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Without relying on external modules, POMATO can directly perform 3D reconstruction along with temporal 3D point tracking and dynamic mask estimation. + +![](images/9d756e08d3e2d94f27849af6b4e03f65b0e8cf5fee25fbbabbc5bbe174eee64c.jpg) + +![](images/bfcaaab9a5ec21305cfa58e3d67b19c49ade436db127ec3a7bcdd3ad0e48ee84.jpg) + +# Abstract + +Recent approaches to 3D reconstruction in dynamic scenes primarily rely on the integration of separate geometry estimation and matching modules, where the latter plays a critical role in distinguishing dynamic regions and mitigating the interference caused by moving objects. Furthermore, the matching module explicitly models object motion, enabling the tracking of specific targets and advancing motion understanding in complex scenarios. Recently, the proposed representation of pointmap in DUSt3R suggests a potential solution to unify both geometry estimation and matching in 3D space, effectively reducing computational overhead by eliminating the need for redundant auxiliary modules. However, it still struggles with ambiguous correspondences in dynamic regions, which limits reconstruction + +performance in such scenarios. In this work, we present POMATO, a unified framework for dynamic 3D reconstruction by marrying POintmap MAatching with Temporal mOtion. Specifically, our method first learns an explicit matching relationship by mapping RGB pixels across different views to 3D pointmaps within a unified coordinate system. Furthermore, we introduce a temporal motion module for dynamic motions that ensures scale consistency across different frames and enhances performance in 3D reconstruction tasks requiring both precise geometry and reliable matching, most notably 3D point tracking. We show the effectiveness of our proposed POMATO by demonstrating the remarkable performance across multiple downstream tasks, including video depth estimation, 3D point tracking, and pose estimation. Code and models are publicly available at https://github.com/wyddmw/POMATO. + +![](images/d4790d7013afc4e3913de26bff86a1058157e1f8f2647138f96914e1b1e2a19f.jpg) +Image1 + +![](images/da7cfadfc356bf2c1cf00c8b8279df0074817de3b6f5c9b690134e137e9a30f0.jpg) +Figure 2. Ambiguity in 3D point matching in dynamic scenes with DUSt3R. Given representative corresponding pixels of background (orange) and moving foreground (red) in two different views, DUSt3R outputs a pair of 3D points within the same coordinate system. In static regions, identical pixels share the same 3D coordinates which provide an accurate matching relationship in 3D space, but in moving regions, the 3D coordinates are inconsistent for corresponding pixels across views, leading to ambiguous 3D matching relationships. + +![](images/80ba9d359d10fae8be286af68910bd22527b49e2e0e9982c65725f9e7b2f3600.jpg) + +# 1. Introduction + +Image-based 3D reconstruction is a fundamental task in computer vision with a wide range of applications including SLAM [39], robotics [19, 48], autonomous driving [52], and novel view synthesis [5]. While substantial progress has been achieved in static 3D reconstruction [16, 23, 26, 44, 50], dynamic scenes remain a major hurdle due to complexities like non-rigid motion and deformation, which may hamper the learning of local structure and camera motion, thereby complicating accurate 3D reconstruction for dynamic scenes. These scenarios require explicit modeling of both scene geometry and object motion. Moreover, downstream reconstruction tasks, such as 3D point tracking, demand precise geometry estimation and robust matching across views. To effectively distinguish dynamic regions, it is essential to establish reliable correspondences between different frames. Some pioneering works have attempted to address dynamic motion by incorporating additional auxiliary matching modules, such as optical flow [42, 51] or 2D tracking [46]. However, these approaches may suffer from domain gaps and accumulated errors between modules, limiting their effectiveness. A unified framework that seamlessly integrates geometry estimation and matching for dynamic 3D reconstruction remains a critical and underexplored challenge. + +Recently, DUSt3R [44] proposes a promising solution to address this challenge. It introduces the concept of a pointmap that assigns each pixel in an image to a corresponding 3D coordinate. The network utilizes a standard transformer-based encoder-decoder architecture and receives a pair of images as input. The system incorporates two parallel decoders to predict pointmaps for each view within the same coordinate system. However, this representation is limited to static matching and struggles in dynamic scenes, as illustrated in Fig. 2. + +To address this problem, we present POMATO, a unified network for dynamic 3D reconstruction by marrying + +POintmap MMatching with Temporal mOtion. We argue that with iterative cross-attention modules across different views, matching features are well preserved in the decoder tokens. We thus introduce an auxiliary pointmap matching head to learn explicit correspondences. Specifically, for each pixel in the second view, the pointmap matching head predicts the corresponding 3D coordinates of its counterpart in the first view, under the shared coordinate system. Our proposed pointmap-based matching representation enables the establishment of explicit correspondences in 3D space, which can be directly leveraged for motion analysis, especially the estimation of dynamic regions. Moreover, we further extend our POMATO to handle 4D video sequences by introducing a temporal motion module that enhances the learning of temporal motions. This motion module promotes scale consistency across different frames and improves performance in tasks where both accurate geometry and reliable matching are paramount, most notably 3D point tracking. Compared with recent temporal 3D reconstruction methods [41, 43] based on an autoregression manner where the previous frames are blocked from the recently added frames, our temporal motion module is based on the self-attention mechanism along the temporal dimension, facilitating a comprehensive interaction across all frames. Our POMATO is trained in a two-stage manner. In the first stage, we used pairwise input images to learn fundamental geometry and matching capabilities. In the second stage, we extend the input to sequential video frames and incorporate the temporal motion module, enabling the model to effectively capture motions over time. + +Our contributions can be summarized in threefold: First, we propose a novel approach that unifies the fundamental geometry estimation and motion understanding for dynamic 3D reconstruction into a single network by incorporating the representation of pointmap matching. Second, we introduce a temporal motion module to facilitate the interactions of motion features along the temporal dimension, which significantly improves the performance in tasks + +where both accurate geometry and precise matching are required for video sequential input, most notably 3D point tracking. Third, we demonstrate promising performance on 3D vision tasks, including video depth estimation, 3D point tracking, and camera pose estimation. + +# 2. Related Work + +Geometry estimation refers to the process of determining the spatial properties and structures from different forms of visual data. Direct recovery of 3D geometry from a single RGB image is by nature an ill-posed problem. Many recent works [3, 16, 23, 50] have tried to leverage strong pre-trained models to learn generalizable depthmaps from large-scale real and synthetic datasets to solve ambiguities. For example, Marigold [23], Geowizard [11], and GenPercept [47] aim at leveraging the generative priors from pre-trained diffusion models by finetuning them on synthetic datasets. Depthanything V2 [50] proposes to estimate scale-and-shift invariant disparity map by finetuning DINOV2 [29] model on synthetic datasets and largescale pseudo labels. Depth Pro [3] further propose a FOV head to estimate the metric depthmap from a single image without relying on camera intrinsics as input. Due to the scale ambiguity in the monocular depth estimation models, ChronoDepth [36], DepthCrafter [17], and Depth-any-video [49] proposes to learn temporal consistent depthmaps by leveraging the priors from a video generative model, i.e. SVD [2]. In another line of the research, multi-view stereo reconstruction (MVS) methods seek to reconstruct visible surfaces from multiple viewpoints. Traditional MVS [12] and SfM pipelines break the reconstruction pipeline into several sub-problems, e.g., feature extraction [8], image matching [1, 27], triangulation, and bundle adjustment [7]. The chain is complicated and accumulates noise for every single step, thus often resulting in unsatisfactory performance in complex real-world scenes. Recognizing the limitations of previous MVS methods, seminal work DUSt3R [44] proposes 3D pointmaps representation, and trains a network from large-scale data to regress the dense and accurate pointmaps from a pair of images. The camera intrinsics and relative camera poses can be implicitly inferred from the two-view pointmaps. However, it still can not handle reconstruction for dynamic scenes. MonST3R [51] directly finetuned the original DUSt3R model upon synthetic datasets that contain dynamic scenes. Motion representation. Optical flow is a commonly used representation for 2D motion. RAFT [38] is a representative work for pairwise optical flow estimation, which employs a 4D cost volume and recurrently estimates the optical flow. Some follow-up methods further extend it to multi-frame (3-5 frames) settings, which is still insufficient for long-range tracking. To resolve the problem, Particle Video [35] represent video motion by using a set of particles. Each + +particle is an image point sample with a long-duration trajectory and other properties. Particle videos have two key advantages over optical flow: (1) persistence through occlusions, and (2) multi-frame temporal context. Some recent works, PIPs [15], TAPIR [9] and Cotracker [22] have renewed interest in this representation and show promising long-term 2D point tracking results. Recognizing the advantage of point representation, SpatialTracker [46] lifts the 2D points into 3D and performs tracking in the 3D space. Though it can handle occlusions and enhance 3D tracking accuracy, it still relies on a separate monocular depth estimator, which prevents it performing 3D point tracking in an end-to-end fashion. + +Multi-view dynamic reconstruction. Our work is closely connected to multi-view dynamic 3D reconstruction techniques. Early works [32, 34] take the straightforward idea that first pre-segment the scene into different regions, each corresponding to a single rigid part of an object, then apply the rigid-SfM technique to each of the regions. Some of the recent Neural Radiance Fields (NeRF) [28] and Gaussian Splatting [24] based methods have achieved state-of-the-art results. However, most of these methods require simultaneous multi-view video inputs or require predefined templates [18]. Shape of motion [42], proposes a new dynamic scene representation to represent the dynamic scene as a set of persistent 3D Gaussians, and optimize the representation from a monocular video by leveraging monocular depth estimation priors and 2D track estimates across frames. + +# 3. Method + +# 3.1. Preliminary + +The overview of our POMATO is demonstrated in Fig.3. We adopt the definition of pointmap $\mathbf{X} \in \mathbb{R}^{H \times W \times 3}$ in DUSt3R [44] as a dense 2D field of 3D points where each point corresponds to its respective RGB pixel. Given a pair of input images $\mathbf{I}^1, \mathbf{I}^2 \in \mathbb{R}^{H \times W \times 3}$ from two different views, a weight-sharing ViT first extracts the corresponding features $\mathbf{F}^1, \mathbf{F}^2$ for each view. Two parallel branches are employed to decode the geometric structures and enhance the feature alignment via cross-attention in decoder modules, following a regression head to estimate pointmaps $\mathbf{X}^{1,1}, \mathbf{X}^{2,1} \in \mathbb{R}^{H \times W \times 3}$ along with a confidence map $\mathbf{C}^{1,1}, \mathbf{C}^{2,1} \in \mathbb{R}^{H \times W}$ for each image view. Generally, $\mathbf{X}^{n,m}$ indicates the pointmap $\mathbf{X}^n$ from camera $n$ expressed in camera $m$ 's coordinate frame, which is obtained by a rigid transformation: + +$$ +\mathbf {X} ^ {n, m} = \mathbf {P} _ {m} \mathbf {P} _ {n} ^ {- 1} h \left(\mathbf {X} ^ {n}\right), \tag {1} +$$ + +where $\mathbf{P}_m, \mathbf{P}_n \in \mathbb{R}^{3 \times 4}$ are world-to-camera poses for camera $m$ and camera $n$ , respectively, and $h(\mathbf{X}^n)$ is a homogeneous mapping for the 3D coordinate in camera coordinate + +![](images/6c2a4e30e8ce899d819fb5ecc880bda38163cdd7993ced19b28b4dd5846716c8.jpg) +Figure 3. Overview of our training pipeline. (1) Stage I: build upon DUSt3R [44] architecture, we introduce a third regression point-matching head: $\mathrm{Head}_3$ , which is in parallel to $\mathrm{Head}_2$ for explicit pointmap matching in 3D space. For each pixel in the second view, the output pointmap coordinate is the 3D point map of the corresponding pixel in the first view. (2) Stage II: we introduce a temporal fusion module in three heads that enables multi-style sequential input for learning temporal motions. + +![](images/605719015a3f01a385bb6b41f66a977cb3406db4d9da2a81979a20f7ae60c171.jpg) + +of camera $n$ + +The task for Decoder 1 and its regression head estimate the 3D points for $\mathbf{I}^1$ in its own coordinate system while Decoder 2 and its regression head are responsible for estimating pixel-wise 3D coordinates for $\mathbf{I}^2$ in $\mathbf{I}^1$ 's coordinate system after a rigid transformation of global rotation and translation. In the following contents, we will first introduce our POMATO with pairwise input images and then extend it to the video sequence input with our temporal motion module. + +# 3.2. Pointmap Matching with Pairwise Input + +As discussed before, the definition of $\mathbf{X}^{2,1}$ depicts a rigid camera transformation that is ambiguous to reflect explicit matching relationships for dynamic regions. To tackle this, we propose to formulate an explicit pointmap matching $\mathbf{X}_m^{2,1} \in \mathbb{R}^{H \times W \times 3}$ that maps dense RGB pixels of $\mathbf{I}^2$ to 3D coordinates of corresponding pixels in $\mathbf{I}^1$ under the first image's coordinate system. Given a 2D query pixel at $(x_2, y_2)$ in $\mathbf{I}^2$ and its corresponding pixel at $(x_1, y_1)$ in $\mathbf{I}^1$ , the matched pointmap at $(x_2, y_2)$ in $\mathbf{I}^2$ is: + +$$ +\mathbf {X} _ {m} ^ {2, 1} \left(x _ {2}, y _ {2}\right) = \mathbf {X} ^ {1, 1} \left(x _ {1}, y _ {1}\right), \tag {2} +$$ + +where $(x,y)$ indicates the coordinates of 2D grid. For the representative dynamic point (red) in Fig. 2, the pointmap matching result is the 3D coordinate of point A in the coordinate system of the first image. As shown in Fig. 3, $\mathbf{X}_m^{2,1}$ and $\mathbf{X}^{1,1}$ are supposed to match perfectly in 3D space on the premise of neglecting occluded regions. We argue that the set of decoder tokens from the second branch preserves abundant matching information with iterative cross-attentions, so we introduce a matching head with the same architecture of $\mathrm{Head}_1$ and $\mathrm{Head}_2$ . The supervision for pointmap matching $\mathbf{X}_m^{2,1}$ still follows the 3D regression loss which is defined as the Euclidean distance: + +$$ +\mathcal {L} _ {\mathrm {m}} = \left\| \frac {1}{z _ {m}} \mathbf {X} _ {m} ^ {2, 1} - \frac {1}{\bar {z} _ {m}} \bar {\mathbf {X}} _ {m} ^ {2, 1} \right\|, \tag {3} +$$ + +where $\bar{\mathbf{X}}_m^{2,1}$ is the ground truth pointmap matching, which can be obtained following Eq. 2 on the 2D tracking dataset + +with the depth and camera information. $z_{m},\bar{z}_{m}$ are the same norm factor defined in DUSt3R. The matching confidence $\mathbf{C}_m^{2,1}$ is also learned following the confidence loss for Head1 and Head2 within valid regions: + +$$ +\mathcal {L} _ {\mathrm {m c o n f}} = \mathbf {C} _ {m} ^ {2, 1} \mathcal {L} _ {\mathrm {m}} - \alpha \log \mathbf {C} _ {m} ^ {2, 1} \tag {4} +$$ + +The final loss $\mathcal{L}$ of our POMATO for pairwise input is a combination of predefined DUSt3R loss $\mathcal{L}_{\mathrm{DUSt3R}}$ , matching loss $\mathcal{L}_{\mathrm{m}}$ , and matching confidence loss $\mathcal{L}_{\mathrm{mconf}}$ . When training our POMATO for pairwise input images at the first stage, the parameters in the encoder are frozen. + +# 3.3. Dynamic Mask Estimation + +Taking advantage of the explicit pointmap matching head, our POMATO can directly perform dynamic mask estimation without introducing an assistant module such as the optical flow model, getting rid of the additional computation cost and the potential domain gap. For an image pair $\{\mathbf{I}^i,\mathbf{I}^j\}$ along with the estimation of $\mathbf{X}^{j,i}$ from $\mathrm{Head}_2$ and $\mathbf{X}_{m}^{j,i}$ from $\mathrm{Head}_3$ , the dynamic mask $\mathbf{D}^{j,i}$ can be obtained by comparing the difference between $\mathbf{X}^{j,i}$ and $\mathbf{X}_{m}^{j,i}$ : + +$$ +\mathbf {D} ^ {j, i} = \left| \left| \mathbf {X} _ {m} ^ {j, i} - \mathbf {X} ^ {j, i} \right| \right| > \alpha , \tag {5} +$$ + +where $\alpha$ is a dynamic threshold defined as $3 \times$ median $(||\mathbf{X}_m^{j,i} - \mathbf{X}^{j,i}||)$ . The explicit dynamic mask can be incorporated into the global alignment process to minimize the interference of moving objects for pose estimation and 3D reconstruction. Details on the incorporation of dynamic masks for global alignment are provided in the supplementary materials. + +# 3.4. Temporal Motion Module + +With the fundamental capability of geometric estimation and pointmap matching for pairwise images, we follow [6] and extend our POMATO to 4D video sequences by inserting a transformer-based motion module into the vanilla DPT head to construct the "temporal DPT head", which is illustrated in Fig.4. For a set of decoder tokens $\mathbf{G} \in \mathbb{R}^{B,T,N,C}$ + +![](images/e73694188c1b8131f76e305cf3ef1fcdd588d7576f6399241e71b55f09d6872f.jpg) +Figure 4. Architecture of our temporal motion module. We insert a transformer-based motion module (in shallow yellow) into the vanilla DPT [33] head to enhance the temporal consistency. + +where $B, T, N, C$ represent the batch size, window length of a video sequence, token number, and token dimension, respectively, we merge the token number dimension into the batch axis and apply the motion module which consists of two blocks of standard multi-head self-attention modules and feed-forward networks along the temporal dimension $T$ . To reduce the computation cost, the temporal motion modules are applied to features of low resolution. + +# 3.5. Downstream Temporal Tasks + +Given a video sequence of $T$ frames $\mathbf{I}^{t_1},\mathbf{I}^{t_2},\dots ,\mathbf{I}^{t_T}$ we construct a unique set of stereo image pairs for each task. As illustrated in Fig. 5, the flexible construction of input pairs—combined with the proposed temporal motion module and pointmap matching head—enables POMATO to seamlessly address downstream temporal tasks, including 3D point tracking, video depth estimation, and 3D reconstruction. The keyframe selection strategy and input formulation for each task are detailed in the following section. + +Besides the default regression losses for $\mathrm{Head}_1$ and $\mathrm{Head}_2$ , and predefined losses Eq. 3 and Eq. 4 for $\mathrm{Head}_3$ , we further employ a temporal consistency loss, $\mathcal{L}_{\mathrm{t}}$ , which will be described in detail below. + +In addition to the default regression losses for $\mathrm{Head}_1$ and $\mathrm{Head}_2$ , and the predefined losses in Eq. 3 and Eq. 4 for $\mathrm{Head}_3$ , we further introduce a temporal consistency loss, $\mathcal{L}_{\mathrm{t}}$ , which will also be described in detail below. + +3D Point Tracking. As illustrated at the top of Fig.5, the keyframe is set to the first image of the global video sequence and fed to the proposed $\mathrm{Head}_3$ to obtain the pointmap matching result of each query point (initialized at the first image) under the coordinate system of each reference frame $\{\mathbf{X}_{m}^{t_{1},t_{1}},\mathbf{X}_{m}^{t_{1},t_{2}},\mathbf{X}_{m}^{t_{1},t_{3}},\dots \mathbf{X}_{m}^{t_{1},t_{T}}\}$ , while the set of reference frames $\{\mathbf{I}^{t_1},\mathbf{I}^{t_2},\mathbf{I}^{t_3},\dots \mathbf{I}^{t_T}\}$ is fed to the $\mathrm{Head}_1$ to obtain the pointmap under each ego coordinate system. The dense tracking results can be further sparsified by indexing the 2D coordinates. When inference on a video + +![](images/03e46edafee22826cca167e638e68f533c2191534b14727c1a972191680c8ac9.jpg) +Figure 5. Inference pipelines for point tracking, video depth, and multi-view reconstruction. $t_k$ indicates the keyframe. With the help of the motion module and flexible input construction, PO-MATO can be easily applied to downstream temporal tasks. + +longer than $T$ frames, a simple sliding-window approach with an overlap of four frames is adopted to enhance the consistency between adjacent video windows. The temporal consistency loss $\mathcal{L}_{\mathrm{t}}$ for tracking is: + +$$ +\mathcal {L} _ {\mathrm {t}} = \frac {1}{T} \sum_ {i = 1} ^ {T} \left\| \frac {\mathbf {X} _ {m} ^ {t _ {1} , t _ {i}}}{z _ {m} ^ {T}} - \frac {\bar {\mathbf {X}} _ {m} ^ {t _ {1} , t _ {i}}}{\bar {z} _ {m} ^ {T}} \right\| + \left\| \frac {\mathbf {X} ^ {t _ {i} , t _ {i}}}{z ^ {T}} - \frac {\bar {\mathbf {X}} ^ {t _ {i} , t _ {i}}}{\bar {z} ^ {T}} \right\|, \tag {6} +$$ + +where $z_{m}^{T} = \mathrm{norm}\left(\mathbf{X}_{m}^{t_{1},t_{1}},\mathbf{X}_{m}^{t_{1},t_{2}},\dots,\mathbf{X}_{m}^{t_{1},t_{T}}\right)$ and $\bar{z}_T =$ norm $(\bar{\mathbf{X}}_m^{t_1,t_1},\bar{\mathbf{X}}_m^{t_1,t_2},\dots,\bar{\mathbf{X}}_m^{t_1,t_T})$ . $z_{m}^{T}$ and $\bar{z}_T$ are defined analogously. + +Video Depth Estimation. As shown in the middle part of the Fig. 5, the input video sequence is formulated to a set of identical image pairs $\{(\mathbf{I}^{t_1},\mathbf{I}^{t_1}),(\mathbf{I}^{t_2},\mathbf{I}^{t_2}),\dots,(\mathbf{I}^{t_T},\mathbf{I}^{t_T})\}$ and fed to $\mathrm{Head}_1$ and $\mathrm{Head}_2$ , where the predictions from each head are identical: $\{\mathbf{X}^{t_1,t_1},\mathbf{X}^{t_2,t_2},\dots,\mathbf{X}^{t_N,t_N}\}$ . We use the output of $\mathrm{Head}_1$ as our final video depth estimation. The temporal consistency loss $\mathcal{L}_{\mathrm{t}}$ is defined as: + +$$ +\mathcal {L} _ {\mathrm {t}} = \frac {1}{T} \sum_ {i = 1} ^ {T} \left\| \frac {\mathbf {X} _ {1} ^ {t _ {i} , t _ {i}}}{z _ {1} ^ {T}} - \frac {\bar {\mathbf {X}} ^ {t _ {i} , t _ {i}}}{\bar {z} ^ {T}} \right\| + \left\| \frac {\mathbf {X} _ {2} ^ {t _ {i} , t _ {i}}}{z _ {2} ^ {T}} - \frac {\bar {\mathbf {X}} ^ {t _ {i} , t _ {i}}}{\bar {z} ^ {T}} \right\|, \tag {7} +$$ + +where $\mathbf{X}_1^{t_i,t_i}$ and $\mathbf{X}_2^{t_i,t_i}$ indicate the output from Head_1 and Head_2, respectively. $\bar{\mathbf{X}}^{t_i,t_i}$ is the pointmap groundtruth. + +3D Reconstruction. Assisted by the temporal motion module, redundant post-process operations such as global alignment can be omitted, allowing the reconstructed 3D point cloud to be obtained in a feed-forward manner. As shown in the bottom part of Fig.5, the keyframe is set to the last frame + +
AlignmentMethodOptim. Onl.Sintel [4]BONN [30]KITTI [13]
Abs Rel ↓δ<1.25 ↑Abs Rel ↓δ<1.25 ↑Abs Rel ↓δ<1.25 ↑
Per-sequence scaleDUSt3R-GA [44]✓0.65645.20.15583.30.14481.3
MASt3R-GA [26]✓0.64143.90.25270.10.18374.5
MonST3R-GA [51]✓0.37855.80.06796.30.16874.4
Spann3R [41]✓0.62242.60.14481.30.19873.7
CUT3R [43]✓0.42147.90.07893.70.11888.1
POMATO✓0.41653.60.07496.10.08593.3
Per-sequence scale & shiftMonST3R-GA [51]✓0.33558.50.06396.40.10489.5
CUT3R [43]✓0.46656.20.11188.30.07594.3
POMATO✓0.34557.90.07296.50.08493.4
+ +Table 1. Video depth evaluation. We report scale-invariant depth and scale & shift invariant depth accuracy on Sintel [4], Bonn [30], and KITTI [13] datasets. Methods requiring global alignment are marked “GA”, while “Optim.” and “Onl.” indicate optimization-based and online methods, respectively. The best and second best results in each category are bold and underlined, respectively. + +$\mathbf{I}^{t_T}$ within the temporal window of length $T$ and is fed to $\mathrm{Head}_1$ with a set output of $\{\mathbf{X}^{t_T,t_T},\mathbf{X}^{t_T,t_T},\dots,\mathbf{X}^{t_T,t_T}\}$ . All the reference frames are input to the $\mathrm{Head}_2$ so the target pointmaps $\{\mathbf{X}^{t_1,t_T},\mathbf{X}^{t_2,t_T},\dots,\mathbf{X}^{t_T,t_T}\}$ are aligned under the coordinate system of the keyframe. The temporal consistency loss $\mathcal{L}_{\mathrm{t}}$ is: + +$$ +\mathcal {L} _ {\mathrm {t}} = \frac {1}{T} \sum_ {i = 1} ^ {T} \left\| \frac {\mathbf {X} ^ {t _ {T} , t _ {T}}}{z _ {1} ^ {T}} - \frac {\bar {\mathbf {X}} ^ {t _ {T} , t _ {T}}}{\bar {z} _ {1} ^ {T}} \right\| + \left\| \frac {\mathbf {X} ^ {t _ {i} , t _ {T}}}{z _ {2} ^ {T}} - \frac {\bar {\mathbf {X}} ^ {t _ {i} , t _ {T}}}{\bar {z} _ {2} ^ {T}} \right\| \tag {8} +$$ + +We further freeze the parameters in Decoder1 and Decoder2 when training the temporal downstream tasks at the second stage. In our work, the temporal window length $T$ is set to 12. Additional explorations on the temporal length can be found in Sec.4. + +# 4. Experiments + +# 4.1. Experimental Details + +Training data. We train our network with a mixture of five datasets: PointOdyssey [53], Tartanair [45], ParallelDomain4D [40], DynamicReplica [21] and Carla (0.9.15) [10]. The specific number and the usage ratio of each dataset can be found in the supplementary materials. All datasets include pixel-accurate ground truth depth, as well as camera intrinsics and extrinsics, and encompass a wide variety of dynamic scenes across both indoor and outdoor environments. Among them, PointOdyssey and DynamicReplica have additional 2D trajectory annotations for dynamic objects which can be used to construct pointmap matching ground truth following Eq. 2. All datasets are used to supervise geometry learning on $\mathrm{Head}_1$ and $\mathrm{Head}_2$ , while only PointOdyssey, DynamicReplica, and TartanAir are used to train the proposed pointmap matching head. + +Training and inference details. Our model architecture is based on the publicly available DUSt3R [51] model, utilizing the same backbone consisting of a ViT-Large encoder + +and a ViT-Base decoder. To fully leverage MonST3R's geometry estimation capabilities in dynamic scenes, we initialize our model using the publicly available MonST3R checkpoint. For the newly introduced pointmap matching head, we initialize its weights from the pretrained $\mathrm{Head}_2$ weights of MonST3R. The temporal motion module is initialized following [14]. We train our network for 10 epochs with a cosine learning rate schedule, with an initial learning rate of 1e-4. In the first stage, which involves pairwise training, we use a batch size of 16 on 4 A100 GPUs (40G). In the second stage, where the temporal motion module is introduced, the batch size is set to 4 with a fixed temporal window length of 12. During each training iteration, we randomly sample a downstream task—3D point tracking, video depth estimation, or 3D reconstruction—to construct the input pairs and apply the corresponding loss function. + +# 4.2. Video Depth Estimation + +Following MonST3R [51] and CUT3R [43], we rescale all predictions from the same video to align them together by conducting two forms of alignment: per-sequence scale and shift alignment and per-sequence scale alignment. Thus, we can measure the per-frame depth quality and inter-frame depth consistency. We employ our proposed motion module for video depth estimation in a feed-forward manner as described in Sec.3.5 and compare our method against several variants of DUSt3R, including DUSt3R [44], MAST3R [26], MonST3R [51], Spann3R [41], and CUT3R [43]. Given 6 frames of $288\times 512$ on an NVIDIA 4070 GPU, POMATO reconstructs the 3D point cloud in 0.7 seconds, whereas global alignment-based methods such as MonST3R require 5.8 seconds. As shown in Tab. 1, our method demonstrates comparable performance to the global alignment (GA)-based MonST3R [51] on the Sintel [4] and BONN [30] datasets, while surpassing it on KITTI dataset. Besides, we + +
MethodPointOdyssey [53]ADT [31]PStudio [20]Average
L-12L-24L-12L-24L-12L-24L-12L-24
SpatialTracker* [46]20.4620.7121.6420.6730.4125.8724.1722.42
DUSt3R [44]19.0319.0329.0225.559.726.5019.2617.03
MASt3R [26]16.5817.3527.3626.4611.788.0918.5717.30
MonST3R [51]27.3127.9228.3026.1316.5011.0624.0321.70
POMATO33.2033.5831.5728.2224.5919.7929.7927.20
+ +Table 2. 3D tracking evaluation. We report the APD metric to evaluate 3D point tracking on the PointOdyssey [53], ADT [31], and PStudio [20] datasets. L-12 and L-24 indicate tracking within the temporal length of 12 frames and 24 frames, respectively. + +![](images/03a55f67a47387cf7a0f1955fb4795a7aa96e25d9492413951874f029abfce2e.jpg) +Figure 6. Qualitative comparison of dynamic scenes. Compared to MonST3R, our POMATO can provide more reliable motion masks, 3D point tracking, and reconstruction performance. + +consistently outperform the state-of-the-art online method, CUT3R [43], across various settings. These results underscore the effectiveness of our approach, specifically (1) the joint learning of geometry and pointmap matching, and (2) the temporal motion module. + +# 4.3. 3D Point Tracking + +For 3D point tracking task, we use the Aria Digital Twin (ADT) [31], and Panoptic Studio (PStudio) [20] benchmarks from the TAPVid-3D [25] dataset along with the validation set on the PointOdyssey [53] dataset. We report the Average Percent Deviation (APD) metric, which quantifies the average percentage of points within a threshold relative to the ground truth depth. The APD metric serves as a direct measure of the accuracy of the predicted tracking. We reformulate the datasets and project all the query points within a temporal window to the first frame. We report tracking results on the length of 12 and 24 frames. As shown in Tab.2, our POMATO achieves the best performance on both PointOdyssey and ADT datasets. It's worth mentioning that SpatialTracker [46] is a state-of-the-art network tailored for 3D point tracking with ground truth camera intrinsic as ad + +ditional input data. POMATO surpasses it on two datasets and improves the average APD metric by $23.3\%$ and $21.4\%$ for 12 frames and 24 frames, respectively. For DUSt3R-based methods, we use the output of $\mathrm{Head}_2$ as tracking results. Obviously, the ambiguous matching representation limits its capability to handle this fine-grained 3D reconstruction task in dynamic scenes. 1 + +# 4.4. Camera Pose Estimation + +Following DUSt3R-based methods, we perform global alignment with the model trained in the first stage on the Bonn [30] and TUM [37] datasets. The sampling stride is set to 5 for the Bonn dataset and 3 for the TUM dataset. Compared with optical-flow assisted global alignment in MonST3R, the dynamic mask is computed according to Eq. 5 while the 2D pseudo label is replaced by projecting the pointmap matching results to 2D coordinates with estimated camera intrinsic. Absolute Translation Error (ATE), Relative Translation Error (RPE trans), and Relative Rotation Error (RPE rot) are reported. The evaluation results over 40 frames are reported in Tab. 4. Notably, POMATO obtains an overall state-of-the-art performance and signifi + +
Temporal LengthVideo DepthTracking (12 Frames)
Sintel [4]Bonn [30]KITTI [13]PointOdyssey [53] ADT [31] PStudio [20]
Abs Rel ↓ δ<1.25 ↑Abs Rel ↓ δ<1.25 ↑Abs Rel ↓ δ<1.25 ↑Abs Rel ↓ δ<1.25 ↑APD↑APD↑APD↑
Pair-wise0.54846.20.08794.00.11389.532.0629.8723.10
6 frames0.43651.30.07695.90.08593.532.6930.9324.52
12 frames0.41653.60.07596.10.08693.333.2031.5724.59
+ +Table 3. Ablation study on the temporal motion module. The introduction of the temporal motion module brings a significant improvement. As the temporal window length enlarges from 6 frames to 12 frames, we obtain an overall consistent improvement. + +
MethodTUM [37]Bonn [30]
ATE ↓RPE trans ↓RPE rot ↓ATE ↓RPE trans ↓RPE rot ↓
DUSt3R [44]0.0250.0132.3610.0300.0252.522
MASt3R [26]0.0270.0151.9100.0310.0252.478
MonST3R [51]0.0210.0061.1420.0250.0212.120
CUT3R [43]0.0230.0160.5100.0280.0332.569
POMATO0.0200.0100.5090.0370.0161.782
+ +![](images/1c6c752e80c60fcd5532fb788c94cf5b5034109a6a0a070aefad9cd940462a1d.jpg) +Figure 7. Effectiveness of our pointmap matching head. Without explicitly filtering out the motion area, both pose and geometry estimation will be degraded. + +Table 4. Pose estimation. Our method achieves an overall best performance and improves the RPE rot metric significantly. + +
MethodBonn [30]PointOdyssey [53]ADT [31]PStudio [20]
ATE ↓RPE trans ↓RPE rot ↓APD ↑APD ↑APD ↑
W/O Head30.0400.0151.72129.1029.6216.94
W/ Head30.0370.0161.78232.0629.8723.10
+ +Table 5. Ablation study on the effectiveness of the pointmap matching head. The comparisons are reported on the pose estimation and 3D point tracking tasks. + +cantly improves the RPE-rot metric, surpassing MonST3R by $55.4\%$ and $13.3\%$ on the TUM and Bonn datasets. + +# 4.5. Ablation Study + +We conduct extensive ablation studies to evaluate the effectiveness of the temporal motion module and the proposed pointmap matching head. As shown in Table 3, we report results for three models: one trained with only pairwise + +images (first-stage training), one using a shorter temporal window of 6 frames, and another using the default temporal window length of 12 frames. Incorporating temporal consistency yields substantial improvements across all datasets for video depth estimation and 3D point tracking. Further improvement is achieved when the temporal window length increases from 6 frames to 12 frames. In Table 5, we evaluate the effectiveness of the pointmap matching head. While it introduces only a modest improvement in the ATE metric, we attribute this to the limited motion and minimal viewpoint variation in the indoor evaluation dataset. As illustrated in Fig. 7, under challenging in-the-wild conditions with significant motion and rapid viewpoint changes, removing the pointmap matching head introduces ambiguity in explicit rigid transformation estimation, resulting in a clear degradation in performance. To further demonstrate the impact of the pointmap matching head on 3D point tracking, we conduct tracking experiments over 12 frames using the pairwise input setup. Clearly, removing the pointmap matching head (using only $\mathrm{Head}_2$ ) leads to an inevitable performance drop, emphasizing explicit correspondence modeling for reliable long-term tracking. + +# 5. Discussion and Conclusion + +We introduce POMATO, a unified framework for geometry estimation and motion understanding in dynamic scenes. By leveraging the proposed pointmap matching head, our method effectively distinguishes moving regions, thereby mitigating the interference introduced by dynamic objects. The temporal motion module further facilitates the learning of temporal dynamics across frames, enhancing scale consistency and improving performance in tasks where both geometry and matching are critical—most notably, 3D point tracking. The downstream temporal tasks including 3D point tracking, video depth estimation, and 3D reconstruction can be easily applied in a feed-forward manner. In future work, we plan to scale up training with more dynamic reconstruction and matching datasets to further enhance 3D reconstruction and tracking performance. + +Acknowledgement. This work was supported by the National Natural Science Foundation of China (No. 62206244) + +# References + +[1] Daniel Barath, Dmytro Mishkin, Luca Cavalli, Paul-Edouard Sarlin, Petr Hruby, and Marc Pollefeys. 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(a) Rain severely degrades event camera data compared to conventional cameras. (b) Unlike frame-based aggregation methods, our approach directly samples raw data, preserving temporal resolution. (c) The multi-scale state space model integrates dual-temporal scales for intra- and inter-window information and multi-spatial scales for rain dynamics. (d) Deraining results of our method. + +![](images/b16275764078c2a8382e2d9085cbfac504c8eb212e79b9dbf756b8f508cb9744.jpg) +(d) Deraining Performance + +# Abstract + +Event cameras excel in high temporal resolution and dynamic range but suffer from dense noise in rainy conditions. Existing event deraining methods face trade-offs between temporal precision, deraining effectiveness, and computational efficiency. In this paper, we propose PRE-Mamba, a novel point-based event camera deraining framework that fully exploits the spatiotemporal characteristics of raw event and rain. Our framework introduces a 4D event cloud representation that integrates dual temporal scales to preserve high temporal precision, a Spatio-Temporal Decoupling and Fusion module (STDF) that enhances deraining capability by enabling shallow decoupling and interaction of temporal and spatial information, and a Multi-Scale State Space Model (MS3M) that captures deeper rain dynamics across dual-temporal and multi-spatial scales with linear computational complexity. Enhanced by frequency-domain regularization, PRE-Mamba achieves superior performance (0.95 SR, 0.91 NR, and 0.4s/M events) with only 0.26M parameters on EventRain-27K, a comprehensive + +dataset with labeled synthetic and real-world sequences. Moreover, our method generalizes well across varying rain intensities, viewpoints, and even snowy conditions. Code and dataset: https://github.com/softword-ii/PRE-Mamba. + +# 1. Introduction + +Event cameras have revolutionized mobile applications with their high temporal resolution (microsecond level), high dynamic range ( $>120$ dB), and low power consumption ( $<10$ mW) [1, 2], driving breakthroughs in high-speed tracking [3, 4], SLAM [5-7], localization [8] and obstacle avoidance [9, 10]. Unlike frame cameras, they asynchronously capture pixel-level intensity changes without global exposure, eliminating motion blur even at extreme speeds. However, despite excelling in dynamic scenes, event cameras suffer significant performance degradation under adverse weather, particularly in rain [11, 12]. The rapid motion of rain streaks triggers excessive intensity changes, generating dense noise that overwhelms valid scene information and exacerbates sampling rates. This severely impacts accuracy and latency in downstream tasks on drones [13-15] and autonomous vehicles [16-18], limiting real-world reliability. + +Despite significant advances in deep learning for frame + +camera deraining [19-22], event camera deraining remains largely unexplored. Existing solutions predominantly follow a frame-based paradigm, converting event streams into grayscale frames [12] and applying frame-based deraining techniques [11], which sacrifice the fine-grained temporal resolution and sparsity of event data. Point-based methods align naturally with event streams' asynchronous, sparse nature, but remain unapplied to deraining due to notable limitations. Point Networks [23, 24], GNNs [25, 26], and SNNs [27-29] still underperform compared to frame-based methods, while Point Transformers face computational bottlenecks under high event rates ( $>10\mathrm{M}$ events/s) due to quadratic attention complexity [30, 31]. As a result, balancing temporal precision, deraining effectiveness, and computational efficiency remains an open challenge. + +Recently, the State Space Model (SSM) [32], particularly Mamba, provides a promising solution with linear complexity and long-range context modeling. However, introducing Mamba to event camera deraining is non-trivial. The original design of the Mamba is aimed at solving causal sequential language tasks, which differ from the asynchronous, sparse, and high-temporal-resolution nature of event data. Rain streaks further complicate this by introducing diverse spatiotemporal patterns, requiring the model to capture complex dependencies across both time and space. + +To address this, we propose PRE-Mamba, the first Point-based deRaining framework for Event camera. As a point-based method, it processes raw events directly instead of quantized frames, fully preserving the sensor's native microsecond $(\mu s)$ temporal resolution and facilitating downstream high-speed vision tasks. Our framework first introduces a 4D event cloud representation (§3.1), integrating inter- and intra-temporal windows to preserve high temporal precision. To handle the spatial irregularity and motion characteristics of rain, we propose a Spatio-Temporal Decoupling and Fusion module (STDF, §3.2), enabling shallow decoupling and interaction of temporal and spatial information. For deeper modeling, we propose a Multi-Scale State Space Model (MS3M, §3.3) that efficiently captures complex rain dynamics across dual temporal and multispatial scales with linear computational complexity. To improve feature discrimination, we introduce a frequency regularization term (§3.4) in the loss function, guiding the model to learn rain distribution patterns in the frequency domain. To evaluate our approach, we construct EventRain27K (§4), the first comprehensive point-based event deraining dataset, comprising 18K labeled synthetic and 9K unlabeled real-world rain sequences. Our model achieves state-of-the-art performance (0.95 SR, 0.91 NR, and 0.4s/M events) with only 0.26M parameters, validated through extensive experiments (§5). Moreover, it generalizes well across diverse rain intensities and snowy conditions. Our contributions are summarized as follows: + +- To the best of our knowledge, we propose the first point-based event deraining framework. +- To effectively extend Mamba for event deraining, we address the asynchronous, sparse nature of event data and the diverse spatiotemporal patterns of rain streaks by introducing a 4D event cloud, an STDF module, and an MS3M enhanced with frequency regularization loss. +- We introduce EventRain-27K, the first point-based event deraining with labeled synthetic and real-world sequences, providing a benchmark for future research. +- We achieve superior performance on synthetic and real datasets with high efficiency and a lightweight design. + +# 2. Related Work + +Existing deraining approaches for frame camera. Deraining methods for frame cameras are categorized into traditional and deep learning-based approaches. Traditional methods, such as dictionary learning and low-rank matrix decomposition [33-36], rely on handcrafted assumptions about the directional nature or sparsity of rain streaks, often failing to generalize to complex real-world scenarios. In contrast, deep learning-based methods, leveraging CNNs and Transformer [37, 38] architectures, have shown significant advances. CNNs effectively model local spatial patterns, capturing rain stripe textures and background structures [19, 39], while Transformer-based models [20-22] enhance performance by capturing long-range dependencies and global context, offering superior deraining capabilities. + +Existing deraining approaches involving event camera. Research on event-based deraining remains limited despite its importance for outdoor applications. Existing methods, such as EGVD [40], RainVID&SS [41], and NESD [42], leverage the high temporal resolution and dynamic range of event cameras to assist frame camera by providing prior knowledge of rain location and density. Other methods designed for event-based deraining typically convert asynchronous event streams into synchronous frames like representations, aligning with image deraining but sacrificing temporal resolution and sparsity. For instance, DistillNet [11] partially preserves temporal resolution through voxel representations but still loses their asynchronous nature. Moreover, the unique motion and spatiotemporal distribution of rain create a domain barrier, limiting the applicability of traditional event denoising methods like filtering [43-45] and clustering [46]. In addition, existing deraining datasets primarily focus on frame camera [47-50] or represent event data in image-like formats [51], further hinder the event camera deraining research. + +Event Data Processing Architectures. Event data processing approaches are broadly categorized into frame-based and point-based frameworks. Frame-based methods [45, 52-54] not only face the aforementioned limitations but also incur redundant computational overhead by + +![](images/1457058ce192e44dcc23e44dd6d41481b45575731f2842eabaf3a9f9cbd274f0.jpg) +Figure 2. Overview of Our Proposed PRE-Mamba. The model takes $n$ temporal windows as input to generate a 4D event cloud, serialized via four scanning modes. The STDF module decouples and enhances spatiotemporal features across dual temporal scales, which flow through a U-Net style encoder-decoder with multiple blocks. Each block employs MS3M as its core, integrating intra- and interwindow branches to capture appearance and motion features, alongside a multi-spatial-scale pathway for handling diverse rain streak scales while preserving local dynamics. Finally, the decoder outputs are fed into a linear layer followed by softmax for per-event predictions. + +processing event-free regions [55], making them inefficient for resource-constrained environments [53, 56]. In contrast, point-based methods process events in their native form, preserving temporal resolution and sparsity. These include Point Networks [57, 58], Graph Neural Networks (GNNs) [59], and Spiking Neural Networks (SNNs) [29, 60], excel in capturing rapid motion and fine-grained temporal dynamics. However, GNNs and SNNs often require specialized hardware or face performance issues, while Point Cloud networks, based on assumptions of permutation and transformation invariance, are poorly suited for temporal event data and require time-aware feature extraction. + +To address these limitations, this paper proposes a novel approach based on selective State Space Models (SSMs) [61-63]. Renowned for its linear computational complexity and parameter efficiency [32, 64], Mamba is well-suited for processing long event sequences exceeding 1M length [30]. It provides a promising direction to bridge performance gap between point-based and frame-based methods [30, 65] while preserving the inherent advantages of event data, facilitating the development of lightweight, real-time deraining systems. + +# 3. Method + +To perform event deraining effectively and efficiently while preserving temporal precision, we propose a novel framework, PRE-Mamba. We formulate event deraining as an event-by-event classification task, akin to event denoising, reducing computational complexity and avoiding artifacts + +compared to reconstruction-based methods. Figure 2 illustrates the architecture of our system. At the input level, a 4D Event Cloud Representation (§3.1) integrates inter- and intra-temporal windows to preserve high temporal precision. For feature extraction, a Spatio-Temporal Decoupling and Fusion module (§3.2) enables effective decoupling and interaction of temporal and spatial information to capture complex rain dynamics. For deep modeling, a Multi-Scale State Space Model (§3.3) captures rain dynamics across dual temporal and multi-spatial scales with linear computational complexity. Finally, a Frequency-Regularized Optimization (§3.4) enhances feature discrimination by learning rain distribution patterns in the frequency domain, ensuring robust deraining accuracy. Together, these components form a unified framework that achieves both computational efficiency and deraining performance. + +# 3.1. 4D Event Cloud Representation + +To preserve fine-grained spatiotemporal information while enabling efficient processing, we transform raw event streams into a structured 4D event cloud representation. The raw event data is represented as a sequence $\mathcal{E} = \{e_i\}_{i=1}^N$ , where each event $e_i = (x_i, y_i, t_i, p_i)$ consists of spatial coordinates $(x_i, y_i)$ , timestamp $t_i$ , and polarity $p_i$ . + +3D Pseudo-Point Cloud Construction: The event sequence is divided into fixed-duration temporal windows $\{\mathcal{W}_k\}_{k=1}^L$ , each spanning a time interval $T$ . Within each window $\mathcal{W}_k$ , events are normalized into a 3D pseudo-point cloud representation: + +$$ +p _ {i} = \left(x _ {i}, y _ {i}, z _ {i}\right) = \left(x _ {i}, y _ {i}, \frac {t _ {i} - t _ {0}}{t _ {e} - t _ {0}}\right), \tag {1} +$$ + +where $t_0$ and $t_e$ denote the window's start and end timestamps, respectively. The normalized coordinate $z_i$ encodes the relative temporal position of the event within the window, mapping event timestamps to a unified temporal scale. 4D Cross-Window Temporal Modeling: To model long-term dependencies across windows, we introduce a fourth dimension, $T_n$ , which represents the global temporal index of the window. This extends the 3D representation to a 4D event cloud $E_n = \{(x_i, y_i, z_i, T_n)\}_{i=1}^{M_n}$ , where $M_n$ is the number of events in window $n$ . The complete 4D event cloud is then $E = \bigcup_{n=1}^{L} E_n$ . + +This hierarchical dual-scale framework captures local intra-window dynamics through normalized timestamp $z$ and models global inter-window evolution via window index $T_{\mathrm{n}}$ . Unlike fixed event-count methods that fragment or regroup events [31, 66], compromising temporal integrity, our approach dynamically adapts to event sparsity and irregularity by processing variable-length sequences within fixed time windows. We also serialize 4D event clouds into SSM-compatible sequences using $z$ -order and Hilbert curves, aligning with point cloud processing paradigms [67, 68]. + +# 3.2. Spatio-Temporal Decoupling and Fusion + +To address the complex spatiotemporal noise in rain events while maximizing the temporal discrimination power of event camera, we propose a Spatio-Temporal Decoupling and Fusion Module (STDF). This module explicitly decouples spatial and temporal features while modeling their interactions across dual scales in the 4D event cloud. + +We extract spatial features $f_{\mathrm{s}}$ via depthwise 1D convolutions on $(x, y, z, p)$ coordinates and temporal features $f_{\mathrm{t}}$ through embeddings of window indices $T_{\mathrm{n}}$ . To exploit rain events' temporal characteristics and event cameras' high resolution, we prioritize temporal information over spatial information through cross-domain feature modulation. Specifically, spatial features $f_{\mathrm{s}}$ are refined through Hadamard products with complementary temporal representations: intra-window dynamics $f_{t}^{\mathrm{intra}}$ from 1D convolutions along $z$ , encoding microsecond correlations within windows, and inter-window trends $f_{t}^{\mathrm{inter}}$ from 1D convolutions on $T_{\mathrm{n}}$ , capturing long-term temporal trends across consecutive windows. This modulation is formulated as: + +$$ +f _ {\mathrm {s}} ^ {*} = f _ {\mathrm {s}} \otimes \left(f _ {\mathrm {t}} ^ {\text {i n t r a}} + f _ {t} ^ {\text {i n t e r}}\right). \tag {2} +$$ + +Finally, the temporally-modulated features are combined with the original spatial and temporal representations via residual addition $(\mathcal{R})$ . The integrated features are sequentially processed by 1D convolution $(\Phi_{1d})$ , batch normalization (BN), and activation $(\sigma)$ to ensure training stability: + +$$ +\begin{array}{l} \mathcal {R} \left(f _ {\mathrm {s}}, f _ {\mathrm {t}}\right) = f _ {\mathrm {s}} + f _ {\mathrm {t}} + f _ {\mathrm {s}} ^ {*}, \tag {3} \\ f _ {\mathrm {S T D F}} = \sigma \left(\mathrm {B N} \left(\Phi_ {1 d} \left(\mathcal {R} (f _ {\mathrm {s}}, f _ {\mathrm {t}})\right)\right)\right). \\ \end{array} +$$ + +# 3.3. Multi-Scale State Space Model + +Building upon the hierarchical input representation and spatiotemporal feature embedding, we propose the Multi-Scale State Space Model (MS3M) to further model deeper rain dynamics from multi-temporal and spatial scales. This framework incorporates parallel intra- and inter-window branches to simultaneously capture appearance features and motion patterns, coupled with a multi-scale spatial pathway that preserves structural details and local rain dynamics. + +Dual-Temporal-Scale Global Modeling: While Mamba excels in sequence modeling, it struggles to leverage temporal features [69] for event deraining. Inspired by the Motion-aware State Space Model (MSSM), which excels in LiDAR-based moving object segmentation [70], we integrate MSSM into our dual-temporal-scale architecture. This enables explicit modeling of rain events' appearance and motion, improving rain-background separation. + +The architecture mainly consists of two complementary branches: an intra-window branch processes spatial appearance features $f_{\mathrm{s}}^{\mathrm{intra}}$ through Reversed Aggregation (RA) and 1D convolution, capturing rain patterns and structural details for rain-background separation; an inter-window branch extracts motion-aware features $f_{\mathrm{m}}^{\mathrm{inter}}$ by analyzing temporal dependencies, enabling separation of dynamic rain streaks from moving objects or scene changes. An adaptive gating mechanism [71] generates weight $f_{\mathrm{G}}$ to emphasize rain-relevant features. Outputs from both branches are fused via cross-product attention with inter-branch interaction, then passed to SSM for global feature learning via scanning [72], followed by gating signal modulation. + +$$ +\begin{array}{l} f _ {\mathrm {s}} ^ {\text {i n t r a}} = \sigma \left(\Phi_ {1 d} \left(\mathrm {R A} \left(f _ {1}\right)\right)\right) \\ f _ {\text {f u s e}} = \sigma \left(f _ {\mathrm {m}} ^ {\text {i n t e r}}\right) \otimes f _ {\mathrm {s}} ^ {\text {i n t r a}} + f _ {\mathrm {m}} ^ {\text {i n t e r}} \tag {4} \\ f _ {\text {d u a l}} = \operatorname {S S M} \left(\sigma \left(f _ {\text {f u s e}}\right)\right) \otimes f _ {\mathrm {G}}. \\ \end{array} +$$ + +Multi-Spatial-Scale Local Pathway: To address rain scale and appearance diversity, we introduce a Multi-Scale Local Spatial Pathway. This pathway extracts multi-scale local features from the intra-window branch using convolutional layers with varying kernel sizes. Small kernel sizes ( $k_{s}$ ) capture fine details of thin rain streaks, while larger kernels model broader and more diffuse rain patterns. This design enhances the model's ability to handle diverse rain scenarios while preserving local structural details. + +$$ +\begin{array}{l} f _ {i} = \sigma \left(\Phi_ {1 d} ^ {k _ {i}} \left(f _ {i - 1}\right)\right), \quad i = 1, 2, \dots , n \\ f _ {0} = \Phi_ {1 d} ^ {k _ {0}} (\mathbb {L} (\mathrm {R A} (f _ {\mathrm {I}}))) \quad f _ {\mathrm {m s}} = \sigma \left(\sum_ {i = 1} ^ {n} f _ {i}\right) \tag {5} \\ \end{array} +$$ + +The multi-scale features $f_{\mathrm{ms}}$ are aggregated and fused with the global outputs $f_{\mathrm{dual}}$ via residual addition, seamlessly integrating local details and global context. Finally, a linear layer $(\mathbb{L})$ refines the fused features, formulated as $f_{\mathrm{out}} = \mathbb{L}(f_{\mathrm{ms}} + f_{\mathrm{dual}})$ , enhancing spatial precision while maintaining structural integrity. + +# 3.4. Training Loss + +![](images/40e0f1483264f087ea2224a6702c67b41a232614b322150a7af6359f9f3d9317.jpg) + +![](images/e4366231ffefaff397d82315ed5ebb9094ad3654b0d42fdd0ddd43be4cc850b4.jpg) + +![](images/ef1afa446e9b7a89434e17d8d7aaf8929bb14e374a2393e659143e9cf6b0cecf.jpg) + +![](images/16bc3bfd3439bfc46fbc0938199f13cd63d51b5a5dd673884f466de4a7a44b62.jpg) +Figure 3. Power Spectrum Heatmap and Segment Length Distribution for Rainfall Intensities (5, 20, 60 mm). Top: Heatmaps show higher frequencies at peak power for lower densities, reflecting sparse rain. Bottom: Distributions of continuous signals reveal longer segments at higher densities, indicating sustained rain. + +![](images/9da8306bcd63da747d601fc2e4d69c90037fb1d43968f949075e751d6222c5c6.jpg) + +![](images/86218fad09f5f9eb62b99210f2095a405eb2933dc1aeea99fe2d48ec74a53166.jpg) + +Our training objective combines a standard binary cross-entropy loss $(\mathcal{L}_{\mathrm{ce}})$ with a frequency-domain regularization term $(\mathcal{L}_{\mathrm{fit}})$ to guide the model in learning both point-wise accuracy and global frequency patterns, forming the joint loss as $\mathcal{L} = \mathcal{L}_{\mathrm{ce}} + \lambda \mathcal{L}_{\mathrm{fit}}$ . + +Frequency-Domain Regularization: Existing image deraining methods integrate frequency layers to capture frequency-domain features [61, 73, 74]. However, for event camera with millions of event data, embedding Fast Fourier Transform (FFT) layer directly introduces significant computational overhead. Alternatively, we propose incorporating $\mathcal{L}_{\mathrm{fft}}$ as a regularization term during model optimization, maintaining efficiency while mitigating overfitting. + +While $\mathcal{L}_{\mathrm{ce}}$ focuses on per-event accuracy, it may overlook global distribution patterns, resulting in unrealistic predictions like isolated rain events. In contrast, $\mathcal{L}_{\mathrm{ftt}}$ enforces statistical consistency by aligning frequency-domain distributions via amplitude and phase constraints: + +$$ +\mathcal {L} _ {\mathrm {f f t}} = \frac {1}{L} \sum_ {i = 1} ^ {L} \left(\frac {| \mathcal {F} (P) _ {i} - \mathcal {F} (Y) _ {i} |}{\operatorname* {m a x} (| \mathcal {F} (P) - \mathcal {F} (Y) | , \epsilon)} + \epsilon^ {\prime}\right) ^ {2}, \tag {6} +$$ + +where $\mathcal{F}(\cdot)$ denotes the 1D FFT, $L$ is the sequence length, and $\epsilon, \epsilon'$ ensure numerical stability, and $Y$ and $P$ denote the ground truth labels and predicted outputs, respectively. Unlike traditional $\mathcal{L}_{\mathrm{fft}}$ used in image reconstruction [61, 75], our formulation operates directly on event labels, leveraging event cameras' microsecond-level resolution to capture rain dynamics. Rainfall intensity directly correlated to event density and label 1's density (rain events labeled as 1). As illustrated in Figure 3, high-density rainfall manifests as low-frequency continuous patterns in the label sequence, while low-density rain exhibits high-frequency sparse patterns. This spectral distinction enables $\mathcal{L}_{\mathrm{fft}}$ to align predictions with physically consistent global patterns [76]. + +![](images/77bf151f5740c1e9b2c617eb867f43577a00b746df66a317940cb87d51ca331a.jpg) +Figure 4. EventRain-27K: The First Point-based Event Deraining Dataset. Additional dataset visualizations with varying rainfall intensities and scenarios are included in the Appendix. + +# 4. Dataset + +To support model training and testing, we published EventRain-27K, the first point-based benchmark dataset for event-based deraining. The dataset comprises over 7K self-generated synthetic rain samples, over 7K self-recorded artificial rain samples, and over 9K real rain samples. + +Synthetic Dataset (labeled). Supervised event deraining relies on labeled data; however, annotating discrete, sparse, and highly dynamic event points is non-trivial. To address this limitation, we use a two-step synthetic data generation approach. We first utilize the KITTI dataset [77] and the SPAC dataset [78] as clean video sources, then synthesize rain effects using state-of-the-art rendering simulators [79, 80]. The KITTI rainy dataset provides videos with varying camera motion speeds and rain intensities (4(a)), covering rainfall rates ranging from light rain (5 mm/hour) to severe storms (200 mm/hour). The SPAC rainy dataset includes 16 diverse scenes, such as cityscapes and natural environments, each augmented with 3 to 4 distinct rain patterns (4(b)). Finally, we generate event sequences from these rainy videos using the Vid2E simulator [81]. + +Self-recorded Artificial Dataset (labeled). To bridge the domain gap between synthetic and real-world event data for model training, we introduce a self-recorded artificial dataset, capturing real event camera data under controlled artificial rainfall. A showerhead was employed to simulate raindrop free-fall motion, captured by a Prophesee EVK4 event camera $(1280\times 720$ resolution, $10\mathrm{k}$ fps, $120\mathrm{dB}$ dy + +
Metrics5mm20mm50mm80mm125mm150mm
SR ↑NR ↑DA ↑SR ↑NR ↑DA ↑SR ↑NR ↑DA ↑SR ↑NR ↑DA ↑SR ↑NR ↑DA ↑SR ↑NR ↑DA ↑
TS[82]0.8880.2650.5760.8870.3050.5960.8830.2310.5570.8810.2710.5760.8770.2370.5560.8720.2430.557
DWF[83]0.7030.3940.5490.7340.4640.5990.7550.3520.5530.7770.4320.6040.7860.3710.5780.7820.3750.578
Knoise[84]0.8600.3750.6180.8700.3770.6240.8840.2410.5630.8900.2570.5740.9010.2110.5560.8960.2140.555
Ynoise[85]0.6790.5330.6060.6770.5680.6230.6630.4810.5720.6580.5250.5910.6470.4820.5640.6340.4870.561
RED[86]0.8620.1720.5170.8530.2510.5520.8330.2080.5200.8220.1850.5030.8080.2070.5070.7890.2080.499
EDnCNN[86]0.9680.9050.9370.9540.9040.9290.9480.8880.9180.9350.8700.9030.9330.8670.9000.9290.8430.886
AEDNet[87]0.9410.8500.8910.9380.8760.9070.9280.7320.8300.9250.6810.8030.9220.6240.7730.9230.5470.735
EDformer[66]0.9810.8180.8990.9620.8320.8970.9240.8440.8840.8940.8340.8640.8760.8400.8580.8390.8340.836
Ours0.9940.9140.9540.9780.9150.9470.9550.9110.9330.9400.9030.9220.9180.8980.9080.9080.8950.902
+ +Table 1. Quantitative Comparisons on Synthetic Dataset with Varying Rainfall Intensities. We mark the best and second best results. + +![](images/f8003e4dee36b93e9df22d63cafc14667dfc2256819b52094e7ef686a6adb4f4.jpg) +Figure 5. Our fixed-point & speed data acquisition system. + +namic range) for both rainy and rain-free data. Slight camera vibrations were applied during captures to obtain complete scene details. Utilizing the K-Nearest Neighbors (KNN) algorithm, background events in rainy data were identified via spatiotemporal alignment with rain-free data, enabling background labeling and isolating rain events. The dataset focuses on urban outdoor scenes (buildings, trees, cars, lakes) and covers diverse rainfall intensities across four scenarios (Figure 4(c)). + +Real-world Dataset (label-free). To validate event deraining effectiveness and generalization, we collect a real-world event dataset. As illustrated in Figure 5, we designed a data acquisition system with fixed-point and fixed-speed (10 cm/s) cruising. We mounted a Propheesee EVK4 event camera on a motion-controlled vehicle, which traversed a slide rail to capture background and rain data simultaneously under controlled dynamic conditions. The dataset includes diverse viewpoints and rain intensities, covering a wide range of real-world scenarios (Figure 4(d)). Additionally, it incorporates 4K samples of real snow data captured to evaluate the model's generalization capability. + +# 5. Experiments + +# 5.1. Experiments Setups + +Evaluation Metrics. We use event Denoising Accuracy (DA), Signal Retention (SR) and Noise Removal (NR) to measure the event rain removal performance on PRE-Mamba. There is $\mathrm{DA} = \frac{1}{2} (\mathrm{SR} + \mathrm{NR}) = (\frac{\mathrm{PB}}{\mathrm{TB}} +\frac{\mathrm{PR}}{\mathrm{TR}})$ , where PB, TB, PR, TR are the predicted background, the predicted rain, the real background, and the number of real rain, respectively. DA measures rain removal while preserving real motion (e.g., vehicles, pedestrians) and structural details + +(e.g., roads, building profiles). SR and NR analyze signal retention and noise suppression, respectively. + +Implementation Details. Our network is implemented in PyTorch and trained using the AdamW optimizer with an initial learning rate of $4.8 \times 10^{-4}$ and a weight decay coefficient of $5 \times 10^{-3}$ . The entire training is conducted on six NVIDIA RTX A6000 GPUs for 50 epochs with a batch size of 6. The model processes a sequence of five temporal windows as input, with each window spanning 0.1 seconds. In the multi-spatial-scale module of the MS3M, we employ kernel sizes of (1, 3, 5) to capture features at different spatial resolutions. Network details can be found in the Appendix. + +# 5.2. Comparisons with State-of-The-Art Methods + +Baselines. As this work represents the first attempt at point-based event deraining, there are no directly comparable baselines in the literature. Alternatively, we adapt state-of-the-art event denoising methods, as deraining can be viewed as a specialized case of noise removal. These include filter-based methods TS [82], DWF [83], Knoise [84], Ynoise [85], RED [86] and learning-based algorithms EDnCNN [86], AEDNet [87], EDformer [66]. Additionally, we qualitatively compare with DistillNet [11], a voxel-based GAN deraining method, but its voxelized processing is incompatible with event point denoising metrics, preventing quantitative evaluation. + +Results on Synthetic and Artificial Datasets. In Table 1, we present SR, NR, and DA results on the synthetic dataset with six rain intensities, ranging from light rain to heavy rain. Our method achieves state-of-the-art performance, with an average SR/NR/DA of $0.95 / 0.91 / 0.93$ . It is notable that learning-based algorithms outperform filtering methods due to their ability to leverage supervised training. When training EDnCNN [86], we replaced its original event probability mask (EPM) labeling framework with our ground truth labels, which improved its performance. In addition, we provide qualitative results in Figure 6. Filtering methods are ineffective for rain removal, as rain streaks exhibit distinct spatiotemporal patterns that deviate from typical noise. Other learning-based methods yield incomplete deraining results, often retaining residual rain streaks. In contrast, our method effectively removes rain streaks and restores details through multi-scale temporal and spatial modeling + +![](images/463d8cc9a2b75a892419f8845159a8aaba16a1653feb2e133b02bcedde199891.jpg) +Figure 6. Qualitative Comparison on Synthetic and Artificial Datasets. PRE-Mamba demonstrates superior deraining capabilities across diverse structural contours and complex textures with enhanced detail preservation. Please zoom in for details. + +
GFLOPsParametersInference time (s)Relative speed
TS[82]N/AN/A0.12961.0 ×
DWF[83]N/AN/A0.09541.36 ×
KNoise[84]N/AN/A0.01986.55 ×
YNoise[85]N/AN/A0.05132.53 ×
RED[86]N/AN/A2.27160.06 ×
EDnCNN[86]234.51614.55K20.18851.0 ×
AEDNet[87]4400.4645.87M43.42500.46 ×
DistillNet[11]255.1718.96M0.202999.50 ×
EDformer[66]8.4149.80K2.49438.09 ×
Ours6.23264.63K0.0987204.54 ×
+ +Table 2. Model complexity comparisons with previous model. + +combined with motion and appearance perception. + +Generalization on Real-World Dataset. To validate practical applicability, we compare our method against baselines on the real-world data of EventRain-27K. Figure 7 (top four rows) visualizes results for four scenarios, including three ground-level and one low-altitude viewpoints. Our method achieves superior performance compared to competitors. In the low-altitude scenario, our method effectively eliminates rain streaks while maintaining the structural integrity of static objects (e.g., buildings) and preserving the motion patterns of dynamic objects (e.g., vehicles). Filter-based methods treat both background and rain equally, resulting in effects similar to downsampling. While EDnCNN [86], AEDNet [87], and EDformer [66] are trained on synthetic data, their denoising-focused designs fail to generalize well to real rain, further hindered by the synthetic-to-real domain gap. DistillNet [11] removes large rain streaks via voxel-based GANs but loses background details and introduces artifacts. In contrast, our method, designed for point-based event deraining, effectively removes rain while preserving both background details and dynamic motion content, demonstrating robust real-world performance. + +Model Complexity and Efficiency Comparison. In Table + +
ModelSTDFMS3MLfitSR↑NR↑DA↑
M10.91230.83940.8759
M2✓0.89830.87470.8865
M3✓0.89410.89060.8923
M4✓✓0.90460.89540.9000
Ours✓✓✓0.90800.89490.9015
+ +Table 3. Ablation about each module in PRE-Mamba on the EventRain-27K validation set. + +2, we compare the computational efficiency of our method and baselines in terms of FLOPs, parameters, and inference time for processing 100K events on an NVIDIA RTX A6000 GPU. Filtering-based methods enable fast inference but suffer from poor deraining performance due to lack of task-specific optimization. EDnCNN [86] and AEDNet [87] incur high computational overhead from encoding or sampling spatial-temporal neighborhoods, resulting in high FLOPs and slow inference. Transformer-based EDformer [66] reduces FLOPs and parameters but suffers from high latency due to the quadratic complexity of its attention mechanism. DistillNet [11] achieves a lower inference time by voxelizing events but at the cost of high computational complexity, large model size, and loss of fine-grained temporal precision. In contrast, our method achieves SOTA performance with only 6.23G FLOPs and 0.26M parameters, processing 100K events in 0.0987s and scaling to 1M events in 0.398s. Compared to EDnCNN and AEDNet, our method reduces FLOPs to $2.66\%$ and $0.14\%$ of theirs, respectively, while achieving $204.5\times$ and $440.0\times$ faster inference. Compared to the lightweight EDformer, our method achieves a $25.3\times$ speedup with comparable model size, excelling in both accuracy and computational efficiency. + +# 5.3. Ablation Studies + +Baseline Design. We conduct systematic ablation studies to validate the efficacy of three proposed components: + +![](images/df93f306664efcbdfdc35074bb31c3ed3965497afb63573d86e6664442e14785.jpg) +Figure 7. Qualitative Comparison on Real-World Datasets. The top four rows highlight our method's superior deraining performance on real rain datasets, while the last two rows showcase its generalization to snow scenes. Please zoom in for details. + +
Window NumberNum = 3Num = 5Num = 8
DA0.82680.90150.9330
Improve (%)-9.0312.84
Inference time (ms)274.02394.16525.68
Relative speed-0.70 ×0.52 ×
+ +Table 4. Ablation about time window number on validation set. the Spatio-Temporal Decoupling and Fusion (STDF) module, Multi-Scale State Space Model (MS3M), and Frequency Loss $(\mathcal{L}_{\mathrm{fft}})$ . Our baseline model ("M1") removes all three components, employing naive summation for spatiotemporal feature fusion, reverting to the original MSSM block [70] for temporal modeling, and using only cross-entropy loss. Building upon "M1", "M2" introduces the STDF module to embed structured spatio-temporal features, while "M3" integrates the MS3M architecture for enhanced multi-scale modeling. And "M4" combines both STDF and MS3M components. Finally, we incorporate the Frequency Loss into "M4" to complete our full model. + +Quantitative Comparison. From Table 3, we observe that both STDF ("M2") and MS3M ("M3") improve the baseline performance by $1.21\%$ and $1.87\%$ in DA, respectively, validating their individual contributions. "M3" achieves greater improvement, demonstrating MS3M's ability to capture deep spatio-temporal features and adapt to diverse rain patterns. By integrating STDF with MS3M, "M4" further enhances performance, demonstrating the complementary nature of these components in modeling multi-scale rain and event characteristics. Finally, our full network outperforms "M4", which verifies the importance of the frequency-domain regularization term in leveraging both amplitude and phase constraints for improved learning. + +Effects of Time Windows Number. In Table 4, we evaluate model performance with time windows of 3, 5, and 8 + +on validation set. Increasing the number of time windows improves the model's ability to capture temporal dependencies, with a $9.0\%$ improvement in DA from 3 to 5 windows and an additional $3.8\%$ improvement from 5 to 8. However, the inference speed decreases by $30\%$ when the window size is increased from 3 to 5, and by $48\%$ when increased from 3 to 8. Therefore, we set the number of time windows to 5, as further increases in time windows yield diminishing returns, emphasizing the need to balance temporal depth and computational efficiency. + +# 5.4. Generalization to Snowy Datasets + +While primarily designed for event-based deraining, our method also generalizes well to snow removal, as demonstrated in Figure 7 (last two rows). Without architectural changes, it delivers promising results under snowy conditions, showcasing robustness to diverse weather patterns. Additional visual results are included in the Appendix. + +# 6. Conclusion + +To the best of our knowledge, PRE-Mamba is the first point-based framework for event camera deraining. It adopts a 4D event cloud to preserve native temporal resolution via inter- and intra-temporal windows, a spatiotemporal decoupling and fusion module for efficient feature extraction, and a multi-scale state space model that captures rain dynamics across spatial and temporal scales with linear complexity. A frequency regularization term and cross-entropy loss guide learning, and we contribute a large-scale dataset with diverse rain scenarios. Extensive experiments demonstrate SOTA performance on synthetic and real-world data. 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Black $^{2}$ + +$^{1}$ Meshcapade, $^{2}$ Max Planck Institute for Intelligent Systems, Tübingen $^{3}$ Stanford University + +![](images/a90aba84fc4f6148b2040aa2dc13b987e48426289058eac7a53af0ed5154c204.jpg) +Figure 1. PRIMAL is a novel generative real-time 3D character animation system that works in Unreal Engine. The avatar reacts to induced impulses promptly and naturally (top). After efficient adaptation, the avatar can be pulled to chase a "magnet" (middle). We also personalize the avatar's movements based on a tiny mocap dataset, captured by Mocapade3.0 [19] from cellphone videos (bottom). As a result, we can control the avatar with discrete commands and continuous signals. Without any control signal, or external perturbations, the avatar moves autonomously in the 3D space without end. PRIMAL is purely data driven; no physical simulation is used. + +# Abstract + +We formulate the motor system of an interactive avatar as a generative motion model that can drive the body to move through 3D space in a perpetual, realistic, controllable, and responsive manner. Although human motion generation has been extensively studied, many existing methods lack the responsiveness and realism of real human movements. Inspired by recent advances in foundation models, we propose PRIMAL, which is learned with a two-stage paradigm. In the pretraining stage, the model learns body movements from a large number of sub-second motion segments, providing a generative foundation from which more complex motions are built. This training is fully unsupervised without annotations. Given a single-frame initial state during inference, the pretrained model not only generates unbounded, realistic, and controllable motion, but also enables the avatar to be responsive to induced impulses in real time. In the adaptation phase, we employ a novel ControlNet-like adaptor to fine-tune the base model effi + +ciently, adapting it to new tasks such as few-shot personalized action generation and spatial target reaching. Evaluations show that our proposed method outperforms state-of-the-art baselines. We leverage the model to create a real-time character animation system in Unreal Engine that feels highly responsive and natural. + +# 1. Introduction + +There has been rapid progress in 3D human motion generation conditioned on text or existing motion sequences [32, 34, 39, 41, 42, 44, 68, 70, 73, 84, 88]. Despite the realism of such approaches, they are not good models of how real humans behave, in that they are not interactive. Autonomous characters need to respond in real-time to commands and environmental inputs such as external forces. To feel "alive", such an agent must be continuously on-line and + +reactive. It must move on its own yet be able to respond to commands. We introduce such an agent using a two-stage approach, in which we first train a low-level motor system from motion capture (mocap) data such that it mimics the dynamics of human motion. This provides a platform upon which to build more complex interactive behaviors in a second stage. This two-stage approach provides a base "motor system" that implicitly models the dynamics of human motion, generalizes beyond the training data, and supports the training of more complex behaviors. + +Our approach, called PRIMAL (Physically Reactive and Interactive Motor model for Avatar Learning), models low-level motor control using an autoregressive diffusion model that is trained to capture human motion movement over short time intervals. Without any physics simulation, we observe that this approach is able to model physically realistic movements, including ground contact, even though we never explicitly model or label contact. This provides a data-driven approach to learning avatar motor control that appears physically realistic without physics simulation. + +We make two key observations that ground our approach. First, existing autoregressive motion models usually predict a future motion conditioned on a past motion. Since a motion sequence implicitly contains semantic information, this ensures the predicted motion is semantically related to the past. However, it raises the risk that the model overfits to the semantics in the training data when the training samples are limited (as they are with existing mocap datasets). This limits generalization, resulting in a model that does not make a good foundation for general motor control. Second, human motion is dominated by physics over short time intervals and by semantics over long ones. We use different approaches to model each of these. We observe that physics plays a critical role in time intervals on the order of 0.5 sec, or 15 frames at 30fps. On longer time horizons, higher level goals dominate. + +In PRIMAL, the first stage models this short-term motion: given an initial condition of the body, including its joint locations and velocities at a single time instant, we predict the motion of the next half second. This assumes that, over a short time horizon, the motion of the future is independent of the past. With this assumption, we have vast amounts of motion capture data with which to train the model; every segment of 15 frames is available for training. We demonstrate that training our generative model in this way mimics the dynamics of human motion without doing any physics simulation. Note that, while we do not explicitly model foot-ground contact, the model learns to produce movements with physically plausible contact. + +Motivated by the representation power of diffusion models [26, 66, 67], the first stage is implemented as a diffusion model, which is trained on diverse half-second motion segments in a fully unsupervised manner. The trained model + +not only generates realistic and autonomous motions in 3D space, but also makes it straightforward to control the avatar in real-time. For example, we simply reset any joint velocities to new values and the model will adapt its future motion appropriately. We can also drive the avatar to reach desired speeds and directions, using a classifier-based guidance (CBG) [14] approach, for which the CBG gradients are analytically derived. + +High-level and long-term behaviors can be composed as a time sequence of consecutive atomic actions. This decouples the learning of movements and semantics, enabling us to learn them individually in a two-stage paradigm with a pretraining stage (motor control) and the adaptation stage (behavior generation). Specifically, we propose a generic adaptation approach based on ControlNet [83] in the second stage. Here, we consider two types of adaptation. One focuses on spatial target reaching and the other on few-shot semantic action generation. To improve the effectiveness of the control signal, we follow [44] to add the control embedding to individual blocks of the transformer. + +We demonstrate the benefits of our interactive avatar with several applications. First, we create an interactive 3D environment in Unreal Engine, in which the agent exhibits perpetual motion (see Fig. 1). The agent's movement is controlled with standard game controllers to move in any direction at varied speeds. Unlike traditional game technology, however, all the motions are uniquely generated in real time based on the commands. We introduce external forces ("pulling" with a "magnet" or an impulsive force that "zaps" the character) that dynamically change the agent's behavior (see Supplemental Video). The agent reacts promptly to interventions in a natural way, without any explicit physics-based training, showing that the first stage learns a generic motor model. Second, we demonstrate how our approach enables training a person/style-specific model using a tiny amount of motion capture data captured with a cell phone. The results illustrate how pre-training a foundational movement stage provides a basic "motor system" upon which to build complex behaviors. + +In summary, PRIMAL produces naturalistic human motion common to methods trained on mocap data together with the physical plausibility and generalization of physics-based methods. To build a motor system for interactive avatars, we use an autoregressive diffusion model with a two-stage pretrain-and-adaptation learning paradigm. This first stage trains the model to capture human motion over short time scales, providing a reactive model that runs in real time. The second stage uses an efficient and generic approach to adapt the base model to different avatar-related tasks. The interactive nature of PRIMAL effectively "breathes life" into an avatar, making it appropriate for applications in gaming, AR/VR, controllable video generation, and interactive agents. + +# 2. Related Work + +Offline motion generation. Enabled by large mocap datasets [20, 50, 58], generative motion models have advanced rapidly, including methods focused on text-to-motion [13, 31, 32, 44, 70, 84], human-scene/object interactions [4, 21, 22, 34, 39, 40, 68, 69, 79, 80, 88], spatial control [15, 35, 45, 61, 78, 81, 86], dance generation [42, 43, 75], and more. Specifically, diffusion models [26, 66, 67] are a promising approach for motion generation, due to their representation power and controllability. For example, MDM [70] proposes a diffusion model with the transformer [77] network, which is trained with text-motion paired data [20] and is able to generate high-fidelity motions given text descriptions. OmniControl [81] leverages ControlNet [83] to create a new adaptor, enabling spatial control of text-to-motion. MotionLCM [13] proposes a consistency model for real-time text-to-motion, and implements autoregressive generation as a spatial control task. Most of these approaches are offline methods and have motion length limitations, making them inappropriate for interactive avatar control. + +More similar to our approach is OMG [44], which proposes a pretrain-then-finetune strategy for text-to-motion. Its pretraining phase trains foundation models with up to 1 billion parameters only with unlabeled mocap data, and the fine-tune phase leverages a ControlNet-like adaptor with a mixture-of-experts. In contrast to our approach, OMG is offline and their pretraining process focuses on generating motions up to 300 frames long, much longer than our short time horizon. Unlike OMG, our model formulation is autoregressive, which not only generates unbounded and controllable motion in real time, but also makes the avatar reactive to external perturbations. + +Physics-based motion generation. A key problem of the data-driven methods above is that they often lack physical plausibility; e.g. feet slide, float, or penetrate the floor, and impacts are not realistic. To address this, many methods have been developed that exploit physical simulation [22, 46, 56, 61, 62, 78]. Hassan et al. [22] employ reinforcement learning (RL) and adversarial imitation learning to produce life-like and physically plausible human-scene interactions. PACER++ [78] generates physically plausible pedestrian locomotion in driving scenarios with fine-grained body part control. Simulation can also be efficiently combined with generative models. For example, PhysDiff [82] projects the generated motion into a physically plausible motion space via physical simulation, which is applied within the reverse diffusion process. CLoSD [71] uses an efficient autoregressive diffusion model, DiP, for planning and applies simulation for tracking, generating unbounded physically plausible motions in 3D. InsActor [62] proposes an hierarchical approach to generate motions given instructions, which contains diffusion-based planning and + +simulation-based motion tracking. An advantage of simulation approaches is that they can generalize to adapt to external forces. However, the resulting motions are usually not yet as natural as those from diffusion models. Additionally, simulations tend to learn policies of a narrow set of motor skills, rather than a generic human motion control system. + +Autoregressive unbounded motion generation. Autoregressive models are trained to generate future frames conditioned on past frames. GAMMA [86] is a VAE [37] model that generates motion primitives recursively and leverages RL to train a policy for spatial target reaching. WANDR [15] is a conditional VAE that generates motions to reach a 3D target with the wrist joint. DIMOS [88] uses scene-aware policies for motion-primitive generation, enabling the synthesis of continuous human-scene interactions. Recently, diffusion models have been used for autoregressive motion modeling. For example, CAMDM [11] exploits a diffusion model that treats motion style, spatial control, and motion history as separate tokens, producing unbounded motions for real-time character animation. Jiang et al. [33] propose a diffusion model that is conditioned on the past 2 frames, as well as text, scene, etc., to generate human-scene interactions. AMDM [64] uses an autoregressive diffusion model with an MLP denoiser. In addition to generating random motions, policy networks are trained with RL for motion control in various tasks. The DiP model proposed in CLoSD [71] is conditioned on the motion history of 20 frames and text tokens, and generates a 40-frame motion in the future. DART [89] uses an online generation method that has an autoregressive VAE tokenizer and a latent autoregressive diffusion model, modeling motion primitives and performing high-fidelity text-to-motion in real time. Latent space optimization and RL policies are used for motion control on the pre-trained model. + +Compared to existing autoregressive diffusion models that generate $N$ future frames based on $M$ past frames, our model formulation generates motions based on an initial state of a single frame that includes joint positions and velocities. With this form, PRIMAL learns human movement from unstructured and unlabeled mocap data directly, without the support of physics or annotations. Despite the lack of explicit physics training, we find that visually plausible physical effects are present in the generated motions. In addition, neither motion tokenizers nor scheduled sampling [5] schemes are necessary in our method, leading to a simple and straightforward training workflow. + +# 3. Autoregressive Diffusion Motion Models + +# 3.1. Preliminaries + +SMPL-X [54]. We employ the SMPL-X gender-neutral body model and denote it as $\mathcal{M}(\beta, r, \varphi, \theta)$ , in which $\beta \in \mathbb{R}^{16}$ represents the body shape parameters, $r \in \mathbb{R}^3$ is the + +root translation, $\varphi \in \mathbb{R}^6$ and $\theta \in \mathbb{R}^{126}$ are the root and joint rotations w.r.t. the continuous 6D representation [91], respectively. Since we focus on the body motion without facial expressions or hand articulations, we extract the 22 joints of the body skeleton and denote their locations and velocities as $J \in \mathbb{R}^{66}$ and $\dot{J} \in \mathbb{R}^{66}$ , respectively. + +Denoising diffusion probabilistic models (DDPM) [26]. Diffusion models are widely used for tasks like motion generation. In this work, we follow the DDPM formulation [26]. Provided a clean sample $\mathbf{X}^0\sim p(\mathbf{X}^0)$ , the forward diffusion process gradually adds Gaussian noise to the sample in $T$ steps, and produces a sequence of samples at different noise levels, i.e. $\{\mathbf{X}^1,\dots ,\mathbf{X}^t,\dots ,\mathbf{X}^T\}$ . Given $q(\mathbf{X}^t |\mathbf{X}^{t - 1}) = \mathcal{N}\left(\sqrt{1 - b_t} X^{t - 1},b_t\mathbf{I}\right)$ with $\{b_{t}\in (0,1)\}_{t = 1}^{T}$ being a set of noise variance scheduler variables, it has + +$$ +\mathbf {X} ^ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {X} ^ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {1} +$$ + +in which $\alpha_{t} = 1 - b_{t}$ , $\bar{\alpha}_{t} = \prod_{t^{\prime} = 1}^{t}\alpha_{t^{\prime}}$ , and $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ . + +The reverse diffusion process gradually removes noise from $\mathbf{X}_t$ to recover the original clean sample $\mathbf{X}_0$ . Following [60, 70], we use a neural network to predict the clean sample in this work, i.e. $\hat{\mathbf{X}}^0 = G(t,\mathbf{X}^t,\mathbf{c})$ , which takes the diffusion time step, the noisy sample, and a condition as input. This network is trained by minimizing a simple loss [26], given by $\mathcal{L}_{\mathrm{simple}} =$ + +$$ +\mathbb {E} _ {\mathbf {X} ^ {0} \sim p \left(\mathbf {X} ^ {0}\right), t \sim U [ 1, T ]} \left[ \left\| \mathbf {X} ^ {0} - G \left(t, \mathbf {X} ^ {t}, \mathbf {c}\right) \right\| ^ {2} \right]. \tag {2} +$$ + +During test-time, the reverse diffusion process can be controlled via classifier-based guidance (CBG) [14] and classifier-free guidance (CFG) [25]. With a pre-trained diffusion model and the guidance objective functions, CBG computes the gradients of the objectives at each denoising step, and hence does not support real-time applications in general. On the other hand, CFG trains the conditional and unconditional diffusion models jointly, and guides the reverse diffusion process via weighted averaging, which is usually much more efficient than CBG. With $G(t,\mathbf{X}^t,\emptyset)$ being the unconditional model, CFG is performed at each denoising step by + +$$ +\hat {X} ^ {0} = G (t, \mathbf {X} ^ {t}, \emptyset) + \gamma (G (t, \mathbf {X} ^ {t}, \mathbf {c}) - G (t, \mathbf {X} ^ {t}, \emptyset)), \tag {3} +$$ + +in which $\gamma \in \mathbb{R}^{+}$ is a hyper-parameter. A larger value of $\gamma$ will increase the influence of the condition. However, invalid results can be produced if it is too large. + +# 3.2. Motion Representation + +We represent an $N$ -frame motion segment as a time sequence of states, $\pmb{X} = \{\pmb{x}_0,\pmb{x}_i,\dots,\pmb{x}_{N - 1}\}_{i = 0}^{N - 1}$ . Each state has $\pmb{x}_i = (r,\varphi ,\theta ,J,\dot{J})\in \mathbb{R}^{267}$ based on SMPL-X. During training, we use the ground truth body shape $(\beta)$ . During testing, we can either leverage a ground truth $\beta$ from the + +![](images/e9b3e644ee8bdefa4ea09caa39d05390c699b57816d673141e4d81967f83ce35.jpg) +Figure 2. Illustration of our network $\hat{\pmb{X}}^0 = G(t,\pmb{X}^t,\pmb{x}_0)$ . The tea-green layers contain trainable parameters and the orange blocks are non-learnable operations. The pink squares denote the tokens at individual frames. + +test set, or draw it from $N(0,\mathbf{I})$ , in order to compute the initial state $\pmb{x}_0$ . During motion generation, $\beta$ is fixed. + +Each motion segment spans 0.5 seconds in this work. This time duration corresponds to the average hang time of human jumps² or nearly half of a walking cycle. This is a time frame during which human motion is dominated more by physical forces than by intentional control. + +Following the canonical coordinate system proposed by [86, 87], the body-centric canonical coordinate is located at the pelvis of the first frame, with X,Y, and Z pointing left, up, and forward, respectively. The neural network is trained with canonicalized motion segments. + +# 3.3. Neural Networks + +Architecture. Following e.g. [11, 64, 71, 89], in this paper the autoregressive diffusion model is defined as a diffusion model that generates $N$ future frames based on $M$ past frames. We formulate our denoising network as $G(t,\mathbf{X}^t,\pmb{x}_0)$ with transformers [55, 77] and illustrate the architecture in Fig. 2. It leverages in-context conditioning, in which the diffusion time embedding and the initial state embedding are first added and then concatenated with the embedding of the noisy motion segment. SiLU [16, 24, 59] is used in the feed-forward layers. + +Training. Unlike existing autoregressive diffusion models, e.g. [11, 71, 89], that leverage annotated training data, our model focuses on modeling the body movements and is trained only with unlabeled short mocap segments. Therefore, the data limitation issue is effectively overcome, since we can collect a huge amount of segments from AMASS [50]. In addition, our motion model is directly trained in + +the motion space, instead of the latent space as in [32, 89]. No separate tokenizers are trained in our method. + +Our training loss is given by + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s i m p l e}} + \gamma_ {1} \mathcal {L} _ {F K} + \gamma_ {2} \mathcal {L} _ {F K V}, \tag {4} +$$ + +which contains a DDPM simple term (see Eq. (2)), two forward kinematics terms on the joint locations and velocities, respectively, and two weights $\gamma_{1}$ and $\gamma_{2}$ . The two forward kinematics losses are given by + +$$ +\mathcal {L} _ {F K} = \frac {1}{N} \sum_ {i = 0} ^ {N - 1} \| \mathcal {M} (\beta , \hat {r} _ {i}, \hat {\varphi} _ {i}, \hat {\theta} _ {i}) - J _ {i} \| _ {2} ^ {2}, \tag {5} +$$ + +and + +$$ +\mathcal {L} _ {F K V} = \frac {1}{N} \sum_ {i = 0} ^ {N - 1} \| \dot {\mathcal {M}} (\beta , \hat {r} _ {i}, \hat {\varphi} _ {i}, \hat {\theta} _ {i}) - \dot {J} _ {i} \| _ {2} ^ {2}, \tag {6} +$$ + +in which the predicted motion state at the $i$ -th frame is denoted by $\hat{\pmb{x}}_i = (\hat{r}_i, \hat{\varphi}_i, \hat{\theta}_i, \hat{J}_i, \hat{J}_i)$ . The ground truth body shape $\beta$ is used. + +Our model is trained in a fully unsupervised manner, and does not use foot contact labels as in [70, 85]. We think the contact information, which is usually defined by the horizontal velocities of the foot joints, can be automatically learned by minimizing the $\mathcal{L}_{FKV}$ term. Incorrect annotations can also degrade model performance. Moreover, we find that our model is self-stabilizing after being trained. Therefore, scheduled sampling [5], which can substantially reduce the training speed, is not employed in our training phase. Compared to existing methods such as [11, 45, 64, 70, 71, 86, 88, 89], our training pipeline is simple and straightforward. + +# 3.4. Inference + +Our motion model learns the distribution of $p(\mathbf{X}|\mathbf{x}_0)$ . Given an initial state, the model generates a motion segment starting with this initial state, and works repeatedly to produce an arbitrarily long motion sequence. The overall inference approach is summarized in Alg. 1 in Sup. Mat. + +In addition, we propose three efficient and effective test-time processing approaches to refine the motion on the fly, i.e. joint re-projection, snapping to the ground, and inertialization blending [8, 27]; see Sup. Mat. for details. + +# 3.4.1. Motion Control with Induced Impulses + +The model generalizes outside the training data, exhibiting behavior typically seen only with physics simulation. Specifically, we perturb the avatar with novel external impulses by changing the velocity at one or more joints. Using this, we can control the avatar with impulses to generate certain actions in a principled manner. For example, we can generate kicks by giving an upward impulse to the joints on + +the leg, or generate runs by pushing the avatars from the back. + +Impulse induction is implemented by perturbing the initial velocities before generating a new segment. We find that such impulses can be defined to reliably generate specific actions; see Sup. Mat. Tab. A1. Future work should explore the automated discovery of impulses for controlling behavior. + +# 3.4.2. Motion Control with Classifier-based Guidance + +Another basic level of controllability needed for an interactive avatar is the ability to move in a given direction at a given speed. To enable that, we propose two intuitive classifier-based guidance (CBG) loss terms to control the movement and the facing direction of the avatar. + +The movement guidance loss is based on the average velocity of all 22 joints in the half-second time horizon, which is given by + +$$ +\mathcal {L} _ {\text {m o v e}} = \left\| \left(\frac {1}{2 2 N} \sum_ {i = 0} ^ {N - 1} \sum_ {j = 1} ^ {2 2} \hat {J}\right) - \boldsymbol {v} _ {\text {g o a l}} \right\| ^ {2}, \tag {7} +$$ + +in which $\pmb{v}_{\text{goal}} \in \mathbb{R}^3$ denotes the target mean speed. + +The facing guidance loss is based on the last frame of the motion segment. Given the avatar's normalized facing directional vector $\mathbf{z}$ and a target facing unit vector $\mathbf{r}_{\text{goal}}$ , the guidance loss is given by + +$$ +\mathcal {L} _ {\text {f a c i n g}} = \left\| \boldsymbol {z} - \boldsymbol {r} _ {\text {g o a l}} \right\| ^ {2}, \tag {8} +$$ + +in which $z$ is computed from the predicted joint locations. + +In order to obtain real-time performance, we derive the analytical gradients of these terms instead of using autodifferentiation. Note that we control motions via manipulating $J$ or $\dot{J}$ in the motion state $\pmb{x}_i$ . The SMPL-X parameters, i.e. $(r,\varphi ,\theta)$ , are not directly controlled. + +# 4. Model Adaptation + +Since it takes 3-4 days to train our autoregressive diffusion model to obtain high-quality results, we regard it as a base model for task-specific adaptation; this reduces the costs of data and computation. Therefore, we do not need to train from scratch to solve new tasks. The effectiveness of this approach has been widely reported in recent advances of foundation models [30, 52, 53, 63, 72, 83]. + +In this work, we take advantage of ControlNet [83] and propose a generic approach for task adaptation, which is illustrated by Fig. 3. For each adaptor, the control embedding and the output from the previous transformer block are added first and then fed into a trainable copy of the current transformer block. The adaptation process only updates the parameters in the adaptors, while keeping the base model parameters frozen. The training loss is identical to Sec. 3.3. + +![](images/b9016faf9dca2d73f5e4f3ed04d3d8cc20e575b485045e5999b2166f21271a90.jpg) +Figure 3. Illustration of our adaptation method. Given a base model, we introduce a ControlNet-like adaptor at each individual transformer block. The control signal $y$ is a generic notation. We adapt the base model for semantic action generation and spatial target reaching. The scale operation manipulates the impact of the control signal, corresponding to $\gamma$ in Eq. (3) of CFG. + +This architecture is different from the ControlNets applied in [81, 90], in which the control embedding is just input once to the adaptor. Our transformer block-wise adaptation is similar to OMG [44]. However, their mixture-of-experts module is specifically designed to fuse the text tokens via cross attention, whereas ours is a generic framework that fuses a generic control embedding via addition. + +Few-shot semantic action generation. Given a small set of personalized mocap sequences with action labels, we adapt our base model to generate actions given the labels. In this case, the control signal $y$ shown in Fig. 3 is an integer action label, and an embedding layer maps this label to a latent vector. After adaptation, our model is able to generate infinite personalized movements based on the action labels, and natural transitions between actions, beyond what this small dataset provides. We can control the impact of the action embedding via classifier-free guidance (CFG). Simultaneously, we can also perturb the joint velocities to generate natural reactions, and control the movement continuously via the CBG method proposed in Sec. 3.4.2. + +Spatial target reaching. In this scenario, the control signal $y$ becomes a 2D target location for the avatar to reach. During finetuning, the pelvis XZ coordinate of the last frame of the canonicalized motion segment is treated as the target. Following [15, 69], we re-scale the target location via $2 \cdot (1 - e^{-\|x\|_2}) \cdot \frac{x}{\|\pmb{x}\|_2}$ , in order to make the model generalize to targets in extreme scenarios. In addition, we use a linear layer to map the scaled target location to a latent variable. After training, target-reaching behavior can be synthe + +sized by specifying the target locations at test time. Since the motion is generated autoregressively, one can control the avatar's motion direction by controlling the target. + +# 5. Experiments + +# 5.1. Evaluations on Body Motion Learning + +A model that learns human body motion well should have two capabilities: 1) It can generate high-fidelity, realistic motions, given an arbitrary initial state; 2) The model's responses to inputs should be natural and human-like. Thus, we have two sets of experiments to measure motion realism and responsiveness, respectively. Below, we denote our PRIMAL architecture in Fig. 2 as InContext. In addition, we compare it with another architecture that exploits adaptive layer normalization [55, 57], denoted as AdaLN, which is illustrated in Sup. Mat. + +# 5.1.1. Motion Realism + +Datasets and metrics. We draw 80 and 160 initial states from the HumanEva [65] and SFU [1] subsets of AMASS, respectively. We use the gender-neutral SMPL-X body and replace the ground truth shapes with random samples from $\mathcal{N}(0,I)$ , testing generalization to unseen identities. From an initial state, we generate a 240-frame motion, ie. 8s. + +We evaluate the motion realism w.r.t. the following terms. 1) Averaged skating ratio (ASR): Following [86-88], we define foot skating as occurring when both foot joints are in contact with the ground (within a tolerance of $5\mathrm{cm}$ ) and their horizontal velocities are both above $15\mathrm{cm/s}$ . We report the averaged ratio of skating frames. 2) Averaged non-collision ratio (ANCR): Similar to [82], we compute the lowest body joint at each frame, and define a collision when the lowest body joint is deeper than $5\mathrm{cm}$ below the ground plane. 3) Averaged neural Riemannian distance (ARD): We employ NRDF [23] to measure the distance of the generated body pose to the pretrained natural pose manifold of AMASS. A smaller value indicates that the generated pose is more natural. 4) Baseline preference ratio (BPR): For each method we render 50 videos and perform perceptual studies to visually compare InContext with individual baselines; we report the percentage of participants who prefer the baseline results. See Sup. Mat. for more details. + +Comparisons to state-of-the-art. We compare our methods with two groups of baselines. The off-the-shelf group includes DiP [71], CLoSD [71] and MotionLCM [13]. The "our implemented" group in Tab. 1 includes versions of DiP and DART [89] where the motion representations and pretraining strategies are identical to ours. For details of how we train and fairly compare the methods, see Sup. Mat. + +Table 1 shows that all methods avoid ground collision. Our PRIMAL-InContext model outperforms data-driven + +![](images/b668a50d43ff8969276a0739155bc58213f1b272a367966435eaf5d35eab8aad.jpg) +Figure 4. Illustration of three random motion generations (one per row). Given different initial states, the model is able to generate high-fidelity future motions of arbitrary lengths in real time. The numbers denote the frame indices. See Supplemental Video. + +
MethodsASR ↓ANCR ↑ARD ×10-3↓BPR ↓
off-the-shelf
DiP [71]0.0671.07.37320.81%
CLoSD [71]0.0191.01.9949.17%
MotionLCM [13]0.1491.0--
our implemented
DART [89]0.0721.00.07734.88%
DiP [71]0.0651.00.17441.15%
our methods
InContext (ours)0.0241.00.074-
AdaLN (ours)0.0361.00.147-
+ +belines w.r.t. foot skating, despite not explicitly training for this. Note that PRIMAL directly outputs SMPL-X parameters, whereas DiP and CloSD need to fit SMPL-X to joint locations. SMPL-X is needed for the ARD and BPR scores and the fit step could negatively impact their scores. Note that InContext is visually preferred to all baselines (ie. low BPR) suggesting the realism of the generated motions. Figure 4 shows generated motions given different initial states; see the Supplemental Video. + +Furthermore, we can see that InContext outperforms AdaLN w.r.t. motion realism. We also find InContext runs slightly faster in our trials. Therefore, we will only use InContext in the following experiments. More details and ablation studies are in Sup. Mat. + +# 5.1.2. Motion Responsiveness + +The ability to respond to external input is necessary for an avatar to feel "alive" (see Fig. 1). We draw 45 random initial states from SFU [1], and replace the ground truth body shape with a random value as before. We compare our In-Context method with our implemented DiP and DART diffusion models, and PRIMAL-InContext-8f, which has an 8-frame time horizon as in DART. + +Table 1. Motion Realism: Comparison with SOTA. Best results are highlighted in boldface. We only compare "InContext" with baselines for the perceptual study (BPR). See text. + +
MethodsASR ↓ANCR ↑ARD ×10-3↓BPR ↓
DART diffusion [89]0.1590.9612.25921.29%
DiP [71]0.1260.9950.64510.50%
InContext-8f0.1720.9957.90330.66%
InContext0.0881.00.511-
+ +Table 2. Results of reactions to induced impulses. The evaluation metrics are the same as in Tab. 1. Best results are in boldface. + +
MethodsASR ↓ARD ×10-3↓R-precision ↑
Finetuning0.2530.0600.87
OmniControlNet [81]0.2990.0630.90
Ours0.2150.0640.96
+ +Table 3. Results of semantic action generation. R-precision indicates classification accuracy. See more results in Sup. Mat. + +Reactions to induced impulses. Here, we perturb the velocities for subsets of the joints and quantify the resulting motions generated by the agent. Depending on the initial velocities, we can make the agent generate kicks, forward runs, back flips, and forward rolls; see Sup. Mat. for the intuitive principles. With PRIMAL, we only perturb the first frame, but apply the velocities to all history frames of DiP and DART to improve their responsiveness. To measure the motion realism, we generate a 3-second motion for each starting state, leading to 225 sequences per method, and compute ASR, ANCR, and ARD. In addition, we render 30 videos per action for a perceptual study that tests how well the models align with human intuitions; see the Sup. Mat. for details. Table 2 shows that InContext outperforms the prior art. Figure 5 visualizes some results; see Supplementary Video. We see that the avatars have realistic reactions to the velocity interventions. + +CBG-based control. The CBG method proposed in Sec. 3.4.2 provides control of the movement direction and speed of the agent. In Context significantly outperforms the baselines on this task - see Sup. Mat. for more details. + +# 5.2. Evaluations on Model Adaptation + +We refer the reader to the Sup. Mat. for the model adaptation experiment details, which include few-shot semantic action generation and spatial target reaching. We evaluate two approaches: 1) We add the control embedding (i.e. the embedding of $y$ in Fig. 3) to the time embedding, and fine-tune the pretrained model directly. 2) We implement the motion ControlNet proposed in [81, 90], in which the control signal is fused to the input of the ControlNet only once. We denote them as finetuning and OmniControlNet, respectively. Overall, we find the ControlNet approach can adapt the PRIMAL base model to novel tasks efficiently and effectively. Compared to OmniControlNet, we find that + +![](images/466ccbb2e9aa35ba718d70d8edd0c770d5f410ac7efa544ac5ffa7aaf98afa10.jpg) +Figure 5. Avatar reactions to induced impulses. Each row shows a motion. The pale orange arrows in the initial frame denote the perturbed velocities, and bars in the future frames denote the generated joint locations and velocities. Darker color means smaller velocity norms. + +![](images/2bc5e34f8ae38a14da5bd83bbf34b42f40204e016a17e028ccb9381d10f951a1.jpg) +Figure 6. Snapshots of personalized mocap dataset, captured by MoCapade3.0 [19] from cellphone videos. + +our proposed adaptor enables the avatar to respond more quickly to the control signal. + +For few-shot semantic action generation, we use Mocapade3.0 [19] to capture 5 classes of actions from video (Fig. 6). Although the dataset is only about 3 minutes in total, it is sufficient to fine-tune the model. Quantitative results are shown in Tab. 3, while visualizations are in Fig. 1. We observe that all these PRIMAL-based methods are effective. The ControlNet approach allows adaptation of the base model to a small set of captured motions, maintaining the controllability and responsiveness of the original model, while being able to mimic the new data. + +# 6. Conclusion + +To create a motor model for interactive agents, we propose a new form of autoregressive diffusion model that generates + +perpetual, controllable, realistic, and responsive motions in real time. Following recent advances in foundation models, our training paradigm has two phases, i.e. 1) unsupervised pretraining to learn body movements, and 2) adaptation to novel tasks. Experimental results show that our model learns motions effectively, adapts to external velocity inputs, and can be efficiently adapted to few-shot personalized action generation and spatial target reaching. We demonstrate the advantages with a real-time character animation system built in Unreal Engine. + +Limitations and future work. First, while most motions exhibit perceptually physical realism, non-physical motions sometimes occur, e.g. when getting up after falling, the avatar sometimes "flies" up. The method generalizes to falls that it has never seen, but more training data of this type would be helpful. We clarify that we do not ensure physical realism. Rather we generate motions that generally look physically realistic. Second, PRIMAL has limited types of control inputs. Extending this to have more natural inputs through text or speech should be explored. For example, we can modify our ControlNet to fuse text and motion features, and fine-tune it on text-motion paired datasets, e.g. BA-BEL [58] and HumanML3D [20]. Third, the agent has no awareness of its environment and does not know about obstacles. Learning to condition on the scene is future work. Finally, the model could eventually replace traditional motion graphs and motion matching (cf. [28, 29, 38]) in video games, however, despite running in real time (i.e. computation takes less than 0.5 second), the computational cost is still too much for this application. + +Acknowledgments. We sincerely thank Radu Alexandru Rosu, Yu Sun, and Aman Shenoy for the Rust-based SMPL-X rendering. We are also heartily grateful to Guy Tevet for the help on CLoSD [71]. Moreover, we thank fruitful discussions with Muhammed Kocabas and Nikolas Hesse. 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VLMs often inherit and amplify biases in their training data, leading to skewed predictions. PRISM is designed to debias VLMs without relying on predefined bias categories or additional external data. It operates in two stages: first, an LLM is prompted with simple class prompts to generate scene descriptions that contain spurious correlations. Next, PRISM uses our novel contrastive-style debiasing loss to learn a projection that maps the embeddings onto a latent space that minimizes spurious correlations while preserving the alignment between image and text embeddings. Extensive experiments demonstrate that PRISM outperforms current debiasing methods on the commonly used Waterbirds and CelebA datasets. We make our code public at: https://github.com/MahdiyarMM/PRISM. + +# 1. Introduction + +Vision-Language Models (VLMs) have emerged as a class of machine learning models capable of understanding and generating multi-modal content by jointly processing images and textual descriptions. Prominent VLMs, such as Contrastive Language-Image Pre-training (CLIP) [20], have demonstrated impressive performance in zero-shot classification and cross-modal retrieval. By aligning textual and visual representations in a shared embedding space, these models enable seamless interactions between vision and language tasks. Despite their unprecedented effectiveness, VLMs inherit and propagate systemic biases from their large-scale pretraining data, leading to inaccurate or skewed predictions. + +Biases in VLMs manifest in various forms, including social [19, 27, 30, 33] and contextual biases [26, 31], of + +![](images/96e971afecb83a4eec7ce8878cf17dc712ef1a8acf11ed45d550611ceca6cb1f.jpg) +(a) Waterbirds. + +![](images/5fb455f6279471084730491adde45c1205be94b9016d0f0e8e3e76c3ac0f4f97.jpg) +(b) CelebA. +Figure 1. Performance comparison among data-free CLIP debiasing methods in terms of debiasing performance (i.e., the accuracy of the worst group) vs. the overall accuracy on (a) Waterbirds and (b) CelebA datasets. Our proposed method, PRISM, achieves state-of-the-art debiasing performance (higher worst-group accuracy) without compromising overall accuracy. + +ten influenced by 'spurious correlations' in training data. Spurious correlations can stem from associating non-target attributes, such as image backgrounds or contextual features, with labels in unintended ways [5]. For instance, CLIP's zero-shot classifiers frequently associate 'camel' with 'desert' and 'panda' with 'bamboo', reflecting underlying biases in training data. These biases can have real-world implications reducing model robustness in diverse settings. Therefore, mitigating implicit bias in VLMs has become a critical research direction. + +Recent research has investigated various strategies to identify, quantify, and reduce spurious correlations in VLMs. These approaches can be classified into three categories: feature-space transformations [7, 29], prompt-based debiasing [1, 5, 6], and adapter design [17]. Methods with a primary focus on the feature space [7, 29] attempt to transform feature embeddings to eliminate spurious correlations. Prompt-based techniques [1, 5, 6] aim to redefine textual inputs to mitigate bias but often struggle with generalization. Meanwhile, adapter-based approaches such as [17] address implicit bias in VLMs by modifying representations at various stages of the model, including but not limited to the final layer. + +Despite the effectiveness of these approaches in addressing spurious bias in VLMs, they fall short in many instances. These methods mostly require fixed predefined bias categories makes them difficult to scale to task-agnostic settings [5-7]. Furthermore, these debiasing solutions either compromise the overall performance of the model by removing essential semantic content [1, 5] or rely on external visual data for debiasing [7, 17, 29]. This underscores the need for a new debiasing method without the reliance on predefined bias categories or any external data that can preserve essential semantic content without compromising overall accuracy. + +To address these limitations, we propose Projection-based Reduction of Implicit Spurious bias in vision-language Models (PRISM). PRISM consists of two key stages. First, we prompt an LLM with labels to return a list of potential spurious connections corresponding to these labels and dynamically generate biased scene disruptions based on the extracted spurious attributes. Next, we find a projection of the embedding space that can effectively remove the impact of spurious attributes using the generated biased scene descriptions. To this end, we propose a novel loss named Latent space Debiasing loss (LD) to learn the debiasing projection in the embedding space effectively. Our proposed LD loss is a contrastive-style debiasing loss that aligns text and image embeddings based on semantic meaning rather than spurious correlations. It ensures that the text embeddings of the same class but different spurious attributes remain similar to each other, and the text embeddings of different classes but the same spurious attribute remain distinct. + +By removing the impact of bias attributes from the embedding space, PRISM generates representations with no or reduced statistical dependence on the bias. To measure this dependency, previously proposed methods mostly employ a metric capable of capturing statistical dependencies, such as Mutual Information [22], Hilbert-Schmidt Independence Criterion (HSIC) [4], or bias scores [7]. In contrast, our proposed method eliminates the need for direct dependency measurement by utilizing an LLM to generate bias-aware descriptions. These descriptions capture common bias attributes in the dataset using only the labels. Our approach facilitates debiasing without the need for predefined bias categories, external text or image datasets, or lossy data conversions to identify bias features. This makes PRISM an effective, task-agnostic, and data-free solution for debiasing VLMs. + +We assess the performance of PRISM on CLIP using different benchmarks, including Waterbirds and CelebA datasets, and compare its performance against various baselines. The results highlight the capability of the proposed PRISM in mitigating spurious biases in VLMs without compromising the overall performance. Figure 1 illustrates + +that our proposed PRISM achieves state-of-the-art debiasing performance without compromising the total accuracy on both Waterbirds and CelebA benchmarks. Our key contributions in this paper can be summarized as follows: + +- We leverage LLMs to generate biased textual descriptions that reflect common spurious correlations found in datasets. This provides a dynamic and adaptable way to identify biases without relying on predefined bias categories. +- We propose a novel task-agnostic data-free debiasing method for VLMs that learns a projection of the embedding space, removing the impact of spurious attributes using a novel contrastive style loss function. +- We demonstrate that our proposed method achieves state-of-the-art debiasing performance without compromising the model's overall accuracy. To allow rapid reproducibility and contribute to the community, we make our code public at: https://github.com/MahdiyarMM/PRISM. + +# 2. Related Works + +Bias identification in VLMs. Recent research has placed considerable emphasis on identifying and assessing bias in foundation models [9], including VLMs [2, 25]. The initial step in debiasing involves recognizing and evaluating the sources of bias. Different frameworks proposed in [31] and [11, 21] comprehensively explored various types of biases in vision and text datasets, respectively. Previous works [2, 25, 28] investigated bias in CLIP's representation space and proposed different methods to mitigate it. These biases cause unfair outcomes in zero-shot classification and reduce performance in certain underrepresented and overlooked categories [25]. + +Debiasing VLMs. The methods proposed in [3, 19, 31] apply mathematical transformations on data to isolate bias in datasets before feeding them into models. However, such transformations may result in information loss. In the field of feature space transformation, FairerCLIP [7] introduced a mathematically rigorous approach to reduce the bias in CLIP's representations by leveraging kernel Hilbert spaces. SFID [15] proposed a selective feature imputation for debiasing, which combines feature pruning and low-confidence imputation to eliminate biases across tasks and modalities. These methods are grounded in rigorous mathematical principles for transformation but can be computationally expensive and risk removing crucial semantic information which compromises the overall accuracy of the model. + +In the field of prompt engineering, VisualDistiller [6] focused on refining visual representations to counter dataset biases. The solutions proposed in [5], namely Orth-cali and Orth-proj, efficiently remove the bias by projecting out the biased components from CLIP's text embeddings using predefined biased prompts. However, because these bi + +ased prompts are fixed, the method may struggle to generalize to biases that weren't anticipated in the prompts. In the field of adapter designing, DFR [17] suggested debiasing by retraining only the model's final layer. On the other hand, contrastive adapter [32] proposed to insert lightweight adapter modules into the pre-trained model architecture. These adapters are trained using a contrastive loss designed to pull representations from similar groups closer while pushing those from different groups apart. + +In a recent study, RoboShot [1] and BendVLM [10] also leveraged language models to extract insights from task descriptions. The primary focus of RoboShot was on improving robustness in underrepresented and adversarial data distributions rather than bias mitigation. BendVLM was proposed to tackle the bias in VLMs by learning task-specific projections via labeled images, with part of the projections computed dynamically during inference. In contrast, our PRISM explicitly targets bias mitigation in CLIP by leveraging LLMs for adaptive bias identification and embedding transformation. PRISM eliminates the need for LLM calls during inference and removes spurious correlations through learning a debiasing projection of the embedding space, ensuring effective bias removal without relying on predefined bias categories or external visual data. Furthermore, unlike prompt-based debiasing techniques that modify only text embeddings, our approach preserves the alignment between text and image representations, ensuring debiased zero-shot classification without compromising the overall accuracy. + +# 3. Method + +# 3.1. Problem formulation + +Let us consider a multimodal foundation model, such as CLIP [20], which maps images and natural language onto a shared $d$ -dimensional space using two encoders: an image encoder $\phi_{\mathrm{I}}(\cdot)$ and a text encoder $\phi_{\mathrm{T}}(\cdot)$ . In the zero-shot setting, given image $x$ and a set of text prompts $\{t_y\}_{y=1}^K$ corresponding to class labels $y \in \{1, \dots, K\}$ , the prediction is made via + +$$ +\hat {y} = \arg \max _ {y} \left\langle \phi_ {\mathrm {I}} (x), \phi_ {\mathrm {T}} \left(t _ {y}\right) \right\rangle , \tag {1} +$$ + +where $\langle \cdot ,\cdot \rangle$ represents the vector inner product. Here, the text prompts are descriptions of the object in each class as: $t_y = "A$ photo of a $< class y>$ + +This formulation presumes that $\phi_I(x)$ predominantly captures the core, task-relevant features of $x$ . However, real-world data often contain spurious correlations that can cause the encoder to also capture irrelevant cues. The image embedding can be modeled as a (normally, unknown) function $f$ of a core component and a spurious component: + +$$ +\phi_ {\mathrm {I}} (x) = f \left(h _ {\text {c o r e}} (x), h _ {\text {s p u}} (x)\right), \tag {2} +$$ + +where $h_{\mathrm{core}}(x)$ represents the features essential for correctly predicting the label $y$ , and $h_{\mathrm{spu}}(x)$ encodes extraneous information (e.g., background elements) that is spuriously correlated with $y$ . + +Assume that the spurious attribute is denoted by $a$ . Accordingly, we define the group identity of each sample as + +$$ +g = (a, y), \quad \text {w i t h} \quad g \in \mathcal {G} = A \times Y, \tag {3} +$$ + +where $A$ is the set of possible spurious attributes $a$ , and $Y = \{1, \dots, K\}$ corresponds to the set of true class labels. For example, in a bird classification task, $x$ is an image of a bird, and $y \in \{0, 1\}$ represents the true class where 0 denotes Landbird and 1 denotes Waterbird. The spurious attribute $a$ belongs to the set $A = \{\text{land background}, \text{water background}\}$ , which indicates the type of background present in the image. Each combination $(a, y)$ defines a distinct group within $G$ , resulting in a total of four groups in this example. + +When the model undesirably relies on the spurious component $h_{\mathrm{spu}}(x)$ , it may assign $x$ to the incorrect group, leading to misclassification. To mitigate this bias, the objective is to minimize the worst-case error over all groups. Formally, we aim to solve + +$$ +\min _ {\theta \in \Theta} \max _ {g \in \mathcal {G}} \mathbb {E} \left[ \ell \left(\left\langle \phi_ {\mathrm {I}} (x), \phi_ {\mathrm {T}} \left(t _ {y}\right) \right\rangle , y\right) | g \right], \tag {4} +$$ + +where $\ell (\cdot ,\cdot)$ denotes the classification loss. + +There are several challenges associated with the optimization of Eq. 4. First, optimizing over the parameter space of $\theta$ is costly due to the number of parameters of the model, CLIP. This is also in contrast to the original purpose of CLIP which is to serve as a universal and general zero-shot classifier (Eq. 1). Second, the identification of spurious attributes $A$ for an arbitrary set of text prompts is challenging and requires prior knowledge about the task, or an external dataset, which is not always accessible. Moreover, we hypothesize that due to the nature of spurious correlations, similar biases should also be present in the text domain. Hence, spurious correlations identified in the text modality can also be leveraged to debias the image modality. We will empirically verify this hypothesis in Section 5. + +# 3.2. PRISM + +To address the challenges mentioned in Section 3.1, we propose Projection-based Reduction of Implicit Spurious bias in vision-language Models (PRISM), which consists of two main steps: (i) PRISM detects potential spurious correlations $A$ by prompting an LLM $\mathcal{F}$ with a set of inputs $\{t_y\}_{y=1}^K$ and instructs the model to generate a set of scene descriptions $\mathcal{T}$ , corresponding to different groups $\mathcal{G}$ . (ii) To preserve CLIP's generality and to avoid the need to fine-tune the network, we then introduce a novel method for + +![](images/9aa0dfa0d9ce2da6cb9b198418b790081f47838bc7e21384a2a03d26e37d21b2.jpg) +Figure 2. An overview of the proposed PRISM. In Stage 1, by passing text prompts as 'A photo of $< y >$ to an LLM, a set of scene descriptions with different labels and spurious attributes is generated. Then, in Stage 2, these scene descriptions are used for learning a debiasing projection of the embedding space, $P$ , using LD loss. Finally, zero-shot classification is performed in the projected debiased embedding space of the VLM. + +finding an embedding projector $P$ that maps the embedding space onto another subspace where the influence of spurious attributes $A$ is minimized. Figure 2 presents a high-level illustration of our proposed method. + +Stage 1: Leveraging LLMs to identify spurious correlations. To propose a fully task-agnostic debiasing method without relying on any external data or predefined bias categories, we propose using pre-trained LLM for bias category discovery. For this purpose, an LLM is prompted with the labels and instructed to return potential spurious correlations. The LLMs' effectiveness in the discovery of spurious correlations stems from their training scheme. These foundation models are trained over a massive corpus $\mathcal{D}$ tokenized to $w_{i}$ by minimizing the following: + +$$ +\frac {1}{N} \sum_ {\left(w _ {1}, \dots , w _ {n}\right) \in \mathcal {D}} \sum_ {i = 1} ^ {n} - \log P _ {\theta} \left(w _ {i} \mid w _ {< i}\right), \tag {5} +$$ + +thereby learning the joint distribution $P_{\theta}(w_1, \ldots, w_n)$ . Whenever a concept $\alpha$ (e.g., 'camel') frequently co-occurs with another concept $\beta$ (e.g., 'desert') in $\mathcal{D}$ , the conditional probability $P_{\theta}(\beta \mid \alpha)$ becomes large, even if $\alpha$ and $\beta$ are merely spuriously correlated rather than causally connected. Hence, for any set of text prompts $\{t_y\}_{y=1}^K$ , the LLM's learned parameters encode high-probability transitions from $\{t_y\}_{y=1}^K$ to $A$ solely due to their co-occurrences in text [24]. This statistical encoding of spurious correlations arises because the model optimizes the likelihood over $\mathcal{D}$ without discriminating between causal and non-causal + +patterns. Consequently, prompting the LLM with queries about $\{t_y\}_{y = 1}^K$ produces $A$ , as follows: + +$$ +A = \mathcal {F} \left(\left\{t _ {y} \right\} _ {k = 1} ^ {K}\right). \tag {6} +$$ + +Then, we use the returned spurious attributes to generate a set of controlled scene descriptions $\mathcal{T}_{a,y}$ correspond to each group $g = (a,y)$ in $\mathcal{G}$ . The full prompts used in this stage of PRISM are provided in Appendix B. + +Stage 2: Learning a debiasing projection of the embedding space. Our method finds a projection $P$ to minimize the impact of $A$ in the embedding space. This is then followed by zero-shot classification in the debiased projected embedding space. To this end, we propose a novel loss, which we call Latent space Debiasing Loss (LD), formulated as: + +![](images/47910dc8426f3474669018278c6c21a0500ee997d13024c023e685e06452f594.jpg) + +where $m$ is the margin hyperparameter. We propose $\mathcal{L}_{\mathrm{LD}}$ to learn a projection that robustly mitigates spurious correlations in the model's joint embedding space. For each iteration of optimization over $P$ , we use a set of scene descriptions $\mathcal{T}$ , generated by the LLM for each group, $g = (a,y)$ . The first component of the loss ((a) Intra-class, inter-attribute term) encourages invariance by minimizing the difference between embeddings of scene descriptions from the same class but differing spurious attributes. Specifically, for each pair $(a,a')$ with $a \neq a'$ , the term $1 - \langle \phi_{\mathrm{T}}((a,y)), \phi_{\mathrm{T}}((a',y')) \rangle$ is minimized. This term ensures that the core class-specific features are consistently represented, independent of the confounding spurious cues. Meanwhile, the second component of the loss ((b) Inter-class, intra-attribute term) employs a margin-based penalty that enforces a minimum separation between embeddings from the same spurious attribute but different classes. For any $y' \neq y$ , the penalty $\max \{0, \langle \phi_{\mathrm{T}}((a,y)), \phi_{\mathrm{T}}((a',y')) \rangle - m\}$ is applied, ensuring that even if the spurious context is shared, class-discriminative features remain distinct. + +The design of $\mathcal{L}_{\mathrm{LD}}$ is inspired by contrastive loss in self-supervised learning, where the objective is to draw semantically similar pairs closer and push dissimilar ones apart. By jointly optimizing for intra-class invariance and inter-class separation, our loss effectively penalizes deviations from the desired embedding structure. Importantly, this approach removes the need to fine-tune the entire CLIP model, as the learnable projection $P$ is optimized independently. Empirical evaluations confirm that minimizing $\mathcal{L}_{\mathrm{LD}}$ not only enhances the robustness of the zero-shot classifier by reducing reliance on spurious cues but also improves worst-group performance and leads to disentanglement of the embedding space. + +Finally, leveraging the learned projection, $P$ , by minimizing Eq. 7, we perform zero-shot classification on the projected embedding space as follows: + +$$ +\hat {y} = \arg \max _ {k} \langle P \left(\phi_ {\mathrm {I}} (x)\right), P \left(\phi_ {\mathrm {T}} \left(t _ {k}\right)\right) \rangle . \tag {8} +$$ + +PRISM-mini. Here, we propose a variation of our method called PRISM-mini, which is mostly different from PRISM in stage 2. Unlike PRISM, which uses scene descriptions for finding $P$ by optimizing over LD loss, PRISM-mini relies on orthogonalizing the embedding space again spurious attributes. Hence, PRISM-mini is less computationally complex and is more suitable for use-cases where computation resources are extremely limited. + +In the first stage, we pass the class prompts to the LLM and obtain a set of spurious attributes rather than full scene descriptions. Then, all these spurious attributes are encoded using CLIP's text encoder as follows: + +$$ +\mathcal {A} = \phi_ {\mathrm {T}} \left(\mathcal {F} \left(\left\{t _ {k} \right\} _ {k = 1} ^ {K}\right)\right), \tag {9} +$$ + +Algorithm 1 PRISM +Require: image $x$ $\{t_y\}_{y = 1}^K$ : Text prompts for $K$ classes $\phi_{\mathrm{I}},\phi_{\mathrm{T}}$ : CLIP's image and text encoders $\mathcal{F}$ LLM +1: Stage 1: Identify Spurious Directions +2: $A = \mathcal{F}(\{t_y\}_{k = 1}^K)$ Extract spurious attributes +3: Stage 2 (PRISM): Learned Projection +4: Generate scene descriptions $\mathcal{T}_{a,y}$ via $\mathcal{F}$ and $A$ +5: Initialize $P$ +6: repeat +7: Compute $\mathcal{L}_{\mathrm{LD}}$ Eq.7 on $\{(a,y)\}$ +8: Update $P$ via gradient descent +9: until converged +10: Stage 2 (PRISM-mini): Simple Orthogonal Projection +11: $\mathcal{A} = \phi_{\mathrm{T}}(A)$ +12: $P\gets I - \mathcal{A}(\mathcal{A}^{\top}\mathcal{A})^{-1}\mathcal{A}^{\top}$ +13: Stage 3: Zero-shot Inference +14: $\mathbf{z}_{\mathrm{I}}\gets P(\phi_{\mathrm{I}}(x)),\quad \mathbf{z}_{\mathrm{T},k}\gets P(\phi_{\mathrm{T}}(t_k))$ +15: $\hat{y}\gets \arg \max_k\langle \mathbf{z}_\mathrm{I},\mathbf{z}_{\mathrm{T},k}\rangle$ + +where $\mathcal{A}$ is a matrix whose columns are the embeddings of bias attributes in $A$ . Inspired by [5], here we seek to reduce the impact of these spurious attributes on the embedding space by orthogonalizing it against $\mathcal{A}$ . To this end, we calculate the projection $P$ as follows: + +$$ +P = I - \mathcal {A} \left(\mathcal {A} ^ {\top} \mathcal {A}\right) ^ {- 1} \mathcal {A} ^ {\top}. \tag {10} +$$ + +The rest of the method is essentially the same as PRISM. PRISM-mini can effectively reduce the impact of spurious correlations in CLIP without the need for any optimization for finding $P$ . As a result, this method is very cost-effective. However, compared to PRISM, it might not be capable of fully mitigating the spurious biases in the embedding space due to its simpler projection mechanism. Algorithm 1 summarizes both variations of the proposed method. + +# 4. Experiment setup + +Datasets. To evaluate the effectiveness of our method, we conduct various experiments on Waterbirds [23] and CelebA [18] datasets, following prior works such as [7]. The Waterbirds dataset consists of images where bird species are paired with specific backgrounds, deliberately inducing spurious correlations between the foreground object and the environmental context. The CelebA dataset includes 200,000 facial images of celebrities annotated with 40 attributes, such as gender, hair color, face shape, etc. + +Evaluation. For performance evaluation, we use Five metrics: Accuracy (Acc), Worst-Group accuracy (WG), which is the lowest accuracy of all subgroups, $\Delta$ WG, which indicates the worst group accuracy improvement compared to + +
ModelWaterbirdsCelebA
WG↑Acc↑ΔWG↑ΔAcc↑Gap↓WG↑Acc↑ΔWG↑ΔAcc↑Gap↓
Baseline
Zero-shot36.4%89.3%——52.9%72.8%87.6%——14.8%
Methods using images for debiasing
WiSE-FT [29]65.9%97.6%29.5%8.3%31.7%80.0%87.4%7.2%-0.2%7.4%
DFR (Sub) [17]51.9%95.7%15.5%6.4%43.8%76.3%92.1%3.5%4.5%15.8%
DFR (Up) [17]65.9%96.1%29.5%6.8%30.2%83.7%91.2%10.9%3.6%7.5%
FairerCLIP [7]78.1%85.1%41.7%-4.2%7.0%86.1%88.0%13.3%0.4%1.9%
Data-free methods
VisualDistiller [6]42.7%90.6%6.3%1.3%47.9%—————
Orth-Proj [5]45.3%86.4%8.9%-2.9%41.1%71.1%87.0%-1.7%-0.6%15.9%
Orth-Cali [5]68.8%84.5%32.4%-4.3%15.7%76.1%86.2%3.3%-1.4%10.1%
RoboShot [1]45.2%79.2%8.8%-10.1%34.0%82.6%85.5%9.8%-2.1%2.9%
PRISM-mini (ours)69.5%92.6%33.1%3.3%23.1%82.6%84.4%9.8%-3.2%1.8%
PRISM (ours)84.2%93.6%47.8%4.3%9.4%84.0%86.9%11.2%-0.7%2.9%
+ +Table 1. The performance of PRISM compared to baselines on CLIP-ViT-L/14 on Waterbirds and CelebA datasets. The top performance in each column is in **bold**, and the second-best is **underlined**. + +the zero-shot clip, $\Delta$ Acc, which indicates the overall accuracy improvement compared to the zero-shot performance of CLIP, and the Gap between Acc and WG. + +Baselines. We compare our method against two categories of baselines: the methods that use auxiliary images for debiasing and data-free methods. The first category employs a set of labeled or unlabeled images in the training process to reduce bias in CLIP. These images are used to keep the alignment of text and image embeddings intact throughout the debiasing process. Three state-of-the-art methods from this category are compared to ours, including WiSE-FT [29], DFR [17], and FairerCLIP [7]. The second category consists of data-free models which do not require any images for debiasing. These methods are inherently task-agnostic as they do not rely on any task-specific visual data to achieve effective debiasing. VisualDistiller [6], Orth [5], and RoboShot [1] are used in the following experiments as state-of-the-art methods in this category. Note that both variations of our method fall into this category. + +Implementation details. All experiments were conducted using PyTorch on an NVIDIA GeForce RTX 3090 GPU with 24 GB VRAM and 64 GB RAM. Each experiment was run three times with different initialization seeds, and the average performance of the models was reported. Adam optimizer [16] with the learning rate of 0.1 (Waterbirds) and 0.01 (CelebA) is used for performing optimization over $P$ . The batch size is set to 64, and the training for the projection step is only performed for a single epoch. + +# 5. Results + +Performance. We evaluate the performance of our method and compare it against prior baselines on two datasets (Waterbirds and CelebA) using the CLIP-ViT-L/14 backbone in Table 1. The results demonstrate that PRISM outperforms prior works, setting a new state-of-the-art over data-free debiasing methods. Specifically, we observe that our proposed PRISM achieves the highest WG in both datasets, meaning it effectively reduces bias without needing additional image data. The effectiveness of our method is further demonstrated as PRISM outperforms the models using auxiliary data in the Waterbirds benchmark and achieve competitive results in the CelebA benchmark. FairerCLIP is the best among image-based methods, improving WG at the cost of some accuracy loss. WiSE-FT and DFR achieve high accuracies but have limited bias mitigation, indicating that fine-tuning might not be a good option to mitigate bias. Orth and RoboShot perform moderately well but struggle in WG gains, demonstrating that although prompt tuning is a viable method for guiding CLIP's outputs, it is not a robust solution for bias removal. Moreover, the efficient variation of our method, PRISM-mini, also achieves the second-best performance in debiasing across all data-free methods while avoiding any optimization, making it a strong candidate for scenarios where resources are very limited. + +Per-group accuracy. In Figure 3, each subfigure shows bar plots of per-group accuracy for three different methods, i.e., Zero-shot, PRISM-mini, and PRISM, on Waterbirds (Figure 3a) and CelebA (Figure 3b) datasets. The groups on the $x$ -axis ( $g(0,0)$ , $g(0,1)$ , $g(1,0)$ , $g(1,1)$ ) represent different + +![](images/91ab97243691c57379bb763cfad9926c74855b0d1b94ee05f972581e05e63b6f.jpg) +(a) Waterbirds. + +![](images/21cd3ea3b7c95741a91e493834e0c14d6f68b0771424737b2f924f2b37cd98a6.jpg) +(b) CelebA. + +![](images/c562215afb88cd8020d8e3ed6967eda3088aed225bb2c2ce198a499035b9912f.jpg) +Figure 3. Per-group accuracy of our method on (a) Waterbirds and (b) CelebA datasets. +(a) CLIP. +Figure 4. The representation map at the output of CLIP (a) without and (b) with PRISM. + +![](images/677e3b85db3f9a71c3da94dd5967841626d122c926314766b5e5a6bbaeb42597.jpg) +(b) CLIP w/ PRISM. + +subpopulations within each dataset, and the $y$ -axis shows the accuracy achieved by each method on those subpopulations. The dashed horizontal lines indicate the WG accuracy achieved by each method, i.e., the lowest accuracy among the four subgroups. By looking at where each bar stands relative to the dashed lines, we can see how each method handles the most challenging subgroup. Across both datasets, PRISM improves accuracy over the zero-shot baseline in each subgroup and tends to raise the WG performance. PRISM-mini also provides gains over the zero-shot baseline, but it may not always reach the same level of WG performance as PRISM. In essence, the figure illustrates that both PRISM variants can help reduce performance disparities across different groups compared to a purely zero-shot approach, with PRISM typically offering the strongest and the most balanced improvements. + +Bias text. We previously hypothesized that since CLIP aligns image and text embeddings, the inherent nature of spurious bias should cause similar biases to emerge in the text domain alone [24]. Consequently, spurious correlations extracted from the text domain can also be applicable to images. To empirically evaluate this hypothesis, we generate a set of scene descriptions featuring different bird species in various locations. We then perform zero-shot classifica + +
Zero shotWG ↑Acc ↑g(0,0)g(0,1)g(1,0)g(1,1)
Image38.3%92.8%99.0%87.6%38.3%59.8%
Scene description33.1%96.0%100%33.1%41.9%96.8%
+ +Table 2. Bias similarity in text and image modalities. + +tion on the embeddings of these descriptions and present the results in Table 2, demonstrating that similar biases can indeed be observed in the text domain. + +Trade-off analysis. Figures 1a and 1b compare different data-free CLIP debiasing methods in terms of accuracy and debiasing performance, measured through WG, on Waterbirds and CelebA datasets. Although some methods exhibit high debiasing performances, their overall performance is drastically degraded. PRISM is the most effective among all compared methods, achieving the best trade-off between these two metrics. + +Feature disentanglement. Figure 4 compares the representation distributions of zero-shot CLIP with PRISM on the Waterbirds dataset, where each color represents a group $(a,y) \in \mathcal{G}$ . In CLIP's representation space (Figure 4a), clusters are highly mixed, indicating that the model heavily relies on spurious background correlations. In contrast, PRISM's representation space (Figure 4b) shows more structured and well-disentangled clusters, demonstrating that it effectively reduces the influence of background information. This analysis confirms that PRISM successfully mitigates bias rather than being influenced by spurious background correlations. + +Number of scene descriptions. Figure 5 shows the effect of varying the number of scene descriptions used during training the projection $P$ . In these experiments, we evaluate how increasing or decreasing the volume of scene descriptions, which serve as bias-aware prompts generated by the LLM, affects the model's ability to mitigate spurious correlations. For both the Waterbirds and CelebA datasets, the results illustrate that there is an optimal range for the number of descriptions: too few may provide insufficient guid + +![](images/8f90683f4ebad2d893afd0b7013cac472dcc7b991ec1d37fba9974922548d660.jpg) +(a) Waterbirds. + +![](images/021fe02f605ed7b87ea1f7302646cc1b755c0982316a2cf7a97d8c3845c5ceeb.jpg) +(b)CelebA. + +![](images/3ed9d37a47260abf02854e6b5b360b0cb1fa1f3ea78f96414479983334b61b12.jpg) +Figure 5. Worst-group performance of PRISM for different numbers of scene descriptions used in training for (a) Waterbirds and (b) CelebA datasets. +(a) Waterbirds. +Figure 6. Worst-group performance of PRISM for different values of margin hyperparameter $m$ for (a) Waterbirds and (b) CelebA datasets. + +![](images/606e3260c8ba1da1a03190ebef9f8b46d44e04e2b7cc4967a05e519dd24b8742.jpg) +(b)CelebA. + +ance for debiasing, while too many might undermine the discriminative signal, ultimately impacting the worst-group accuracy. + +$m$ in LD loss. Figure 6 shows the sensitivity of PRISM's performance to the hyperparameter $m$ in the LD loss function, which determines the margin in the contrastive component of the loss. This parameter influences how aggressively the model penalizes similarities between embeddings of different classes with the same spurious attribute. The results, demonstrate that for both datasets, an $m$ of 0.6 maximizes WG performance by separating the representations across different groups, achieving an optimal balance between preserving essential semantic information and removing spurious correlations. + +Role of LLMs. Table 3 shows that the effectiveness of PRISM in reducing bias, measured by WG and Acc, can be significantly influenced by the choice of LLM. Selecting a more capable LLM for bias identification can improve debiasing without severely compromising the overall classification performance. The table compares several LLMs that vary in size and capability, where we see that GPT-40 achieves the best WG performance with score of $84.0\%$ and an overall accuracy of $86.9\%$ . + +Limitations. While PRISM demonstrates strong performance in mitigating spurious biases in VLMs, it has some + +
LLMWG ↑Acc ↑
Llama 3.2 (70B) [8]58.9%90.1%
DeepSeek r1 (8B) [12]68.3%89.2%
GPT 4o mini (~8B) [13]81.6%86.6%
GPT o1 (~300B) [14]77.9%83.9%
GPT 4o (~1.7T) [13]84.0%86.9%
+ +Table 3. The performance of PRISM on CelebA dataset using different LLMs. + +limitations. First, PRISM relies on LLMs to generate spurious attribute descriptions, and the quality of these descriptions can vary depending on the specific LLM used. While our results show that more capable LLMs yield better biasing performance, less powerful models may struggle to extract meaningful spurious correlations, potentially reducing effectiveness. Additionally, our approach focuses on linear projections to remove bias in the embedding space, which may not always capture highly complex or non-linear biases present in real-world data. + +# 6. Conclusion + +We propose PRISM, a data-free debiasing framework for vision-language models that mitigates spurious correlations in CLIP's embedding space without requiring any weight updates. PRISM has two stages. In the first stage, an LLM is leveraged with simple class prompts to generate scene descriptions that unravel common spurious correlations in the training data. In the second stage, these generated descriptions guide the learning of an optimized projection mapping, which is carried out via our novel LD loss to systematically reduce spurious biases while preserving the semantic alignment between image and text embeddings. Through extensive evaluations on benchmark datasets (Waterbirds and CelebA), we demonstrated that PRISM significantly improves worst-group accuracy while maintaining overall classification performance. Beyond its empirical effectiveness, PRISM offers a data-free and task-agnostic solution to debiasing multimodal representations. Future research directions include exploring non-linear projections for embedding space debiasing, which could potentially better capture complex spurious correlations beyond linear transformations. + +# Acknowledgment + +We would like to thank Geotab Inc., the City of Kingston, and NSERC for their invaluable and continued support of this work. + +# References + +[1] Dyah Adila, Changho Shin, Linrong Cai, and Frederic Sala. Zero-shot robustification of zero-shot models. In International Conference on Learning Representations, 2024. 1, 2, 3, 6 +[2] Sandhini Agarwal, Gretchen Krueger, Jack Clark, Alec Radford, Jong Wook Kim, and Miles Brundage. Evaluating clip: towards characterization of broader capabilities and downstream implications. arXiv preprint arXiv:2108.02818, 2021. 2 +[3] Ibrahim Alabdulmohsin, Xiao Wang, Andreas Peter Steiner, Priya Goyal, Alexander D'Amour, and Xiaohua Zhai. CLIP the bias: How useful is balancing data in multimodal learning? 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Previous large reconstruction models typically prepare training images under fixed and simple lighting, offering minimal photometric cues for precise reconstruction. Furthermore, images containing specular surfaces are treated as out-of-distribution samples, resulting in degraded reconstruction quality. To handle these challenges, PRM renders images by varying materials and lighting, which not only improves the local details by providing rich photometric cues but also increases the model's robustness to variations in the appearance of input images. To offer enhanced flexibility, we incorporate a real-time physically-based rendering (PBR) method and mesh rasterization for ground-truth rendering. By using an explicit mesh as 3D representation, PRM ensures the application of differentiable PBR for predicted rendering. This approach models specular color more accurately for images with varying materials and illumination than previous neural rendering methods and supports multiple supervisions for geometry optimization. Extensive experiments demonstrate that PRM significantly outperforms other models. + +# 1. Introduction + +Recent advancements in generative models [12, 27, 38] have spurred notable progress in 2D content creation, driven by fast growth in data volumes. In contrast, the development in 3D field remains encumbered due to limited 3D assets, which are essential for diverse applications including game modeling [8], computer animation [23, 32], and virtual reality [35]. Traditional approaches to generating 3D assets have utilized optimization-based techniques from multi-view posed images [42, 49, 50] or have harnessed SDS-based distillation methods from 2D diffusion models [25, 26, 34]. Despite their effectiveness, these methods often require increased computational costs, making them less + +suitable for rapid deployment in real world. + +Feed-forward 3D generative models [13, 15, 51] have been developed to address the limitations of per-scene optimization by training a generalizable model on large-scale 3D assets. Notably, the Large Reconstruction Model (LRM) [13] has demonstrated promising results, exhibiting exceptional reconstruction speeds. The subsequent LRM series [13, 39, 43, 46, 48] utilizes a Transformer-based architecture to encode either single or multi-view images, and decoding them into 3D representations, such as triplanes [3], Flexicubes [36] or 3D Gaussians [39]. These 3D representations enable differentiable neural rendering from arbitrary viewpoints, which is crucial for calculating multi-view reconstruction loss for optimization. + +While the LRM series effectively reconstructs globally coherent 3D assets, it struggles with capturing fine-grained details. This limitation stems from its reliance on images rendered under fixed, simple lighting, which provide insufficient photometric information for detailed surface reconstruction. Additionally, the LRM series is sensitive to variations in input image appearance, particularly with glossy surfaces, as these are out-of-distribution samples that rarely occur in the training data. Moreover, the use of neural rendering for predicted rendering exacerbates this issue [41], since the view-dependent effect is not considered. + +To address the challenges, we introduce PRM, a photometric stereo based large reconstruction model. This model is adept at capturing fine-grained local details and ensures robustness against the complex appearances of input images. We achieve these objectives by leveraging images with varying materials and illumination [10]. Specifically, we render ground-truth images by varying camera pose, materials (i.e., metallic and roughness), and lighting. However, rendering these images is not trivial since there are infinite possible combinations of camera pose, materials and lighting. In the recent LRM series, images are typically rendered offline using Blender's Cycles engine [11]. While this approach produces high-quality, noise-free images, it requires numerous samples of lighting directions, significantly increasing the time cost and making it expensive to maximize the training sample distribution. + +![](images/0896bd3c4bd1244de8b9f0605c559b4e24f14442940c62e1e6199170301c255d.jpg) +Figure 1. Top left: PRM is capable of reconstructing high-quality meshes with fine-grained local details even under complex image appearances, such as specular highlights and dark appearances. Right: We demonstrate a scene comprising diverse 3D objects generated by our models. Bottom left: A zoomed-in visualization of the scene highlights these details more clearly. + +![](images/08daf036044bc9b59b4ed0ed7531072423011e51f36f56ee31454133e3c4bbec.jpg) + +To handle this issue, we incorporate a real-time, physically based rendering technique known as split-sum approximation [19], along with mesh rasterization for online rendering. This approach offers greater flexibility compared to traditional offline methods. We discuss two training strategies in the Supplement. Images with varying materials and illumination offer two distinct advantages. First, they provide additional photometric cues, thereby enhancing the capacity to recover fine-grained local details. Second, the PRM model demonstrates remarkable robustness to variations in the appearances of inputs. For instance, it is capable of accurately reconstructing the geometry of images with glossy surfaces. Moreover, by utilizing mesh as 3D representation, we can employ differentiable PBR for predicted rendering, producing intermediate shading variables such as albedo, specular and diffuse light maps, along with geometric cues like normals and depth. These variables provide multiple supervisions, including photometric and geometric supervision for high-quality reconstruction. Furthermore, differentiable PBR can better disentangle the specular component, making the geometry be correctly recovered when the images are characterized with glossy surfaces. + +To summarize, our contributions are listed as follows. + +- We introduce PRM, a model that is capable of reconstructing geometry with fine-grained local details and robust to variations in the appearance of input image by utilizing images with varying materials and illumination. +- We employ differentiable PBR for predicted rendering by utilizing mesh as the 3D representation. This approach is advantageous for modeling reflective components and enables the incorporation of multiple supervisions for high-quality geometry reconstruction. + +- Extensive experiments on multiple datasets demonstrate the effectiveness of the proposed framework, which significantly outperforms previous methods, particularly on glossy objects. + +# 2. Related Work + +# 2.1. Feed-forward 3D Generative Models + +Large-scale 3D assets [5] facilitate the training of generalizable reconstruction models. Recent works have focused on generating 3D objects using feed-forward models [13, 14, 24, 39, 43, 47, 48, 51], demonstrating impressive results in terms of speed and quality. Specifically, Clay [51] utilizes occupancy for direct supervision. X-ray [15] explores novel 3D representations by converting a 3D object into a series of surface frames at different layers. The LRM series [13, 24, 43, 46, 48] shows that a transformer backbone can effectively map image tokens to 3D triplanes, benefiting from multi-view supervision. Instant3D [24] employs multi-view images to provide additional 3D information for triplane prediction, yielding promising outcomes. CRM [43] and InstantMesh [46] opt for an explicit mesh representation, supporting mesh rasterization and rendering additional geometric cues for supervision. Despite these achievements, the existing LRM series typically render low-frequency images under fixed and simple lighting, which compromises the model's adaptability to complexity in the appearance of input images and the model's capability to recover local details due to limited photometric cues. In response, we render images with varying materials and illumination that significantly enhance the photometric cues necessary for the recovery of fine-grained local details. + +# 2.2. Photometric Stereo + +Photometric stereo (PS) is a technique for recovering surface normals from the appearance of an object under varying lighting conditions. Traditional methods, inspired by the seminal work [44], assume calibrated, directional lighting. Recently, uncalibrated photometric stereo methods have emerged, which assume Lambertian integrable surfaces and aim to resolve the General Bas-Relief ambiguity [9] between light and geometry. However, these methods are still constrained to single directional lighting. More contemporary research [16, 17, 29] has shifted focus towards natural lighting conditions. Despite the significant progress, these approaches generally concentrate on single-view photometric stereo, relying solely on photometric cues and neglecting multi-view information, which is crucial for accurately reasoning geometric features. Some studies [10, 20–22, 33, 53] leverage both photometric and geometric cues for reconstruction. These cues are complementary: photometric stereo provides precise local details, while multiview information yields accurate global shapes [53]. For example, UA-MVPS [20] utilizes complementary strengths of PS and multi-view stereo for geometry reconstruction. NeRF-MVPS [21] utilizes surface normal estimated from images with varying materials and illumination to enhance the reconstruction performance of NeRF. Our approach integrates the principles of photometric stereo into LRM, aiming to harness the strengths of photometric cues for enhanced reconstruction accuracy. + +# 2.3. Physically-based Rendering + +Physically based rendering (PBR) is a computer graphics approach that renders photo-realistic images. PBR offers a physically plausible approach to modeling radiance by simulating the interaction between lighting and materials. PBR has proven to be effective in improving the geometry for multi-view reconstruction task. For example, incorporating the principles of PBR into volume rendering significantly improves the accuracy [7, 28, 41], especially for glossy surfaces. Since geometry and predicted radiance are closely entangled, improving radiance modeling can also enhance geometry reconstruction. Besides, PBR is also widely used in inverse rendering task [1, 4, 31]. The task aims at decomposing image appearance into intrinsic properties. Unlike previous LRM methods that predict radiance without explicitly considering the interactions between materials and lighting, we leverage advancements from the multi-view reconstruction field and employ PBR for improved radiance modeling and geometry reconstruction. To this end, we predict albedo instead of color, which is more reasonable as albedo is view-independent. The final color is derived using the predicted albedo and the ground truth metallic, roughness, and lighting. + +# 3. Method + +We begin with a succinct overview of large reconstruction model, physically based rendering and photometric stereo in Section 3.1. Then, we introduce how to prepare images with varying materials and illumination in Section 3.2. Subsequently, we introduce PRM in Section 3.3, with our proposed comprehensive objectives and applications. An overview of our framework is provided in Figure 2. + +# 3.1. Preliminaries + +Large Reconstruction Model aims to reconstruct 3D assets given a single image. LRM first utilizes a pre-trained visual transformer [2], to encode the images into image tokens. Subsequently, it employs an image-to-triplane transformer decoder that projects these 2D image tokens onto a 3D triplane using cross-attention [13]. Following this, images can be differentiable rendered from any viewpoint, supporting photometric supervision and optimization. + +Physically-based Rendering aims to produce 2D images using specified geometry, materials, and lighting. Central to this process is the rendering equation [18] formulated by + +$$ +C (\boldsymbol {x}, \omega_ {o}) = \int_ {\Omega} f (\boldsymbol {x}, \omega_ {o}, \omega_ {i}) L _ {i} (\boldsymbol {x}, \omega_ {i}) (\omega_ {i} \cdot \mathbf {n}) d \omega_ {i}, \tag {1} +$$ + +where $\omega_{o}$ is the viewing direction of the outgoing light, $L_{i}$ is the incident light of direction $\omega_{i}$ sampled from the upper hemisphere $\Omega$ of the surface point $\mathbf{x}$ , and $\mathbf{n}$ is the surface normal. $f$ is the BRDF properties. The function $f$ consists of a diffused and a specular component + +$$ +f (\boldsymbol {x}, \boldsymbol {\omega} _ {o}, \boldsymbol {\omega} _ {i}) = (1 - m) \frac {\boldsymbol {a}}{\pi} + \frac {D F G}{4 (\boldsymbol {\omega} _ {i} \times \mathbf {n}) (\boldsymbol {\omega} _ {o} \times \mathbf {n})}, \quad (2) +$$ + +where $m\in [0,1]$ is the metallic, $\pmb {a}\in [0,1]^3$ is the albedo. We detail the expression of $D,F$ and $G$ in the Supplement. With Eq.(1) and Eq.(2), the outgoing radiance is given by + +$$ +\boldsymbol {C} (\boldsymbol {x}, \boldsymbol {\omega} _ {o}) = \boldsymbol {C} _ {\mathrm {d}} (\boldsymbol {x}, \boldsymbol {\omega} _ {o}) + \boldsymbol {C} _ {\mathrm {s}} (\boldsymbol {x}, \boldsymbol {\omega} _ {o}), \tag {3} +$$ + +$$ +\boldsymbol {C} _ {\mathrm {d}} (\boldsymbol {x}, \boldsymbol {\omega} _ {\boldsymbol {o}}) = (1 - m) \boldsymbol {a} \int_ {\Omega} L _ {i} (\boldsymbol {x}, \boldsymbol {\omega} _ {\boldsymbol {i}}) \frac {(\boldsymbol {\omega} _ {\boldsymbol {i}} \cdot \mathbf {n})}{\pi} d \boldsymbol {\omega} _ {\boldsymbol {i}}, \tag {4} +$$ + +$$ +C _ {\mathrm {s}} (\boldsymbol {x}, \omega_ {o}) = \int_ {\Omega} \frac {D F G}{4 (\boldsymbol {\omega} _ {i} \times \mathbf {n}) (\boldsymbol {\omega} _ {o} \times \mathbf {n})} L _ {i} (\boldsymbol {x}, \omega_ {i}) (\boldsymbol {\omega} _ {i} \cdot \mathbf {n}) d \boldsymbol {\omega} _ {i}, \tag {5} +$$ + +$C_{\mathrm{s}}$ and $C_\mathrm{d}$ are specular and diffuse color, respectively. + +Photometric Stereo aims to estimate the surface normals by observing an object under varying lightings [44]. When considering a Lambertian surface illuminated by a single + +![](images/e7f63656e2a252119f11e3f00b82d4f7c491a7e03d7c40e6190c9dbf115d4d4e.jpg) +Figure 2. Overview of our framework. During training, images with varying materials and illumination are rendered using PBR with randomly varied materials, lighting, and camera poses, along with depth, normal, albedo, and lighting maps. Images are encoded as a mesh through the network. All associated maps are used for supervision. During inference, an optional multi-view diffusion model outputs multi-view images, which are then fed into the network for mesh prediction. Relighting and material editing functionalities are also supported. + +point-like, distant light, the color is determined solely by the diffuse term, which can be formulated by + +$$ +\boldsymbol {C} (\boldsymbol {x}) = \boldsymbol {a} (\boldsymbol {L} \cdot \boldsymbol {n}), \tag {6} +$$ + +where $L = L\cdot \omega$ $\omega$ and $L$ are the direction and the intensity of the lighting, respectively. When we observe the object under different lighting conditions $L_{i}$ ,we have multiple such equations. We assume that both the direction and intensity of the lighting are known, and the shading colors $C(x)$ is also observed. Under these conditions, determining the surface normals $\pmb{n}$ and the albedo $\pmb{a}$ is effectively equivalent to solving a system of equations derived from these observations. More lighting indicates more equations, which effectively constrain the solution space. + +# 3.2. images with varying materials and illumination + +Previous methods typically prepared training data by rendering multi-view images with fixed, simple lighting and materials in Blender [11]. This approach resulted in images with low-frequency appearances, offering limited photometric cues. Consequently, these methods struggled to reconstruct geometry with precise local details. Additionally, they often failed when processing images with glossy surfaces, as these are out-of-distribution samples for the model. + +We provide some examples in the Supplement. + +In contrast, we prepare images with varying materials and illumination by varying materials and lighting. A naive solution is to prepare these images offline, as with previous methods, but this approach poses significant challenges due to the infinite number of potential combinations of materials and lighting. Moreover, rendering high-quality images requires large sample counts, making traditional data preparation methods infeasible. To overcome these issues, we incorporate a real-time rendering method known as split-sum approximation [19] along with mesh rasterization, which facilitates rapid rendering. This method enables online data preparation and significantly enhances flexibility. + +Split-sum approximation. High-quality estimation of physically based rendering typically requires Monte Carlo sampling to approximate the integral in Eq.(1). However, this process demands large sample counts, making it time-consuming. Instead, we employ a real-time rendering method known as the split-sum approximation [19]. According to the split-sum approximation, the specular component in Eq.(5) can be rewritten as: + +$$ +\boldsymbol {C} _ {\mathrm {s}} (\boldsymbol {x}, \boldsymbol {\omega} _ {o}) \approx \int_ {\Omega} \frac {D F G}{4 (\boldsymbol {\omega} _ {o} \cdot \boldsymbol {n})} d \boldsymbol {\omega} _ {i} \int_ {\Omega} L (\boldsymbol {x}, \boldsymbol {\omega} _ {i}) D (\hat {\boldsymbol {d}}, \rho) d \boldsymbol {\omega} _ {i}, \tag {7} +$$ + +The first term is the integral of the BRDF, which is approximated by specular albedo $\pmb{a}_{\mathrm{s}} = ((1 - m)*0.04 + m*\pmb {a})*F_1 + F_2$ , where $F_{1}$ and $F_{2}$ are pre-computed scalars and stored in a 2D lookup texture related to $\rho ,n$ and $\omega_{o}$ . The second term is the integral of lights on the normal distribution function $D(\hat{\pmb{d}},\rho)$ , which can also be pre-computed and stored as mipmaps $M_{\mathrm{s}}$ . $\hat{\pmb{d}} = 2(-\omega_o\cdot n)\pmb {n} + \omega_o$ is the reflective direction. Then the Eq.(7) is modified as + +$$ +\boldsymbol {C} _ {\mathrm {s}} (\boldsymbol {x}, \omega_ {o}) = \boldsymbol {a} _ {\mathrm {s}} (\boldsymbol {a}, m, \boldsymbol {n}, \omega_ {o}) \boldsymbol {L} _ {\text {s p e c}} (\boldsymbol {x}, \boldsymbol {n}, \omega_ {o}, \rho , \boldsymbol {M} _ {\mathrm {s}}), \tag {8} +$$ + +where $L_{\mathrm{spec}} = \mathrm{Tex\_Sample}(\pmb{x},\hat{\pmb{d}},\rho ,M_{\mathrm{s}})$ , Tex Sample indicates texture sampling based on different levels of roughness $\rho$ in pre-computed lighting map $M_{\mathrm{s}}$ . A low-resolution map $M_{\mathrm{d}}$ is also created to represent low-frequency diffuse lighting and the diffuse part in Eq.(4) is simplified as + +$$ +\boldsymbol {C} _ {\mathrm {d}} (\boldsymbol {x}, \omega_ {o}) = \boldsymbol {a} _ {\mathrm {d}} (\boldsymbol {a}, m) \boldsymbol {L} _ {\text {d i f f}} (\boldsymbol {x}, \boldsymbol {n}, \boldsymbol {M} _ {\mathrm {d}}), \tag {9} +$$ + +where $\mathbf{a}_{\mathrm{d}} = (1 - m)\mathbf{a}$ indicates the diffuse albedo and $L_{\mathrm{diff}} = \mathrm{Tex\_Sample}(\mathbf{x},\mathbf{n},M_{\mathrm{d}})$ . We show some rendered examples in the Supplement. + +Discussion. We render images with varying materials and illumination using varied camera poses, materials, and lighting conditions rather than solely changing the lighting. Please refer to the Supplement for more details. This approach offers two distinct advantages. Firstly, multi-view images provide more geometric cues than single-view images, which are crucial for reconstructing globally reasonable geometry [20-22]. Secondly, by varying materials, we can create images with glossy appearances, particularly when the metallic component is high and roughness is low. These varied images serve as inputs, enhancing the model's robustness to variations in appearance. Furthermore, the core principles of photometric stereo remain applicable. In equations Eq.(8) and Eq.(9), the observation direction $\omega_{o}$ , metallic value $m$ , roughness $\rho$ , and mipmaps $M_{\mathrm{d}}$ and $M_{\mathrm{s}}$ are all known. Predicting the surface normals $\pmb{n}$ and the albedo $\pmb{a}$ still equates to solving these equations. Moreover, compared to merely changing lighting, altering the metallic and roughness values allows for diverse shading color rendering, which produces a richer set of equations. + +Mesh Rasterization Rendering. Given an object with explicit mesh $O$ , rasterization is utilized to determine surface points $x$ , along with corresponding depth $d$ , surface normals $n$ , and mask $m$ . After obtaining the surface points $x$ and their surface normals $n$ along with selected camera pose, materials and lighting, we leverage split-sum approximation to estimate the specular and diffuse color as Eq.(8) and Eq.(9), respectively. During the process, besides the shading color, we can also render albedo, specular light, and diffuse light maps. The entire process can be formulated as + +$$ +\left\{C, \boldsymbol {n}, \boldsymbol {d}, \boldsymbol {m}, \boldsymbol {a}, L _ {\text {s p e c}}, L _ {\text {d i f f}} \right\} = \operatorname {P B R} (\text {R a s t e r i z a t i o n} (O)), \tag {10} +$$ + +where $C$ , $n$ , $d$ , $m$ , $a$ , $L_{\mathrm{spec}}$ , and $L_{\mathrm{diff}}$ are the rendered color, normal, depth, mask, albedo, specular light, and diffuse light maps, respectively. + +# 3.3. PRM + +Mesh as 3D Representation. The previous LRM series typically integrate triplane as 3D representation. In contrast, we opt for an explicit representation using mesh as our 3D format, which enables the use of differentiable PBR method for better radiance modeling. As a result, specular and diffuse lighting maps are also renderable, providing extra photometric cues that are only related to surface normals. Moreover, PBR can effectively model the specular component, leading to improved geometry reconstruction results [7, 41]. Specifically, we leverage differentiable isosurface extraction module, namely FlexiCubes [36]. + +Two Stage Optimization. Inspired by InstantMesh [46], we have similarly designed a two-stage optimization framework. The first stage mirrors Instantmesh, using triplane and volume rendering for optimization with offline rendered data. In the second stage, FlexiCubes is used as the 3D representation. To reuse the knowledge in the first stage, we load the pretrained model as in InstantMesh [46]. The original color MLP is repurposed as an albedo MLP to incorporate color priors. Since our focus is on reconstruction, we directly utilize the ground-truth metallic and roughness during training. Given that an explicit mesh serves as our 3D representation, novel views can be rendered as described in Eq.(10). The difference is that the mesh $\hat{O}$ is extracted using the dual marching cubes algorithm [30], which utilizes predicted SDF values, deformation, and weights derived from the triplane formulated by + +$$ +\{\hat {\boldsymbol {C}}, \hat {\boldsymbol {n}}, \hat {\boldsymbol {d}}, \hat {\boldsymbol {m}}, \hat {\boldsymbol {a}}, \hat {\boldsymbol {L}} _ {\text {s p e c}}, \hat {\boldsymbol {L}} _ {\text {d i f f}} \} = \mathrm {P B R} (\text {R a s t e r i z a t i o n} (\hat {\boldsymbol {O}})). \tag {11} +$$ + +Optimization. During the training process, our total loss function is + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\mathrm {M S E}} (\boldsymbol {C}, \hat {\boldsymbol {C}}) + \lambda_ {\mathrm {L P I P S}} \mathcal {L} _ {\mathrm {L P I P S}} (\boldsymbol {C}, \hat {\boldsymbol {C}}) \\ + \mathcal {L} _ {\mathrm {M S E}} (\boldsymbol {a}, \hat {\boldsymbol {a}}) + \lambda_ {\mathrm {L P I P S}} \mathcal {L} _ {\mathrm {L P I P S}} (\boldsymbol {a}, \hat {\boldsymbol {a}}) \\ + \mathcal {L} _ {\mathrm {M S E}} \left(\boldsymbol {l} _ {*}, \hat {\boldsymbol {l}} _ {*}\right) + \lambda_ {\mathrm {L P I P S}} \mathcal {L} _ {\mathrm {L P I P S}} \left(\boldsymbol {l} _ {*}, \hat {\boldsymbol {l}} _ {*}\right) \tag {12} \\ + \lambda_ {\text {n o r m a l}} \hat {\boldsymbol {m}} \otimes (1 - \boldsymbol {n} \cdot \hat {\boldsymbol {n}}) + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}} \\ + \lambda_ {\text {d e p t h}} \hat {\boldsymbol {m}} \otimes \| \boldsymbol {d} - \hat {\boldsymbol {d}} \| _ {1} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {M S E}} (\boldsymbol {m}, \hat {\boldsymbol {m}}), \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{MSE}}$ and $\mathcal{L}_{\mathrm{LPIPS}}$ indicates the mean square error loss and LPISP loss [52], respectively. $* \in \{\mathrm{spec}, \mathrm{diff}\}$ denotes specular light and diffuse light maps, respectively. $\mathcal{L}_{\mathrm{reg}}$ is the regularization terms used in FlexiCubes [36]. During training, we set $\lambda_{\mathrm{LPIPS}} = 2.0$ , $\lambda_{\mathrm{normal}} = 0.2$ , $\lambda_{\mathrm{depth}} = 0.5$ , $\lambda_{\mathrm{mask}} = 1.0$ and $\lambda_{\mathrm{reg}} = 0.01$ . + +For both the specular $L_{\mathrm{spec}}$ and the diffuse lighting map $L_{\mathrm{diff}}$ , which are directly influenced by surface normals, effectively optimizing these light maps significantly enhances + +![](images/ce0665adb94175989846b24499ac8558cc829d3c4a3df972d2d436a0e45788bb.jpg) +Figure 3. Qualitative comparisons with state-of-the-art methods and ground truth for single-view reconstruction task. PRM reconstructs the highest quality 3D mesh and provides a more accurate texture prediction from input photographs compared to the others. + +the surface normals, thereby refining the precision of local details. This process is analogous to photometric stereo. The key difference is that these maps are exclusively related to surface normals without considering albedo, as demonstrated in Eq.(8) and Eq.(9), in contrast to shading color. + +Applications. PRM achieves high-quality geometry reconstruction with predicted albedo. This capability enables us to render the object under novel lighting conditions and also to modify its material properties. Examples of these applications are provided in the Supplement. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Protocol + +Datasets. For training, we used Objaverse [5], a dataset comprised of synthetic 3D assets, that allows us to control the lighting, geometry, and material properties. We first filter Objaverse to get a high-quality subset for training. The filtering process aims to exclude objects lacking texture maps or those of inferior quality, such as those with low-poly properties. Texture maps are essential as they provide detailed albedo maps; in their absence, vertex colors are used as a substitute for albedo. Moreover, low-poly + +meshes result in uneven surface lighting. During rendering, we maintained the original albedo unchanged and randomly selected a material combination from a total of 121 possibilities, which were derived by varying the metallic and roughness properties from 0 to 1 in increments of 0.1. For lighting, we utilized environment maps sampled from a collection of 679 maps available on Polyhaven.com, thereby ensuring a diverse range of lighting conditions. + +For evaluation, We performed quantitative comparisons using two public datasets, including Google Scanned Objects (GSO) [6] and OmniObject3D (Omni3D) [45]. We randomly picked out 300 objects as the evaluation set both datasets, respectively. To show the robust capabilities of our model on appearance variations, we rendered the input view of each object with a randomly sampled combination of materials and lighting. We also report extra comparison results, following previous methods that utilized fixed lighting and did not change materials. + +Evaluation Protocol. We evaluated both the 2D visual quality and the 3D geometric quality. For the 2D visual evaluation, we rendered novel views from the reconstructed 3D mesh and compared them with the ground truth views, using PSNR, SSIM, and LPIPS. Since other methods do not + +Table 1. Quantitative comparison with methods on the GSO and Omni3D datasets, showcasing 3D reconstruction and 2D rendering metrics. + +
DatasetGSOOmniObject3D
MetricCD↓FS@0.1↑PSNR↑SSIM↑LPIPS↓CD↓FS@0.1↑PSNR↑SSIM↑LPIPS↓
TripoSR0.1090.87215.2470.8590.1970.0830.94015.2370.8650.176
CRM0.2020.70717.2930.8540.1420.0880.90718.2930.8940.112
LGM0.1440.80017.6430.8690.1580.1380.82317.8930.8840.139
InstantMesh0.0760.93119.9880.9010.0960.0960.89218.6080.9030.096
PRM0.0500.98125.1250.9290.0610.0530.97925.0630.9320.063
+ +predict albedo, we compared their shading color in novel views. For our method, we rendered the shading color based on the predicted mesh and albedo, then performed the metric calculations. For the 3D geometric evaluation, we first aligned the coordinate systems of the reconstructed meshes with those of the ground truth meshes. Subsequently, we repositioned and rescaled all meshes into a cube of size $[-1,1]^3$ . We reported the Chamfer Distance (CD) and F-Score (FS) at a threshold of 0.1, which were computed by uniformly sampling 16K points from the mesh surfaces. + +# 4.2. Implementation Details + +Our model was developed based on InstantMesh [46]. The architecture of the Transformer encoder, triplane transformer, and the FlexiCubes decoder mirrors that of InstantMesh. Our model underwent training for 7 days and 3 days on 32 NVIDIA RTX A800 GPUs for the first stage and second stage, respectively. During inference, we used a single RGB image to generate six fixed views by Zero123++ [37] as the input of PRM. For more details, please see our Supplement. + +# 4.3. Comparison with State-of-the-Art Methods + +We compared the proposed PRM with four baselines. These include TripoSR [40], an open-source LRM implementation renowned for its superior single-view reconstruction performance; CRM [43], a UNet-based Convolutional Reconstruction Model that reconstructs 3D meshes from generated multi-view images and canonical coordinate maps (CCMs); LGM [39], a unet-based Large Gaussian Model + +Table 2. Comparison on GSO dataset. "Random m&r" indicates whether materials and lighting were randomly changed. + +
MethodRandom m&RCD↓FS@0.1↑PSNR↑
InstantMesh✓0.0610.93421.115
InstantMesh×0.0480.97223.644
PRM✓0.0530.98224.602
PRM×0.0430.99126.377
+ +Table 3. Quantitative results of the ablation study. + +
MetricCD↓FS@0.1↑PSNR↑
Only albedo supervision0.0990.88717.532
w/o PBR0.0890.90919.143
w/o lighting supervision0.0730.91920.114
w/o change materials0.0890.89419.662
Full model0.0660.94820.992
+ +that reconstructs Gaussians from generated multi-view images; and InstantMesh [46], a transformer-based LRM that employs a two-stage training strategy for direct 3D mesh reconstruction. We reported both quantitative and qualitative comparative results for a complete comparison analysis. + +Quantitative Results. We reported quantitative results with randomly selected lighting and materials in two different datasets in Table 1. We also report quantitative results without changing materials and using fixed lighting as previous methods compared with cutting-edge method Instantmesh on GSO in Table 2, where ground-truth rendered multi-view images were used as input. + +For 3D reconstruction metrics, PRM achieves significant improvements over all state-of-the-art methods on both datasets, as shown in Table 1. The qualitative comparison with other methods is presented in Figure 3. We attribute these improvements to our use of images with varying materials and illumination for both input and supervision. This approach not only enables the model to learn fine-grained geometric details by providing photometric cues but also enhances the model's robustness to variations in image appearance. Further validation of these results in the test setting without material changes and using fixed lighting is shown in Table 2. + +For 2D visual metrics, our approach effectively mitigates the impact of lighting variations to accurately restore the original colors of objects, as shown in Table 1. We surpass all current methods across all metrics. + +![](images/cbd830ded9bdfbf34f137a9240560ddb58c33b76372fe94827013d2f808de2c3.jpg) +Figure 4. Visualization of our ablation study to validate the effectiveness of each component in our framework. + +![](images/26b18e524b265c93477290a05c04e49db406dc525dd20d33d08cd485dbd9818d.jpg) +Figure 5. Shading color offers significant photometric cues for perceiving geometry, whereas albedo lacks this information. + +Qualitative Results. For the qualitative comparison, we randomly selected four images from the GSO dataset to serve as inputs for 3D model reconstruction. For each reconstructed mesh, we visualized both the albedo (ours) and the shading color (others), as well as the pure geometry. + +As shown in Figure 3, the results reconstructed by PRM exhibit more accurate geometry and appearance. Our model can reconstruct precise geometry and accurately predict albedo from images with specular highlights, whereas other methods fail. For instance, InstantMesh often predicts uneven geometric surfaces and tends to reconstruct incorrect geometry. Similarly, both CRM and LGM struggle to produce satisfactory results, falling short in both geometry accuracy and texture prediction. This underscores the robustness and superior performance of our PRM method in handling complex lighting conditions and intricate surface details, making it a more reliable choice for high-quality 3D model reconstruction. + +# 4.4. Ablation Study + +We conducted the ablation study to validate the effectiveness of each component in our framework. We reported quantitative results of our ablation study in Table 3. For ablations, we reduce the training set from $120\mathrm{K}$ to $30\mathrm{K}$ for faster experiments due to the heavy cost. + +The effectiveness of PBR. PBR plays a crucial role in improving geometry, especially for glossy surfaces. To validate the effectiveness of PBR, we conducted experiments by directly predicting shading colors using an MLP, rather than deriving results with PBR. However, direct prediction of shading color, without accounting for view-dependent appearances, struggles to model such effects and thus fails to accurately reconstruct geometry. We presented these results as "w/o PBR" in Table 3 and Figure 4. + +Albedo supervision. To avoid the interference caused by specular color on the surface, an intuitive approach is to directly use albedo instead of shading color for supervision. However, this method proves ineffective in practice, as albedo contains few photometric cues, thereby hindering geometry reconstruction. For example, a concave surface + +![](images/092277a6cd64b7bea80cdeaa773606fc0566fcf1b11005f97e6618f590fc4fb5.jpg) +Figure 6. Ablation study of the effect of changing materials. + +with uniform albedo may appear planar without the presence of cast shadows, while shading color provides significant photometric cues critical for accurately perceiving geometry, as illustrated in Figure 5. We conducted an ablation study within our framework by excluding shading color and light maps from supervision. The qualitative comparison is shown in and Table 3 and Figure 4 denoted as "Only albedo supervision". The results demonstrate that photometric cues are crucial for accurate geometry reconstruction. + +Lighting maps supervision. We conducted the ablation study within our framework by excluding the lighting maps loss. The results, denoted as "w/o lighting supervision", are displayed in Table 3 and Figure 4. Since lighting maps are exclusively related to surface normals and do not include albedo, optimizing these maps proves particularly beneficial for enhancing the optimization of fine-grained local details. + +Variations in materials. We conducted an ablation study to illustrate the effectiveness of varying materials during training. The results are shown in Table 3 and Figure 6. Without changing the materials, some details are lost. Moreover, the model has lost the capability to reconstruct glossy surfaces. + +# 5. Conclusion and Limitation + +Limitation. Despite the high-quality results achieved in this work, there remain several limitations for future research to explore: 1) Firstly, the reconstructed 3D model is sensitive to the quality of multi-view images. 2) Secondly, the accuracy of the estimated albedo appears to be somewhat entangled with the lighting conditions. + +Conclusion. In this work, we introduce PRM, a novel feedforward framework designed to reconstructed high-quality 3D assets with fine-grained local details, even amidst complex image appearances. To achieve this goal, we utilize images with varying materials and illumination as both input and supervision, providing sufficient photometric cues for fine-grained geometry recovery and enhancing the model's robustness to variations in image appearance. Using a mesh as our 3D representation, we employ differentiable PBR for predicted rendering, underpinning the utilization of multiple supervisions for optimization. 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However, most prior art indiscriminately uses a fixed prompt distribution across different tasks, neglecting the importance of each block varying depending on the task. In this paper, we introduce adaptive distribution optimization (ADO) by tackling two key questions: ① How to appropriately and formally define ADO, and ② How to design an adaptive distribution strategy guided by this definition? Through empirical analysis, we first confirm that properly adjusting the distribution significantly improves VPT performance, and further uncover a key insight that a nested relationship exists between ADO and VPT. Based on these findings, we propose a new VPT framework, termed PRO-VPT (iterative Prompt Relocation-based VPT), which adaptively adjusts the distribution built upon a nested optimization formulation. Specifically, we develop a prompt relocation strategy derived from this formulation, comprising two steps: pruning idle prompts from prompt-saturated blocks, followed by allocating these prompts to the most prompt-needed blocks. By iteratively performing prompt relocation and VPT, our proposal can adaptively learn the optimal prompt distribution in a nested optimization-based manner, thereby unlocking the full potential of VPT. Extensive experiments demonstrate that our proposal significantly outperforms advanced VPT methods, e.g., PRO-VPT surpasses VPT by 1.6 pp and 2.0 pp average accuracy, leading prompt-based methods to state-of-the-art performance on VTAB-1k and FGVC benchmarks. The code is available at https://github.com/ckshang/PRO-VPT. + +# 1. Introduction + +Fine-tuning pre-trained vision models (PVMs) [26] has proven remarkably effective in adapting to a variety of + +![](images/827bc2189f20a003217341ba80cce94f37759915d6021c21de68ab428c0edcff.jpg) +Figure 1. PRO-VPT (ours) vs. prior art in VPT. Existing VPT approaches typically insert trainable prompts into the PVM with a pre-specific static distribution, whether shallow or deep, and optimize these prompts to drive the PVM to conduct downstream tasks. Compared to the prior art, our proposal (PRO-VPT) adaptively adjusts prompt distribution by treating it as an optimization objective and coupling the distribution optimization with prompt tuning. + +downstream tasks [14, 30, 65]. However, the computational and storage costs associated with full fine-tuning are prohibitively high, particularly as model sizes continue to grow [1, 40, 57]. To overcome these challenges, parameter-efficient fine-tuning (PEFT) methods [2, 20, 61, 62], such as visual prompt tuning (VPT) [22], have emerged as more promising alternatives, garnering significant attention. + +Instead of updating all model parameters directly, VPT inserts lightweight learnable prompt tokens into the input space of Transformer blocks, with either a shallow distribution (inserted only in the first block) or a deep distribution (uniformly inserted across all blocks), while keeping the PVM frozen. This approach significantly reduces the number of parameters that need to be fine-tuned, thereby lowering the computational and memory overhead [14]. Follow-up + +research further enhances this pipeline by improving aspects such as prompting architecture [13, 50, 52], prompt initialization [58], and prompt propagation structure [5, 63, 71]. + +Despite these advancements, most of the prior art still relies on a preset fixed prompt distribution, either shallow or deep, across various downstream tasks, as illustrated in Fig. 1. However, recent findings reveal that the importance of each pre-trained block varies significantly across different tasks [12, 28, 43, 49, 60], underscoring the need to dynamically tailor the fine-tuning intensity for each block to improve task performance [11, 25, 29, 45, 53]. This implies that indiscriminately using a fixed prompt distribution may not fully exploit the potential of VPT, motivating us to adaptively adjust the distribution to better accommodate each task. + +In this paper, we naturally consider prompt distribution as one of the optimization objectives, which we refer to as adaptive distribution optimization (ADO). As the focus pivots towards the ADO problem, new questions arise. First, since the underlying nature of distribution optimization is still unexplored, the definition of ADO remains unclear. For instance, defining it as a one-shot process or an iterative one leads to a critical consideration, namely whether the effectiveness of distribution adjustments is influenced by ongoing prompt updates. This leads us to our first key question: ① How can we appropriately and formally define ADO? (§ 3.2) Second, once the definition of ADO is established, a more essential question emerges: ② How can we achieve adaptive distribution derived from this definition? (§ 3.3) + +To address these questions, we first empirically analyze the ADO problem. Our findings confirm the significance of ADO and further reveal two key insights: the effectiveness of distribution adjustments is indeed impacted by prompt updates, and a nested relationship exists between ADO and VPT. Based on these insights, we propose PRO-VPT (iterative Prompt RelOcation-based VPT), a novel iterative framework derived from a nested optimization definition. Specifically, building on this definition, we develop a prompt relocation (PR) strategy for ADO, which comprises two optimization steps: pruning and allocating. The pruning step first identifies and releases idle prompts from prompt-saturated blocks, while the subsequent allocation step determines the most prompt-needed blocks for redistributing these prompts. By iteratively performing PR and VPT, PRO-VPT can adaptively learn the optimal prompt distribution for each task in a nested optimization manner, thereby unlocking the full potential of VPT. Our main contributions are fourfold. + +- We explore the ADO problem within VPT and reveal the nested relationship between ADO and VPT. +- Building upon our insights into prompt distribution, we propose the first ADO-VPT co-design framework, termed PRO-VPT, with a nested optimization definition. +- Derived from the definition, we present a PR strategy for ADO, which introduces an idleness score to prune under + +utilized prompts from prompt-saturated blocks and then allocates them to prompt-needed blocks using reinforcement learning (RL). + +- Extensive experiments show that PRO-VPT exhibits superior performance, e.g., it attains state-of-the-art average accuracies of $78.0\%$ on VTAB-1k and $91.7\%$ on FGVC, with 1.6 pp and 2.0 pp advantages over the VPT baseline. + +# 2. Related Work + +Visual Prompt Tuning. VPT [22], one of the leading techniques in PEFT, draws inspiration from language-domain prompting works [19, 32, 37, 38] to fine-tune a small portion of prompts while keeping the pre-trained model frozen. Subsequent research has improved VPT in three main aspects: (1) Extending prompts to other Transformer components (e.g., key and value matrices or the patch embedding layer) to better suit the Transformer architecture [13, 50, 52]; (2) Initializing prompts with prototypes of image tokens to accelerate convergence [58]; (3) Refining the propagation structures of prompts to strengthen cross-layer interactions [5, 63, 71]. However, most existing methods depend on a fixed prompt distribution for all tasks, resulting in less effective prompting performance. In contrast, our approach adaptively adjusts the prompt distribution for each task, enabling prompt-based methods to achieve state-of-the-art performance. + +Layer-wise Fine-Tuning. Recent research has highlighted the importance of treating each pre-trained block differently during downstream fine-tuning, emphasizing the need for layer-wise adaptive strategies to calibrate the fine-tuning intensity for each block [12, 25, 31, 43, 54]. For instance, [29] first revealed that some pre-trained blocks may already be near-optimal for specific tasks, indicating that fine-tuning demands of each block vary significantly for different tasks. This work then proposes freezing these near-optimal blocks and selectively fine-tuning the remaining ones to improve performance. Similarly, [45, 49] proposes to adaptively assign different learning rates to each block, tailoring the fine-tuning intensity at a layer level to achieve more fine-grained layer-wise adaptation. Inspired by these findings, we hypothesize that the prompting intensity for each block, i.e., the overall distribution of prompts, may also play a crucial role in task adaptation, leading us to focus on adaptively adjusting the prompt distribution within VPT. + +# 3. Methodology + +# 3.1. Notation + +Visual prompt tuning (VPT) aims to learn lightweight tunable prompts $\mathbf{P}$ that are inserted into the vision Transformer (ViT) $f(\cdot)$ with a specific distribution $\mathcal{D}$ . In particular, for a set of $N$ prompts $\mathbf{P} = \{\mathbf{p}_k\}_{k=1}^N$ and their distributed blocks $\mathcal{D} = \{d_k\}_{k=1}^N$ where $d_k \in \{0,1,\dots,L\}$ ( $d_k = 0$ for undistributed), the prompted ViT model is denoted as $f_{\mathbf{P},\mathcal{D}}(\cdot)$ . Given a training set $\mathcal{T}_{tr}$ of input-label pairs $(\mathbf{x},y)$ , the model + +![](images/fabb879534ef035f291e9250b930bf54e09c5b6477a2229003a717896d609d24.jpg) +Figure 2. Performance gaps from distribution adjustments using prompts from epochs 25, 50, and 75. Adjusting prompt distribution appropriately leads to enhanced performance; however, effective adjustments vary significantly across different epochs. + +is then trained by minimizing the task loss $\mathcal{L}(f_{\mathbf{P},\mathcal{D}}(\mathbf{x}),y)$ . For convenience in later sections, we define the loss difference as $\Delta \mathcal{L}(f_1,f_2) = \mathcal{L}(f_1(\mathbf{x}),y) - \mathcal{L}(f_2(\mathbf{x}),y)$ . + +# 3.2. Analysis and Formulation of ADO + +We first explore the underlying nature of ADO and its formal definition, in response to question ①. + +Intuitively, ADO can be defined in two distinct ways: one-shot (independently adjusting the distribution) or iterative (integrating with prompt tuning through iteratively adjusting the distribution). These definitions are distinct in whether the distribution is adjusted concurrently with prompt tuning. Specifically, an iterative process is more appropriate when distribution adjustments are affected by ongoing changes in prompts, as independent optimization may lead to suboptimal results by failing to account for these dynamics. Otherwise, one-shot adjustments may be sufficient. + +To investigate which definition better matches the underlying nature, we experiment to examine how distribution adjustments behave when applied to prompts from different epochs. We use two intuitive adjustment strategies: incrementally adding to a small initial prompt set and repositioning existing prompts. As shown in Fig. 2, adding or repositioning prompts to specific blocks can effectively improve performance; however, the effective adjustments differ significantly when prompts are updated. Comprehensive results with detailed analysis are provided in Appendix C. In conclusion, we summarize our key findings as follows: + +Finding 1. Properly adjusting the prompt distribution significantly enhances performance, confirming the necessity to reconsider its optimization. + +Finding 2. Distribution adjustments are sensitive not only to different blocks but also to the updated prompts themselves, highlighting the need for an iterative process that continuously adjusts the distribution during training. + +Finding 3. The effectiveness of distribution adjustments can + +only be properly evaluated after prompt tuning, indicating that the prompt tuning process should be nested within the distribution optimization process (see Appendix C). + +Building on these insights, we propose integrating ADO with VPT into an iterative optimization framework. Formally, we present the definition of this ADO-VPT co-design framework through the lens of nested optimization, where the objectives of ADO and VPT are expressed as: + +$$ +\mathcal {D} ^ {*} = \underset {\mathcal {D}} {\arg \min } \mathbb {E} _ {(\mathbf {x}, y) \in \mathcal {T} _ {t r}} \left[ \mathcal {L} \left(f _ {\mathbf {P} ^ {*}, \mathcal {D}} (\mathbf {x}), y\right) \right], \tag {1} +$$ + +$$ +\mathbf {P} ^ {*} = \underset {\mathbf {P}} {\arg \min } \mathbb {E} _ {(\mathbf {x}, y) \in \mathcal {T} _ {t r}} \left[ \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D} ^ {*}} (\mathbf {x}), y\right) \right]. \tag {2} +$$ + +This formulation clearly illustrates the intertwined relationship between visual prompts $\mathbf{P}$ and their distribution $\mathcal{D}$ , with its framework presented in Fig. iii. In this framework, prompt tuning is integrated into the ADO process, forming a closed-loop workflow of 'distribution adjustment $\rightarrow$ prompt tuning $\rightarrow$ adjustment evaluation $\rightarrow$ new adjustment', thereby achieving a co-design process aligning with the observed iterative and nested nature. + +Remark. This nested optimization framework offers a universal approach capable of incorporating various distribution adjustment strategies, e.g., adding or repositioning. However, we empirically observe that adding-based adjustments often lead to unstable performance (see Appendix D). Therefore, in the following section, we focus on developing a prompt relocation (PR) strategy based on this formulation to effectively tackle the ADO problem. + +# 3.3. Iterative Prompt Relocation-based VPT + +Following the relocation objective defined in Eq. (1), we introduce the PR strategy derived from this definition and provide a detailed overview of the PRO-VPT framework, in response to question ②. + +Building on the aforementioned findings, the discrete PR objective is further complicated by the non-stationary nature of effective relocation (Finding 2) and the necessity to predict the effectiveness of relocation operations (Finding 3). Nonetheless, these three properties make a RL framework [24, 33] a natural and well-suited approach for optimizing the PR objective. However, a naive RL implementation needs to model all possible relocation operations as actions, resulting in $L^2$ possible arrangements (e.g., 144 actions for ViT-B). Such a large action space necessitates numerous iterations to achieve convergence (cf. § 4.3). + +To address this, we propose decomposing the PR process into two sequential steps: pruning and allocating. The pruning step first identifies and releases idle prompts for relocation, while the allocating step then employs RL to determine optimal blocks for these freed prompts. By focusing solely on allocatable blocks instead of all block arrangements, this approach effectively reduces the action space from $L^2$ to $L$ . More importantly, this approach has an intuitive explanation: idle prompts typically exist within the prompt-saturated + +![](images/99e613aac9f769b9798fb836d99510999807b463e1f5b0720ecc8488a0c954b9.jpg) +Figure 3. Overview of our proposed PRO-VPT. Left: The streamlined workflow of PRO-VPT. Right: Illustration of the PR process. + +![](images/e334a4a16adad44f6c9b4b11adb3492cac7637121733737b24297a63bf388b85.jpg) + +blocks, thus relocating them to prompt-needed blocks may enhance the effectiveness of prompt distribution. Decomposed from the relocation objective in Eq. (1), the pruning and allocation steps1 can be formalized as: + +$$ +k ^ {*} = \underset {k} {\arg \max } \mathbb {E} _ {(\mathbf {x}, y) \in \mathcal {T} _ {t r}} \left[ \Delta \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D}}, f _ {\mathbf {P}, \mathcal {D} \mid d _ {k} = 0}\right) \right], \tag {3} +$$ + +$$ +a ^ {*} = \underset {a} {\arg \max } \mathbb {E} _ {(\mathbf {x}, y) \in \mathcal {T} _ {t r}} \left[ \Delta \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D} ^ {-}}, f _ {\mathbf {P} ^ {\prime}, \mathcal {D} | d _ {k ^ {*}} = a}\right) \right], \tag {4} +$$ + +where $\mathcal{D}^{-} = \{d_{k}\in \mathcal{D}|d_{k^{*}} = 0\}$ and $\mathcal{D}^{+} = \{d_{k}\in \mathcal{D}|d_{k^{*}} = a^{*}\}$ denote the prompt distributions after pruning and allocation with $a\in [L]$ as the allocation block, and the allocation step uses the tuned prompts $\mathbf{P}'$ for evaluation following Finding 3. These two equations are specifically designed to identify the $k^*$ -th prompt suitable for pruning and to determine the optimal block $a^*$ for allocating. + +Following this, we utilize Eqs. (3) and (4) to approach the pruning and allocation stages, respectively, with the overall PRO-VPT framework illustrated in Fig. 3 and Algo. i: + +Idleness Score-based Pruning. To measure whether a prompt is idle for its current block and suitable for relocation, we take Eq. (3) as the idleness score: + +$$ +\mathcal {I} _ {k} = \Delta \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D}}, f _ {\mathbf {P}, \mathcal {D} \mid d _ {k} = 0}\right). \tag {5} +$$ + +Intuitive Interpretation. If $\mathcal{I}_k = \Delta \mathcal{L} > 0$ , pruning the prompt $\mathbf{p}_k$ from its current block can enhance performance. This indicates that $\mathbf{p}_k$ is negative for its current block, which tends to be prompt-saturated and therefore suitable for its relocation to a more prompt-needed block. Conversely, $\mathcal{I}_k \leq 0 \forall k$ suggests that no blocks are saturated and thus the prompt distribution is near-optimal. + +Pruning Implementation. Since computing $\mathcal{I}_k$ for each individual prompt $\mathbf{p}_k$ is significantly inefficient, we approximate $\mathcal{I}_k$ using its first-order Taylor expansion (see Appendix F for detailed derivation): + +$$ +\widehat {\mathcal {I}} _ {k} \approx \mathbf {g} _ {k} ^ {T} \mathbf {p} _ {k}, \tag {6} +$$ + +where $\mathbf{g}_k = \frac{\nabla\mathcal{L}}{\nabla\mathbf{p}_k}$ represents the elements of the gradient $\mathbf{g}$ . + +To this end, by calculating the estimated scores as in Eq. (6), we can effectively identify and prune the idle prompt $\mathbf{p}_{k^*}$ with the maximum $\widehat{\mathcal{I}}_{k^*}$ from the prompt-saturated block (when $\max \widehat{\mathcal{I}}_k > 0$ ), thereby fulfilling Eq. (3) and forming the pruned distribution $\mathcal{D}^{-}$ . + +RL-based Allocation. After pruning an idle prompt, the following key step is to leverage RL to determine its optimal allocation to the prompt-needed block. Specifically, we take Eq. (4) as the optimization objective for the RL problem, i.e., the allocation reward, as follows: + +$$ +r = \Delta \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D} ^ {-}}, f _ {\mathbf {P} ^ {\prime}, \mathcal {D} | d _ {k ^ {*} = a}}\right). \tag {7} +$$ + +Intuitive Interpretation. The optimal allocation block $a^*$ , which achieves the maximum $r^* = \max \Delta \mathcal{L}$ , is identified as the block where assigning a prompt leads to the highest performance improvement, implying that this block is the most prompt-needed. + +Allocation Implementation. We detail the RL-based allocation under a Markov decision process framework, where the main components are: + +(1) State. We leverage all available information to represent the state of the current prompt distribution. Specifically, the state incorporates the block-wise idleness scores, the current distribution, and the pruned prompt's location, formally defined as $s = \{\sum_{d_k = i}\widehat{\mathcal{I}}_k\}_{i = 1}^L\bigcup \mathcal{D}^{-}\bigcup \mathrm{OneHot}(k^*)$ . After PR and VPT, the state transitions to $s'$ . +(2) Action. The action determines which block the pruned prompt will be allocated to, represented as $a \in [L]$ . +(3) Reward. Although the allocation reward $r$ is defined in Eq. (7), calculating the intermediate loss of $f_{\mathbf{P},\mathcal{D}^{-}}$ is computationally inefficient. To address this, we approximate $r$ by incorporating the idleness score as: + +$$ +\hat {r} \approx \Delta \mathcal {L} \left(f _ {\mathbf {P}, \mathcal {D}}, f _ {\mathbf {P} ^ {\prime}, \mathcal {D} | d _ {k ^ {*} = a}}\right) - \widehat {\mathcal {I}} _ {k ^ {*}}, \tag {8} +$$ + +where the idleness score $\widehat{\mathcal{I}}_{k^*} \approx \Delta \mathcal{L}(f_{\mathbf{P},\mathcal{D}}, f_{\mathbf{P},\mathcal{D}^-})$ provides an approximation of the intermediate loss of $f_{\mathbf{P},\mathcal{D}^-}$ . + +To this end, by leveraging RL to maximize the estimated reward as in Eq. (8), we can efficiently determine the optimal allocation to the prompt-needed block $a^{*}$ even within the non-stationary environment, thereby fulfilling Eq. (4) + +and forming the relocated distribution $\mathcal{D}^+$ . Particularly, we accomplish this by employing proximal policy optimization (PPO) [48], a state-of-the-art RL algorithm. + +Remark. Although the relocation process is decomposed into two-step sequential steps, the overall optimization objective, whether based on the expected objectives in Eqs. (3) and (4) or the estimated objectives in Eqs. (6) and (8), can be expressed as $\max_{k,a} \mathbb{E}_{(\mathbf{x},y) \in \mathcal{T}_{tr}}[\Delta \mathcal{L}(f_{\mathbf{P},\mathcal{D}}, f_{\mathbf{P}'', \mathcal{D}|d_k = a})]$ . This formulation remains equivalent to the original PR objective (i.e., the ADO objective) defined in Eq. (1). Consequently, leveraging the nested optimization formulation, the proposed PR strategy can effectively address the ADO problem and adaptively construct the optimal distribution. + +# 3.4. Discussion + +We note that some prior works have indirectly achieved adaptive distribution [13, 27, 67]. Specifically, pruning-based techniques [13, 27] introduce mask variables to iteratively prune redundant prompts from the original distribution, and NOAA [67] uses an evolutionary algorithm to search for an optimal sub-distribution within the original distribution in a one-shot manner. PRO-VPT is distinct and advantageous compared to these methods as: + +Distinct Goals. These methods aim to enhance performance through the lottery ticket hypothesis [8, 41, 47], focusing on searching for a more effective sub-distribution within a given hyper-distribution by circumventing negative prompts and retaining essential ones. However, they are limited to pruning prompts from prompt-saturated blocks and fail to tackle prompt-deficient blocks (cf. § 4.5). In contrast, our approach actively learns an optimal distribution of all prompts, adaptively relocating them from prompt-saturated blocks to prompt-needed blocks through our PR strategy, thereby maximizing the effectiveness of the entire prompt distribution. This fundamental distinction sets our approach apart from the methods discussed above. + +Efficient. While effective, we argue that these approaches typically incur considerable unnecessary training costs to identify an optimal sub-distribution, as numerous trained prompts are pruned and left unused (cf. § 4.3). This fundamentally contradicts the goal of parameter efficiency. Conversely, our work directly adjusts the distribution of the entire prompt set through prompt relocation, thereby minimizing extra costs and improving efficiency. + +Effective. These methods straightforwardly apply one-shot or iterative processes without considering the underlying distribution dynamics. For instance, NOAA [67] adopts a one-shot approach post-training, leading to suboptimal results (cf. § 4.2). Conversely, our work conducts empirical analyses and accordingly proposes a nested optimization-based method, enabling prompt-based methods to reach state-of-the-art performance. + +# 4. Experiments + +# 4.1. Experiment Setups + +Datasets. We evaluated our proposed PRO-VPT on a series of datasets grouped into three categories: (1) VTAB-1k. The visual task adaptation benchmark (VTAB) [66] encompasses 19 classification tasks categorized into three group: Natural, Specialized, and Structured, aiming to assess adaptation capabilities under low-shot training conditions. (2) FGVC. Fine-grained visual classification (FGVC) includes 5 classification tasks: CUB-200-2011 [56], NABirds [55], Oxford Flowers [42], Stanford Dogs [6], and Stanford Cars [10], aiming to assess task adaptation in large-scale, fine-grained settings. (3) COCO and ADE20k. These widely-used benchmarks for detection and segmentation are employed to assess the generalizability of our method across diverse downstream visual tasks. + +Implementation Details. We mainly use ViT-B/16 [7] supervised pre-trained on ImageNet-21k [46] as the initialization. We employ the SGD optimizer with a batch size of 64 and fine-tune models for 100 epochs. The number of prompt tokens per task in our method is set in accordance with [22]. Following [51], we evaluate our method using Inception normalization instead of ImageNet normalization, and for fair comparisons, we present the results of other counterparts using both normalization techniques. Notably, unlike most approaches [9, 22, 34, 68], our method employs a fixed learning rate instead of using a learning rate schedule, as we necessitate ensuring timely rewinding after prompt relocation [44]. More details about the hyper-parameters are provided in Appendices G. + +# 4.2. Main Results + +VTAB-1k. We evaluate the proposed PRO-VPT on VTAB-1k and compare it with other methods. We provide results for full fine-tuning and linear probing as baselines of traditional fine-tuning. As competing advanced adapter- or reparameterization-based methods, we include SSF [34], SPT-Adapter [16], Adapter+ [51], LoRA [20], FacT-TK [23], and Consolidator [15]. Furthermore, we benchmark against state-of-the-art prompt-based methods including VPT [22], NOAA [67], SPT [58], and iVPT [71]. + +Tab. 1 presents results on VTAB-1k with the best-performing normalization techniques (i.e., ImageNet or Inception) for each method (see Appendix H for complete results). Among all prompt-based methods, the previous best performance of $77.1\%$ average accuracy achieved by iVPT falls short of the advanced adapter-based method Adapter+, which reaches $77.6\%$ . Nevertheless, with the introduction of the optimization-based adaptive distribution, the proposed PRO-VPT sets a new state-of-the-art performance among all evaluated methods with an average accuracy of $78.0\%$ , highlighting the significant potential of prompt-based approaches. Additionally, compared to the one-shot optimization-based + +Table 1. Detailed results on the VTAB-1k datasets. Performance results are reported as the highest of ImageNet normalization (○) or Inception normalization (●), presented in % after a complete training schedule with ViT-B/16 supervised pre-trained on ImageNet-21k. The best results of prompt-based methods and other PEFT approaches are highlighted in bold. f: Early-stopping based on the test set. †: Lack of complete code or hyperparameter configurations for the method, hence results are reported as presented in the original paper. ¹Average across the average accuracies of the VTAB-1k groups, following previous work. + +
Param (M)NaturalSpecializedStructuredGlobal Avg.1
Cifar100Caltech101DTDFlower102PetsSVHNSun397Group Avg.Group Avg.Clev-CountClev-Dist.DMLabKITTI-Dist.dSpr-Loc.dSpr-Ori.sNORB-Azi.sNORB-Ele.Group Avg.
Full •85.873.292.670.497.986.290.639.678.687.196.687.574.086.366.661.049.879.782.651.933.537.057.874.2
Linear •0.0478.188.169.099.190.036.056.973.979.890.773.773.779.532.430.535.961.911.226.214.324.529.661.0
LoRA • [20]0.2983.091.771.699.290.983.856.782.486.295.783.571.984.377.762.349.080.282.251.731.047.060.175.6
FacT-TKs • [23]0.0574.992.773.799.191.385.557.782.186.894.984.170.984.281.964.149.277.283.853.128.244.760.375.5
FacT-TK≤32 • [23]0.1074.693.773.699.390.688.757.582.687.695.485.570.484.784.362.651.979.285.552.036.446.662.376.5
Consolidator † [15]0.3074.290.973.999.491.691.555.582.486.995.786.675.986.381.268.251.683.579.852.331.938.560.976.5
SSF f o [34]0.2469.092.675.199.491.890.252.981.687.495.987.475.586.675.962.353.380.677.354.929.537.959.075.7
SPT-Adapter f o [16]0.2372.993.272.599.391.484.655.281.385.396.084.375.585.382.268.049.380.082.451.931.741.260.875.8
SPT-Adapter f o [16]0.4372.993.272.599.391.488.855.882.086.296.185.575.585.883.068.051.981.282.451.931.741.261.476.4
Adapter+ r=16 • [51]0.3583.794.271.599.390.688.255.883.387.597.087.472.986.282.960.953.780.888.455.237.346.963.377.6
Prompt-based Methods:
VPT-Deep • [22]0.6083.093.071.299.091.384.156.082.584.996.682.574.584.677.558.749.779.686.256.137.950.762.176.4
NOAH f o [67]0.4369.692.770.299.190.486.153.780.284.495.483.975.884.982.868.949.981.781.848.332.844.261.375.5
SPT-Dept † [58]0.2279.392.673.299.591.089.151.282.385.496.884.974.885.570.364.854.275.279.349.536.541.558.975.6
iVPT † [71]0.6082.794.272.099.191.888.156.683.587.796.187.177.687.177.162.649.480.682.155.331.847.660.877.1
PRO-VPT (ours)0.6184.594.173.299.491.888.257.284.187.796.886.675.586.778.861.050.681.386.756.438.151.763.178.0
+ +![](images/48083588549ffa71739fc7376c8b3ff95e05f0f7cbf7b0e0a42432cfd540e51f.jpg) +Figure 4. Performance gains achieved by VPT w/ ADO (PRO-VPT) compared to VPT w/o ADO (VPT-Deep). PRO-VPT consistently outperforms VPT-Deep. + +NOAH, our nested optimization-based PRO-VPT achieves an average accuracy gain of 2.5 pp, validating the effectiveness of our proposed nested optimization framework. + +Furthermore, Fig. 4 illustrates the performance differences between VPT w/ ADO (PRO-VPT) and w/o ADO (VPT-Deep) on the VTAB-1k datasets. The accuracies of PRO-VPT are consistently higher than those of VPT-Deep, yielding an average accuracy improvement of $1.6\mathrm{pp}$ . This emphasizes the significance of optimizing the prompt distribution to unlock the full potential of VPT. + +FGVC. Next, we evaluate PRO-VPT on the FGVC benchmark. Among the aforementioned contenders, only a portion have conducted evaluations on FGVC and released the code and configurations. + +Tab. 2 presents the FGVC results with the best-performing normalization (see Appendix H for complete results). PRO-VPT achieves the best average accuracy of $91.7\%$ over all five FGVC datasets, surpassing the second-best performance of $91.4\%$ achieved by Adapter+ and SPT-Deep. This demonstrates that PRO-VPT also delivers state-of-the-art results for task adaptation when training data is large-scale. + +Table 2. Detailed results on the FGVC datasets. Performance results are reported as the highest of ImageNet normalization (○) or Inception normalization (●), presented in % after a complete training schedule with ViT-B/16 supervised pre-trained on ImageNet-21k. The best results of prompt-based methods and other PEFT approaches are highlighted in bold. †: Same as Tab. 1. + +
Param (M)CUB200NABirdsOxford FlowersStanford DogsStanford CarsGlobal Avg.
Full •86.088.081.599.285.690.689.0
Linear •0.1888.981.899.592.652.883.1
SSF o [34]0.3989.585.799.689.689.290.7
SPT-Adapter † [16]0.4089.183.399.291.186.289.8
SPT-LoRA † [16]0.5288.683.499.591.487.390.1
Adapter+ • [51]0.3490.485.099.792.689.191.4
Prompt-based Methods:
VPT-Deep • [22]0.8590.183.399.690.385.089.7
SPT-Deep † [58]0.3690.687.699.889.889.291.4
iVPT † [71]0.4189.184.599.590.885.689.9
PRO-VPT (ours)0.8690.686.799.791.889.691.7
+ +# 4.3. Ablation Study + +To comprehensively assess the advantages of our proposed PR strategy, we compare it with the following alternative strategies, as shown in Tab. 3: + +Strategies (A), (B) represent alternatives for extracting a sub-distribution from a hyper-distribution (see § 3.4). We utilize the pruning-based technique as in [13], applying pruning percentages ranging from $10\%$ to $90\%$ with $10~\mathrm{pp}$ intervals. (B) prunes from a huge hyper-distribution to obtain a sub-distribution with the same final parameter count as the VPT + +Table 3. Ablation study on various alternative ADO strategies. Results are presented using ViT-B/16 on two instances: Natural SVHN and Specialized Resisc45. The best and second-best results are highlighted in bold and underline. *Our proposed PR strategy. + +
Alternatives for the ADO ProblemSVHNResisc45
Param (M)Acc (%)Param (M)Acc (%)
VPT Baseline0.46884.100.12782.50
(A) Pruning0.46883.760.12783.81
(B) Pruning2.54384.170.54184.86
(C) Naive RL0.48283.510.14083.02
(D) Prn1 & Alc10.46884.880.12784.06
(E) Prn1 & Alc20.48286.990.14085.68
(F) Prn2 & Alc10.46885.820.12784.76
(G) Prn2 & Alc2*0.48288.190.14086.56
+ +baseline, and (A) prunes from a smaller hyper-distribution to match the number of trained parameters in the VPT baseline. + +Strategies (C)-(G) represent alternatives of prompt relocating, each incorporating different components. Particularly, (C) frames the PR process as a naive RL problem (see § 3.3) and utilizes the PPO algorithm. (D)-(G) are various combinations of the following components: + +Prn1. Randomly pruning prompts. + +Prn2. Pruning underutilized prompts based on the idleness score. + +Alc1. Modeling the allocation task as a multi-armed bandit problem, which is well-suited for stationary discrete decision-making, and then adopting the widely used Thompson sampling for prompt allocation. + +Alc2. Modeling the allocation task as a vanilla RL problem, which is more suited to non-stationary decision-making, and then using the popular PPO algorithm for prompt allocation. + +In summary, the key observations are as follows: + +Observation 1. Relocation-based methods are more efficient and effective compared to pruning-based methods. Pruning strategies (A) and (B) typically underperform relocation strategies (D)-(G), indicating that pruning is less effective in adaptive distribution. Specific to pruning, while (B) outperforms (A), it incurs high storage costs (e.g., 2.075M trained but unused parameters in SVHN) and still lags behind our proposed PR strategy. In contrast, RL-based relocation strategies (E) and (G) require only 0.014M extra parameters for PPO's policy networks, which is relatively negligible. + +Observation 2. The decomposition for $RL$ is remarkably effective. Strategy (C) significantly underperforms the two-step PR strategies (D)-(G), underscoring the benefits of decomposing the PR process for simplifying decision-making. + +Observation 3. Both the pruning and allocation components in PRO-VPT exhibit significantly effective, especially RL-based allocation. Comparing strategies (D) vs. (F) and (E) vs. (G), $Prn2$ indicates superior performance improvements (averaging 1.07 pp for SVHN and 0.79 pp for Resisc45), highlighting the effectiveness of the proposed idleness score. Moreover, strategies (G) and (E) achieve the best results, with Alc2 delivering remarkable gains over Alc1 (2.24 pp and 1.71 pp), highlighting the advantage of framing the allocation task as a non-stationary RL problem. + +Table 4. Generalizability study on distinct backbones. Results are presented in % on two instances: VTAB-1k Natural Cifar100 and Structured DMLab. + +
BackboneCifar100DMLab
ViT-B/16VPT-Deep83.0049.70
PRO-VPT84.49 1.49 ↑50.64 0.94 ↑
ViT-L/16VPT-Deep85.8245.98
PRO-VPT87.07 1.25 ↑46.57 0.59 ↑
ViT-H/14VPT-Deep78.4944.12
PRO-VPT79.73 1.24 ↑45.17 1.05 ↑
Swin-BVPT-Deep81.3349.86
PRO-VPT82.67 1.34 ↑50.78 0.92 ↑
+ +Table 5. Generalizability study on different pre-training strategies. Results are presented in % on two instances: VTAB-1k Natural Cifar100 and Structured DMLab. + +
Pre-Training StrategyCifar100DMLab
SupervisedVPT-Deep83.0049.70
PRO-VPT84.49 1.49 ↑50.64 0.94 ↑
Self-Supervised:
MAEVPT-Deep32.6543.58
PRO-VPT34.36 1.71 ↑46.07 2.49 ↑
MoCo-v3VPT-Deep72.4846.56
PRO-VPT73.62 1.14 ↑47.63 1.07 ↑
+ +# 4.4. Generalizability Analysis + +We evaluate the generalizability of PRO-VPT across different backbones and pre-training strategies, as well as in detection and segmentation tasks. + +**Backbone.** We experiment with three different scales of the ViT backbone: ViT-Base (ViT-B/16), ViT-Large (ViT-L/16), and ViT-Huge (ViT-H/14) [7], along with the hierarchical Swin Transformer (Swin-B) [39]. All backbones are supervised pre-trained on ImageNet-21k [46]. As shown in Tab. 4, PRO-VPT delivers higher accuracy compared to VPT with various scales and architectures. + +Pre-Training Strategy. In addition to the supervised pretraining strategy, we experiment with two self-supervised strategies: the masked image modeling method (MAE) [18] and the contrastive self-supervised method (MoCo-v3) [3]. As illustrated in Tab. 5, PRO-VPT consistently outperforms VPT regardless of the pre-training strategy, highlighting its strong generalizability. + +Detection and Segmentation. We also experiment on detection and segmentation tasks in Appendix H, where PRO-VPT still maintains advantages over VPT. + +# 4.5. Observations on PRO-VPT + +We design several experiments to thoroughly understand PRO-VPT. The key insights are concluded as follows: + +Observation 1. PRO-VPT effectively learns task-specific prompt distributions. We visualize the learned distributions of PRO-VPT under different total numbers of prompts, as shown in Fig. 5. Notably, the distributions remain consistent + +![](images/5210786e215a241ce9998933cff03dc5a05d0c511ae83ec4110d1be70a6431c8.jpg) +Figure 5. Visualization of prompt distributions learned by PRO-VPT on VTAB-1k Natural CIFar100, Specialized Resisc45, and Structured Clevr-Count with varying numbers of prompts. PRO-VPT effectively learns task-specific distributions. + +![](images/30bccd057695e84caebe13024780a8c5b855acb7b95984d5d40994a0a88538b0.jpg) + +![](images/955516fcd9c5d540bddb9a28ae547496d8766a0ee8f9de080880e16c0d8f9958.jpg) + +![](images/a4fc96948910094b2bd06bd2c3a423b90cddc75a5797876e39f93a50d7235e70.jpg) +Figure 7. Cosine similarity of feature changes and the corresponding test accuracy. The PR strategy has a minimal impact on features, and PRO-VPT demonstrates better stability than VPT in both representation and performance. + +![](images/4ba24fb2c9b6780513312ea743b264265ff8ea61fb98e7ce4551706b02147fc2.jpg) + +![](images/9b718002cedb2c59eb33918d97dc728e1b0724a30c6cebf24258af4d44d208fa.jpg) + +![](images/f4f4a7b6b2bd491c54185d3f5f5a068a32f4b07dc74dc39847242dbe53316be5.jpg) + +across different prompt numbers but exhibit significant variations across different tasks. This indicates that the prompting importance of each block indeed varies by task, and PROVPT effectively captures and adapts to these task-specific distributions to better accommodate each task. + +Observation 2. PRO-VPT effectively meets the block-specific prompt requirements via prompt relocation. We visualize the attention weights from representation features (i.e., [CLS] embeddings) to prompts across different blocks on Cifar100. Each attention weight represents the importance of a given prompt for its corresponding block. As depicted in Fig. 6, the attention weights in VPT reveal phenomena of prompt saturation (e.g., blocks 2 and 5) and prompt deficiency (e.g., blocks 4 and 12), confirming that different blocks exhibit significantly varying prompt demands. However, due to its fixed prompt distribution, VPT lacks the flexibility to adapt to these diverse needs. Even pruning-based methods can only prune negative prompts from prompt- + +saturated blocks while failing to address prompt-deficient blocks. In contrast, PRO-VPT effectively meets these block-specific prompt demands through adaptive prompt relocation. Such a fine-grained tuning strategy maximizes the effectiveness of the prompt distribution, thereby enhancing downstream task performance. + +![](images/045489051476a645121b46227c8a7c99de60ed81c57f7d2eff71c88f2519a626.jpg) +Figure 6. Visualization of prompt attention weights. + +Observation 3. PRO-VPT demonstrates enhanced stability and robustness. One might be skeptical that runtime modifi + +cations of the prompt distribution could compromise stability. To investigate this, we evaluate both the representation stability and performance stability in PRO-VPT and VPT. Specific to feature stability, we measure cosine similarity between representations (i.e., [CLS] embeddings) from the previous epoch and after each stage of pruning, allocation, and tuning. This similarity reflects the extent of feature changes resulting from each stage. Fig. 7 illustrates the similarity at different blocks and the corresponding test accuracy on Cifar100. Surprisingly, the orange and green lines indicate that the PR strategy has little impact on the learned features, as the features remain nearly unchanged after pruning and allocation. Moreover, PRO-VPT exhibits superior stability compared to VPT, both in terms of representation stability and performance stability. Additionally, as shown in Fig. vi, PRO-VPT demonstrates remarkable robustness to variations in prompt quantity compared to VPT, whereas the performance of VPT fluctuates significantly while PRO-VPT remains consistent. Overall, we argue that these benefits stem from our proposed optimization-based approach, which effectively identifies the optimal road for relocation, thereby minimizing its impact on stability and enhancing robustness. + +# 5. Conclusion + +This paper investigates the ADO problem within VPT. Based on our experimental insights into the nested relationship between ADO and VPT, we formalize an ADO-VPT co-design framework through the lens of nested optimization. Upon this formalization, we propose a novel PRO-VPT algorithm, which iteratively optimizes the distribution by integrating the PR (prompt relocation) strategy with VPT. Across 26 datasets, we show our method's significant performance improvement over VPT with superior robustness. + +# Acknowledgements + +This work was supported in part by the National Natural Science Foundation of China under Grants 62376233, 62306181, 62476063, and 62306313; in part by the NSFC / Research Grants Council (RGC) Joint Research Scheme under Grant N_HKBU214/21; in part by the General Research Fund of RGC under the Grant 12202622; in part by the RGC Senior Research Fellow Scheme under Grant SRFS2324-2S02; in part by the Guangdong Basic and Applied Basic Research Foundation under Grant 2024A1515010163; in part by the National Key Laboratory of Radar Signal Processing under Grant JKW202403; and in part by Xiaomi Young Talents Program. + +# References + +[1] Aochuan Chen, Yuguang Yao, Pin-Yu Chen, Yihua Zhang, and Sijia Liu. Understanding and improving visual prompting: A label-mapping perspective. 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In CVPR, pages 633–641, 2017. vi +[71] Nan Zhou, Jiaxin Chen, and Di Huang. ivpt: Improving task-relevant information sharing in visual prompt tuning by cross-layer dynamic connection. arXiv preprint arXiv:2404.05207, 2024. 2, 5, 6, vi, vii \ No newline at end of file diff --git a/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/images.zip b/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fde553ea2e2b78312dc902e03c501f16886b91f4 --- /dev/null +++ b/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5781fcfd44aa706a373da1e882339c6177e476ee9691d46d749b1482aeb9d4ee +size 629345 diff --git a/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/layout.json b/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ad6dccecc179f4870c26f74aa397222d1adfbe63 --- /dev/null +++ b/ICCV/2025/PRO-VPT_ Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:036ca93ac2f22358bc5c63d13f28753fa1ac48a3217383bb5e73ff68006950dd +size 435325 diff --git a/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_content_list.json b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..cc95ad0e29fbc6e19b29bae6f42f8d8734b10221 --- /dev/null +++ b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9fe4c83d87268ac40a9d98ebef43d8bf11b8fc0c865caf5f18280dc18297eded +size 75492 diff --git a/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_model.json b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..229fb770b694b8f9c34369059c7eb507e7adb25a --- /dev/null +++ b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:81586b72b5f648863e73e4c2d9a9394404732f1ef22f9734b69a2ff48893bebf +size 97909 diff --git a/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_origin.pdf b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..45ff1bb2b57e294871c260c7178e7ccdeab773a6 --- /dev/null +++ b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/91086143-b5ba-4d82-87ab-d2e978da69f3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2820b0c5decf248774ef37a9b373e37d9ae41799c148596e653e4c405b4b8d0b +size 11321066 diff --git a/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/full.md b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ac5b315f10973c08b24b7c1b3f973f4324f84d6b --- /dev/null +++ b/ICCV/2025/PROGRESSOR_ A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement/full.md @@ -0,0 +1,339 @@ +# PROGRESSOR: A Perceptually Guided Reward Estimator with Self-Supervised Online Refinement + +Tewodros W. Ayalew $^{1}$ Xiao Zhang $^{*,1}$ Kevin Yuanbo Wu $^{*,1}$ Tianchong Jiang $^{2}$ Michael Maire $^{1}$ Matthew R. Walter $^{2}$ + +1University of Chicago 2Toyota Technological Institute at Chicago + +https://ripl.github.io/progressor + +# Abstract + +We present PROGRESSOR, a novel framework that learns a task-agnostic reward function from videos, enabling policy training through goal-conditioned reinforcement learning (RL) without manual supervision. Underlying this reward is an estimate of the distribution over task progress as a function of the current, initial, and goal observations that is learned in a self-supervised fashion. Crucially, PROGRESSOR refines rewards adversarially during online RL training by pushing back predictions for out-of-distribution observations in order to mitigate distribution shift inherent in non-expert observations. Utilizing this progress prediction as a dense reward together with an adversarial pushback, we show that PROGRESSOR enables robots to learn complex behaviors without any external supervision. Pre-trained on large-scale egocentric human video from EPIC-KITCHENS, PROGRESSOR requires no fine-tuning on indomain task-specific data for generalization to real-robot offline RL under noisy demonstrations, outperforming contemporary methods that provide dense visual reward for robotic learning. Our findings highlight the potential of PROGRESSOR for scalable robotic applications where direct action labels and task-specific rewards are not readily available. + +# 1. Introduction + +Practical applications of reinforcement learning (RL) require that a domain expert design complex reward models that encourage desired behavior while simultaneously penalizing unwanted behavior [34, 37, 38]. However, manually constructing dense rewards that enable effective learning is difficult and can yield undesired behaviors [5, 14]. Sparse rewards require far less effort, but the sparsity of supervision typically results in a significant loss of sample efficiency. These issues are exacerbated for long-horizon + +![](images/360f7ae4000bdeffb294d7a27089711b4d4bf33fa79cae23c26f3916072bd43d.jpg) +Figure 1. Trained in a self-supervised manner on expert videos, PROGRESSOR predicts an agent's progress toward task completion, providing a reward signal for reinforcement learning. During online reinforcement learning, we employ an adversarial technique to refine this reward estimate, addressing the distribution shift between expert data and non-expert online rollouts. + +tasks, where credit assignment is particularly difficult. + +A promising alternative is to learn effective rewards from unlabeled (i.e., action-free) videos of task demonstrations [2, 8, 19, 25, 29, 41]. Large-scale video data is readily available on the internet, providing a effective alternative to costly, intensive task-specific data collection. An effective way to incorporate diverse video data into a single model without learning a new policy for each task is to condition the model on a goal image that visually specifies the desired environment changes upon task completion [9, 25]. + +To that end, we propose PROGRESSOR, a self-supervised framework that learns a task-agnostic reward function from videos for goal-conditioned reinforcement learning that only requires image observations, without the need for corresponding action labels. Following Yang et al. [41], we assume that expert demonstrations make monotonic progress towards the goal and employ a self-supervised temporal learning approach that utilizes a proxy objective aimed at + +estimating task completion progress. PROGRESSOR predicts the distribution of progress of the current observation (i.e., the current image) relative to the initial and goal observations. This estimation provides dense supervision of an agent's progression toward reaching the goal—and thereby completing the task—guiding exploration in alignment with expert execution trajectories. However, during RL exploration, agents will often encounter states that were not visited as part of the expert trajectories. PROGRESSOR accounts for this distribution shift via an online adversarial refinement that pushes back predictions for out-of-distribution observations. + +We evaluate the effectiveness of PROGRESSOR on robot manipulation tasks in both simulation and the real world. These results demonstrate the benefits that PROGRESSOR's self-supervised reward has on policy learning, particularly in settings where existing methods otherwise require intricate reward design. Additionally, PROGRESSOR can be used in imitation learning with suboptimal demonstrations to guide the learning of optimal task execution. The key contributions of this paper are as follows: + +- We present PROGRESSOR, a self-supervised reward model trained on unlabeled videos that guides a reinforcement learning agent by providing dense rewards based on predicted progress toward a goal. +- PROGRESSOR achieves state-of-the-art performance on six diverse tasks from the Meta-World benchmark [44] without the need for environment reward. +- Pretrained on large-scale egocentric human videos from EPIC-KITCHENS [6], PROGRESSOR enables few-shot offline learning on real robots, even in scenarios where half of the demonstrations are unsuccessful. + +# 2. Related Work + +Learning from expert videos has gained traction due to the potential to scale the acquisition of complex skills using the vast amount of video content readily available online. + +Inverse RL Inverse reinforcement learning (IRL) is a framework for learning reward functions from expert demonstrations as an alternative to specifying them manually. In contrast to traditional RL, where the reward function is predefined and the goal is to learn an optimal policy, IRL focuses on deducing the underlying reward structure that results in the expert's behavior [1, 40, 47]. Recent IRL methods leverage adversarial techniques to learn reward functions [10, 11, 23], such as in Generative Adversarial Imitation Learning (GAIL) [18]. A key limitation of typical approaches to IRL is that they require action-labeled demonstrations, which are only available in small quantities. Another is the ambiguity that results from having multiple rewards that can explain the observed behavior [27], potentially leading to ill-shaped reward functions. In contrast, our notion of progress enables the learning of well + +shaped dense rewards. + +Imitation learning from video Several methods [4, 45] infer an inverse dynamics model from a small amount of action-annotated videos and then use this model to pseudolabel large-scale action-free videos for policy learning. Other methods employ hand pose estimation as an intermediate annotation followed by standard imitation learning [3, 32], but they are sensitive to the accuracy of the pose estimators and rely on camera calibration. + +Learning reward from video Recent methods learn visual representations useful for RL from video data using self-supervised temporal contrastive techniques [9, 25, 29, 36, 42]. Time-contrastive objectives treat observations close in time as positive pairs and those that are temporally distant as negative pairs. They then learn embeddings that encourage small distances between positive pairs and large distances between negative pairs. The learned embeddings can then be used to define reward functions, i.e., as the distance from the goal image in embedding space. Time-contrastive objectives can be sensitive to frame rate, and extracted rewards are assumed to be symmetric [25]. In comparison, our approach is agnostic to the sampling rate and can learn asymmetric dynamics depending on the specified initial and goal images. + +Additionally, generative approaches have been used for reward learning. VIPER [8] estimates the log-likelihood of an observation and uses it as a reward function by training on an expert dataset using a VideoGPT-based autoregressive model. Similarly, Huang et al. [19] employ a diffusion-based approach to learn rewards by leveraging conditional entropy. However, these methods necessitate costly generative processes to estimate rewards. + +Particularly relevant, Rank2Reward [41] demonstrates that learning the ranking of visual observations from a demonstration helps to infer well-shaped reward functions. By integrating ranking techniques with the classification of expert demonstration data vs. non-expert data obtained through on-policy data collection, Rank2Reward guides robot learning from demonstration. A key limitation of the method is that it necessitates training distinct models for each task due to the task-dependent nature of ranking frames. In contrast, our approach employs a single reward model for all tasks. Additionally, we utilize an adversarial training approach that tackles the domain shift observed during online RL, rather than incorporating a separate classifier as used in Rank2Reward. + +# 3. Preliminaries + +We formulate our method in the context of a finite-horizon Markov decision process (MDP) $\mathcal{M}$ defined by the tuple $(\mathcal{O},\mathcal{A},\mathcal{P},\mathcal{R},\gamma ,\rho_0)$ that represents the observation space, action space, transition probability function, reward function, discount factor, and initial state distribution, respec + +tively. The agent starts from an initial state with observation $o_0 \in \mathcal{O}$ and at each step performs an action $a \in \mathcal{A}$ . + +The fundamental objective in RL is to learn an optimal policy $\pi^{*}$ that maximizes the expected discounted reward, i.e., $\pi^{*} = \arg \max_{\pi}\mathbb{E}_{\pi_{\theta}}[\sum_{t = 1}^{T}(\gamma^{t - 1}\mathcal{R}(\boldsymbol {o}_t))]$ . + +In this work, we assume a fully observable environment, where each observation $\pmb{o}_k \in \mathbb{R}^{H \times W \times 3}$ corresponds to a high-dimensional RGB image. We assume access to a dataset $\mathcal{D}_e = \{\tau_k\}_{k=1}^N$ of expert demonstrations, where each demonstration $\tau_k$ is a trajectory (sequence) of observations $\tau_k = \{o_0^{\tau_k}, o_1^{\tau_k}, \dots, o_n^{\tau_k}\}$ . + +However, we assume that neither the reward function $\mathcal{R}$ nor the demonstrated actions $a_{t} \sim \mathcal{A}$ are known. This setup mirrors the real-world robot task-learning scenario in which we have a plethora of videos of human-performed tasks, without knowledge of the human actions or the rewards being received. Indeed, the primary objective of this paper is to construct a model capable of predicting a well-structured dense reward from a dataset of expert demonstrations, without access to demonstrated actions or rewards. This model can subsequently serve as a reward estimating mechanism when training an agent using online RL in the absence of any environment rewards. + +# 4. Method + +We propose to learn a unified reward model via an encoder $\pmb{E}_{\theta}(\pmb{o}_i, \pmb{o}_j, \pmb{o}_g)$ that estimates the relative progress of an observation $\pmb{o}_j$ with respect to an initial observation $\pmb{o}_i$ and a goal observation $\pmb{o}_g$ , all of which are purely pixel-based. Figure 2 illustrates PROGRESSOR's framework for task progress estimation. Here, the objective is to learn the temporal ordering of observations that lead to the correct execution of a task. By learning this progress estimation, we can create a reward model that incentivizes progress toward the goal. Similar to Yang et al. [41], our method relies on the assumption that the values of states in optimal policies increase monotonically towards task completion. + +# 4.1. Learning the Self-Supervised Reward Model + +We measure an observation $o_j$ 's progress towards a goal in terms of its relative position with respect to the initial observation $o_i$ and the goal observation $o_g$ . In order to learn this progress estimate, we first represent the relative position of an observation $o_j$ within an expert trajectory $\tau_k$ as + +$$ +\delta \left(\boldsymbol {o} _ {i} ^ {\tau_ {k}}, \boldsymbol {o} _ {j} ^ {\tau_ {k}}, \boldsymbol {o} _ {g} ^ {\tau_ {k}}\right) = \frac {| j - i |}{| g - i |}. \tag {1} +$$ + +Here, $\delta (\pmb{o}_i^{\tau_k},\pmb{o}_j^{\tau_k},\pmb{o}_g^{\tau_k})$ calculates the ratio of the relative frame position differences between $\pmb{o}_j$ and $\pmb{o}_i$ and between $\pmb{o}_g$ and $\pmb{o}_i$ within a given expert trajectory $\tau_{k}$ . This progress label is always such that $\delta (\pmb{o}_i^{\tau_k},\pmb{o}_j^{\tau_k},\pmb{o}_g^{\tau_k})\in [0,1]$ + +Predicting progress based on real-world video is challenging due to factors like camera motion and repetitive sub-trajectories. We address this by formulating the problem as one of estimating a Gaussian distribution over progress, allowing the model to represent the uncertainty in the estimate. With this approach, we approximate the ground-truth distribution for a triplet of frames $(\pmb{o}_i^{\tau_k},\pmb{o}_j^{\tau_k},\pmb{o}_g^{\tau_k})$ within a video $\tau_{k}$ as a normal distribution with mean $\mu_{\tau_k} = \delta (\pmb{o}_i^{\tau_k},\pmb{o}_j^{\tau_k},\pmb{o}_g^{\tau_k})$ and standard deviation $\sigma_{\tau_k} = \max \left(\frac{1}{g - i},\epsilon\right)$ : + +$$ +p _ {\text {t a r g e t}} \left(\boldsymbol {o} _ {i} ^ {\tau_ {k}}, \boldsymbol {o} _ {j} ^ {\tau_ {k}}, \boldsymbol {o} _ {g} ^ {\tau_ {k}}\right) = \mathcal {N} \left(\mu_ {\tau_ {k}}, \sigma_ {\tau_ {k}} ^ {2}\right) \tag {2} +$$ + +Our $\epsilon$ upper-bound of $\sigma_{\tau_k}$ downweights the penalty for triplets in which there are many frames between the initial and goal images, which we empirically find to improve robustness during training. + +We optimize our reward model $\boldsymbol{r}_{\theta}$ to predict the distribution of progress on the expert trajectories. The architecture consists of a shared visual encoder to compute the per-frame representation, followed by several MLPs to produce the final estimate: + +$$ +\boldsymbol {E} _ {\theta} \left(\boldsymbol {o} _ {i}, \boldsymbol {o} _ {j}, \boldsymbol {o} _ {g}\right) = \mathcal {N} \left(\mu , \sigma^ {2}\right). \tag {3} +$$ + +Following Kingma and Welling [22], we estimate $\log \sigma^2$ and then compute $\sigma$ as $\sigma = \exp \left(0.5\log \sigma^2\right)$ . We learn the parameters of the network by optimizing the Kullback-Leibler divergence loss between the ground-truth and the predicted distributions: + +$$ +\mathcal {L} _ {\text {e x p e r t}} = D _ {\mathrm {K L}} \left(p _ {\text {t a r g e t}} \left(\boldsymbol {o} _ {i} ^ {\tau_ {k}}, \boldsymbol {o} _ {j} ^ {\tau_ {k}}, \boldsymbol {o} _ {g} ^ {\tau_ {k}}\right) \| \boldsymbol {E} _ {\theta} \left(\boldsymbol {o} _ {i} ^ {\tau_ {k}}, \boldsymbol {o} _ {j} ^ {\tau_ {k}}, \boldsymbol {o} _ {g} ^ {\tau_ {k}}\right)\right) \tag {4} +$$ + +During training of our reward model $\boldsymbol{r}_{\theta}$ , we randomly select and rank three frames from a video sequence of expert trajectories as a training triplet. Additionally, since these triplets can be randomly drawn from any trajectory within the dataset of different robotics tasks, a single reward model suffices to handle a variety of tasks. + +Using the Reward Model in Online RL: Due to the monotonic nature of task progress in our problem formulation, the estimates derived from the trained model can serve as dense rewards for training, replacing the unknown true reward. We create the reward model by defining a function in terms of the model's predicted outputs given a sample triplet of frames $(\pmb{o}_i,\pmb{o}_j,\pmb{o}_g)$ from a trajectory as: + +$$ +\boldsymbol {r} _ {\theta} \left(\boldsymbol {o} _ {i}, \boldsymbol {o} _ {j}, \boldsymbol {o} _ {g}\right) = \mu - \alpha \mathcal {H} \left(\mathcal {N} \left(\mu , \sigma^ {2}\right)\right), \tag {5} +$$ + +where $r_{\theta}$ denotes PROGRESSOR's reward estimate and $\mathcal{H}$ is the entropy. The first term $\mu$ in Eqn. 5 uses the mean prediction from the progress estimation model to determine the position of the current observation relative to the goal. The second term penalizes observations that yield high variance. Here, $\alpha$ is hyperparameter, which we set to $\alpha = 0.4$ in all our experiments. + +![](images/1a00e33c8480131565db3712afd01f92efd1b666a2c713fe070d85c5a27abb66.jpg) + +![](images/5d535dcc9dce3eb5bf22ef49f51cf1a1573a478a26c1c900fa3debea4b5977fd.jpg) + +![](images/176b73f331fa235a4416366a671273fb19a3956efae432e3fc9b5b59139f951c.jpg) +Figure 2. Top Left: Initial phase of reward model pretraining on expert data, where the model learns to predict the parameters of a Gaussian distribution centered on normalized progress, reflecting expected progress as demonstrated by experts. Top Right: In online reinforcement learning (RL) training, an adversarial online refinement (i.e., push-back) is applied to counteract non-expert predictions made by the reward model, effectively distinguishing expert from non-expert progress. Bottom: During online RL, the reward model is updated on expert and non-expert data. + +# 4.2. Adversarial Online Refinement via Push-Back + +Our reward model $r_{\theta}$ can be used to train a policy that maximizes the expected sum of discounted rewards as: + +$$ +\pi^ {*} = \arg \max _ {\pi} \mathbb {E} _ {\pi_ {\theta}} \left[ \sum_ {t = 1} ^ {T} \gamma^ {t - 1} \boldsymbol {r} _ {\theta} \left(\boldsymbol {o} _ {i} ^ {\tau^ {\prime}}, \boldsymbol {o} _ {t} ^ {\tau^ {\prime}}, \boldsymbol {o} _ {g} ^ {\tau^ {\prime}}\right) \right] \tag {6} +$$ + +The reward encourages the agent to take actions that align its observed trajectories $\tau'$ with those of the expert demonstrations $\tau$ , thereby promoting task completion. However, the all-but-random actions typical of learned policies early in training result in out-of-distribution observations relative to the expert trajectories. As a result, optimizing the policy using a reward $r_{\theta}$ that is only trained on an expert trajectory $\tau$ can result in unintended behaviors, since $r_{\theta}$ does not reflect the actual progress of $\tau'$ . To tackle this distribution shift, we propose an adversarial online refinement strategy [12, 13], which we refer to as "push-back", that enables the reward model $r_{\theta}$ to differentiate between in- and out-of-distribution observations from $\tau$ and $\tau'$ , improving estimation accuracy. Specifically, for a frame triplet $(o_i^{\tau_k}, o_j^{\tau_k}, o_g^{\tau_k})$ sampled from $\tau_k'$ and the estimated progress $\mu_{\tau_k'}$ from $E_{\theta}(3)$ , we update $E_{\theta}$ so that it learns to push-back + +# Algorithm 1 Training PROGRESSOR with Online RL + +Require: Expert demonstration data $\mathcal{D}_e = \{\tau_k\}_{k=1}^N$ +1: Initialize policy $\pi$ , empty replay buffer $\mathcal{D}_{RB}$ +2: Initialize reward model $\mathbf{r}_{\theta}$ +3: // Pretraining PROGRESSOR +4: for step $n$ in $\{1, \dots, N_{\text{pretrain}}\}$ do +5: Sample triplets $(\pmb{o}_i^{\tau_k},\pmb{o}_j^{\tau_k},\pmb{o}_g^{\tau_k})$ from $\tau_{k}\in \mathcal{D}_{e}$ +6: Learn $\boldsymbol{r}_{\theta}$ with objective Eqn. 4 +7: end for +8: // Policy optimization and reward model fine-tuning +9: for step $n$ in $\{1, \dots, N\}$ do +10: With $\pi$ , collect transitions $\{\tau_l\}_{l=1}^M$ and store in $\mathcal{D}_{RB}$ +11: if $n \%$ reward_update频率 $= 0$ then +12: Update $\boldsymbol{r}_{\theta}$ with Eqn. 4 using samples from $\mathcal{D}_e$ +13: Update $\pmb{r}_{\theta}$ with Eqn. 7 using samples from $\mathcal{D}_{RB}$ +14: end if +15: Sample batch of transitions $s_{\pi}$ from $\mathcal{D}_{RB}$ +16: Update $\pi$ to maximize returns using Eqn. 5 +17: end for + +the current estimate as $\beta \mu_{\tau_k'}$ , where $\beta \in [0,1]$ is the decay factor. In our experiments, we use $\beta = 0.9$ (see Section 10 + +![](images/8ef753083cc86bda59447c94938d1ffc3dda0c357eb617890769b1e7e6e8b1f5.jpg) +(a)Drawer-Open + +![](images/7d358f391b54bdb2b37a978deea2c4f778a50b2d11ec72a61a9374096bca782a.jpg) +(b)Drawer-Close + +![](images/9c1e78b9f15b94e093078fedddfbdfc5ba3d2c39d521d8431b8d70bc0e0d83c7.jpg) +(e) door-open + +![](images/dc9f919d63070feb97b69e2d333d27a283d5cc7ef3981be53225e0a3274c25a0.jpg) +(f) drawer-open + +![](images/d27dc575cb125502a04af3e1c3a93d8f3a10ce08fbecd6a29725dfd110e397e2.jpg) +(g) hammer + +![](images/8ece76161aad36138e3fea56afb574f4e4a1a4897b622239fa1bcddac1cc7df8.jpg) +(c)Push +Figure 3. Visualization of the robotic tasks: (a-d) Real world environments with a UR5 arm, (e-j) simulation environments for evaluation using the Meta-World [44] benchmark. + +![](images/77075d99d86291147d77d899d0ad5a2a1f3148d1c0f61ca5803ec952e2d30642.jpg) +(d) Pick-Place-Cup + +![](images/a0ade43f6cfcdd286f1c582a5b15a721cdcdc72286a97bff2c81df59c48aa7b4.jpg) +(h) peg-insert-side + +![](images/7d995282ac819cc92f1ce3319bfc63a2bdf4c7202472c28fb61cdbf7ca23237a.jpg) +(j) pick-place + +![](images/be06301878795182375c86c32dfa58dd6588975d537320e6361d6e309f692e00.jpg) +(i) reach + +for an ablation of $\beta$ . We formulate our online refinement objective as: + +$$ +p _ {\text {p u s h - b a c k}} = \operatorname {s g} \left(\mathcal {N} \left(\beta \mu_ {\tau_ {k} ^ {\prime}}, \frac {1}{(g - i) ^ {2}}\right)\right) +$$ + +$$ +\mathcal {L} _ {\text {p u s h - b a c k}} = D _ {\mathrm {K L}} \left(p _ {\text {p u s h - b a c k}} \| \boldsymbol {E} _ {\theta} \left(\boldsymbol {o} _ {i} ^ {\tau_ {k} ^ {\prime}}, \boldsymbol {o} _ {j} ^ {\tau_ {k} ^ {\prime}}, \boldsymbol {o} _ {g} ^ {\tau_ {k} ^ {\prime}}\right)\right), \tag {7} +$$ + +where $\mathrm{sg}(\cdot)$ denotes the stop gradient operator. With this approach, we differentiate between the two sources of trajectories by treating observations from the (inferior) online roll-out trajectories $\tau'$ as corresponding to lower progress compared to expert trajectories $\tau$ . In this case, optimizing for $\pi^*$ would encourage the agent to consistently improve its actions until the policy trajectories are well aligned with the distribution of expert trajectories $\tau_k$ . + +During online training, we fine-tune $E_{\theta}$ (3) using hybrid objectives: we optimize $\mathcal{L}_{\mathrm{push - back}}$ based on $\tau_k^{\prime}$ sampled from the most recent buffers and at the same time, we optimize $\mathcal{L}_{\mathrm{expert}}$ using samples from $\tau_k$ , preventing $E_{\theta}$ from being biased by $\tau_k^{\prime}$ . + +# 5. Experimental Evaluation + +We evaluate the effectiveness with which PROGRESSOR learns reward functions from visual demonstrations that enable robots to perform various manipulation tasks in simulation as well as the real world. The results demonstrate noticeable improvements over the previous state-of-the-art. + +# 5.1. Simulated Experiments + +In our simulation experiments, we use benchmark tasks from the Meta-World environment [44], selecting six table-top manipulation tasks (Figure 3 e-j): door-open, drawer-open, hammer, peg-insert-side, pick-place, and reach. For all tasks, we train the model-free reinforcement learning algorithm DrQ-v2 [43] using the reward predicted by PROGRESSOR in place of the environment reward. + +We compare our method to five baselines. TCN [35] is a temporal contrastive method that uses optimized embed + +dings to measure task progress. GAIL [17] is an adversarial approach that aligns the state-action distribution of a policy with that of an expert. GAIL's discriminator is used as a reward function for our baseline following Yang et al. [41]. SOIL [33] jointly trains an inverse dynamics model and policy by predicting actions from state-only demonstrations. ROT [15] leverages optimal transport to match the expert and agent's trajectory to provide extra regularization for robot learning. Finally, Rank2Reward [41] is a state-of-the-art reward learning method that combines temporal ranking and classification of expert demonstrations to estimate rewards. Unlike our method, which uses a single model for all tasks, Rank2Reward requires a separate model for each task and needs an additional classifier for online adaptation. + +We collected 100 expert trajectories for each of the six tasks using the Oracle from Meta-World. All methods were trained for 1.5 million steps, relying solely on the reward estimates produced by their respective models. To ensure a fair comparison, we used the default hyperparameters reported for each method under the same experimental setup. + +We evaluate performance using episodic return, which measures the cumulative reward an agent receives during each episode. To ensure robustness, we average the episodic returns over five different seeds for both our approach and the baselines. This setup enables a comprehensive and controlled comparison across all tasks, allowing us to assess the impact of our proposed method in a simulated environment. + +We present the results in Figure 4. Our method significantly outperforms the baseline methods across most tasks, with a notable advantage in efficiency. In the drawer-open and hammer tasks, PROGRESSOR requires only $10\%$ of the total training budget to achieve higher rewards than the baselines. In the door-open and peg-insert-side tasks, where almost all other methods fail entirely, our approach demonstrates strong performance and a higher success rate. + +Ablating Push-back We examine the impact of adversarial online refinement via push-back in our framework. Across various tasks (Figure 4), we find that online pushback significantly enhances PROGRESSOR's performance, particularly on challenging tasks such as door-open and hammer. These tasks demand more precise discrimination between expert behavior and online roll-outs to provide an informative reward signal. Notably, PROGRESSOR without push-back still outperforms every baseline on the drawer-open and reach tasks. + +In the case of the reach task, we observe that PROGRESSOR with push-back shows a decrease in return as training progresses, a trend that is less pronounced in the version without push-back. We hypothesize that this occurs because the model initially achieves a high success rate—reaching a peak with only $10\%$ of the total steps—leading + +![](images/98ef3a101aa21e2fc028c4d1eb65d24d53b1312fe229f4ebd725f72bc68cceb3.jpg) +Figure 4. Visualization of policy learning in the Meta-World [44] simulation environment. We compare PROGRESSOR to five contemporary baselines on six diverse tasks of various levels of difficulty. We also run PROGRESSOR without online push-back as an ablation. We follow the standard evaluation protocol and plot the mean and standard deviation of (left) the environment reward during training and (right) the task success rate from ten rollouts averaged over five seeds. PROGRESSOR demonstrates clear advantages in both metrics, especially at early stages of training. + +the refinement process to overly penalize the agent even when its behavior closely resembles the expert. + +Online training with non-expert data is crucial for robust performance. TCN, which is only trained on expert demonstrations without online updates, fails at every task due to the domain shift between pretraining and online RL. + +# 5.2. Real-World Robotic Experiments + +Going beyond simulation, we use experiments with a real-world manipulator to demonstrate how PROGRESSOR, pretrained on the egocentric EPIC-KITCHENS dataset [6, 7], can efficiently learn robotic tasks from a limited number of demonstrations, even when some are unsuccessful. Our approach enhances sample efficiency and robustness to noisy data in offline RL, making it more effective than traditional behavior cloning (BC) methods. + +# 5.2.1. Pretraining on Kitchen Dataset + +Using ResNet34 [16] as a backbone, we first pretrain our encoder $E_{\theta}$ to minimize $\mathcal{L}_{\mathrm{expert}}$ (Eqn. 4) using the P01-P07 sequences from the EPIC-KITCHENS dataset that consist of approximately 1.29M frames. We randomly sample frame triplets $(o_i, o_j, o_g)$ from the videos ensuring a maximal frame gap $\| i - g \| \leq 2000$ . To improve the robustness + +
TaskBehavior of Failed Demonstrations
Drawer-OpenThe robot approaches the drawer but misses the handle by a few centimeters, failing to open it.
Drawer-CloseThe robot misses the drawer by a few centimeters, failing to close it.
Push-BlockThe robot moves the block halfway toward the target cup but stops before reaching it.
Pick-Place-CupThe robot lowers to pick up the cup but misses it by a few centimeters and remains in that position.
+ +Table 1. Failure modes in the collected suboptimal trajectories for the real-world robotic experiments. For each task we collected 20 failed demonstrations to go with the 20 expert demonstrations. + +of $E_{\theta}$ , we additionally train with distractor frames where we replace the current observation $o_j$ with a frame $o_{j'}$ randomly sampled from a different video sequence as a negative example. For negative triplets, we replace $\mu$ in Eqn. 3 with -1 as the label. We train our model with batch size + +![](images/1a7bf6c63ad2fc5b1b59f75648fce36dd349ddbbb94ddb006e5dc1de631a173b.jpg) +Figure 5. Success rates for four real-world tasks, where RWR- ACT is trained on a combination of correct and failed demonstrations using PROGRESSOR, GVL, R3M, and VIP as reward models. + +128 for 30000 iterations using the Adam optimizer [21] with constant learning rate $2e - 4$ . + +# 5.2.2. Baselines + +We compare PROGRESSOR with GVL [26], R3M [28], and VIP [24]. VIP and R3M are self-supervised visual representations shown to provide dense reward functions for robotic tasks. GVL frames value estimation as a temporal ordering task over shuffled video frames, leveraging pretrained vision-language models (VLMs). To compare with GVL, we use Gemini-1.5-Pro as the VLM following Ma et al. [26]. R3M is trained via time contrastive learning, where the distance between frames closer in time is smaller than for images farther apart in time. Additionally, they leverage L1 weight regularization and language embedding consistency losses. VIP uses a contrastive approach treating frames close in time as negative pairs and those farther away as positive pairs towards learning visual goal-conditioned value functions. For fair evaluation, we pretrained both R3M and VIP on the same EPIC-KITCHENS subsets that our method was trained on. + +# 5.2.3. Real-World Few-Shot Offline Reinforcement Learning with Noisy Demonstrations + +Following the offline reinforcement learning experiments of Ma et al. [24], we use the reward-weighted regression (RWR) method [30, 31]. Our aim in applying RWR is to show that a reward model trained on human videos can help robots learn to perform tasks even when the training data contains noisy, suboptimal trajectories. In scenarios with highly suboptimal trajectories, vanilla behavior loning (BC) approaches often struggle to learn performant policies, essentially regressing to the mean [20]. However, goal-conditioned reward weighting provides a signal that focuses learning from the correct sub-trajectories, enabling the visual imitation learning model to effectively learn accurate action executions. + +To this end, we start with a vanilla BC model and adapt the loss function to be weighted by a pretrained reward model. Specifically, we employ Action-Chunking + +Transformer (ACT) [46], a BC model designed for learning fine-grained manipulation tasks. We modified ACT's reconstruction loss—originally defined as the mean absolute error between the predicted action and the ground-truth action—to incorporate RWR as follows: + +$$ +\mathcal {L} _ {\text {r e c o n s t}} = \exp (\omega \cdot \hat {\mathbf {r}}) \cdot \| \pi_ {\mathrm {A C T}} (\boldsymbol {o} _ {j}) - a _ {j} \| _ {1}, \tag {8} +$$ + +where $\hat{\mathbf{r}}$ is the reward prediction for the current observation $o_j$ , $\omega$ is a temperature parameter, $a_{j}$ is the ground-truth action, and $\pi_{\mathrm{ACT}}(o_j)$ is the action predicted by ACT by taking the current observation image $(o_j)$ as input. We refer to ACT trained with the reconstruction loss in Equation 8 as RWR-ACT, to distinguish it from the standard ACT. + +We compare PROGRESSOR with GVL, R3M and VIP by freezing the pretrained models and using them as reward prediction models to train RWR-ACT on downstream robot learning tasks. We use the reward predictions from these models in place of $\mathbf{u}_{\theta}$ in Equation 8. In both VIP and R3M, the reward prediction is parameterized by the current observation, previous observation, and goal observation. Following Ma et al. [24], we define the reward for a given transition tuple $(o_{t}, o_{t+1})$ as $R(o_{t}, o_{t+1}; \phi, o_{g}) := S_{\phi}(o_{t+1}; o_{g}) - S_{\phi}(o_{t}; o_{g})$ , where $S_{\phi}$ is the distance function in the $\phi$ -representation space extracted from VIP and R3M, defined as $S_{\phi}(o_{t}; o_{g}) := -\|\phi(o_{t}) - \phi(g)\|_{2}$ . + +In contrast, our method parameterizes reward using the initial observation, current observation, and goal observation. Additionally, we include vanilla ACT as a baseline, which applies uniform weighting (i.e., $\omega = 0$ ) across all observations in the training trajectories. + +We design four tabletop robotic manipulation tasks (Figure 3 a-d): **Drawer-Open**, **Drawer-Close**, **Pick-Place-Cup**, and **Push-Block**. For each task, we collect 40 demonstrations, half of which are suboptimal and fail to complete the task. Table 1 summarizes the behaviors in failed demonstrations. Including these failed demonstrations is crucial for evaluating whether the learned reward model can accurately signal progress toward a goal by assigning high reward to transitions that lead toward completion and low reward to those that do not. We categorize **Drawer-Close** as an easy task and the other three as hard tasks. This distinction in difficulty is based on the complexity of the tasks and the level of suboptimality in the failed demonstrations. Section 9 provides detailed task and data descriptions along with frame sequences from both successful and failed trajectories. + +We train all policies using the same hyperparameters employed by Zhao et al. [46] for training ACT in their real-world behavior cloning experiments (see Section 9.4 for more details). For all RWR experiments, we set $\omega = 0.1$ . We evaluate each method over 20 rollouts and report the success rate considering the criteria in Table 4. + +The results presented in Figure 5 highlight the significant + +![](images/9efea4bd8c4b9271a753e78cc7451551a1208ff515d255864350a90a3b1370b3.jpg) +Figure 6. Estimated progress curves for correct and incorrect demonstrations in the Push-Block task from PROGRESSOR, GVL[R1], R3M, and VIP. PROGRESSOR exhibits the most distinct separation for incorrect demonstrations, contributing to the superior performance + +advantage of PROGRESSOR-RWR-ACT, which on average outperforms all baseline methods. This advantage is particularly pronounced on the more challenging tasks, such as Push-Block and Open-Drawer, for which other methods struggle. While GVL-RWR-ACT performs comparably to PROGRESSOR-RWR-ACT on the Pick-Place-Cup and Close-Drawer tasks, its performance drops significantly on the more challenging Open-Drawer and Push-Block tasks. Similarly, R3M-RWR-ACT and VIP-RWR-ACT show moderate success on simpler tasks, such as Driver-Close, yet their performance drops significantly for the Push-Block and Open-Drawer tasks. As shown in Figure 6, PROGRESSOR provides significantly more accurate progress estimates for both failed and successful trajectories compared to GVL, R3M, and VIP, particularly starting from around step 55 when the robot starts to deviate from the goal observation. This supports our hypothesis that PROGRESSOR provides more distinct reward weighting for both correct and failed trajectories compared to the baselines. Vanilla ACT performs poorly, especially on difficult tasks. Since ACT assigns equal weight to all sub-trajectories, it cannot prioritize better transitions or filter out noise effectively, leading to poor performance. + +Figure 7 shows reward predictions for a sample frame sequence from EPIC-KITCHENS and a trajectory from our Pick-Place-Cup robot task. The figure shows that, despite being pretrained solely on human videos, PROGRESSOR generates well-formed reward predictions for the robotic task in a zero-shot setting. + +# 6. Conclusion + +In this work, we presented PROGRESSOR, a self-supervised framework that learns task-agnostic reward functions from video via progress estimation. By learning to estimate progress between observations in expert trajectories, PROGRESSOR generates dense rewards that effectively guide policy learning. During online RL training, PROGRESSOR further refines this progress estimation through an adversar + +![](images/c42e99b3f94fb811498a0592ae6f024a9b1a80cbfd166384b1d9596c043d3edc.jpg) +(a) The evolution of the episodic reward on human video + +![](images/31073b920ea3009132a81590d5dd27c7aa2cae8f24e0835498648d9ef7cadd3c.jpg) +(b) The evolution of the episodic reward on robot video +Figure 7. Visualization of the predicted rewards from Epic Kitchen pretrained PROGRESSOR, evaluated on a sample clip from EPIC-KITCHENS (top) and on sample frames from an unseen Pick-Place-Cup demonstration on our robot (bottom). + +ial push-back strategy, helping the model handle non-expert observations and minimize distribution shift. Our method outperforms previous state-of-the-art approaches across a range of simulated experiments. Through real-world experiments, we show that by pretraining on in-the-wild human videos, PROGRESSOR enables robots to learn from limited and noisy task demonstrations, outperforming other visual reward models. Meanwhile, our framework opens several avenues for future improvement. Currently, it assumes that progress is monotonic, which may not be valid for all tasks. One means of relaxing this assumption may be to learn a multimodal or cycle-aware model of task progress. 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Anwar Ma'sum $^{1,*}$ , Mahardhika Pratama $^{1}$ , Savitha Ramasamy $^{2}$ , Lin Liu $^{1}$ , Habibullah Habibullah $^{1}$ , and Ryszard Kowalczyk $^{1,3}$ + +$^{1}$ STEM University of South Australia, $^{2}$ Institute for Infocomm Research, A*STAR & IPAL, CNRS@CREATE + +3Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland + +# Abstract + +The data privacy constraint in online continual learning (OCL), where the data can be seen only once, complicates the catastrophic forgetting problem in streaming data. A common approach applied by the current SOTAs in OCL is the use of memory-saving exemplars or features from previous classes to be replayed in the current task. On the other hand, the prompt-based approach performs excellently in continual learning, but at the cost of a growing number of trainable parameters. The first approach may not be applicable in practice due to the data openness policy, while the second approach has the issue of throughput associated with the streaming data. In this study, we propose a novel prompt-based method for online continual learning that includes 4 main components: (1) single light-weight prompt generator as a general knowledge, (2) trainable scalar-and-shifter as specific knowledge, (3) pre-trained model (PTM) generalization preserving, and (4) hard-soft updates mechanism. Our proposed method achieves significantly higher performance than the current SOTAs in CIFAR100, ImageNet-R, ImageNet-A, and CUB dataset. Our complexity analysis shows that our method requires a relatively smaller number of parameters and achieves moderate training time, inference time, and throughput. For further study, the source code of our method is available at https://github.com/anwarmaxsum/PROL. + +# 1. Introduction + +Continual learning (CL) has become a spotlight in the world of artificial intelligence (AI) involving dynamic environments, as it tackles catastrophic forgetting for a continually evolving sequence of tasks [5, 38]. CL methods are proven to be promising in various domains, e.g., computer vision, automation, NLP and graph analysis [1, 21, 31, 35]. Online continual learning (OCL) is an advanced subproblem of CL where CL is conducted in streaming data. + +The limitation of seeing data only once in OCL leads to insufficient learning of a deep learning model that results in difficulty in gaining knowledge of a new task while maintaining knowledge of previously learned tasks. In other words, it complicates how to resolve the catastrophic forgetting problem. To handle such a limitation, most of the state-of-the-art OCL methods (SOTAs) save previous task exemplars for a rehearsal process to maintain the knowledge from previously learned tasks [30, 39, 49]. Practically, this approach is not reliable since, due to privacy constraints or data openness policy, previously learned data can be unavailable anymore. In addition, the rehearsal process increases memory consumption and computational costs. + +Leveraging the recent advancement of the foundation model, recent SOTAs utilized a pre-trained model (PTM) that carries a generalization attribute as initial weight [22, 25, 48]. However, the SOTAs still store and replay previously learned exemplars or features in their memory. The insight tells us that rehearsal-free online continual learning remains an open problem. On the other hand, the prompt-based approach has been proven to be effective in rehearsal-free continual learning. Specifically, the growing prompt components methods [17, 28, 33] outperform the prompt-pool method [44] and task-wise prompt methods [7, 37, 42, 43] both in terms of accuracy and forgetting measure. However, from the perspective of OCL, the growing components prompt methods violate the throughput aspects, as the model parameters grow with the increasing number of classes. This growth incurs more operations and longer training time, leading to more skipped (unprocessed) data streams. Thus, the approach is not favorable for dealing with catastrophic forgetting in streaming data. + +These intriguing insights motivate us to develop a novel rehearsal-free method that can effectively address the OCL problem. We develop our proposed method based on two fundamental goals in OCL, i.e., (1) achieving stability-plasticity and (2) being efficient both in the training and inference phases. To achieve these goals, we design our method with the following components: (1) a single + +lightweight prompt generator for all tasks, (2) a set of scalers and shifters associated with the class-wise learnable keys, (3) preservation of PTM generalization via cross-correlation matrices, and (4) hard-soft learning updates for a better parameter tuning. The generator is trained only on the first task to avoid forgetting and achieve stability, while scalers and shifters are trained on every task to achieve plasticity. To achieve high throughput, our lightweight generator has fewer parameters than a single generator in [28] and fewer than a single task-specific prompt in [43]. The third component is adapted from SAFE[51] to the OCL problem. + +In this study, our contributions are: (1) We highlight rehearsal-free constraint in online continual learning and propose a novel prompt online learning (PROL) that addresses the two essential goals of OCL. (2). We design a new mechanism to generate prompts by a single generator with a few smaller-shifter parameters. We also propose a joint loss function for our method. (3). Our rigorous experiment and analysis prove the superiority of our method compared to the existing SOTAs in general and historical performance. Our analysis shows that our method has relatively low parameters, moderate training, inference time, and throughput compared to the SOTAs. (4). We provide a complexity analysis of our method and complete numerical results for further study; please see the supplementary. + +# 2. Literature Review + +Online Continual Learning (OCL): Recent OCL studies shed light on various approaches to handle catastrophic forgetting in streaming data. The backbone tuning approach tunes the whole model with unique mechanisms, e.g. cross-task class discrimination as in GSA [10], dual-view as in DVC [8], proximal point method as in LPR [49], real-synthetic similarity maximization as in ESRM [39], and adaptive layer freezing as in ALF [30]. The other approaches tune the class prototype along with the backbone as in ONPRO [45], augmenting and refining the prototype as in DSR [13], or generating multiple features in angular space as in EARL [29]. Another unique approach uses a student-teacher model and knowledge distillation between them, as in MKD [23], CCLDC [40], and MOSE [41]. The recent development of the foundation model gives rise to the PTM-based OCL, e.g., NSCE [48] that transfers PTM weight and fine-tunes it, RandDumb [25] that trains RBF kernel from PTM generated features, and RanPAC [22] that projects the feature with a randomized matrix. Tackling OCL can be achieved by a customized optimization technique, e.g., POCL [47] that utilizes Pareto optimization, and CAMA [14] that performs confidence-aware moving average. However, these aforementioned methods still save exemplar or features for rehearsal. It is not always applicable in real-world applications since the old data may not be available or accessible. Note that rehearsal-based CL meth + +ods [2, 3, 24, 26, 46] work poorly in OCL and even worse than the aforementioned methods. + +PTM-Based Continual Learning: The prompt-based approach is one of the most popular approaches in CL due to its simplicity and scalability. The prompt can be generated by learnable latent parameters or a vector generated by trainable generator networks and then prepended into visual transformer (ViT) multi head self attention (MSA) [18, 19]. The prompt structure can be organized by a pooling approach as in L2P [44], task-specific and task-shared structure as in DualPrompt, S-Prompt, HiDePrompt and CPrompt [7, 37, 42, 43], evolving prompt component as in CODA-P[33], evolving prompt generator as in ConvPrompt and EvoPrompt [17, 28]. The other approach utilizes Low-Rank Adaptation (LoRA) where it extends the frozen ViT weight $W$ with learnable matrices $A$ and $B$ [6, 20, 32]. The adapter-based approach emerges as a new PTM approach for CL by extending the ViT with a sequence of (growing) adapters [34, 52]. Rather than extending the inner level, such as ViT weight, adapters work on the feature level by projecting the ViT feature into a more discriminative form. Last but not least, recent works focused on learning mechanisms, i.e., slow-learner rather than structures to elevate PTM model discrimination [50, 51]. Except for the adapters approach, all the mentioned methods were developed for rehearsal-free CL. Even thought they have been proven effective in rehearsal-free CL, the methods are not yet proven in rehearsal free OCL where the data is streaming and can be seen only once. + +# 3. Preliminary + +(a) Problem Formulation: Class incremental learning (CIL) problem is defined as the problem of learning a sequence of fully supervised tasks $\{\mathcal{T}^t\}_{t = 1}^T$ , where after finishing learning a task $\mathcal{T}^t$ , a model must recognize all learned tasks i.e. $\mathcal{T}^1,\mathcal{T}^2,\dots \mathcal{T}^{t - 1},\mathcal{T}^t$ . Symbol $T$ represents the number of consecutive tasks. Each task carries pairs of training samples, i.e., $\mathcal{T}^t = \{(x_i^t,y_i^t)\}_{i = 1}^{|\mathcal{T}^t|}$ where $x_{i}\in \mathcal{X}^{t}$ and $y_{i}\in \mathcal{V}^{t}$ denotes input image and its label, while $|\cdot |$ denotes cardinality. $\mathcal{C}^t$ denotes the unique class labels in $\mathcal{V}^t$ , i.e., $\mathcal{C}^t = \text{unique} (\mathcal{V}^t)$ , and $|\mathcal{C}^t|$ denotes the number of classes in $\mathcal{T}^t$ . The task ID is visible only during the training phase of CIL, unlike in task incremental learning (TIL), which is visible in both the training and inference phases. + +Online Class incremental learning (OCIL) is similar to CIL but the data comes in streams $s_1, s_2, s_3, \ldots$ where $s_j = \{(x_i^t, y_i^t)\}_{i=1}^{|s_j|}$ rather than in a storable $\mathcal{T}^t = \{(x_i^t, y_i^t)\}_{i=1}^{|\mathcal{T}^t|}$ manner. $|s_j|$ is relatively small, e.g., 10. The data can be seen only once, as the data will not be available (stored) after streaming. Following [15], there are three main settings in OCL, i.e., disjoint task where each task $t$ is disjoint from another task $t'$ , i.e., $\forall t, t' \neq t$ , $(\mathcal{T}^t \cap \mathcal{T}^{t'} = \emptyset)$ , blurry task + +![](images/e895f685824edad59f3c173cf0a4cdaab6a74e241d16f5edccfda9cf408f3cba.jpg) +Figure 1. Topology of OCL and prompt-based CL methods (a) OCL Methods without pre-trained model (PTM), (b) OCL methods with PTM as weight initiation, (c) Prompt-based CL method. Majority of the OCL method requires memory from previously learned classes to be replayed along with the currently learned classes, while the prompt-based method is rehearsal-free. + +![](images/9ca3cb7d4539984bcb313f52275a37280458987bf8d98614e2569621b08485f2.jpg) + +![](images/bcf42e2a61ebdfcc23a7c527d27a4f603d104b7a3af6162148c346ecc30ea465.jpg) + +setting where there is no explicit boundary between tasks, and iBlurry setting where consist of $N\%$ of the classes are put into disjoint tasks and the other $(100 - N)\%$ classes appear in every task. In this study, we focus on the disjoint task setting that is the most common in OCL and CL. + +(b) The OCL Method and Its Gap: Figure 1 shows a topology that the OCL methods can be divided into 2 main categories, i.e., OCL method without PTM (Non-PTM) and with PTM. In the perspective of available foundation model, the main gap of this category is that it tunes the whole backbone $f_{\theta}(.)$ and classifier $g_{\phi}(.)$ from scratch in the case of streaming data where the data can be seen only once. In addition, the backbone training in every task increases the chance of the model forgetting. Even with the presence of sample memory to avoid forgetting, the methods can not perform well since its weight is not yet convergent. A customized backbone tuning technique such as the proximal point method, real-synthetic similarity maximization, dual view, or adaptive layer freezing [8, 10, 30, 39, 49], or customized optimization method as in [14, 47] can not compensate the insufficient training and avoid model forgetting. The other approach trains dual models, i.e., student $(f_{\theta}^{student})$ and teacher $(f_{\theta}^{teacher})$ backbones. Even though one of the model is frozen, this approach requires higher training complexity (longer training time) and reduces model throughput. The prototype approach replaces the MLP classifier $(g_{\theta})$ with a prototype-based classifier $(g_{Z})$ . Despite reducing model forgetting, the prototypes do not optimally discriminate the learned classes since the prototypes are calibrated with once-seen data. + +On the other side, the PTM-based method leverages PTM generalized weight as its initial values. NSCE[48] transfers the PTM weight and then fine-tunes its weight along with the classifier to adapt to the streaming data. Despite achieving better performance than non-PTM methods, + +it still requires memory samples that may not be applicable in real-world applications due to data privacy or openness policy. Feature projection network, e.g., RanPAC[22] and RanDumb[25] transform PTM features into a more discriminative form by a projection network $Prj_{\psi}$ . Similarly, this approach requires memory (in feature space) from a previous task to be replayed in the currently learned class. The adapter methods [34, 52] that were originally for offline CL are considered as baselines in OCL. Aside from utilizing sample memory, this method has a growing number of adapters ( $A_1, A_2, \dots, A_t$ ) along with the increasing of learned classes. This mechanism is bounded to increase model complexity and reduce model throughput. F-OAL [53] forms a feature fusion from its PTM layers then classify it with analytical learning (AL). Despite working in rehearsal-free setting, the method requires more operation for AL since the least square solver requires higher computation than standard MLP or prototype-based classifier. + +(c). Prompt-based CL Methods and its Drawback: The pool-based prompting, e.g., L2P[44] selects top-k prompts from the pool $[P^1, P^2, \ldots, P^M]$ where $M$ is the pool size. Any prompt $P^m$ in the pool can be trained for any task $t \in [1..T]$ . The task-wise prompting, e.g., DualPrompt[43] trains only the corresponding prompt $P^t$ that associated to task-wise key $K^t$ during the training process on task $t$ , while the prompts and keys associated with the previous tasks i.e $[P^1, P^2, \ldots, P^{(t-1)}]$ and $[K^1, K^2, \ldots, K^{(t-1)}]$ are frozen. The growing component approach dynamically increases the number of prompt components, e.g., $p^i, p^{i+1}, \ldots, p^M$ to learn new classes while maintaining knowledge on previously learned classes. The final prompt is generated by weighted summing the components, i.e., $P = \sum_{i=1}^{M} p^i \alpha^i$ where $\alpha^i$ denotes similarity value. The prompt components $p^t$ can be a learnable latent parameter as in [33] or generated by prompt generator + +network, i.e., $p^i = G^i(x)$ as in [28]. + +The pool-based approach has a high risk of forgetting since all the prompts $[P^1, P^2, \dots, P^M]$ are possible to be trained in all tasks $t \in [1..T]$ . A prompt $P^i$ is optimal for the $t^{th}$ task but is tuned again in the $t + 1^{th}$ task. Therefore, it is no longer optimal for $t^{th}$ task and leads to forgetting. Task-specific prompting has the risk of high similarity keys between two different tasks, e.g., $K^t \approx K^{t'}$ for $t \neq t'$ , which leads to inaccurate task prediction during inference. The growing component prompting adds new components, i.e., $p^i, p^{i+1}, \dots, p^M$ that could disrupt the previous components, i.e., $p^1, p^2, \dots, p^{i+1}$ that are already optimal for previous tasks. Similar to the adapters method, this approach could lead to higher model complexity and reduce its throughput due to the growing prompt components or prompt generators. + +# 4. Proposed Method + +In this study, we propose prompt online learning (PROL) to handle catastrophic forgetting in streaming data. The goal of the method is to achieve stability-and-plasticity and high throughput. Thus, we utilize only a single lightweight generator for all classes in all tasks. The generator is trained only in the base task, then frozen afterwards to maintain stability, and assisted by learnable scalers and shifters to achieve plasticity. Figure 2 shows the architecture and flow of PROL, i.e., part 2(a) shows the generator and learnable parameters, part 2(b) shows the prompt generation mechanism, and part 2(c) shows the model forward, loss, and parameter updates. The following subsections explain the details of the components and the learning mechanism. + +# 4.1. Learnable Parameters: + +(a). Single Lightweight Generator for All: We design a lightweight generator $(G_{K}, G_{V})$ to achieve the highest possible throughput in online continual learning that is trained only in the first task yet can be utilized in all tasks. We design it in a pair following the prompt structure in prefix tuning [19] that divides prompt $P$ into two parts, i.e., $P_{K}$ and $P_{V}$ that prepend into $K$ and $V$ of the ViT layer's MSA, respectively. Following ConvPrompt [28], the generator is distributed into all MSA heads of the ViT layers. Thus, the generator can be noted as $(G_{K}, G_{V}) = \{(G_{K,l,h}, G_{V,l,h})\}, l \in [1..L]h \in [1..H]$ , where $L$ and $H$ are the number of heads and MSA heads per layer respectively. Each $G_{K,l,h}$ or $G_{V,l,h}$ is a 1DCNN kernel with the size of 3, thus only saving 3 parameters. Therefore, the total parameters of our generator are only $2 \times H \times L \times 3$ , which is generally less than 1K. + +(b). Learnable Scalers-and-Shifters and Class-wise Key: To assist the generator in achieving plasticity, we train a learnable scalers-and-shifters $(a_{K}^{c},b_{K}^{c},a_{V}^{c},b_{V}^{c})$ associated with a learnable class-wise key $K^c$ (figure 2(a)), where $c$ is + +the class label that is represented by $K^c$ . Following the generator pair, we can specify that $(a_K^c, b_K^c)$ and $(a_V^c, b_V^c)$ are the scalars-and-shifters for $G_K$ and $G_V$ respectively. However, the scaller and shifters are not distributed into all MSA heads and layers but are expanded based on prompt length $l$ . Thus, each element of the tuple, e.g., $a_K^c$ is a vector with $l - 1$ elements. Note that the first length $(l = 1)$ is not scaled or shifted, but left original $G(x)$ . Our method utilizes small prompt length as in DualPrompt [43], i.e., $l = 5$ to maximize the model throughput. Based on that setting, the total scalars and shifters for each class are $4 \times 4 = 16$ parameters. To avoid uncontrollable values of $(a_K^c, b_K^c, a_V^c, b_V^c)$ we deploy upper and lower bounds both for $K$ and $V$ scalars and shifters formulated by the expression below: + +$$ +\left(1 - \epsilon_ {a}\right) \leq a ^ {c} \leq \left(1 + \epsilon_ {a}\right), \text {a n d} - \epsilon_ {b} \leq b ^ {c} \leq \epsilon_ {b} \tag {1} +$$ + +where $\epsilon_{a}$ and $\epsilon_{b}$ are small positive real numbers. The boundaries are deployed to avoid too much perturbation of $G_{K}(x)$ and $G_{V}(x)$ that leads to degraded performance. $K^{c}$ is a $\mathbb{R}^D$ learnable vector that represents class $c$ , where $D$ is the embedding size. By representing class $c$ , $K^{c}$ plays as a reference to select the appropriate scalars and shifters during the inference time based on its similarity to input $x$ . + +# 4.2. Prompt Generation + +We propose a novel prompt generation mechanism i.e., by single lightweight generators and scalers-and-shifters. The mechanism is unique to existing prompt-generation methods [17, 28, 33]. Given prompt generator $(G_K, G_V)$ and scalar-and-shifters $(a_K^c, b_K^c, a_V^c, b_V^c)$ where each element as $l$ -elements vector, the prompt is generated by executing equation 2. + +$$ +\begin{array}{l} P _ {K} = \left[ P _ {K, 1}; P _ {K, 2}; \dots ; P _ {K, l} \right], P _ {V} = \left[ P _ {V, 1}; P _ {V, 2}; \dots ; P _ {V, l} \right] \\ P _ {K, i} = a _ {K, i - 1} ^ {c} G _ {K} (x) + b _ {K, i - 1} ^ {c}, \tag {2} \\ P _ {V, i} = a _ {V, i - 1} ^ {c} G _ {V} (x) + b _ {V, i - 1} ^ {c}, i \in [ 2.. l ] \\ \end{array} +$$ + +where $"$ ;" denotes the concatenation operation. We add similarity factor $s$ to $G(x)$ , i.e., $G(x) = s.G(x)$ where $s$ is the cosine similarity between input and closest key, i.e., $s = \text{cosine}(x, K^c)$ . The addition of the similarity factor acts as a controller if the input chooses the wrong key. Following the previous study[28, 43], the matched input $x$ can be pached embedding, class token, or class feature that we set as default in this study. + +# 4.3. Current-to-Previous Classes Orthogonality + +We apply current-to-previous classes orthogonality to increase the discriminative capability of our method. Let the method currently at task $t$ that learns class $j, j + 1, j + 2 \ldots m$ . The model must discriminate any currently learned class $c \in [j, j + 1,..m]$ to any previously learned class $c' \in [1, 2,..j - 1]$ . Due to rehearsal-free constraints, our model can not replay any samples from class $c'$ with the samples of + +![](images/ea5f26d048486e916966f698a49908d159032b9a728eb13c4700fcc0ce319da6.jpg) +Figure 2. The proposed PROL diagram. PROL utilizes a single generator $(G_K, G_V)$ for all classes in all tasks, learnable scalars $(a_K^i, a_V^i)$ , and shifters $(b_K^i, b_V^i)$ parameters associated to the class-wise key $K^i$ . The generator is trained only in the first task and frozen afterward, while the scalers, shifters, and class-wise keys are trained in every task. The prompt is generated by scaling and shifting $G(x)$ by the selected scalers and shifters associated with the highest similarity key. The model is updated by joining the loss function consisting of intra-task loss $\mathcal{L}_{intra}$ , inter-task loss $\mathcal{L}_{intra}$ , orthogonality loss $\mathcal{L}_{ort}$ , input-to-key similarity loss $\mathcal{L}_{sim}$ and generalization loss $\mathcal{L}_{gen}$ . + +$c$ . Dealing with the constraint, we utilize $K^c$ and $K^{c'}$ that represent $c$ and $c'$ respectively, thus the model can always improve its discrimination capability. Following the vector principle, that states 2 orthogonal vectors have a zero dot product, our method optimizes $K^c$ so that $K^c.K^{c'} = 0$ . + +# 4.4. Preserving Generalization Property + +We utilize PTM that has generalization capability as the initial weight of our method. Dealing with the sequence of streaming data that may be infinite, the generalization capability must be preserved so that it can be taken advantage of by the upcoming data. Following the previous study[51], we preserve the generalization capability by cross correlating the feature of PTM (only), i.e., $f_{\theta}(x)$ and the feature of PTM and prompt, i.e., $f_{\theta;P}(x)$ into a matrix $M$ by executing equation 3. + +$$ +M = 1 / B \left[ f _ {\theta} (x) \right] ^ {T} \left[ f _ {\theta ; P} (x) \right] \tag {3} +$$ + +$\mathbf{M}$ is $D\times D$ matrix, while $f_{\theta}(x)$ and $f_{\theta ;P}(x)$ are $B\times D$ where $B$ and $D$ is batch and embedding sizes respectively. The total quantity of the diagonal elements of $\mathbf{M}$ shows the alignment between the PTM feature $(f_{\theta}(x))$ and the PTM+prompt tuning feature $(f_{\theta ;P}(x))$ . The higher the quantity, the higher the generalization preserving. + +# 4.5. Learning, Losses, and Final Objectives + +In this subsection, we explain the learning objective of our method. For a better understanding, we explain it in a per-component way as follows. + +(a) Tuning Generators and scalar-and-shifters: These 2 components work together to generate the prompt that is prepended into ViT layers and go through until the last module, i.e., MLP classifier. Along with the MLP classifier, these two components are tuned by using cross entropy loss that is derived into two types, i.e., intra-task loss $(\mathcal{L}_{intra})$ + +and inter-task loss $\mathcal{L}_{inter}$ . $\mathcal{L}_{intra}$ improves model discrimination within a task, specifically, currently learned classes, while $\mathcal{L}_{inter}$ improves model discrimination for all learned classes, including current and old classes. The intra and inter-task loss are formulated as in equations 4 and 5. + +$$ +\mathcal {L} _ {i n t r a} = - \sum_ {c \in C ^ {t}} \log \frac {\exp \left(g _ {\phi} \left(f _ {\theta ; P} (x)\right) [ c ]\right)}{\sum_ {c ^ {\prime} \in C ^ {t}} \exp \left(g _ {\phi} \left(f _ {\theta ; P} (x)\right) [ c ^ {\prime} ]\right)} \tag {4} +$$ + +$$ +\mathcal {L} _ {\text {i n t e r}} = - \sum_ {t = 1} ^ {t = T} \sum_ {c \in \mathcal {C} ^ {t}} \log \frac {\exp \left(g _ {\phi} \left(f _ {\theta ; P} (x)\right) [ c ]\right)}{\sum_ {t = 1} ^ {t = T} \sum_ {c ^ {\prime} \in \mathcal {C} ^ {t}} \exp \left(g _ {\phi} \left(f _ {\theta ; P} (x)\right) [ c ^ {\prime} ]\right)} \tag {5} +$$ + +(b) Tuning Task-wise learnable key: $K^c$ has two important roles in our method, i.e., as the class representation to select scalers-and-shifters and improving model discrimination through orthogonality. As the class representation, we tune $K^c$ tuned closer to the input sample of class $c$ with similarity loss $\mathcal{L}_{sim}$ as expressed in the equation 6. + +$$ +\mathcal {L} _ {s i m} = - \left(x. K ^ {c}\right) / \left(\max \left(\left| | x | | _ {2}. \right| \left| K ^ {c} \right| | _ {2}, \epsilon\right)\right) \tag {6} +$$ + +To improve class discrimination, we tune any $K^c$ from currently learned classes to be orthogonal to any $K^{c'}$ from previously learned classes. Let $y = [c_1, c_2, \dots, c_B]$ is the class labels of batch-wise input $x$ , $K_{new} = [K^{c_1}, K^{c_2}, \dots, K^{c_B}]$ is the class-wise keys matched with $y$ , and $K_{old} = [K^{c_1'}, K^{c_2'}, \dots, K^{c_B'}]$ , then the model will be improved by orthogonality loss $\mathcal{L}_{\text{ort}}$ as formulated in equation 7. + +$$ +\mathcal {L} _ {o r t} = \frac {1}{B} \sum_ {i = 1} ^ {B} K ^ {c i}. K ^ {c ^ {\prime} i} \tag {7} +$$ + +(c) Tuning Generalization preserving Matrix: The diagonal elements of matrix $M$ represent the agreement between PTM only prototype $(f_{\theta}(x))$ and PTM+Prompt prototype $(f_{\theta;P}(x))$ , while the non-diagonal represent the disagreement between them. Thus we tune the generalization matrix + +$M$ with generalization loss $\mathcal{L}_{gen}$ as formulated in the equation 8. The first term of $\mathcal{L}_{gen}$ push the model towards the agreement, while the second term of the $\mathcal{L}_{gen}$ avoids the disagreement of the prototypes. + +$$ +\mathcal {L} _ {\text {g e n}} = \frac {1}{D} \sum_ {i = 1} ^ {D} \left(1 - M _ {i, i}\right) ^ {2} + \frac {1}{D (D - 1)} \sum_ {i = 1} ^ {D} \sum_ {j \neq i} M _ {i, j} ^ {2} \tag {8} +$$ + +(d) Joint Loss and Final Objective: Finally, accommodating the losses for all components of our proposed method, i.e., single lightweight generators, scalers-and-shifter, class-wise keys, and generalization matrix, we define a new joint loss function as in equation 9. To enhance the flexibility of our model we add losses coefficient $\lambda_{1},\lambda_{2},\lambda_{3},\lambda_{4},\lambda_{5}$ . + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {i n t r a}} + \lambda_ {2} \mathcal {L} _ {\text {i n t e r}} + \lambda_ {3} \mathcal {L} _ {\text {s i m}} + \tag {9} \\ \lambda_ {4} \mathcal {L} _ {o r t} + \lambda_ {5} \mathcal {L} _ {g e n} \\ \end{array} +$$ + +(e) Hard-Soft Update (HSU) Strategy: Dealing with streaming data that the learning cannot be repeated into several epochs, we devise a learning strategy for updating the model. We utilize Hard-Soft Update (HSU) where the model adaptively switches from-and-into hard update, i.e., update with constant and high learning rate, and soft update, i.e., update with decayed learning rate. The hard update is started when the model see new class labels and switch into soft update if the cross entropy loss, i.e., $\mathcal{L}_{ce} = \lambda_1\mathcal{L}_{intra} + \lambda_2\mathcal{L}_{inter}$ less than a loss threshold $\mathcal{L}_{thres}$ . The decay is executed by a cosine annealing scheduler. + +# 5. Result and Analysis + +# 5.1. Experiment Setting + +We evaluate our method in 4 of the most popular datasets in CL i.e. CIFAR100[11], ImageNet-R [16], ImageNet-A [12], and CUB[36]. CIFAR100 contains 100 classes images, while the other has 200 classes. We uniformly split the dataset into 10 tasks. We compare our proposed method with the current SOTAs of PTM-based OCL, i.e., RanDumb [25], RanPAC [22], and MOS [34], the extension of EASE [52]. We adapt the official code of RanDumb and RanPAC from [25] into our rehearsal free and disjoint setting. We also adapt the rehearsal version (denoted with -R) with 5 samples per class as memory, and the joint version (denoted with -J) for both of them. We adapted MOS from its official code into rehearsal free setting. We add L2P [44], DualPrompt [43], and ConvPrompt [28] as representation of pool-based, task-specific, and growing components prompting, respectively. To ensure fairness, all the consolidated methods are run with the same dataset split, backbone, i.e., ViT-B/16 pre-trained on Imagenet-21K, and a 10 chunk size. We also compare our method to non-PTM methods [3, 4, 9, 10, 27, 39, 45] as reported in [39]. The learning rates for all methods are set by grid search from the range + +of [0.001,0.005,0.01,0.05,0.1]. All the methods are run under the same environment, i.e., a single NVIDIA A100 GPU with 40 GB RAM, with 3 different random seeds. We utilize Adam optimizer for PROL, while the rest follows their official implementation. We evaluate final average accuracy (FAA), cumulative average accuracy (CAA), and final forgetting measure (FM), see supplementary. + +# 5.2. Result and Analysis + +a) Overall Performance: Table 1 shows the summarized performance of the consolidated method in 4 benchmark datasets. In term of accuracy, our method outperforms the existing SOTAs with a significant gap, i.e., $2 - 76\%$ FAA and $2 - 64\%$ CAA, respectively, except in the CUB dataset. Surprisingly, our method outperforms the joint version of RanDumb and RunPAC with a $2 - 20\%$ gap both for FAA and CAA, even though those methods join all the samples' features together. Our method outperforms their replay versions (RanPAC-R and RanDumb-R) with a high margin, i.e., $20 - 35\%$ FAA and CAA margins. The rehearsal free of those methods perform extremely poor indicated by the very low FAA and CAA. Our method outperforms the prompt-based methods with a significant margin, i.e., $2 - 20\%$ margin both for FAA and CAA. ConvPrompt is the closest competitor to our method with $2 - 3\%$ difference in all cases. Our method outperforms the adapter method (MOS) with a significant margin, i.e., $2 - 21\%$ FAA and $2 - 10\%$ CAA, respectively. In CUB dataset, our method has lower performance than RanPAC-J and RanDumb-J, comparable performance with RanPAC-R and RanDumb-J, and outperforms the other methods with a convincing gap, i.e., $2 - 63\%$ FAA and $2 - 52\%$ CAA, respectively. In terms of forgetting, our method achieves a fairly low forgetting rate, i.e., slightly higher than Convprompt methods in many cases but significantly lower than RanPAC, RanDumb, and MOS. Our method even achieves lower forgetting in 2 of 4 datasets than RanPAC-J and RanDumb-J. Table 2 shows that despite having a smaller backbone size, our method outperform the non-PTM methods with a significant gap, i.e., $\geq 16\%$ . It shows that PTM and parameter-efficient tuning are preferable to a bigger size backbone and memory. + +b) Historical Performance: Figure 3 plots the detailed performance of the consolidated methods after finishing each task. The figure shows that in CIFAR100, ImageNet-R, and ImageNet-A datasets, our method consistently achieves the highest average accuracy from the first task until the last task. In addition, the figure shows that our method has the smallest slope, indicating that it suffers from the smaller performance degradation in the learning process. In CUB dataset, our method consistently achieves higher performance than all rehearsal-free methods and competes with RanPAC-R and RanDumb-R, even though it has lower performance than RanPAC-J and RanDUmb-J. Note that both the -R and -J methods replay the previous data, and those + +Table 1. Summarized performance of consolidated methods in 4 benchmark dataset, i.e., CIFAR100, Magnet-R, Magnet-A, and CUB200. The official code of ConvPrompt is not runnable on Imagenet-A due to its descriptor unavailability to determined new generators for continual tasks. PET and Rhsl denotes parameter efficient tuning and rehearsal respectively. + +
MethodPET TypeRhslCIFAR100ImageNet-RImageNet-ACUB200
FAACAAFMFAACAAFMFAACAAFMFAACAAFM
RanPAC-J [22]Rand. matrixyes79.9485.916.4352.0956.216.6345.0353.306.9785.2086.312.63
RanDumb-J [25]RBF kernelyes80.3986.156.2552.6356.136.0444.0752.304.9885.8286.842.52
RanPAC-R [22]Rand. matrixyes59.6669.3534.3028.1635.3739.8128.5435.1632.0575.6379.3714.65
RanDumb-R [25]RBF kernelyes50.9362.1447.3521.9129.9048.8124.8630.8234.7973.8178.7017.45
RanPAC [22]Rand. matrixno9.5227.9294.527.2418.8167.273.7714.8657.769.5227.0688.98
RanDumb [25]RBF kernelno9.5627.9494.517.3218.8067.673.6914.5655.159.5327.2189.69
L2P [44]Prompt (Latent)no80.9986.666.7152.0855.905.6714.6421.885.3561.9871.469.81
DualPrompt [43]Prompt (Latent)no82.5388.064.5361.1762.733.7520.0521.571.9158.0649.956.23
ConvPrompt [28]Prompt Gen.no84.7988.192.3870.9274.663.39---70.1277.487.21
MOS [34]Adaptersno83.9989.5311.3452.1367.9735.7244.7955.1415.5061.7477.0325.25
PROL (Ours)Prompt. Gen+SSno86.3291.356.3473.5078.134.8247.7258.963.2972.5179.898.92
+ +![](images/f141733a5de79fbdfef2d833a4df7a2a599dd79329d2434e7023479391dae467.jpg) + +![](images/2865be8c9f8dc4a16c73ff27f865cdbb0ea927fa025e37810ed72a950ef6a17d.jpg) + +![](images/5cb85924c451de2a2961e3b9f2bc0cabf5256d5d4a769059ff20ba2a0d7bda6c.jpg) + +![](images/a56457c0a51107d2238ff4575ffab94a139a831aba019f86824f1a2fc3690e28.jpg) + +Figure 3. Historical performance plot of the consolidated methods in CIFAR100, Magnet-R, Magnet-A, and CUB200 dataset +![](images/eaa1d16473819804eb94ab55b7c2f978adbbf35a5bea91913eeabf50d019555b.jpg) +RanPAC-J RanDumb-J RanPAC-R RanDumb-R RanPAC RanDumb L2P DualPrompt ConvPrompt MOS PROL + +![](images/faa8e50c8978fcc0ffa2fd984eab09f741e47cba0fc72e1d4f322cb0c5efb1ca.jpg) + +![](images/1b4484e226b373c9a6eabf038c7c2a29a764b845fdaafc3bc6d166fce2b73b17.jpg) + +![](images/6a3b5b9b5f8dd722dd7fbaaa9fb06234fe37ac0963cf656ca46402c0b677340a.jpg) + +Table 2. Comparison of proposed method to non-PTM method on CIFAR100 dataset, the result is copied from ERSM[39] + +
MethodMemBackboneFAA on CIFAR100
TypeSizePTM
ER [27]5000ResNet-1811.2Mno38.70
DER++ [3]5000ResNet-1811.2Mno37.62
ERACE [4]5000ResNet-1811.2Mno39.82
OCM [9]5000ResNet-1811.2Mno42.01
GSA [10]5000ResNet-1811.2Mno42.27
OnPro [45]5000ResNet-1811.2Mno41.47
ERSM [39]5000ResNet-1811.2Mno47.72
PROL (Ours)-ViT-Tiny5.6Myes64.59
+ +methods are significantly outperformed by PROL in the other 3 datasets. In terms of the forgetting measure, PROL consistently achieves a fairly low forgetting rate along with the prompt-based methods. The plot shows that our method is consistently in the bottom group while RanPAC, RanDumb, and MOS are in the middle and upper groups. + +c) Parameter, Throughput and Execution time: Table 3 presents the parameter and summarized throughput and execution time while the detailed version is presented by fig.4. The throughput is computed in the training phase, where the + +learning process is conducted. The table shows that PROL requires one of the smallest number of trainable parameters, i.e., only slightly bigger than RanPAC and L2P and far smaller than the rest of the methods. RanDumb saves the biggest (> 7M) RBF kernel parameters, while ConvPrompt and MOS require 1.4M and 3.2M parameters, respectively. The table show that PROL has a moderate throughput, i.e., comparable with L2P and DualPrompt, lower than RanDumb and RanPAC. In line with this, PROL achieves moderate training and inference time. RanDumb and RanPAC have higher throughput and lower execution time since the methods update their feature projection and classifier only once, not iteratively per data stream. In the streaming process, it only extracts the input feature, stores it in memory, and then updates the projection and classifier only once after the current task is finished. The weakness of this mechanism is that it can not handle any time inference where a request for inference comes in the middle of the streaming. Figure 4 confirms that PROL has moderate throughput, training time, and testing time from the first task until + +Table 3. Trainable Parameter (including classifier), summarized throughput and execution time of consolidated methods in, ImageNet-R dataset. + +
Method#Trainable +Parameter +In million (M)Average +Throughput +(sample/s)Average +Training +Time (s)Average +Inference +Time (s)
RanPAC-J [22]0.15482.9229.6055.24
RanDumb-J [25]7.83477.0332.0053.79
RanPAC-R [22]0.15489.4628.3084.20
RanDumb-R [25]7.834116.8921.2043.36
RanPAC [22]0.15486.8327.7045.21
RanDumb [25]7.83485.9029.9046.81
L2P [44]0.20040.9459.8054.50
DualPrompt [43]0.70146.5053.2052.60
ConvPrompt [28]1.43411.77235.70103.92
MOS [34]3.19716.06165.70322.20
PROL (Ours)0.21335.4268.7055.39
+ +the last task. In terms of throughput, it competes with DualPrompt and L2P and is far better than ConvPrompt and MOS. ConvPrompt and MOS low throughput and high execution time confirm our preliminary analysis on growing prompt components/adapters. + +![](images/89dce0af13be97e66954199ece8a4fba0ee6854853f3641499c508249bd0830e.jpg) +Figure 4. Detailed throughput and execution time of consolidated methods in, Magnet-R dataset. + +d) Robustness Analysis: Table 4 shows the robustness of our method in comparison to the closest competitor, i.e., ConvPrompt, on different prompt lengths and the number of ViT layers pre-pended. The table shows that PROL successfully maintains its performance in different prompt lengths and numbers of layers, even in the smaller prompt length or fewer layers. In addition, it maintains the performance gap to the ConvPrompt as the closest competitor with the convincing margin, i.e. $\geq 2\%$ . The table shows that PROL achieves a higher CAA in a higher number of layers. The table also shows that PROL has a better performance stability than ConvPrompt with $2\%$ performance swing. +e) Ablation Study: We conducted an ablation study to evaluate the contribution of each component of our method as presented in table 5. The table shows that fine-tuning (FT) alone can not handle OCL problem since the performance is too low. However, combining both inter-task loss $\mathcal{L}_{inter}$ and intra-task loss $\mathcal{L}_{intra}$ has $1 - 2\%$ better accuracy than utilizing only one. The generator (G) plays the most important role as it tremendously boosting the accuracy and reduce the forgetting i.e. up to $57\%$ . The learnable scalar-and-shifetrs (SS) and class-wise keys (K) and input-to-key similarity + +Table 4. Robustness analysis of the proposed method compared to the competitor methods in ImageNet-R dataset. + +
Robustness on Different Prompt Length
Method3571015
FAACAAFAACAAFAACAAFAACAACAA
ConvPrompt69.8872.8970.9274.6670.6874.1170.0274.1869.45
PROL73.4277.7173.5078.1373.4377.9273.4578.0373.30
Robustness on Different Number of ViT Layers
Method3579-
FAACAAFAACAAFAACAAFAACAA-
ConvPrompt71.4375.9570.9274.6669.3874.2172.1277.47-
PROL73.7277.8073.5078.1373.5578.1473.7578.69-
+ +Table 5. Ablation study of our method in ImageNet-R dataset. + +
ComponentLossFAACAAFM
FTLinter11.9826.2575.72
FTLinter+Lintra12.6828.1381.15
FT+GLinter+Lintra69.7774.433.25
FT+G+SS+KLinter+Lintra+Lsim70.8275.833.96
FT+G+SS+KLinter+Lintra+Lsim+Lort71.1376.094.31
FT+G+SS+K+HSULinter+Lintra+Lsim+Lort72.5377.244.95
FT+G+SS+K+HSU+MLinter+Lintra+Lsim+Lort+Lgen73.5078.134.82
+ +loss $\mathcal{L}_{sim}$ improve the performance with $1\%$ margin. At this point, our method is comparable to ConvPrompt as the closest competitor and even achieves higher CAA. Adding orthogonality loss $\mathcal{L}_{ort}$ on K improves both FAA and FAA even though with a small margin. Applying the hard-soft-update strategy improves the model accuracy with $1.5\%$ FAA and $1.2\%$ CAA improvement, respectively. However, it increases the forgetting along with the accuracy. Finally, preserving the PTM generalization property by matrix M and generalization loss $\mathcal{L}_{gen}$ improves the accuracy with $1\%$ margin, and reduces a slight magnitude of forgetting. + +# 6. Concluding Remark + +We highlight the rehearsal-free aspect of continual learning in streaming data and propose a novel rehearsal-free method that incorporates four key concepts (1) Single lightweight prompt generator for all instances in all classes (2) learnable scalers-and-shifters parameters associated with learnable class-wise keys (3) cross-correlation matrix for preserving PTM generalization (4) hard-soft update for adaptive learning rate assignment. Our experiment and analysis show the superiority of our method to existing SOTAs in CIFAR100, ImageNet-R, ImageNet-A, and CUB dataset with significant margins, i.e., $2 - 76\%$ and $2 - 64\%$ margin for FAA and CAA, respectively. Our method significantly outperforms the joint version of existing SOTAs in 3 datasets while running in a rehearsal-free manner. Our historical analysis shows the consistency of our method in maintaining stability-plasticity in every task. Our method achieves moderate training time, and throughput. Our method achieves significantly higher throughput and lower training and testing time than the growing prompt generator and adapters methods. Our robustness analysis shows that our method consistently achieves the highest performance in various prompt lengths and numbers of ViT layers. + +# Acknowledgement + +M. Anwar Ma'sum acknowledges the support of Tokopedia-UI Centre of Excellence for GPU access to run the experiments. + +# References + +[1] Magdalena Biesialska, Katarzyna Biesialska, and Marta R Costa-Jussa. Continual lifelong learning in natural language processing: A survey. arXiv preprint arXiv:2012.09823, 2020. 1 +[2] Matteo Boschini, Lorenzo Bonicelli, Pietro Buzzega, Angelo Porrello, and Simone Calderara. Class-incremental continual learning into the extended der-verse. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(5):5497-5512, 2022. 2 +[3] Pietro Buzzega, Matteo Boschini, Angelo Porrello, Davide Abati, and Simone Calderara. 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Despite recent progressive, existing methods often struggle to handle severe object appearance changes and cluttering background in the video due to lacking sufficient target cues, leading to degradation. Addressing this, we introduce PRVQL, a novel Progressive knowledge-guided Refinement framework for EgoVQL. The core is to continuously exploit target-relevant knowledge directly from videos and utilize it as guidance to refine both query and video features for improving target localization. Our PRVQL contains multiple processing stages. The target knowledge from one stage, comprising appearance and spatial knowledge extracted via two specially designed knowledge learning modules, are utilized as guidance to refine the query and videos features for the next stage, which are used to generate more accurate knowledge for further feature refinement. With such a progressive process, target knowledge in PRVQL can be gradually improved, which, in turn, leads to better refined query and video features for localization in the final stage. Compared to previous methods, our PRVQL, besides the given object cues, enjoys additional crucial target information from a video as guidance to refine features, and hence enhances EgoVQL in complicated scenes. In our experiments on challenging Ego4D, PRVQL achieves state-of-the-art result and largely surpasses other methods, showing its efficacy. Our code, model and results will be released at https://github.com/fb-reps/PRVQL. + +# 1. Introduction + +The egocentric visual query localization (EgoVQL) task [9] aims at answering the question "Where was the object $X$ last seen in the video?", with "X" being a visual query specified by a single image crop outside the search video. In specific, given a first-person video, its goal is to search and locate the + +![](images/af7ebde89806e999309ade5550e096636087695a4cad09aec38556550c647d29.jpg) +Figure 1. Comparison between current EgoVQL approaches in (a) and proposed PRVQL with progressive knowledge-guided refinement in (b). Best viewed in color and by zooming in for all figures. + +visual query, spatially and temporally, by returning the most recent spatio-temporal tube. Owing to its important roles in numerous downstream object-centric applications including augmented and virtual reality, robotics, human-machine interaction, and so on, EgoVQL has drawn extensive attention from researchers in recent years. + +Current approaches (e.g., [9, 14, 28, 29]) simply leverage the provided visual query as the sole cue to locate the target in the video (see Fig. 1 (a)). However, since the given visual query is cropped outside the search video, there often exists a significant gap between the query and the target of interest, due to rapid appearance variations in first-person videos caused by many factors, such as object pose change, motion blur, occlusion, and so forth. As a result, relying only on the given object query, as in existing methods, is insufficient to describe and distinguish the target from background in complicated scenarios with heavy appearance changes, resulting in performance degeneration. In addition, to achieve precise + +localization, it is essential for an EgoVQL model to enhance target and meanwhile suppressing background regions from videos. Yet, this is often overlooked by existing approaches, making them easily suffer from cluttering background and therefore leading to suboptimal target localization. + +The aforementioned issues faced by current methods naturally raise a question: In addition to the given visual query, is there any other information that could be leveraged for enhancing EgoVQL? We answer yes, and show the information directly explored from the video itself, as a supplement to the given target cue, is effective in improving EgoVQL. + +Specifically, we propose a novel Progressive knowledge-guided Refinement framework for EgoVQL (PRVQL). The core idea of our algorithm is to continuously exploit target-relevant knowledge from the video and leverage it to guide refinements of both query and video features, which are crucial for localization, for improving EgoVQL (see Fig. 1 (b)). Concretely, PRVQL consists of multiple processing stages. Each stage comprises two simple yet effective modules, including appearance knowledge generation (AKG) and spatial knowledge generation (SKG). In specific, AKG works to mine visual information of the target from videos as the appearance knowledge. It first estimates potential target regions from a video using the query, and then selects top few highly confident regions to extract appearance knowledge from video features. Different from AKG, SKG focuses on exploring target position cues from videos as spatial knowledge by exploiting the readily available target-aware attention maps. In PRVQL, the appearance knowledge is used to guide the update of query feature, making it more discriminative, while the spatial knowledge is employed to enhance target and meanwhile suppressing unconcerned background in video features, enabling more focus on the target. The extracted appearance and spatial knowledge in one stage are used as guidance to respectively refine query and video features for next stage, which are adopted to learn more accurate knowledge for further feature refinement. Through this progressive process in PRVQL, the target knowledge can be gradually improved, which, in turn, results in better refined query and video features for target object localization in the final stage. Fig. 2 illustrates the framework of PRVQL. + +To our best knowledge, PRVQL is the first method to exploit target-relevant appearance and spatial knowledge from the video to improve EgoVQL. Compared with existing solutions, PRVQL can leverage target information from both the given visual query and mined knowledge from the video for more robust localization. To verify its effectiveness, we conduct experiments on the challenging Ego4D [9], and our proposed PRVQL achieves state-of-the-art performance and largely outperforms other approaches, evidencing effectiveness of target knowledge for enhancing EgoVQL. + +In summary, our main contributions are as follows: $\spadesuit$ We propose a progressive knowledge-guided refinement frame + +work, dubbed PRVQL, that exploits knowledge from videos for improving EgoVQL; $\spadesuit$ We introduce AKG for exploring visual information of target as appearance knowledge; $\clubsuit$ We introduce SKG for learning spatial knowledge using target-aware attention maps; $\spadesuit$ In extensive experiments on Ego4D, PRVQL achieves state-of-the-art performance. + +# 2. Related Work + +Egocentric Visual Query Localization. Egocentric visual query localization (EgoVQL) is an emerging and important computer vision task. Since its introduction in [9], EgoVQL has received extensive attention in recent years owing to its importance in numerous applications. Early methods [9, 28, 29] often utilize a bottom-up multi-stage framework, which sequentially and independently performs frame-level object detection, nearest peak temporal detection across the video, and bidirectional object tracking around the peak, to achieve EgoVQL. Despite the straightforwardness, this bottom-up design easily causes compounding errors across stages, thus degrading performance. Besides, the involvement of multiple detection and tracking components in this design leads to high complexities as well as inefficiency of the entire system, limiting its practicability. To deal with these issues, the recent method of [14] introduces a single-stage end-to-end framework for EgoVQL with Transformer [25], eliminating the need for multiple components and meanwhile showing promising performance. The method of [15] presents a training-free EgoVQL framework using foundational models ans shows excellent results. Unlike existing models, the work of [20] introduces an online setting for EgoVQL. + +In this work, we exploit target knowledge directly from the video to refine features for better localization. Different from previous works, PRVQL leverages cues from both the given query and mined target information for EgoVQL, significantly improving robustness, especially in presence of severe appearance variations and cluttering background. + +Query-based Visual Localization. Query-based visual localization, broadly referring to localizing the target of interest from images or videos given a specific query (image or text), is a crucial problem in computer vision, and consists of a wide range of related tasks, including one-shot object detection [12, 32, 38], visual object tracking [1, 4, 17], visual grounding [6, 18, 39], spatio-temporal video grounding [10, 31], pedestrian search [16, 35], etc. Despite sharing some similarity with the above tasks in localizing the target, this work is distinctive by focusing on spatially and temporally searching for the target from egocentric videos, which is challenging due to frequent and heavy object appearance variations under the first-person views. + +Progressive Learning Approach. Multi-stage progressive learning is a popular strategy to improve performance, and has been successfully applied for various tasks. For exam- + +![](images/cf01bb464d3b79c5d410dd61636ee14f544b4e9f6234479015649db1004f44dd.jpg) +Figure 2. Overview of PRVQL, which aims to explore target knowledge directly from videos via AKG and SKG and applies it as guidance to refine query and video features with QFR and VFR for improving localization in EgoVQL through a multi-stage progressive architecture. + +ple, the works of [2, 27, 34] introduce the cascade architecture to progressively refine the bounding boxes or features for improving object detection. The work in [33] presents a spatio-temporal progressive network for video action detection. The methods in [13, 37] introduce progressive refinement network for multi-scale semantic segmentation. The methods of [3, 36] apply progressive learning to improve features for saliency detection. The method in [8] proposes to progressively learn more accurate anchors for enhancing tracking. The work from [40] progressively transfers person pose for image generation. Different than these works, we focus on progressive refinement for improving EgoVQL. + +# 3. The Proposed Method + +Overview. In this paper, we propose PRVQL by exploiting crucial target knowledge directly from videos for improving target localization in EgoVQL. Our PRVQL is implemented as a progressive architecture. After feature extraction of the visual query and video frames, PRVQL performs iterative feature refinement guided by the target knowledge for localization through multiple stages (Sec. 3.1). As displayed in Fig. 2, each stage, expect for the final stage for prediction, consists of two crucial modules, comprising AKG (Sec. 3.2) and SKG (Sec. 3.3), for generating target appearance and spatial knowledge. The knowledge is leveraged as the guidance to refine query and video features (Sec. 3.4), which are applied in the next stage to generate more accurate target knowledge for further feature refinement. Through such a progressive process, the target knowledge can be gradually enhanced, which finally benefits learning more discriminative query and video features for improving EgoVQL. + +# 3.1. Our PRVQL Framework + +Visual Feature Extraction. In our PRVQL, we first extract features for the visual query and video frames. Specifically, + +given the query $q$ and a sequence of $L$ frames $\mathcal{I} = \{I_i\}_{i=1}^L$ from the video, we utilize a shared backbone $\Phi(\cdot)$ [21] for extracting their features $\mathbf{q} = \Phi(q) \in \mathbb{R}^{H \times W \times C}$ and $F = \{\mathbf{f}_i\}_{i=1}^L$ with each $\mathbf{f}_i = \Phi(I(i)) \in \mathbb{R}^{H \times W \times C}$ , where the $H$ and $W$ represent the spatial resolution of the features and $C$ denotes the channel dimension. For subsequent processing, we flatten $\mathbf{q}$ and $F$ to obtain $\mathbf{Q} = \text{flatten}(\mathbf{q}) \in \mathbb{R}^{HW \times C}$ and $\mathbf{V} = \{\mathbf{v}_i\}_{i=1}^L$ with each $\mathbf{v}_i \in \mathbb{R}^{HW \times C}$ . + +Progressive Knowledge-guided Feature Refinement for EgoVQL. As mentioned earlier, the core idea of PRVQL is to exploit target knowledge directly from videos and apply it as guidance to enhance query and video features for target localization. For this purpose, PRVQL is implemented as a progressive architecture with multiple stages in a sequence. Each but the last stage involves target knowledge learning and knowledge-guided feature refinement, as in Fig. 2. + +More specifically, for the $k^{\mathrm{th}}$ $(1\leq k < K)$ stage of our PRVQL, let $\mathcal{Q}_k$ and $\nu_{k}$ denote the query and video features. For the first stage $(k = 1)$ , $\mathcal{Q}_1$ and $\nu_{1}$ are initialized using query and video features extracted from the backbone, and $\mathcal{Q}_1 = \mathbf{Q}$ and $\nu_{1} = \mathbf{V}$ . Otherwise, $\mathcal{Q}_k$ and $\nu_{k} = \{v_{i}^{k}\}_{i = 1}^{L}$ are refined features in the last stage $(k - 1)$ . To mine target-specific knowledge from the video, we perform feature fusion between $\mathcal{Q}_k$ and $\nu_{k}$ , aiming to inject target information into video feature for improving its target awareness. In specific, we leverage cross-attention from [25] for feature fusion owing to its powerfulness in feature modeling. Mathematically, this process can be expressed as follows, + +$$ +\mathcal {X} _ {k} = \left\{x _ {i} ^ {k} \mid x _ {i} ^ {k} = \mathrm {C A B} \left(v _ {i} ^ {k}, \mathcal {Q} _ {k}\right) \right\} \quad i = 1, 2, \dots , L \tag {1} +$$ + +where $\mathcal{X}_k$ is the fused feature in stage $k$ , and $v_i^k$ the feature in frame $i$ . $\mathrm{CAB}(\mathbf{z},\mathbf{u})$ is the cross-attention (CA) block with $\mathbf{z}$ generating query and $\mathbf{u}$ key/value. Due to space limitation, please see supplementary material for detailed architecture. Besides fused feature, we also obtain target-aware + +spatial attention maps $\mathcal{S}_k = \{s_i^k\}_{i=1}^L \in \mathbb{R}^{L \times HW \times HW}$ for $L$ frames in Eq. (1), with each $s_i^k \in \mathbb{R}^{HW \times HW}$ the attention map from the cross-attention operation in $\mathsf{CAB}(v_i^k, \mathcal{Q}_k)$ . + +To further capture spatio-temporal relations from videos for enhancing features, we apply self-attention [25] on $\mathcal{X}_k$ by propagating the query information spatially and temporally. Considering that targets in nearby frames are highly correlated, we restrict the attention operation in a temporal window using a masking strategy, similar to [14]. To reduce the computation, we downsample $\mathcal{X}_k$ to decrease the spatial dimension of each frame feature to $h\times w$ . Then, we add a position embedding $\mathcal{E}_k^{\mathrm{pos}}$ to the video feature. This process can be written as follows, + +$$ +\tilde {\mathcal {X}} _ {k} = \text {D o w n s a m p l e} \left(\mathcal {X} _ {k}\right) + \mathcal {E} _ {k} ^ {\text {p o s}} \tag {2} +$$ + +where $\mathrm{Downsample}(\cdot)$ represents the downsampling operation implemented with convolution operation. Afterwards, masked self-attention is applied on as $\tilde{\mathcal{X}}$ as follows, + +$$ +\mathcal {H} _ {k} = \operatorname {M a s k e d S A} \left(\tilde {\mathcal {X}} _ {k}\right) \tag {3} +$$ + +where $\mathcal{H}_k$ represents enhanced video feature. MaskedSA(z) denotes the masked self-attention block with $\mathbf{z}$ generating query/key/value. In this block, each feature element from frame $i$ only attends to feature elements from frames in the temporal range $[(i - u),(i + u)]$ , which can be easily implemented using masking strategy [5, 25]. From Eq. (3), besides the $\mathcal{H}_k$ , we also gain the temporal-aware spatial attention maps, denoted as $\mathcal{T}_k\in \mathbb{R}^{L\times hw\times Lhw}$ , for the target in the video, which will be used for knowledge generation. + +With video feature $\mathcal{H}_k$ and attention maps $S_{k}$ and $\mathcal{T}_k$ , the target knowledge can be extracted with the AKG and SKG modules (as explained later in Sec. 3.2 and 3.3), as follows, + +$$ +\mathcal {K} _ {k} ^ {a} = \mathrm {A K G} \left(\mathcal {H} _ {k}, \mathcal {V} _ {k}\right) \quad \mathcal {K} _ {k} ^ {s} = \operatorname {S K G} \left(\mathcal {S} _ {k}, \mathcal {T} _ {k}\right) \tag {4} +$$ + +where $\mathcal{K}_k^a$ represents the appearance knowledge and $\mathcal{K}_k^s$ the spatial knowledge. Guided by $\mathcal{K}_k^a$ and $\mathcal{K}_k^s$ in stage $k$ , we can refine query and video features using two update modules QFR and VFR (as described later in Sec. 3.4) as follows, + +$$ +\mathcal {Q} _ {k + 1} = \mathrm {Q F R} \left(\mathcal {K} _ {k} ^ {a}, \mathcal {Q} _ {k}\right) \quad \mathcal {V} _ {k + 1} = \mathrm {V F R} \left(\mathcal {K} _ {k} ^ {s}, \mathcal {V} _ {1}\right) \tag {5} +$$ + +where $\mathcal{Q}_{k + 1}$ and $\nu_{k + 1}$ are refined features guided by target knowledge, which are fed to the next stage $(k + 1)$ to generate more accurate knowledge for further feature refinement. Fig. 3 compares the attention maps from the masked self-attention with and without using our approach. We can see that, our method with refined features guided by knowledge can better focus on the target in the video and thus improves target localization, showing its efficacy. + +For the final $K^{\mathrm{th}}$ stage in PRVQL, since no knowledge is extracted, the AKG and SKG modules are removed. Given the visual query and video features $\mathcal{Q}_K$ and $\nu_{K}$ from the $(K - 1)^{\mathrm{th}}$ stage, we can then obtain the final enhanced video feature $\mathcal{H}_K$ through Eqs. (1)-(3) in the $K^{\mathrm{th}}$ stage. With $\mathcal{H}_K$ , + +![](images/c82db6153d50588f0080a1236b7352dbc1de75ab347549433bb6589378aefdd7.jpg) +visual query + +![](images/79cbd6076d9098417125c33464824c7db6a3c74d1d307135e8b1a0aae3e1193a.jpg) +(a) Attention maps in frames without progressive refinement + +![](images/9b93e63fbb3c30985565d0b668b1496cf5057c3825ad0f61a52470409321be24.jpg) + +![](images/3b28cf6ad21229e391b80aebb807559b622017345312bb342300280504ca3419.jpg) + +![](images/6dc5bee484eca61f5a78f34cebd2c6435182a4b7de6c09741f7f4dbe791c9674.jpg) + +![](images/fed0441089bfd390f32262b5b1eff173d8e72c0dfc32b70025f4699dad402c2a.jpg) +(b) Attention maps in frames with progressive refinement + +![](images/8117a0a129614283719bfa6100f967e62a69e9abe0c1f05a92ad6a8d558613ab.jpg) +Figure 3. Comparison of attention maps for video frames from the masked self-attention block without (a) and with (b) our progressive refinement. As shown, our method can better focus on the target regions, and hence can improve target localization in EgoVQL. The red boxes indicate the foreground object to localize. + +![](images/8c3f491959a44b9a55ef273c4bfe554c9c316513452383f4d3fccc259e84c39d.jpg) + +![](images/936a320d250b30eaa01788d5e99fe9a9a4cc0b070f08cf0d9b4e603cb26ec906.jpg) + +we use the prediction heads as in [14] for target localization via regression and classification. For details of the adopted prediction heads, please kindly refer to [14]. + +# 3.2. Appearance Knowledge Generation (AKG) + +In order to extract discriminative visual information of target directly from the video, we introduce a simple yet highly effective module, named appearance knowledge generation (AKG), for appearance knowledge learning. Specifically, it first estimates the potential target regions from the video using target-aware video features. Then, based on confidence scores of these regions, we select the top few ones to extract target features from the video as the appearance knowledge. + +Specifically, given the target-aware video feature $\mathcal{H}_k$ , we first reshape it to the 2D feature map, and then increase its spatial resolution back to $H\times W$ as follows, + +$$ +\tilde {\mathcal {H}} _ {k} = \text {U p s a m p l e} (\text {R e s h a p e} (\mathcal {H} _ {k})) \tag {6} +$$ + +where $\mathrm{Upsample}(\cdot)$ denotes the upsampling operation. After this, we apply $\mathcal{H}_k$ to produce temporal confidence scores and spatial box regions for target in each frame. More concretely, we first split $\tilde{\mathcal{H}}_k$ along the channel dimension into two equal halves $\tilde{\mathcal{H}}_k^t$ and $\tilde{\mathcal{H}}_k^s$ via $\tilde{\mathcal{H}}_k^t$ , $\tilde{\mathcal{H}}_k^s = \mathrm{Split}(\tilde{\mathcal{H}}_k)$ . Inspired by [14], we perform classification and regression to predict temporal confidence scores and spatial boxes using multi-scale anchors [23]. Specifically, two Conv blocks are applied on $\tilde{\mathcal{H}}_k^t(i)$ and $\tilde{\mathcal{H}}_k^s(i)$ for prediction as follows, + +$$ +\tilde {\mathcal {C}} _ {k} = \operatorname {C o n v B l o c k} \left(\tilde {\mathcal {H}} _ {k} ^ {t}\right) \quad \Delta \tilde {\mathcal {B}} _ {k} = \operatorname {C o n v B l o c k} \left(\tilde {\mathcal {H}} _ {k} ^ {s}\right) \tag {7} +$$ + +where $\tilde{\mathcal{C}}_k\in \mathbb{R}^{L\times H\times W\times m}$ denotes the temporal confidence scores for target in $L$ frames with $m$ the number of anchors at each position. $\Delta \tilde{\mathcal{B}}_k\in \mathbb{R}^{L\times H\times W\times 4m}$ is the offsets to the anchor boxes $\bar{B}$ , and target boxes $\tilde{\mathcal{B}}_k = \Delta \tilde{\mathcal{B}}_k + \bar{\mathcal{B}}$ . With $\tilde{\mathcal{C}}_k$ , the confidence score in each frame is determined by the highest classification score of anchors, and the target region is the box corresponding to the box with the highest classification score. This way, we can obtain the confidence scores + +![](images/0b0cfbe68871431805766285256426caf0f6b04c140a36bfd9f894d03739fb6e.jpg) +Figure 4. Illustration of appearance knowledge generation (AKG). + +$\bar{\mathcal{C}}_k$ and target regions $\bar{B}_k$ in each frames as follows, + +$$ +\bar {\mathcal {C}} _ {k} = \left\{c _ {k} ^ {i} \mid c _ {k} ^ {i}, d _ {k} ^ {i} = \operatorname {M a x} (\tilde {\mathcal {C}} _ {k} (i)) \right\} \tag {8} +$$ + +$$ +\tilde {\mathcal {B}} _ {k} = \left\{b _ {k} ^ {i} | b _ {k} ^ {i} = \operatorname {I n d e x} \left(\tilde {\mathcal {B}} _ {k} (i), d _ {k} ^ {i}\right) \right\} +$$ + +where $i\in [1,L]$ is the frame index. $c_k^i$ is the highest value selected from the classification scores $\tilde{\mathcal{C}}_k(i)\in \mathbb{R}^{H\times W\times m}$ of anchors in frame $i$ and $d_k^i$ is its index. $b_{k}^{i}$ is the target box corresponding to $c_k^i$ in frame, and extracted from $\tilde{\mathcal{B}}_k(i)\in$ $\mathbb{R}^{H\times W\times 4m}$ . $\mathrm{Max}(\cdot)$ is to select the maximum and its index, and Index $(\cdot)$ to extract the box from $\tilde{\mathcal{B}}_k(i)$ given its index. + +With $\bar{\mathcal{C}}_k\in \mathbb{R}^{L\times 1}$ and $\vec{B}_k\in \mathbb{R}^{L\times 4}$ , we first sample target regions with high confidence scores as follows, + +$$ +\mathcal {B} _ {k} = \operatorname {S a m p l e} \left(\bar {\mathcal {B}} _ {k} (i), \bar {\mathcal {C}} _ {k} (i), \tau\right) = \left\{\bar {\mathcal {B}} _ {k} (i) \mid \bar {\mathcal {C}} _ {k} (i) > \tau \right\} \tag {9} +$$ + +Then, we extract $n$ regions from $\mathcal{B}_k$ with the top confidence scores via $\mathcal{B}_k^{\mathrm{top}} = \mathrm{Top}_n(\mathcal{B}_k)$ . If the number of regions in $\mathcal{B}_k$ is less than $n$ , we keep all regions. After this, RoIAlign [11] is used to extract the appearance knowledge from $\mathcal{V}_k$ via + +$$ +\mathcal {K} _ {k} ^ {a} = \operatorname {R o I A l i g n} \left(\mathcal {V} _ {k}, \mathcal {B} _ {k} ^ {\text {t o p}}\right) \tag {10} +$$ + +where $\mathcal{K}_k^a$ represents the appearance knowledge from AKG in the $k^{\mathrm{th}}$ stage. Please notice that, in Eq. (10), we only perform RoIAlign in frames corresponding to $\mathcal{B}_k^{\mathrm{top}}$ . Since $\mathcal{K}_k^a$ is generated from the video itself, when using it as guidance to refine the query feature, we can reduce the discrepancy between the query and the foreground target. By deploying AKG in each but the last stage, $\mathcal{K}_k^a$ could be gradually improved with better refined query feature in each stage. Fig. 4 illustrates AKG for appearance knowledge generation. + +# 3.3. Spatial Knowledge Generation (SKG) + +In addition to appearance knowledge, we explore target spatial knowledge from the video for improving video features. Specifically, inspired by the observation that intermediate attention maps from previous attention operations reflect the spatial cues of target in each frame to some extent, similar to the concept of "saliency" but for the target, we propose the spatial knowledge generation (SKG) module, which works to leverage readily available attention maps as guidance for enhancing target while suppressing background in the video + +![](images/69e4a00710d5068f8af6bba2a083a4d4f3cf29d49b0ab44106bce29faafd5355.jpg) +Figure 5. Illustration of spatial knowledge generation (SKG). + +features, enabling more focus on the target in PRVQL. + +Concretely in our SKG, we exploit the target-aware spatial attention maps $S_{k}$ from cross-attention block in Eq. (1) and temporal-aware spatial attention maps $\mathcal{T}_k$ from masked self-attention block in Eq. (3) for spatial knowledge learning. Specifically, given $S_{k}$ and $\mathcal{T}_k$ , we first extract the interframe spatial attention maps $\mathcal{T}_k^{\mathrm{d}}$ by extracting diagonal elements from $\mathcal{T}_k$ as follows, + +$$ +\mathcal {T} _ {k} ^ {\mathrm {d}} = \phi_ {\operatorname {d i a g}} (\mathcal {T} _ {k}) = \left\{t _ {i} ^ {k} \right\} _ {i = 1} ^ {L} \tag {11} +$$ + +where $\phi_{\mathrm{diag}}$ denotes the operation to extract diagonal elects, and $t_i^k\in \mathbb{R}^{hw\times hw}$ represents the attention maps for frame $i$ . To match the spatial dimension of $\mathcal{T}_k^{\mathrm{d}}$ and $\mathcal{S}_k$ , we first perform bilinear interpolation on $\mathcal{T}_k^{\mathrm{d}}$ to increase its spatial resolution to $HW\times HW$ , and then combines these two attention maps to obtain spatial knowledge. Mathematically, this process can be expressed as follows, + +$$ +\mathcal {K} _ {k} ^ {s} = \alpha \cdot \varphi_ {\text {i n t}} \left(\mathcal {T} _ {k} ^ {\mathrm {d}}\right) + (1 - \alpha) \cdot \mathcal {S} _ {k} \tag {12} +$$ + +where $\varphi_{\mathrm{int}}$ denotes the bilinear interpolation operation, $\mathcal{K}_k^s$ is the target spatial knowledge, and $\alpha$ is a parameter to balance different attention maps. Since $\mathcal{K}_k^s$ indicates the target position cues in each frame in some degree, we can use it to highlight target while restraining background in videos for improving localization. Similar to AKG, SKG is deployed in each but the last stage of PRVQL. Fig. 5 illustrates SKG. + +# 3.4. Feature Refinement with Knowledge + +With target appearance knowledge $\mathcal{K}_k^a$ and spatial knowledge $\mathcal{K}_k^s$ obtained from AKG and SKG in stage $k$ ( $1 < k \leq K$ ), we then apply them as guidance to refine the query and video features through query feature refinement (QFR) and video feature refinement (VFR) modules. + +Query Feature Refinement (QFR). QFR aims to refine the query feature with guidance from learned target appearance knowledge. Specifically, it adopts a cross-attention block to fuse appearance knowledge $\mathcal{K}_k^a$ into the query. Given the query feature $\mathcal{Q}_k$ and appearance knowledge $\mathcal{K}_k^a$ in stage $k$ , we first apply a Conv block on $\mathcal{K}_k^a$ and then perform refine + +ment via QFR as follows, + +$$ +\mathcal {Q} _ {k + 1} = \mathrm {Q F R} \left(\mathcal {Q} _ {k}, \mathcal {K} _ {k} ^ {a}\right) = \operatorname {C A B} \left(\mathcal {Q} _ {k}, \operatorname {C N B} \left(\mathcal {K} _ {k} ^ {a}\right)\right) \tag {13} +$$ + +where $\mathcal{Q}_{k + 1}$ is refined query feature and fed to next stage for learning more accurate knowledge, which in turn leads to better query feature for localization in the final stage. It is worth noting that, besides cross-attention, we explore different strategies to combine $\mathcal{Q}_k$ and $\kappa_{k}^{a}$ , including addition and concatenation operations. We observe that using cross-attention achieves the best performance, as exhibited in our experiments provided in the supplementary material. + +Video Feature Refinement (VFR). VFR uses the target spatial knowledge to refine initial video feature by enhancing target while suppressing the background. Given the initial video feature $\mathcal{V}_1$ and learn spatial knowledge $\kappa_k^s$ in stage $k$ , we use residual connection to refine $\mathcal{V}_1$ as follows, + +$$ +\mathcal {V} _ {k + 1} = \beta \cdot \left(\mathcal {K} _ {k} ^ {s} \odot \mathcal {V} _ {1}\right) + (1 - \beta) \cdot \mathcal {V} _ {1} \tag {14} +$$ + +where $\nu_{k + 1}$ denotes the refined video feature that is used for the next stage, $\beta$ is a balancing parameter, and $\odot$ represents the pixel-wise multiplication. + +# 3.5. Optimization and Inference + +Optimization. Given a video and a visual query, we predict confidence scores $\tilde{\mathcal{C}}_k$ and target boxes $\tilde{\mathcal{B}}_k$ ( $\tilde{\mathcal{B}}_k = \Delta \tilde{\mathcal{B}}_k + \tilde{\mathcal{B}}$ ) in each stage $k$ ( $1 \leq k \leq K$ ). During training, given the groundtruth boxes $\mathcal{B}^*$ and temporal occurrence scores $\mathcal{S}^*$ , we design the following loss function $\mathcal{L}_k$ for stage $k$ , + +$$ +\mathcal {L} _ {k} = \mathcal {L} _ {\mathrm {L} _ {1}} \left(\tilde {\mathcal {B}} _ {k}, \mathcal {B} ^ {*}\right) + \lambda_ {1} \mathcal {L} _ {\mathrm {G I o U}} \left(\tilde {\mathcal {B}} _ {k}, \mathcal {B} ^ {*}\right) + \lambda_ {2} \mathcal {L} _ {\mathrm {B C E}} \left(\tilde {\mathcal {S}} _ {k}, \mathcal {S} ^ {*}\right) \tag {15} +$$ + +where $\mathcal{L}_{\mathrm{L}_1}$ , $\mathcal{L}_{\mathrm{GloU}}$ , and $\mathcal{L}_{\mathrm{BCE}}$ represent the $L_{1}$ loss, generalized IoU (GIoU) [24] loss, and binary cross-entropy (BCE) loss, respectively. $\lambda_{1}$ and $\lambda_{2}$ are two balancing parameters. With Eq. (15), the total training loss $\mathcal{L}_{\mathrm{total}}$ can be obtained via $\mathcal{L}_{\mathrm{total}} = \sum_{k=1}^{K} \mathcal{L}_k$ . Following [9, 14, 29], we perform hard negative mining during training to decrease false positive prediction. For details, please refer to [9, 14, 29]. + +Inference. We employ the same strategy as in [14] to obtain the prediction result. Specifically, during inference, we first obtain the target region in each frame by selecting target box with the highest confidence score. Please note that, the target regions with confidence scores smaller than a threshold, set to 0.79, will be discarded. After this, we select the most recent peak and generate a response track via bidirectional search from the peak. Details can be seen in [14]. + +# 4. Experiments + +Implementation. Our PRVQL is implemented using PyTorch [22]. Similar to [14], we apply the ViT [7] pretrained with DINOv2 [21] as the backbone. PRVQL is end-to-end trained for 50 epochs (60K iterations in total) with a batch size of 12, utilizing the AdamW optimizer [19] with a peak + +Table 1. Comparison on the Ego4D validation set. + +
MethodstAP25stAP25rec%Succ
STARK [ICCV'21]0.100.0412.4118.70
SiamRCNN [CVPR'22]0.220.1532.9243.24
NFM [VQ2D Challenge'22]0.260.1937.8847.90
CocoFormer [CVPR'23]0.260.1937.6747.68
VQLoC [NeurIPS'23]0.310.2247.0555.89
PRVQL (ours)0.350.2747.8757.93
+ +Table 2. Comparison on the Ego4D test set. + +
MethodstAP25stAP25rec%Succ
SiamRCNN [CVPR'22]0.210.1334.041.60
NFM [VQ2D Challenge'22]0.240.1736.3845.07
CocoFormer [CVPR'23]0.260.1843.2048.10
VQLoC [NeurIPS'23]0.320.2445.1155.88
PRVQL (ours)0.370.2845.7059.43
+ +Table 3. Comparison of speed on Ego4D. + +
STARKSiamRCNNNFMCocoFormerVQLoCPRVQL
FPS333333630
+ +learning rate of $10^{-4}$ and a weight decay of $5 \times 10^{-2}$ . The query image and video frames are resized to $480 \times 480$ . The number of stages $K$ in PRVQL is empirically set to 3, and the pooling size for RoIAign is 5. The number of selected boxes $n$ for appearance knowledge is 3, and the threshold $\tau$ is set to 0.7. The parameters $\alpha$ and $\beta$ are empirically set to 0.5 and 0.1. $\lambda_{1}$ and $\lambda_{2}$ are 0.3 and 100. The video frame length $L$ , similar to [14], is set to 30 with frames randomly selected to ensure coverage of at least a portion of the response track. For the anchor boxes in localization, we employ four scales $(16^{2}, 32^{2}, 64^{2}, 48^{2})$ with three different aspect ratios (0.5, 1, 2) for each anchor box, similar to [14]. + +# 4.1. Dataset and Evaluation Metrics + +Dataset. Following [14, 29], we conduct the experiments on Ego4D [9], a recently proposed large-scale dataset dedicated to first-person video understanding. Similar to [14], we use videos from the VQ2D task, with 13.6K, 4.5K, 4.4K pairs of queries and videos for training, validation, and test. + +Evaluation Metrics. Following [14, 29], we adopt the metrics provided by Ego4D [9] for evaluation, including temporal average precision $(\mathrm{tAP}_{25})$ , spatio-temporal average precision $(\mathrm{stAP}_{25})$ , recovery $(\mathrm{rec}\%)$ , and success (Succ). For more details of these metrics, please refer to [9]. + +# 4.2. State-of-the-art Comparison + +To verify the effectiveness of PRVQL, we compare it with other methods on Ego4D, including STARK [30], SiamR-CNN [26], NFM [28], CocoFormer [29], and VQLoC [14]. Tab. 1 displays results on the Ego4D validate test. As in Tab. 1, we can clearly see that PRVQL achieves the best performance on all four metrics. In particular, it achieves 0.35 + +![](images/5aa7f9fb83a280814285313d9994be18752efcb5eec8e674951cdfa8bd513703.jpg) + +![](images/92dadc553949ad8b769f26cb9ba91deef8bd29fa8a1ae890f380165cf295e20c.jpg) +visual query + +![](images/b61183a0f9e23670559911defa5b58f717ac8657a1f5b569acfa6b82254c5011.jpg) + +![](images/8c0e75ce4f0aa17550241bda72fc9dd150bf4961c709e5215d75f532576310b2.jpg) +Stage 1 + +![](images/63396fb698b3270c6f4c2015158ec73cc455ad746de95ea398218cb7a4de8278.jpg) + +![](images/2d511957ca26d49d1d7be84e70afaf72aee6e1f551d241cd0c62671fd61aa5bb.jpg) +Stage 2 +Figure 6. Visualization of refinement in different stages. The red bounding boxes indicate the groundtruth. + +![](images/12aba10ae34c0d2e954602a93bba662c455c7647a1e56dec22bdabf882a97d9b.jpg) + +![](images/432c86d6964cd955340559934ec4802c390bb97f02b91e0c826cffd319978acc.jpg) +Stage 3 + +Table 4. Ablation studies of AKG and SKG. + +
AKGSKGtAP25stAP25rec%Succ
1--0.320.2345.2455.37
2✓-0.340.2647.3457.27
3-✓0.330.2446.3356.46
4✓✓0.350.2747.8757.93
+ +Table 5. Ablation studies on the number of stages. + +
# StagestAP25stAP25rec%Succ
1K=10.320.2345.2455.37
2K=20.340.2747.2556.43
3K=30.350.2747.8757.93
4K=40.330.2645.9155.29
+ +$\mathrm{tAP}_{25}$ and $0.27 \, \mathrm{stAP}_{25}$ scores, which outperforms the second best VQLoC with $0.31 \, \mathrm{tAP}_{25}$ and $0.22 \, \mathrm{stAP}_{25}$ scores by $4\%$ and $5\%$ . Besides, the rec and Succ scores of PRVQL are $47.87\%$ and $57.93\%$ respectively, which surpasses the $47.05\%$ rec and $55.89 \, \mathrm{Succ}$ scores of VQLoC, evidencing its effectiveness. Besides, in Tab. 2, we further report the experimental results on Ego4D test set. As in Tab. 2, PRVQL again achieves the best results on all four metrics. Specifically, PRVQL obtains $0.37 \, \mathrm{tAP}_{25}$ and $0.28 \, \mathrm{stAP}_{25}$ scores. Compared to VQLoC, our approach shows gains of $5\%$ and $4\%$ , respectively, on $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ . All these show the efficacy of target knowledge in improving EgoVQL. + +Moreover, we show the speed, measured by frames per second (FPS), for different methods in Tab. 3. PRVQL runs fast at 30 FPS. Despite being slightly slower than VQLoC running at 36 FPS, PRVQL is more robust in localization, showing a better balance between accuracy and speed. + +# 4.3. Analysis of Refinement by Multiple Stages + +Our PRVQL improves the localization performance through multiple stages of refinement guided with target knowledge. In Fig. 6, we show the attention maps of the visual query from different stages of PRVQL in the video frame. From Fig. 6, we can clearly see that, the attention maps are gradually focused on the target regions via refinement in multiple stages and benefit better target localization, which evidences the effectiveness of our PRVQL. + +Table 6. Ablation studies on the threshold $\tau$ . + +
ThresholdtAP25stAP25rec%Succ
1τ = 0.60.320.2444.8255.97
2τ = 0.70.350.2747.8757.93
3τ = 0.80.340.2646.5357.33
+ +Table 7. Ablation studies on the number of target boxes in AKG. + +
tAP25stAP25rec%Succ
1n = 20.340.2647.2756.03
2n = 30.350.2747.8757.93
3n = 40.360.2646.5957.62
4n = 50.350.2446.8456.95
+ +Table 8. Ablation studies on RoIAlign feature size. + +
SizetAP25stAP25rec%Succ
130.330.2646.9456.06
250.350.2747.8757.93
370.340.2747.5857.38
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+ +# 4.4. Ablation Study + +For better understanding of PRVQL, we conduct extensive ablation studies on Ego4D validation set as follows. + +Impact of AKG and SKG. AKG and SKG are two key modules in PRVQL for knowledge generation. To analyze these two modules, we conduct thorough ablation studies in Tab. 4. From Tab. 4, we can see that, without AKG and SKG, the $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ scores are 0.32 and 0.23, respectively (1). By applying AKG alone for refinement with appearance knowledge, they are significantly improved to 0.34 and 0.26 with performance gains of 0.02 and 0.03 (2 v.s. 1). When using only SKG for refinement with spatial knowledge, $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ are improved to 0.33 and 0.24 (3 v.s. 1). From this table, we also observe that, using appearance knowledge for refinement in PRVQL brings more gains than the spatial knowledge (2 v.s. 3). When using both AKG and SKG in our PRVQL, we achieve the best performance with 0.35 $\mathrm{tAP}_{25}$ and 0.27 $\mathrm{stAP}_{25}$ scores (4 v.s. 1), which clearly evidences the efficacy of target knowledge for improving the robustness of EgoVQL. + +Impact of the number of stages. PRVQL is a progressive architecture with $K$ stages to explore the target knowledge for refinement. We conduct an ablation study on $K$ in PRVQL in Tab. 5. From Tab. 5, we observe that, when setting $K = 1$ , which means only one stage is used and the target knowledge is not used due to one-stage design, the $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ scores are 0.32 and 0.23 (1). When adding the second stage, $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ are largely improved by $2\%$ and $4\%$ to 0.34 and 0.27, respectively (2). With three stages, the $\mathrm{tAP}_{25}$ and $\mathrm{stAP}_{25}$ scores are further boosted to 0.35 and 0.27 (3). When setting $K = 4$ with 4 stages, the performance is decreased with 0.33 $\mathrm{tAP}_{25}$ and + +![](images/05ff5abcee8c70232912c3c95a08c6c49c888a3aab1166cfbdae724c3c58f7dc.jpg) +Figure 7. Qualitative analysis and comparison between our PRVQL and state-of-the-art VQLoC in representative videos with different challenges. We observe that, owing to our target knowledge from videos, PRVQL can more robustly localize the target of interest. + +$0.26\mathrm{stAP}_{25}$ scores (4). Hence, we set $K$ to 3 in PRVQL. + +Impact of threshold $\tau$ in AKG. The threshold $\tau$ is used to filter out less confident target regions in AKG, aiming to avoid noisy features in appearance knowledge generation. In this work, we conduct an ablation to study the impact of $\tau$ on the final performance in Tab. 6. As shown in Tab. 6, we can see that, when setting $\tau$ to 0.7, PRVQL achieves the best performance on all four metrics (2). + +Impact of number of target boxes in AKG. In AKG, we extract visual features from the top $n$ highly confident target regions for appearance knowledge generation. We conduct an ablation on $n$ in Tab. 7. From Tab. 7, we can observe that, when using the top 3 target regions for knowledge learning in AKG, we achieve the best overall performance (2). + +Impact of RoIAlign Feature Size. With the top $n$ selected target regions, we perform the RoIAlign operation [11] to obtain target appearance knowledge. The RoIAlign feature size may have an impact on the target appearance knowledge. A too small size may result in the coarse spatial information of the target, while a too large size may lead to losing discriminative local features for the target, both degrading performance. In this work, we study different RoIAlign feature sizes in Tab. 8. As shown, when setting the size to 5 in RoIAlign, PRVQL shows the best overall performance. + +# 4.5. Qualitative Analysis + +To provide further analysis of our PRVQL, we show the visualization results of its localization and compare it with VQLoC in Fig. 7. Specifically, we show results on several representative videos, including video in (a) with pose variation, video in (b) with cluttering background and out-of-view, video in (c) with occlusion and low resolution, video + +in (d) with pose variation and cluttering background, and video in (e) with motion blur and distractor. From Fig. 7, we can see that, our method can robustly and accurately localize the target in all these challenges, owing to the help of target knowledge from videos, while VQLoC is prone to drift to the background due to lack of discriminative target information, evidencing the effectiveness of our method. + +Due to limited space, we demonstrate more results, analysis, and ablation studies in the supplementary material. + +# 5. Conclusion + +In this paper, we present a multi-stage architecture, dubbed PRVQL, for improving EgoVQL via exploring the target knowledge to refine features for robust localization. In each stage, two key modules, including AKG and SKG, are used to extract target appearance and spatial knowledge from the video. The knowledge from one stage is used as guidance to refine query and video features in the next stage, which are adopted for learning more accurate knowledge for further refinement. Through this progressive process, PRVQL learns gradually improved knowledge, which in turn leads to better refined features for localization in the final stage. Our experiments on Ego4D show that PRVQL achieves promising results and largely surpasses other methods. + +Acknowledgment. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of U.S. Naval Research Laboratory (NRL) or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. + +# References + +[1] Luca Bertinetto, Jack Valmadre, Joao F Henriques, Andrea Vedaldi, and Philip HS Torr. Fully-convolutional siamese networks for object tracking. In ECCVW, 2016. 2 +[2] Zhaowei Cai and Nuno Vasconcelos. Cascade r-cnn: Delving into high quality object detection. In CVPR, 2018. 3 +[3] Shuhan Chen and Yun Fu. Progressively guided alternate refinement network for rgb-d salient object detection. In ECCV, 2020. 3 +[4] Xin Chen, Houwen Peng, Dong Wang, Huchuan Lu, and Han Hu. Seqtrack: Sequence to sequence learning for visual object tracking. 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Progressive pose attention transfer for person image generation. 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Despite its importance in real-world applications, human pose sequence refinement has received less attention than human pose estimation. In this paper, we propose PS-Mamba, a novel framework that refines human pose sequences by integrating spatial-temporal graph learning with state space modeling. Specifically, we introduce the Spatial-Temporal Graph State Space (STGSS) block, which captures spatial and temporal dependencies across joints to smooth pose sequences while preserving structural integrity. The spatial-temporal graph learns intricate joint interactions, while the state space component effectively manages temporal dynamics, reducing both short- and long-term pose instability. Besides, we incorporate a dynamic graph weight matrix to adaptively model the relative influence of joint interactions, further mitigating pose ambiguity. Experiments on challenging benchmarks show that our PS-Mamba outperforms SOTAs, achieving $-14.21\mathrm{mm}$ MPJPE $(+18.5\% \uparrow)$ , $-13.59\mathrm{mm}$ PA-MPJPE $(+22.1\% \uparrow)$ , and $-0.42\mathrm{mm} / s^2$ ACCEL $(+9.7\% \uparrow)$ compared to SynSP on AIST++, significantly reducing jitters and enhancing pose stability. The code is available at https://github.com/donghaoye/ps-mamba. + +# 1. Introduction + +Human pose sequence refinement focuses on improving the smoothness of pose estimation across frames. It is essential for applications such as animation and virtual reality [4, 10-14, 28, 33, 55-59, 67], where stable and realistic motion is crucial. However, traditional image-based estimators [16, 17, 21, 24, 27, 35, 36, 43-45] often produce jittery outputs due to the frame-by-frame processing, which lacks temporal coherence. To address this limitation, video-based methods [6, 25, 26, 29, 42, 46, 54, 68] incorporate temporal information to improve stability. Despite these efforts, human pose estimations still show inconsistencies, highlighting the need for dedicated refinement techniques. This has + +![](images/6b5178b1ac6d5d8dab9abfd1d856a2f81af5f54508714577e3a42f503ad2efbd.jpg) + +![](images/f1279ef0b357a9ca37d93ed5be463f1ef0d790366dae7460e56097ba82a7beb3.jpg) +Figure 1. (a) PA-MPJPE and MPJPE results after human pose refinement on the AIST++ [32], all initialized by VIBE [25], show that our PS-Mamba significantly reduces ambiguity and outperforms existing refinements in improving pose accuracy. (b) The acceleration error on the Human3.6M [23] shows that we achieve best performance in the denoising task, with the lowest acceleration error and enhancing smoothness across varying noise levels. + +led to recent efforts to establish human pose sequence refinement as a distinct research task [9, 52, 66]. + +Recent methods for human pose sequence refinement, such as SmoothNet [66] focused solely on temporal refinement, capturing temporal relationships for each joint independently. Although this approach effectively reduced jitter, it does not fully resolve pose ambiguity. SynSP [52] extended human pose sequence refinement to a multi-view set- + +ting by learning a synergy between smoothness and precision, mitigating ambiguity through the integration of similar poses across views. MoManifold [9] leveraged a neural distance field combined with a joint acceleration manifold to model high-dimensional motion dynamics, improving the naturalness of pose sequences. However, these existing refinement models overlook the preservation of intrinsic spatial relationships and struggle to fully capture the dynamics of pose sequences, making it difficult to reduce jitter and ambiguity. As a result, they remain limited in their ability to adapt to dynamic temporal variations and achieve smooth, jitter-free pose sequences in practical scenarios. + +To address those challenges, we present PS-Mamba, a novel spatial-temporal graph-guided Mamba framework that integrates spatial-temporal graph learning (ST-GCN) [61] with selective state space modeling (Mamba) [18] to achieve accurate and dynamic temporal coherent human pose sequences. We propose a Spatial-Temporal Graph State Space (ST-GSS) block to model dynamic joint relationships between joints across frames, leveraging temporal dependencies to enhance motion coherence. Our ST-GSS consists of two key components: ST-Graph (Spatial-Temporal Graph network) and ST-SSM (Spatial-Temporal State Space Modeling). The ST-Graph aims to learn the spatial relationships with human pose graphs, while ST-SSM utilizes GST-Scanning (Graph-guided Spatial-Temporal Scanning) to improve smoothness through graph-guided state space modeling. We also apply a dynamic graph weight matrix that learns the relative influence of edges in the human pose graph, enabling the model to adaptively learn intrinsic relationships between joints. The proposed PS-Mamba is the first framework to integrate spatial-temporal graph learning and state space modeling for pose sequence refinement. As illustrated in Figure 1, the proposed PS-Mamba achieves SOTA performance in the human pose sequence refinement task, significantly improving both accuracy and smoothness. + +We summarize the contributions as follows: + +- Our PS-Mamba is the first to incorporate spatial-temporal graph learning with Mamba for the human pose sequence refinement task. +- We design an effective ST-GSS block that captures spatial-temporal relationships across frames to improve motion coherence and reduce jitter artifacts. +- We introduce a dynamic graph weight matrix that learns the relative impacts of edges, adaptively capturing intrinsic spatial relationships between joints. +- Extensive experiments on challenging benchmarks validate the effectiveness of PS-Mamba, demonstrating its consistent improvement over SOTAs in refining human pose sequences with reduced jitter and ambiguity. + +# 2. Related Work + +Human Pose Sequence Refinement. Several human pose sequence refinements [9, 52, 66] have been proposed recently. SmoothNet [66] reduced jitter by using temporally-only features with few full connections. SynSP [52] refined pose sequences by balancing smoothness and precision. MoManifold [9] used neural distance fields and joint acceleration manifolds for refinement. KITRO [62] introduced a mesh refinement using human kinematic tree structures and bone directions. HiMoReNet [53] refined pose sequences with a hierarchical neural network that distinguishes motion patterns across joint groups. D3PRefiner [60] used a diffusion-based method with a Gaussian distribution to reduce noise. Energy-based method [49] smoothed pose trajectories by filtering noise during occlusions. However, they overlooked joint graph relationships in the temporal context. We address this by incorporating state space modeling with graph learning to refine human pose sequences. + +Physical-based Pose Refinement. PhysDiff [65] used a physics-guided motion diffusion model to prevent floating and penetration artifacts but increased computation time and required ground and contact labels. The dynamics-regulated method [38] integrated kinematics, dynamics, and scene object data for object-aware 3D egocentric pose estimation, but required first-person view data with object interactions. DAMP [63] introduced a meta-algorithm for five pose estimation tasks, leveraging primitive alignment and rigid body dynamics, but it is not tailored for human pose sequence refinement. These methods relied on additional constraints such as physics simulation, object interactions, or rigid body dynamics, limiting their ability to resolve jitter and ambiguity when only pose sequences are available. + +State Space Modeling. Mamba [18] is a selective state space model that removes attention, enabling efficient scaling and faster inference. STG-Mamba [31] integrated Mamba with graph learning via Kalman Filtering GNNs, focusing solely on the traditional graph learning task. Graph-Mamba [51] introduced input-dependent node selection for improving long-range modeling with lower computational costs. VideoMamba [30] optimized Mamba for video understanding by handling local redundancy and global dependencies. GMNs [1] applied Mamba to GNNs without complex message passing or positional encodings. PoseMamba [22] replaced self-attention with a graph-based Mamba block for 2D-to-3D lifting. Hamba [15] improved 3D hand reconstruction by modeling joint sequence relations with graph and SSMs. MV-SSM [5] leveraged state space models to estimate 3D human poses in multi-view scenarios. However, none of these methods focus on human pose sequence refinement. We are the first to integrate spatial-temporal graphs with state space modeling for this task, effectively addressing jitter and reducing ambiguity. + +![](images/6cf58c38225604c09595034d7162244a705aac8c0fc963cd6f92fca4dc488840.jpg) +Figure 2. Architecture of our PS-Mamba. Our framework can take 2D, 3D, or SMPL representation as input, and generate structurally coherent pose sequences in the respective representation. Our model consists of two main modules: ST-Graph (Spatial-Temporal Graph network) and ST-SSM (Spatial-Temporal State Space Modeling). ST-Graph aims to learn the joint relationship with a dynamic graph weight matrix $\mathbf{W}$ of the pose skeleton graph. ST-SSM leverages GST-Scanning (Graph-guided Spatial-Temporal Scanning) to enhance the smoothness via state space modeling. ST-Graph and ST-SSM collaboratively improve the model's accuracy and stability. + +# 3. Our Proposed Method + +We present PS-Mamba, a novel framework to refine human pose sequences by integrating spatial-temporal graph learning and Mamba. We first define the task in Section 3.1, provide the motivation in Section 3.2, and outline the preliminaries in Section 3.3. Next, we describe the model architecture in Section 3.4. We then provide a detailed clarification of the ST-GSS in Section 3.5, including the ST-Graph, STSSM, and the dynamic graph weight matrix $W$ . Finally, we introduce the loss functions in Section 3.6. + +# 3.1. Problem Formulation + +Given a human pose sequence $\mathbf{Q} = \{\mathbf{Q}_1, \mathbf{Q}_2, \dots, \mathbf{Q}_t\}$ , our objective is to model a transformation that enhances structural coherence, temporal consistency, and kinematic plausibility in $\mathbf{Q}$ . To this end, we learn a function $f(\mathbf{Q}) \in \mathbb{R}^{B \times T \times J \times D}$ that constructs an optimized pose sequence representation while preserving natural motion dynamics. Here, $B, T, J,$ and $D$ denote batch size, temporal window size (in frames), number of joints, and joint dimensions. + +# 3.2. Why Mamba? + +Learning a function to construct an optimized pose sequence representation while preserving natural motion dynamics is challenging due to persistent jitter and ambiguity in the given human pose sequence. While video-based pose estimation methods [6, 25, 26, 29, 42, 46, 54, 68] leverage + +![](images/3cfe75d756bf822850e80926033cf16b71285f6657ad01fa53587aabd8021af5.jpg) +(a) ST-Scanning + +![](images/543460b0cad914c279f988c5d10802017f0aa359584b1d0461d7fb80f783ed8d.jpg) +(b) GST-Scanning (Ours) +Figure 3. Motivation. (a) Traditional ST-Scanning (Spatial-Temporal Scanning) [18] involves redundant tokens, failing to capture the dependencies between joints. (b) Our GST-Scanning (Graph-guided Spatial-Temporal Scanning), under the guidance of the human joint relationship graph, effectively captures joint dependencies while preserving temporal coherence. + +temporal data to reduce jitter, they often overlook spatial relationships between joints, which are crucial for resolving ambiguity. Existing approaches [9, 52, 66] partially mitigate jitter, as they neglect spatial joint dependencies across frames, leading to unsatisfactory results. + +We integrate Mamba [18] with spatial-temporal graph learning [61] to address these limitations by combining long-range temporal modeling with an understanding of joint graph dependencies. The spatial-temporal graph captures spatial relationships between joints, reducing ambiguity, while the state space modeling of Mamba [18] han + +dles temporal dynamics, effectively smoothing sequences for coherent motion. This combination makes Mamba [18] ideal for refining pose sequences by enhancing temporal stability and preserving joint-structural accuracy across frames. Specifically, we design the ST-GSS block with a Graph-guided Spatial-Temporal Scanning (GST-Scanning), leveraging the capability of Mamba [18] to capture temporal dependencies while dynamically focusing on key joint interactions through graph learning, as illustrated in Figure 3. + +# 3.3. Preliminaries + +State Space Models. Mamba [18] is a Selective SSM, which has shown exceptional capability in managing sequences, transforming the input sequence $x(t) \in \mathbb{R}$ into the output sequence $y(t) \in \mathbb{R}$ via the latent state representation $h(t) \in \mathbb{R}^N$ utilizing ordinary linear differential equations: + +$$ +h ^ {\prime} (t) = \boldsymbol {A} h (t) + \boldsymbol {B} x (t), \quad y (t) = \boldsymbol {C} h (t) + D x (t), \tag {1} +$$ + +where parameters $\mathbf{A} \in \mathbb{R}^{N \times N}$ , $\mathbf{B} \in \mathbb{R}^{N \times 1}$ , $\mathbf{C} \in \mathbb{R}^{1 \times N}$ and $D \in \mathbb{R}^1$ define the dynamics of the transformation to learn temporal dependencies in the joint sequence. + +$$ +h _ {t} = \bar {\boldsymbol {A}} h _ {t - 1} + \bar {\boldsymbol {B}} x _ {t}, \quad y _ {t} = \boldsymbol {C} h (t), \tag {2} +$$ + +where + +$$ +\begin{array}{l} \overline {{\boldsymbol {A}}} = \exp (\Delta \boldsymbol {A}), \\ \overline {{\boldsymbol {\mathbb {R}}}} = (A A) ^ {- 1} (A A) ^ {- 1} A B. \end{array} \tag {3} +$$ + +$$ +\overline {{\boldsymbol {B}}} = (\Delta \boldsymbol {A}) ^ {- 1} (\exp (\Delta \boldsymbol {A}) - \boldsymbol {I}) \cdot \Delta \boldsymbol {B}, +$$ + +are the discretization of the continuous dynamical systems in Eq. 2, utilizing the zero-order hold discretization, and $\Delta$ denotes the discrete step size. S4 [19] is a linear time-invariant model, while Mamba [18] extends it via selective scanning to capture the full sequence. + +# 3.4. Model Architecture + +In Figure 2, given a human pose sequence $Q$ initialized by off-the-shelf models, we first pass it through an encoder to extract high-dimensional features. We then design $N$ Spatial-Temporal Graph State Space (ST-GSS) blocks to process these features, where each block contains the Spatial-Temporal Graph network (ST-Graph) and the Spatial-Temporal State Space Model (ST-SSM) with a residual skip connection. The ST-Graph consists of a Graph Convolutional Network (GCN), a dynamic graph weight matrix $W$ , and a Temporal Convolutional Network (TCN). Our ST-GSS employs a Graph-guided Spatial-Temporal Scanning strategy (GST-Scanning) to construct four bidirectional spatial-temporal scanning sequences, which are then passed through the SSM [18, 37]. The feature sequences are passed through Layer Normalization (LN), a Linear layer, and a Feed-Forward Network (FFN). We combine the joint pose features from the ST-SSM with those from the ST-Graph to enhance overall model performance. Finally, the combined features are fed into a decoder to produce the refined human pose sequences $\hat{Q}$ . + +# 3.5. ST-GSS Block + +We first introduce the ST-Graph, explaining how graph-based approaches effectively capture the spatial relationships between joints using a dynamic weight matrix $W$ . We then present the ST-SSM, providing a detailed explanation of state space modeling to enhance human pose refinement. + +# 3.5.1. ST-Graph + +We leverage a tailored version of ST-GCN [61], transforming its original classification focus to model joint-level spatial-temporal dynamics. To this end, we first define the initial representation of the human pose graph as follows: + +$$ +\boldsymbol {G} _ {\text {p o s e}} = \left(\boldsymbol {V} _ {\text {j o i n t}}, \boldsymbol {E} _ {\text {s p a t i a l}}, \boldsymbol {E} _ {\text {t e m p o r a l}}\right), \tag {4} +$$ + +where + +$$ +\boldsymbol {V} _ {\text {j o i n t}} = \left\{\boldsymbol {h} _ {v _ {i}} \right\} _ {i = 1} ^ {V}, \tag {5a} +$$ + +$$ +\boldsymbol {E} _ {\text {s p a t i a l}} = \left\{\left(\boldsymbol {h} _ {v _ {i}}, \boldsymbol {h} _ {v _ {l}}\right) \mid \left(v _ {i}, v _ {l}\right) \in \mathcal {P} \right\}, \tag {5b} +$$ + +$$ +\boldsymbol {E} _ {\text {t e m p o r a l}} = \left\{\left(\boldsymbol {h} _ {v _ {i}} ^ {t - 1}, \boldsymbol {h} _ {v _ {i}} ^ {t}\right) \right\} _ {i = 1, t = 2} ^ {V, T}. \tag {5c} +$$ + +Here, $V_{\mathrm{joint}}$ represents the set of joints, $E_{\mathrm{spatial}}$ is the spatial edges that connect neighboring joints according to the structure of the human pose $\mathcal{P}$ , and $E_{\mathrm{temporal}}$ denotes the temporal edges that link the joints across frames. Additionally, $h_{v_i} \in R^{C \times T}$ represents the features of joint $v_i$ , with $C$ as the feature channel number and $T$ as the temporal frame number. We denote $F_{\mathrm{in}}$ as the input joint features for the ST-Graph, which are also obtained from the encoder. The output features are computed as: + +$$ +\boldsymbol {F} _ {\text {o u t}} = \sum_ {i} ^ {n} \boldsymbol {\Lambda} _ {i} ^ {- \frac {1}{2}} \boldsymbol {A} _ {i} \boldsymbol {\Lambda} _ {i} ^ {- \frac {1}{2}} \boldsymbol {F} _ {\text {i n}}, \tag {6} +$$ + +where $\Lambda_i^{jj} = \sum_k(A_i^{jk}) + \alpha$ . We set $\alpha = 0.001$ to mitigate the issue of empty rows. $n$ denotes the number of adjacency matrices. We set four ST-GSS blocks and one adjacency matrix per block ( $n = 4$ ). $A_i^{jk}$ indicates if joint $h_{v_k}$ is included in the spatial sampling subset of joint $h_{v_j}$ . + +Dynamic Graph Weight Matrix $W$ . For human pose estimation, jitter and ambiguity are common challenges. To address these issues, we follow [61] to introduce a learnable graph weight matrix $W$ for the model to dynamically adjust the connectivity between joints in the spatial-temporal space. This facilitates the preservation of consistent spatial relationships between pose joints across frames. Since joints can appear across different frames and body parts with varying influence, the learnable matrix $W$ at each layer modulates the influence of the feature of a joint on its neighboring joints. The formulation is as follows: + +$$ +\hat {\boldsymbol {F}} _ {\text {o u t}} = \sum_ {i} ^ {n} \boldsymbol {F} _ {\text {o u t}} \boldsymbol {W} _ {i}, \tag {7} +$$ + +where $n$ denotes the number of adjacency matrices, and $W_{i}$ represents the weight of the $i$ -th adjacency matrix. + +# 3.5.2. ST-SSM + +Mamba [18] was initially designed to operate on one-dimensional sequential data. Although [34, 37] and [1, 51] have applied the Mamba to 2D/3D tasks and graph learning, respectively, its potential for Mamba- and graph-based human pose sequence refinement remains largely unexplored. We thus propose a GST-Scanning technique for spatial-temporal data with graph-guided bidirectional scanning. Using GST-Scanning, our approach effectively learns the joint relationship within pose sequences. + +The graph features $\pmb{F}$ from ST-Graph are fed into the STSSM block, which contains $N$ SSM blocks to enhance the features. As shown in Figure 2, each ST-SSM block applies layer normalization (LN), residual connections, depth-wise convolution [7] (DW), and SS2D. The detailed architecture of the ST-SSM block is illustrated at the bottom of Figure 2, and is formulated as follows: + +$$ +\begin{array}{l} \boldsymbol {F} _ {i - 1} ^ {\prime} = \operatorname {L N} \left(\boldsymbol {F} _ {i - 1}\right), \\ \boldsymbol {F} _ {i - 1} ^ {\prime \prime} = \sigma \left(\mathrm {D W} \left(\operatorname {L i n e a r} \left(\boldsymbol {F} _ {i - 1} ^ {\prime}\right)\right)\right), \\ \boldsymbol {F} _ {i} ^ {\prime \prime} = \operatorname {L i n e a r} \left(\operatorname {L N} \left(\operatorname {S S 2 D} \left(\boldsymbol {F} _ {i - 1} ^ {\prime \prime}\right)\right)\right), \tag {8} \\ \boldsymbol {F} _ {i} ^ {\prime} = \boldsymbol {F} _ {i} ^ {\prime \prime} + \boldsymbol {F} _ {i - 1}, \\ \boldsymbol {F} _ {i} = \operatorname {F F N} \left(\operatorname {L N} \left(\boldsymbol {F} _ {i} ^ {\prime}\right)\right) + \boldsymbol {F} _ {i} ^ {\prime}, \\ \end{array} +$$ + +where $F_{i}$ is the output of the $i$ -th block, and $\sigma$ represents the SiLU activation [20]. SiLU enables stable training and better gradient flow via smooth, non-monotonic activation. The SS2D component is a 2D-Selective-Scan (SS2D) module [37] designed to adapt Mamba [18] to vision data. It enables every pixel to gather contextual cues from all directions, forming comprehensive global awareness across the entire 2D space. The "2D space" refers to the spatial-temporal map we construct by flattening pose dimensions (e.g., joints × channels) across time steps, treating each joint-channel pair at a given time as a "pixel". This allows SS2D to operate effectively on poses. We apply this strategy to capture the spatial-temporal relationships in human pose sequences. + +# 3.6. Loss Functions + +The objective of PS-Mamba is to reduce MPJPE [23], PA-MPJPE [24], and acceleration error [66]. We define the MPJPE and PA-MPJPE loss functions as follows: + +$$ +\mathcal {L} _ {\mathrm {m p j p e}} = \frac {1}{T \times J} \sum_ {t = 1} ^ {T} \sum_ {i = 1} ^ {J} \| Q _ {(t, i)} - \hat {Q} _ {(t, i)} \| _ {2}, \tag {9} +$$ + +$$ +\mathcal {L} _ {\mathrm {p a - m p j p e}} = \frac {1}{T \times J} \sum_ {t = 1} ^ {T} \sum_ {i = 1} ^ {J} \| Q _ {(t, i)} - \mathbf {P} (\hat {Q} _ {(t, i)}) \| _ {2}, \tag {10} +$$ + +where $Q_{(t,i)}$ denotes the ground truth joint positions at time $t$ for joint $i$ , and $\hat{Q}_{(t,i)}$ denotes the predicted joint $i$ positions at time $t$ , and $J$ is the joint number. $\mathbf{P}$ function denotes ProcrustesAlign, which adjusts the estimated + +poses for PA-MPJPE by removing differences in scale, rotation, and translation, ensuring that the estimated poses align more accurately with ground truth joints. We define the acceleration as follows: + +$$ +\mathcal {L} _ {\text {a c c e l}} = \frac {1}{(T - 2) \times J} \sum_ {t = 1} ^ {T - 2} \sum_ {i = 1} ^ {J} \left| M _ {(t, i)} - \hat {M} _ {(t, i)} \right|, \tag {11} +$$ + +where $M(t,i)$ and $\hat{M}(t,i)$ denote ground truth data and predicted accelerations, respectively. The acceleration is computed as: + +$$ +\boldsymbol {M} _ {(t, i)} = \left(\boldsymbol {Q} _ {(t + 2, i)} - \boldsymbol {Q} _ {(t + 1, i)}\right) - \left(\boldsymbol {Q} _ {(t + 1, i)} - \boldsymbol {Q} _ {(t, i)}\right), \tag {12} +$$ + +where $Q_{(t,i)}$ denotes the joint positions at time $t$ for joint $i$ . + +We train PS-Mamba using a combined loss function that consists of the MPJPE loss $\mathcal{L}_{\mathrm{mpjpe}}$ , PA-MPJPE loss $\mathcal{L}_{\mathrm{pa - mpjpe}}$ , and acceleration loss $\mathcal{L}_{\mathrm{accel}}$ . The total loss $\mathcal{L}_{\mathrm{total}}$ is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {\mathrm {m p j p e}} \mathcal {L} _ {\mathrm {m p j p e}} + \lambda_ {\mathrm {p a - m p j p e}} \mathcal {L} _ {\mathrm {p a - m p j p e}} + \lambda_ {\text {a c c e l}} \mathcal {L} _ {\text {a c c e l}}, \tag {13} +$$ + +where $\lambda_{\mathrm{mpjpe}}$ , $\lambda_{\mathrm{pa - mpjpe}}$ , and $\lambda_{\mathrm{accel}}$ represent the weights assigned to each loss term, respectively. + +# 4. Experiments + +# 4.1. Experiment Settings + +Datasets. We conduct experiments using four benchmark datasets: Human3.6M [23], 3DPW [50], AIST++ [32, 47] and CMU-Mocap [48]. These datasets are preprocessed using SmoothNet [66], which includes outputs from various SOTA pose estimation models. For the denoising task, we follow the approach in [8, 52] to simulate noisy for input poses on Human3.6M [23] and CMU-Mocap [48]. + +Implementation Details. The learning rate is set to 0.001, the batch size to 128, and the window size to either 8 or 32. All models were trained on an NVIDIA RTX A6000 GPU. + +Evaluation Metrics. To evaluate the generalizability of PS-Mamba, we perform experiments in all three representations of human poses (2D, 3D, and SMPL). We follow the evaluation protocol of [66]. This includes MPJPE [23], PA-MPJPE [2, 24], and Acceleration error (Accel) [25]. + +# 4.2. Comparison in Different Representations + +SmoothNet [66] conducted experiments with a window size of 32, while SynSP [52] did not achieve better results at this setting (see analysis for this limitation in Table 3 of the SynSP [52] supplementary). Since SynSP [52] had no publicly available code by the submission deadline, we reproduced their method based on the paper's descriptions and evaluated it with a window size of 32. The results for a window size of 8 and multi-view experiments are taken directly from their paper. For a fair comparison, we conduct + +
MethodWSHuman3.6M / 2DHuman3.6M / 3DAIST++ / SMPL
MPJPE↓PA-MPJPE↓Accel↓MPJPE↓PA-MPJPE↓Accel↓MPJPE↓PA-MPJPE↓Accel↓
InputN/A9.427.641.5454.5542.2019.17107.7274.4033.20
One-Euro [3]110.697.980.3455.2042.733.80108.9775.2714.70
Gaussian1d [64]329.377.560.5153.6741.602.43104.8472.1810.05
Savitzky-Golay [40]329.357.550.1753.4841.191.34104.5872.306.07
SmoothNet [66] (ECCV22)329.257.570.1552.7240.921.03103.0071.195.72
SynSP†[52] (CVPR24)3212.726.690.8262.8648.110.9689.8463.687.42
PS-Mamba (Ours)327.315.740.1449.6038.360.9274.0452.985.51
SynSP [52] (CVPR24)88.136.090.1551.3640.131.0284.6359.026.08
PS-Mamba (Ours)87.525.860.1551.2239.631.7272.5452.956.88
SynSP [52] (MV, CVPR24)87.625.640.1541.7833.320.98---
PS-Mamba (MV, Ours)86.904.530.1628.6321.831.0---
+ +Table 1. Comparison with SOTAs on Human3.6M / 2D, Human3.6M / 3D, and AIST++ / SMPL, respectively. WS means window size. MV denotes Multi-View. Results with $\dagger$ are reproduced from the original paper. + +![](images/7b9d3dec6d899d7dad2da1740073463033d6024ecce6deb1d8b86f84486325e9.jpg) +Figure 4. Qualitative comparisons on Human3.6M [23]. Our PS-Mamba achieves accurate 3D poses, initialized by FCN [39], particularly in ambiguous or occluded scenarios. + +experiments with both window sizes (8 and 32) and follow SynSP's setup for multi-view evaluations. Table 1 presents quantitative comparisons with SOTAs on Human3.6M [23] and AIST++ [32, 47] datasets. Figure 5 demonstrates that our PS-Mamba achieves more accurate pose refinement than SynSP [52]. These results collectively validate the effectiveness of our PS-Mamba across 2D, 3D, and SMPL. + +2D Representation. As shown in Table 1, with a window size of 8, PS-Mamba achieves $7.52\mathrm{mm}$ MPJPE and 5.86 mm PA-MPJPE on the "Human3.6M / 2D" column, outperforming SynSP [52] (8.13 mm MPJPE). In the multi-view setting, PS-Mamba achieves the lowest MPJPE and PA-MPJPE, demonstrating minimal jitter and superior smoothness in 2D human pose sequences. + +3D Representation. As shown in the "Human3.6M / 3D" column of Table 1, our PS-Mamba achieves the lowest MPJPE of $28.63\mathrm{mm}$ and PA-MPJPE of $21.83\mathrm{mm}$ in the multi-view setting. In the single-view setting, it also achieves competitive MPJPE and PA-MPJPE. Our PS- + +![](images/1c7bf698630374cbbc1fa51f4ea553e65df3b3882656bd81de83be4251170e97.jpg) +Figure 5. Qualitative comparisons on AIST++ [32, 47]. Our PS-Mamba achieves accurate 3D mesh and outperforms SynSP [52] and SmoothNet [66], all initialized by SPIN [27]. + +Mamba achieves the best Accel value of $0.92 \, \mathrm{mm/s}^2$ with a window size of 32, outperforming SynSP [52] and Smooth-Net [66]. Figure 4 shows our PS-Mamba's superiority in handling pose ambiguities and occlusions, producing more accurate and visually coherent 3D poses. + +SMPL Representation. As shown in the "AIST++/SMPL" column of Table 1, our PS-Mamba achieves significant improvements, reducing MPJPE to $72.54\mathrm{mm}$ and PA-MPJPE to $52.95\mathrm{mm}$ with a window size of 8, while maintaining an Accel of $5.51\mathrm{mm/s^2}$ with a window size of 32. These results are remarkably better than SynSP [52] at $84.63\mathrm{mm}$ MPJPE and $59.02\mathrm{mm}$ PA-MPJPE. The SMPL representation is a 3D human shape model prone to ambiguity, requiring precise body parameter estimation to avoid unrealistic poses and shapes. The low Accel error, MPJPE, and PA-MPJPE highlight our PS-Mamba's ability to produce accurate poses with reduced ambiguity. + +
MethodWSHuman3.6M DatasetCMU-Mocap Dataset
N(0,100)N(0,400)U(0,50)U(0,100)N(0,100)N(0,400)U(0,50)U(0,100)
M↓A↓M↓A↓M↓A↓M↓A↓M↓A↓M↓A↓M↓A↓M↓A↓
Noisy inputN/A65.6160.3131.1320.594.8231.3189.5462.761.2143.8122.5287.688.7207.9177.4415.8
GFpose [8] (CVPR23)142.8-64.6-50.9-89.4-40.4-60.0-45.6-84.4-
SmoothNet [66] (ECCV22)3242.410.757.914.249.410.274.316.335.14.341.54.937.74.244.95.1
SynSP [52] (CVPR24)837.68.856.113.045.610.969.415.720.63.728.04.424.44.132.44.6
PS-Mamba (Ours)836.78.754.312.944.510.863.613.111.72.517.33.610.72.413.62.9
PS-Mamba (Ours)3232.63.954.94.839.14.153.84.812.71.317.31.511.61.214.21.3
+ +# 4.3. Motion Denoising + +We evaluate PS-Mamba for 3D motion denoising on the Human3.6M [23] and CMU-Mocap [48] datasets, applying various noise types as summarized in Table 2. With a window size of 32, PS-Mamba achieves substantial improvements across all noise types. + +For Human3.6M, with a window size of 8, our PS-Mamba achieves MPJPE of $36.7\mathrm{mm}$ and Accel of $8.7\mathrm{mm/s^2}$ under Gaussian noise with a variance of 100, outperforming both SmoothNet [66] and SynSP [52]. Even at a higher Gaussian variance of 400, PS-Mamba maintains strong robustness, achieving MPJPE of $54.3\mathrm{mm}$ and Accel of $12.9\mathrm{mm/s^2}$ , further outperforming SynSP [52]. Our PS-Mamba also demonstrates strong denoising performance under uniform noise. With uniform-50 noise, it reduces MPJPE to $44.5\mathrm{mm}$ and Accel error to $10.8\mathrm{mm/s^2}$ , outperforming SynSP [52]. Under uniform-100 noise, PS-Mamba achieves an MPJPE of $63.6\mathrm{mm}$ and an Accel of $13.1\mathrm{mm/s^2}$ , surpassing SynSP [52]. These results highlight PS-Mamba's robustness across varying levels of noise. + +For CMU-Mocap, with a window size of 8, our PS-Mamba achieves an MPJPE of $11.7\mathrm{mm}$ and an Accel of $2.5\mathrm{mm/s^2}$ under Gaussian noise with a variance of 100, significantly outperforming SmoothNet [66] and SynSP [52]. At a Gaussian variance of 400, our PS-Mamba demonstrates exceptional stability, achieving about $50\%$ improvement in both MPJPE and Accel error compared to SynSP [52] and SmoothNet [66], highlighting its robustness across varying noise levels. Under uniform-50 noise, our PS-Mamba achieves an MPJPE of $10.7\mathrm{mm}$ and an Accel error of $2.4\mathrm{mm/s^2}$ . With uniform-100 noise, it attains an MPJPE of $13.6\mathrm{mm}$ and an Accel of $2.9\mathrm{mm/s^2}$ , outperforming SynSP [52] and SmoothNet [66]. These results demonstrate PS-Mamba's superior accuracy and smoothness over other SOTA methods in the motion denoising task. + +# 4.4. Comparison with Video-based SOTAs + +To further validate the performance, we conduct experiments with video-based methods [6, 25, 26] on the 3DPW [50] and AIST++ [32, 47] datasets. As reported in Table 3, while SmoothNet [66], SynSP [52], and MoManifold [9] offer some improvements when integrated + +Table 2. Comparison of 3D motion denoising performance on the Human3.6M [23] and CMU-Mocap [48] under various noise types: $\mathcal{N}(0,100)$ , $\mathcal{N}(0,400)$ , $\mathcal{U}(0,50)$ , and $\mathcal{U}(0,100)$ . Results are shown in terms of MPJPE (M↓) and Accel (A↓). + +
DatasetMethodMPJPE↓Accel↓
AIST++VIBE [25]106.931.60
VIBE [25] + MoManifold [9]104.856.34
VIBE [25] + SmoothNet [66]97.474.15
VIBE [25] + SynSP [52]77.004.32
VIBE [25] + PS-Mamba (Ours)62.793.90
TCMR [6]106.726.4
TCMR [6] + SmoothNet [66]105.514.24
TCMR [6] + SynSP [52]--
TCMR [6] + PS-Mamba (Ours)80.803.97
3DPWPARE [26]79.0025.60
PARE [26] + SmoothNet [66]78.105.91
PARE [26] + SynSP [52]76.206.16
PARE [26] + PS-Mamba (Ours)75.435.84
+ +Table 3. Comparison with different video-based estimators, where "+" denotes the integration of estimators with pose refinement. + +
MethodParams(M)FLOPs(M) / FrameMPJPE↓Accel↓
SmoothNet [66]0.691.1035.14.3
PS-Mamba-T (Ours)0.640.4414.81.6
SynSP [52]2.793.7620.63.7
PS-Mamba (Ours)1.433.5212.71.3
+ +Table 4. Comparison of Params and FLOPs on CMU-Mocap [48]. PS-Mamba-T denotes the tiny version of our PS-Mamba. + +with baseline video-based methods such as TCMR [6], PARE [26], and VIBE [25], our PS-Mamba achieves superior performance across all evaluations, with the lowest MPJPE and Accel error, thanks to its strong capacity for modeling spatial-temporal features. through its ST-Graph and leverage state space modeling with ST-SSM, making it a highly effective method for pose sequence refinement. + +# 4.5. Efficiency Analysis + +We evaluate the efficiency of our approach on the CMU-Mocap [48] using Gaussian noise from $\mathcal{N}(0,100)$ . Table 4 compares SmoothNet [66], SynSP [52], our PS-MambaT, and our PS-Mamba models in terms of parameters (Params), FLOPs per frame, MPJPE, and Accel. SmoothNet [66] has small parameters (0.69M) and small FLOPs (1.10M) but compromises accuracy with higher MPJPE (35.1 mm) and Accel (4.3 mm/s²). SynSP [52] uses large 2.79M Params and 3.76M FLOPs, improving MPJPE (20.6 mm) and Accel (3.7 mm/s²), but remains less efficient. Our + +
MethodMPJPE↓PA-MPJPE↓Accel↓
Input54.5542.2019.17
w/o ST-GSS370.23181.883.01
w/o ST-SSM51.9740.271.25
w/o ST-Graph50.7538.520.97
w/o W50.7439.400.94
w/o Temporal50.2738.790.98
w/o Residual50.2139.240.94
w/o mpjpe loss446.50181.290.98
w/o pa-mpjpe loss51.0239.280.95
w/o accel loss50.6339.490.95
PS-Mamba (Full)49.6038.360.92
+ +PS-Mamba obtains a balance with 1.43M parameters and 3.52M FLOPs, achieving the best MPJPE (12.7 mm) and Accel (1.3 mm/s²). Our tiny version of PS-Mamba (PS-Mamba-T) has only two blocks and a hidden dimension of 32 and achieves the lowest parameters (0.64M) and FLOPs (0.44M) while keeping strong performance (MPJPE 14.8 mm, Accel 1.6 mm/s²). PS-Mamba-T shows superior performance compared to SmoothNet [66] and SynSP [52], offering an optimal balance of accuracy and efficiency. + +# 4.6. Ablation Study + +Impact of ST-GSS. As shown in Table 5, removing the ST-GSS block reduces the model to a standard encoder-decoder, leading to a significant performance drop: with MPJPE increasing to $370.23\mathrm{mm}$ (from $49.60~\mathrm{mm}$ ), PA-MPJPE rising to $181.88\mathrm{mm}$ (from $38.36\mathrm{mm}$ ), and Accel increasing to $3.01\mathrm{mm} / \mathrm{s}^2$ (from $0.92\mathrm{mm} / \mathrm{s}^2$ ). This significant decline demonstrates the critical role of the ST-GSS block in human pose sequence refinement. + +Effect of ST-SSM, ST-Graph, and Others. When the STSSM module is removed, we observe a significant increase in MPJPE (51.97 mm vs. 49.60 mm) and PA-MPJPE (40.27 mm vs. 38.36 mm), along with an increase in Accel to $1.25\mathrm{mm / s^2}$ , indicating that ST-SSM substantially enhances temporal smoothness and consistency. The removal of the ST-Graph leads to a drop in MPJPE (50.75 mm vs. 49.60 mm) and PA-MPJPE (38.52 mm vs. 38.36 mm), while omitting the graph weight matrix $W$ similarly affects performance (50.74 mm MPJPE, 39.40 mm PA-MPJPE, and Accel at $0.94\mathrm{mm / s^2}$ ). When the temporal strategy is removed, MPJPE increases to $50.27\mathrm{mm}$ , PA-MPJPE to 38.79 mm, and Accel increases to $0.98\mathrm{mm / s^2}$ . Omitting residual connections slightly degrades performance, while removing the MPJPE loss causes a significant increase, emphasizing its importance for motion consistency. Removing the PA-MPJPE or Accel loss leads to moderate declines, with Accel increasing when the Accel loss is omitted. Overall, Table 5 confirms the effectiveness of each model component + +Impact of Window Size. We conduct experiments to exam- + +Table 5. Ablation study on Human3.6M [23]. + +
Input4816304050
MPJPE54.5553.2652.7950.6951.5350.1351.91
PA-MPJPE42.2040.5340.2539.5338.9838.9339.16
Accel19.173.221.741.190.940.910.90
+ +Table 6. Impact of window size on Human3.6M. + +ine how variations in sliding window size impact model performance. The input 3D poses are initialized by FCN [39] on Human3.6M [23] dataset. As reported in Table 6, the model's performance consistently improves across all metrics as the window size increases, despite occasional variations in individual results. This suggests that a larger window size enhances the model's effectiveness. For MPJPE, the baseline FCN value of $54.55\mathrm{mm}$ decreases as the window size increases, reaching a minimum of $50.13\mathrm{mm}$ at window size 40 before slightly rising at larger window sizes. PA-MPJPE improves from $42.20\mathrm{mm}$ to a minimum of $38.93\mathrm{mm}$ at window size 40. The acceleration error also decreases significantly as the window size increases, stabilizing at $0.90\mathrm{mm/s^2}$ at window size 50. These results highlight the impact of window size on temporal consistency. + +# 5. Data-driven vs. Physics-based Methods + +While physics-based methods can ensure physical plausibility, they often require additional labels (e.g., contact, environment interaction) or simulation environments, which increase complexity and computational cost [41, 65]. In contrast, we adopt a data-driven approach that refines pose sequences without such supervision, following the setup in prior works like SynSP [52] and SmoothNet [66]. Our method learns from real-world motion data, which implicitly encodes physical consistency, and achieves strong performance (e.g., $+18.5\%$ MPJPE on AIST++) without physics modeling. This highlights the potential of data-driven learning for efficient and scalable pose refinement. + +# 6. Conclusion + +We propose PS-Mamba, a novel framework that refines human pose sequences by incorporating spatial-temporal graph learning with Mamba, using our effective GST-Scanning. Specifically, we design the ST-GSS block to capture intricate spatial-temporal relationships and manage temporal dynamics. We apply a dynamic graph weight matrix to further enhance performance. Extensive experiments show that PS-Mamba outperforms SOTAs in reducing jitter and enhancing pose stability, paving the way for robust human pose sequence refinement with applications in animation, virtual avatars, and 3D human modeling. + +Acknowledgements. This research/project is supported by the National Research Foundation, Singapore, under its NRF-Investigatorship Programme (Award ID. NRF-NRFI09-0008). + +# References + +[1] Ali Behrouz and Farnoosh Hashemi. Graph Mamba: Towards learning on graphs with state space models. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 119-130, 2024. 2, 5 +[2] Abdallah Benzine, Florian Chabot, Bertrand Luvison, Quoc Cuong Pham, and Catherine Achard. 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632445 diff --git a/ICCV/2025/PS3_ A Multimodal Transformer Integrating Pathology Reports with Histology Images and Biological Pathways for Cancer Survival Prediction/full.md b/ICCV/2025/PS3_ A Multimodal Transformer Integrating Pathology Reports with Histology Images and Biological Pathways for Cancer Survival Prediction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4652375c2f4708319dc17980f974b9a8320d4bff --- /dev/null +++ b/ICCV/2025/PS3_ A Multimodal Transformer Integrating Pathology Reports with Histology Images and Biological Pathways for Cancer Survival Prediction/full.md @@ -0,0 +1,345 @@ +# PS3: A Multimodal Transformer Integrating Pathology Reports with Histology Images and Biological Pathways for Cancer Survival Prediction + +Manahil Raza Ayesha Azam Talha Qaiser Nasir Rajpoot University of Warwick, UK + +{manahil.raza, ayesha.azam, talha.qaiser, n.m.rajpoot}@warwick.ac.uk + +# Abstract + +Current multimodal fusion approaches in computational oncology primarily focus on integrating multi-gigapixel histology whole slide images (WSIs) with genomic or transcriptomic data, demonstrating improved survival prediction. We hypothesize that incorporating pathology reports can further enhance prognostic performance. Pathology reports, as essential components of clinical workflows, offer readily available complementary information by summarizing histopathological findings and integrating expert interpretations and clinical context. However, fusing these modalities poses challenges due to their heterogeneous nature. WSIs are high-dimensional, each containing several billion pixels, whereas pathology reports consist of concise text summaries of varying lengths, leading to potential modality imbalance. To address this, we propose a prototype-based approach to generate balanced representations, which are then integrated using a Transformer-based fusion model for survival prediction that we term PS3 (Predicting Survival from Three Modalities). Specifically, we present: (1) Diagnostic prototypes from pathology reports, leveraging self-attention to extract diagnostically relevant sections and standardize text representation; (2) Histological prototypes to compactly represent key morphological patterns in WSIs; and (3) Biological pathway prototypes to encode transcriptomic expressions, accurately capturing cellular functions. PS3, the three-modal transformer model, processes the resulting prototype-based multimodal tokens and models intra-modal and cross-modal interactions across pathology reports, WSIs and transcriptomic data. The proposed model outperforms state-of-the-art methods when evaluated against clinical, unimodal and multimodal baselines on six datasets from The Cancer Genome Atlas (TCGA). The code will be released upon publication. + +# 1. Introduction + +Patient prognosis in oncology refers to the predicted progression and outcome of cancer, often determined by clinical, pathological and molecular factors [44, 71]. It is essential to guide treatment strategies, inform risk assessment and facilitate patient-centered decision-making to optimize survival and quality of life [13, 38]. Recently, integrating multiple data modalities have been shown to improve survival prediction in cancer research, with most studies focusing on combining genomic data such as transcriptomic data with histology whole slide images (WSIs) [7, 52, 54]. These approaches leverage the strengths of each modality—genomics captures molecular subtypes, while WSIs provide spatial and morphological insights into tumor characteristics [72]. However, pathology reports remain an under-utilized resource despite providing essential information to clinicians for estimating the prognosis of cancer patients. Generated by expert pathologists, they are mandatory for definitive cancer diagnosis [42] and contain critical clinical and prognostic information including biomarker status, tumor grading, staging and histological subtypes [24, 27, 41]. They often complement histology and genomic data by incorporating expert-driven diagnostic insights [1, 53]. Moreover, as routinely produced components of clinical workflows, pathological reports serve as a readily available source of medical knowledge [23]. Despite their clinical significance, they remain largely untapped in computational survival prediction models. + +Early multimodal approaches often relied on late fusion techniques [6, 31, 64], which integrated unimodal representations only at the final decision stage [12]. However, these methods struggled to model cross-modal interactions, which may be crucial for accurate prognosis. In contrast, more recent studies have investigated early fusion approaches for integrating WSIs and genomic data. Although early fusion captures fine-grained cross-modal interactions more effectively [5, 20, 51, 67], it remains computationally demanding due to the high dimensionality and heterogeneity of the data. + +Another key challenge in early fusion of WSIs, genomics and pathology reports is modality imbalance, arising from differences in structure and scale of the data modalities. WSIs are gigapixel-scale images typically divided into thousands of high-dimensional patches containing spatial and morphological information [46]. To process these vast amounts of image data, Multiple Instance Learning (MIL) [11, 63] is commonly employed, allowing models to extract and aggregate relevant features from individual patches. In contrast, pathology reports provide concise textual summaries with significantly fewer raw data points. Further, genomic data, such as RNA-Seq expression levels are typically represented as isolated scalar values, lacking contextual information about their biological functions. This imbalance can lead to modality dominance, where data-rich modalities (e.g. WSIs) can disproportionately influence the model compared to modalities with fewer tokens (e.g. pathology reports). Addressing this imbalance is crucial for developing an effective multimodal fusion framework that ensures fair contributions from all modalities and improves predictive performance. + +To address these challenges, we propose a prototype-based multimodal fusion framework that standardizes and balances representations across three modalities. The prototypes represent large, variable-length inputs as compact embeddings, enabling more effective multimodal fusion. We exploit the inherent morphological redundancy in WSIs by identifying recurring histological patterns within tissue patches [62]. Inspired by previous works [25, 50, 51], we use a Gaussian Mixture Model (GMM) to represent slides, with each mixture component corresponding to a distinct histological prototype. This clustering of similar morphological patterns enables compact WSI representations using key histological prototypes. Pathology reports, which contain significantly less raw data than WSIs, often exhibit unstructured or semi-structured formats, inconsistent formatting, varying lengths and levels of detail [41, 47, 59]. Rather than truncating their content, we construct diagnostic prototypes—standardized representations designed to capture the most diagnostically relevant sections of each report using self-attention-based mechanisms [60]. To ensure a biologically meaningful representation of transcriptomic data, we draw inspiration from prior methods [20, 51, 72] and transform the values into a set of 50 Cancer Hallmark pathway prototypes [33]. This representation aligns gene expression patterns with well-established cellular processes, providing a structured and interpretable genomic feature set. + +We propose a multimodal transformer-based framework PS3, designed to Predict Survival by integrating information from three (3) different data modalities: WSIs, transcriptomics and pathology reports. By transforming raw data into compact prototype-based representations, we reduce the disparity in token counts across modalities, + +achieving a more balanced token distribution. This allows our transformer-based method to effectively model self-attention and cross-attention mechanisms, thereby facilitating the fusion of complementary information from all three modalities. As a result, our approach enhances predictive performance, leading to robust survival prediction. We evaluate the proposed method on six cancer cohorts from The Cancer Genome Atlas (TCGA) [65] and demonstrate that it outperforms both unimodal and multimodal baselines. + +To summarize, our main contributions are: (1) a novel framework for representing pathology reports, WSIs and transcriptomic profiles using diagnostic, histological and pathway prototypes, respectively; (2) development of a multimodal transformer, PS3, to predict survival using three modalities; and (3) comprehensive experiments and ablation studies on six cancer cohorts, showcasing the effectiveness of PS3 for cancer survival prediction. + +# 2. Related Work + +# 2.1. Survival Prediction with Whole Slide Images + +Given the large number of patches in WSIs, many methods adopt MIL-based methods for efficient processing and analysis [2]. MIL typically involves three key steps: (1) dividing the WSI into hundreds or thousands of smaller patches (or instances), (2) extracting patch embeddings using a feature encoder and (3) aggregating the patch embeddings to obtain a slide-level representation [63]. For survival prediction, various MIL-based approaches have been explored, including graph-based [4, 30, 35] and attention-based MIL models [18, 70] both of which aim to capture global WSI representations for survival analysis. More recently, transformer-based architectures leveraging self-attention mechanisms [10, 21, 60] have been introduced, including hierarchical transformer architectures designed to capture multi-scale WSI representations [49, 68]. + +# 2.2. Multimodal Survival Prediction + +While unimodal methods have demonstrated strong prognostic capabilities, multimodal approaches have led to further improvements in survival prediction. Most existing multimodal fusion methods integrate genomic or transcriptomic data with multi-gigapixel histology WSIs [6]. Early studies primarily relied on late fusion using techniques such as concatenation [39], Kronecker product [3, 64] or factorized bilinear pooling [31, 45]. However, since late fusion merges unimodal representations only at the final stage [12], it fails to capture cross-modal interactions, leading to suboptimal integration. Similarly, text-based fusion using concatenation [15] and weighted sum [40] to combine patient health records and medical images suffer from similar limitations. + +In contrast, early fusion approaches have gained signif + +cant attention for their effectiveness in modeling cross-modal interactions. Many models utilize transformers [66], incorporating co-attention [5, 34, 74] and cross-attention mechanisms [9, 20, 37, 51] to enhance feature integration. Some extend transformer architectures with hierarchical transformers [29] while others employ prototyping techniques to reduce data dimensionality before fusion, improving efficiency and minimizing the number of tokens processed [50]. Additionally, other approaches such as optimal transport-based methods [51, 67], information bottlenecking techniques [72] and graph-based methods [73] have been explored as alternatives to transformers. + +# 3. Methodology + +We introduce PS3, a prototyping-based multimodal framework for survival prediction that integrates histology images, transcriptomic data and pathology reports. We explain the construction of the diagnostic prototypes, histological prototypes and pathway prototypes in Sections 3.1, 3.2 and 3.3, respectively. Section 3.4 describes the Transformer-based multimodal approach, while Section 3.5 outlines the post-fusion processing steps taken for survival prediction. + +# 3.1. Diagnostic Prototypes from Pathology Reports + +Feature Extraction: Each pathology report $(t)$ , denoted as $R_{i}$ , is first divided into smaller text segments or sections: $R_{i} = \{x_{1}^{t}, x_{2}^{t} \ldots x_{N_{t,i}}^{t}\}$ , where $N_{t,i}$ is the number of segments in the $i^{th}$ report. These text segments are tokenized and subsequently passed through a pre-trained and frozen text encoder $E_{T}$ which extracts feature embeddings for each text segment: $\mathbf{h}_{i}^{t} = E_{T}(x_{i}^{t}) \in \mathbb{R}^{d_{t}}$ . The set of embeddings for the $i^{th}$ pathology report are then defined as: $\mathbf{H}_{i}^{t} = \{\mathbf{h}_{1}^{t}, \mathbf{h}_{2}^{t} \ldots \mathbf{h}_{N_{t,i}}^{t}\}$ . + +Self-Attention Mechanism: For a batch of $b$ pathology reports, the input can be modeled as $\mathbf{H}^t = \{\mathbf{H}_1^t,\mathbf{H}_2^t\dots \mathbf{H}_b^t\} \in \mathbb{R}^{b\times N_{t,i}\times d}$ where $N_{t,i}$ is the number of text segments in the $i^{th}$ report. Since reports vary in length, they are padded to ensure uniformity within the batch. The resulting padded batch is represented as: $\tilde{\mathbf{H}}^t = \{\tilde{\mathbf{H}}_1^t,\tilde{\mathbf{H}}_2^t\dots \tilde{\mathbf{H}}_b^t\} \in \mathbb{R}^{b\times m\times d_t}$ where $m$ is the length of the longest report in the training set. A corresponding binary mask $\mathcal{M}\in \{0,1\}^{b\times m}$ is created to differentiate between the real tokens and padded positions, ensuring they do not contribute to the attention scores. + +We aim to standardize report representations while preserving the most clinically and pathologically relevant information. To achieve this, we employ a Transformer-based self-attention mechanism [60] to construct the Diagnostic Prototypes. In particular, we project the padded report embeddings into query, key and value vectors using learnable linear transformations: + +$$ +\mathbf {Q} ^ {t} = \mathbf {W} _ {Q} \cdot \tilde {\mathbf {H}} ^ {t}, \quad \mathbf {K} ^ {t} = \mathbf {W} _ {K} \cdot \tilde {\mathbf {H}} ^ {t}, \quad \mathbf {V} ^ {t} = \mathbf {W} _ {V} \cdot \tilde {\mathbf {H}} ^ {t} (1) +$$ + +where $\mathbf{W}_Q, \mathbf{W}_K, \mathbf{W}_V \in \mathbb{R}^{d_t \times d_t}$ are learnable matrices. The scaled dot-product attention $A^t$ is then computed as: + +$$ +\mathbf {A} ^ {t} = \sigma \left(\frac {\mathbf {Q} ^ {t} \mathbf {K} ^ {t} {} ^ {\top}}{\sqrt {d _ {t}}}\right) \tag {2} +$$ + +The padded positions are masked during the self-attention process to prevent them from influencing the results. The attention weights are further used to compute a weighted sum of the values $\mathbf{Z}^t = \mathbf{A}^t\cdot \mathbf{V}^t\in \mathbb{R}^{b\times m\times d_t}$ representing the post-attention embeddings of the pathology reports. + +Prototype Selection: To extract the most diagnostically relevant segments (or prototypes) from each pathology report, we compute a single importance score for each segment, by averaging its attention weights across all query positions. This process produces a vector of importance scores for all sections in a report: $\mathbf{s}^t = [s_1^t,s_2^t,\dots s_m^t ]\in \mathbb{R}^m$ showing, on average, how much the entire report attends to each segment. Mathematically, if $\mathbf{A}_n^t\in \mathbb{R}^{m\times m}$ is the attention matrix for the $n$ -th report, we define the importance score $s_{n,j}^{t}$ of section $j$ as: + +$$ +s _ {n, j} ^ {t} = \frac {1}{m} \sum_ {i = 1} ^ {m} A _ {n, i, j} ^ {t} \tag {3} +$$ + +where $A_{n,i,j}^{t}$ is the attention weight from query position $i$ to key position $j$ . The sections are then ranked in descending order of their importance scores. Segments that are more relevant for diagnosis (e.g. those describing tumor size or pathology findings) typically receive higher scores. From the post-attention representation $\mathbf{Z}_i^t$ , we select embeddings corresponding to the top $N_{\mathcal{T}}$ sections, yielding fixed-length Diagnostic Prototypes: $\mathbf{Z}_{i,\mathrm{proto}}^t\in \mathbb{R}^{N_\mathcal{T}\times d_t}$ , where $N_{\mathcal{T}}$ is the number of prototypes and $d_{t}$ is the embedding dimension for the $i^{th}$ report. To facilitate multimodal fusion, we align the dimensions of the prototype representations derived from the three modalities. For this reason, we apply a linear transformation $f_{\alpha}^{t}$ to the text prototype embeddings, resulting in: $\mathbf{Z}_{\alpha}^{t} = f_{\alpha}^{t}(\mathbf{Z}_{\mathrm{proto}}^{t})\in \mathbb{R}^{d_{e}}$ . + +# 3.2. Histological prototypes from WSIs + +Feature Extraction: For each WSI, we first identify and isolate the tissue regions [43] to ensure that diagnostically irrelevant background regions are excluded from further analysis. The retained tissue region in each histology image $(h)$ , denoted as $X_{i}$ , is divided into non-overlapping patches [36] as follows: $X_{i} = \{x_{1}^{h}, x_{2}^{h} \ldots x_{N_{h,i}}^{h}\}$ where $x_{j}^{h} \in \mathbb{R}^{H \times W \times 3}$ denotes the $j^{th}$ patch, $H$ and $W$ represent the height and width of the patch, respectively and $N_{h,i}$ represents the total number of patches in the $i^{th}$ slide. Each patch is processed by a pre-trained and frozen image encoder $E_{I}$ to extract visual features: $\mathbf{h}_{j}^{h} = E^{I}(x_{j}^{h}) \in \mathbb{R}^{d_{h}}$ , where $d_{h}$ represents the dimensions of the extracted visual + +![](images/bf072f5099f44e50c89646c978a884a163f0834ffe1a0ec566435ce25608fd6c.jpg) +a) + +![](images/e75920cd5d8d71968700f1d22207076d849d5f3ae953a7991be8d0b60a1ab065.jpg) +b) For each report: + +![](images/7475e63d1e738264c5d83541c2b4b5809da3e7ac024f867d4e3f770d660d2390.jpg) +c) + +![](images/50aaea88c1015ccb71f9eeab961d1ae9024044a87b240900d9f17bbfd0a6a8b7.jpg) +d) +Figure 1. (a) Whole Slide Image $X_{i}$ patches are processed by a frozen image encoder $E_{I}$ to extract visual features $\mathbf{H}^{h}$ , which are clustered into $C$ histological prototypes using a Gaussian Mixture Model (GMM) to obtain a slide-level representation. (b) Feature embeddings $\mathbf{H}_{i}^{t}$ are extracted from the text segments of a single pathology report $R_{i}$ , using a frozen text encoder $E_{T}$ . For a batch of pathology reports $\mathbf{H}^{t}$ we construct Diagnostic prototypes by applying Transformer-based self-attention mechanisms and sorting the text segments within each report based on their importance scores. (c) Gene-expression vector $\mathbf{x}^{p}$ are multiplied with the binary pathway vectors (B) to create pathway prototypes. These are processed through $f_{\alpha}$ MLPs to generate feature embeddings. (d) Prototypes from each modality are projected into key, value and query representations, followed by self- and cross-modal attention to integrate information. The resulting outputs are used for survival risk prediction. + +feature vector. The set of extracted feature vectors for slide $i$ are collectively represented as $\mathbf{H}_i^h = \{\mathbf{h}_1^h,\mathbf{h}_2^h\dots \mathbf{h}_{N_{h,i}}^h\}$ + +Prototype Construction: To summarize the recurring morphological patterns in WSIs, we cluster patches into $C$ histological prototypes using GMM, inspired by previous methods [50, 51]. Before applying the GMM, we first obtain an initial estimate of the histological prototypes by randomly initializing cluster centers in the feature space. Each prototype mean $(\mu)$ is sampled from a Gaussian distribution, ensuring that the cluster centers are spread out. The diagonal covariance matrices $(\Sigma)$ are initialized as identity matrices while the mixture weights $(\pi)$ are uniformly initialized. Mathematically we represent this as: + +$$ +\mu_ {c} \sim \mathcal {N} (0, 0. 1 ^ {2} I), \quad \Sigma_ {c} = I, \quad \pi_ {c} = \frac {1}{N _ {\mathcal {H}}} \qquad (4) +$$ + +$\forall c \in \{1, 2, \dots, N_{\mathcal{H}}\}$ where $N_{\mathcal{H}}$ denotes the number of prototypes $c$ . Unlike traditional clustering methods, GMM allows soft assignments, meaning each patch is assigned to multiple prototypes with varying probabilities, enabling a more flexible representation of the morphological diversity found in the tissue structures [50]. The likelihood of a patch embedding under the GMM is given by: + +$$ +p \left(\mathbf {h} _ {j} ^ {h}\right) = \sum_ {c = 1} ^ {N _ {\mathcal {H}}} \pi_ {c} \cdot \mathcal {N} \left(\mathbf {h} _ {j} ^ {h}; \mu_ {c}, \Sigma_ {c}\right) \tag {5} +$$ + +where: $\pi_c$ is the probability of selecting prototype $c$ and $\mathcal{N}(\mathbf{h}_j^h;\mu_c,\Sigma_c)$ represents the Gaussian density function and models the likelihood of $\mathbf{h}_j^h$ given prototype $c$ . For an entire + +WSI, the joint probability over all patches is: + +$$ +p \left(\mathbf {H} ^ {h}\right) = \prod_ {j = 1} ^ {N _ {h}} \sum_ {c = 1} ^ {N _ {\mathcal {H}}} \pi_ {c} \cdot \mathcal {N} \left(\mathbf {h} _ {j} ^ {h}; \mu_ {c}, \Sigma_ {c}\right) \tag {6} +$$ + +This formulation ensures that the WSI is summarized using a compact set of histological prototypes. The GMM parameters $(\mu, \Sigma, \pi)$ are optimized using the Expectation-Maximization (EM) algorithm [8, 25]. Over successive EM iterations, the prototypes are progressively updated, ultimately converging to meaningful cluster centers. After convergence, the final slide representation is obtained by concatenating the estimated mixture parameters: + +$$ +\mathbf {Z} _ {\text {p r o t o}} ^ {h} = \left[ \pi_ {1}, \mu_ {1}, \Sigma_ {1}, \dots , \pi_ {N _ {\mathcal {H}}}, \mu_ {N _ {\mathcal {H}}}, \Sigma_ {N _ {\mathcal {H}}} \right] \in \mathbb {R} ^ {N _ {\mathcal {H}} \times (1 + 2 d _ {h})} \tag {7} +$$ + +where: $\pi_c$ quantifies the prevalence of each prototype in the slide, $\mu_c$ represents the average morphological characteristics of each prototype and $\sum_{c}$ captures the variation within the patches belonging to each prototype. This prototype-based embedding significantly reduces the dimensionality of WSI patch features whilst still preserving key morphological characteristics. To align the dimensionality of histology prototypes with those from other modalities, we apply a linear transformation $f_{\alpha}^{h}$ to the prototype embeddings, yielding: $\mathbf{Z}_{\alpha}^{h} = f_{\alpha}^{h}(\mathbf{Z}_{\mathrm{proto}}^{h})\in \mathbb{R}^{d_{e}}$ + +# 3.3. Pathway Prototypes from Genomic Data + +Prototype Construction: The transcriptomic profile for each sample can be represented by a gene-expression vector $\mathbf{x}^p\in \mathbb{R}^{N_G}$ , where $N_{G}$ is the total number of genes. We aim to group these genes $(p)$ into $N_{\mathcal{P}}$ pre-defined biological pathways, each acting as a prototype. For each pathway $i$ we define a binary mask $\mathbf{B}_i\in \{0,1\}^{N_G}$ , where each element indicates whether a gene is included in a given pathway (1) or not (0). To construct the pathway prototypes, we perform an element-wise product of the gene expression vector $(\mathbf{x}^p)$ with the binary pathway vectors (B) [51]. This operation generates a pathway-specific representation: + +$$ +\mathbf {Z} _ {\text {p r o t o}, i} ^ {p} = \mathbf {x} ^ {p} \odot \mathbf {B} _ {i}, \quad \forall i \in [ 1, N _ {\mathcal {P}} ] \tag {8} +$$ + +where $N_{\mathcal{P}}$ denotes the number of pathways. The resulting vector $\mathbf{Z}_{\mathrm{proto},i}^{p}$ is then reduced to remove any zero entries, yielding a dense but variable-length representation (since different pathways involve different gene counts). To ensure a fixed size embedding for each pathway, we employ self-normalizing neural networks (SNNs) [20, 26]: + +$$ +\mathbf {Z} _ {i, \alpha} ^ {p} = f _ {\alpha , i} ^ {p} \left(\mathbf {Z} _ {\text {p r o t o}, i} ^ {p}\right) \in \mathbb {R} ^ {d _ {e}}, \forall i \in [ 1, N _ {\mathcal {P}} ] \tag {9} +$$ + +where $f_{\alpha,i}^{p}$ is a trainable network dedicated to pathway $i$ . By treating each pathway as a "prototype" we are able to preserve biologically relevant groupings of genes while ensuring that the final representation for each pathway shares the same dimensionality with itself and aligns with the other modalities. + +# 3.4. Multimodal Fusion + +We aim to design a multimodal fusion model that extends the standard Transformer attention mechanism [10, 60] to capture both intra-modal and cross-modal interactions. Specifically, we seek to learn interactions among: diagnostic prototypes from pathology reports $(t)$ represented as $\mathbf{Z}_{\alpha}^{t}\in \mathbb{R}^{N_{\mathcal{T}}}$ , histological prototypes from histology images $(h)$ represented as $\mathbf{Z}_{\alpha}^{h}\in \mathbb{R}^{N_{\mathcal{H}}}$ and pathway prototypes from transcriptomic data $(p)$ represented as $\mathbf{Z}_{\alpha}^{p}\in \mathbb{R}^{N_{\mathcal{P}}}$ . Each modality-specific embedding consists of $N_{\mathcal{M}}$ prototypes, where $\mathcal{M}\in \{\mathcal{P},\mathcal{H},\mathcal{T}\}$ . To allow the model to dynamically enhance the prototype representations, we also append a learnable and randomly initialized embedding $\mathbf{e}_r\in \mathbb{R}^{d_r}$ to the prototypes [19, 32, 51]. The modified embeddings are then represented as $\mathbf{Z}_{\alpha}^{h,p,t}\in \mathbb{R}^{d = d_e + d_r}$ . + +To integrate the three modalities, we concatenate the modality-specific prototypes into a single multimodal embedding: $\mathbf{Z}^{mm} = [\mathbf{Z}_{\alpha}^{p}\parallel \mathbf{Z}_{\alpha}^{h}\parallel \mathbf{Z}_{\alpha}^{t}]\in \mathbb{R}^{(N_{\mathcal{P}} + N_{\mathcal{H}} + N_{\mathcal{T}})\times d}$ where $d$ is the feature dimension. Following the standard Transformer architecture, we introduce three learnable projection matrices, $\mathbf{W}_Q,\mathbf{W}_K,\mathbf{W}_V\in \mathbb{R}^{d\times d}$ to map the multimodal embedding $\mathbf{Z}^{mm}$ into queries, keys and values: + +$$ +\mathbf {Q} = \mathbf {W} _ {Q} \cdot \mathbf {Z} ^ {m m}, \quad \mathbf {K} = \mathbf {W} _ {K} \cdot \mathbf {Z} ^ {m m}, \quad \mathbf {V} = \mathbf {W} _ {V} \cdot \mathbf {Z} ^ {m m} \tag {10} +$$ + +However, rather than treating $\mathbf{Z}^{mm}$ as a unified sequence, we decompose it into modality-specific components and compute attention for all possible pairwise interactions. Concretely, we split each $\mathbf{Q},\mathbf{K},\mathbf{V}$ into three modality-specific blocks: + +$$ +\mathbf {Q} = \left[ \begin{array}{c c c} \mathbf {Q} ^ {p} & \parallel \mathbf {Q} ^ {h} & \parallel \mathbf {Q} ^ {t} \end{array} \right], +$$ + +$$ +\mathbf {K} = \left[ \mathbf {K} ^ {p} \parallel \mathbf {K} ^ {h} \parallel \mathbf {K} ^ {t} \right], \tag {11} +$$ + +$$ +\mathbf {V} = \left[ \begin{array}{l l l} \mathbf {V} ^ {p} & \parallel & \mathbf {V} ^ {h} \end{array} \right. \parallel \left. \mathbf {V} ^ {t} \right], +$$ + +where $\mathbf{Q}^p, \mathbf{K}^p, \mathbf{Q}^p \in \mathbb{R}^{N_{\mathcal{P}} \times d}$ for pathways (and likewise for histology and text). + +The approach results in a total of nine attention mechanisms categorized into (1) three self-attention (intra-modal) interactions: $\mathbf{A}^{p\to p}$ (pathways attending to pathways), $\mathbf{A}^{h\to h}$ (histology attending to histology) and $\mathbf{A}^{t\to t}$ (text attending to text) (2) six cross-attention (inter-model) interactions: $\mathbf{A}^{p\to h},\mathbf{A}^{p\to t}$ (pathways attending to histology and text), $\mathbf{A}^{h\to p},\mathbf{A}^{h\to t}$ (histology attending to pathways and text) and $\mathbf{A}^{t\to p},\mathbf{A}^{t\to h}$ (text attending to pathways and histology). Each attention component is computed as: $\mathbf{A}^{m\to n} = \mathbf{Q}^m (\mathbf{K}^n)^\top$ where $\mathbf{A}^{m\to n}$ represents the attention logits from modality $m$ to modality $n$ . + +After computing all intra- and cross-modal attention scores, we concatenate the sub-blocks within each modality and apply a row-wise softmax operation, producing a single probability distribution over key tokens for each query modality. This ensures that each modality attends to the + +most relevant information from both itself and the other modalities. Once the attention scores are computed, they are multiplied by the corresponding value representations from all modalities. The final modality-specific embeddings after fusion are: + +$$ +\begin{array}{l} \left(\begin{array}{c}\mathbf {Z} _ {\text {f u s i o n}} ^ {p}\\\mathbf {Z} _ {\text {f u s i o n}} ^ {h}\\\mathbf {Z} _ {\text {f u s i o n}} ^ {t}\end{array}\right) = \sigma \left[ \frac {1}{\sqrt {d}} \left(\begin{array}{c c c}\mathbf {A} ^ {p \rightarrow p}&\mathbf {A} ^ {p \rightarrow h}&\mathbf {A} ^ {p \rightarrow t}\\\mathbf {A} ^ {h \rightarrow p}&\mathbf {A} ^ {h \rightarrow h}&\mathbf {A} ^ {h \rightarrow t}\\\mathbf {A} ^ {t \rightarrow p}&\mathbf {A} ^ {t \rightarrow h}&\mathbf {A} ^ {t \rightarrow t}\end{array}\right) \right] \left(\begin{array}{c}\mathbf {V} ^ {p}\\\mathbf {V} ^ {h}\\\mathbf {V} ^ {t}\end{array}\right) \\ = \sigma \left[ \frac {1}{\sqrt {d}} \left( \begin{array}{c c c} \mathbf {Q} ^ {p} \left(\mathbf {K} ^ {p}\right) ^ {\top} & \mathbf {Q} ^ {p} \left(\mathbf {K} ^ {h}\right) ^ {\top} & \mathbf {Q} ^ {p} \left(\mathbf {K} ^ {t}\right) ^ {\top} \\ \mathbf {Q} ^ {h} \left(\mathbf {K} ^ {p}\right) ^ {\top} & \mathbf {Q} ^ {h} \left(\mathbf {K} ^ {h}\right) ^ {\top} & \mathbf {Q} ^ {h} \left(\mathbf {K} ^ {t}\right) ^ {\top} \\ \mathbf {Q} ^ {t} \left(\mathbf {K} ^ {p}\right) ^ {\top} & \mathbf {Q} ^ {t} \left(\mathbf {K} ^ {h}\right) ^ {\top} & \mathbf {Q} ^ {t} \left(\mathbf {K} ^ {t}\right) ^ {\top} \end{array} \right) \right] \binom {\mathbf {V} ^ {p}} {\left( \begin{array}{l} \mathbf {V} ^ {h} \\ \mathbf {V} ^ {t} \end{array} \right)} \tag {12} \\ \end{array} +$$ + +where $\sigma[\cdot]$ is the row-wise softmax operation. Finally, the full multimodal representation is obtained by concatenating the post-fusion modality-specific embeddings: + +$$ +\mathbf {Z} _ {\text {f u s i o n}} ^ {m m} = \left[ \mathbf {Z} _ {\text {f u s i o n}} ^ {p} \| \mathbf {Z} _ {\text {f u s i o n}} ^ {h} \| \mathbf {Z} _ {\text {f u s i o n}} ^ {t} \right] \tag {13} +$$ + +# 3.5. Survival Prediction + +After the multimodal fusion step, the resulting embeddings are processed by a series of multi-layer perceptrons (MLPs) for further transformation. Within each modality, these embeddings undergo layer normalization and are subsequently averaged to create compact, modality-specific representations [51]. + +$$ +r i s k = f _ {r i s k} \left[ \frac {1}{N _ {\mathcal {X}}} \sum_ {i = 1} ^ {N _ {\mathcal {X}}} f _ {\beta} \left(\mathbf {Z} _ {i, \text {f u s i o n}} ^ {x}\right) \right] _ {\mathcal {X} \in \{\mathcal {P}, \mathcal {H}, \mathcal {T} \}} \tag {14} +$$ + +The final patient-level representation is obtained by concatenating these averaged modality-specific embeddings, which are then passed through a linear layer $f_{\mathrm{risk}}$ to generate a patient-level prediction. + +# 4. Datasets and Implementation + +# 4.1. Datasets + +We evaluate our proposed method using publicly available datasets from The Cancer Genome Atlas (TCGA) across six types of cancer [65]: Bladder urothelial carcinoma (BLCA) $(n = 328)$ , Lung adenocarcinoma (LUAD) $(n = 391)$ , Kidney renal clear cell carcinoma (KIRC) $(n = 328)$ , Stomach adenocarcinoma (STAD) $(n = 253)$ , Colon and Rectum adenocarcinoma (CRC) $(n = 269)$ and Head and Neck Squamous Cell Carcinoma (HNSC) $(n = 385)$ . + +Hematoxylin and Eosin (H&E) stained WSIs for all patients were obtained from the National Cancer Institute (NCI) Genomic Data Commons (GDC) [65]. The corresponding pathology reports were obtained from Kefeli et + +al.[23], who curated 9,523 machine-readable reports from TCGA by converting PDF documents into text format. Bulk RNA sequencing data for TCGA cohorts was accessed from the UCSC Xena database [14], measured using the Illumina HiSeq 2000 system. To stabilize variance and mitigate the impact of extreme values, we applied and $\log_2(x + 1)$ transformed with RSEM normalization [28]. To structure the data into pathways, we utilized 50 Hallmark gene sets from the Molecular Signatures Database (MSigDB) [33, 55], covering approximately 4000 unique genes in total. Further implementation details can be found in Supplementary Material, Implementation Details. + +# 4.2. Baselines + +# 4.2.1. Unimodal Baselines + +The following unimodal baselines were separately implemented for each data modality: + +Text: We employ a unimodal text-only variant of the proposed method (with prototypes), $\mathrm{PS3}_{\mathrm{t}}$ . Additionally, we use an Attention-based MIL [18] on the pathology reports. Gene: We use a unimodal transcriptomics-only variant of the proposed method (with prototypes), $\mathrm{PS3}_{\mathrm{p}}$ . Additionally, we use a 2-layer MLP as a non-prototype baseline [20, 51]. Histology: We utilize TransMIL [48], $\mathbb{R}^2$ -TMIL [57] and CLAM [36, 69] as our histology baselines. We also implement a unimodal histology-only variant of the proposed method (with prototypes), $\mathrm{PS3}_{\mathrm{WSI}}$ . + +# 4.2.2. Multimodal Baselines + +We implement MOTCat [67], MCAT [5], SurvPath [20], SurvivMIL [40], CMTA [74], FSM [73] and both variants of MMP [51] - $\mathrm{MMP}_{\mathrm{Trans}}$ and $\mathrm{MMP}_{\mathrm{OT}}$ — as our multimodal baselines. Additional details can be found in Supplementary Material, Multimodal Baselines. + +# 5. Results + +# 5.1. Survival Prediction Results + +Table.1 presents the C-Index results for PS3 and all baseline models in predicting disease-specific survival. PS3 demonstrates the highest overall (average) performance, outperforming the next-best multimodal and unimodal methods with percentage improvements of $6.72\%$ and $7.21\%$ , respectively. In addition, it achieves among the highest performance in 5 of the 6 cancer types evaluated. We summarize the key findings below. Additional results can be found in Supplementary Material, Kaplan-Meier Analysis and Attention Visualization. + +# 5.1.1. Comparison with Clinical Baseline + +Clinical variables such as age, sex and histologic grade have been identified as important prognostic factors for survival prediction [22, 56, 58, 61]. In Table.1 our analysis demonstrates that all subsequent methods achieve superior perfor + +
ModelBLCALUADKIRCSTADCRCHNSCAvg (↑)
Gene exp [20]Clinical0.557 ± 0.0620.494 ± 0.0930.723 ± 0.0440.583 ± 0.0510.496 ± 0.0990.516 ± 0.0900.561
PS3p0.656 ± 0.0470.508 ± 0.0640.764 ± 0.0420.578 ± 0.0800.678 ± 0.0690.595 ± 0.0760.630
0.643 ± 0.0620.578 ± 0.0680.765 ± 0.0400.614 ± 0.0590.710 ± 0.0630.601 ± 0.0600.652
Text ABMIL [18]PS3t0.522 ± 0.0690.560 ± 0.0530.598 ± 0.0790.594 ± 0.0670.772 ± 0.1370.507 ± 0.0670.592
0.629 ± 0.0650.536 ± 0.0870.623 ± 0.0750.548 ± 0.0780.805 ± 0.1300.550 ± 0.0800.615
HistologyCLAM [36]0.562 ± 0.1000.606 ± 0.1040.684 ± 0.0550.510 ± 0.0780.680 ± 0.1270.560 ± 0.0750.600
TransMIL [48]0.585 ± 0.0490.594 ± 0.0960.736 ± 0.0850.558 ± 0.0350.671 ± 0.1200.594 ± 0.0700.623
RRTMIL [57]0.550 ± 0.0650.557 ± 0.0910.704 ± 0.1280.603 ± 0.0880.575 ± 0.0350.556 ± 0.0560.591
PS3wSI0.539 ± 0.0330.597 ± 0.0710.759 ± 0.1020.542 ± 0.0850.586 ± 0.1970.502 ± 0.0530.588
MultimodalSurvivMIL [40]0.484 ± 0.0500.568 ± 0.0480.654 ± 0.1010.492 ± 0.0680.663 ± 0.0570.552 ± 0.0860.569
SurvPath [20]0.613 ± 0.0360.567 ± 0.0550.761 ± 0.0540.608 ± 0.0480.640 ± 0.0540.536 ± 0.0550.621
MOTCat [67]0.636 ± 0.0570.533 ± 0.0390.766 ± 0.0490.553 ± 0.0820.677 ± 0.0670.586 ± 0.0440.625
MCAT [5]0.636 ± 0.0680.512 ± 0.0400.762 ± 0.0300.572 ± 0.0740.661 ± 0.1010.578 ± 0.0640.620
CMTA [74]0.637 ± 0.0670.565 ± 0.0450.741 ± 0.0440.578 ± 0.0650.659 ± 0.0580.579 ± 0.0300.627
FSM [73]0.642 ± 0.0500.565 ± 0.0820.776 ± 0.0480.609 ± 0.0680.663 ± 0.0590.577 ± 0.0640.639
\( MMP_{Trans} \) [51]0.641 ± 0.0530.606 ± 0.0680.776 ± 0.0590.639 ± 0.0630.689 ± 0.0780.566 ± 0.0750.653
\( MMP_{OT} \) [51]0.645 ± 0.0300.617 ± 0.0580.774 ± 0.0260.660 ± 0.0730.689 ± 0.0740.545 ± 0.0410.655
PS30.684 ± 0.0260.640 ± 0.0930.776 ± 0.0610.638 ± 0.0450.826 ± 0.1010.627 ± 0.0660.699
+ +mance (by a minimum of $1.4\%$ ) compared to the clinical baseline, which relies solely on these variables. This highlights the benefits of integrating additional data modalities such as histology images, transcriptomic data and pathology reports. Additional details can be sound in Supplementary Material, Clinical Baselines. + +Table 1. Survival prediction results comparing the proposed method, PS3, with multimodal and unimodal baselines for disease-specific survival prediction using the C-Index. Pathology Language and Image Pre-Training (PLIP) [16] is used as a feature encoder across all methods. Performance is evaluated over five runs, with standard deviation reported. The best-performing results are highlighted in bold. + +
AblationModelAvg.
PS30.699
Text Proto NTAvg ⇒ p900.691 (-1.14%)
Encoder EI, ETPLIP ⇒ QUILT-Net0.676 (-3.29%)
Modalitiesp,h,t ⇒ h,t0.644 (-7.87%)
p,h,t ⇒ p,t0.687 (-1.72%)
p,h,t ⇒ p,h0.653 (-6.58%)
Fusion MethodFull ⇒ Late0.669 (-4.29%)
Full ⇒ Hierarchical0.660 (-5.58%)
Embeddings erRandom ⇒ None0.688 (-1.57%)
MLP fβMultiple ⇒ Single0.690 (-1.29%)
+ +Table 2. Ablation study analyzing the impact of modifying individual model components on the C-Index, with results averaged across six cohorts. + +# 5.1.2. Comparison of Histology, Gene and Text-Based Methods + +Table.1 also demonstrates that gene-based methods (with C-Index results $0.63 - 0.65$ ) outperform other unimodal baselines, highlighting the strong prognostic value of transcriptomics data for survival prediction. In contrast, histology (with C-Index results $0.58 - 0.62$ ) and text-based methods (with C-Index results $0.59 - 0.61$ ) achieve similar performance, likely due to their shared reliance on histopathological features. While WSIs provide direct morphological insights and pathology reports summarize these observations, both modalities may be more affected by feature extraction challenges and variability in reporting, making them less discriminative than genomic features. + +# 5.1.3. Impact of Prototypes in Unimodal and Multimodal Approaches + +In unimodal settings, prototype-based methods outperform non-prototype approaches for gene and text data. However, for histology, non-prototype methods achieve higher performance, as seen in Table.1, where TransMIL, CLAM and $\mathbb{R}^2$ -TMIL outperform $\mathrm{PS3}_{\mathrm{WSI}}$ . This decline can be attributed to the compression effect of histological prototyping. Reducing thousands of image patches to a compact set of prototypes reduces data dimensionality and complexity but can lead to the loss of fine-grained histological details. + +However, prototyping can enhance multimodal learning by facilitating better integration across modalities. While + +MIL-based methods perform well in unimodal settings, they tend to struggle with multimodal integration. In contrast, prototyping-based approaches significantly outperform MIL-based methods when combining histology with transcriptomics and/or text. As shown in Table.1, PS3, $\mathrm{MMP}_{\mathrm{Trans}}$ and $\mathrm{MMP}_{\mathrm{OT}}$ outperform SurvPath, MCAT, CMTA and MOTCat, demonstrating the benefits of prototyping for multimodal fusion. A similar trend is observed in the histology-text configuration where the histology + text method $(h,t)$ ablation study in Table.2 outperforms MIL-based method, SurvivMIL by $13.18\%$ . Data scale disparities across modalities can lead to modality dominance and imbalance, hindering effective multimodal integration. Prototyping mitigates this by normalizing data scale while preserving essential information, ensuring more balanced multimodal integration where each modality contributes meaningfully to survival prediction. + +# 5.1.4. Two-Modal vs. Three-Modal Approaches + +As shown in Table.1, integrating all three modalities outperforms both dual-modality and unimodal approaches, achieving $6.72\%$ and $7.21\%$ improvement compared to the next-best multimodal (with C-Index 0.655) and unimodal (with C-Index 0.652) methods, respectively. This underscores the value of incorporating pathology reports into the workflow. Further supporting this, Table.2 presents an ablation study (Impact of Modality Combinations), which evaluates our model's performance across different two-modality combinations. The results show that the proposed three-modal approach, PS3 $(h,p,t - 0.699)$ achieves $8.54\%$ higher performance than Histology + Text $(h,t - 0.644)$ , $1.75\%$ higher performance than Pathways + Text $(p,t - 0.687)$ and $7.04\%$ higher performance than Pathways + Histology $(p,h - 0.653)$ . Notably, Pathways + Text outperforms both other dual-modality combinations, highlighting the prognostic value of pathology reports. These results highlight the advantage of multimodal integration in improving patient prognostication. + +# 5.2. Ablation Study + +We conducted extensive ablation studies in Table.2 to evaluate the impact of various design choices on multimodal learning performance. Below, we summarize our key findings: (1) Number of Diagnostic Text Prototypes : Instead of setting the number of text prototypes $N_{\mathcal{T}}$ to the average length of text segments in the training dataset, we experimented with setting it to the 90th percentile (p90). However, this introduced additional noise, which reduced the overall performance. (2) Feature Encoder Performance: We compared different vision-language feature encoders and discovered that PLIP-based [16] features outperformed those derived from QUILT-Net [17]. (3) Impact of Modality Combinations: As explained previously in Section.5.1.4 the proposed model which incorporates all three + +modalities $(h,p,t)$ outperforms all two-modality combinations, highlighting the importance of integrating multiple complementary data sources. (4) Fusion Methods Comparison: We evaluated two different fusion strategies: Late Fusion: This approach only applies attention within each modality, without capturing any cross-modal interactions. Modalities are only merged at the final stage before prediction. Hierarchical Fusion: This approach employs a two-step process. First, it models cross- and self-modal interactions between histology and text. Then, the fused (histology + text) representation undergoes additional self and crossattention with transcriptomics. We note that the proposed method outperforms both aforementioned fusion strategies. (5) Effect of Learnable Embeddings: We experimented without adding the randomly initialized embeddings, $\mathbf{e}_r$ to the feature representations of each modality. Our results indicate that these embeddings improve model performance by allowing the model to learn richer feature representations. (6) MLPs: Instead of separate MLPs for the prototypes we experiment with implementing a single shared MLP for all prototypes across different modalities. + +# 6. Conclusions + +Pathology reports contain critical diagnostic and prognostic insights, yet remain under-utilized in computational survival prediction models. While transcriptomic and histological data capture molecular and spatial characteristics, pathology reports offer expert-driven interpretations that complement these modalities. However, existing approaches often overlook this valuable resource in multimodal survival analysis. To address this, we proposed a prototype-based multimodal fusion framework that integrates cancer aggressiveness-related signals from WSIs, pathology reports and transcriptomic data for improved survival prediction. By transforming each modality into structured representations – histological prototypes for WSIs, diagnostic prototypes for pathology reports and pathway prototypes for transcriptomic data – we mitigated modality imbalance and improved predictive performance. The PS3 multimodal transformer effectively modeled cross-modal interactions across all three modalities, leading to superior predictive performance. We evaluated our proposed model across six cancer types, outperforming both unimodal and multimodal baselines. + +Future work can further enhance this approach by incorporating additional multi-omics modalities, radiology images and patient metadata, to provide a more comprehensive view of patient characteristics. 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0000000000000000000000000000000000000000..cd208f7ae21dcca43ad4933c145dc570a1840114 --- /dev/null +++ b/ICCV/2025/PUMA_ Empowering Unified MLLM with Multi-granular Visual Generation/full.md @@ -0,0 +1,396 @@ +# PUMA: Empowering Unified MLLM with Multi-granular Visual Generation + +Rongyao Fang $^{1*†}$ Chengqi Duan $^{3*}$ Kun Wang $^{4}$ Hao Li $^{1,5}$ Linjiang Huang $^{6}$ Hao Tian $^{4}$ Xingyu Zeng $^{4}$ Rui Zhao $^{4}$ Jifeng Dai $^{5}$ Hongsheng Li $^{1,2‡}$ Xihui Liu $^{3‡}$ + +$^{1}$ CUHK MMLab $^{2}$ CPII under InnoHK $^{3}$ HKU $^{4}$ SenseTime $^{5}$ Shanghai AI Lab $^{6}$ BUAA + +a) The Diversity and Controllability Requirements of Different Visual Generative Tasks + +Generate images of a puma in different postures. + +![](images/1aaa4a26a5a33627a5be2a0018d64480c973a1c5c4fe8e2c72efcf436bf2f544.jpg) +Diverse Text-to-Image Generation + +![](images/189b53c6f73d041f0abb1d854297f7befaee160ed90462b688b33933408f6abb.jpg) + +![](images/78e098137950303c8b91db56ac17814a44b4e0e909364d9a9da7e36366529f73.jpg) + +Draw an image based on canny input. + +![](images/995dcaa8fc8c7b9882256ca3f82e7eb6f426cf275027aea373d879e7c65a31e9.jpg) +Conditional Image Generation + +![](images/536992201bd5bd142565daeb81342f094c209f133b9810edf0631af354ceb18b.jpg) + +Remove the tractor from the field. + +![](images/359c09f3c3f9619a373db2bdba0070f1ff906769da6431712ba39a5a73de08ab.jpg) +Image Manipulation + +![](images/dc595064f9c5519a9b91676aebbb71b816d51b5d910a17380ebb17bd7f7ccf43.jpg) + +Diversity + +Controllability + +b) PUMA for Various Visual Generation and Understanding Tasks + +The image should convey On the way to Eggum. + +Use inpainted image as input to generate an image + +![](images/24b348113f15e3bbd162960efe33f8baccaf0d23433236fc725ceba9e5f891e2.jpg) +Image Editing + +![](images/8b370006e349e0e5be07a7960331eaf0d8d56903d2d19bce95b6a2a6b91b565b.jpg) +Image Inpainting + +![](images/2937054dd165e0508ac602059a080cd68100a2a323cbabe63f4aa2e73a298054.jpg) +Conditional Image Generation + +Produce a visual with canny edge +Portrait Preparing for Examinations, 1864 by Ilya Efimovich Repin. + +![](images/3a8ef2c15837621dc69d0428003b37a59afa5c2bbdbedf570dfc1233a9c7773b.jpg) +Image Understanding + +![](images/86fd00628c8efde4e4221afb72209b24456aaf33717bc427f4f58f1893a7e289.jpg) + +Please remove the black cow statue from the bench. + +![](images/60d01a206bd382da0fb56ec2ef38936bf9ca9e83164890207d3dd2b4d62a4dd8.jpg) + +![](images/762c3f88ef787cecbc236b09f2691c79b17cbc8c285557922992337dac7a2df5.jpg) +Figure 1. a) Diversity and controllability trade-off in image generation tasks: diverse text-to-image generation requires high diversity and fidelity, while tasks like conditional generation and manipulation require high controllability on the image. b) The introduced PUMA, a unified multimodal large language model that processes and generates multi-granular visual representations, balancing diversity and controllability across visual generation tasks. It excels in image understanding, diverse text-to-image generation, editing, inpainting, colorization, and conditional image generation. + +What is the purpose of the sign? + +![](images/0679a7d723dfd843fe139f07a146afc63c5871bbc31bc0e54335682dae533163.jpg) + +It encourages people to take advantage of the service without the need for prior scheduling, making it more accessible and convenient for potential customers. + +Generate an image with the caption: a cute fox artwork by James Gilliard vibrant colors + +![](images/1d744cf20c34426e2885660cc69a7e80ef0e4984eabd0d13e03405c719798906.jpg) +Diverse Text-to-Image Generation + +![](images/4d202b86b7fcffa0772ecd3311fa0bc6725486ee39867647ff9ba199da5d6fe1.jpg) + +![](images/2adb373658d6b81ff68e9976fa8ff27ac6017ecd5bfc1295fab9f1823c3f0a9a.jpg) + +![](images/c1cdd4ec3c0bf245a10731c823d1919edec032f640bb2dd4d2094d7791f7a100.jpg) + +# Abstract + +Recent advancements in multimodal foundation models have yielded significant progress in vision-language understanding. Initial attempts have also explored the potential of multimodal large language models for visual content generation. However, existing approaches face a trade-off between generation diversity and controllability, struggling to meet the varying granularity demands of different image generation tasks within a unified MLLM framework. In this work, we propose PUMA, emPowering Unified MLLM with Multi-grAnular visual generation, a novel paradigm + +that tackles the diversity-controllability trade-off. PUMA achieves this by unifying multi-granular visual features as both inputs and outputs of MLLMs, thus effectively meeting the distinct granularity needs for diverse generation and precise manipulation within a single framework. Following multimodal pretraining and instruction tuning, PUMA demonstrates remarkable capabilities in a wide range of multimodal tasks, including image understanding, diverse text-to-image generation, editing, inpainting, colorization, and conditional generation. This work marks a significant stride towards realizing truly unified MLLMs capable of seamlessly adapting to the diverse granularity demands and task requirements inherent in various visual tasks. + +# 1. Introduction + +Unifying multimodal understanding and generation capabilities is a critical milestone toward artificial general intelligence (AGI), as it paves the way for more versatile and human-like AI systems capable of rich interactions with the world. Towards this goal, recent advancements [2, 31, 66] in multimodal large language models (MLLMs) have made significant progress in integrating visual understanding with natural language interfaces. However, developing a unified framework that excels at both comprehending and generating visual content remains a challenge. + +To unify visual understanding and generation, a promising recent research direction leverages MLLMs to generate visual conditions to feed into diffusion-based image decoders [11, 17, 47, 48, 67]. This architecture capitalizes on MLLMs' semantic understanding capabilities while harnessing diffusion modules' visual generation strengths. Such methods successfully support different tasks within a single framework, including image understanding, text-to-image generation, and image editing. + +However, these approaches consistently encounter a fundamental trade-off between diversity and controllability. The challenge arises from a fundamental mismatch: achieving diversity benefits from coarse-grained conditioning that focuses on semantic concepts, while controllability requires fine-grained conditioning to capture detailed visual features. This contrasts with the single-granularity conditioning typically passed from the MLLM to the diffusion decoder. As shown in Fig. 2, we conduct a pilot study that clearly demonstrates this trade-off. In this study, we train diffusion decoders using different numbers of CLIP visual tokens [40] as conditional inputs and observe a clear trade-off relationship. Specifically, more visual tokens yield stronger conditions of image details but reduce the diversity of the decoded images. Conversely, using fewer visual tokens focused more on semantic concepts, leading to diverse decoded images that are semantically aligned with the conditions but lack fine-grained visual details. This trade-off poses a significant problem because different visual generation tasks have inherently different requirements. For example, text-to-image generation benefits from higher diversity to create varied and creative outputs that faithfully match text descriptions. In contrast, tasks like image editing and inpainting require precise control through fine-grained visual features to ensure accurate reproduction of specific image elements. A recent work [17] also identifies the tradeoff problem and tries to solve it by using condition images directly as diffusion inputs for fine-grained control. However, even this approach still fails to provide a unified solution to the broader multi-granularity challenge. + +Towards the multi-granular demands of various tasks, we propose a novel paradigm emPowering Unified MLLM with Multi-grAnular visual generation (PUMA). PUMA facilitates the seamless integration of image generation and understanding within a unified framework by incorporating + +![](images/06aa5862707758a22d5105fccd149df0d8159ab1d09a4a5cc88405da75e26a54.jpg) +Figure 2. Pilot study on the controllability-diversity trade-off. Results from diffusion decoders trained with different numbers of CLIP visual tokens [40]. Moving from left (256 tokens) to right (1 token), we observe finer-grained conditioning produces high controllability but limited diversity, while coarser-grained conditioning enables greater diversity but reduced control over details. + +multi-granular features. By leveraging multi-scale features, PUMA empowers MLLMs to excel in both diverse image generation and precise control for various visual manipulation tasks, all within a unified framework. + +Our PUMA method comprises four key modules: 1) An image encoder that extracts multi-granular representations, which serve as the foundation for visual generation and understanding; 2) An autoregressive MLLM that processes and progressively generates multi-scale image features; 3) A lightweight granularity selection router that automatically determines optimal feature granularity based on task requirements, enabling adaptive control over the controllability-diversity trade-off; and 4) A set of dedicated diffusion-based image decoders that transform MLLM-generated features into images at multiple granularities. To optimize this framework, we employ a staged training strategy: first fine-tuning pre-trained diffusion models as our image decoders, where each model decodes images conditioned on the corresponding feature granularities from the encoder; then training the autoregressive MLLM with regression loss supervised by the multi-scale encoder features. Finally, a lightweight router is trained on a small set of data to learn which granularity level best suits different instructions and visual tasks. PUMA leverages largescale pre-training followed by instruction tuning, enabling our model to handle diverse tasks including image understanding, text-to-image generation, editing, inpainting, colorization, and conditional generation. + +In summary, we introduce a novel multi-granularity paradigm for MLLMs that addresses the limitations of existing single-scale methods. By simultaneously processing and generating features at multiple granularities, it handles a wide range of tasks, from diverse image generation + +to precise editing and highly controllable generation. This unified framework represents a significant advancement towards more versatile and capable MLLMs, contributing to the broader goal of achieving AGI in multimodal domains. + +# 2. Related Work + +# 2.1. Multimodal Understanding + +The rapid advancement of large language models (LLMs) has catalyzed significant progress in multimodal large language models (MLLMs) for multimodal understanding tasks [8, 9, 24, 27, 28, 61, 63]. Pioneering works such as LLaVA [31] and MiniGPT-4 [66] have demonstrated remarkable performance across diverse image understanding tasks. These approaches typically employ visual encoders, such as the CLIP encoder [40], to extract continuous image features, which are then projected into the LLM's embedding space for subsequent tasks. While successfully unifying various image understanding tasks within a single model, these methods mostly adhere to a multimodal-input, text-output paradigm. Matryoshka [6] has explored the use of multi-granular visual features, but its focus is on enhancing image understanding capabilities rather than a unified framework for both generation and understanding. These methods excel at text-based responses to visual inputs but cannot generate multimodal outputs beyond text, limiting applicability in tasks requiring visual content generation. + +# 2.2. Unified Understanding and Generation for MLLMs + +Recent research has focused on equipping MLLMs with multimodal output capabilities [49, 55, 58, 67]. GILL [22] pioneered the integration of image generation abilities into MLLMs. Subsequently, SEED-LLaMA [15] and Emu [47] further advanced image generation and understanding capabilities within MLLMs, while DreamLLM [11] proposed an end-to-end training approach for enhanced performance. + +More recent works, such as SEED-X [17] and Emu2 [48], have scaled up MLLMs for unified generation, adopting continuous feature-based methods. These approaches utilize pre-trained vision encoders to extract continuous semantic features, which MLLMs then autoregressively regress. However, these single-scale image feature generation pipelines struggle to address tasks with varying granularity demands. SEED-X attempts to address the multi-granularity issue by introducing conditional image input to the diffusion-based decoder for fine-grained control. However, it limits applicability to image editing tasks encountered during decoder training. In contrast, our work proposes a novel multi-granularity paradigm that addresses these limitations by simultaneously handling multiple levels of feature granularity within a single, unified framework. + +Alternative approaches have also been investigated. Chameleon [50] explored using discrete image tokens to bridge image understanding and generation, but the vector quantization process leads to information loss, hinder + +ing high-performance image understanding. TransFusion [65] and show-o [57] proposed transforming the MLLM backbone itself into a denoiser in a diffusion-based or demasking-based approach. However, these methods require numerous denoising steps for each image generation, resulting in substantial computational costs given the scale of current MLLM backbones. + +# 3. Method + +Existing approaches that utilize MLLMs to generate visual conditions to feed into diffusion-based image decoders typically optimize for either fine or coarse-grained features, resulting in a trade-off between precise control and generation diversity. To overcome this limitation, we propose PUMA, a unified multi-granular MLLM. Our approach simultaneously processes multiple levels of feature granularity within a unified MLLM framework, enabling seamless adaptation across a wide spectrum of image generation tasks, accommodating both coarse and fine-grained requirements. + +Our framework consists of four components: an image encoder that extracts multi-granular visual representations (Sec. 3.1), a set of diffusion-based image decoders each specialized for different granularity levels (Sec. 3.2), an autoregressive MLLM that processes and generates multiscale image features (Sec. 3.3), and a granularity selection router that dynamically determines the optimal feature resolution based on task requirements (Sec. 3.4). These components work synergistically to address the fundamental controllability-diversity trade-off by adaptively selecting the appropriate granularity for different visual tasks. Our approach employs a staged training strategy (Sec. 3.5): first fine-tuning the diffusion decoders, then training the MLLM with regression loss, and finally optimizing the router on a small dataset to learn task-specific granularity selection. This enables PUMA to excel at diverse tasks including image understanding, generation, editing, and conditional image generation. + +# 3.1. Image Encoding and Multi-granular Feature Extraction + +Our unified multi-granularity paradigm leverages a semantic image encoder to extract multi-scale features, forming the foundation for diverse visual task processing. We employ a CLIP [40] semantic image encoder to process input images $x$ and generate the initial set of high-resolution features $f_0 \in \mathbb{R}^{H \times W \times C}$ , with $H$ and $W$ representing the spatial dimensions of the highest resolution feature grid, and $C$ denoting the channel dimension. In our setting, the feature size is $H = W = 16$ , thus the highest resolution feature $f_0$ has 256 visual tokens. + +To obtain multi-granular representations, we derive lower resolution features through successive applications of 2D average pooling with kernel size 2 and stride 2: + +$$ +f _ {i} = \operatorname {A v g P o o l} \left(f _ {i - 1}\right), \quad i = 1, 2, \dots , N \tag {1} +$$ + +![](images/37a29011813feec713a4a7d5e8f31f61eb3624e7e14bf56364872c194c01c513.jpg) +Figure 3. PUMA architecture overview showing the unified multi-granular autoregressive model that processes text and images through multiple feature scales ( $f_{N}$ to $f_{0}$ ). + +where $N$ is the number of additional granular levels. This process generates feature grids at progressively coarser resolutions, from fine-grained features preserving spatial details and textures, through mid-level features capturing object parts and regional structures, to coarse-grained semantic concepts. The features are denoted as $f_0, f_1, f_2, f_3$ , and $f_4$ , with 256, 64, 16, 4, and 1 visual tokens, respectively. + +# 3.2. Multi-Granular Visual Decoding + +Image features at different granularities encode varying levels of information. We employ diffusion-based models as the image decoders. When processing coarse-grained features, the decoders can effectively synthesize missing fine-grained information with their learned image priors and generate diverse, semantics-aligned images. On the other hand, when handling fine-grained features, they accurately decode precise image details. This versatility in decoding images across different granularities makes diffusion-based models suitable for our multi-granularity approach. + +We develop a set of dedicate diffusion-based decoders $D_0, D_1, \ldots, D_N$ corresponding to the feature scales $f_0, f_1, \ldots, f_N$ . These decoders enable the visual decoding of images at various levels of granularity. We formulate the image decoding process for each granularity level $i$ as $\hat{x}_i = D_i(f_i, z)$ , where $\hat{x}_i$ is the decoded image, $f_i$ is the feature map at granularity level $i$ , and $z$ is a random noise vector for the diffusion process. + +We leverage the pre-trained SDXL models [38] as our decoding framework and fine-tune these pre-trained models to decode images conditioned on different granular features. By modifying the conditional input mechanism through cross-attention in SDXL to accept our multi-granular features $f_{i}$ , we harness the models' inherent ability to decode coherent images. + +During the training process of different granular image decoding, the image encoder is frozen to preserve semantic property. Fig. 2 illustrates the visual decoding capabilities + +of multi-granular decoders. The visualizations demonstrate the fidelity of decoded images across different granularities, with finer-grained features yielding decoded images closer to the original input, and coarser-grained features leading to guided by the semantics of the input image. This validates the effectiveness of our approach in preserving and utilizing multi-granular visual information. + +This multi-granular decoding framework, combined with hierarchical feature extraction, establishes a foundation for subsequent stages of our MLLM architecture, enabling diverse visual tasks in later training phases. + +# 3.3. Progressive Multi-Granular Image Modeling in Autoregressive MLLM + +Driven by the goal of utilizing a unified framework capable of adapting to a wide range of visual-linguistic tasks with varying granularity requirements, we design a unified autoregressive MLLM to process and generate both text tokens and multi-granular image features. + +Our autoregressive MLLM, denoted as $M$ , processes text and multi-granular image features progressively, as illustrated in Fig. 3. The model generates visual features token by token, predicting each token sequentially within each granularity level and progressing from the coarsest level $N$ to the finest level 0. + +We structure the input sequence as a concatenation of text tokens and flattened image feature tokens across multiple granularity levels. This unified and progressive approach enables the model to capture dependencies from coarse global structures to fine local details. The total token count for each input or output image is $1 + 4 + 16 + 64 + 256 = 341$ , representing only a $33\%$ increase over the 256 tokens typically used in popular image understanding MLLMs. This design keeps the additional computation manageable, allowing for enhanced granularity without significantly impacting efficiency. + +The MLLM is trained using an autoregressive next token prediction objective, combining both text and image losses: + +$$ +\mathcal {L} = - \sum_ {i} \log P \left(t _ {i} \mid t _ {< i}, F _ {< i}\right) + \sum_ {i = 0} ^ {N} \alpha_ {i} \sum_ {j = 1} ^ {k _ {i}} \left| f _ {i, j} - \hat {f} _ {i, j} \right| ^ {2} \tag {2} +$$ + +The first term represents the cross-entropy loss for text token prediction, where $t_i$ are text tokens. The second term is the regression loss for image feature prediction, where $f_{i,j}$ and $\hat{f}_{i,j}$ are the ground truth and predicted feature tokens, respectively, at the $i$ -th granularity level. $k_i$ is the number of visual tokens at the $i$ -th granularity level. The coefficient $\alpha_i$ allows for adjusting the importance of each granularity level during training. For the setting of $\alpha_i$ , refer to Appendix. + +# 3.4. Automatic Granularity Selection Router + +After training the MLLM, we introduce a lightweight granularity selection router that automatically determines the appropriate visual feature granularity for different generation tasks. This router employs a two-layer Q-former [25] architecture to classify which granularity level best suits each input. To create the training dataset, we use our trained MLLM and visual decoders to generate 10,000 visual outputs across different tasks, preserving the instruction text embeddings, multi-granularity output features, and the corresponding decoded images for all five granularity levels. The router takes instruction embeddings and multi-granularity features as input and produces granularity selection scores. We train this classifier using cross-entropy loss, where the training labels are derived from perceptual loss metrics computed on the decoded images. For diversity-oriented tasks, we assign positive labels to granularity levels that maximize perceptual differences between two decoded images with different random seeds. For precision-oriented tasks, we assign positive labels to granularity levels that minimize perceptual loss against ground truth images. This label assignment process is formalized as follows: + +For diversity-focused tasks: + +$$ +g ^ {*} = \arg_ {\max g \in 1, N} \mathcal {L} _ {p} \left(D _ {g} \left(f _ {g} ^ {s 1}\right), D _ {g} \left(f _ {g} ^ {s 2}\right)\right) \tag {3} +$$ + +For precision-focused tasks: + +$$ +g ^ {*} = \arg_ {\min g \in 1, N} \mathcal {L} _ {p} \left(D _ {g} \left(f _ {g}\right), I _ {g t}\right) \tag {4} +$$ + +where $g^{*}$ represents the optimal granularity level, $D_{g}$ is the decoder at granularity $g$ , $f_{g}^{s1}$ and $f_{g}^{s2}$ are features from different random seeds, $I_{gt}$ is the ground truth image, and $\mathcal{L}_{p}$ denotes perceptual loss. + +# 3.5. Multimodal Pretraining and Instruct Tuning + +To demonstrate the effectiveness of our unified multi-granularity paradigm, we implement a comprehensive two-stage training pipeline for PUMA: multimodal pretraining followed by task-specific instruct tuning. This approach allows our model to first acquire broad multimodal capabilities before specializing in targeted visual-linguistic tasks during the subsequent instruct tuning stage. + +Multimodal Pretraining: Our multimodal pretraining leverages a diverse set of large-scale datasets: Laion-2B [43], Laion-Aesthetics [5], GRIT [37], The Pile [14], OCR-VQA-200K [36], and LLaVAR [64]. This combination of datasets provides a rich mixture of image-text pairs, textual data, and specialized visual question-answering samples. To enhance the model's bidirectional understanding of image-text relationships, we employ a dynamic training strategy that randomly alternates between text-to-image and image-to-text tasks for each image-text pair. + +Instruct Tuning: Following pretraining, we conduct instruct tuning to adapt our model to a wide range of visual-linguistic tasks within a single unified model. This unified approach enables our model to handle diverse visual generation and understanding tasks within a single framework. + +For our unified PUMA, we combine multiple datasets spanning various visual-linguistic capabilities. We include Laion-Aesthetics [5], JourneyDB [45] and images generated by FLUX.1 [dev] [23] for high-quality text-to-image generation; SEED-Edit [16] for precise image editing; and a subset of MultiGen-20M [39] covering conditional generation tasks such as canny-to-image, inpainting, and colorization. For visual understanding capabilities, we incorporate subsets of LLaVA-OneVision [24] and Cambrain [51] datasets, excluding math/reasoning data and removing duplicates across datasets. + +# 4. Experiments + +We present our experimental results as follows: Sec. 4.1 details our experimental setup. In Sec. 4.2, we demonstrate that our $f_{0}$ scale feature achieves significantly better visual decoding performance compared to previous works using CLIP as the image encoder. Sec. 4.3 shows the evaluation of our router's adaptive granularity selection for balancing diversity and controllability. We then showcase PUMA's versatility across a range of tasks: diverse text-to-image generation (Sec. 4.4), image editing (Sec. 4.5), conditional image generation (Sec. 4.6), and vision-language understanding (Sec. 4.7). + +# 4.1. Setup + +Our unified multi-granular MLLM employs LLaMA-3 8B [52] as the language model backbone and CLIP-Large $(224\times 224$ input) [40] as the image encoder. The image decoders are initialized from pretrained SDXL models [38]. For details on the experimental setup, refer to the Appendix. + +# 4.2. Fine-grained Image Decoding + +Fine-grained image decoding is crucial for preserving image details, yet it has posed significant challenges for models like SEED-LLaMA [15], SEED-X [17], and Emu2 [48]. Fig. 4 visually illustrates our method's superior decoding quality. While SEED-LLaMA and SEED-X struggle with detailed decoding, limiting their precise image manipulation capabilities without additional techniques such as conditional image input (as used in SEED-X), Emu2 attempts + +![](images/7cad58f233aa2a35503c5d899f4baa56e741ab98bf826104572edeaf8d115960.jpg) +Rec. LPIPS: 0.675↓ Rec. LPIPS: 0.515↓ Rec. LPIPS: 0.253↓ Rec. LPIPS: 0.221↓ Rec. PSNR: 9.73↑ Rec. PSNR: 10.861 Rec. PSNR: 15.72↑ Rec. PSNR: 18.16↑ + +
TaskAttributef0(256)f1(64)f2(16)f3(4)f4(1)
T2IDiversity0.000.000.7418.6980.12
EditingPrecision98.971.030.000.000.00
Cond.Precision43.9754.101.930.000.00
+ +Table 1. Task-specific granularity selection distribution with granularity selection router, showing the probability $(\%)$ of each granularity level selected by our router across different tasks. Text-to-image generation (T2I) favors coarser granularity for higher diversity, while editing and conditional generation (cond.) tasks prefer finer granularity for greater precision. + +to improve fine-grained decoding by scaling up its image encoder to 4 billion parameters. Our approach achieves superior decoding quality with a more efficient architecture. We employ the CLIP-Large encoder (0.3 billion parameters), which is over 10 times smaller than Emu2's, and implement fine-grained level image embedding with 256 tokens. Our method using $f_{0}$ scale features achieves 18.16 PSNR and 0.221 LPIPS [62] on the ImageNet validation set. These results outperform Emu2's fine-grained decoding performance and significantly surpass SEED-LLaMA and SEED-X (without conditional input). + +# 4.3. Automatic Granularity Selection + +Tab. 1 presents the distribution of granularity levels selected by our router across different tasks, evaluated on COCO test set [29] (text-to-image), Emu-Edit test set [44] (editing), and MultiGen20M dev set [39] (conditional generation). The results reveal task-dependent selection patterns: text-to-image generation strongly favors coarser granularities $(f_{3}$ and $f_{4})$ , with $80.12\%$ selection of the coarsest level, enabling greater diversity in open-ended generation. Conversely, image editing tasks select the finest granularity $(f_{0})$ at $98.97\%$ , maximizing precise control over visual details. Conditional generation shows an intermediate pattern, primarily leveraging fine-grained features $(f_{0}$ and $f_{1})$ with a balanced distribution between these levels. These selection patterns demonstrate our router's effectiveness in automati + +![](images/5ae0001ba413ffb4b99fc1b2bf32a44b77c9775248e90f411d01f3145e85c9b7.jpg) +Anthropomorphic rat, wearing harajuku street wear, decora kei, hyper realistic, clothing shops, shop signs. + +![](images/3fdb85a5e7d2cfe090028c210737144b0cc8012fb8df47de6fb9a2dfeb7abdc5.jpg) +Figure 4. Fine-grained image reconstruction of SEED-LLaMA [15], SEED-X [17], Emu2 [48] and PUMA ( $f_0$ scale). Rec. LPIPS and PSNR denotes the reconstruction performance on ImageNet [10] validation set, in which our $f_0$ scale achieves the best reconstruction performance. +Figure 5. Diversity visualization of text-to-image generation results from PUMA, and Emu2 [48]. The generated features are input to corresponding diffusion-based decoders with different random seeds. +Figure 6. Visualization of diverse text-to-image generation results from PUMA. + +cally adapting to different task requirements, balancing diversity and controllability without manual intervention. + +# 4.4. Diverse Text-to-image Generation + +Our method generates diverse outputs by primarily utilizing coarse-grained features ( $f_4$ and $f_3$ scales), as indicated by the router selection probabilities in Tab. 1. This capability enables our model to produce varied images that accurately correspond to text conditions. Fig. 5 demonstrates that PUMA's outputs exhibit higher diversity while keeping the consistency with the text prompt. In contrast, generation results from Emu2 [48] show limited diversity. + +For quantitative evaluation, we assess our model on two benchmarks. First, on the MSCOCO 30K validation dataset [29], we present CLIP-I, CLIP-T, FID, and $\mathrm{LPIPS}_d$ in Tab.3, where the first three metrics measure consistency while $\mathrm{LPIPS}_d$ measures generation diversity. $\mathrm{LPIPS}_d$ measures the average difference between two generated images with different random seeds of the same prompt, reflecting generation diversity. Second, we evaluate on the GenEval benchmark [18] in Tab. 2, which assesses compositional generation capabilities across multiple categories. PUMA achieves an overall score of 0.61, on par with the best unified model (Janus) and specialized model (SD3), while excelling in single object generation (0.98), two object composition (0.73), and color attributes (0.85). Notably, PUMA significantly outperforms other unified models in counting + +
MethodArchitectureOverallSingle Obj.Two Obj.CountingColorsPositionAttr. Binding
Specialized Models
SDv1.5 [42]UNet+CLIP0.430.970.380.350.760.040.06
SDv2.1 [42]UNet+CLIP0.500.980.510.440.850.070.17
SD-XL [38]UNet+CLIP0.550.980.740.390.850.150.23
DALLE-2 [41]UNet+CLIP0.520.940.660.490.770.100.19
SD3 (d=24) [12]MMDIT+CLIP+T50.620.980.740.630.670.340.36
LlamaGen [46]Autoregressive0.320.710.340.210.580.070.04
Unified Models
Chameleon [50]Autoregressive0.39------
LWM [32]Autoregressive0.470.930.410.460.790.090.15
SEED-X [17]UNet+LLaMA0.490.970.580.260.800.190.14
Emu3-Gen [53]Autoregressive0.540.980.710.340.810.170.21
Janus [54]Autoregressive0.610.970.680.300.840.460.42
PUMAUNet+LLaMA0.610.980.730.600.850.300.22
+ +![](images/a9e3cd4a2344068445cc47a4db81f7751304421e5c16d91926aba051dfdc77bd.jpg) +Figure 7. Left: Visualizations of PUMA's editing result which utilizes $f_{0}$ scale feature to preserve fine-grained detail of input image. Right: Visualization of PUMA's conditional generation results. ①: canny-to-image generation; ②: image inpainting; ③: image colorization. + +Table 2. Evaluation of text-to-image generation on GenEval benchmark [18]. Obj.: Object. Attr.: Attribution. + +
ModelCLIP-I↑CLIP-T↑FID↓LPIPSd↑
SD-v1.5 [42]0.6670.3029.930.692
DALL-E 2 [41]-0.31410.93-
SDXL [38]0.6740.31013.760.600
DALL-E 3 [3]-0.320--
GILL [22]--12.20-
SEED-LLaMA [15]0.682-16.040.652
Emu [47]0.6560.28611.600.700
Emu2 [48]0.6860.29724.750.329
SEED-X [17]0.7290.31414.680.493
Unified-IO 2 [35]--13.39-
Emu3-DPO [53]0.6800.31219.30-
PUMA0.7110.32115.210.603
+ +tasks (0.60), demonstrating our framework's strong compositional abilities. Fig. 6 visually demonstrates our model's text-to-image generation capabilities with various prompts. + +Table 3. Diverse text-to-image generation evaluation on MSCOCO 30K validation set. CLIP-I, CLIP-T, and FID measure the similarity between generated images and ground truth images or prompts. $\mathrm{LPIPS}_d$ quantifies the difference between two images generated from the same prompt, reflecting generation diversity. + +
ModelCLIP-I↑CLIP-T↑DINO↑
InstructPix2Pix [4]0.8340.2190.762
MagicBrush [60]0.8380.2220.776
EMU-Edit [44]0.8590.2310.819
OmniGen [56]0.8360.2330.804
PUMA0.8390.2620.780
+ +Table 4. Image editing evaluation on Emu-edit testset [44]. + +# 4.5. Image Editing + +To assess PUMA's image editing capabilities, we evaluated it on the Emu-Edit test benchmark [44]. Tab. 4 presents the results using CLIP-I, CLIP-T, and DINO [7] scores. CLIP-I and DINO scores measure the model's ability to preserve elements from the source image, while CLIP-T reflects the consistency between the output image and the target caption. Our results demonstrate that PUMA exhibits strong preservation ability, second only to the current state-of-the-art model, EMU-Edit. Notably, PUMA achieves significantly better CLIP-T scores, even surpassing the state-of-the-art model. This indicates superior alignment between + +![](images/06bab38c21b37e9ac1ca2db11a38b49bb6a8938c0b8ccb563223026c5f7b085f.jpg) +Input image + +![](images/6dd186c0cc93c1e35ec0d63e5034dc770189c49dba9d1a87aad7b90e764b2d48.jpg) +PUMA $f_{0}$ scale + +![](images/380f2daede3322125c9a8b91b0490cdcb7a262c7d83714101e4dc057f0e8fc8f.jpg) +PUMA $f_{1}$ scale +Replace the trees with palm trees. + +![](images/13aa003632471edb2e1258a4a0e06c1219496590577f14337fbdac103c413fbf.jpg) +Input image +Turn the grayscale image into an image. +Figure 8. Comparison of $f_{0}$ and $f_{1}$ feature scales for tasks requiring precise controllability. + +![](images/67e4e879ae1e7e5152153c3b12b9d67cc1a18f774415bce0cf146197e04d62b8.jpg) +PUMAf0 scale + +![](images/89287f6783ff4404b535d56e9db0c5770057c248070eb9b2e48d1ce4f97df71a.jpg) +PUMA $f_{1}$ scale + +
TypeModel# ParamsMMB↑MME↑GQA↑VQAv2(test)↑POPE↑Vizwiz↑
Und. OnlyLLaVA-v1.5 [30]7B64.31510.762.078.585.950.0
InstructBLIP [9]13B-1212.849.5-78.933.4
Qwen-VL-Chat [2]7B-1487.557.578.2-38.9
mPLUG-Owl2 [59]7B64.51450.256.179.485.854.5
Und. and Gen.Emu [47]13B---57.2--
NExT-GPT [55]7B58.0--66.7-48.4
SEED-X [17]17B75.41457.047.9-84.2-
Chameleon [50]34B---66.0--
Emu2Chat [48]40B--65.184.9-54.9
PUMA8B67.11472.760.175.684.246.5
+ +Table 5. Evaluation on multimodal understanding benchmarks. PUMA utilizes CLIP-Large encoder with ${224} \times {224}$ resolution input and 341-token multi-granular visual feature. Und. and Gen. denote "understanding" and "generation", respectively. + +
ModelT2I-AdapterControlNetPUMA
SSIM0.2310.3120.313
+ +Table 6. Conditional generation evaluation on canny-to-image on Multigen-20M. + +edited images and target captions. For qualitative evaluation, Fig. 7 provides visualizations of the editing results, illustrating PUMA's effectiveness in image manipulation. + +# 4.6. Conditional Image Generation + +PUMA demonstrates strong performance on conditional image generation tasks including canny-to-image, inpainting, and colorization. As shown in Fig. 7, our approach preserves image details effectively, particularly for inpainting and colorization, while maintaining good overall visual fidelity with appropriate diversity. Quantitatively, our canny-to-image generation achieves a SSIM score of 0.313 on the multigen-20M test set (Tab. 6), outperforming T2I-Adapter (0.231) and matching ControlNet (0.312). + +# 4.7. Image Understanding + +We evaluate PUMA's image understanding performance on several MLLM benchmarks, including MMB [33], MME [13], GQA [20], VQAv2 [1], POPE [26], and Vizwiz [19]. Tab. 5 presents the results of this evaluation. Despite PUMA's relatively few 8B parameters and the use of an image encoder with $224 \times 224$ resolution input, it demonstrates competitive and often superior image understanding performance compared to other unified understanding and generation models. Notably, PUMA's performance on some metrics even surpasses that of understanding-only baselines. This performance can be attributed to PUMA's use of multi- + +granular continuous visual tokens as input to the MLLM. A detailed ablation study examining the impact of different scale features as input on image understanding tasks is provided in the Appendix. + +# 4.8. Ablation + +We conduct an ablation study to examine the impact of feature scale selection on tasks requiring fine-grained controllability. Fig. 8 compares the outputs of $f_{0}$ and $f_{1}$ feature scales for image editing and colorization tasks. The results demonstrate that $f_{1}$ scale features are insufficient for preserving crucial image details, while $f_{0}$ scale features maintain the necessary fine-grained information for precise manipulation tasks. More ablation studies are in the Appendix. + +# 5. Conclusion + +In this paper, we introduce PUMA, a novel unified multi-granular MLLM that unifies various granular tasks in visual generation and understanding. By leveraging multi-granular representations, PUMA effectively addresses the challenge of balancing diversity and controllability in image generation tasks. Our approach demonstrates superior performance across a spectrum of visual tasks, including diverse text-to-image generation, image editing, inpainting, colorization, conditional generation, and understanding. PUMA's ability to adapt to varying granularity requirements within a single framework represents a significant advancement in MLLM capabilities. This work opens up new possibilities for more versatile and powerful multimodal AI systems, contributing to the broader goal of achieving artificial general intelligence in multimodal domains. + +# 6. Acknowledgment + +This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, and in part by NSFC-RGC Project N_CUHK498/24. + +# References + +[1] Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. Vqa: Visual question answering. In Proceedings of the IEEE international conference on computer vision, pages 2425-2433, 2015. 8 +[2] Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. 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0000000000000000000000000000000000000000..96cbef8a5854fe83c7871c62552e21fca97b9a9f --- /dev/null +++ b/ICCV/2025/PUMPS_ Skeleton-Agnostic Point-based Universal Motion Pre-Training for Synthesis in Human Motion Tasks/full.md @@ -0,0 +1,310 @@ +# PUMPS: Skeleton-Agnostic Point-based Universal Motion Pre-Training for Synthesis in Human Motion Tasks + +Clinton Ansun Mo $^{1,2}$ , Kun Hu $^{3,*}$ , Chengjiang Long $^{4}$ , Dong Yuan $^{1}$ , Wan-Chi Siu $^{5}$ , Zhiyong Wang $^{1}$ + +$^{1}$ School of Computer Science, The University of Sydney, NSW 2006, Australia + +2The University of Tokyo, Bunkyo City, Tokyo, Japan + +$^{3}$ School of Science, Edith Cowan University, WA 6027, Australia + +Meta Reality Labs, Burlingame, CA, USA + +$^{5}$ Hong Kong Polytechnic University, Hong Kong, China + +clinton.mo@weblab.t.u-tokyo.ac.jp, k.hu@ecu.edu.au, clong1@meta.com + +{dong.yuan, zhiyong.wang}@sydney.edu.au, enwcsiu@polyu.edu.hk + +# Abstract + +Motion skeletons drive 3D character animation by transforming bone hierarchies, but differences in proportions or structure make motion data hard to transfer across skeletons, posing challenges for data-driven motion synthesis. Temporal Point Clouds (TPCs) offer an unstructured, cross-compatible motion representation. Though reversible with skeletons, TPCs mainly serve for compatibility, not for direct motion task learning. Doing so would require data synthesis capabilities for the TPC format, which presents unexplored challenges regarding its unique temporal consistency and point identifiability. Therefore, we propose PUMPS, the primordial autoencoder architecture for TPC data. PUMPS independently reduces frame-wise point clouds into sampleable feature vectors, from which a decoder extracts distinct temporal points using latent Gaussian noise vectors as sampling identifiers. We introduce linear assignment-based point pairing to optimise the TPC reconstruction process, and negate the use of expensive pointwise attention mechanisms in the architecture. Using these latent features, we pre-train a motion synthesis model capable of performing motion prediction, transition generation, and keyframe interpolation. For these pre-training tasks, PUMPS performs remarkably well even without native dataset supervision, matching state-of-the-art performance. When fine-tuned for motion denoising or estimation, PUMPS outperforms many respective methods without deviating from its generalist architecture. The code is available at: https://github.com/MiniEval/PUMPS. + +![](images/8ffe6387ecfdc99d025daea679a299691aeda60a14222942b5200454ba13c8b2.jpg) + +![](images/a8a475819db4f43d05391ff230703b05655d702008966d59075358cd54507fee.jpg) +Figure 1. Overview of PUMPS pre-training, zero-shot evaluation, and fine-tuning pipelines. PUMPS consists of an auto-encoder (encoder-decoder modules) and latent synthesis component, which are pre-trained successively. + +# 1. Introduction + +3D motion skeletons serve as the backbone of computer animation pipelines for character motions. A skeleton is a hierarchical structure of joints in 3D space, used to deform the vertices of character meshes and other 3D features through positional and rotational transforms [25]. By representing joints as line segments, i.e. as bones, skeletons provide an intuitive interface for controlling charac + +ter poses. However, the diversity of skeletal configurations, with varying joint hierarchies and resting positions, has been a long-standing challenge for data-driven motion learning [19]. In particular, the lack of standardization for skeletons disables machine learning methods from generalizing across different characters, ultimately limiting their applicability in animation pipelines that often target specific character setups. This is demonstrated by the joint position and rotation-based output format used conventionally in deep motion synthesis architectures, such as for motion completion [5, 30, 31], and conditional motion generation [14, 53]. Attempts to standardize skeleton control systems [23, 26, 32] have largely traded off flexibility and expressiveness, making them less suitable for creative workflows. This limitation underscores the need for a non-intrusive approach to motion standardisation, which does not conflict with existing character animation processes. + +The concept of the Temporal Point Cloud (TPC) recently emerged as a geometric motion representation that obfuscates hierarchical differences of skeletons. Compared to standard point clouds, TPCs maintain consistent point identities over a temporal dimension, allowing individual points to represent trajectories that reflect the dynamics of a motion. Crucially, trajectories allow TPCs to reconstruct skeletal motion data without supervision [29]. While TPCs have enabled cross-skeleton motion transfer, the motion synthesis pipelines remain skeleton-specific, requiring motion synthesis to be learned independently for any new skeleton. This would be suboptimal and redundant if a unified motion synthesis solution can be achieved within the TPC medium natively, which, by definition, requires TPC synthesis. However, TPC synthesis presents significant challenges due to the curse of dimensionality from combining spatial and temporal dimensions. Temporal awareness is necessary for operating with motion features, whereas spatial awareness enables the production of evenly distributed points as expected of Gaussian-sampled TPC poses. Conventional architectures for capturing spatio-temporal awareness, such as attention mechanisms, are either hindered by excessive memory footprints due to large quantities of feature vectors, or exhibit high parameter redundancy from improper handling of point permutations. + +To address these issues and enable motion feature learning without skeletal representations, we propose Point-based Universal Motion Pre-training for Synthesis (PUMPS) - an efficient two-stage pipeline for pre-training various motion tasks directly within the TPC medium. As illustrated in Fig. 1, PUMPS begins with an auto-encoder stage that learns a latent representation of point cloud frames, and reconstructs TPCs from these latent features. We employ conventional point attention networks [69] for the encoding stage, and introduce a novel decoder architecture tailored for TPC reconstruction. Its key innovation is its + +incorporation of Gaussian noise vectors, which induce point identity-awareness into the decoding process, achieving efficient trajectory-centric TPC generation without point-wise attention. This practice grants our approach a significantly more simplified yet capable decoding process, with highly efficient utilisation of memory and parameters. + +We leverage the resulting latent embedding space to pre-train the motion synthesis model of PUMPS, using masked data modelling tasks including keyframe interpolation, motion transition, and short-term motion prediction [5, 30]. Our pre-trained model achieves state-of-the-art motion completion capabilities and is capable of zero-shot motion completion for any skeleton through the TPC-to-skeleton conversion [29]. Moreover, it can be effectively fine-tuned for various skeleton-specific motion tasks. We provide demonstrations of fine-tuning capabilities with 2D-to-3D motion estimation and motion denoising. + +In summary, we present the following contributions: + +1. We propose motion synthesis pre-training in the TPC medium, enabling universal human motion learning in a skeleton-agnostic manner. +2. To address memory and redundancy issues with TPC reconstruction, a noise vector-based architecture is proposed to imitate point cloud sampling processes and avoid expensive spatio-temporal attention mechanisms. +3. We demonstrate state-of-the-art motion completion capabilities of our approach through extensive experiments, as well as its adaptability in two fine-tuned tasks: motion denoising and 2D-to-3D motion estimation. + +# 2. Related Work + +This section reviews existing research on machine learning approaches in the point cloud domain, along with common tasks and methods for motion synthesis in the current field. Since our proposed method aims to be readily usable in practice, we incorporate an appropriate variety of these synthesis tasks into the model's pre-trained capabilities. + +# 2.1. Permutation-Invariant Learning for Points + +Point cloud data, as an unordered set of 3D vectors, presents a unique challenge in neural network design: the requirement for permutation invariance, where models should be order-insensitive. Early attempts approximated point clouds as volumes [37, 59], leveraging order-insensitive voxel aggregations to feed into neural networks. However, volumetric representations universally suffer from resolution limitations due to their dense structure. In response, attention mechanisms on randomly-ordered sets were demonstrated on recurrent networks [51] as a method to directly operate on set data, though consistent ordering was still preferred. A breakthrough occurred with the development of pooling-based attention architectures, which performed true permutation-invariant aggregation using maximum or + +average pooling.[38-40, 47]. Subsequently, Transformer-based architectures [56, 57, 69] further expanded the range of learnable point-based tasks, including point cloud completion [54, 63] and point-based 3D shape synthesis [58]. + +Despite these advances, reconstructing point clouds from latent features has remained unexplored for temporally-consistent points. Tokenisation-based reconstruction [34, 60, 63] lacks point identities upon which temporal points can be conditioned, whereas 2D-to-3D point folding [33, 41, 62] struggles to represent volumes, which are crucial for obfuscating skeletal structures. Our method addresses this limitation by leveraging a sequence-wise noise vector mechanism to condition and stochastically generate temporal points independently and in a volumetric manner. + +# 2.2. Data-Driven Motion Modelling and Synthesis + +Motion synthesis encompasses all tasks that produce motions based on a variety of conditions. Deep learning has established itself as the premier approach in this field, and primarily takes two forms: statistical motion prior-based optimisation [35, 49, 67], and end-to-end motion synthesis learning [5, 8, 30, 31, 36, 42, 48]. Motion priors model natural motion dynamics, and serve as the optimisation objective in synthesis problems with initial estimates, such as motion denoising from noisy motions [11, 49], and motion completion starting from classical interpolation [2, 20, 49]. In contrast, end-to-end motion learning can process any synthesis condition, including those without initial estimates, such as 3D pose/motion estimation from 2D keypoints or videos [21, 27, 70, 71], sign language translation [15, 61, 64], and text-to-motion generation [17, 52, 66]. Unlike motion priors, end-to-end learning generally requires training data that specifically pertains to the synthesis task. As end-to-end solutions become increasingly prominent in motion synthesis, the necessity of compatible task-specific motion datasets stands out as a major obstacle towards their practicalities outside of lab environments. + +# 3. PUMPS Architecture + +PUMPS consists of three components: 1) Point cloud frame encoder $\Phi^{\mathrm{enc}}$ to transform TPCs into a rich latent space, 2) TPC reconstruction decoder $\Phi^{\mathrm{dec}}$ to reconstruct temporal-aware point clouds, and 3) Latent motion synthesiser $\Phi^{\mathrm{LMS}}$ to learn motion synthesis through masked self-supervision. + +# 3.1. Point Cloud Frame Encoder + +The frame encoder $\Phi^{\mathrm{enc}}$ is a crucial component of PUMPS, designed to extract rich latent features of pose patterns from individual point cloud frames sampled from skeletal poses. By using point clouds as a universally compatible representation, the encoder can be trained on various motion datasets, regardless of their native skeleton structure. The + +![](images/654fa44c0fef046be182a537ccbfdab6032bd8ad6cb6336f067b95b5f9c7dad5.jpg) +Figure 2. Training strategy of the PUMPS auto-encoder components $\Phi^{\mathrm{enc}}$ and $\Phi^{\mathrm{dec}}$ . The primary objectives of the auto-encoder are to learn a TPC reconstruction process for $\mathcal{P}'$ , and produce a regularised latent space $\mathcal{V}$ of point cloud frame features. + +![](images/728e8e27b7dc0ae32139e92fed3d819319ecebcd72b8a4572c37c6fef6db12a4.jpg) + +resulting skeleton-agnostic latent space serves as a foundation for learning a wide range of motion synthesis tasks. + +To begin, we generate point cloud data from the proximate volumes of posed skeletons using the TPC sampling setup in [29]. Formally, given a pose $x$ , we can sample its point cloud representation as $\mathcal{P}_x = \{p_0, p_1, \dots, p_{|\mathcal{P}| - 1}\}$ where $|\mathcal{P}|$ indicates the number of points in the point cloud. Each point $p \in \mathcal{P}$ consists of a 3D position and a one-hot body group based on the bone with which it is associated, assigned to one of the following classes: {body, left arm, right arm, left leg, right leg}. The encoder converts $\mathcal{P}_x$ into a $|v|$ -element vector $v_x \in \mathbb{R}^{|v|}$ . For point aggregation, our setup trains a PointTransformer backbone [69] from scratch. + +$\Phi^{\mathrm{enc}}$ is trained using an auto-encoder objective: reconstructing the input point cloud from its latent representation (discussed in Sec. 3.2). To make reconstructions of latent vector $v$ learnable with scalar error-based objectives (in Sec. 3.3), the latent space must 1) maintain a consistent distribution between features and 2) ensure near-equal importance for each feature in the decoding process. In detail, we employ non-affine layer normalisation after $\Phi^{\mathrm{enc}}$ to restrain features within a normal $\mathcal{N}(0,1)$ distribution, and a sequence-wise dropout strategy in $\Phi^{\mathrm{dec}}$ to regularise individual feature importances. Sequence-wise dropout omits the same feature indices throughout a given sequence, ensuring that remaining features retain continuity, as opposed to frame-independent omission with standard dropout. + +![](images/e5a686bab08a515beffe638ff4f1901bbe22f565452c2e6112fa397f76a968c2.jpg) +Figure 3. Motion completion pre-training for the latent motion synthesiser $\Phi^{\mathrm{LMS}}$ , using a frozen pre-trained checkpoint for $\Phi^{\mathrm{enc}}$ . Gray latent feature vectors are masked out from the $\Phi^{\mathrm{LMS}}$ input. + +# 3.2. Point Cloud Reconstruction Decoder + +TPCs present several significant challenges for the reconstruction process. A TPC decoder should account for point identities to maintain temporal consistency when tracking points across frames. Intuitively, spatio-temporal self-attention could enable conditioning on both point identity and position; however, this approach is prohibitively expensive due to the quadratic complexity of self-attention. Given an encoded latent vector sequence $\mathcal{V} = \{v_0,v_1,\dots,v_{|\mathcal{V}| - 1}\}$ , spatio-temporal attention would result in a complexity of $O((|\mathcal{P}||\mathcal{V}|)^2)$ , where $|\mathcal{V}|$ is the frame length of the motion. + +We propose the construction of a latent space sampling system that can extract and reconstruct independent points from latent features, eliminating the need for costly pointwise attention. The architecture of $\Phi^{\mathrm{dec}}$ , illustrated in Fig. 2, is designed to reconstruct $|\mathcal{P}|$ point sequences from the latent vector sequence $\mathcal{V}$ . Since each $v \in \mathcal{V}$ is derived independently, without temporal awareness, $\Phi^{\mathrm{dec}}$ uses rotary self-attention (RoPE) [46] to produce a temporally-aware transformation $\mathcal{T} = \{t_0, t_1, \dots, t_{|\mathcal{V}| - 1}\}$ . + +To produce distinct temporal points for reconstructing the TPC, we introduce stochasticity via a $|z|$ -element Gaussian noise vector $z \in \mathbb{R}^{|z|} \sim \mathcal{N}(0,1)$ for each point, which is appended to each latent vector in $\mathcal{T}$ . This results in a set of $|\mathcal{P}| \times |\mathcal{V}|$ vectors: $\{t_0 \oplus z_0, t_1 \oplus z_0, t_2 \oplus z_0, \ldots, t_0 \oplus z_1, t_1 \oplus z_1, t_2 \oplus z_1, \ldots\}$ , where $t_\alpha \oplus z_\beta$ represents the $\alpha$ -th frame of the $\beta$ -th point. Each point maintains a consistent identity across different frames by having the same $z_\beta$ . In addition, we condition the body group of each point, similarly to the encoding process of $\Phi^{\mathrm{enc}}$ . Finally, each vector of this vector set is independently decoded into a 3D position sequence + +using multi-layer perceptron (MLP) layers, producing a reconstructed TPC. By deferring attention mechanisms before expanding to the point dimension, $\Phi^{\mathrm{dec}}$ achieves a complexity of $O(|\mathcal{V}|^2)$ for the RoPE attention step, followed by a set of $O(|\mathcal{P}||\mathcal{V}|)$ independent attention-free operations. + +The absence of point attention causes a lack of interpoint awareness in $\Phi^{\mathrm{dec}}$ . Consequently, common Chamfer distance-based objectives [29, 55, 63] often cause predicted points to collapse toward the centroid of body group clusters. This is because Chamfer distance addresses the presence, but not the expected distribution, of points within the reconstructed cloud. We propose the use of linear assignment. Given the expected and predicted TPCs $\mathcal{P}$ and $\mathcal{P}'$ , assignments methods like the Hungarian method [6] can deduce the optimal set of unique point pairs with the minimum total distance measured in Mean Squared Error (MSE). We denote the pairing set as $H(\mathcal{P}, \mathcal{P}') = \{(p_0, p_{h_0}', (p_1, p_{h_1}', \ldots)\}$ , where $\{h_0, h_1, \ldots, h_{|\mathcal{P}| - 1}\} = \{0, 1, \ldots, |\mathcal{P}| - 1\}$ , from which $\Phi^{\mathrm{enc}}$ and $\Phi^{\mathrm{dec}}$ can optimise the reconstruction objective $\mathcal{L}_{\mathrm{rec}}$ : + +$$ +\mathcal {L} _ {\text {r e c}} = \sum_ {0 \leq k < | \mathcal {P} |} \| p _ {k} - p _ {h _ {k}} ^ {\prime} \| _ {2} ^ {2}. +$$ + +# 3.3. Latent Motion Synthesiser + +We train our motion synthesis (pre-training) tasks on an existing Transformer-based architecture, which was proposed for motion interpolation learning [30], denoted as $\Phi^{\mathrm{LMS}}$ . Latent encodings of the pose data are created by a frozen $\Phi^{\mathrm{enc}}$ checkpoint. The tasks involve keyframe interpolation, motion transition, and short-term motion prediction, which can all be defined as masked data modelling problems, as illustrated in Fig. 3. Formally, our masked data modelling involves predicting an expected $|\mathcal{V}|$ -frame latent sequence $\mathcal{V} = \{v_0, v_1, \dots, v_{|\mathcal{V}| - 1}\}$ from a subset of given data $\mathcal{V}' = \{v_{k_0}, v_{k_1}, \dots\}$ , determined by a keyframe set $K = \{k_0, k_1, \dots\}$ , $K \subset \{0, 1, 2, \dots, |\mathcal{V}| - 1\}$ . + +- For keyframe interpolation learning, all $|K|$ keyframes are randomly selected, except the first and last frames which are always selected, i.e. $K = \{0, |\mathcal{V}| - 1\} \cup \{\mathbb{N}^{|K| - 2} \sim \mathcal{U}_{[1, |\mathcal{V}| - 2] \cap \mathbb{N}}\}$ . +- For motion transition learning, keyframes produce a masked interval between two known motion sequences, i.e. $K = \{k \in \mathbb{N} \mid 0 \leq k < |\mathcal{V}| \} \setminus \{k \in \mathbb{N} \mid a \leq k \leq b, a > 0, b < |\mathcal{V}| - 1\}$ . +- For short-term motion prediction learning, a continuous segment is removed from the end of the sequence, i.e. $K = \{k \in \mathbb{N} \mid 0 \leq k < b, b < |\mathcal{V}| - 1\}$ . + +To optimise $\Phi^{\mathrm{LMS}}$ , we minimise the MSE between $\nu$ , and predicted latent vectors $\mathcal{W} = \{w_0, w_1, \dots, w_{|\mathcal{V}| - 1}\}$ , i.e. $\mathcal{L}_{\mathrm{LMS}} = \sum_{0 \leq f < |\mathcal{V}|} ||v_f - w_f||_2^2$ . Normalisation steps in $\Phi^{\mathrm{enc}}$ are critical to ensuring consistent variances between features, validating the use of MSE as an objective. + +
Keyframe interpolationL2P↓L2Q↓NPSS↓Motion transitionL2P↓L2Q↓NPSS↓
515305153051530153060153060153060
LERP0.1700.5881.1660.2850.7651.1730.3541.3332.420LERP0.2480.7431.8890.2940.6731.2660.2481.0982.916
SLERP0.1700.5911.1720.2860.7661.1810.3571.3692.488SLERP0.2490.7451.8960.2920.6791.2660.2431.1002.953
TGcomplete0.1690.5421.1380.2830.7281.1820.3511.2022.200TGcomplete0.2220.6761.9130.2790.6631.2060.2161.0302.579
BERT0.2030.4930.9980.3250.7361.1700.5411.2992.213BERT0.2010.5171.3310.2960.6561.1650.2261.0492.127
Pose-NDF0.2060.6091.1800.3220.7921.1960.3691.3502.441Pose-NDF0.3040.7891.9250.3600.7471.3280.2551.1272.954
MAE0.1820.5020.9780.3020.7391.1280.4711.3162.192MAE0.1880.4561.2340.2830.6441.1590.2211.0042.169
Δ0.1540.4760.9410.2630.6741.0580.3221.1702.073Δ0.2390.6581.7070.2740.6311.1680.2181.0182.691
CITL0.1860.4660.9080.3070.6881.0560.5361.2712.023CITL0.2550.6321.6560.3340.7181.2300.2691.1172.300
PUMPS0.1370.4580.9480.2600.6931.0950.2491.0801.973PUMPS0.1680.4430.9000.2710.6091.2230.2410.9462.766
+ +Table 1. Keyframe interpolation (left) and motion transition (right) $\ell_2$ position, $\ell_2$ quaternion, and NPSS performance. Keyframe interpolation is tested on 121-frame motion sequences, given regular 5, 15, and 30-frame intervals between keyframes. Motion transition is tested on 15, 30, and 60-frame intervals between 15-frame motion windows. The top performer for each scenario is highlighted in bold. + +# 4. Masked Motion Synthesis Pre-Training + +# 4.1. Motion Datasets + +We evaluate the effectiveness of our proposed method on the pre-training motion completion tasks, comparing it to existing methods in the field. The data we use for training and evaluation are sourced from the following datasets: + +- AMASS [26] is a large collection of motion datasets retargeted to various SMPL skeletons [23] via manual vertex mesh-based weighting and optimisation. +- LaFAN1 [9] consists of production quality, long-form human motions for dynamic action classes commonly used in video games, such as firearm aiming. +- Human3.6M [12, 13] contains a large set of natural human motions, captured on a compact stage. This dataset generally features slower, more static movements. +- 100STYLE [28] contains 100 distinct motion styles focused on locomotion, such as walking and running. + +We designate all datasets for pre-training PUMPS, excluding testing splits from LaFAN1 and 100STYLE. + +# 4.2. Experimental Settings + +PUMPS operates on TPCs consisting of 256 points, sampled from skeletons using a distribution of $\sigma \sim \mathcal{U}_{[0.025,0.075]}$ for point offsets from their associated bones [29]. The encoder $\Phi^{\mathrm{enc}}$ initially learns feature vectors of size 32 per point. $\Phi^{\mathrm{enc}}$ employs 4 layers of farthest-first pooling [63], with each layer doubling the feature size while reducing the ratio of point vectors by $\frac{1}{4}$ , resulting in a singular feature vector of size 512. For the point cloud decoder $\Phi^{\mathrm{dec}}$ , we employ 4 layers of RoPE self-attention on the latent sequence, and 3 linear MLP layers to reduce point feature sizes to 512, 32, and 3 respectively. A dropout ratio of 0.1 is used for the sequence-wise dropout mechanism. $\Phi^{\mathrm{LMS}}$ uses 8 attention heads and layers for each attention stage. For training, we employ an AdamW optimiser [24], using a learning rate of $10^{-4}$ with exponential decay [50]. + +Each pre-training task is configured as follows, on 128- + +frame motion sequences: + +- Keyframe interpolation: $5 \leq |K| \leq 32$ keyframes are given as input, and missing frames are predicted. +- Motion transition: A contiguous masked section of $10 \leq 128 - |K| \leq 32$ frames is to be predicted. +- Motion prediction: The last $10 \leq 128 - |K| \leq 32$ frames are to be predicted. + +We compare our keyframe interpolation and motion transition results with several state-of-the-art machine learning methods, as well as standard linear and spherical interpolation (LERP & SLERP) techniques [44]. The learned methods include the recurrent network-based $\mathrm{TG}_{\mathrm{complete}}$ architecture [9], a prior-based interpolation approach PoseNDF [49], and several attention-based approaches, namely a BERT adaptation [5], $\Delta$ -interpolator [31], masked autoencoders (MAE) [10], and CITL [30]. We measure accuracy based on $\ell_2$ distances between global bone positions and quaternions (L2P & L2Q), as well as the signal similarity metric, NPSS [7]. To retrieve skeletal motion data from our TPCs, we adapt a RoPE variant of the unsupervised point cloud-to-skeletal motion model, PC-MRL, from [29]. To further address imperfections in motion data retrieval, we correct our model by applying offsets measured between predicted and known keyframes. + +# 4.3. Motion Synthesis Results + +As shown in Table 1, PUMPS demonstrates surprisingly superior interpolation and transition performance to existing natively supervised methods, given that PUMPS relies on non-native motion data in training. The main strength of PUMPS lies in its L2P performance, which is to be expected as point clouds directly represent positional data. Positional accuracy is essential for strong synthesis performance, as joint positions influence visual similarity more directly than rotations and frequencies. Nonetheless, the rotational representation capabilities of TPCs, as first shown in [29], remain effective with PUMPS, given its near-equal L2Q performance with existing methods. PUMPS strongly compensates its lack of native supervision with its ability to simulta- + +![](images/40dfcd36f6e02bf76e7ac412bf9746e5aca5b59dc6f50606340ac838ffe28b1b.jpg) +Figure 4. Keyframe interpolation (left) and motion transition (right) examples on a 61-frame sequence. We leave 15 frames between keyframes for interpolation, and 31 frames between 15-frame windows for transition. For visibility purposes, only every 5th frame is shown. Grey regions indicate frames provided by the input. The ground truth is overlaid in each row for direct comparison. + +neously learn from multiple large motion datasets, utilising homogenised TPC-based motion representations. + +The running motion example in Fig. 4 highlights a key advantage of interpolating within our point cloud latent space compared to direct skeletal data predictions. It illustrates a sequence with motion patterns that are unlikely to be present in the training portion of the dataset. In such cases, masked motion synthesis models often default to a LERP-like strategy, which may fail to respect the expected inertial properties of movements. The behaviour primarily arises from LERP's status as a relatively straightforward solution for interpolating skeletal data [30, 31], which most machine learned approaches tend to converge as default behaviour. In contrast, LERP does not exhibit any notable efficacy in the PUMPS latent space, as the relation between our latent features and its resulting point clouds is both non-linear and stochastic, structured by $\Phi^{\mathrm{dec}}$ . Furthermore, since PUMPS is able to learn from a significantly larger dataset than existing methods, its solution is much more generalised and exhibits inertial behaviour more strongly than other methods. The combination of these factors makes PUMPS a new state-of-the-art solution for masked motion synthesis. + +# 4.4. Ablation Study on TPC Reconstruction + +The core technical contributions of our work are centred around TPC reconstruction. As such, in Table 2, we demonstrate the performance contributions of the various components in the PUMPS auto-encoder. Of the basic component studies, the only alternative configuration that converged to some semblance of motion was sinusoidal positional embeddings, used in the original Transformer model [50]. Conventional element-wise dropout induced erratic motion dynamics that prevented convergence to a consis + +![](images/e1ad7735f04da2cb6c265bfc57c338291e9e4124a4c6c06b6ff0deec8bccb9ea.jpg) + +Table 2. Component ablation results of the PUMPS auto-encoder architecture, measured in linearly assigned point distances $(\mathcal{L}_{\mathrm{rec}})$ . + +![](images/5d42274013a809b503e9bab38523fb5fd9d23504cc3598051de129e940cc79e4.jpg) +Figure 5. TPC reconstructions comparisons between our method and FoldingNet [62], from the same TPC motion representation. + +tent motion, while Chamfer distances collapsed into distinct point clusters rather than evenly distributed point volumes. + +We further showcase two existing point cloud reconstruction strategies that exhibit point identity conditioning mechanisms for TPCs: PointIVAE [3] with VAE-based sampling, and FoldingNet [41] with 2D-to-3D point map folding. The implementation of these components are centred around producing the TPC from $\mathcal{T}$ . The volatility of latent vectors in VAE decoders under conventional Kullback-Leibler divergence regimes [18] appears to make point cloud modelling impossible to converge with a temporal + +axis. On the other hand, FoldingNet [62] shares a key similarity with our method in modelling point identities, using uniform 2D coordinates rather than noise vectors, and demonstrates a reasonable level of TPC modelling capability. However, two identifier variables alone cannot reasonably produce a volumetric point cloud representation, exemplified by FoldingNet's inability to model the distributive features of TPCs, as illustrated in Fig. 5. + +# 5. Fine-Tuning for Motion-based Tasks + +For fine-tuning demonstrations, we train skeleton-specific models for 3D motion estimation and denoising tasks. For both tasks, we include an input and output MLP layer in $\Phi^{\mathrm{LMS}}$ to project the skeleton's pose space into our latent space, and vice versa, as shown in Fig. 1. + +# 5.1. 2D-to-3D Motion Estimation + +3D motion estimation from video sequences often begins with 2D keypoint estimation to track body parts. Given 2D perspective projections of 3D skeletal motions as input, motion estimation models aim to reconstruct the original motion by predicting skeletal bone rotations. Using joint-wise $\ell_2$ position and quaternion objectives, we perform end-to-end fine-tuning of the pre-trained $\Phi^{\mathrm{LMS}}$ model on supervised motion estimation to demonstrate the adaptability of our method. Since 2D skeletons cannot be represented by 3D point clouds, this fine-tuned model directly learns latent projections from 2D to 3D skeletal data. + +We evaluate two variants of our $\Phi^{\mathrm{LMS}}$ model - one fin-tuned and one trained from scratch - against multiple state-of-the-art 2D-to-3D motion estimation methods, including the spatio-temporal transformer-based models MixSTE [65], PoseFormer v1/v2 [70, 71], and MHFormer [21], as well as a motion pre-training approach, MotionBERT [72]. To obtain 2D keypoints, we simply evaluate perspective projection maps of 3D joint positions from a random camera position, with a rotation that sets the camera's principal point to the skeleton's root joint position. + +Motion estimation accuracy is commonly measured with mean per-joint positional error (MPJPE) and velocity error (MPJVE) [12, 70], metrics that we adopt for our benchmark. As shown in Table 3, our fine-tuned model produces competitive results against state-of-the-art methods in terms of both MPJPE and MPJVE, and notably outperforms its own architecture if trained from scratch. The respective $\sim 40\%$ and $\sim 30\%$ reduction in each metric strongly demonstrate the importance of the pre-training process for effective motion estimation learning. This improvement enables our method to consistently outperform all existing methods except MHFormer, which demonstrates strong generalisability through its sophisticated dropout setup. It should be noted that most existing approaches utilise spatial attention mechanisms, which is absent from our $\Phi^{\mathrm{LMS}}$ model. + +
MPJPE↓Motion category
AimDanceFallFightObst.PronePushWalk
MixSTE61.0558.2680.9560.5854.4795.1358.2047.68
PoseFormer v171.2182.3492.7277.3572.65102.7171.5171.90
MotionBERT57.8059.0573.8659.8352.2776.1851.7448.99
MHFormer40.3845.4355.5943.4938.3662.8737.4737.67
PoseFormer v259.1959.8087.7260.0148.8293.5749.1745.32
PUMPS (scratch)73.5684.9899.4684.3967.02119.8065.9457.79
PUMPS (finetune)44.1548.6357.3045.1237.9773.2638.5338.65
+ +
MPJVE↓Motion category
AimDanceFallFightObst.PronePushWalk
MixSTE23.4439.3822.5927.9022.8326.4126.4423.01
PoseFormer v114.9236.6122.1627.1018.1619.7121.8118.70
MotionBERT18.3032.9925.4428.5318.5021.2823.4519.72
MHFormer9.6622.5515.9918.0710.6513.3913.4911.01
PoseFormer v216.6430.1323.5226.6814.6619.8619.5514.74
PUMPS (scratch)18.6942.3331.6035.1519.8427.2127.1919.53
PUMPS (finetune)12.6527.1418.3719.9212.9116.6917.9615.36
+ +Table 3. 2D-to-3D motion estimation method comparisons on 128-frame sequences, using MPJPE (top) and MPJVE (bottom). + +
Input 2D Keypoints12345678910
MixSTE1111111111
PoseFormer v11111111111
MotionBERT1111111111
MHFormer1111111111
PoseFormer v21111111111
PUMPS1111111111
Ground truth1111111111
+ +Figure 6. Motion estimation on a dance motion sample, given a sequence of 2D keypoints (top row). Predictions are rotated by $90^{\circ}$ around the vertical axis for better visual comparison. + +In future work, we may consider more sophisticated fin-tuning strategies involving such mechanisms. + +# 5.2. Motion Denoising + +Motion denoising is crucial for regularising raw motion capture sequences, which are typically obtained through camera-based systems. Challenges during performance capture, including body part occlusion, camera synchronisation issues, and image noise, can cause defects into the captured motions. In response, motion denoising techniques aim to identify such defects and refine raw motions to ensure they adhere to realistic physical constraints and natural motion patterns. Like motion estimation, we employ joint-wise $\ell_2$ position and quaternion objectives. To generate noisy motion data for both training and evaluation, we introduce Gaussian noise into the pose space, with standard deviations of $\sigma \in (0, 0.1]$ for the 3D root joint position, and $\sigma \in (0, 0.2]$ for quaternion values. The noise is applied to between $20\%$ and $80\%$ of all frames per sequence. + +
MPJPE↓Motion category
AimDanceFallFightObst.PronePushWalk
Laplacian61.2769.8064.4069.8963.3962.1464.5563.97
Pose-NDF70.1784.6976.9181.5372.8771.1278.0173.75
HuMoR75.74107.0697.93105.6876.5180.9193.3876.73
U-ViT64.39101.4291.85105.0079.5198.7769.3659.16
Transformer58.6870.0577.4472.8061.6264.4956.4051.22
PUMPS (scratch)70.2098.0684.25101.5480.0685.6871.0465.26
PUMPS (finetune)49.8373.0765.1268.7858.0059.2954.1853.04
+ +
Accel.↓Motion category
AimDanceFallFightObst.PronePushWalk
Laplacian24.0136.2228.0235.9726.6424.9928.9828.12
Pose-NDF54.9368.2660.2166.8357.5455.9460.3758.38
HuMoR29.6152.2742.6351.3833.7936.6436.6735.42
U-ViT19.1044.9728.8541.2125.9728.9926.6922.22
Transformer18.5433.9524.2932.7022.6522.2323.7320.42
PUMPS (scratch)8.9233.0515.8931.4114.4611.9917.9014.79
PUMPS (finetune)10.4532.2716.5530.5115.3112.7618.8716.33
+ +Table 4. Motion denoising method comparisons on 128-frame sequences, using MPJPE (top) and acceleration error (bottom). + +![](images/76fb8b03dc812cf8e623e87b55360164581627f3a656ab9f89f5df14c7b5a9f5.jpg) +Figure 7. Motion denoising examples given a noisy falling motion sequence (top row). Though only every 5th frame is shown, all frames are included in the trajectory representation (grey lines). + +Like with motion estimation, we compare two variants of PUMPS against several existing state-of-the-art methods. Our variants include a $\Phi^{\mathrm{LMS}}$ denoising model trained from scratch, and a fine-tuned $\Phi^{\mathrm{LMS}}$ denoising model. Motion denoising performance is measured in the aforementioned MPJPE for visual similarity, as well as per-joint acceleration error [43] for motion smoothness. To compare with state-of-the-art methods, we conducted experiments with the VAE-based motion prior model HuMoR [43], the neural distance field optimisation method Pose-NDF [49], as well as end-to-end denoisers used in text-to-motion diffusion, specifically U-ViT [1, 4] and the conventional Transformer model [22, 50]. Furthermore, we provide results from Laplacian smoothing [45] as a classical reference point. For all learned methods, we use our LaFAN1 training split. + +The performance for each method is shown in Table 4. Our fine-tuned method clearly demonstrates superior motion denoising performance compared to state-of-the-art approaches and Laplacian smoothing. Variable motion priors appear to be ineffectual for MPJPE, as they typically end + +up measuring simple velocity and pose validity, rather than temporal motion naturalness features. End-to-end models, including our method, are stronger in this regard. In contrast, our approach's temporal attention mechanisms leverage pre-trained motion understanding to produce strong denoising results, significantly outperforming existing methods. As shown in Figure 7, pre-trained motion knowledge allows PUMPS to recognise walking and falling motions, and generate a clean motion accordingly. + +Like with motion estimation, our method observes a notable improvement when fine-tuned from pre-trained weights, as opposed to training from scratch. This strongly suggests that the implicit motion patterns in the fine-tuned $\Phi^{\mathrm{LMS}}$ model provides a crucial foundation for the synthesis component of motion denoising. Overall, these pre-trained features have led to a $\sim 25\%$ decrease in MPJPE, albeit at a minor but acceptable cost to acceleration loss. + +# 6. Limitations and Future Work + +Our method's ability to work in skeleton-specific pose space without supervision faces similar limitations as PC-MRL [29], the method we use to decode temporal point clouds into skeletal motion data. To re-iterate, the method requires either native or non-native motion datasets during training, and at least one known pose during evaluation due to its temporal offset-based evaluation. Furthermore, skeletal bones of undefined or zero length are incompatible with the method. In our experiments, all such bones were removed. + +Modern diffusion-based motion synthesis models are primarily built on convolutional networks [16, 68], and the applicability of attention-based architectures has been seldom explored in this emerging field. Since our method has shown strong efficacy in motion denoising processes, our future work entails explorations into motion diffusion applications. Additionally, as temporal point clouds are a relatively new medium for representing motion data, we are excited to expand to a broader range of motion-related tasks. + +# 7. Conclusion + +This paper primordially explores pre-training approaches for motion synthesis processes in the medium of skeleton-agnostic point clouds. The non-hierarchical nature of TPCs and its convertibility with skeletal data makes the representation medium ideal for producing unified motion synthesis models, which are preferred over skeleton-specific methods due to their universal applicability. Our proposed method, PUMPS, employs a highly efficient latent sampling system using Gaussian noise vectors to enable an effective TPC auto-encoder architecture, which serves to train a foundational motion model in the TPC medium. PUMPS strongly demonstrates superior performance for motion understanding and synthesis despite its non-native supervision strategy. + +# Acknowledgements + +This work was supported by the Australian Research Council (ARC) Linkage Project #LP230100294, ARC Discovery Project #DP210102674 and ECU Science Early Career and New Staff Grant Scheme. + +# References + +[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A ViT backbone for diffusion models. In CVPR, pages 22669-22679, 2023. 8 +[2] Jinxiang Chai and Jessica K Hodgins. Constraint-based motion optimization using a statistical dynamic model. pages 8-es, 2007. 3 +[3] Jingyi Chen, Ge Li, Ruonan Zhang, Thomas H Li, and Wei Gao. PointIVAE: invertible variational autoencoder framework for 3D point cloud generation. In ICIP, pages 3216-3220. IEEE, 2022. 6 +[4] Xin Chen, Biao Jiang, Wen Liu, Zilong Huang, Bin Fu, Tao Chen, and Gang Yu. 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To address this limitation, we propose a one-shot learning framework PVChat, the first personalized ViLLM that enables subject-aware question answering (QA) from a single video for each subject. Our approach optimizes a Mixture-of-Heads (MoH) enhanced ViLLM on a synthetically augmented video-QA dataset, leveraging a progressive image-to-video learning strategy. Specifically, we introduce an automated augmentation pipeline that synthesizes identity-preserving positive samples and retrieves hard negatives from existing video corpora, generating a diverse training dataset with four QA types: existence, appearance, action, and location inquiries. To enhance subject-specific learning, we propose a ReLU Routing MoH attention mechanism, alongside two novel objectives: (1) Smooth Proximity Regularization for progressive learning through exponential distance scaling and (2) Head Activation Enhancement for balanced attention routing. Finally, we adopt a two-stage training strategy, transitioning from image pre-training to video fine-tuning, enabling a gradual learning process from static attributes to dynamic representations. We evaluate PVChat on diverse datasets covering medical scenarios, TV series, anime, and real-world footage, demonstrating its superiority in personalized feature understanding after learning from a single video, compared to state-of-the-art ViLLMs. Code is PVChat. + +# 1. Introduction + +Recent advancements in Video Large Language Models (ViLLMs) have showcased impressive capabilities across + +![](images/a283f2eb547cb76c05b27830437eacde579ac283ed6cceca5bd677a63373b851.jpg) +Figure 1. Examples of PVChat's ability with one-shot learning (e.g., $<\mathrm{Nz}>$ and $<\mathrm{Ab}>$ ). PVChat can answer questions about the personalized information correctly while other models [5, 51] fail. a wide range of tasks, e.g., video captioning, temporal action localization, and video question answering [5, 32, 50, 51]. These models, trained on vast datasets, exhibit broad knowledge across multiple domains, such as medical assistance [17] and autonomous driving [56], significantly extending the functional scope of ViLLMs. + +Despite these achievements, current ViLLMs are largely confined to general-purpose content understanding and struggle in personalized scenarios that require distinguishing specific individuals. For instance, when analyzing a video featuring a person named "Alex", even state-of-the-art models fail to consistently recognize "Alex" in novel contexts, such as identifying him from others or describing his specific actions. This limitation arises because existing training data predominantly focus on general knowledge rather than learning identity-specific information about an individual. As a result, ViLLMs are ill-equipped for real-world applications that demand personalized comprehension, e.g., smart + +home [61], intelligent healthcare [15] and human-computer interaction [6]. + +To enhance the ability of LLMs in capturing personalized cues, recent research has focused on personalized image understanding [35, 38, 39]. For example, Yo-LLaVA [35] acquires the capability to encode a customized subject into a collection of latent tokens by utilizing a small number of sample images representing the subject. Other studies [38, 39] construct specialized training datasets curated with expert annotations to enable personalized image recognition. While these methods have demonstrated promising results, they are inherently limited to static image-based understanding and cannot model dynamic, temporally evolving visual cues present in videos. Given that videos contain significantly richer personalized information, including motion patterns, interaction dynamics, and contextual dependencies, there is a pressing need for solutions that enable identity-aware comprehension in video-based contexts. + +To address these limitations, we propose PVChat, the first personalized video understanding LLM capable of learning individual characteristics and supporting subject-specific question answering from a single reference video. To enable one-shot learning, we propose a data augmentation pipeline that synthesizes high-quality personalized samples. It generates identity-preserving positives while incorporating visually similar negatives for enhanced discrimination. The process begins with facial attribute extraction and demographic categorization, followed by high-fidelity video synthesis using ConsisID [57] and PhotoMaker [21]. Hard negatives are introduced by retrieving similar faces from Laion-Face-5B [60] and CelebV-HQ [62] with corresponding video synthesis. Finally, question-answer pairs covering four key categories—subject existence, appearance, action, and location—are generated via InternVideo2 [51] and ChatGPT-4o to ensure linguistic coherence and personalization. + +To improve subject-specific feature learning, we introduce a ReLU Routing Mixture-of-Heads (ReMoH) attention mechanism, which replaces conventional softmax-based and top-k head selection with a ReLU-driven dynamic routing strategy, enabling smooth and scalable training. Additionally, we propose two novel optimization objectives: Smooth Proximity Regularization, which promotes progressive learning via exponential distance scaling, and Head Activation Enhancement, which balances shared and routed attention heads, effectively mitigating gradient explosion and inactive heads in multi-head attention mechanisms. To optimize our ReMoH-inspired PVChat under limited data conditions, we adopt a two-stage training strategy transitioning from static image learning to video temporal modeling. In the first stage, the model is trained on images with a simple summary task to capture static identity attributes. In the second stage, it is fine-tuned on video QA tasks to develop dynamic action recognition and multi-person interaction capabilities. This + +progressive learning framework enables a structured transition from static representations to complex spatiotemporal reasoning. We verify PVChat across a diverse range of personalized scenarios, including healthcare, TV series, anime, and real-world scenes, requiring the recognition of one, two, or three individuals. Experimental results demonstrate that PVChat achieves state-of-the-art performance in individual information comprehension and identity-aware reasoning from a single reference video. + +In summary, our main contributions of this work are listed as follows: + +- We introduce PVChat, the first ViLLM that extends LLMs with personalization capability from a single reference video. This enables personalized video understanding and user-specific question-answering with only one-shot learning, laying a strong foundation for future individual video comprehension. +- We develop a systematic video augmentation and QA generation pipeline from a single reference video. The key is to exploit off-the-shelf toolboxes to generate identity-preserving positives and synthesize hard negatives for confusingly similar faces. To support the research, we construct a diverse dataset containing 6 individual scenarios, 304 original videos, 2,304 extended generated videos with over 30,000 QA pairs, which will be publicly released to facilitate future research. +- We design the ReLU Routing Mixture-of-Heads module to enhance the effective extraction of individual-specific characteristics from videos. Additionally, we introduce Smooth Proximity Regularization and Head Activation Enhancement to improve training stability and attention head activation. + +# 2. Related Works + +# 2.1. Image Large Language Models + +The remarkable language comprehension and reasoning capabilities of Large Language Models (LLMs) [1, 3, 46, 48] have spurred significant interest in extending them into multimodal understanding. Pioneering works demonstrate different approaches for vision-language alignment: Flamingo [48] processes interleaved image-text inputs through cross-attention layers for diverse multimodal tasks, while BLIP-2 [16] employs a Querying Transformer (Q-Former) to bridge frozen visual encoders with LLMs. Simpler architecture like LLaVA [24] achieves effective feature alignment using lightweight MLP projectors. Recent research systematically explores critical components of Multimodal LLMs (MLLMs), including dynamic high-resolution processing strategies [4, 26], instruction-tuning methodologies [18, 29], and optimal visual encoder selection [47, 53]. Comprehensive design space analyses from MM1 [33] and Idefics2 [14] further establish foundational principles for + +MLLM development. + +# 2.2. Video Large Language Models + +With progress in image-based multimodal language models (MLLMs), video understanding research has garnered great attention. Video-ChatGPT [31] and Vally [30] aggregate temporal features into compact tokens, while Video-LLaVA [22] unifies image-video representations through aligned projections before LLM integration. Video-Teller [23] underscores modality alignment in pre-training objectives, whereas PLLaVA [55] examines feature pooling impacts on video Question-Answering tasks. For extended sequences, LLaMA-VID [19] encodes frames with dual tokens to balance efficiency and information retention, while MovieChat [45] employs memory optimization for processing ultra-long videos ( $>10\mathrm{K}$ frames). Weng et al. [54] enhance local segment features by injecting global semantics through hierarchical fusion mechanisms. These approaches collectively address spatiotemporal modeling challenges across varied input scales. However, these models are still incapable of understanding videos with personalization. + +# 2.3. Personalized Large Language Models + +Personalization in generative models exhibits distinct implementations across domains. For image generation, existing approaches focus on pixel-level subject fidelity through either concept token optimization [8, 13] or model parameter adaptation [41]. In natural language processing contexts, personalization typically involves shaping LLMs' behavioral patterns (e.g., conversational style) via prompt engineering or metadata-driven retrieval mechanisms [28, 36, 59]. Recent personalized modeling approaches employ parameter-efficient adaptation through few-shot learning. MyVLM [2] implements a Q-former-based architecture with trainable projection heads for concept extraction and visual feature augmentation, whereas Yo'LLaVA [34] extends the LLaVA framework by integrating novel concepts as specialized tokens within the LLM's embedding space. To the best of our knowledge, our model is the first to support videos input while others only accept images as inputs. + +# 3. PVChat + +# 3.1. Overview + +To achieve video personalization understanding, we first establish a promising and systematic data augmentation pipeline in 3.2 to deal with the severe lack of diverse video data for individuals. To enhance the subject-specific learning, we propose a ReLU Routing MoH Attention mechanism in 3.3, alongside two novel objectives: (1) Smooth Proximity Regularization (SPR) for progressive learning through exponential distance scaling; (2) Head Activation Enhancement (HAE) for balanced attention routing. Finally, a two-stage + +training strategy is adopted in 3.4 to progressively learn from static features to dynamic features of the target. + +# 3.2. Data Collection + +To address the challenge of limited training data and achieve one-shot learning, we propose a novel and comprehensive data augmentation pipeline as illustrated in Fig.2, which starts from two key principles: 1) enabling automated personalized data collection directly from a wide range of natural videos; 2) ensuring that the generated personalized data encompasses different scenes, actions, and contextual elements while preserving the identity information. + +Identity-Preserving Positives Generation. Maintaining the identity information is key to obtaining diverse data of a specific individual. To achieve that, our pipeline starts with facial extraction from original videos using DeepFaceLab [37]. When multiple faces are present, we carefully design a two-stage approach: first, we extract facial embeddings via FaceNet [42], then apply DBSCAN [7] clustering to differentiate between subjects. After that, the faces are evaluated using several metrics, including Eye Aspect Ratio (EAR) to determine eye openness (with a threshold of 0.25), facial orientation, image clarity, and presence of facial landmarks. These metrics allow us to identify the highest-quality facial image (HQ-face) for subsequent steps. + +To further enhance the stability of identity preservation, the characteristics of individuals in the videos are determined using InternVideo2 [51], which are categorized by gender (male/female) and age group (young/middle-aged/elderly) based on the video content and our designed prompt. With these demographic characteristics, we can more accurately preserve the identity, and employ ConsisID [57] with our extensive prompt library Fig. 5 to generate a wide range of videos in different scenarios (e.g., gym, restaurant, school, etc) with identity consistency. Although videos from ConsisID [57] contain rich content and we extract multiple types of identity information, their ID consistency is still poor, leading to a decline in data quality. + +With the aim of incorporating more ID consistent data, we utilize PhotoMaker [21] with the identified characteristics to generate additional high-fidelity images of the subject across different environments, and adopt LivePortrait [9] to animate these images to generate high-identity-consistency videos with a facial motion and expression library (including nodding, head-shaking, questioning, anger, and smiling). Meanwhile, we also directly input the HQ-face image to LivePortrait [9], generating the motion video. These videos exhibit strong ID consistency but include simple contents, complementing the data from ConsisID [57]. + +Hard Negatives Retrieval. Avoiding the misidentification of personalized subjects is crucial for personalized video chatting. As observed in previous VLM research [35] and our video chat experiments, training with only positive data + +![](images/938bb9806d32eb69ebe68236cfd3b2da8f08fda41085b1ad79bf74b0daf0154a.jpg) +Figure 2. The systematic data collection pipeline. For positive data collection, the original videos are processed by DeepFaceLab [37] for high-quality face and InterVideo2 [51] for demographic characteristics, which boost identity preservation. ConsisID [57] and LivePortrait [9] with PhotoMaker [21] utilize the identity information to generate videos of various background or different motion/expression, respectively. For model's robust perception, hard negative samples are selected from either similar face retrieval to generate negative videos, or sampled from the CelebV-HQ dataset [62]. These negative samples guarantee the model's accurate recognition of both identity and content. + +can lead to the model losing its ability to recognize personalized subjects. Considering these factors, we introduce challenging negative samples by retrieving top-k visually similar faces from the Laion-face-5b dataset [60] utilizing CLIP [40]. Similarly, these facial images are animated by LivePortrait [9] to serve as negative data, which enables the model to learn to robustly identify the personalized subjects. In addition, these negative samples also contain relatively simple movements and other content, which inspires us to supplement them with 30 randomly selected videos from the CelebV-HQ dataset [62] that possesses rich and high-resolution content. Combining them together, the personalized video chat model is equipped with robustness to both subjects and content. + +Question-Answer Pairs Generation. Having various positive and negative samples, the final stage involves generating question-answer pairs using InternVideo2 [51] across four categories: existence verification, appearance description, location identification, and action recognition. To enhance the linguistic naturalness, we refine these responses using ChatGPT-4o, converting generic human references into subject-specific references. The QA generation is illustrated in Fig. 3. + +Through this comprehensive pipeline, each input natural video is transformed into 81 different videos accompanied by 1,455 question-answer pairs, significantly expanding our training dataset while maintaining subject identity consistency and guaranteeing the model's robustness. + +# 3.3. ReLU Routing Mixture-of-Heads Attention + +Multi-Head attention. We begin by reviewing the standard multi-head attention mechanism [49] which is based on scaled dot-product attention. For $T_{1}$ input tokens $X_{1} \in \mathbb{R}^{T_{1} \times d_{in}}$ where $d_{in}$ is the input dimension, and $T_{2}$ tokens $X_{2} \in \mathbb{R}^{T_{2} \times d_{in}}$ , attention is conducted as follows: + +$$ +\text {A t t e n t i o n} \left(\boldsymbol {Q}, \boldsymbol {K}, \boldsymbol {V}\right) = \operatorname {S o f t m a x} \left(\frac {\boldsymbol {Q} \boldsymbol {K} ^ {\top}}{\sqrt {d _ {k}}}\right) \boldsymbol {V}, +$$ + +$$ +\text {w h e r e} Q = X _ {1} W _ {Q}, K = X _ {2} W _ {K}, V = X _ {2} W _ {V}. \tag {1} +$$ + +To enhance the representation of the attention layer, Vaswani [49] proposed to use multiple attention heads to operate on the projection of the input. The transformer computes $h$ different projection of $(Q, K, V)$ , and the concatenation form of multi-head attention is + +$$ +\operatorname {M H A} \left(\boldsymbol {X} _ {1}, \boldsymbol {X} _ {2}\right) = \operatorname {C o n c a t} \left(\boldsymbol {H} ^ {1}, \boldsymbol {H} ^ {2}, \dots , \boldsymbol {H} ^ {h}\right) \boldsymbol {W} _ {O}, +$$ + +$$ +\boldsymbol {H} ^ {i} = \text {A t t e n t i o n} \left(\boldsymbol {X} _ {1} \boldsymbol {W} _ {Q} ^ {i}, \boldsymbol {X} _ {2} \boldsymbol {W} _ {K} ^ {i}, \boldsymbol {X} _ {2} \boldsymbol {W} _ {V} ^ {i}\right), \tag {2} +$$ + +where $\pmb{W}_{Q}^{i},\pmb{W}_{K}^{i},\pmb{W}_{V}^{i}$ represent the $i_{th}$ projection matrices of the query, key and value. $\pmb{W}_{O}$ is the final projection matrix, which is decomposed by $\pmb{W}_{O} = \left[\pmb{W}_{O}^{1},\pmb{W}_{O}^{2},\dots,\pmb{W}_{O}^{h}\right]$ . The summation form is as follows: + +$$ +\operatorname {M H A} \left(\boldsymbol {X} _ {1}, \boldsymbol {X} _ {2}\right) = \sum_ {i = 1} ^ {h} \boldsymbol {H} ^ {i} \boldsymbol {W} _ {O} ^ {i}. \tag {3} +$$ + +# 3.3.1. Heads as Experts with ReLU Routing + +Motivation of ReMoH. Recent study Mixture-of-Heads [12] targets to allow each token to select the Top-k relevant + +![](images/3669eede57668848b8a85b3913f8a6e13c1a61a3f77d5b03c5f66eea65aaba2b.jpg) +Figure 3. We illustrate the process of automatically generating question-answer pairs using InternVideo2 [51] and ChatGPT [1]. A positive and a negative sample are shown at the bottom. + +heads, improving inference efficiency without sacrificing accuracy or increasing the parameters, compared with traditional multi-head attention. Moreover, MoH [12] finds it can learn domain-specific information, which is consistent with our personalized video understanding with only one-shot learning. However, the vanilla Top-k choice of MoH limits the performance and domain-specific information learning, which is because: 1) Top-k choice is not fully differentiable for training; 2) The choice of heads is not adaptive and flexible, and interferes with the domain-specific knowledge learned by expert heads. Thus, inspired by [52], our ReLU Routing Mixture-of-Heads Attention (ReMoH) aims at enhancing MoH with much more efficient and adaptive learning especially for the personalized subject's information, with only an increase of 2 MLP parameters. The detailed design for ReMoH can be seen in Fig. 4 (b). + +ReMoH with Head and ReLU Routers. Specifically, ReMoH consists of $h$ attention heads $H = \{H^1, H^2, \dots, H^h\}$ and uses a head routers with a ReLU router to modulate the output of different expert heads. Formally, given input tokens $X_1$ and $X_2$ , the output of ReMoH is the weighted sum of outputs of the heads: + +$$ +\operatorname {R e M o H} \left(\boldsymbol {X} _ {1}, \boldsymbol {X} _ {2}\right) = \sum_ {i = 1} ^ {h} s _ {i} \boldsymbol {H} ^ {i} \boldsymbol {W} _ {O} ^ {i}, \tag {4} +$$ + +where $s_i$ is the score corresponding to $H^i$ . In the attention mechanism, some attention heads capture common knowledge across different contexts, such as grammatical rules in language, while others focus on context-specific knowledge [43]. Following MoH [12], we divide the heads into shared + +![](images/ffd69a712e36984a226beaadd82f6f1b837c52141a81260372aa5648cdd8790a.jpg) +Figure 4. (a) The training pipeline of our method. (b) The proposed ReMoH technique for better specialized characteristics learning. + +heads and routed heads, where shared heads are always activated, and routed heads will only be activated if the ReLU routing score is non-zero. Specifically, the score for each head is defined as: + +$$ +s _ {i} = \left\{ \begin{array}{l l} \alpha_ {1}, & \text {i f} 1 \leq i \leq n, \\ \alpha_ {2} \operatorname {R e L U} \left(\boldsymbol {W} _ {r} \boldsymbol {x} _ {t}\right) _ {i}, & \text {i f} n < i \leq n + m, \end{array} \right. \tag {5} +$$ + +where $n$ and $m$ are the number of shared heads and routed heads, respectively. $\pmb{W}_r\in \mathbb{R}^{m\times d_{in}}$ denotes the projection matrix of the ReLU router. $\alpha_{1}$ and $\alpha_{2}$ , which come from the shared router, will be used to balance the contributions of the shared and routed heads, and are defined as: + +$$ +\left[ \alpha_ {1}, \alpha_ {2} \right] = \operatorname {S o f t m a x} \left(\boldsymbol {W} _ {h} \boldsymbol {x} _ {t}\right). \tag {6} +$$ + +With the utility of ReLU router to choose specific routed heads to be activated, the decision process becomes fully differentiable and offers greater flexibility. This boosts the learning of the personalized video information, avoiding a fixed number of activated experts to limit the performance or cause computational redundancy. A more detailed analysis can be found in our ablation study. + +# 3.3.2. Controlling Sparsity Strategy + +One important issue found in [52] is that most experts are always activated during training. Our ReMoH aims to control computation cost by managing the sparsity of the ReLU output, targeting a sparsity of $T_{s} = (1 - \frac{b}{m})$ , where $b$ is the number of routed heads we set for encouraging the activation. To encourage the sparsity of activation, which helps to + +reduce computational cost and boost specific-domain learning, we propose the Smooth Proximity Regularization (SPR) Loss to make the training more flexible: + +$$ +\mathcal {L} _ {S P R} = \beta_ {p} \cdot \mathcal {L} _ {R e g}, \tag {7} +$$ + +where $\beta_{p}$ is a step- $p$ adaptive weight which adjusts the strength of $L_{Reg}$ . Following prior work [20, 44], to effectively encourage sparsity by penalizing the average activation values, $L_{Reg}$ always uses the $L_{1}$ regularization: + +$$ +\mathcal {L} _ {R e g} = \left\| \frac {1}{n} \left(\boldsymbol {W} _ {\boldsymbol {r}} \boldsymbol {x} _ {\boldsymbol {t}}\right) \right\|, \tag {8} +$$ + +$$ +\beta_ {p + 1} = \beta_ {p} \cdot e ^ {k \cdot \left(T _ {s} - R _ {s}\right)}, \tag {9} +$$ + +where $R_{s}$ is the current sparsity and $R_{s} = 1 - \frac{1}{n} (W_{r}\pmb{x}_{t})$ , $k$ is a scaling factor to control the change of the step-wise weight. Such a design will make the training process more flexible, more stable, and with less extreme loss. + +However, $L_{Reg}$ just focuses on increasing the sparsity, forcing the model to be more sparsely activated, which usually makes all output prone to 0. Considering this, we design a Head Activation Enhancement (HAE) Loss to activate more heads to avoid some experts always being asleep: + +$$ +\mathcal {L} _ {H A E} = e ^ {2 \cdot \left(R _ {s} - T _ {s}\right)} - 1 \quad \text {i f} R _ {s} > T _ {s}. \tag {10} +$$ + +$\mathcal{L}_{HAE}$ helps some heads to be more active when they fall into a state of zero. Combining the SPR and HAE, a balanced activation ratio can be guaranteed. Our final training objective is designed with the language-model used cross-entropy loss $\mathcal{L}_{LM}$ : + +$$ +\mathcal {L} = \mathcal {L} _ {L M} + \mathcal {L} _ {S P R} + \mathcal {L} _ {H A E}. \tag {11} +$$ + +# 3.4. Training Pipeline + +We implement a two-stage training strategy, transitioning from image-summary pretraining to video-QA fine-tuning, teaching the model to progressively learn both static and dynamic subject-specific features. This strategy adapts our PVChat model from static image understanding to dynamic video reasoning. The architecture is shown in Fig. 4(a). + +Stage 1: Image Understanding. In the first stage, the model focuses on learning static subject-specific knowledge from separate images, where we extract the first frame of each video as input. To preserve the pre-trained visual encoder's capability, we freeze the visual encoder and only train the ReMoH components, by employing Low-Rank Adaptation (LoRA) [10] to efficiently fine-tune the Mistral-7B-Instructv0.3 language model [11], which significantly reduces trainable parameters while maintaining performance. + +The QA pairs used in this stage primarily consist of existence verification (e.g., "Is visible in this video?") and attribute description questions (e.g., "What is wearing + +![](images/a23e465c9d0b184e94b54b22650a79d9303719543a7bf240711e29d3b98bf075.jpg) +Figure 5. The hierarchical structure of our prompt library, which is carefully divided into four levels, such as gender, age, and scenarios, and provides different descriptions according to the specific subject. in this video?"). These questions guide the model to focus on static subject-specific features, which helps the model to do personalized image chat. + +Stage 2: Video Reasoning. In the second stage, we extend the model to capture temporal dynamics and environmental interactions. We selectively train several later blocks in the visual encoder to enhance cross-frame feature integration in the personalized scenarios. This modification enables the model to recognize how subjects interact with their environments and what the subject is doing over time. + +Here, we expand our QA dataset with action recognition questions (e.g., "What movements or actions does perform here?") and location identification questions (e.g., "Can you describe 's location relative to others?"). Utilizing both positive and negative samples for training, our PVChat model becomes robust and precise. + +# 4. Experiments + +# 4.1. Settings + +Implementation Details. Our LLM backbone is based on the Mistral-7B-Instruct-v0.3 [11]. All models are trained on one NVIDIA L20 GPU. The first stage of training takes one epoch, and the second stage takes seven epochs. We set the batch size to 2, the learning rates of token embedding, ReMoH, LLM Lora to $1 \times 10^{-4}$ , $1 \times 10^{-5}$ , and $1 \times 10^{-5}$ , training time needs $3h$ , video resolution is $1080 \times 1920$ . For visual encoder each video will evenly sample 8 frames. + +Datasets. To establish the dataset, we collect six different scenarios, including (Friends(6), Good Doctor(5), Ne Zha(2), doctor(3), patient(3), Big Bang(6)) 25 characters (including doctor, patient, cartoon character, engineer, professor, etc.), and collect 304 original videos and 2,304 extended videos with over 30,000 QA pairs. 300 prompt descriptions for different scenarios are designed for different ages and genders. The structure and distribution of our dataset can be found in Fig. 5. For each character, we randomly select one video for the training set as our refer video and the other for the evaluation set as query video. We show more details and + +![](images/62abe71f720b9db59f4d63c59db8b96f58b52a5f1a935e709298634774066505.jpg) +Figure 6. Examples of PVChat's ability with a learned video (e.g., a man named $<\mathrm{Sh}>$ and another man named $<\mathrm{Ho}>$ ). PVChat can recognize and answer questions about the personalized concept in various scenarios, such as medical scenarios (left) and TV series (right). + +examples in our supplementary. + +Evaluation Metrics across Multiple Datasets. Following the evaluation of LLaVA [25] and YoLLaVA [35], we rigorously assess PVChat with state-of-the-art ViLLMs using five complementary metrics across four question categories: existence, appearance, action, and location queries. The final results presented represent the averaged performance across all datasets, offering a holistic view of model capabilities. + +Our evaluation metrics incorporate: (1) Accuracy (Acc) to measure the correctness of the presence or absence of subjects; (2) BLEU and BERTScore (BS) to quantify the textual similarity between model's response and the ground truth; (3) Entity Specificity (ES) to assess if responses contain personalized information; (4) Descriptive Completeness (DC) to measure the quality of details inside responses. More details about the evaluation metrics can be found in the supplementary. For appearance, action, and location queries, we employ BLEU, BS, ES, and DC to comprehensively evaluate both semantic accuracy and conversational quality of generated responses. + +# 4.2. Comparison with State-of-the-Art Models + +Quantitative Results. To verify PVChat's effectiveness, we present the quantitative results in Tab. 1, which is compared with state-of-the-art ViLLMs, including InternVideo2 [51], VideoLLaMA2 [5]. + +The result demonstrates that our PVChat exhibits a strong ability for personalized video understanding, offering high-accuracy and comprehensive responses. Especially for the negative sample, another model always replies that the object character is existent and no real understanding of the char + +
Model TypeAcc↑BLEU↑BS↑ES↑DC↑
InternVideo2 [51]0.3420.0460.8753.0411.812
VideoLLaMA2 [5]0.4700.0820.8903.0123.301
PVChat (Ours)0.9010.5620.9524.9404.201
+ +Table 1. Quantitative evaluation of our method against state-of-the-art methods [5, 51]. Compared with these SOTA models, our model exhibits superior performance across five metrics. + +acteristic of the object. Since these models do not support multi-video input in a single-round conversation, we are not able to input the reference video and query video simultaneously. To ensure fairness, we find that InternVideo2 [51] supports the multi-round conversation, allowing us to use the reference video in the first round conversation, and input our query video in the second round. VideoLLaMA2 [5] does not support the multi-round conversation, so we input a detailed description of the reference video, and then test the query video using the character's detailed description. + +Qualitative Analysis. We conduct qualitative assessments on some challenging scenarios, including single-subject and multi-subject settings in various interactive environments and actions in Fig. 6. The result shows that our PVChat outperforms other models [5, 51] in different settings, demonstrating our superior personalized video understanding ability. Due to the shortage of personalized training and subject-specific data, previous models cannot concisely capture personalized information and show reasonable responses with correct identity. + +# 4.3. Ablation Study + +Analysis of ReMoH. To explore the impact of ReMoH, we conduct experiments as shown in Tab. 2 and visualize the + +![](images/282daa2ed13ae78b347e506a832053742f025ed92b0057d1074539a1b4197af4.jpg) +Figure 7. The comparison of expert heads activation between MoH [12] and ReMoH in different layers, where $\mathrm{H}_i$ represents the $i^{th}$ head. Orange refers to the video without the target individual, while blue represents the video having the character. + +
MethodAcc↑BLEU↑BS↑ES↑DC↑
Baseline0.7330.5500.9044.7354.142
Baseline + MoH [12]0.8130.5580.9264.9394.191
Baseline + ReMoH0.9010.5620.9524.9404.201
+ +heads of expert activation ratio in Fig. 7. We choose the typical transformer architecture Q-former [58] with the LLM backbone [11] as our baseline. Compared with the baseline and incorporating the typical MoH [12], our ReMoH results in respective improvements of $18.6\%$ , $9.8\%$ on the Acc, where our ReMoH significantly enhances the model's capability of personalizing understanding and chatting. + +In Fig. 7, we find that ReMoH effectively allocates some certain heads of expert to extract the video feature about the target character, while MoH [12] almost evenly distributes expert heads to learn the knowledge. For example, if using MoH [12], in most layers, no matter the character appears in the video or not, the first and second heads are always activated for video reasoning, verifying that these heads of expert actually do not learn about specific information. On the contrary, with the utility of ReMoH, in most layers it is observed that the activation of expert heads undergoes significant changes from no characters to having characters. This pattern supports that the model can learn personalized knowledge with ReMoH better, improving the QA performance related to specific identity, as presented in Tab. 2. + +Influence of SPR and HAE. We conducted ablations to verify the effectiveness of SPR and HAE losses. As shown in Tab. 3, the introduction of SPR successfully smooths loss fluctuations and enhances training stability compared with MoH [12]. However, models with only SPR suffer from very low expert head activation ratio, limiting personalized feature extraction. Adding HAE loss alongside SPR, the head activation diversity increases significantly, allowing the model to capture more nuanced personalized representations. + +Contribution of Each Type of Data. We conduct an ablation on the dataset creation. Tab. 4 presents all metrics + +Table 2. Ablations on the proposed ReMoH, where ReMoH significantly outperforms MoH in Acc. + +
MethodActivate Rateloss↓Acc↑BLEU↑BS↑ES↑DC↑
PVChat w/o SPR and MAE-nan-----
PVChat w/o MAE0.2170.0850.7460.5550.9264.9134.112
PVChat0.5520.0280.9010.5620.9524.9404.201
+ +Table 3. Ablations on SPR and HAE losses. It verifies that SPR and HAE guarantee stability and enhance learning of the expert heads. + +
Data TypeAcc↑BLEU↑BS↑ES↑DC↑
one positive0.4640.4170.9054.8263.947
+Negative0.5840.4180.9314.8994.120
+ConsisID Positive0.7810.5320.9274.9294.132
+LivePortrait Positive0.9010.5620.9524.9404.201
+ +Table 4. Ablations on the dataset collection, where combining all types of designed data, the model performs accurately and robustly for the personalization conversion. Using vanilla datasets (with only one positive sample) fails to perform well on personalized questions, always responding with "yes" to all questions. After injecting the negative samples, it could recognize the identity of the character to a certain degree, but still suffers from some complex questions about action and location. After training with the generated data from ConsisID [57] and LivePortrait [9], the model is capable of understanding the specific information more accurately and robustly. + +Influence of Token Numbers. We set each question prompt corresponding to $N = 16$ tokens per character. As the token number increases, the metrics overall increase, but decrease when larger than 16. This is because too many tokens make the model hard to capture the characteristics of the subject. 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However, Mamba models struggle with structured 2D visual data using sequential computing, thereby lagging behind their attention-based counterparts. In this paper, we propose a Parallel Vision Mamba (PVMamba), a novel SSM architecture tailored for visual data. PVMamba encompasses two key designs: 1) Based on the sparsity and adjacency of visual signals, we parallelize the sequential computing through three core steps, termed Dynamic State Aggregation (DSA), i.e., parallelization, alignment, and aggregation. DSA generates the hidden state in SSM by a feasible spatial aggregation, thereby overcoming the inherent sequential constraints. 2) Along with maintaining linear computational complexity, we apply a dynamic operator to learn the spatial samplings for each hidden state. To further boost the local modeling capability, we restrict the dynamic operator to the neighboring pixels in shallow layers. We also devise a layer multiplexing technique to stabilize the training and reduce the learning redundancy. PVMamba is a versatile backbone network with dynamic operators for various vision tasks, such as image classification and dense prediction. Extensive experiments show that PVMamba achieves state-of-the-art performance on a range of benchmarks. The code is available at https://github.com/VISION-SJTU/PVMamba. + +# 1. Introduction + +The architecture of Structured State Space Models (SSMs) [8, 9, 13, 26, 38] has become increasingly popular due to their remarkable computational efficiency in long sequence modeling. Recently, there has been a growing trend in applying Mamba [25, 31, 62, 71], an improved SSM variant, as the core module for various vision tasks, such as im + +![](images/a494245c0bf85dc99129e84a2a68c228fe840bad6cca0758f52d26e58f9c64f1.jpg) +(a) attention + +![](images/e2f95d0dbc98fcc81d83bccf2e3c9a0cfcaad256db2162fa55ab1b2d5a32394c.jpg) + +![](images/6c0112acc84c2099747b61755682f96917aeb6a6f5caca8a51d3049859b8750b.jpg) +(b) Mamba +(c) PVMamba +Figure 1. (a) shows attention [33, 49, 65], whose computational costs are expensive, while it is implemented by hardware-friendly matrix operations. (b) is Mamba scheme [22, 31, 71] with linear complexity while suffering from recursive computation and sequential transformation. (c) Our PVMamba aims to preserve the merits of complexity and break the sequential constraints. + +age classification [31, 71], dense prediction [28, 36, 41, 62], and generative tasks [7, 14, 20, 47]. These applications show the potential of Mamba in the visual domain. + +Despite their advances in model efficiency, SSMs, which originated from sequential language tasks [54], lack inherent adaptation for the visual domain. This limitation makes many existing SSM architectures lag behind their transformer [5, 33, 49] counterparts in performance on vision understanding tasks. We carefully examine the merits and demerits of the visual operators as illustrated in Fig. 1. The transformer can flexibly attend to the pixels in 2D regions and be efficient in matrix calculation while suffering from quadratic computational costs. In contrast, Mamba benefits from linear complexity and processes each pixel in sequence, maintaining awareness of their relative order. However, the sequential nature [8, 13] in Mamba introduces two main constraints when handling 2D visual data: 1) Vision Mamba needs to convert 2D visual data into 1D sequential + +![](images/4dac4aeb6538fbeb082e3a4be6d11f7b305c655b841cedccc2df3f40745e0688.jpg) +(a) sequential computing in Mamba + +![](images/620658b85329c3baa2bc5d12e616cb229743dcaadc83b556fe09afa9b2a4225b.jpg) +Figure 2. (a) the sequential pipeline of hidden state computing in Mamba, which conditions on previous state and input feature; (b) DSA parallelizes the hidden state computation through a feasible spatial aggregation from the input feature. + +forms, which limits its spatial modeling capabilities. 2) A recursive pipeline brings latency, which is unfriendly to the current parallel deep learning paradigm [39]. While the two mentioned sequential constraints are partially addressed by developing more complex scanning strategies [22, 31] and hardware-aware optimizations [8], the core operator of vision Mamba still follows a sequential pipeline, as shown in Fig. 2(a). Thus, it raises a natural question: Can we parallelize the Mamba operator to break the sequential constraints while preserving the merits of the Mamba? + +In this work, we propose a novel PVMamba scheme, which parallelizes the Mamba scheme via three core steps: parallelization, alignment, and aggregation. Our intuitive idea comes from the fact that the visual signal has much lower information density than language [19], making them insensitive to the order of computing. In the first step, instead of recursive calculation conditioning on previous hidden states (Fig. 2(a)), we compute the hidden state by directly aggregating a set of learnable spatial samplings from the input feature (Fig. 2(b)). In the second step, we conduct spatial alignment through simplifying the matrix generation in SSM equations, which enables a feasible spatial aggregation. The additional benefit is that the simplification facilitates the SSM computation. In the last step, to maintain position awareness, we compute the spatial aggregation among the aggregated pixels and sampling pixels to solve the SSM, thus overcoming the inherent sequential constraints. Specifically, instead of recursive calculation, we generate the hidden state by directly aggregating a set of learnable spatial samplings from the input feature as illustrated in Fig. 2(b). + +It is noteworthy that improper sampling operators, such as similarity comparison [49, 68], impose a quadratic complexity, and dense sampling easily leads to training collapse. To maintain efficiency and ease the training burden, we propose a Dynamic State Aggregation (DSA) operator with two variants: the local operator (Lo-DSA) and the spatial-adaptive operator (Sa-DSA). In the shallow layers, the Lo-DSA adopts a pooling layer to aggregate the neighboring image pixels, which aims to enhance local modeling. In the deep layers, the De-DSA learns to predict a set of learnable sampling points from arbitrary spatial locations. We also + +propose a sparsification technique, dubbed layer multiplexing, to stabilize the training and reduce the model cost. + +We conduct extensive experiments to validate the PV-Mamba on various vision tasks, i.e., image classification [42], object detection [27], and segmentation [70]. In summary, the contributions of this work are threefold: + +- We introduce three core steps to parallelize the Mamba pipeline, overcoming the inherent sequential constraints and maintaining high efficiency. +- We develop two variants of DSA operators, which aggregate neighboring and learnable sampling points for the shallow and deep layers. Several practical implementations are proposed, including layer multiplexing. +- Our PVMamba achieves state-of-the-art results in various vision downstream tasks, outperforming recent transformer and Mamba-based vision models. + +# 2. Related Work + +State Space Models. State space models (SSMs) [8, 10, 13, 26, 38, 44, 54] are newly emerged model architectures in the deep learning paradigm, with remarkable advances in linear complexity with sequence length. SSMs originated from the continuous state space models [11] in control systems and are applied to the long-sequence modeling problem in language tasks [15, 37]. Later, a series of improvements, such as initialization [9, 44] and normalization techniques [12], further enhance the sequence modeling ability of SSMs. Mamba [8] introduces hardware-optimized parallel scanning (S6), achieving both great efficiency and effectiveness in causal sequence processing. Since then, SSMs have been applied in the vision domain [17, 31, 36, 43, 71] and have shown the potential to be a compelling alternative to CNN/Transformers. ViM [71] and VMamba [31] are pioneers in integrating the Mamba with the modern vision backbone architecture. Before processing by the SSMs, vision Mamba methods have to rearrange the 2D visual components into a 1D sequential format using bidirectional or four-directional scans. The succeeding vision Mamba works [40, 60, 64] optimize the scanning strategies, such as quadtree-based partition [60], to preserve 2D locality and network search [22] to find the optimal scanning. Instead of + +improving the scanning strategies, we propose three steps to parallelize the SSM with reasonable assumptions, which overcomes the sequential constraint inherently. Our work provides a vision-specific alternative for the SSMs, which has a hardware-friendly computing pipeline. + +Vision Backbone Models. Convolutional Neural Networks (CNNs) [18, 23, 35, 45, 46, 61] and Vision Transformers (ViTs) [5, 33, 48, 50, 52] are two mainstream choices of model architecture, which generally serve as versatile vision backbones for various downstream vision tasks, such as image classification [42], segmentation [70], and object detection [27] and tracking [55]. The CNN was originally developed for image recognition [23], while the transformer was first proposed for language modeling and later adapted into the vision domain for its global modeling ability. The local convolutional operators in CNNs are restricted in global modeling but still prove the necessity of local modeling at the shallow feature layers [59]. In contrast, transformers [49] excel in long-range modeling but at the expense of quadratic computation complexity [33]. Recent Mamba vision models [8, 31, 71] achieve linear complexity with sequence length but show only marginal performance gains compared to transformers. MLLA [16] and VSSD [43] reformulate SSM as a non-causal linear attention model, while our PVMamba still maintains the causal modeling ability. To adapt Mamba for vision, we decouple DSA operators at both shallow and deep levels, creating a hybrid model structure [17]. + +Dynamic Operators in Vision Models. Dynamic operators [3, 57, 67, 72] have been widely applied in CNN and vision transformer architectures. To enhance the transformation modeling capability of CNNs, the pioneer Deformable Convolution (DCN) series [3, 53, 63, 72] adapts convolution filters to attend to flexible spatial locations by learning a group of offsets. Later, vision transformers [57, 67] adopt dynamic operations to reduce the computation redundancy in the attention scheme. Deformable DETR [73] learns a small set of key sampling points for each query point in the last model stage, which greatly improves the training convergence. For the visual backbone models, PS-ViT [67] and DAT [57] learn a group of spatial sampling points that are shared for the whole feature map in all model stages. Our method can also be viewed as the first vision Mamba model equipped with a spatial adaptive scheme to compute the hidden states for solving the SSM. + +# 3. Method + +We first recap the SSM in Sec. 3.1. Then, we elaborate on our two key designs that well-adapt SSM models to visual data, i.e., the parallel state space model (Sec. 3.2) and dynamic state transition (Sec. 3.3). Finally, we depict the overall model architecture in Sec. 3.4. + +# 3.1. Revisiting Selective State Space Model + +The core modeling of State Space Models (SSMs) [8, 13] is inspired from the continuous linear time-invariant systems [29]. A hidden state embedding $h(t) \in \mathbb{R}^N$ incorporates the mappings from the input $x(t) \in \mathbb{R}$ to output signal $y(t) \in \mathbb{R}$ . The detailed mappings are described by linear ordinary differential equations: + +$$ +h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} x (t), \quad y (t) = \mathbf {C} h (t), \tag {1} +$$ + +where $\mathbf{A} \in \mathbb{R}^{N \times N}$ , $\mathbf{B} \in \mathbb{R}^{N \times 1}$ , and $\mathbf{C} \in \mathbb{R}^{1 \times N}$ are weighting coefficients. + +Discretization. For implementation in the deep learning paradigm [39], the continuous system described by Eqn. 1 is discretized using a zero-order hold assumption. It effectively transforms the continuous-time parameters (A, B, C, D) into corresponding discrete parameters over the specified sampling time-scale $\Delta \in \mathbb{R}^C > 0$ : + +$$ +\bar {\mathbf {A}} = e ^ {\Delta \mathbf {A}}, \bar {\mathbf {B}} = (\Delta \mathbf {A}) ^ {- 1} (e ^ {\Delta \mathbf {A}} - I) \Delta \mathbf {B}, \bar {\mathbf {C}} = \mathbf {C}. \tag {2} +$$ + +Selective Mechanism. Mamba [8] applies an input-dependent scheme to generate the parameters $\{\mathbf{B}_k\}_{k=1}^L$ , $\{\mathbf{C}_k\}_{k=1}^L$ and $\{\pmb{\Delta}_k\}_{k=1}^L$ from the input sequence $\{x_k\}_{k=1}^L$ . Then, it introduces a dynamic selection mechanism to process the sequential states $\{h_k\}_{k=1}^L$ . Thus, the output sequence $\{y_k\}_{n=1}^L$ can be calculated with input-dependent parameters: + +$$ +h _ {k} = \bar {\mathbf {A}} _ {k} h _ {k - 1} + \bar {\mathbf {B}} _ {k} x _ {k}, \quad y _ {k} = \mathbf {C} _ {k} h _ {k}. \tag {3} +$$ + +To ease the difficulties of parallelism, Mamba [8] applies hardware-aware optimization when computing the hidden states $\{h_k\}_{k=1}^L$ in Eqn. 3. Mamba2 [4] further unifies the SSM and attention in the concept of state space duality. + +Vision SSM. Vision Mamba methods [22, 31, 60, 71] adopt various scanning strategies $S$ , which flatten the 2D image $x \in \mathbb{R}^{H \times W}$ into 1D sequences $x_{s} \in \mathbb{R}^{L = H \times W}$ . To gain global context modeling, vision Mamba generates multiple sequences. Our method dynamically models the spatial context, removing the complex scanning strategies. + +# 3.2. Parallel State Space Model + +To overcome the sequential constraints in SSM, we illustrate three core steps in Fig. 3. Our assumption comes from the observation that the information density in visual signal is far more sparse than the language [19], so that the visual modeling is insensitive to the sequential order. + +Parallelization. On this basis, we assume that hidden state $h_k$ can be parallelly aggregated by a selection of input pixel embedding $x$ . Fig. 3(a) shows that we replace the previous hidden state $h_{k-1}$ in the SSM equation with the spatial aggregation from input $x$ . Thus, we do not need to compute the hidden states in Eqn. 3 recursively. Then, a spatial + +![](images/1cd0184090cc51979ca6b3d717e7984f324c35a282428bb9cb62c55609d7d811.jpg) +(a) Step 1: parallelization + +![](images/06e27d98a6c66fa6eea77db4f73a1b2e5bb7a8151dfb2dc45c31e03599a3d7ac.jpg) +(b) Step 2: alignment + +![](images/69c9d44d4f6b86261bbf6e9ffcdc49fb1283501d19b2c51fb1d0f2638a042e97.jpg) +(c) Step 3: aggregation + +sampling operator $\mathcal{P}_{\Omega}(\cdot \cdot \cdot)$ is adopted to generate the hidden state $h_k$ instead of recursive computation: + +$$ +h _ {k} = \sum_ {i \leq k} \left(\prod_ {i} ^ {k} \bar {\mathbf {A}} _ {i}\right) x _ {k} \xrightarrow {\text {P a r a l l e l i z e}} \sum_ {\forall w \in \Omega} \mathcal {P} _ {\Omega} (\bar {\mathbf {A}}) x _ {w}, \tag {4} +$$ + +where index $w$ belongs to the index set $\Omega$ of corresponding embeddings. We omit the $\bar{\mathbf{B}}$ for clarity. The details of the index selection operator $\Omega$ are in Sec. 3.3. + +Alignment. In order to conduct matrix calculation in the parallel SSM, we simplify the matrix $\bar{\mathbf{A}}$ in Eqn. 3 from $\mathbb{R}^{L\times C}$ to $\mathbb{R}^{L\times 1}$ , where $L = H\times W$ . We omit the batch size dimension $B$ here for simplicity. Thus, the matrix parameters in Eqn. 3 can be spatially aligned with the feature $x\in \mathbb{R}^{H\times W}$ , which enables a feasible spatial aggregation for the hidden state computation. + +Aggregation. In contrast to the cumulative multiplication of transition matrix $\bar{\mathbf{A}}_k$ from the previous hidden state $h_a$ to $h_b$ , we reformulate it as a weighted summation which can aggregate the feature states from any two embedding indices: + +$$ +\vec {\mathbf {T}} _ {a b} = \prod_ {i = a} ^ {b} \bar {\mathbf {A}} _ {i} \xrightarrow {\text {R e f o r m u l a t e}} (\bar {\mathbf {A}} _ {b} - \bar {\mathbf {A}} _ {a}), \tag {5} +$$ + +where $\vec{\mathbf{T}}_{ab}$ is the transition matrix for the transition from the index $a$ to $b$ . A faster approximation, which directly applies $\overline{\mathbf{A}}_b$ as the transition matrix, also works well. Then, the current hidden state $h_k$ can be obtained by an aggregation of all the transition states: + +$$ +h _ {k} = \sum_ {\forall w \in \Omega} \vec {\mathbf {T}} _ {w k} x _ {w}. \tag {6} +$$ + +Finally, $h_k$ can be applied to compute the output $y_k$ using the second formula in Eqn. 3. We omit $\bar{\mathbf{B}}$ , $\mathbf{C}$ for clarity, as it can be calculated by matrix operations. + +![](images/0cae7be8bf117e2537e8830e799a0a563fdb224eabc34bb4a8282b6649b3bd0f.jpg) +Figure 3. Three core steps of parallelizing the sequential Mamba scheme. (a) shows how we parallelize the sequential SSM solving for hidden states. (b) illustrates the alignment for parallelizing the SSM computation. We simplified parameter generation. For clarity, we omit the batch dimension and other parameter matrices. (c) depicts the computation of transition matrices and spatial aggregation. + +![](images/36cfe4ab60c504da7803a1f2a8f29dc654c10f373075eca993d44fe48d498d6c.jpg) +Figure 4. Implementations of local and spatial-adaptive state aggregation. + +# 3.3. Dynamic State Aggregation Layer + +With the proposed parallel state space scheme, we describe the DSA layer, which is built upon a vision Mamba block with gated structure [31, 43, 64]. As shown in Fig. 4, we introduce two variants of the DSA operator: local (Lo-DSA) and spatial-adaptive (Sa-DSA) state transition. + +Local State Aggregation. In the shallow layers, we focus on enriching the feature representation from the local context in small $K_{l} \times K_{l}$ local neighborhoods. The deformable-style $\mathcal{P}_{\Omega_{loc}}$ is transformed to a 2D local operator for each token index $x_{k}$ and its corresponding 2D coordinates $x_{(i,j)}$ . The aggregated state $h_{(i,j)}$ is computed as: + +$$ +h _ {(i, j)} = \sum_ {\forall (m, n) \in \Omega_ {l o c}} \vec {\mathbf {T}} _ {m n} x _ {(m, n)}, \tag {7} +$$ + +where $\Omega_{loc}$ denotes the indices located at a local window region $\{m\in (i - \frac{K_l - 1}{2},i + \frac{K_l - 1}{2}),n\in (j - \frac{K_l - 1}{2},j + \frac{K_l - 1}{2})\}$ . Neglecting the scalar item, all the hidden states $\mathbf{H}$ can be efficiently implemented by the average pooling layer $\mathbf{Pool}_{(K_l,K_l)}(.)$ with kernel size of $K_{l}\times K_{l}$ : + +$$ +\mathbf {H} = \mathbf {P o o l} _ {\left(K _ {l}, K _ {l}\right)} (\bar {\mathbf {A}} \odot \mathbf {X}), \tag {8} +$$ + +where $\{\vec{\mathbf{A}},\mathbf{H},\mathbf{X}\}$ are the embeddings of $\{\vec{\mathbf{A}}_k,h_k,x_k\}_{k = 1}^N$ in 2D format and $\odot$ is the element-wise multiplication operator. We here adopt a faster implementation that directly + +![](images/905d355b4493f2bba8c1e5dac538c7f633e2509cc7bc668beb342c7e0d32c201.jpg) +Figure 5. The stacked Sa-DSA layers with layer multiplexing. + +applies $\bar{\mathbf{A}}$ as the transition matrix. The implementation details are in the supplementary materials. Our hidden states are efficient parallel forms in contrast to the recurrent forms in Mamba. + +Spatial-Adaptive Aggregation. We aim to model the long-range dependencies in the deep layers and enable a dynamic state aggregation among the most relevant regions. To maintain a linear complexity with the length of visual tokens, we adopt a lightweight linear layer $\phi(.)$ to predict sampling points $\{\mathbf{p}_k\}_{k=1}^N \in \mathbb{R}^{2 \times K_d \times N}$ for feature tokens $\{x_k\}_{k=1}^N \in \mathbb{R}^{C \times N}$ instead of a pair-wise similarity comparison: + +$$ +\mathbf {p} _ {k} = \left\{p _ {k} ^ {1}, p _ {k} ^ {2}, \dots , p _ {k} ^ {K _ {d}} \right\} = \phi (x _ {k}), \tag {9} +$$ + +where $K_{d}$ is the pre-defined number of sampling points for each visual token $x_{k}$ . The sampling points $\mathbf{p}_k$ also denote the $\Omega_{De}$ for the Sa-DSA layer. Then, to formulate a spatial-adaptive state transition path for each visual token $x_{k}$ , we adopt a bilinear interpolation and sampling operation $\mathbf{Bi-Samp}(.|.)$ to obtain the sampling features and corresponding transition matrices: + +$$ +\left\{x _ {k} ^ {1}, x _ {k} ^ {2}, \dots , x _ {k} ^ {K _ {c}} \right\} = \mathbf {B i - S a m p} (\mathbf {X} | \mathbf {p} _ {k}), \tag {10} +$$ + +$$ +\{\vec {\mathbf {T}} _ {k} ^ {1}, \vec {\mathbf {T}} _ {k} ^ {2}, \dots , \vec {\mathbf {T}} _ {k} ^ {K _ {c}} \} = \mathbf {B i} - \mathbf {S a m p} (\bar {\mathbf {A}} | \mathbf {p} _ {k}) - \bar {\mathbf {A}} _ {k}, \tag {11} +$$ + +where the $\mathbf{Bi}$ -Samp(.|.) operation is differentiable w.r.t. both the embeddings $\{\mathbf{X},\bar{\mathbf{A}}\}$ and the sampling locations $\mathbf{p}_k$ . In the final, the deformable aggregated hidden state $h_{(i,j)}$ is computed as follows: + +$$ +h _ {k} = \sum_ {\forall l \in \Omega_ {d e}} \vec {\mathbf {T}} _ {k} ^ {l} x _ {k} ^ {l}. \tag {12} +$$ + +Layer Multiplexing. In practice, we reuse the learned sampling points in stacked Sa-DSA layers, which we call layer multiplexing. As shown in Fig. 5, in a stacked Sa-DSA unit, sampling points $\mathbf{p}_k$ are learned from scratch only in the beginning Sa-DSA layer. Subsequent layers learn to refine or leverage the previous sampling points. The layer multiplexing technique eases the network's training burden and + +reduces the overall computation overhead. Details of the stacked pattern can be found in Sec. 4.4. + +Complexity Analysis of DSA Layers. The proposed DSA scheme enables directional sparse modeling while maintaining the linear computation complexity. For Lo-DSA, the implementation using an average pooling layer brings no additional model parameters and acceptable computation overhead. For Sa-DSA, the additional overhead comes from the prediction sub-network for sampling. We remove the independent linear projection, which is widely adopted in deformable operators [53, 72]. Thus, the offsets are directly predicted, resulting in an additional complexity $O(2HWCK_d)$ . Typically, consider the tiny model for image classification where $H = W = 14$ , $K_{d} = 5$ , $C = 512$ , the additional computational cost for Sa-DSA in a single block is only 1.003M FLOPs. The layer multiplexing further reduces the overall complexity. + +Connections to CNN, Attention, and Graph. Lo-DSA adopts a fixed local operator, which is similar to the depthwise convolution [66]. Sa-DSA adds learnable offsets to the sampling points, which excels at long-range modeling, like attention [57]. Our DSA scheme is partially inspired by the concept of directed graphs [56, 68]. The difference is that our DSA functions in the hidden states of SSM and dynamically generate the edge weight in a directional style. + +# 3.4. Model Architecture + +PVMamba follows a hierarchical architecture from vision transformers [21, 33, 33, 34, 50, 69] and gated block from vision Mamba [31, 43] and Mamba2 [4]. An image $I \in \mathbb{R}^{H_{im} \times W_{im} \times 3}$ is first partitioned into patches, resulting in $N = \left\lfloor \frac{H_{im}}{4} \right\rfloor \times \left\lfloor \frac{W_{im}}{4} \right\rfloor$ tokens. The tokens are firstly mapped to hidden embeddings with dimension $C$ and then passed into four model stages. In between each stage, a downsampling layer is to reduce the size of feature maps by half and double their channel dimension. Specifically, in the first and second model stages, we stack the Lo-DSA layer. In the third model stage, which consumes the most parameters, we choose the Sa-DSA layers. For layer multiplexing, the first Sa-DSA layer predicts the sampling points at the scratch. Then, two subsequent layers reuse the sampling points, and one last layer refines the points. We build three model variants, i.e., Tiny/Small/Base: + +- Tiny: $C = 64$ , layer number: $\{2, 4, 8, 4\}$ +- Small: $C = 64$ , layer number: $\{3,4,21,5\}$ +- Base: $C = 96$ , layer number:{3,4,21,5} + +# 4. Experiments + +We conduct experiments on various vision benchmarks, i.e., ImageNet-1K [42] for image classification, COCO [27] for object detection, and ADE20K [70] for semantic segmenta + +
CostModelParmas (M)FLOPs (G)Top1-acc (%)
small model ~ 4.5GCoAtNet-T [35]294.582.1
UniRepLKNet-T [35]294.582.1
ConvNeXt-T [35]294.582.1
MambaoutOut-T274.582.7
InternImage-T [53]305.083.5
DeiT-S [48]224.679.9
Swin-T [32]294.581.3
DAT294.682.0
Vim-S265.180.3
VMamba-T225.682.2
LocalVMamba265.782.7
MLLA-T [16]254.283.5
PVMamba-T244.583.9
base model ~ 9.0GConvNeXt-S [35]508.783.1
MambaoutOut-S489.084.1
PVTv2-b3 [51]456.983.2
Swin-S [32]508.783.0
DAT-S509.083.7
InternImage-S [53]508.084.2
Swin-S [32]508.783.0
UniFormer-B* [24]508.385.1
VMamba-S4411.283.5
PlainMamba-L2258.181.6
LocalVMamba-S5011.483.7
PVMamba-S407.484.2
large model ~ 18.0GConvNeXt-B [35]8915.483.8
Swin-B [32]8815.483.5
DAT-B8617.584.0
PVTv2-L [51]8211.883.8
InterImage-B [53]9716.084.9
VMamba-B8915.483.9
PlainMamba-L35014.482.3
PVMamba-B8916.184.8
+ +tion. In the following, we compare with the previous state-of-the-art (sota) methods and present ablation studies. + +# 4.1. Image Classification on ImageNet-1K + +Settings. We benchmark the proposed PVMamba on ImageNet-1K [42], which contains 1.28M training images and 50K validation images from 1K classes. For a fair comparison, we follow the training settings in [31, 33]. The Top-1 accuracy is reported. + +Results. We compare PVMamba against previous CNN, transformer, and Mamba-based SOTA models in Tab. 1. The results in the table show that PVMamba consistently outperforms previous models at different levels. Moreover, PVMamba-S shows a significant improvement over previous Mamba and transformer models, which achieves $84.5\%$ Top1-accuracy with 7.1G FLOPs. It outperforms the VMamba-T [31] and LocalMamba-T [22] by $1.5\%$ and $1.0\%$ in Top1-accuracy, respectively. When scaling up the model size, PVMamba-B also outperforms the VMamba-B [30] by $0.9\%$ in Top1-accuracy. + +Table 1. Comparison with the state-of-the-art methods on ImageNet-1K classification. + +
BackboneParams FLOPsMask R-CNN 1×+MS
(M)(G)APbAPb50APb75APmAPm50APm75
ResNet-504426038.258.841.434.755.737.2
Swin-T4826742.765.246.839.362.242.2
VMamba-T5027146.568.552.042.165.545.3
LocalVMamba-T4529146.768.750.842.265.745.5
PVMamba-T4426647.169.351.942.666.545.7
ResNet-1016333638.258.841.434.755.737.2
Swin-S6935444.868.649.440.965.344.2
VMamba-S7034948.269.752.543.066.646.4
LocalVMamba-S6941448.469.952.743.266.746.5
PVMamba-S6032148.670.253.443.767.147.3
Swin-B8849646.9--42.366.346.0
ConvNeXt-B10748647.069.451.742.766.346.0
VMamba-B10848549.271.454.044.168.347.7
PVMamba-B10850949.771.854.444.568.548.1
+ +Table 2. Comparison to other backbones using Mask R-CNN with "1 × +MS" schedule. + +
BackboneParams FLOPsMask R-CNN 3×+MS
(M)(G)APbAPb50APb75APmAPm50APm75
Swin-T4826746.068.150.341.665.144.9
ConvNeXt-T4826246.267.950.841.765.044.9
VMamba-T5027148.870.453.543.767.447.0
PVMamba-T4426649.170.853.843.967.947.0
Swin-S6935448.269.852.843.267.046.1
ConvNeXt-S7034847.970.052.742.966.946.2
VMamba-S7034949.970.954.744.268.247.7
LocalVMamba-S6941449.970.554.444.167.847.4
PVMamba-S6032150.280.155.044.668.447.9
+ +Table 3. Comparison to other backbones using Mask R-CNN with "3 × +MS" schedule. + +# 4.2. Object Detection on COCO + +Settings. We conduct object detection and instance segmentation experiments in the COCO 2017 [27] benchmark, which contains 118K, 5K, and 20K images for training, validation, and testing, respectively. We consider two typical object detection settings to validate the effectiveness of our backbone: Mask R-CNN [1] with "1" and "3 × +MS" schedule. For these detection frameworks, we utilize similar settings and follow the SwinT [33] and VMamba [31]. + +Results. We compare PVMamba against SOTA models in Tab. 2 and Tab. 3. The results demonstrate that PVMamba consistently outperforms the CNN/transformer variants and improves the Mamba-based models at different model levels and settings. For the Mask R-CNN with "1×" schedule, PVMamba-T achieves $47.1\%$ AP and $42.6\%$ mask AP, significantly surpassing the VMamba-T [30] by $1.6\%$ AP and $0.5\%$ AP mask with similar model cost. For the Mask R-CNN with "3×" schedule, PVMamba-T/S also outperforms recent sota transformer and Mamba methods, SwinT [33] and VMamba [31]. + +
BackboneMethodParams(M)FLOPs(G)mIoU(%)
Swin-T [33]UperNet60M945G44.4
InternImage-T [53]UperNet59M944G47.9
VMamba-T [31]UperNet62M949G48.0
LocalMamba-T [22]UperNet57M970G47.9
PVMamba-TUperNet54M941G48.2
Swin-T [57]UperNet81M1039G47.6
InternImage-S [53]UperNet80M1017G50.1
VMamba-S [31]UperNet82M1028G50.6
LocalMamba-S [22]UperNet81M1095G50.0
PVMamba-SUperNet70M1004G50.8
Swin-B [33]UperNet121M1188G48.1
InternImage-B [53]UperNet128M1185G50.8
VMamba-B [31]UperNet122M1170G51.0
PVMamba-BUperNet120M1192G51.4
+ +# 4.3. Semantic Segmentation on ADE20K + +Settings. ADE20K [70] is a widely used semantic segmentation dataset covering 150 semantic categories. It comprises a total of $25\mathrm{K}$ images, with $20\mathrm{K}$ for training, $2\mathrm{K}$ for validation, and $3\mathrm{K}$ for testing. We utilize UperNet [58] in mmseg [2] as our base framework for a fair comparison. More details are in the supplementary materials. + +Results. We compare PVMamba with sota CNN/transformer and Mamba models in Tab. 4. The table shows that PVMamba achieves competitive results and outperforms the state-of-the-art models InternImage [53] and Vmamba [31] in pixel-level tasks. PVMamba-T with $48.2\%$ mIoU even surpasses Swin-T [33] with fewer FLOPs. + +# 4.4. Ablation Studies + +In this section, we ablate important designs in PVMamba. The ablations adopt image classification, object detection, and semantic segmentation accordingly. To be efficient in ablation studies, we implement a lite version with roughly 13M/2.4G model costs. + +DSA Layer. Tab. 5 shows that SSM heavily relies on the additional acceleration [8, 44] to achieve a normal latency (0.613 ms). Our DSA slightly increases the model cost and latency while removing additional complex speeding-up tricks. In Tab. 6, we observe an improvement of $0.5\%$ in Top1-accuracy when replacing the original SS2D with the Sa-DSA operator, showing the effectiveness of the proposed DSA. Moreover, Tab. 6 shows the various improvements from the existing well-designed modules, such as the embedding and MESA [6]. + +Sampling Points. The core hyperparameter is the number of sampling points for each pixel, which analyzes the impacts on both classification and dense prediction tasks in Tab. 7. For image classification in ImageNet [42], the Top1-accuracy in ImageNet [42] begins to saturate around $82.2\%$ when the number of points is larger than 4. For dense prediction tasks in COCO [27], the improvement increases + +Table 4. Comparison with the state-of-the-art on ADE20K. + +
ModelPipelineAccelerationParams (M)FLOPs (G)Latency (ms)
SSMsequentialw/o325.3212 × 103
SSMsequentialw associative scan [44] w hardware optim. [8]325.30.613
DSAparallelw/o345.50.702
+ +Table 5. Efficiency comparison between SSM and DSA. + +
StepMethodParams (M)FLOPs (G)Top1 (%)
0Baseline304.882.5
1SS2D → Sa-DSA314.983.0
2Hybrid model stage304.883.2
3{Block, Channel Number} ↓234.283.4
4Simple Embed.→More Embed. layers234.283.5
5+ MESA244.583.9
+ +Table 6. The ablation experiments demonstrate the roadmap from the Mamba-based vision backbone to PVMamba. The tiny model is adopted. + +
KdParams (M)FLOPs (G)Memory Cost (512 img)Top1 (%)APb (%)APm (%)
313.52.325.8GB82.145.240.9
413.52.325.8GB82.245.441.0
513.52.335.8GB82.245.441.2
713.52.345.8GB82.245.641.3
913.52.356.5GB82.345.741.5
+ +Table 7. Comparison of performance and speed across various sampling point settings in the lite model. The size of the testing image is $224 \times 224$ . + +![](images/d8b612247b2a0810538e0fd8f632d68d3427ed12a2b4c14ddbf6354d7adfcfef.jpg) +Figure 6. Training curves of w pattern A (collapse), w pattern B (stable), and w/o layer multiplexing (collapse) technique. + +more consistently when the number of points rises. For the memory cost and model efficiency, the memory cost only rises significantly to 6.5 GB when the number of points $(K_{d} = 9)$ is too large, while the model efficiency decreases more linearly. Considering the balance of performance in various downstream tasks and efficiency, the $K_{d} = 5$ can be set for performance, and $K_{d} = 3$ for efficiency. + +Layer Multiplexing. The layer multiplexing technique is + +
Stage1Stage2Stage3Stage4Params (M)↓FLOPs (G)↓Throughput (img/s)↑Top1 (%)
Sa-DSASa-DSASa-DSASa-DSA14.92.42112882.0
Lo-DSALo-DSASa-DSASa-DSA14.92.39142382.2
Lo-DSALo-DSASa-DSAAttention13.52.32152482.2
+ +Table 8. The performance and efficiency comparisons on different hybrid model stage configurations. + +
ModelParams (M)FLOPs (G)Throughput (imgs/s)Top1 (%)
ConvNeXt-T [35]294.577582.9
Focal-T [65]294.958282.2
Swin-S [33]508.8100683.0
PVMamba-Tiny244.5103883.9
ConvNeXt-S [35]508.744783.1
Focal-S [65]519.135183.5
PVMamba-Small407.461184.2
ConvNeXt-B [35]8915.429383.8
Focal-B [65]9016.425684.0
PVMamba-Base8916.140584.8
+ +Table 9. Comparison of inference speed. We measure with an A800 GPU platform. + +key to applying our DSA scheme to the visual backbone. As shown in Fig. 6, a training collapse phenomenon is observed when applying DSA operators without layer multiplexing. The potential reason is that the dense sampling is easy to overfit, as the semantic-meaning area is limited. It indicates that the Sa-DSA operator requires a sparsification technique to ease the learning burden. Multiplexing the sampling points in previous layers can significantly ease the risk of overfitting, which also reduces the overall computational cost and improves convergence to a degree. We also explore the pattern of multiplexing: pattern A refers to learning the sampling points in the beginning and multiplexing them in the remaining layers; pattern B is an interleaved style that stacks several repeated units. Thus, each unit can learn the sampling points separately. The training curve of pattern B successfully overcomes the collapse, validating the effectiveness of the interleaved design. + +Hybrid Operator. The effectiveness of the cooperation of different operators in four model stages is validated in Tab. 8. Restricting the dynamic operator into the neighboring window in the first two model stages improves the $0.2\%$ Top1-accuracy in ImageNet [42] classification. In the fourth model stage, which generally includes 2 layers and the smallest spatial size of the feature map, we replace the DSA with vanilla attention [5, 43], which has negligible negative impacts on the performance and model cost while raising the throughput from 1423 to 1524 img/s. + +Inference Speed. We compare the PVMamba's inference speed with the recent strong CNN/transformer backbones in Tab. 9. Our models show competitive inference speed and superior performance across various model levels. + +![](images/777068c8aca91ed983cc270f6a6622cd1cde6ef7ebc8088c1316d927fa516177.jpg) +Figure 7. Model cost and GPU memory cost (32 images with the size of $224 \times 224$ ) when scaling up. + +Scaling Capability. We compare the scaling capability of different deformable operator implementations: DCNv2-style [72], DCNv3-style [53], and ours. In Fig. 7, our implementation shows superior scaling capability with high model efficiency and performance. Our model consumes nearly less $52.6\%$ GPU memory than the DCNv2-style in the base model. It is attributed to the lightweight design in PVMamba, in which we remove the independent projection layers for weight and offset in DCNv2 [72] and further omit the in-out projection layers in DCNv3 [53]. + +# 5. Limitations + +The number of sampling points can be increased to enhance performance at the cost of lower speed. Our PVMamba shares similarity with the DCN series [3, 53, 63], which could benefit from hardware optimizations in future work. Though PVMamba exhibits strong performance and competitive efficiency compared to the previous methods, the application to the multi-modality task, i.e., text [8], image [31], and video data [25], remains under-explored. + +# 6. Conclusion + +This paper parallelizes the vision Mamba with a dynamic state aggregation scheme, which can naturally handle the 2D visual data. PVMamba is the first parallel SSM variant equipped with a spatial adaptive operator, overcoming the inherent sequential constraints. PVMamba achieves state-of-the-art performance on various vision downstream tasks, such as classification, detection and semantic segmentation, significantly surpassing previous transformer and Mamba-based methods. We hope that PVMamba will provide an insightful solution to bridge the gap between sequence-based language models and vision models. + +Acknowledgments. This work was supported by NSFC (62322113, 62376156), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Zhaowei Cai and Nuno Vasconcelos. Cascade r-cnn: Delving into high quality object detection. In CVPR, 2018. 6 +[2] MMSegmentation Contributors. Mmsegmentation, an open source semantic segmentation toolbox, 2020. 7 +[3] Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen Wei. Deformable convolutional networks. In ICCV, 2017. 3, 8 +[4] Tri Dao and Albert Gu. Transformers are SSMs: Generalized models and efficient algorithms through structured state space duality. In ICML, 2024. 3, 5 +[5] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. 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PacGDC generalizes effectively across unseen scenarios with a wide range of scene semantics/scales and depth sparsity/patterns. The data include real ones from Ibims [20], Void [58], and KITTI [11], as well as synthetic ones from Sintel [3]. The sparse depths are captured from $0.1\% / 10\%$ uniform sampling, 16 line vehicle LiDAR, and visual-inertial odometry (VIO) system with 1500 feature points. + +# Abstract + +Generalizable depth completion enables the acquisition of dense metric depth maps for unseen environments, offering robust perception capabilities for various downstream tasks. However, training such models typically requires large-scale datasets with metric depth labels, which are often labor-intensive to collect. This paper presents PacGDC, a label-efficient technique that enhances data diversity with minimal annotation effort for generalizable depth completion. PacGDC builds on novel insights into inherent ambiguities and consistencies in object shapes and positions during 2D-to-3D projection, allowing the synthesis of numerous pseudo geometries for the same visual scene. This process greatly broadens available geometries by manipulating scene scales of the corresponding depth maps. To leverage this property, we propose a new data synthesis pipeline that uses multiple depth foundation models as scale manipulators. These models robustly provide pseudo depth labels with varied scene scales, affecting both local objects and global layouts, while ensuring projection consistency + +that supports generalization. To further diversify geometries, we incorporate interpolation and relocation strategies, as well as unlabeled images, extending the data coverage beyond the individual use of foundation models. Extensive experiments show that PacGDC achieves remarkable generalizability across multiple benchmarks, excelling in diverse scene semantics/scales and depth sparsity/patterns under both zero-shot and few-shot settings. Code: https://github.com/Wang-xjtu/PacGDC. + +# 1. Introduction + +Depth completion aims to infer dense metric depth maps from paired images and sparse depth measurements [7], providing accurate spatial representations that can support various downstream applications, such as robotics [4] and autonomous driving [27]. Despite its notable advancements, most existing methods suffer from poor generalization toward various new domains [50]. Recently, generalizable depth completion resorts to domain-agnostic models that learn from source data but enable effective deployment across various unseen downstream environments + +![](images/738688d2016b4edf371493f60da4cc5e6cefd8bf1ea2d347b8c1053e12bf1c5e.jpg) +(a) + +![](images/b52b88d4b8e2b0305f4cc5146e9d1db5e13275bc6691e1db43fc04faad405c1e.jpg) +(b) +Figure 2. Illustration of the ambiguity and consistency in 2D-to-3D projections for generalizable depth completion. (a) Ambiguity: shape ambiguity refers that the same 2D object can correspond to different 3D shapes, while position ambiguity refers that the same 3D shape can vary in size and position. (b) Consistency: shape consistency denotes that the 3D shape aligns with the semantics of image input, while position consistency denotes that the 3D position is regularized by sparse depth input. The possible 3D objects are marked with $\checkmark$ . + +[51, 65]. However, the success of these studies relies heavily on large-scale dense metric depth annotations to effectively cover real-world distributions, while collecting such annotated data is often laborious and time-consuming [49]. + +This paper introduces PacGDC, a label-efficient technique that is designed to maximize training data coverage with minimal annotation effort for generalizable depth completion. PacGDC is grounded in 2D-to-3D projection ambiguity, where the same 2D image can be projected from multiple possible 3D geometric scenes [36, 72]. To leverage this ambiguity, we decompose it into two orthogonal components: shape and position, as shown in Fig. 2 (a). This decomposition reveals that each 3D geometry, defined by a depth map, can be uniquely identified by both shape and position cues. Meanwhile, these two cue types align well with the two input types in depth completion. As illustrated in Fig. 2 (b), the shape cues (e.g., "sphere") are consistent with semantic information (e.g., "ball") in images, while sparse depth points help regularize spatial positions. Such consistency mitigates ambiguity in generalizable depth completion, enabling accurate estimation of target metric depths across unseen scenarios, as shown in Fig. 1. + +Building on these insights, this paper exploits these ambiguities to synthesize diverse pseudo geometries for the same visual scene, while maintaining consistencies among synthesized training triplets (i.e., images, sparse depths, and dense depth labels). It is achieved by manipulating scene scales of the corresponding depth maps, significantly expanding available geometries without requiring additional labeled samples. Since sparse depths with consistent positions can be sampled from dense labels, as introduced in + +[51, 82], our primary focus is to synthesize a large volume of pseudo dense depth labels that have consistent shapes. + +Specifically, we exploit multiple foundation models of monocular depth estimation to synthesize qualified depth labels. These models can robustly predict dense depth maps with consistent shapes/semantics from a single image [2, 69], even across diverse unseen scenes. However, their predictions typically suffer from inaccurate scene scales, for both local objects and global layouts, due to the inherent scale ambiguity problem [56, 72]. These characteristics allow generating pseudo dense depth maps that diverge from ground-truth labels in terms of scene scales, while preserving consistency in shape cues. To further diversify geometry, we incorporate interpolation and relocation strategies, enabling additional variations beyond the predictions of any individual foundation model. With the inclusion of unlabeled data, PacGDC significantly enriches the data diversity. The full synthesis pipeline is illustrated in Fig. 4. + +We conduct extensive experiments to validate the effectiveness of PacGDC in two practical applications: (1) zero-shot testing on seven unseen datasets with diverse sparse depth inputs, including those captured from uniform sampling, visual-inertial odometry system, and vehicle LiDAR; (2) few-shot testing on the KITTI dataset [11] with fewer than $1\%$ training data. The results show that our method achieves superior generalizable depth completion. + +The major contributions of this paper are threefold: + +- We exploit a novel insight into 2D-to-3D projection ambiguity and consistency for generalizable depth completion, enriching data diversity without additional real labels. +- We propose a new data synthesis pipeline that manipu + +![](images/afc927a7ca7576c84c3a9f56c1ac7ff14fc1d6f87ad9e9910a71ec6f0f0f8b4f.jpg) +Figure 3. Data distribution of our synthesis method on 1000 samples from UnrealCV dataset [50], visualized by mean and variance. From left to right, the data diversity increases progressively with each step. Notably, this statistic is based on a single foundation model, DepthAnything [69], and a single instance of interpolation and relocation for simplicity. In the final implementation, multiple foundation models and randomized interpolation and relocation can be adopted to further enhance the data distribution. + +lates local and global scene scales, enabling effective generalization to unseen domains with metric depths. + +- Our approach achieves state-of-the-art performance in zero-/few-shot depth completion, validated across multiple benchmarks with different setups. + +# 2. Related Work + +Depth Completion. The success in deep learning has enabled depth completion methods to explore various dimensions including surface normal cues [34, 66, 77], semantics cues [28, 76], refinement strategies [7, 29, 45, 54], advanced backbone architectures [39, 41, 78], and sophisticated feature fusion modules [25, 55, 68, 79]. These approaches have effectively improved performance for intradomain learning, where their training and testing data share similar scenes, such as KITTI [11] and NYUv2 [42]. However, they suffer degraded performance in unseen domains. + +To address this limitation, G2-MonoDepth [50] explored a generalized framework for zero-shot scenarios. TDDC [65] incorporated pre-trained depth estimation models as a preprocessing step for enhanced image analysis. SPNet [51] investigated an important property of scale propagation within network architectures, while OMNI-DC [82] introduced multi-resolution depth guidance. + +In practical applications, a limited number of training samples can be collected for cost-efficient deployment in specific environments. Conventional intra-domain methods can be directly applied in such scenarios. Recently, UniDC [30] explored few-shot depth completion using hyperbolic representation [31], while DDPMDC [35] leveraged pretrained diffusion models to mitigate data overfitting. + +Monocular Depth Estimation. Existing monocular depth estimation methods can be broadly categorized into three main types. First, most methods focused on predicting metric depth maps within familiar training domains [9, 74], while they struggle to generalize to unseen domains. To improve robustness, some approaches predicted relative depth + +maps with normalized scales [17, 36, 37, 62, 69], which disregarded scene scales for superior generalization. Recently, the community explored predicting metric depth maps from unseen scenes by incorporating the camera focal length [2, 33, 73]. Our method manipulates the scene scales of depth maps using their dense predictions. + +Pseudo Labeling. As a popular topic in semi-supervised learning, pseudo-labeling methods focused on leveraging unlabeled data by synthesizing pseudo labels [22]. The dominant methods aimed to improve pseudo label quality for reliable supervision, employing techniques such as threshold-based selection [18, 43, 53, 75], teacher-student frameworks [64, 80], and advanced regularization strategies [21, 43, 63]. These approaches have successfully enriched the training data of many foundational models [19, 38, 69]. In contrast, our method investigates pseudo labels upon projection ambiguity for both labeled and unlabeled data. + +# 3. Method + +# 3.1. Problem Definition + +The training data of depth completion comprises annotated triplets, denoted $\mathcal{T} = \{I,p,d\}$ , where $I$ represents the input image, $p$ is the sparse depth map captured by the depth sensors, and $d$ is the dense depth map of ground truth. The objective is to train a model $\mathcal{F}$ , that can predict the dense depth map $\mathcal{F}(I,p)$ using both the input image and sparse depth map. The model is optimized by minimizing the difference between the predicted dense depth $\mathcal{F}(I,p)$ and the ground truth $d$ , formulated as: $\min_{\mathcal{F}}|\mathcal{F}(I,p) - d|$ . + +In the context of generalizable depth completion, the objective is updated to train the model $\mathcal{F}$ on source datasets with triplets $\mathcal{T}$ , while enabling it to effectively generalize to unseen target data, achieving strong zero-shot performance. + +This paper aims to achieve superior generalizable depth completion with minimal annotation effort. We develop a label-efficient solution, PacGDC, that synthesizes pseudo triplets $\hat{\mathcal{T}}$ to substitute for original triplets $\mathcal{T}$ . This signifi + +![](images/71353af5300eb82c958f8ceb1d5bb286c012ec0d51870939b2a7f2c6dc8fd9a9.jpg) +Figure 4. Overview of the proposed data synthesis pipeline, which leverages multiple depth foundation models, interpolation and relocation strategies, and unlabeled data. Sparse depth maps are then sub-sampled to form pseudo triplets (marked by $\checkmark$ ). This process significantly enhances data diversity through projection ambiguity while ensuring projection consistency that contributes to generalization. + +cantly enhances the diversity of source data, enabling better coverage for real-world data. + +Our approach addresses two main challenges: + +- The theoretical process of enhancing data diversity, which we tackle by leveraging the 2D-to-3D projection ambiguity and consistency, as detailed in Sec. 3.2. +- The practical solution of synthesizing qualified data that contributes to generalization, for which we employ multiple depth foundation models, as detailed in Sec. 3.3. + +# 3.2. Geometry Diversity from Projection Ambiguity and Consistency + +Projection Ambiguity. In the pin-hole camera model [52], the 2D coordinate $(u_i, v_i)$ in the image plane is mapped to their corresponding 3D position $(x_i, y_i, z_i)$ at pixel $i$ using the following projection relationship: + +$$ +d _ {i} P ^ {- 1} \left[ \begin{array}{l} u _ {i} \\ v _ {i} \\ 1 \end{array} \right] = \left[ \begin{array}{l} x _ {i} \\ y _ {i} \\ z _ {i} \end{array} \right], \tag {1} +$$ + +where $P$ is the projection matrix and $d_{i}$ is the depth value at pixel $i$ . By applying a scaling factor $\alpha_{i}$ to both sides of the equation, the same 2D coordinate $(u_{i}, v_{i})$ can correspond to a new depth value $\hat{d}_{i} = \alpha_{i} d_{i}$ and a scaled 3D position $(\alpha_{i} x_{i}, \alpha_{i} y_{i}, \alpha_{i} z_{i})$ . This reveals that multiple 3D geometries can project onto the same 2D visual appearance $I$ , by manipulating the scene scale of depth pixel $d_{i}$ . This phenomenon is commonly referred to as projection ambiguity or scale ambiguity [36, 72]. + +In this paper, we decompose the projection ambiguity into two orthogonal sources, as illustrated in Fig. 2 (a): + +- Shape ambiguity refers to that one 2D object can correspond to different 3D shapes in the same position. This implies that corresponding depth maps may share similar means but differ in variances. +- Position ambiguity means that the same 3D shape can vary in size and position. This suggests that their depth maps may have similar variances but varied means. + +Remark. These ambiguities indicate that each 3D geometry can be uniquely identified by both shape and position. + +Projection Consistency. The ambiguities suggest that predicting target 3D geometry, defined by the target depth map, requires identifying both its shape and position. In the training triplets $\mathcal{T}$ , the input image $I$ provides semantic cues to identify the target shape. As illustrated in Fig. 2 (b), the 2D object with semantic of "Ball" should correspond to the 3D shape of "Sphere", rather than an unrealistic "Cone" or "Cylinder". Meanwhile, the input sparse depth $p$ offers sparse depth points to regularize the target position. + +These consistencies of shape and position are the foundation for achieving generalizable depth completion, where metric depths can be effectively identified by these shape and position cues, even across diverse unseen scenarios. + +Geometry Diversity. Building on these insights, we leverage projection ambiguity to synthesize numerous pseudo geometries for the same visual scene, while maintaining projection consistency between the input data $I,p$ and the synthesized depth labels $\hat{d}$ . This process can significantly enhance the geometry diversity of training data, thus achieving superior generalizability for depth completion. + +We introduce the theoretical process of forming pseudo triplets $\hat{\mathcal{T}}$ to substitute for original triplets $\mathcal{T}$ . First, we synthesize a set of dense depth maps $\{\hat{d^j}\}_{j = 1}^N$ , where $N$ is the number of pseudo depth labels per image. The specific synthesis method ensuring shape consistency is detailed in Sec. 3.3. Next, sparse depth maps are directly sub-sampled from each pseudo depth label, i.e., $\{\hat{p}^{j,k}\}_{j = 1,k = 1}^{N,M}$ , where $M$ is the number of sparse depth maps per dense depth label. In this paper, we adopt the uniform sampling pipeline in [51] combined with the LiDAR&SFM patterns sampling in [82]. The sub-sampling naturally maintains consistent positions. Finally, the pseudo triplets consist of the original visual image, the pseudo depth labels, and the sampled sparse depth maps, i.e., $\hat{\mathcal{T}} = \{I,\{\hat{d^j}\}_{j = 1}^N,\{\hat{p}^{j,k}\}_{j = 1,k = 1}^{N,M}\}$ . This process generates additional data combinations from the same visual images, beyond the original triplets $\mathcal{T}$ . + +# 3.3. Qualified Synthesis with Scale Manipulation + +Our synthesis method aims to achieve two key objectives: (1) ensuring that the shape of the pseudo dense labels is consistent with the semantics of the input images, and (2) + +![](images/dc7d6f41726c036da22638d9e7807432978ee3b3e714c65517c49472e2989e25.jpg) +Figure 5. Illustration of basic geometry synthesis. + +capturing diverse shapes and positions in the synthesized geometries. We leverage foundation models of monocular depth estimation to accomplish the two goals. + +Pseudo Labels from Depth Foundation Model. Depth foundation models, such as DepthAnything [69] and DepthPro [2], are capable of robustly predicting dense depth maps with consistent semantic information from a single image, even across diverse unseen visual scenes. However, their predictions typically suffer from inaccurate scene scales due to the scale ambiguity inherent in single images [36]. For instance, the top-ranking depth estimation method [33] on the KITTI leaderboard achieves 8.24 iRMSE, significantly weaker than the top-ranking depth completion method [55] with 1.83 iRMSE. Furthermore, although many methods adopt the global affine-invariant hypothesis, their predictions exhibit scale variations not only in the global layouts but also for local objects, as discussed in [56, 72]. These characteristics enable the manipulation of local and global scene scales of pseudo depth labels to generate diverse geometries, while maintaining consistency in shape cues. + +Therefore, we denote the pseudo depth labels generated by the depth foundation model $\mathcal{R}$ from visual inputs $I$ as $\hat{d} = \mathcal{R}(I)$ . Unfortunately, a single $\mathcal{R}$ only generates one type of dense prediction $\mathcal{R}(I)$ , depending on its network architecture, training data, and training strategy. To diversify synthesized geometries, we further incorporate interpolation and relocation strategies. First, we randomly interpolate the original ground-truth depth maps $d$ with pseudo dense labels $\mathcal{R}(I)$ . This operation can fill the geometry coverage between them, as illustrated in Fig. 5. One limitation is that the filled coverage depends on the initial spatial positions of the two dense maps. To address this, we randomly relocate the interpolated results into new positions. The pseudo depth labels are formalized as: + +$$ +\hat {d} = \theta (\lambda \mathcal {R} (I) + (1 - \lambda) d), \tag {2} +$$ + +where $\lambda$ and $\theta$ are the random factors for interpolation and relocation, respectively. The diversity introduced by these strategies is demonstrated in Fig. 3, and their effects are also verified in the ablation study in Sec. 4.4. + +Extensions to Multiple Foundation Models and Unlabeled Images. The basic synthesis pipeline can be extended by using multiple depth foundation models and incorporating unlabeled images. First, instead of relying on a single + +
DatasetsIndoorOutdoorLabelSize
Matterport3D [5]✓RGB-D194K
HRWSI [62]✓✓Stereo20K
VKITTI [10]✓Synthetic21K
UnrealCV [50]✓✓Synthetic5K
BlendedMVS [71]✓✓Stereo115K
SA1B [19] (subset)✓✓None390K
+ +Table 1. The details of training datasets. + +model $\mathcal{R}$ , we update it to a set of models $\{\mathcal{R}^t\}_{t=1}^L$ , where $L$ denotes the number of depth foundation models. This expansion increases the variety of pseudo dense labels, yielding $\mathcal{R}^t(I)$ . By combining these models with the interpolation and relocation strategies from Eq. (2), the pseudo depth labels are updated as follows: + +$$ +\hat {d} = \theta \left(\sum_ {t = 1} ^ {L} \lambda^ {t} \mathcal {R} ^ {t} (I) + \left(1 - \sum_ {t = 1} ^ {L} \lambda^ {t}\right) d\right), \tag {3} +$$ + +where $\lambda^t$ is random interpolation factor for each foundation model, with the constraint $\sum_{t=1}^{L} \lambda^t \leq 1$ . This paper adopts two foundation models with quite different designs as examples, including DepthAnything [69] and DepthPro [2]. + +As discussed in Sec. 3.2, PacGDC emphasizes assigning multiple pseudo depth labels to a single visual scene. This design shifts the model's focus from regular fitting dataset priors to ours learning geometric alignment. It suggests that pseudo data, even without ground truth scene scale, can still contribute effectively to training generalizable depth completion models. This insight motivates us to incorporate unlabeled images $I^{u}$ into our synthesis pipeline, further enriching data diversity from additional semantics and scene scales. Consequently, the set of visual images expands to $\hat{I} = \{I, I^{u}\}$ . In this study, we incorporate 390K unlabeled images from SA1B dataset [19] for validation. + +Remark. The final triplets $\hat{\mathcal{T}}$ are constructed by three elements: visual images $\hat{I}$ , pseudo dense labels $\hat{d}$ generated by Eq. (3) from $\hat{I}^1$ , and sparse depth maps $\hat{p}$ sampled from $\hat{d}$ . + +The synthesis pipeline is illustrated in Fig. 4, which significantly enhances data diversity without requiring any additional real annotations. The ablation study of these strategies is provided in Sec. 4.4. + +# 3.4. Learning from Synthesized Triplets + +Learning from such large-scale, diverse, and ambiguous training data presents a challenge for existing depth completion frameworks. To effectively leverage our synthesized data, we integrate our data settings into the SPNet [51] + +
MethodsETH3DIbimsNYUv2DIODESintelKITTIMean ↓
RMSEMAERMSEMAERMSEMAERMSEMAERMSEMAERMSEMAERMSEMAE
LRRU [54]522639327965991924138790145714182501324910783745076655389
ImprovingDC [55]36479523110218452279180994516562182561378711705839681986105
NLSPN [29]228313672391164142105172237943424342214170191192846701
CFomer [78]1821810215714211745176219726415218074400196064084503
G2MD [50]142069119658382150502621143612917369016072387923
SPNet [51]154456917747399154507020783312659312412402271791
OMNI-DC [82]9294201654635713948482076773339893050119128471310
Ours90745416046376147472119842961580267311721966731
+ +Table 2. Zero-shot depth completion on the six datasets with sparse depth maps obtained by uniformly sampling $10\% /1\% /0.1\%$ valid pixels. The bold indicates the best result, and the underline indicates the second-best result. + +
MethodsVoid-1500Void-500Void-150KITTI-64LKITTI-16LKITTI-4LMean ↓
RMSEMAERMSEMAERMSEMAERMSEMAERMSEMAERMSEMAERMSEMAE
LRRU [54]835530937637100068521247424968294312658946637532501
ImprovingDC [55]95059511608501251949220011184281232511421804435442313
NLSPN [29]43115648419257124716275012174711413316901570583
CFomer [78]42614446017052220815133592221601476818351652553
G2MD [50]38311741714148418115703522138572394116481489502
SPNet [51]35310437511943015115233312108537326811481343398
OMNI-DC [82]3911214221434781771191270168244129819971191358
Ours3481023631144091411375337170246026858961147342
+ +Table 3. Zero-shot depth completion on Void dataset with 1500/500/150 sparsity levels from visual-inertial odometry system, and KITTI dataset with 64/16/4 beam lines from vehicle LiDAR. + +framework, known for its efficiency and strong generalization ability. The source training datasets, detailed in Tab. 1, include 355K labeled samples and 390K unlabeled samples. Computational Cost Analysis. Since our work focuses on training data diversity, it does not introduce any additional computational cost during inference. This ensures that our model fully retains the efficient inference of SPNet, whose "Tiny" model achieves 126.6 image/s on a single 3090 GPU at $320 \times 320$ resolution. In comparison, competing methods such as G2-MonoDepth [50] and OMNI-DC [2] achieve only $69.5\%$ and $8.4\%$ of SPNet's speed, respectively. + +The computational cost is primarily introduced during training. Our method consists of four main components: depth foundation models, unlabeled images, interpolation, and relocation. The latter two introduce only minimal additional multiplication and addition operations. For depth foundation models, their predictions can be precomputed and loaded on demand. Therefore, the primary additional cost derives from unlabeled images, resulting in an additional 390K/355K computations in our implementation. + +# 4. Experiment + +Our experiments consider two practical applications: zero-shot depth completion in Sec. 4.2 and few-shot depth completion in Sec. 4.3. Additional experimental results are included in the supplementary materials. + +# 4.1. Settings + +Evaluation Protocol. Zero-shot depth completion: Following zero-shot depth estimation [69], we impose no restrictions on the model training, evaluating only released models on the same test setups. The test datasets include two types: (1) sparse depth maps obtained by uniformly sampling $10\% / 1\% / 0.1\%$ of valid pixels from the ETH3D [40], Ibims [20], NYUv2 [42], DIODE [46], Sintel [3], and KITTI [11] datasets, as used in [50, 51]; (2) sparse depth points captured by visual-inertial odometry system with 1500/500/150 sparsity levels on Void [58] dataset, and by vehicle LiDAR with 64/16/4 beam lines on KITTI dataset. Few-shot depth completion: All models are trained on sequentially selected subsets of 1, 10, 100, and 1000 samples from the KITTI training set (i.e., 86K samples), and evaluated on its validation set with 1000 test samples. + +Implementation Details. Zero-shot depth completion: We adopt the "Large" model of SPNet for the best performance, while sacrificing $47\%$ inference speed. The model is trained using the AdamW optimizer with batch size 192, running on six 3090 GPUs. The initial learning rate is 0.0002 with cosine learning rate decay using 100 epochs. Few-shot depth completion: Our models are initialized by pre-trained weights from the zero-shot phase. We adopt 1/10 initial learning rate for this fine-tuning. The batch sizes are set to $\{1, 1, 4, 4\}$ when using $\{1, 10, 100, 1000\}$ training samples. + +
ShotMethodsRMSE ↓MAE ↓iRMSE ↓iMAE ↓
1LRRU [54]213867995.692.94
ImprovingDC [55]13583374.681.43
SparseDC [25]17576368.303.65
UniDC [30]1684522--
Ours10782502.900.98
10LRRU [54]13373425.541.38
ImprovingDC [55]13163154.131.26
SparseDC [25]143838010.221.86
UniDC [30]1385407--
Ours9692382.700.96
100LRRU [54]12612954.021.17
ImprovingDC [55]12413044.011.27
SparseDC [25]12033254.421.48
UniDC [30]1224339--
Ours9112292.540.96
1000LRRU [54]11052663.341.09
ImprovingDC [55]11212793.791.15
SparseDC [25]10492633.571.14
Ours8302202.280.91
+ +![](images/d8c199c2a615144905ee2ef53e7fd08ef1ba434cdfa14dfb86b3e4b2d91005d5.jpg) +Figure 6. "Few-shot vs full-shot" on KITTI with 64 line Li-DAR. The horizontal axis denotes that our models use 1, 10, 100, and 1000 training samples, while the baselines use 86K samples. The self-supervised baselines include VLO [44], KBNet [57], AugUndo [61], and DesNet [67]. The supervised baselines include S2D [26], TWISE [16], GAENet [6], and ImprovingDC [55]. + +Baseline Details. Zero-shot depth completion: The baselines include several generalizable depth completion methods: G2-MonoDepth (G2MD) [50], OMNI-DC [82], and SPNet [51], as well as fully supervised methods: NLSPN [29], CFormer [78], LRRU [54], and ImprovingDC [55]. To ensure zero-shot testing, the fully supervised methods are retrained on large-scale datasets provided by SPNet. Few-shot depth completion: We retrained recent methods, LRRU [54], ImprovingDC [55], and SparseDC [25] in the same few-shot setting for direct comparison. The official results of UniDC [30] are listed for reference. To highlight our + +Table 4. Few-shot depth completion on KITTI with 64 line Li-DAR using 1, 10, 100, and 1000 training samples. + +
ShotMethodsRMSE ↓MAE ↓iRMSE ↓iMAE ↓
1LRRU [54]55583708259.5923.60
ImprovingDC [55]3322147312.697.22
SparseDC [25]5950399712598.67250.22
Ours16624553.541.42
10LRRU [54]3206132912.305.56
ImprovingDC [55]3092135013.066.20
SparseDC [25]3507165950.569.61
Ours15244263.321.37
100LRRU [54]2646101414.144.37
ImprovingDC [55]2642104310.074.55
SparseDC [25]223579819.303.47
Ours14253393.071.29
1000LRRU [54]20927136.212.79
ImprovingDC [55]22598437.823.67
SparseDC [25]18636065.792.36
Ours12973712.821.22
+ +Table 5. Few-shot depth completion on KITTI with 64/32/16/8/4 lines LiDAR using 1, 10, 100, and 1000 training samples. + +![](images/528fdf119022532334a866a98b7aa082c821595861bc984d3a68e7b1e7b74b74.jpg) +Figure 7. "Few-shot vs full-shot" on KITTI with 64/32/16/8/4 lines LiDAR. Our model is trained with 1000 samples, while the baselines use 86K samples including SparseDC [25], PackNet-SAN [13], PeNet [15], and SPAgNet [8]. + +model, we further evaluate it, using less than 1000 samples, against full-shot baselines, trained with 86k samples. Their results are directly taken from the original papers. + +Metric Details. We use standard evaluation metrics including root mean square error (RMSE), mean absolute error (MAE), root mean square error of the inverse depth (iRMSE), and mean absolute error of the inverse depth (iMAE). All results are reported in millimeters (mm). + +# 4.2. Zero-Shot Depth Completion + +In this section, we show model capability across zero-shot environments, which is unobserved during training. + +Uniformly Sampled Depths. We begin evaluation on sparse depth maps with uniformly sampled valid pixels at $10\% / 1\% / 0.1\%$ sparsity levels, across six unseen datasets. + +
FrameworkSpeed (image/s)Basic Synthesis MethodExtensionsRMSE ↓MAE ↓
DepthAnything [69]P(Interpolation)RelocationDepthPro [2]SA1B (subset) [19]
SPNet [51] (Tiny)126.6✓0.02484990
✓0.252463956
✓0.52380912
✓1.02344889
✓1.0✓2330889
✓1.0✓2277857
✓1.0✓✓2241854
✓1.0✓✓✓2143792
G2MD [50]88.0✓1.0✓✓✓26691101
✓1.0✓✓✓2192817
+ +Table 6. Ablation study of our synthesis method based on two types of generalizable depth completion frameworks. + +The average results are summarized in Tab. 2, in which our model performs the best in most scenarios, with the lowest RMSE $1966\mathrm{mm}$ and MAE $731\mathrm{mm}$ on average. + +Sensor Captured Depths. Next, we evaluate sparse depth points captured by physical sensors on two unseen datasets: VOID [58] dataset with 1500/500/150 sparsity levels, and KITTI [11] dataset with 64/16/4 lines LiDAR. Tab. 3 shows that our model still outperforms all baseline models with the lowest RMSE $1147\mathrm{mm}$ and MAE $342\mathrm{mm}$ on average. + +Visual Results. Fig. 1 has presented several visual results. Additional results can be found in supplementary material. + +# 4.3. Few-Shot Depth Completion + +In this section, we fine-tune our model in the specific environment to compete for intro-domain learning methods, on KITTI dataset with 1, 10, 100, and 1000 samples. + +64 line LiDAR Depths. We train and test all models using 64 line LiDAR under the few-shot setting. Tab. 4 shows that our model significantly outperforms these baselines designed for intro-domain learning. We attribute this strong performance to powerful pre-trained weights by our synthesis method. These weights provide an excellent starting point to regularize this few-shot learning. + +Additionally, we compare our few-shot model against baselines trained on the full 86K samples. As shown in Fig. 6, our model achieves competitive results, outperforming all self-supervised baselines in MAE with just a single annotated sample. When using 1000 training samples, our model even outperforms supervised baselines such as S2D and TWISE in RMSE, as well as S2D and GAENet in MAE. + +64/32/16/8/4 lines LiDAR Depths. We also train all models on randomly sampled 64/32/16/8/4 lines LiDAR, and test them in each beam line. Tab. 5 shows the average results across these beam lines, and our models also outperform baseline methods. As shown in Fig. 7, our few-shot model, trained with just 1000 samples, achieves competitive results of full-shot baselines. Notably, our model achieves the best RMSE and MAE on 8/4 lines LiDAR data. + +# 4.4. Ablation Study + +In this section, we verify each component of our synthesis method. Due to computational constraints, we adopt the "Tiny" model of SPNet using $25\%$ of the full data. + +Basic Synthesis Method. Our synthesis method consists of three components to implement the basic approach outlined in Eq. (2): the incorporation of a depth foundation model (i.e., DepthAnything [69]), interpolation operation (i.e., P(Interpolation) = 1.0), and relocation operation. As shown in Tab. 6, each of these steps progressively improves prediction quality by enhancing the geometry diversity. + +Extension Examples. The basic synthesis method can be extended by integrating multiple depth foundation models and unlabeled data, as discussed in Sec. 3.3. For verification, we further incorporate an depth foundation model, DepthPro [2], and 390K unlabeled images from SA1B [19]. The effectiveness of these extensions is shown in Tab. 6. + +Interpolated vs Original Labels. To further show the effectiveness of interpolated labels, we adjust the probability of using interpolated labels (i.e., P(Interpolation)) from 0.0 to 1.0. The remaining probability is used for randomly selecting original dense depth maps, including ground-truth depth maps and dense predictions from DepthAnything. As shown in Tab. 6, when using fully interpolated depth labels (i.e., P(Interpolation) = 1.0), the model achieves the best performance due to maximized data diversity. + +# 5. Conclusion + +In this paper, we propose a label-efficient method, PacGDC, to expand training data coverage with minimal annotation effort for generalizable depth completion. This is achieved by a data synthesis pipeline based on the 2D-to-3D projection ambiguities and consistencies. This pipeline includes multiple depth foundation models, interpolation and relocation strategies, and unlabeled data. Extensive experiments demonstrate that PacGDC achieves superior generalizable depth completion in both zero-shot and few-shot settings. + +# Acknowledgment + +This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 62088102 and 62373298, and by the Singapore Ministry of Education (MOE) Tier-2 Grant MOE-T2EP20123-0003. + +# References + +[1] Luca Bartolomei, Matteo Poggi, Andrea Conti, Fabio Tosi, and Stefano Mattoccia. Revisiting depth completion from a stereo matching perspective for cross-domain generalization. In 2024 International Conference on 3D Vision (3DV), pages 1360-1370. IEEE, 2024. 1 +[2] Aleksei Bochkovskii, Amael Delaunoy, Hugo Germain, Marcel Santos, Yichao Zhou, Stephan R Richter, and Vladlen Koltun. Depth pro: Sharp monocular metric depth in less than a second. arXiv preprint arXiv:2410.02073, 2024. 2, 3, 5, 6, 8 +[3] Daniel J Butler, Jonas Wulff, Garrett B Stanley, and Michael J Black. 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Existing approaches typically rely on costly test-time optimizations (often based on NeRF) to consolidate 2D predictions of off-the-shelf panoptic segmentation methods into 3D. Instead, in this work, we propose a unified and integrated approach PanSt3R, which eliminates the need for test-time optimization by jointly predicting 3D geometry and multi-view-consistent panoptic segmentation in a single forward pass. Our approach harnesses the 3D representations of MUSt3R, a recent scalable multi-view version of DUSt3R, and 2D representations of DINOv2, then performs joint multi-view panoptic prediction via a mask transformer architecture. We additionally revisit the standard post-processing mask merging procedure and introduce a more principled approach for multi-view segmentation. We also introduce a simple method for generating novel-view predictions based on the predictions of PanSt3R and vanilla 3DGS. Overall, the proposed PanSt3R is conceptually simple yet fast and scalable, and achieves state-of-the-art performance on several benchmarks, while being orders of magnitude faster. More information and examples available on our project page. + +# 1. Introduction + +Robust understanding of the semantics of 3D scenes is key to many applications like virtual reality, robot navigation, or autonomous driving. Such use cases require an accurate decomposition of the 3D environment into separate object instances of known classes. In 2D vision, this joint task of semantic and instance segmentation, denoted as panoptic image segmentation [24], consists of instance segmentation of things classes (i.e. countable objects such as cars) and semantic segmentation of stuff classes (i.e. uncountable classes such as road or sky). Following [24], a large number of solutions have been proposed for 2D panoptic segmentation, based on CNNs [8, 30, 33, 37, 64], Transformers [14, 15, 29, 43, 67, 79], or more recently diffusion mod + +![](images/aca33f576c1fe03bd85f2da1dc501d8acc5448e1047cf9bed6cad37622de5710.jpg) +Figure 1. PanSt3R jointly predicts 3D geometry and panoptic segmentation of a scene in a single forward pass. + +![](images/2e3f280dc9a48b69e8439b8a97e010c32e78622e9c5224eb460f0495d16da793.jpg) + +els [6, 56, 60, 65]. + +Several recent works [21, 27, 45, 51, 66] have extended panoptic segmentation to 3D scenes represented as point clouds, meshes or voxels. These methods typically take a 3D representation (e.g. a point cloud) as input and label it using neural networks, such as PointNet [41, 42], designed for direct operation on such data. However, acquiring dense and accurate point clouds requires dedicated sensors and recent models [26, 49, 55, 58, 61] struggle with noisy or sparse point clouds derived from unposed images. + +Instead, in this work, we propose to jointly perform 3D reconstruction and panoptic segmentation given an unconstrained set of unposed images or video frames. In this sense our method is closer to NeRF-based [2, 16, 25, 50, 57, 75] or 3DGS-based methods [62] that start from a collection of images. These approaches typically rely on posed images and off-the-shelf 2D panoptic segmentation models [15], followed by lifting and fusing the 2D panoptic predictions to 3D via NeRFs [36] or 3DGS [22]. + +While this allows for aggregation of potentially inconsistent and noisy 2D panoptic labels from multiple images into consistent 3D labels, these methods have several limitations: (1) they depend on accurate camera poses, (2) they require costly test-time optimization to align 2D segmentations with 3D geometry, and (3) they inherently separate the 2D segmentation and 3D reconstruction pipelines, potentially sacrificing efficiency and accuracy. + +We argue that 3D reconstruction and 3D panoptic segmentation are two intrinsically connected tasks, both involving reasoning in terms of 3D geometry of the scene and its instance decomposition. Therefore, we propose to + +model the 3D geometry and its panoptic segmentation in a unified, end-to-end framework that performs directly multiview consistent panoptic segmentation. Existing works for such panoptic 3D reconstruction usually focus on single-image inputs [11, 74] or require posed video inputs [63]. + +Instead, building on top of the recent 3D reconstruction network MUsT3R [61], we propose PanSt3R (Panoptic MUsT3R) which jointly predicts the 3D scene geometry and its panoptics from an unconstrained collection of unposed images in a single forward pass. PanSt3R leverages two pre-trained feature extractors to encode frames in both semantic (2D) and 3D-aware information, then directly regresses 3D geometry via a 3D head, and performs multiview instance mask prediction via a Mask2Former-like decoder. These mask predictions are finally filtered using a lightweight novel quadratic binary optimization framework (QUBO). This turns out to be a crucial step in our method, as we show that the standard filtering technique is poorly suited for multi-view predictions. Finally, we demonstrate that it is straightforward to generate novel view panoptic predictions based on the outputs of our method via simple test-time uplifting of labels to 3DGS [35]. + +In summary, our main contributions are as follows. We introduce a method for joint 3D reconstruction and panoptic segmentation, which tackles the problem with a single forward pass. The approach is simple, fast, and operates on hundreds of images without requiring any camera parameters or test-time optimization. Second, we propose a novel and mathematically grounded mask prediction merging strategy to further improve the quality of multi-view panoptic predictions. Third, we introduce two distinct and simple approaches for novel-view synthesis with panoptic segmentation, leveraging our framework and 3D Gaussian Splatting. Finally, we conduct extensive evaluation and ablative studies on several datasets, obtaining state-of-the-art results, both in terms of panoptic quality and inference speed. + +# 2. Related work + +2D Panoptic Segmentation is a unification of semantic and instance segmentation tasks. Its goal is to decompose an image into different regions, each region corresponding to an individual object (denoted as thing) or uncountable concepts like 'sky' or 'ground' (denoted as stuff). The first panoptic methods extended Mask R-CNN [19] to design a deformable-convolution-based semantic segmentation head and solve the two subtasks simultaneously [13, 23, 24, 37, 64]. Another set of models [8, 40, 59, 68] build upon the DeepLab architecture [31]. Instead, [30] combines a proposal attention module with a mask attention module, [33] proposes an end-to-end occlusion-aware pipeline, and [52] introduces a fully differentiable end-to-end network for + +class-agnostic instance segmentation jointly trained with a semantic segmentation branch. Gao et al. [17] jointly trains semantic class labeling with a pixel-pair affinity pyramid, and Yuan et al. [71] generalizes object-contextual representations to panoptic segmentation. + +With the success of Vision Transformers, Mask2Former [15], inspired by DETR [4], adopted a more unified approach to directly produce panoptic output, posing the task as a mask prediction and classification problem. Several recent extensions also aim for open-vocabulary segmentation capabilities (e.g. using a CLIP text encoder) [7, 14, 18, 20, 29, 43, 67, 70]. Recently, several diffusion-based methods were also proposed for this task [6, 56, 60, 65]. + +3D Panoptic Segmentation is a direct extension of 2D panoptic segmentation for 3D scenes. We can distinguish between several categories of approaches. First, methods that directly process an input 3D point cloud, typically obtained by dedicated sensors (ToF or LIDAR), thereby assuming prior knowledge of the 3D scene geometry [21, 27, 45, 51, 66]. + +The second category of methods, closer to our approach, requires only a set of input images and respective camera parameters (if not provided directly, the latter is usually obtained via standard SfM techniques [48]). Existing approaches in this category are either based on NeRF [36], or Gaussian Splatting [22], with implicit or explicit labeled 3D representations as output, respectively. These methods typically perform 3D panoptic segmentation by lifting 2D segmentation masks obtained with pre-trained 2D panoptic segmentation models (e.g. Mask2Former [15]) to 3D. Zhi et al. [75] showed that noisy 2D semantic segmentations can be fused into a consistent volumetric model by a NeRF, and their model was extended to instance and panoptic segmentation in [16, 25, 57]. + +Panoptic NeRF [16] starts from a set of sparse images, coarse 3D bounding primitives and noisy 2D predictions to generate panoptic labels via volumetric rendering. Panoptic Neural Fields (PNF) [25] learns a panoptic radiance field with a separate instance MLP and a semantic MLP by explicitly decomposing the scene into a set of objects and amorphous background. These MLPs collectively define the panoptic-radiance field describing 3D point color, semantic and instance labels. DM-NeRF [57] introduced an object field component to learn unique codes for all individual objects in 3D space from 2D supervision and panoptic segmentation with an extra semantic branch parallel to object code branch. Panoptic Lifting (PanLift) [50] relies on TensoRF [5] on top of which they introduce lightweight output heads for learning semantic and instance fields. The core idea of Contrastive Lift [2] is a slow-fast clustering objective function well suited for scenes with a large number of objects. They lift 2D segments to 3D fusing them by + +means of a neural field representation, which encourages multi-view consistency across frames. + +On the Gaussian Spatting side, PLGS [62] learns to embed an additional semantic and instance probability vectors for each Gaussian, which can be rendered on novel views in parallel to RGB. To handle noisy panoptic predictions, they rely on Scaffold-GS architecture [34] where additional depth maps are provided as input and 3D Gaussians are initialized with semantic anchor points used for smooth regularization during training. Instead, PCF-Lift [78] addressed the degradation of performance in complex scenes caused by noisy and error-prone 2D segmentations by introducing Probabilistic Contrastive Fusion (PCF), which learns to embed probabilistic features to robustly handle inaccurate segmentations and inconsistent instance IDs. + +Alternatively, a category of methods explores joint prediction of 3D geometry and panoptics of the scene. However, these approaches are either limited to single-image inputs [10, 11, 74], or rely on posed and ordered collection of input frames [63, 77]. + +In contrast to all these methods, our approach works on collections of unordered and unposed input images without camera parameters or depth maps, and directly outputs a 3D reconstruction annotated with panoptic labels in a single forward pass (see examples in Fig. 1). + +# 3. Method + +Problem statement. Given a set of $N$ images $I_{1}\ldots I_{N}\in \mathbb{R}^{W\times H\times 3}$ , we aim to jointly perform 3D reconstruction and panoptic segmentation, producing a global 3D point, a semantic class, and an instance ID for every pixel in each input image. Formally, these outputs materialize as 3D point-maps $\mathbf{X}\in \mathbb{R}^{N\times W\times H\times 3}$ , semantic segmentation masks $\mathbf{M}^{\mathrm{CLS}}\in \{1\dots C\}^{N\times W\times H}$ , and instance segmentation masks $\mathbf{M}^{\mathrm{INST}}\in \{1\dots m\}^{N\times W\times H}$ , where $W$ and $H$ denote the image width and height, $C$ the number of classes and $m$ the maximum number of instances in the scene. + +Summary. Our method builds upon recent progress made in the 3D reconstruction community. Specifically, our approach is based on MUsT3R [3], a Transformer-based powerful and scalable 3D reconstruction method, which we augment with panoptic capabilities inspired by Mask2Former [9]. In Sec. 3.1 we detail the overall architecture of our network. Since the network outputs raw mask predictions that are potentially overlapping, a merging step is necessary to select a globally optimal set of instances (Sec. 3.2). In order to generate panoptic segmentations for novel viewpoints, we optionally project the labeled point cloud into a set of 3D Gaussians (Sec. 3.3). + +# 3.1. PanSt3R + +The overall PanSt3R architecture is illustrated in Fig. 2 and detailed below. It consists of a feature extraction step that leverages foundational models for 2D and 3D feature extraction, followed by instance mask proposal generation. + +Feature extraction. Our network starts by extracting dense semantic and 3D-aware representations from the set of input images by leveraging two pretrained backbones. Namely, we extract DINOv2 features for each input image, which have been shown to capture dense and semantically meaningful representations of the scene [38]. Likewise, we extract MUsT3R [3] features for each input image. MUsT3R is a recent extension of DUSt3R [26, 61], a foundation model for 3D vision, excelling at reconstructing the geometry of a scene given only sparse views. In practice, MUsT3R processes images sequentially while maintaining an internal memory of the previously seen images, thereby allowing the encoding of multi-view-consistent representations. Like DINOv2, MUsT3R is a Transformer-based network, but it contains an additional decoder to leverage its internal memory. This way, it can encode both local and global scene geometry using its encoder and decoder, respectively. + +Formally, we denote by $\mathbf{E}_n^D = \mathrm{ENC}^{\mathrm{D}}(I_n)$ the DINOv2 feature maps of image $I_{n}$ and by $\mathbf{E}_n^M = \mathrm{ENC}^{\mathrm{M}}(I_n)$ and $\mathbf{D}_n^M = \mathrm{DEC}(\mathbf{E}_n^M)$ the encoder and decoder feature maps from MUSt3R. Note that by feature maps, we refer to an array of tokens, where each token corresponds to a small $16\times 16$ patch in the image, i.e. we have in reality $\mathbf{E}_n^D,\mathbf{E}_n^M,\mathbf{D}_n^M$ multi-channel feature maps of size $\frac{W}{16}\times \frac{H}{16}$ and the number of channels corresponding to the respective feature dimensions $d_{ED} = d_{EM} = 1024$ and $d_{DM} = 768$ . As shown in Fig. 2, the three token maps are concatenated along the feature dimension and passed through an MLP to form compact joint 3D-semantic token representations $\{\mathbf{f}_n\}$ with $\mathbf{f}_n\in \mathbb{R}^{d_t}$ , where $d_{f} = 768$ . The concatenated feature maps are also used to construct high-resolution mask features $\mathbf{F}_n\in R^{\frac{W}{2}\times \frac{H}{2}\times d_F}$ used for mask prediction, with $d_{F} = 256$ . For that, we perform a series of MLP and $2\times$ upsampling operations to gradually upscale them until we reach the output resolution. + +3D geometry. We leverage MUs3R's innate capabilities to reconstruct 3D point clouds. For every image, MUs3R predicts a global point cloud in the first image's coordinate frame, a local point cloud, and a confidence map. Specifically, given the decoder features $\mathbf{D}_n^M$ , a prediction head $\mathrm{HEAD}^{3D}$ regresses 3D coordinates and confidences for each pixel, i.e. $\mathbf{X}_n^g, \mathbf{X}_n^l, \mathbf{C}_n = \mathrm{HEAD}^{3D}(\mathbf{D}_n^M) \in \mathbb{R}^{W \times H \times 3}$ . + +Mask prediction and classification. We follow Mask2Former [15] in formulating panoptic segmentation as a binary mask prediction and classification problem. We extend this formulation to the multi-view setting, generating globally consistent masks for each instance, i.e., the same + +![](images/f51e2ceb76926378cf528fdda387ec752ddbbc7b79e4bafd427128c5fbc982c1.jpg) +1. Extracting frame-wise features + +![](images/95c6a2b4c85216824a33f4c90ddac326391bbe6e5aa59a2d892b6792d759df97.jpg) +2. Panoptic prediction +Figure 2. PanSt3R architecture. 1) input unposed RGB frames are passed through pretrained DINOv2 and MUsT3R to extract 2D semantic and globally aligned 3D geometric features respectively. Frame tokens and mask features are constructed from per-frame concatenated features. 2) A mask transformer is used to decode instance masks and their class probabilities, by cross-attending learnable instance queries with extracted frame tokens. + +instance ID is assigned to a 3D object instance across all views it appears in. + +This is achieved by a series of learnable queries denoted by $\{\mathbf{q}_j^0\}$ , shared by all views and used to represent different instances of things and stuff classes in the input scene. These learnable query features can hence be seen as region proposals. They are input to a mask transformer $\mathrm{DEC}^{\mathrm{P}}$ that attends to multi-view frame tokens $\{\mathbf{f}_n\}$ using cross-attention. This results in a set of refined queries $\{\mathbf{q}_j\} = \mathrm{DEC}^{\mathrm{P}}(\{\mathbf{q}_j^0\}, \{\mathbf{f}_n\})$ , which serve as the base for instance classification and mask prediction. + +To enable training across multiple datasets with diverse labeling conventions, we adopt an open-vocabulary approach for instance classification. Specifically, the class probabilities for each query are computed as the cosine similarity between the query embeddings and SigLIP [39, 72] generated text embeddings of class names $^{2}$ . Second, the mask prediction of each query is obtained via a dot product with the high-resolution mask features $\mathbf{F}_n$ . We denote the resulting instance mask for the image $I_{n}$ and query $j$ as + +$$ +\mathbf {M} _ {j, n} = \operatorname {s i g m o i d} \left(\mathbf {F} _ {n} \cdot \mathbf {q} _ {j} ^ {\mathrm {M}}\right) \in \mathbb {R} ^ {\frac {W}{2} \times \frac {H}{2}}, \tag {1} +$$ + +where $\mathbf{q}_j^{\mathrm{M}} = \mathrm{LIN}^{\mathrm{M}}(\mathbf{q}_j)$ is the mask embedding of $\mathbf{q}_j$ . + +Training loss. We follow the training protocol of Mask2Former [15], which comprises three losses: a focal loss $\mathcal{L}_{cls}$ for instance classification [28], and a combination of dice loss $\mathcal{L}_{dice}[54]$ and binary cross-entropy $\mathcal{L}_{bce}$ for mask prediction. The final loss is a weighted combination + +$$ +\mathcal {L} = \lambda_ {c} \mathcal {L} _ {c l s} + \lambda_ {d} \mathcal {L} _ {d i c e} + \lambda_ {b} \mathcal {L} _ {b c e}. \tag {2} +$$ + +Discussion. While our panoptic prediction network is largely inspired by Mask2Former [15], we would like to + +point out a few key innovations. Most notably, our network is inherently multi-view, processing multiple images simultaneously and directly predicting consistent panoptic segmentation across all views. This is enabled by leveraging 3D-aware features from MUSt3R and employing a shared set of queries, where each query explicitly targets the same object instance across all view. Unlike [15], we do not construct a multi-resolution feature pyramid, but instead we retain the original frame tokens to limit the memory footprint. We adapt an open-vocabulary classification head [73], facilitating training on heterogeneous datasets and improving test-time performance. + +# 3.2. Merging mask predictions + +Given the set of multi-view mask predictions from Eq. (1), denoted $\mathbf{M}_i\in \mathbb{R}^{N\times \frac{W}{2}\times \frac{H}{2}}$ for each query $i$ , our goal is to find a subset of masks that optimally cover the $N\times \frac{W}{2}\times \frac{H}{2}$ output pixel space, minimizing the overlap between selected masks while reducing the area of empty regions (i.e., holes). Mathematically, this can be formalized as a quadratic unconstrained binary optimization (QUBO) problem: + +$$ +u ^ {\star} = \max _ {u \in \{0, 1 \} ^ {m}} \sum_ {i} u _ {i} Q _ {i} - \sum_ {i < j} u _ {i} u _ {j} Q _ {i, j}, \tag {3} +$$ + +where $u$ is a boolean assignment of proposals, the weight $Q_{i} = \sum_{k}\mathbf{M}_{i,k}$ represents the area $|\mathcal{M}_i|$ covered by mask proposal $i$ , and $Q_{i,j}$ represents the area in excess when selecting both mask proposals $i$ and $j$ due to their overlap: + +$$ +Q _ {i, j} = \left| \mathcal {M} _ {i} \cap \mathcal {M} _ {j} \right| = \sum_ {k} \min \left(\mathbf {M} _ {i, k}, \mathbf {M} _ {j, k}\right), +$$ + +since $|\mathcal{M}_i \cup \mathcal{M}_j| = |\mathcal{M}_i| + |\mathcal{M}_j| - |\mathcal{M}_i \cap \mathcal{M}_j|$ . + +To limit the selection of overlapping regions, we further multiply $Q_{i,j}$ by a penalty $\lambda_p > 1$ , (typically $\lambda_p = 2$ ). Since QUBO is an NP-hard problem, we rely on simulated annealing [47] to find a near-optimal solution efficiently. + +Given $u^{\star}$ , we construct instance masks $\mathbf{M}^{\mathrm{INST}}$ by merging the final assigned masks via per-pixel arg max. $\mathbf{M}^{\mathrm{CLS}}$ is obtained by assigning the highest probability class $c_{j} = \arg \max_{i} p_{i,j}$ within the mask area of an instance. + +Discussion. The standard mask merging procedure as introduced in MaskFormer [9] is substantially different from ours. In a nutshell, it consists of first filtering out low-confidence mask predictions to get a pool of candidate masks. This is followed by a pixel-wise voting process to select the most confident mask at each location. Finally, additional filtering is applied to remove predictions that lack sufficient vote support. While this heuristic procedure is simple and typically performs well for single images, it often fails to integrate the multi-view constraints essential for 3D panoptic segmentation. Indeed, as shown in Sec. 4.5, our QUBO procedure results in a large boost in performance, thanks to its global optimization of instance masks across all views. + +# 3.3. Panoptic labels on novel views with 3DGS + +In order to compare our model with other methods [2, 16, 25, 50, 57, 62], which evaluate the panoptic performance on unseen views, we additionally rely on Gaussian Splatting (3DGS) [22]. We explore two possible strategies: (i) we simply generate novel RGB views with vanilla 3DGS and predict the panoptic segmentation by a simple forward pass of PanSt3R on the rendered images; or (ii) we uplift the predicted panoptic segmentations to 3D and render the segmentations on novel views. Since the first strategy is trivial and self-explanatory, we now describe the second strategy in more detail. In the following, we denote 2D images $I_{1},\ldots ,I_{N}$ and instance mask predictions $\mathbf{M}^{\mathrm{INST}}$ as output by the QUBO mask merging described above. + +Scene optimization. The 3DGS optimizes the means and covariances of the Gaussian densities, their opacities, and the color function parametrized by spherical harmonics [22]. Denoting by $\theta$ the color-related parameters and by $\psi$ the other parameters, the 3DGS optimizes the following reconstruction loss: + +$$ +\mathcal {L} _ {r g b} = \frac {1}{N} \sum_ {n = 1} ^ {N} \mathcal {L} \left(I _ {n}, \hat {I} _ {n} (\theta , \psi)\right), \tag {5} +$$ + +where $\hat{I}_n(\theta)$ is the image rendered in the direction corresponding to view $n$ , and $\mathcal{L}$ is a combination of $\mathcal{L}_1$ and SSIM loss functions [22]. + +Panoptic regularization. Optimizing Gaussians using only RGB supervision may cause them to span multiple object instances or semantic boundaries, which can negatively impact subsequent label uplifting. To address this, we propose an additional regularization term to align Gaussians to the predicted panoptic masks. + +Concretely, we assign a unique RGB color to each instance ID in $\mathbf{M}_n^{\mathrm{INST}}$ , producing an instance color map $P_{n} \in \mathbb{R}^{3 \times W \times H}$ for each image $I_{n}$ , which we use as a lightweight supervision signal. We introduce an additional set of Gaussian color parameters $\hat{\theta}$ , and an auxiliary loss and an auxiliary loss that supervises the rendering of instance color maps during Gaussian optimization: + +$$ +\mathcal {L} _ {r e g} (\theta , \phi) = \frac {1}{N} \sum_ {n = 1} ^ {N} \mathcal {L} _ {1} \left(P _ {n}, \hat {P} _ {n} (\hat {\theta}, \psi)\right), \tag {6} +$$ + +where $\hat{P}_n(\theta, \phi)$ is the rendered panoptic image. We optimize the Gaussians with the following weighted combination of the two losses: + +$$ +\min _ {\theta , \phi} \quad \mathcal {L} _ {r g b} (\theta , \psi) + \lambda \mathcal {L} _ {r e g} (\hat {\theta}, \psi) \tag {7} +$$ + +with weight $\lambda$ set to 1 in all our experiments. + +Uplifting with LUDVIG. To uplift the instance labels into the optimized Gaussian Splatting scene, we opt for LUDVIG [35], a recent 3DGS-based feature uplifting method that simply averages 2D pixel features across all views. Instead of using LUDVIG to uplift features, we utilize it to uplift one-hot encoded instance labels $M_{n}^{0} \in \{0,1\}^{m \times W \times H}$ obtained from $\mathbf{M}_{n}^{\mathrm{INST}}$ . We define $S_{i}$ as the set of view-pixel pairs $(n,u)$ impacted by Gaussian $G_{i}$ during forward rendering. This impact is quantified by the weight $w_{i}(n,u)$ resulting from $\alpha$ -blending. LUDVIG defines the 3D feature $\mathbf{g}_{i}$ for the Gaussian $G_{i}$ as the following weighted sum: + +$$ +\mathbf {g} _ {i} = \sum_ {(n, u) \in \mathcal {S} _ {i}} \frac {w _ {i} (n , u)}{Z _ {w}} M _ {n} ^ {0} (u), \quad Z _ {w} = \sum_ {(n, p) \in \mathcal {S} _ {i}} w _ {i} (n, p), \tag {8} +$$ + +After uplifting to 3D and and reprojecting to 2D, the final 2D rendered instance label is obtained as the arg max along the instance label dimension. + +# 4. Experimental evaluation + +# 4.1. Implementation details + +Training datasets. To train our method, we employ a mix of 2D (single-view) and 3D (set of multi-view posed images) datasets for which ground truth panoptic segmentations are available (see Tab. 1). ScanNet++ [69] is comprised of 1006 high-resolution 3D indoor scenes with dense semantic (100 class labels) and instance annotations. We use the V2 version of the dataset and follow the official split, i.e. 850 scenes for training and 50 scenes for validation. Aria Synthetic Environments (ASE) [1] is a procedurally-generated synthetic dataset containing 100K unique multi-room interior scenes populated with around 8K 3D objects from which we randomly sampled 750 scenes. With InfiniGen [44], another tool for procedural generation of 3D data, + +Table 1. Statistics for datasets used during training (top) and evaluation (bottom). "MV" denotes available multi-view data. + +
DatasetrealMV#scenes#classes
TrainingScanNet++ [69]✓✓855100
ASE [1]x✓75044
Infinigen [44]x✓93676
COCO [32]✓x118k80
ADE20k [76]✓x20k150
EvalScanNet++ [69]✓✓50100
ScanNet [12]✓✓1220
Hypersim [46]x✓620
Replica [53]x✓720
+ +we generate 936 indoor scenes of 25 images each. Finally, we also leverage two widely used 2D panoptic segmentation datasets, COCO [32] and ADE20K [76], which consist of high-resolution images with precise manual annotations. Adding these datasets is useful to improve generalization and robustness, since they offer a larger visual diversity. To simulate multi-view data on 2D images, we sample several geometric and photometric variants of the input image including crops, rotations, and color jittering. + +Training details. The DINOv2 and MUs3R backbones (resp. ViT-L, and ViT-L+ViT-B architectures) are initialized with their pretrained weights and frozen during PanSt3R training. In preliminary experiments, we observed that finetuning MUs3R does not have a big impact on the final performance, but incurs significant additional training cost. Since each dataset comes with a different set of classes, we restrict the focal loss supervision $\mathcal{L}_{cls}$ to within the set of ground-truth classes of each dataset during training. Additional training details are provided in the Supplementary. + +Test-time keyframes. Since the number of test views can be large during inference (e.g. hundreds), we adopt the same technique as in [3] to reduce the computational and memory footprint. Namely, we efficiently cluster the set of input images using retrieval techniques and select a small set of 50 keyframes using the farthest-point-sampling (FPS) algorithm to maximize coverage. Frame tokens $\{\mathbf{f}_n\}$ are then only selected from these keyframes, which is enough to generate relevant queries $\{\mathbf{q}_j\}$ , as shown in Sec. 4.5. We then process the remaining views frame-by-frame, only extracting the per-frame features $\mathbf{F}_n$ and directly performing mask prediction via Eq. (1), with the decoded queries $\{\mathbf{q}_j\}$ obtained from the keyframes. + +# 4.2. Evaluation metrics + +Panoptic Quality (PQ). The Panoptic Quality (PQ) score [24] is defined as + +$$ +\mathrm {P Q} = \frac {2 \sum_ {(p , g) \in T P} \operatorname {I o U} (p , g)}{2 | T P | + | F P | + | F N |}, \tag {9} +$$ + +where $p$ is a predicted instance and $g$ is a GT class instance. Intuitively, this score averages IoU of matched segments + +Table 2. We report results for direct predictions of PanSt3R on rendered test images (with and without QUBO), as well as results obtained via the simple 3DGS uplifting approach with LUDVIG. Timing for building the 3DGS. Note that given access to target view images, PanSt3R can make predictions without the need for 3DGS (and camera parameters). + +
MethodReq. +PosesHyper- +simRep- +licaScan +NetTime +(min)
DM-NeRF [57]✓51.644.141.7~900
PNF [25]✓44.841.148.3-
PanLift [50]✓60.157.958.9~450
Contrastive Lift [2]✓62.359.162.3~420
PLGS [62]✓62.457.858.7~120
PCF-Lift [78]✓--63.5-
PanSt3R w/o QUBO†51.657.359.5~4 (+35†)
PanSt3R†56.562.065.7~4.5 (+35†)
PanSt3R + LUDVIG✓66.360.667.5~40
+ +![](images/e1eec826b720098643836f444f45a4f4fa0a62cc05b94f451b69d5c2209e035c.jpg) + +![](images/e0d6a708a83254cc421c753481647766ed44707cd70b69f64740905078fb4cc2.jpg) +Figure 3. Qualitative examples of novel-view panoptic segmentation on Hypersim and Replica scenes. Predictions are overlaid on top of original images, and colors and their nuances denote different classes and object instances respectively. + +![](images/8c2919900daa5de55240ec762d993228719c6a706c004ae1457b4638744022b4.jpg) + +![](images/730211471dfaa45cfd65a828a12e95becbb4b060efb43507964fe324552fe044.jpg) + +![](images/170a653d950af08e47b44fed6a2ebfc3fa094083ab693a9a67e41abb59d7e7af.jpg) + +![](images/8cc7757d10a96799edaf27bb83fc215aaefede1296213524799fbee0f658a957.jpg) + +![](images/2515118e8621bf3687c2b1dbe24113124fdfdd063d45dadcfbfb83c21c971062.jpg) + +![](images/cf8d9a5810a1538c996283c0b17e1a3769f64571ab8298350dcc67daba403fe3.jpg) + +while penalizing segments with wrong matches (False Positives) or without matches (False Negatives). It can be seen as a combination of two terms, segmentation quality $\mathrm{SQ} = 1 / |TP|\sum_{(p,g)\in TP}\mathrm{IoU}(p,g)$ , and a recognition quality $\mathrm{RQ} = TP / (2\cdot |TP| + |FP| + |FN|)$ . + +Extension to 3D scenes. PQ can be trivially computed at the scene level by pretending that the scene is a concatenation of all images, effectively tying predictions between all images. This metric, coined scene-PQ $(\mathrm{PQ}^{sc})$ , was first proposed in [50] to evaluate the results of 3D panoptic segmentation. As we always use the scene-PQ metric, we omit the upper-script $^{sc}$ for brevity in the following. To compute the overall results for a dataset, we average the per-scene PQs across all scenes. + +# 4.3. Evaluation on the PanLift benchmark + +We first evaluate our method on the Panoptic Lifting (PanLift) benchmark [50]. It comprises 12 scenes from ScanNet [12], 6 scenes from Hypersim [46] and 7 scenes from Replica [53] (see details in [50]). We use the same splits between seen and unseen (novel) views as in [2, 50]. + +For PanSt3R, we experiment with the two strategies presented in Sec. 3.3: (i) we simply render a novel image of the target viewpoint using an off-the-shelf 3DGS model, and + +![](images/29a9e2bc91ad1cb2393c9b038a90e1fe5324cbc052de152626a233a8ca713306.jpg) +Figure 4. Qualitative comparison of novel-view panoptic segmentation on ScanNet [12] scenes. Colors and their nuances denote different classes and object instances respectively. + +perform a forward pass on rendered images with PanSt3R; or (ii) we utilize the LUDVIG uplifting strategy to directly construct a panoptic 3DGS-based scene representation. Given access to target-view images, PanSt3R can directly predict panoptic segmentation in a forward pass, in principle not requiring poses or 3DGS. However, to be more inline with the competing methods, which predict panoptic segmentation based on test poses, not images, we compute the PQ results for PanSt3R (and PanSt3R w/o QUBO) on test images rendered with vanilla 3DGS built with posed training images3. + +Comparison with existing methods. 3D panoptic segmentation methods either directly process an input 3D point cloud (see discussion in Supplementary), or they revolve around the idea of performing 3D panoptic segmentation by lifting 2D segmentation masks obtained with off-the shelf pre-trained 2D panoptic segmentation models, often Mask2Former [62] pretrained on COCO [32]. Then they map the COCO panoptic classes to the following 21 classes: wall, floor, cabinet, bed, chair, sofa, table, door, window, counter, shelves, curtain, ceiling, refrigerator, television, person, toilet, sink, lamp, bag and other. In general, these methods lift and align the 2D predictions to 3D with a test-time optimization of a NeRF or 3DGS. + +We compare our PanSt3R variants on the PanoLift datasets against state-of-the-art methods in Tab. 2, where DM-NeRF [57], PNF [25], PanLift [50] and Contrastive Lift [2] are NeRF-based approaches, and PLGS [62] and PCF-Lift [78] rely on 3DGS to uplift 2D panoptic segmentation masks. PanSt3R inference is performed using the full training class set, then classes are re-mapped to the target 21 classes, similar to existing work. In Fig. 3 we provide visual examples for PanSt3R+LUDVIG on different datasets and scenes, and in Fig. 4 we provide qualitative comparisons between PanSt3R, PanSt3R+LUDVIG, PanLift and Contrastive Lift. + +Table 3. Results on the ScanNet++ val set. We report result of our default model PanSt3R (full) and one trained only on ScanNet++. PanSt3R is compared with PanLift [50] and Contrastive Lift [2], utilizing Mask2Former [15] finetuned on ScanNet++. + +
MethodPQ\( PQ_{th} \)\( PQ_{st} \)Time (min)
PanLift [50]29.515.659.4~ 500
Contrastive Lift [2]28.414.856.3~ 460
PanSt3R (ScanNet++) + LUDVIG46.743.255.8~ 2.3
54.852.462.4~ 35
PanSt3R (full) + LUDVIG49.145.858.7~ 2.3
54.751.762.4~ 35
+ +Discussion. PanSt3R + LUDVIG set a new state-of-the-art, except on Replica, where direct forward pass prediction of PanSt3R on rendered views performs slightly better. On Hypersim and ScanNet, uplifting the panoptic segmentations performs much better than direct forward with PanSt3R due to the noise reduction effect of multi-view feature aggregation (Fig. 4). Notably, PanSt3R accomplishes this while being far more computationally efficient than previous methods, even when uplifting to 3DGS via LUDVIG. Additionally, using a simple direct prediction with PanSt3R on re-rendered images is enough to outperform all previous methods on two out of three datasets (except Hypersim), with potentially no need for camera parameters in contrast to existing methods. + +# 4.4. Evaluation on ScanNet++ + +We also evaluate PanSt3R on the validation set of the ScanNet++ [69]. For each of the 50 validation scenes, we randomly select 100 frames (only iPhone images) and use PanSt3R to predict multi-view consistent panoptic segmentations for these images in a single forward pass. We then randomly select 50 images from the remaining pool of images to serve as test views in order to evaluate the panoptic segmentation on novel unseen viewpoints with the same process as used in the PanLift benchmark. A major difference compared to PanLift is a much larger number of classes (100 instead of 20), including small objects (e.g. crate, paper, socket, cup, smoke detector, soap dispenser), hence requiring much more fine-grained segmentation. To better assess the performance of the models, we also report $\mathrm{PQ_{th}}$ and $\mathrm{PQ_{st}}$ , denoting panoptic quality computed separately on thing and on stuff classes. + +Comparison with existing methods. Due to a lack of published results for panoptic segmentation on ScanNet++, we compare our method to PanLift [50] and Contrastive Lift [2] using the official code and uplift the predictions of Mask2Former, finetuned on the ScanNet++ training set. To ensure a fair comparison, we also evaluate a variant of PanSt3R trained only on the ScanNet++ training set, de + +![](images/70ec8ffd91b93df219c71ffa81283592a6f328c037c820b9f12e59dbba5d2a83.jpg) +Figure 5. Qualitative results of novel-view panoptic segmentation on various ScanNet++ [12] scenes. Colors and their nuances denote different classes and their instances. Note that due to the large number of classes (100), some may share similar colors. + +noted as PanSt3R (ScanNet++) alongside our full model4. Quantitative and qualitative results are presented in Tab. 3 and Fig. 5 respectively. + +Discussion We observe that all PanSt3R variants (full or ScanNet++ only, with or without LUDVIG) largely outperform both PanLift and Contrastive Lift by more than $10\%$ in PQ, while being an order of magnitude faster. Analysis reveals, that related approaches encounter difficulties with thing instances, especially small objects (see $\mathrm{PQ}_{\mathrm{th}}$ scores). Additionally, we observe that NeRF optimization struggles when using 'only' 100 training views. In comparison, PanSt3R's performance is relatively invariant to the number of views, since it builds upon the sparse view reconstruction framework of DUSt3R and MUsT3R (see ablations in Sec. 4.5). When we compare PanSt3R and PanSt3R (ScanNet++, we observe that the model trained on more data is slightly better, but the gap disappears when using LUDVIG. Finally, we once again observe that uplifting labels with LUDVIG results in a significant improvement both quantitatively and qualitatively (see Fig. 5). + +# 4.5. Ablative studies + +We perform a range of comparative experiments and ablative studies to evaluate the impact of various components and model configurations on the method's performance. We primarily assess the role of using 2D DINOV2 and 3D MUsT3R encoders, as well as the impact of QUBO and GS regularization. Further ablative experiences can be found in the Supplementary. + +Impact of 2D & 3D features. We ablate the contribution of our two feature extraction backbones on the final performance. For this study, we use a smaller architecture, + +Table 4. Ablating the importance of 3D (MUSt3R [3]) and 2D (DINOv2 [38]) features on the ScanNet++ validation set. Results are shown for PanSt3R (224, ScanNet++)+LUDVIG. + +
featuresPQPQthPQst
3D + 2D50.445.461.1
3D46.440.758.8
2D35.728.451.9
+ +Table 5. Analyzing the effect of the QUBO merging strategy (Sec. 3.2). Results are reported for PanSt3R+LUDVIG. + +
QUBOHypersimReplicaScanNetScanNet++
x58.160.860.250.8
✓66.760.767.352.0
+ +starting from MUSt3R/DINOv2 with a 224x224 input resolution and trained on the ScanNet++ training set only. Result obtained using only the 2D (DINOv2) or 3D (MUSt3R) features are presented in Tab. 4. We observe a clear complementarity effect between 2D semantic features of DINOv2 and 3D geometric features of MUSt3R. + +Mask merging strategy. We evaluate the impact of the QUBO-based mask merging strategy (Sec. 3.2). In Tab. 2 and Fig. 5, we compare two versions of PanSt3R, with and without QUBO (i.e. using the standard merging strategy from MaskFormer [9]). The same experiments are performed with additional LUDVIG uplifting in Tab. 5. We observe an overall large gap in terms of PQ (except for PanSt3R+LUDVIG on Replica), which highlights the inadequacy of the standard merging scheme when dealing with multi-view segmentation. In a sense, this is expected, as the standard scheme is purely heuristic and instances are selected only locally, without considering any global consistency. + +# 5. Conclusion + +We have presented PanSt3R, a novel approach for joint 3D reconstruction and 3D panoptic segmentation operating on unposed and uncalibrated collections of images. The proposed approach, building upon recent progress in 2D and 3D foundation models, is conceptually simple yet effective, achieving state-of-the-art results on multiple benchmarks. 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Most existing methods fall in the joint diffusion paradigm, but their complex and heuristic crop connection designs often limit their ability to achieve multilevel coherence. By deconstructing this challenge into its core components, we find it naturally aligns with next-token prediction, leading us to adopt an autoregressive (AR) paradigm for PIg modeling. However, existing visual AR (VAR) models are limited to fixed-size generation, lacking the capability to produce panoramic images. In this paper, we propose PanoLlama, a novel framework that achieves endless and coherent panorama generation with the autoregressive paradigm. Our approach develops a training-free strategy that utilizes token redirection to overcome the size limitations of existing VAR models, enabling next-crop prediction in both horizontal and vertical directions. This refreshes the PIg pipeline while achieving SOTA performance in coherence $(47.50\%)$ , fidelity $(28.16\%)$ , and aesthetics $(15\%)$ . Additionally, PanoLlama supports applications other PIg methods cannot achieve, including mask-free layout control, multi-scale and multi-guidance synthesis. To facilitate standardized evaluation, we also establish a dataset with 1,000 prompts spanning $100+$ themes, providing a new testing benchmark for PIg research. The code is available at https://github.com/0606zt/PanoLlama. + +# 1. Introduction + +Panoramic Image Generation (PIG) [3] is the task of generating images with arbitrarily long dimensions. It has gained significant attention as a subtask in image generation, especially with the growing interest in artistic expression, user control, and historical restoration [42]. The objective of this task is to generate coherent and endless panoramicas under a planar perspective. + +In recent years, diffusion models [29] have become the mainstream method in image generation, proving effective in visual editing [14], restoration [19], augmentation [7], + +and multi-modal tasks [15, 25]. They employ diffusion and denoising Markov chains to map the data distribution to a Gaussian distribution, as exemplified by DDPM [13], DDIM [30], and LDM [24]. So far, the most effective paradigm for PIG is joint diffusion [3, 17, 22], where the panoramic latent space is segmented into individual crops, then denoised and fused into a panorama through the connection strategy (Fig. 1 right). While effective, these approaches face limitations in the following aspects. + +1. Multilevel-Coherence Challenge: Existing methods often rely on heuristic, rule-based connection strategies, such as performing weighted averaging [3], introducing gradient guidance [17, 46], or deepening attention layers [22], struggling to achieve multi-coherence across both low-level and high-level features. +2. **Complex Designs:** Achieving crop-wise generation is non-trivial. These methods require complex designs to reconcile denoising paths across image crops, lacking unity, stability, and scalability. + +Achieving low-level coherence (e.g., color, edges) relies on adjacent crop connections, while achieving high-level coherence (e.g., semantics, layout) requires considering the overall transition across a sequence of crops, which naturally aligns with the next-token prediction paradigm. This insight motivates us to handle SIG tasks through an autoregressive (AR) architecture, which has been widely used in large language models (LLMs) [4, 36]. Visual AR (VAR) approaches [2, 31, 43] introduce a tokenizer to quantize image features into discrete tokens, generating an image in the next-token prediction manner. + +However, unlike LLMs' ability to produce long text, existing VAR models are limited to fixed-size image generation (typically $512 \times 512$ ) constrained by the training paradigm of image data. + +To address these challenges, we propose PanoLlama (Fig. 1 left), a novel framework that achieves endless and coherent panorama generation with the autoregressive paradigm. Our key contributions are as follows: + +1. New Paradigm: We define a new paradigm for SIG, modeling it as a next-token prediction task to better solve the multilevel coherence challenge. + +![](images/f06f1dcb800c86422b7633f173b708ebbb73d6ffb6afcacc617af34930058003.jpg) +Figure 1. PanoLlama vs. the most effective current FIG method, joint diffusion. Joint diffusion methods (right) denoise each image crop individually and require complex designs to connect them, which face challenges in achieving multilevel coherence. To address this, our PanoLlama (left) redefines FIG as a next-crop prediction task. Leveraging the autoregressive properties that inherently align with the FIG objective, we generate endless panoramas with higher continuity. + +![](images/a6d39a8ebe7cdbd8c44016301f299574e5d15811dc8ed35c3558c307f8e25b9d.jpg) + +2. New Strategy: Based on token redirection, we develop a training-free next-crop prediction strategy that enables endless FIG with existing VAR models. Compared to current methods with complex designs, PanoLlama offers a more straightforward and efficient framework, achieving SOTA performance in coherence (47.50%), fidelity & diversity (28.16%), and aesthetics (15%). +3. Additional Applications: Beyond basic panorama generation, we support applications other SIG methods cannot achieve, including multi-scale generation, mask-free layout control, and multi-guidance synthesis. +4. New Benchmark: Given the lack of a standardized testing prompt in prior FIG works, which typically rely on 5-20 specific ones, we construct a dataset of 1,000 detailed prompts across $100+$ themes. Along with a comprehensive set of baselines and metrics, this establishes a new benchmark for panorama generation. + +# 2. Related Work + +Panorama Generation While panoramas often refer to $360^{\circ}$ spherical projections [8, 18, 37, 40], we define them more broadly as arbitrarily long images, aiming for endless and coherent extension in a planar view. Existing studies mainly focus on extending pre-trained diffusion models for panorama upscaling, which can be summarized into two branches. (i) The main branch is joint diffusion, aiming to develop a connection strategy that seamlessly fuses image crops into a panorama. This branch is pioneered by MultiDiffusion [3], where the panoramic space is split into smaller crops, then denoised and merged together through a linear interpolation function. Building on this, many studies [16, 17, 22, 45, 46] are devoted to optimizing the connection process, resulting in improved generation outcomes. However, as discussed in Sec. 1, these methods of + +ten rely on intuitively designed connection strategies, limiting their ability to achieve multilevel coherence. (ii) Another branch utilizes image inpainting techniques to establish regional correlations for extrapolating subsequent image content [1, 24]. Yet, they infer the next crop's content solely from the masked region of the previous one, lacking consideration for the overall layout and structure, and requiring long generation times. + +Autoregressive Models for Image Generation Visual AR models [41] introduce a tokenizer to enable sequential modeling for image data, with its generation process following the next-token prediction paradigm. VQVAE [35] pioneers this approach by incorporating a codebook to convert continuous image embeddings into discrete tokens. VQGAN [5, 11] further improves VQVAE by integrating adversarial and perceptual losses. Recent studies [6, 20, 33, 38, 43] attempt to incorporate image generation with LLMs (e.g., GPT [4], Gemini [32], and Llama [34]), which have demonstrated their effectiveness in understanding and generating visual content. For example, LlamaGen [31] explores the vanilla Llama architecture [34] for image generation and yields promising results. While we propose that the autoregressive paradigm can better tackle the multilevel-coherence problem, current VAR methods lack the capability for panorama generation. This provides insights for our work, which bridges this gap and addresses the key challenge of FIG tasks. + +# 3. Methodology + +# 3.1. Panorama Generation as a Next-Token Prediction Task + +In FIG tasks, we aim to extend a pre-trained reference model $\Phi$ , which operates within a limited image space + +![](images/c14371c594dae1b29d6fadb134aa6b10284bf9c441b417bd3a5f5a11fc737aca.jpg) +(i) + +![](images/73d868787e36efe62791f25e647d33be3bb71d7b936fa2c745442e89df1d2307.jpg) +(ii)-Horizontal +$v_{i}^{j} = f_{\mathcal{G}}(v_{i - 1,\epsilon (v_{i - 1}^{j}) - \sqrt{p} +c},\dots ,v_{i - 1,\epsilon (v_{i - 1}^{j})})$ + +![](images/a6d241667d9ba65f4e4902b31c5a199e5b172248c076a14c93ddc5aa28ea1488.jpg) +(iii) +Figure 2. The framework of PanoLlama consists of three parts: (i) Textual Conditioning: The given prompt $y$ is encoded into a conditional embedding $s$ using the text encoder $f_{\mathcal{E}}$ (Eq. (4)). (ii) Next-Crop Prediction: With $s$ as a prefilling, the token generator $f_{\mathcal{G}}$ autoregressively generates a sequence of $p$ image tokens (Eq. (5)). After reaching the token limit, vertical expansion is achieved by setting $v_{i}$ to start with the last $p - r\sqrt{p}$ tokens of $v_{i-1}$ via Eq. (6); while horizontal expansion extends rows interleavingly by Eq. (8), redirecting the last $\sqrt{p} - c$ tokens of each preceding row $v_{i-1}^{j}$ as the starting condition for $v_{i}^{j}$ . (iii) Decoding Tokens into Panorama: After $n$ rounds of expansion, the concatenated token sequence $V$ is converted into the panorama $x'$ through the image tokenizer decoder $f_{\mathcal{T}d}$ (Eq. (10)). + +![](images/0bdc0f605b4ca28ed5b0d9dfeeb897c589a4189c698c70ce986d72e2d639e935.jpg) +(ii) - Vertical + +![](images/5f66215b5305519194066bb6080c0629caef96ccf32e94d62d4b2b030492d7a7.jpg) + +![](images/c06b8142e93921521cbb4fd30d9b0dbcc40ae760de5e5b22d62c4097d7a11a98.jpg) +(iii) + +$\mathcal{I} = \mathbb{R}^{h\times w\times ch}$ , to enable panorama generation over an arbitrarily large space $\mathcal{I}' = \mathbb{R}^{h'\times w'\times ch}$ , where $h' > h$ and $w' > w$ . Specifically, the panorama $x' \in \mathcal{I}'$ is constructed by a series of spatial-ordered image crops $\mathcal{X} = \{x_i \mid x_i \in \mathcal{I}, i = 1,2,\dots,n\}$ , where each $x_i$ represents an individual image segment. + +PanoLlama defines a joint probability distribution to learn how these crops interrelate to form a panorama $x'$ : + +$$ +\begin{array}{l} P \left(x ^ {\prime}\right) = P \left(x _ {1}, x _ {2}, \dots , x _ {n}\right) \\ = \prod_ {i = 1} ^ {n} P \left(x _ {i} \mid x _ {1}, x _ {2}, \dots , x _ {i - 1}\right) \tag {1} \\ \end{array} +$$ + +where each $P(x_{i} \mid x_{1}, x_{2}, \ldots, x_{i-1})$ represents the conditional probability of generating the $i$ -th image crop given the preceding ones. This draws from the inspiration of next-token prediction in language modeling, creatively applied to generate a coherent crop series for panorama. + +Taking the logarithm of both sides of Eq. (1), we obtain our loss function: + +$$ +\begin{array}{l} \mathcal {L} (\theta) = - \log P \left(x ^ {\prime} \mid \theta\right) \\ = - \sum_ {i = 2} ^ {n} \log P \left(x _ {i} \mid x _ {1}, x _ {2}, \dots , x _ {i - 1}; \theta\right) \tag {2} \\ \end{array} +$$ + +Formally, the optimization task is: + +$$ +\begin{array}{l} \theta^ {*} = \arg \min _ {\theta} \mathcal {L} (\theta) \\ = \arg \min _ {\theta} - \sum_ {i = 2} ^ {n} \log P \left(x _ {i} \mid x _ {1}, x _ {2}, \dots , x _ {i - 1}; \theta\right) \tag {3} \\ \end{array} +$$ + +By leveraging a pre-trained autoregressive model as $\Phi$ , we can well estimate the $\theta^{*}$ that maximizes the likelihood of $x^{\prime}$ , leading to enhanced multi-coherence of the panorama data. + +# 3.2. Framework of PanoLlama + +However, as discussed in Sec. 1 and 2, existing VAR models are limited to generating images $x \in \mathcal{I}$ with the token constraint of $p$ . To address this, we develop a simple yet effective approach that extends next-token prediction within a single crop to next-crop prediction across crops, enabling image generation in a panoramic space $\mathcal{I}'$ . + +Given the model's property of arranging image tokens in a raster scan order, we treat each token sequence as a 2D block to achieve next-crop expansion in a row-wise, training-free manner. Distinct strategies are designed for both horizontal and vertical expansion, with the entire process recapped in Fig. 2 and Appendix A. + +Firstly, the textual prompt $y$ is encoded into an embedding $s$ using the text encoder function $f_{\mathcal{E}}$ : + +$$ +s = f _ {\varepsilon} (y) \tag {4} +$$ + +where $f_{\mathcal{E}}:\mathcal{V}\to \mathcal{E}$ maps the prompt space $\mathcal{V}$ to the textual embedding space $\mathcal{E}$ . + +With $s$ as a conditional prefilling, the token generator $f_{\mathcal{G}}$ autoregressively produces a sequence of $p$ image tokens, labeled as the first block: + +$$ +v _ {1} = f _ {\mathcal {G}} (s) = \left\{v _ {1, k} \mid k = 1, 2, \dots , p \right\} \tag {5} +$$ + +Vertical Expansion When the position index $k$ reaches the token limit $p$ for the first block, it is redirected to $p - r\sqrt{p}$ to start a new round, extending $r$ rows as $v_{2}$ . To ensure continuity and maximize token usage, we let $v_{2}$ begin with the condition of $v_{1,r\sqrt{p}}, \ldots, v_{1,p}$ , i.e., the last $p - r\sqrt{p}$ tokens of $v_{1}$ . The generation process then advances as follows: + +$$ +v _ {2} = f _ {\mathcal {G}} \left(v _ {1, r \sqrt {p}}, \dots , v _ {1, p}\right) = \left\{v _ {2, k} \mid k = 1, 2, \dots , r \sqrt {p} \right\} \tag {6} +$$ + +This redirection process is iteratively applied for $n$ times, resulting in a series of token sequences $\mathcal{V} = \{v_{i} \mid i = 2, \dots, n\}$ , with each $v_{i}$ corresponds to the image crop $x_{i}$ . Then the entire panorama is constructed by: + +$$ +\begin{array}{l} V = v _ {1} \oplus_ {i = 2} ^ {n} v _ {i} \\ = \left\{v _ {1, k} \mid k = 1, 2, \dots , p \right\} \tag {7} \\ \oplus \left\{v _ {i, k} \mid i = 2, \dots , n, k = 1, 2, \dots , r \sqrt {p} \right\} \\ \end{array} +$$ + +where $\oplus$ refers to the vertical concatenation operator. + +Horizontal Expansion Unlike vertical expansion, which naturally aligns with the original token arrangement, horizontal expansion disrupts this order. Thus, we propose an interleaved expansion method as an effective solution. + +Let $v_{i}^{j}$ denote the $j$ -th row in the $i$ -th block, $\epsilon(v_{i}^{j})$ denote the index of the end token in $v_{i}^{j}$ . In the horizontal case, each adjacent row $v_{i-1}^{j}$ and $v_{i}^{j}$ need to be connected with successive and cohesive conditions. Thus, we modify the redirection strategy Eq. (6) to let the last $\sqrt{p} - c$ tokens of each $v_{i-1}^{j}$ serves as the start condition for $v_{i}^{j}$ . In each iteration, the length of each row is extended by $c$ columns: + +$$ +\begin{array}{l} v _ {i} ^ {j} = f _ {\mathcal {G}} \left(v _ {i - 1, \epsilon \left(v _ {i - 1} ^ {j}\right) - \sqrt {p} + c}, \dots , v _ {i - 1, \epsilon \left(v _ {i - 1} ^ {j}\right)}\right) \tag {8} \\ = \left\{v _ {i, k} \mid j = 1, 2, \dots , \sqrt {p}, k = c (j - 1) + 1, \dots , c j \right\} \\ \end{array} +$$ + +Accordingly, Eq. (7) should be modified as: + +$$ +\begin{array}{l} V = v _ {1} \cup_ {i = 2} ^ {n} v _ {i} \\ = \left\{v _ {1, k} \mid k = 1, 2, \dots , p \right\} \tag {9} \\ \cup \left\{v _ {i, k} \mid i = 2, \dots , n, k = 1, 2, \dots , c \sqrt {p} \right\} \\ \end{array} +$$ + +and $\cup$ corresponds to the horizontal concatenation operator. + +After vertical / horizontal expansion, we convert $V$ into a panorama $x^{\prime}$ through the decoder of image tokenizer $f_{\mathcal{T}d}$ : + +$$ +x ^ {\prime} = f _ {\mathcal {T} d} (V) \tag {10} +$$ + +where $f_{\mathcal{T}d}:\mathcal{T}\to \mathcal{I}'$ maps tokens to the pixel space, and $\mathcal{T}$ denotes the discrete token set. + +# 3.3. PanoLlama vs. Existing FIG Methods + +As outlined in Sec. 2, current FIG methods fall into two branches: joint diffusion and inpainting. To provide a more in-depth comparison and analysis of PanoLlama against these methods, we unify their paradigms into the modeling form presented by Sec. 3.1. + +PanoLlama vs. Inpainting For the inpainting strategy, each crop $x_{i}$ acts as the masked part of the previous one, inferring content from it. The conditional dependency can be expressed as: + +$$ +P \left(x ^ {\prime}\right) = \prod_ {i = 2} ^ {n} P \left(x _ {i} \mid x _ {i - 1}\right) \tag {11} +$$ + +This can be viewed as a simplification of our paradigm in Eq. (1), considering features only from the left neighbor $x_{i-1}$ , whereas our approach accounts for all preceding crops $x_1, x_2, \ldots, x_{i-1}$ , facilitating better coherence. + +PanoLlama vs. Joint Diffusion The key to joint diffusion is devising an effective connection strategy between adjacent crops. This leads to the joint probability: + +$$ +P \left(x ^ {\prime}\right) = \prod_ {i = 2} ^ {n} P \left(x _ {i} \mid x _ {i - 1}, x _ {i + 1}\right) \tag {12} +$$ + +where each crop $x_{i}$ is generated based on its left and right neighbor. + +While existing joint diffusion methods have explored a range of connection strategies for this task, their heuristic and tailored designs face difficulties in achieving multicoherence holistically. In contrast, our approach leverages the autoregressive properties that inherently align with the FIG objective, forming an effective framework that surpasses these methods. + +# 4. Experiments + +We conduct a comprehensive evaluation of PanoLlama, comparing it with multiple baselines from both qualitative and quantitative perspectives. Since some baselines do not support vertical generation, the experiments discussed in Sec. 4.1 and 4.2 focus on the horizontal case. + +Figure 3. Qualitative comparisons between six baselines and ours. Our approach minimizes unnatural connections commonly found in existing methods, producing high-quality panoramas with significantly extended dimensions of $512 \times 5120$ . +![](images/d89663b1e70f5100cad01b61439206a1021e79b394cb2540352cdc3e861fec44.jpg) +"A photo capturing a serene landscape featuring a range of mountains reflected in the still waters of a clear lake, surrounded by lush greenery. People engaged in activities like kayaking and fishing, and colorful boats gently bobbing on the water. The sky is a soft blue, dotted with a few wispy clouds, adding to the peaceful ambiance of this natural setting." + +# 4.1. Comparison + +Evaluation Dataset To ensure a comprehensive and fair evaluation, we design the dataset with a focus on diversity and difficulty across content types. It contains 1,000 detailed long prompts for text-to-panorama generation, covering 25 main themes and $100+$ sub-themes, encompassing both photorealistic and artistic styles. See Appendix D for more construction details. + +Implementation Details Using all prompts in the dataset and 25 sets of random seeds, we generate 2,000 panoramas in total. Specifically, these panoramas are produced with an expansion stride of $u = \frac{3}{4}$ and dimensions of $h' = 512$ , $w' = 5120$ , 10x wider than the original $\Phi$ . + +Evaluation Metrics We apply nine quantitative metrics to evaluate our approach across four aspects: (i) coherence at crop connections, (ii) fidelity and diversity of generated panoramas, (iii) compatibility with input prompts, and (iv) + +efficiency of the inference process. Since the performance of PIG methods is closely tied to their reference model $\Phi$ , we also measure $\Phi$ ’s performance on (ii) and (iii) as a reference score ((i) and (iv) are panorama-specific and cannot be evaluated for $\Phi$ ), a common practice in related studies [3, 17, 46]. The score gap between the PIG method and its corresponding $\Phi$ reflects the degradation (or improvement) introduced during panorama expansion. + +- Coherence: We use LPIPS [44] and DISTS [10] to capture perceptual differences of high-level features; SSIM [39] and TV [26] to measure pixel differences for low-level features. The first three metrics are calculated between pairs of adjacent but non-overlapping crops, and the TV score is computed along the connection between crops. +- Fidelity & Diversity: FID [12] and IS [27] describe both fidelity and variety of the results. We randomly take one crop of each panorama in a size aligned with $\Phi$ , forming a generated image set $\mathcal{D}_x$ . We correspondingly construct + +Table 1. Quantitative comparison of PanoLlama with multiple baselines. The best, second-best, and relative scores are marked in bold, underlined, and parentheses. Our method achieves the best overall performance, excelling in coherence, fidelity, and aesthetics. + +
CoherenceFidelity & DiversityCompatibilityEfficiency
LPIPS↓DISTS↓TV↓SSIM↑FID↓IS↑CLIP↑CLIP-aesthetic↑time↓
SD----36.147.4933.036.74-
LlamaGen----37.826.4331.626.74-
BLD0.8290.3690.0830.00889.51 (+53.37)5.81 (-1.68)32.29 (-0.74)5.76 (-0.98)10670.35s
MD0.6940.2690.0610.18439.30 (+3.16)6.36 (-1.13)33.19 (+0.16)6.84 (+0.10)1808.95s
TD0.6510.2390.0590.26142.10 (+5.96)6.22 (-1.27)33.78 (+0.75)6.88 (+0.14)2045.79s
SyncD0.5820.2310.0580.26344.89 (+8.75)6.13 (-1.36)33.21 (+0.18)6.94 (+0.20)7232.70s
MAD0.5200.2090.0400.26859.23 (+23.09)4.99 (-2.50)31.30 (-1.73)6.90 (+0.16)1923.99s
SMD0.6370.2230.0550.25789.64 (+53.50)6.45 (-1.04)30.95 (-2.08)6.75 (+0.01)241.06s
Ours0.4100.1960.0210.30540.09 (+2.27)5.97 (-0.46)31.56 (-0.06)6.97 (+0.23)726.33s
+ +two reference sets $\mathcal{D}_{\Phi}^{1}$ and $\mathcal{D}_{\Phi}^{2}$ , each with an equal number of images generated by the reference model $\Phi$ . For FIG methods, IS is computed on $\mathcal{D}_x$ , and FID compares distributions of $\mathcal{D}_x$ with $\mathcal{D}_{\Phi}^{2}$ . For $\Phi$ models, IS is measured on $\mathcal{D}_{\Phi}^{1}$ , and FID compares $\mathcal{D}_{\Phi}^{1}$ with $\mathcal{D}_{\Phi}^{2}$ . + +- Compatibility: CLIP [23] assesses the compatibility between input prompts and generated images, while CLIP-aesthetic [28] reflects the overall aesthetic quality. We also use the aforementioned image sets $\mathcal{D}_x$ and $\mathcal{D}_{\Phi}^{1}$ to calculate these scores. +- Efficiency: We measure the model's runtime speed by the inference time taken to generate a batch of 50 pancreas on an A100 GPU. + +Baselines and Reference Models We compare our PanoLlama with six recent methods: Blended Latent Diffusion (BLD) [1], MultiDiffusion (MD) [3], TwinDiffusion (TD) [46], SyncDiffusion (SyncD) [17], Merge-AttendDiffuse (MAD) [22], and StreamMultiDiffusion (SMD) [16], using default optimal parameters for each, where $u$ is typically $\frac{1}{4}$ . As for the reference model $\Phi$ , we take the widely used VAR architecture LlamaGen [31], while other baselines utilize Stable Diffusion (SD) [24]. More comparisons with its variants, such as Stable Diffusion XL (SDXL) [21], are provided in Appendix C. + +Qualitative Results As shown in Fig. 3, BLD exhibits artificial seams and repetitive segments during its extrapolation process. As the basic joint diffusion method, MD also suffers from abrupt transitions between crops. While TD and SyncD improve on this, they still show unnatural junctions and layouts. MAD achieves seamless results, but with excessive content repetition and blurred textural details. SMD obtains smoother transitions at the cost of simplifying image content, which results in a loss of features and unstable performance. In contrast, our method con + +sistently generates high-quality panoramas even at $10\mathrm{x}$ extended dimensions of the original $\Phi$ , preserving diversity and detail while demonstrating significantly higher coherence. See Appendix B for additional qualitative results. + +Quantitative Results Tab. 1 reports the mean scores for each metric, with the best in bold and the second-best underlined. The first two rows present results for the reference models, followed by the baselines and our method. As previously mentioned, aspects (i) and (iv) consider absolute scores, while (ii) and (iii) compare relative scores against the reference model, as labeled in parentheses. PanoLlama outperforms baselines in almost all aspects. Coherence, the key factor in panoramic images, is greatly enhanced by our method. Compared to the best baseline MAD, we achieve improvements of $21.15\%$ in LPIPS, $6.22\%$ in DISTS, $47.50\%$ in TV, and $13.81\%$ in SSIM. An improvement in the CLIP-aesthetic metric is also observed, indicating that the enhanced coherence contributes to better aesthetic quality. As for fidelity and diversity, PanoLlama also achieves the best results, demonstrating that our next-crop prediction strategy introduces less relative loss during the panoramic expansion process. Regarding efficiency, except for the real-time generation method SMD, our generation speed is $3x - 10x$ faster than other FIG frameworks. + +# 4.2. Ablation + +Our ablation studies further investigate the key factors of PanoLlama's performance, demonstrating its advantages in robustness, adaptability, etc. + +As coherence is the most critical attribute for panoramas, we select LPIPS, DISTS, TV, and SSIM metrics for our ablation analysis, constructing a coherence score (COH) based on their weighted sum. Specifically, we replace SSIM with 1-SSIM to ensure monotonicity and normalize all scores to the same range before weighting. + +Expansion Stride As described in Sec. 3.2, each horizontal iteration expands the 2D token block by $c$ columns, creating an overlapping region of $\sqrt{p} - c$ columns between $x_{i-1}$ and $x_i$ . This yields an expansion stride of $u = \frac{c}{\sqrt{p}}$ , which controls the balance between quality and efficiency. Higher coherence comes with a smaller $u$ , but at the cost of longer generation time. To investigate the effectiveness of our approach in improving this trade-off, we record the COH score and generation time under $u = 1, \frac{3}{4}, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ , and plot the quality-efficiency curves for different methods. + +As seen in Fig. 4a, at the same value of $u$ , our method's runtime is comparable to other training-free baselines (MD, TD, MAD). However, as $u$ increases, the performance of other baselines degrades significantly, while our method maintains a consistently low COH score, demonstrating superior robustness and insensitivity to the expansion degree. This results in a superior quality-efficiency balance, with additional visual support presented in Fig. 4b. + +![](images/ca033faefe79fcd1ca8f9a600f48ed5f2756fb26017c4021fc65c7d0916979c2.jpg) + +![](images/643c30cc8ca233d84b0e6255dda3d1a2bd6f2429a81945cdb05b472c2ebb7fc7.jpg) +(a) Quality-efficiency curves for different methods, with markers corresponding to $u = 1, \frac{3}{4}, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ from left to right. PanoLlama achieves the optimal quality-efficiency trade-off, with less generation time and consistently low COH score. +Figure 4. The quantitative and qualitative results demonstrate our method's high robustness to the expansion stride $u$ , leading to a better quality-efficiency trade-off. + +![](images/09b0db64f120764477c220fbef084d2c82b0d2e733d225572c8a1f24154c171b.jpg) +(b) Visual support for the quantitative results. As $u$ increases, our method (left) shows minimal quality degradation, while seams in the baseline (right) become increasingly noticeable. + +Panorama Size Generating larger panoramas inherently increases the number of crop connections, making it more challenging to maintain coherence. We test five different sizes of $w' = 1024, 2048, 3072, 4096, 5120$ , corresponding to $2\mathrm{x}, 4\mathrm{x}, 6\mathrm{x}, 8\mathrm{x}$ , and $10\mathrm{x}$ the resolution of $\Phi$ , to ex + +![](images/4fd6308e84285e3edbc5c4ad86f18858e9dfe64cd89afa3a1323b1a28d4b3ced.jpg) +Figure 5. Ablation studies on different panorama sizes $w'$ . While other PIG methods degrade as $w'$ increases, our PanoLlama maintains stable coherence, effectively handling larger panoramas. + +amine PanoLlama's capability in maintaining coherence as panorama length increases. + +As shown in Fig. 5, except for BLD, other methods exhibit comparable performance when the size is doubled on $\Phi$ (i.e., $w' = 1024$ ). However, as $w'$ scales up, other PIG methods become less satisfactory, while our PanoLlama remains stable, effectively reducing the increased potential for incoherence in larger panoramicas. + +![](images/e8cddba958610d14e071fe8b5ab17aa4c1cd95aa42d42b87b89f636fb02e4f25.jpg) +Figure 6. Exploration on a wide range of prompt themes. Our method outperforms MAD and SyncD overall, excelling in grand scenes but facing challenges in complex, dense scenes. + +Prompt Theme We test each of the 25 main themes in our dataset, generating 80 prompts per theme, to explore which prompt content types pose the greatest challenge for panorama generation. + +To streamline, Fig. 6 only displays comparison results with two best-performing baselines, MAD and SyncD. Our method achieves a better overall COH score, exhibiting greater adaptability to prompt contents. Specifically, it often performs well in grand scenes with large, uniform color areas (e.g., 'seascape', 'grassland', 'weather'), but is weaker in complex, dense scenes (e.g., 'crowd', 'pattern'). + +# 4.3. Applications + +Beyond basic panorama generation, we implement a range of applications that other PIG methods cannot achieve, with implementation details provided in Appendix E. + +![](images/dbfcbdbc12d0d2cff3d00f437d692cc47e0c749794bb42eea5931e88c41180c6.jpg) +(i) Multi-Scale Expansion + +![](images/b22775c3f197e2e3b0c3b0fb0428bb7067628e6856619584e6f093ee8580b416.jpg) +(ii) Mask-Free Layout Control + +![](images/2a257ba5bfc831515666ae801929f14026821f9f8e8f581a35a0fb2765a6ae11.jpg) +(iii) Multi-Guidance Generation +Figure 7. PanoLlama enables versatile applications that other FIG methods cannot achieve, including multi-scale expansion, mask-free layout control, and multi-guidance generation. + +Multi-Scale Expansion We support expansion in horizontal, vertical, and both directions. Fig. 7 shows the multiscale results, with sizes of $3072 \times 512$ and $3072 \times 3072$ . + +Mask-Free Layout Control Our method allows for flexible adjustments in rows $(r)$ , columns $(c)$ , and prompts $(y)$ , enabling mask-free layout control. As demonstrated in Fig. 7, PanoLlama effectively blends different token regions guided by different prompts into a cohesive, storytelling panorama. + +Multi-Guidance Generation Besides text-guided generation, our framework also accommodates image guidance and mixed guidance. Input images are tokenized by the encoder of image tokenizer $f_{\mathcal{T}e}$ , which then serves as the condition for generation. Fig. 7 illustrates two examples where the text and image collaboratively guide the generation process, resulting in an effect similar to image inpainting. + +# 5. Conclusion + +Multilevel coherence is one of the major pending challenges in panoramic image generation. In this paper, we introduce PanoLlama as a novel solution, which has several key advantages over the existing methods: (i) We introduce the + +next-token prediction paradigm to SIG, offering a better alignment with the core characteristics of multilevel coherence. (ii) We use token redirection to develop a training-free next-crop prediction method, achieving endless SIG upon fixed-size VAR models, with comprehensive experiments demonstrating its SOTA performance in coherence, fidelity, aesthetics, and more. (iii) We support additional applications that other SIG approaches do not achieve. (iv) We establish a new dataset and evaluation benchmark for standardized SIG research. + +Limitations Due to the fixed token capacity of pre-trained VAR models, we approximate global dependencies by leveraging a partial set of preceding tokens, balancing context range with architectural constraints. 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Although existing methods have shown remarkable performance across various benchmarks, they are predominantly reliant on accurate pose information. In real-world scenarios, the acquisition of precise pose often requires additional computational resources and is highly susceptible to noise. These limitations hinder the broad applicability and practicality of such methods. In this paper, we present PanoSplatt3R, an unposed wide-baseline panorama reconstruction method. We extend and adapt the foundational reconstruction pretrainings from the perspective domain to the panoramic domain, thus enabling powerful generalization capabilities. To ensure a seamless and efficient domain-transfer process, we introduce RoPE rolling that spans rolled coordinates in rotary positional embeddings across different attention heads, maintaining a minimal modification to RoPE's mechanism, while modeling the horizontal periodicity of panorama images. Comprehensive experiments demonstrate that PanoSplatt3R, even in the absence of pose information, significantly outperforms current state-of-the-art methods. This superiority is evident in both the generation of high-quality novel views and the accuracy of depth estimation, thereby showcasing its great potential for practical applications. Project page: https://npucvr.github.io/PanoSplatt3R + +# 1. Introduction + +Panorama images capture $360^{\circ}$ scene information from a single viewpoint, providing immersive visuals that can recreate the surrounding environment in full detail. This + +capability has found wide applications across various domains. In Virtual Reality (VR) [3, 16], Augmented Reality (AR) [34] and real estate [45], panorama images enhance user experiences by offering a more natural and engaging interaction with digital environments, enabling users to explore spaces remotely or in immersive settings. In autonomous driving and robotics [30], panorama images contribute to situational awareness, allowing systems to navigate complex environments with a broader context. These popular applications highlight the need for methods capable of accurately reconstructing entire 3D structures from panorama images while delivering photorealistic synthesis that allows users to freely explore and interact with the scene. Given a pair of panorama images, generalized panorama reconstruction methods [8, 10, 72] offer efficient and scalable solutions to this challenge. + +Existing methods address the challenge of reconstructing scene geometry and synthesizing novel views from two-view wide-baseline panorama images by constructing specialized cost volumes for panoramic data to estimate $360^{\circ}$ depth maps. However, these approaches have two significant limitations. First, they require camera pose information as input, which not only demands additional computational resources but also introduces vulnerability to noise in real-world scenarios. Second, depth estimation from panoramic cost volumes constitutes a domain-specific problem, creating substantial barriers to the effective transfer of established knowledge from the perspective domain. For practical applications, there is a clear need for an unposed general method that demonstrates robust generalization capability across diverse scenarios. + +Utilizing more than 8 million training samples, foundational stereo models in the perspective domain significantly advanced stereo matching, optical flow [63], depth estimation, pose regression [61], visual localization and 3D reconstruction [32]. Given the broader knowledge base established in the perspective imagery, transfer learning from perspective to panoramic domains offers a promising approach to enhance model generalization abilities. Existing methods typically employ teacher-student frameworks + +that require frequent projection transformations between domains, which not only lacks efficiency but also continues to depend heavily on limited panoramic data. A fundamental challenge remains in how to effectively transfer general knowledge to this specialized domain. Development of a seamless and efficient knowledge transfer procedure would significantly advance this field, enabling more robust performance across diverse panoramic scenarios without the computational overhead of current approaches. + +In this paper, we propose PanoSplatt3R, a novel approach for unposed wide-baseline panorama reconstruction. Our network adopts a vision transformer backbone and is trained to represent geometric structures from two viewpoints in a unified coordinate system, eliminating the need for camera poses [62]. By leveraging a pretrained foundational model from the perspective domain, we transfer its strong generalization ability to work with panoramic data. Additionally, our framework incorporates specialized modeling to capture the geometric periodicity of panorama images. Enhanced with Gaussian Splatting for rendering, PanoSplatt3R faithfully reconstructs the 3D scene and generates photorealistic novel views. + +We summarize our contributions as follows: + +- We introduce PanoSplatt3R, a novel unposed method for two-view wide-baseline panorama scene reconstruction and novel view synthesis, providing Gaussian Splatting based photorealistic renderings at novel viewpoints. +- We adapt a foundational stereo model for panorama images and demonstrate that general knowledge from the perspective domain can be effectively transferred to the panoramic domain, significantly improving wide-baseline panorama reconstruction. +- We propose RoPE rolling, a specialized variant of rotary positional embedding for panorama images, capturing geometric periodicity with minimal modifications to ensure seamless domain transfer. +- Extensive experiments show that PanoSplatt3R significantly outperforms state-of-the-art pose-dependent methods in both novel view synthesis quality and depth accuracy—even without known camera poses. + +# 2. Related Work + +# 2.1. Novel View Synthesis + +Novel View Synthesis (NVS) aims to generate visual representations of a scene from new viewpoints, given a set of known observations as input. This task typically involves either implicit scene reconstruction, such as Neural Radiance Fields (NeRF) [20, 42], or explicit reconstruction methods, such as 3D Gaussian Splatting (3DGS) [28, 40]. + +Optimization-based NVS methods achieve high fidelity reconstruction through gradient-based scene fitting but are often computationally intensive. In contrast, generalized + +NVS methods are designed to operate with fewer input views and follow a feed-forward approach, enabling faster inference and better scalability to diverse scenes. + +Generalized Neural View Synthesis methods learn scene priors from diverse multi-view data, enabling robust 3D scene reconstruction. These methods can either implicitly infer 3D geometry (e.g., pixelNeRF [68]) or explicitly express it using techniques like 3D Gaussian splats (e.g., pixelSplat [4], MVSplat [7]). + +While explicit NVS methods benefit from better geometry estimation, this often becomes challenging in sparse-view scenarios, such as those involving only two images. In such cases, Dust3R [61] addresses these challenges by predicting two point maps in a shared coordinate frame, which not only enhances geometry estimation but also encodes camera intrinsics and relative pose information. Leveraging a diverse training dataset, Dust3R demonstrates strong generalization capabilities, enabling high-quality 3D scene reconstruction and improving 3D consistency in video generation tasks [33, 70]. + +Dust3R's advanced spatial understanding has been especially beneficial for generalized 3D Gaussian reconstruction, applying both at the object level [5, 65] and the scene level [6, 17, 27, 43, 50, 67]. Its impact also extends to scene understanding [18] and SLAM [36], highlighting its versatility across various 3D vision applications. + +To address challenges in processing longer sequences, several adaptations of the Dust3R architecture have been proposed [9, 55, 58, 66]. Furthermore, the pre-trained Dust3R model has shown effectiveness in dynamic scene reconstruction, as demonstrated in works like [26, 39, 60, 74]. + +# 2.2. 3D Reconstruction from Panoramic Images + +Panorama images present unique challenges compared to standard perspective images due to their equirectangular projection. This projection creates a horizontal loop and encodes varying ray densities across rows, complicating feature extraction and holistic scene understanding. These distinctive properties necessitate specialized approaches to effectively process and analyze panoramic data. + +To address these challenges, several approaches adopting convolutional networks introduce distortion-aware convolutions to expand the horizontal receptive field and mitigate projection-induced distortions [11, 12, 14, 56, 75, 76]. For transformer-based networks, solutions include deformable patch embeddings [73], spherical token localization models [49], and attention mechanisms incorporating spherical distance biases [71]. + +An alternative strategy involves projecting panorama images into multiple perspective images [15]. Common techniques include tangent projection [2, 44, 47] and cubemap projection [25, 57]. Since most models are pre-trained on perspective images, it enables better generalization while + +![](images/3777659b5cadf7f58fb89487aabf6d8d6caf78f4a99e08e0c0904a9a8737ede2.jpg) +Figure 1. Overview of our proposed PanoSplatt3R. Given two panorama images as input and without knowing their relative pose, our model reconstructs the entire 3D scene using Gaussian Splats. The estimated geometry can provide photorealistic renderings at novel view points. We removed two walls from the final reconstruction to better display the room. + +producing feature representations that are more compatible with standard networks. After feature extractions or direct applications of pre-trained models, the features of projected perspective images are fused back to the panoramic ones. + +Other methods capture the intrinsic properties of panorama images through tailored representations. For instance, some approaches adopt column-wise [53] or panellike structures [69], some introduce spherical 3D point features to better model the geometry of panoramic scenes [1]. + +Further advancements have been made for sparse panorama inputs, particularly with two wide-baseline panorama inputs. These methods typically construct a cost volume by using the extracted features and corresponding poses. PanoGRF [8] aggregates geometry from predicted depths and appearance features from the given panoramas to build the cost volume, but its computational cost is prohibitively high. Other methods enhance image quality by incorporating cube map images and depth features [10], or focus on high-resolution inputs and efficient training and rendering [72]. + +Panorama reconstruction methods can be broadly categorized into two main streams: varied wide baseline and fixed baseline. In the first setting, input panoramas are captured from arbitrary poses, introducing significant geometric variations and making the reconstruction process more challenging. In contrast, fixed-baseline methods [72] assume that the principal points of the input panoramas are aligned, and the goal is to synthesize an intermediate view. These methods inherently benefit from a predefined spatial relationship between views. A direct comparison would be unfair, as fixed-baseline methods operate within a controlled setup, but methods that handles varied wide baseline are more flexible in real-world applications. Our approach not only can handle varied-baseline inputs, but also eliminates the need for precise pose input, extending the application scenario of stereo panorama reconstruction. + +# 3. Method + +# 3.1. Overview + +Given two wide-baseline panoramic images $I_{1}$ and $I_{2}$ , our goal is to densely reconstruct the scene using Gaussian Splatting. The model makes pixel-wise Gaussian parameter predictions $G_{1}$ and $G_{2}$ , where each point is parameterized by $\{\pmb{x}_i, \alpha_i, \pmb{r}_i, \pmb{s}_i, \pmb{c}_i\}_{i=1,\dots,2\times H\times W}$ ; specifically, the center location $\pmb{x} \in \mathbb{R}^3$ , opacity $\alpha \in \mathbb{R}$ , rotation $\pmb{r} \in \mathrm{SO}(3)$ , scaling $s \in \mathbb{R}^3$ (For 2DGS [24], scaling $s \in \mathbb{R}^2$ ) and color $c$ expressed with spherical harmonics. + +An overview of our model is illustrated in Figure 1. Our model adopts a vision transformer backbone. Two panorama images $I_{1}$ and $I_{2}$ are first tokenized and feed into a shared encoder. Then the image features $F_{1}$ and $F_{2}$ from two branches attend each other in the decoder, which is composed of cross-attention blocks. Finally, the Gaussian parameters are predicted for each viewpoint. + +Reconstructing a scene from stereo panoramic images presents unique challenges. The remarkable generalization ability of foundational stereo models [32, 61] does not directly apply to panoramic images, because they are predominantly trained on perspective data, leaving them ill-equipped to handle the inherent distortions and structural differences of panoramic inputs. Adaptation strategies are needed to bridge this domain gap and enable foundational stereo model to operate on panoramic inputs. + +In the following sections, we first detail our approach, explaining how we achieve an unposed reconstruction in Section 3.2. Then we outline the key modifications that allow the model to overcome the challenges posed by panoramic imagery in Sec. 3.3. Next, we introduce a Gaussian parameter prediction head to enhance the visual realism of the reconstructions, as outlined in Sec. 3.4. A progressive training strategy is introduced in Sec. 3.5, to ensure optimal performance in the panoramic context. + +# 3.2. Unposed Stereo Panorama Reconstruction + +While previous methods [8, 10, 72] tackle stereo panorama reconstruction by building cost volumes and finding correspondences, they rely on accurately known camera poses. However, in real-world scenarios, wide-baseline panoramic images are often captured without precise relative pose information, making these pipelines impractical. Moreover, estimating camera pose from two wide-baseline panoramic images is a challenging task. As a result, pose-dependent methods struggle when given inaccurate pose estimates, leading to degraded reconstruction quality. + +Inspired by recent foundational stereo models [32, 61], we design our method to operate without requiring known camera poses. Our approach consists of three key components: (1) a shared ViT encoder that extracts features from both input images $I_{1}$ and $I_{2}$ , (2) a transformer decoder that performs cross-attention between the encoded features $F_{1}$ and $F_{2}$ , and (3) a Gaussian parameter prediction head that estimates the scene geometry. The model learns to establish correspondences between views through cross-attention and represents geometry in a unified coordinate system. Unlike cost volume-based methods, this approach removes the reliance on pose input, enabling wide-baseline panorama reconstruction without requiring known camera poses. + +We build our backbone network upon the architecture of Dust3R [61]. However, the original model fails to account for the horizontal periodicity of panoramic images, resulting in inconsistencies at the left and right boundaries. To overcome this limitation, we incorporate targeted enhancements, which we describe in detail in the next section. + +# 3.3. Adapting Perspective Models for Panorama + +Positional embeddings enable vision transformers to sense the location of tokens, which is vital for precisely understanding 3D scenes. We start from a brief review of positional embeddings. Currently, absolute positional embeddings are widely adopted in popular models [13, 37], recent efforts to introduce relative positional embeddings have shown superior performance and greater flexibility [23, 41]. Rotary Positional Embedding (RoPE) [52] has been shown to be advantageous over absolute positional embeddings in tasks that rely on two-view correspondences [63], and is adopted in our backbone model [32]. + +As a relative positional embedding technique, RoPE applies a series of rotations at different frequencies to deep features, ensuring that the attention result after query and key transformations depends only on their relative spatial positions. When extending RoPE to 2D images, the feature vector is split into two halves: one undergoes rotation based on the $x$ -axis position, while the other is rotated according to the $y$ -axis position. For example, for a token located at $(p_n^x, p_n^y)$ , the rotation matrices for feature dimension $t$ are: + +![](images/994bc4f3ec042e06b7ac306862c6a09b6585d296fdbc5e9f0c77547d068d3234.jpg) +Figure 2. Visual illustration of RoPE rolling. Multiple attention heads mark the location of A, B and C using different 'RoPE's to avoid always distancing A and C in positional embeddings. + +$$ +\mathbf {R} (n, 2 t) = e ^ {i \theta_ {t} p _ {n} ^ {x}}, \quad \mathbf {R} (n, 2 t + 1) = e ^ {i \theta_ {t} p _ {n} ^ {y}}. \qquad (1) +$$ + +In vision transformers, the rotation frequencies are typically set as $\theta_t = 100^{-t / (d_{head} / 4)}$ , for an attention head with $d_{head}$ channels. Using pixel locations allows RoPE to effectively capture spatial relationships in perspective images. + +However, when applied to panorama images, this approach encounters fundamental challenges. Since panoramic images form a continuous horizontal loop, the left and right edges of the image are adjacent in the physical scene but are assigned the maximum possible horizontal separation in RoPE's embedding space. A straightforward approach might be to set the largest rotation angle in RoPE to $2\pi$ to enforce periodicity. However, this does not resolve the issue, as the frequency $\theta_{t}$ decreases with increasing feature dimension $t$ . Intuitively, this means higher-dimensional features undergo slower rotations. Consequently, even if we increase $\theta_{t}$ by $2\pi$ , only a small subset of feature dimensions would complete a full circular rotation, making it ineffective in modeling the continuous nature of panoramic images. + +To address this, we propose a simple yet effective solution called RoPE rolling. While a single RoPE application inherently follows a one-directional measurement without looping, it can be extended across multiple attention heads with varying offsets. For the $m^{\text{th}}$ attention head, we apply a horizontal roll to the $x$ -coordinate by an offset of $Wm / M$ , where $W$ is the feature map width and $M$ is the total number of attention heads. The resulting pixel location for the rotation matrices is formulated in Equation 2. + +$$ +p _ {n} ^ {x} \leftarrow \left(p _ {n} ^ {x} + W m / M\right) \mod W. \tag {2} +$$ + +We apply RoPE rolling in both the encoder and decoder. Figure 2 provides an intuitive illustration of this mechanism. This strategy minimally alters the original RoPE mechanism, preserving its compatibility with transfer learning while effectively modeling the periodic structure of panoramic images. + +# 3.4. Gaussian Parameter Prediction + +We use the DPT head [46] to predict the Gaussian parameters $G_{1,2}$ for each view. Each view uses two DPT heads. The first one takes features from the transformer decoder and predicts the Gaussian center location $x$ . The second head predicts remaining Gaussian parameters, utilizing features from the ViT decoder and the RGB image. The RGB image serves as a shortcut to directly incorporate texture information, which is essential for capturing fine details in 3D reconstruction [67]. + +Since our model learns to predict the geometric structures in a common coordinate system, we fuse $G_{1}$ and $G_{2}$ by direct concatenation, then Gaussian rasterization kernels can render them at an arbitrary novel view. + +# 3.5. Model Training + +We employ a progressive training strategy where the model first learns to predict Gaussian centers before optimizing other Gaussian parameters with photometric loss. This staged optimization stabilizes training and improves convergence. During the first stage, we exclude the Gaussian parameter head responsible for predicting the remaining Gaussian parameters, focusing solely on learning accurate Gaussian centers. These centers $\hat{\pmb{x}}_i$ are supervised using ground truth 3D points $\pmb{x}_i$ obtained from depth projection. The loss for a valid pixel is formulated as the combination of $L_{1}$ and $L_{2}$ loss: + +$$ +\mathcal {L} _ {\text {s t a g e 1}} = \sum_ {i = 1} ^ {2 \times H \times W} \left(\frac {1}{2} \| \boldsymbol {x} _ {i} - \hat {\boldsymbol {x}} _ {i} \| + \frac {1}{2} \| \boldsymbol {x} _ {i} - \hat {\boldsymbol {x}} _ {i} \| ^ {2}\right). \tag {3} +$$ + +To supervise the model to express points of $I_{2}$ in the coordinate of $I_{1}$ , we project the points in $I_{2}$ to 3D using its ground truth depth $D_{2}$ , then transform these points to $I_{1}$ 's coordinate using the relative pose between them. + +In the second stage, we supervise all Gaussian parameters at a novel view. To provide holistic supervision of the entire reconstructed scene, we use the cubemap projection to capture the surrounding scene of a viewpoint. Specifically, we render 6 images with $90^{\circ}$ field of view (FOV) at the same position but faces 6 different directions. Utilizing the rendered image $\hat{I}$ and depth $\hat{D}$ , the full model is trained under both image and depth losses. For image supervision, we use the mean squared error (MSE) and LPIPS loss, with weights of 1.0 and 0.05, respectively. For depth supervision, we use $L_{2}$ loss with a weight of 0.08. + +$$ +\begin{array}{l} \mathcal {L} _ {\text {s t a g e 2}} = \sum_ {j = 1} ^ {6} \left[ \left\| I _ {j} - \hat {I} _ {j} \right\| _ {2} + 0. 0 8 \left\| D _ {j} - \hat {D} _ {j} \right\| _ {2} \right. \\ \left. + 0. 0 5 \cdot \operatorname {L P I P S} \left(I _ {j}, \hat {I} _ {j}\right) \right], \tag {4} \\ \end{array} +$$ + +where $I_{j}$ and $D_{j}$ are the ground truth image and depth for the $j^{\mathrm{th}}$ cube map view at a novel viewpoint. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. To compare with existing methods, we evaluate PanoSplatt3R on two synthetic datasets: HM3D [45] and Replica [51]. We follow the data split of Splatter-360 [10] to render panoramic videos with AI-Habitat simulation tool [48] by sampling random trajectories, and train on HM3D. All panoramic images are at a resolution of $512 \times 1024$ . Since the data preparation process involves random sampling, reported metrics are not identical as in previous works [10], but are still highly consistent with them. + +Comparing Methods. We adhere to the evaluation protocol established in Splatter-360 and present performance comparisons with wide-baseline panorama reconstruction methods including Splatter-360 [10] and PanoGRF [8], along with perspective methods that takes cubemap images, including HiSplat [54], MVSplat [7] and DepthSplat [64]. + +Evaluation Metrics. We evaluate the quality of novel view synthesis using PSNR, SSIM, and LPIPS. Additionally, we compare the rendered depth map errors to assess the accuracy of 3D reconstruction, including absolute relative error (AbsRel), root mean squared error (RMSE) and accuracy under threshold $\delta_{1}(\delta < 1.25)$ . + +Scale Recovery. While we supervise the model using data in metric units, recovering metric geometry from two viewpoints with an unknown baseline distance remains an ill-posed problem. This results in misalignment between the ground truth view and the estimation view rendered with a metric pose. + +To address this, we adopt a straightforward strategy by applying a uniform scaling to the model's estimated geometry. Specifically, we begin by estimating the relative pose of the second input view and solve a Perspective-n-Point (PnP) [31] problem. Since the geometry of the second viewpoint is expressed in the coordinate frame of the first viewpoint, we directly construct the 3D-2D correspondences using the point map of the second view and its 2D image coordinates. Once the relative pose, denoted as $\hat{\mathbf{P}}_2 = [\hat{\mathbf{R}} | \hat{\boldsymbol{t}}]$ , is obtained, we compute a scaling factor $\lambda$ based on the ratio of the norms of the translation vectors: $\lambda = |\boldsymbol{t}| / |\hat{\boldsymbol{t}}|$ , where $\boldsymbol{t}$ is the translation from the ground truth pose and $\hat{\boldsymbol{t}}$ is the estimated translation. + +We apply the scaling to both the location and scale of the 3D Gaussians: $\boldsymbol{x} \gets \lambda \boldsymbol{x}, \quad \boldsymbol{s} \gets \lambda \boldsymbol{s}$ . Please note that this process only scales the reconstruction up to a global factor, and does not affect the quality of the reconstruction; rather, it is applied to eliminate scale ambiguity, allowing the photometric indicators to more accurately reflect the true reconstruction quality. + +Table 1. Quantitative comparisons on wide-baseline panorama reconstructions. We compare our model with methods that require accurate known pose, including those with cube map inputs and panorama inputs. Our model, even in the absence of camera pose, presents the best performance in both novel view synthesis quality and depth estimation accuracy. Models with $\dagger$ are trained on HM3D by [10]. + +
Problem SettingMethodHM3DReplica
PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑
posed perspectiveHiSplat [54]17.3580.6200.4860.6780.90729.99017.1570.6420.4170.7401.02525.824
MVSplat [7]18.0150.6270.5111.1861.36724.88418.0050.6310.5121.4231.79821.229
DepthSplat [64]18.4870.6520.4560.5700.69337.79119.3690.7320.3340.3730.55050.364
posed 360°PanoGRF[8]25.8630.8100.3040.1950.30885.16827.9200.8920.1710.1280.25888.057
MVSplat†[7]27.2270.8520.1750.0940.27090.50528.3990.9080.1150.0880.24789.913
Splatter-360 [10]28.3080.8750.1540.0780.22493.62729.8880.9240.0970.0630.19794.572
unposed 360°PanoSplatt3R28.9380.8690.1470.0440.14797.65431.5220.9350.0820.0340.12698.115
+ +Table 2. Relative pose estimation comparison. Results are measured on the Replica dataset and metrics are averaged. + +
MethodRRARTA
SIFT+8PA20.53°14.07°
Ours+PnP0.541°0.584°
Ours+8PA0.477°0.239°
+ +Table 3. Quantitative comparisons on unposed pipelines. We use SIFT to get point matches and use the 8-points algorithm (8PA) to estimate the relative pose, then apply posed methods with it. Current methods are vulnerable towards pose inaccuracy. Our model does not require pose input, performs significantly better. + +
MethodHM3DReplica
PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑
8PA+PanoGRF [8]18.5220.6600.4880.3960.65854.96817.7330.6990.4300.3170.65354.422
8PA+MVSplat† [7]16.3860.5810.5120.4290.83140.74714.3460.6070.4650.4540.94231.534
8PA+Splatter-360 [10]14.7650.5370.4960.4480.85840.22512.9160.5700.4630.4360.92034.223
PanoSplatt3R28.9380.8690.1470.0440.14797.65431.5220.9350.0820.0340.12698.115
+ +# 4.2. Implementation Details + +PanoSplatt3R is implemented in Pytorch, with a 2DGS [24] renderer implemented in CUDA. We initialize our model using pre-trained weights of Mast3R [32]. We train the model with 50k steps in stage 1 and 100k steps in stage 2. To improve efficiency and reduce GPU memory usage, we replace the original attention mechanism with xFormers' memory-efficient attention [29] and utilize auto mixed precision training. Experiments are conducted on 8 NVIDIA L40 48G GPUs. + +# 4.3. Experimental Results + +We present performance comparisons in Table 1. As an unposed approach, PanoSplatt3R significantly outperforms existing pose-dependent methods in both novel view synthesis quality and depth accuracy. Visualization results in Figure 3 further highlight its effectiveness, showcasing photorealistic novel views and highly accurate 3D structures. Please find more visualization results in the supplementary. + +# 4.4. Further discussions + +# 4.4.1. Applying posed methods to the unposed setting. + +Current wide-baseline panorama reconstruction methods rely on accurate pose information, which is often difficult to obtain in real-world applications. To evaluate their robustness, we first conduct an experiment on the relative pose + +estimation on wide-baseline panorama images, results are displayed in Table 2, using inputs from the Replica [51] dataset. The relative pose derived using SIFT [38] and 8-point algorithm [22] with RANSAC [19] (SIFT+8PA) is highly inaccurate measured by Relative Rotation Angle (RRA) and Relative Translation Angle (RTA). + +In contrast, our model's PnP-based relative pose estimation (as detailed in Section 4.1) is significantly more accurate. We also use the estimated 3D points from two images to find 2D correspondences and apply 8-point algorithm to recover the relative pose, the results are even more accurate, the relative rotation and translation angle are both $< 0.5^{\circ}$ . + +We further conduct experiments using estimated relative poses (with translations properly scaled) and present the results in Table 3. Since estimating accurate pose from wide-baseline panoramic images is itself a challenging problem, pose-dependent methods are highly sensitive to pose inaccuracies, resulting in degraded performance. This underscores the need for a pose-free wide-baseline panorama reconstruction approach. + +# 4.4.2. Comparison with fixed baseline methods. + +We compare our model against methods trained and evaluated under a fixed-baseline setting, as shown in Table 4. Here, the principal axes of the two panoramic images are aligned, which makes the stereo reconstruction task significantly easier for posed methods. Since these methods are trained under different assumptions and data splits, direct + +Table 4. Quantitative comparisons with fixed baseline methods. Results are measured on the novel view panorama synthesis. All models above the horizontal line are trained on Matterport3D with a baseline of 1.0 meter, their results are measured by [72]. + +
MethodMatterport3D (1.0m)Matterport3D (1.5m)Matterport3D (2.0m)Replica (1.0m)Residential (~0.3m)
WS-PSNR↑SSIM↑LPIPS↓WS-PSNR↑SSIM↑LPIPS↓WS-PSNR↑SSIM↑LPIPS↓WS-PSNR↑SSIM↑LPIPS↓WS-PSNR↑SSIM↑LPIPS↓
S-NeRF [42]15.250.5790.54614.160.5630.58013.130.5230.60716.100.7230.44322.470.7410.435
IBRNet [59]25.720.8550.25821.690.7510.38220.040.7060.43122.650.8540.29122.470.7350.498
NeuRay [35]24.920.8320.26021.920.7660.34719.850.7150.40725.900.8990.18722.380.7530.427
PanoGRF [8]27.120.8760.19523.380.8110.28220.960.7610.35229.220.9370.13431.030.9090.207
MVSplat [7]29.290.9120.10522.510.8070.23013.380.5950.55431.250.9580.05931.320.9060.200
PanSplat [72]30.010.9310.09124.760.8490.18121.190.7770.26531.670.9620.06931.360.9170.172
Splatter-360[10]21.970.7500.27319.910.6970.35418.500.6590.39524.560.8750.19122.950.7350.366
PanoSplatt3R27.470.8760.14525.560.8440.18523.650.8040.24128.640.9310.10628.860.8520.264
+ +![](images/f8a6cc344d85a2c0a45128aff8d62b937cc9c3f665ff87cb4e0e0fd13985a0b0.jpg) +MVSplat† [7] + +![](images/891aa59c5d4d47194784d68f90c8f06d09eb91cb59c38aec75cc20897fd3d5eb.jpg) +Splatter-360[10] + +![](images/618d64dea37e19846d3f318f0b6caf7022c159101ae76408ad5d001e7f5b397a.jpg) +PanoSplatt3R + +![](images/1304ad8e36c2a48bc038a6e7b399ca457d8f76a99bc6d37adedbc98fc7b80732.jpg) +GT + +![](images/f44f9bfbd8fc6420815bf94d1e6af5fed0450a8673568b9fca29d1404613b34d.jpg) + +![](images/94e9f6d08dc62c1d712b5f91eefae8e2ac81cb99d61648a3433034b0c0f06d97.jpg) + +![](images/22d897545619833e9b1da6bc0e424854a8e3d94d2160bc0697e92122b36417ab.jpg) + +![](images/191005ecdd4c09e2fabafb4309eb5dcddcee3524be33a8cc8f9ac09489ff162c.jpg) + +![](images/0a201249df62d05b3313875b0a5561fcc4812642bdc2177d9598cb7367a471f2.jpg) + +![](images/afee3c33a1a7d6477c488f11190c665062d4eaf884dd7db463f78f3ab6982238.jpg) + +![](images/32699419b556ad470513f683de89ca52d407041dde70eb988993a73645b0e585.jpg) + +![](images/4ac7c185d82a0a23f9239d9880a9878318842754ebfd769e19af353e262b10a3.jpg) + +![](images/7a45ffc615d129bfb31571e6cf619bb7e61b2d0e2d7c902cc6cb245d7a34dab1.jpg) + +![](images/e03d837be63c97d041e38882f03617b2415c825d80806b179687406644aa2521.jpg) + +![](images/c7af1b981b9a8e8622dbf974e75c98098d0cd383d31c4037a39bb4d9df278cb0.jpg) + +![](images/82878a6b81cd6a5062daea428432b2b732b0ff691c9ed23189d13c6f11ca03e8.jpg) + +![](images/96fd5823a468e0590dd1866e9a11aaa87bc3bcf79f901f855693bcd2892604ab.jpg) + +![](images/d196acc1bd31b24f35920444811da2522febf73dbec27a9001d71bc90eff2a0e.jpg) + +![](images/a713479af52dc1c5d671366f0492de70bc4791db1531d2356a5d090a38090929.jpg) + +![](images/fb7691a247b6b3579ddd9a26d54c7db362016d1e325a7c362d9b8d5a1614dc8e.jpg) + +![](images/ab04e23bbf74da7fdde98d495404cc58a772c05d2698acaaf4e9ff34a300cc1e.jpg) +Figure 3. Visual Comparison on reconstructed image (above) and depth (below). Each row comes from different pairs of input. + +![](images/4652499fc67fc4b6c286544172e03867f068b78dd0248b078531ac4dbb4a3138.jpg) + +![](images/0e6610d3dbbe550350718dd2491bb70a7d2a0114071492c0b67ce22865c65020.jpg) + +![](images/18b580f4736a49ebb0f3623243e794c20fc4edc9465dc4f851b36bc6d447cd67.jpg) + +comparisons are not entirely fair. We add Splatter-360 [10], who is trained on the same data as ours for a fair comparison. Our model outperforms Splatter-360 by a large margin, showcasing its strong generalization ability. + +Despite not being trained on Matterport3D [45] and being designed to handle more challenging and unconstrained inputs, our model achieves comparable performance to these methods with narrow-baseline panorama images on + +Table 5. Ablation studies on method details (model components and design principles). + +
ConfigurationHM3DReplica
PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑PSNR↑SSIM↑LPIPS↓Rel↓RMS↓δ1↑
a. × RoPE rolling27.9160.8430.1650.0530.16197.24727.8520.8770.1220.0670.17896.398
b. → RoPE 2π26.8490.8180.1870.0670.18196.15026.6950.8620.1480.0840.21393.408
c. × Mast3R weight23.3310.7310.2810.1570.32185.00623.6730.8150.2120.1720.36479.310
d. × Progressive training27.2170.8270.1820.0600.17396.70727.9180.8820.1280.0670.17995.255
e. × 2DGS → 3DGS28.0490.8460.1620.0510.16097.29128.0690.8800.1180.0670.17496.645
Full PanoSplatt3R28.2000.8480.1600.0510.15797.39728.1810.8820.1170.0630.16897.055
+ Scale28.9380.8690.1470.0440.14797.65431.5220.9350.0820.0340.12698.115
+ +![](images/2d88c06f6b64cbd20fed3450a5de59ea6755fd0ca5ad8c4da04e3b803dc923e9.jpg) +$I_{1}$ in input views + +![](images/cb945cc82c952a9545fe9642c1418679c89d7201d9e18c3a9639efd66931ecb5.jpg) +Figure 4. Model without RoPE Rolling estimates broken geometry at panorama image boundaries, while the full PanoSplatt3R reconstructs the wall without a hole. + +![](images/cea9ac77e1774ed2e4745112c35f53dfd3c8cb0c8f1c9a660f8fbbe52d8bf679.jpg) +w/o RoPE Rolling +Full model + +Replica [51] and Residential [21], and even outperform them in the wider-baseline setting. Moreover, as the baseline distance increases, our model performance stably decreases, while fixed baseline methods face a sharp decline. + +# 4.5. Ablation Studies + +In this section, we conduct various ablation studies to analyze the effectiveness of our model components and design principles. The results are reported in Table 5. + +Important of perspective pre-training. Configuration c) (Cfg.c) adopts a random initialization while our full model uses pretrained weights of Mast3R. There is a significant performance gap between Cfg.c and full model, demonstrating the effectiveness of Dust3R's and Mast3R's perspective pre-training, while highlighting the necessity of we adopting a transfer learning paradigm. + +Effectiveness of RoPE rolling. Configuration a) uses the standard RoPE implementation from Dust3R and Mast3R, which performs worse than the full model. This indicates that RoPE rolling is crucial in improving geometric predictions for panoramic data. To better illustrate its impact, we visualize the Gaussian prediction $G_{1}$ separately. As shown in Figure 4, the input panorama image $I_{1}$ contains a wall spanning across its right and left edges. Without RoPE rolling, the model fails to capture the continuity of the wall's geometry, leaving a gap in the final reconstruction. In contrast, our full model, equipped with RoPE rolling, successfully estimates the complete and continuous structure. + +As explained in Section 3.3, changing the maximum ro + +tating angle to $2\pi$ does not yield a horizontally periodical positional encoding. What's worse, it changes the RoPE mechanism, hindering the knowledge transfer process. Its effect is further validated in Cfg.b. + +Importance of progressive training of the model. Configuration d) skips stage 1 and directly trains the model in stage 2. For a fair comparison, we train it for 150K steps—the total number of steps across both stages in our full model. In the early training phase, the model produces random point predictions, and each Gaussian point has a limited receptive field for backpropagating gradients after being rasterized to 2D. Directly optimizing with photometric loss at this stage hinders learning. Instead, we first stabilize the model's 3D point predictions before introducing photometric supervision, leading to a more effective training process. + +What if model directly regresses metric predictions? We apply scaling to the final reconstruction to resolve the scale ambiguity inherent in unposed inputs. For completeness, we also evaluate our model without this scaling step, denoted as "Full PanoSplatt3R". Even without scaling, the model achieves leading performance, demonstrating its strong generalization ability in unposed wide-baseline panorama reconstruction. + +Furthermore, Cfg.e in Table 5 implies that using 2DGS can bring superior performance than using 3DGS. + +# 5. Conclusion + +In this paper, we proposed PanoSplatt3R, a novel framework for reconstruction and view synthesis that operates directly on unposed wide-baseline panoramic images. 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Seminal works in natural language processing, e.g. Low-Rank Adaptation (LoRA), leverage the low "intrinsic rank" of parameter updates during adaptation. In this paper, we argue that incorporating stronger inductive biases on both the data and the models can enhance the adaptation of Geospatial Foundation Models (GFMs), pretrained on RGB satellite images, to other types of optical satellite data. Specifically, the pretrained parameters of GFMs serve as a strong prior for the spatial structure of multispectral images. For this reason, we introduce DEFLECT (Deflecting Embeddings for Finetuning Latent representations for Earth and Climate Tasks), a novel strategy for adapting GFMs to multispectral satellite imagery with very few additional parameters. DEFLECT improves the representation capabilities of the extracted features, particularly enhancing spectral information, which is essential for geoscience and environmental-related tasks. We demonstrate the effectiveness of our method across three different GFMs and five diverse datasets, ranging from forest monitoring to marine environment segmentation. Compared to competing methods, DEFLECT achieves on-par or higher accuracy with $5 - 10\times$ fewer parameters for classification and segmentation tasks. The code is available at https://github.com/Vmarsocci/DEFLECT. + +# 1. Introduction + +In recent years, the diversity and availability of satellite data have skyrocketed. This unprecedented access to multi/hyper-spectral satellite imagery has opened up new prospects for monitoring the Earth's biosphere. Real-world applications of Remote Sensing (RS) include several tasks such as agricultural monitoring from multispectral images [49], canopy + +![](images/3eafa274a1b20ab5fbf720af9d19078892c6b6e13ca426e9046a722806a80d35.jpg) +(a) + +![](images/dc8eec54ef0e334fb999790249c54555a284d4ac007a56d3a7d3530eba0ed338.jpg) +(b) +Figure 1. (a) Performance (IoU and F1-score) averaged across tasks, datasets and models, against the proportion of tuned GFM parameters. Our method, DEFLECT, performs almost as well as full fine tuning (oracle), while adjusting $< 1\%$ of the encoder parameters. (b) Performance averaged across models for each dataset. DEFLECT consistently performs competitively for classification and semantic segmentation across five datasets, spanning from the urban domain to the forestry domain. + +traits mapping from hyperspectral images [43], and building damage assessment from very high-resolution optical imagery [15]. Furthermore, combining multimodal satellite data with heterogeneous spatial, spectral and temporal resolutions has proved crucial, for instance for the detection of pluvial flood-induced damages [4], or for the quantification of toxic plumes released by industries and power plants [3]. + +Given the scarcity of ground truth on the one hand, and the massive amount of unlabeled data on the other, Geospatial Foundation Models (GFMs) $^{1}$ have gained considerable traction to tackle a wide variety of RS downstream tasks [28, 39, 53]. GFMs are large neural networks pretrained on large-scale data sets, usually through self-supervised pretext tasks [32, 41], to learn task-generic latent representations. Then, task-specific predictors can be trained on top of the (frozen) features extracted by GFMs. However, many GFMs are pretrained on a single modality, e.g. (very high-resolution) RGB images [32, 41, 46]. Therefore, such models require end-to-end finetuning to handle new heterogeneous satellite data. + +Conventional finetuning strategies, e.g. end-to-end full finetuning, are resource-intensive and require the storage of large parameter sets for each task [30]. In natural language processing (NLP), Low-Rank Adaptation (LoRA) [21] has been a pioneering work that mitigates this issue. LoRA leverages the low "intrinsic rank" of parameter updates during adaptation to finetune large models at the cost of very few additional parameters. Many Parameter-Efficient Finetuning (PEFT) techniques in Computer Vision (CV) take inspiration from this low-rank bias [10, 66]. In RS, [50] introduced a data-agnostic framework for adapting GFMs to new modalities via a LoRA-like technique. + +In this paper, we investigate a novel paradigm for adapting GFMs in a parameter-efficient way. We argue that stronger inductive biases on the data, i.e. satellite images, and models, i.e. Vision Transformers (ViT) (that are ubiquitous in GFMs [39]), can significantly enhance the adaptation of GFMs pretrained on RGB satellite images to multispectral satellite data. We introduce an untangled patch embedding (UPE) layer that decomposes the data embeddings into RGB embeddings and spectral embeddings. UPE disentangles the geometric information from the radiometric information provided by multispectral channels. Based on this decomposition, we propose a modified version of the self-attention module in the GFM, named untangled Attention (uAtt). Our untangled attention module allows, on the one hand, the use of the GFM pretrained parameters to process the RGB geometric and radiometric information without any updates, and on the other hand, to leverage the new radiometric information. In order to ensure minimal disruption to the structure of the GFM's latent space, that captured high-level spatial patterns + +through pretraining, we introduce a principle of embedding deflection. Inspired by the work of [23], that links neural networks to dynamical systems, embedding deflection consists in deviating the trajectory of patch embeddings in the latent space of ViTs. Our method, DEFLECT (Deflecting Embeddings for Finetuning Latent representations for Earth and Climate Tasks), requires fewer parameters than low-rank adaptation techniques. Moreover, DEFLECT can work in combination with LoRA techniques, differently from other methods. Finally, we empirically study the benefits of DEFLECT for classification and semantic segmentation against existing adaptation methods. The contributions of this paper are summarized as follows: + +- We provide strong inductive biases on the data and the models, tailored to multispectral satellite imagery and vision transformers. +- Concretely, these inductive biases translate into two new architectural elements. Firstly, a patch embedding layer, called UPE, which disentangles the different kinds of information of multispectral images. Secondly, a novel attention mechanism, called uAtt, which unties pretrained parameters and new multispectral information. +- We introduce a principle of **embedding deflection** that deviates the latent trajectory of the embeddings, based on the additional spectral information, while the global structure of the latent space is preserved. +- We empirically demonstrate the adaptation capabilities of DEFLECT across diverse tasks, datasets and models, with fewer parameters than low-rank adaptation techniques. + +# 2. Related Works + +Section 2.1 provides an overview of state-of-the-art algorithms to pretrain GFMs, both from scratch and in a continual fashion. Section 2.2 reviews the PEFT methods to adapt GFMs to downstream tasks and to new data domains. + +# 2.1. Geospatial Foundation Models + +In regards to the large amount of satellite data, and to the scarcity of labels for Earth observation (EO) tasks (e.g. land cover annotations, canopy height measurements), self-supervised learning (SSL) has become central to train GFMs [54, 56]. + +Self-supervised learning for multi-source satellite images Most learning algorithms rely on Masked Image Modeling (MIM) [5, 7, 45, 59], and on Contrastive Learning (CL) [12, 37, 57] to learn task-agnostic latent representations. To cope with the heterogeneity of spatial resolutions across RGB imagery, Scale-MAE [46] introduced resolution-aware positional encodings, while Cross-scale MAE [52] combined contrastive and generative losses. Other models, such as OmniSAT [2] and CROMA [12], combine MIM and CL to learn multimodal representations. + +Continual pretraining Continual pretraining involves adding new pretraining stages to an existing model to enhance or specialize its representations for specific tasks or domains. Initially shaped for NLP [16, 34], continual pretraining boosts the performance of SSL [47]. In EO, where vast unlabeled datasets are common, continual pretraining helps tailor large models for EO-specific tasks [38, 42, 55]. Techniques like those in [40, 44, 63] combine SSL and continual learning to manage the non-stationarity of remote sensing data. Unlike PEFT, which minimizes parameter updates to adapt models to new tasks, continual pretraining emphasizes expanding the model's core representations through ongoing updates. + +Despite recent efforts, through SSL and continual pretraining, to train task-agnostic and sensor-agnostic GFMs, their generalization remains limited [60]. Many recent GFMs are still confined to the processing of RGB satellite images [32, 42, 46, 52]. Therefore, PEFT techniques are required to extend the use of GFMs to multispectral satellite images, and to a wider range of tasks, especially for environmental applications. + +# 2.2. Parameter-Efficient Finetuning + +PEFT was first introduced in NLP, aiming to adapt large pretrained models to specific tasks with minimal adjustments to the model parameters [17]. In RS, PEFT is of great interest as far as many specialized models need to be trained, stored, and deployed. PEFT techniques can be divided into three main categories [31]: additive, selective, and low-rank adaptation techniques. + +Additive techniques In NLP, [20] introduced adapter modules, paving the way to additive techniques. Adapter modules extend the pretrained model with few task-specific parameters. In order to decrease the computation overhead of finetuning, [11] introduced additive modules with computation and parameter sharing across multiple tasks. In RS, many PEFT techniques rely on adapter modules in order to cope with multi-source data of varying dimensions [6, 9, 19, 22, 61]. Among them, [19] add additional modules for extracting multimodal-specific representations for scene classification. + +Selective techniques In contrast to additive methods, selective techniques finetune only a specific subset of the model parameters [14]. Data-agnostic methods include norm-tuning [64] and BitFit [62], that only tune the layer normalization parameters and the biases, respectively, with very convincing results. Other approaches leverage sparse parameter updates, such as [1] that ignores the structure of the model or [51] that estimates parameters' importance from the Fisher information. + +Low-Rank Adaptation The paradigm of Low-Rank Adaptation was introduced in [21]. While it could be casted as + +an additive technique, LoRA has opened the path towards a myriad of methods [8, 18, 33, 35, 36] that leverage the low "intrinsic" rank of parameter updates in order to dramatically reduce the cost of finetuning. Recently, SLR [50] proposed a combination of LoRA and a scaling strategy to adapt GFMs to new RS modalities, both in the finetuning and continual pretraining stages. + +Main limitations On the one hand, some methods are either constrained by the tasks they address (e.g. change detection [6, 29, 61], classification [19]) or by the architectures they employ (e.g. the Segment Anything Model [25] in [6, 65]). On the other hand, many techniques inspired by research in NLP do not address the specificities of CV or remote sensing. Our strategy, DEFLECT, leverages inductive biases on the data and on the ubiquitous ViT, such that it can be applied to any ViT-based GFM and to any downstream task. + +# 3. Preliminary & Motivation + +Setup Let us consider a downstream task, for which we have a labeled dataset of multispectral images. In order to solve the task, consider using a ViT-based GFM, pretrained on RGB satellite images, which typically have higher spatial resolution than multispectral images. Finally, consider one instance from the dataset, i.e. a satellite multispectral image $\mathbf{X} \in \mathbb{R}^{C \times H \times W}$ , that comprises $H \times W$ pixels with $C$ spectral channels. + +Vision Transformers Data processing in ViTs can be considered in three stages [23]: i) dimensionality change, ii) data transport, and iii) task-specific predictions. First, the input image $\mathbf{X}$ is divided into $n$ patches. Each patch is encoded into a $d$ -dimensional embedding, resulting in a latent representation $\mathbf{x} = [\mathbf{x}_1 \dots, \mathbf{x}_n]^T \in \mathbb{R}^{n \times d}$ . Second, ViTs transport the embeddings in the latent space through $m$ attention blocks. We denote the input of the $l^{th}$ attention block as $\mathbf{z}^{(l)}$ , e.g. $\mathbf{z}^{(1)} = \mathbf{x}$ . The $l^{th}$ layer computes the displacement from $\mathbf{z}^{(l)}$ to $\mathbf{z}^{(l+1)}$ . Third, task-specific layers map the latent representations to predictions. Attention blocks themselves process the data in two steps. First, a self-attention module, comprising query, key and value matrices denoted as $W_l^Q$ , $W_l^K$ , $W_l^V \in \mathbb{R}^{d \times d}$ , respectively, computes a first displacement: + +$$ +\Delta_ {1} \boldsymbol {z} _ {i} ^ {(l)} = \sum_ {j = 1} ^ {n} \frac {\exp \left(\alpha_ {i j}\right)}{\sum_ {j ^ {\prime} = 1} ^ {n} \exp \left(\alpha_ {i j ^ {\prime}}\right)} \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {l} ^ {V}\right), \tag {1} +$$ + +$$ +\text {w h e r e} \alpha_ {i j} = \frac {1}{\sqrt {d}} \left(\boldsymbol {z} _ {i} ^ {(l)} W _ {l} ^ {Q}\right) \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {l} ^ {K}\right) ^ {T}. \tag {2} +$$ + +Second, a standard MLP computes a second displacement: + +$$ +\Delta_ {2} \boldsymbol {z} _ {i} ^ {(l)} = \operatorname {M L P} ^ {(l)} \left(\boldsymbol {z} _ {i} ^ {(l)} + \Delta_ {1} \boldsymbol {z} _ {i} ^ {(l)}\right) \tag {3} +$$ + +All in all, the embeddings are transported in the latent space as follows: + +$$ +\boldsymbol {z} _ {i} ^ {(l + 1)} = \boldsymbol {z} _ {i} ^ {(l)} + \Delta_ {1} \boldsymbol {z} _ {i} ^ {(l)} + \Delta_ {2} \boldsymbol {z} _ {i} ^ {(l)} \tag {4} +$$ + +For readability, we omitted the normalization layers, and considered a single-head self-attention module. + +Embedding decomposition In multispectral images, spectral channels beyond RGB provide crucial information for many environmental applications. We refer to geometric information as the signal derived from the spatial arrangement of multiple pixels – capturing features such as edges, textures, or contextual patterns. In contrast, we use radiometric and spectral information interchangeably to describe pixel-level reflectance values, which result from the pre-processed atmospheric correction of raw sensor signals. The additional multispectral radiometric information is highly informative of the physical and chemical properties of the Earth's biosphere. The geometric information of the additional spectral channels, however, is redundant with the geometric information of the RGB channels. In that regard, we assume that the patch embeddings $\mathbf{x}$ , computed by an arbitrary neural network, can be decomposed as follows: + +$$ +\boldsymbol {x} = \boldsymbol {x} _ {P} + \boldsymbol {x} _ {A} \tag {5} +$$ + +where $\pmb{x}_P$ encodes the radiometric and geometric information of the RGB channels, while $\pmb{x}_A$ encodes the spectral information beyond RGB. Practically, $\pmb{x}_P$ is the patch embedding computed by the pretrained foundation model. On the contrary, $\pmb{x}_A$ corresponds to auxiliary information that the pretrained model is unable to handle. + +Limitations of low-rank methods Low-rank methods fine-tune a small amount of new parameters, denoted as $\Delta W$ , in addition to pretrained parameters, denoted as $W_{P}$ , resulting in task-specific parameters $\tilde{W}$ : + +$$ +\tilde {W} = W _ {P} + \Delta W \tag {6} +$$ + +Therefore, assuming the existence of the embedding decomposition defined in Eq. 5, the attention product of the first attention block, defined in Eq. 2, becomes: + +$$ +\begin{array}{l} \alpha_ {i j} ^ {\mathrm {L R}} = \frac {1}{\sqrt {d}} \left(\left(\boldsymbol {x} _ {i P} + \boldsymbol {x} _ {i A}\right) \tilde {W} ^ {Q}\right) \left(\left(\boldsymbol {x} _ {j P} + \boldsymbol {x} _ {j A}\right) \tilde {W} ^ {K}\right) ^ {T} \\ = \frac {1}{\sqrt {d}} \left[ \left(\boldsymbol {x} _ {i P} \tilde {W} ^ {Q}\right) \left(\boldsymbol {x} _ {j P} \tilde {W} ^ {K}\right) ^ {T} + \left(\boldsymbol {x} _ {i P} \tilde {W} ^ {Q}\right) \left(\boldsymbol {x} _ {j A} \tilde {W} ^ {K}\right) ^ {T} \right. \\ \left. + \left(\boldsymbol {x} _ {i A} \tilde {W} ^ {Q}\right) \left(\boldsymbol {x} _ {j P} \tilde {W} ^ {K}\right) ^ {T} + \left(\boldsymbol {x} _ {i A} \tilde {W} ^ {Q}\right) \left(\boldsymbol {x} _ {j A} \tilde {W} ^ {K}\right) ^ {T} \right] \tag {7} \\ \end{array} +$$ + +Eq. 7 shows that the patch embeddings $\mathbf{x}_P$ and $\mathbf{x}_A$ are entangled. Therefore, the projection matrices $\tilde{W}^Q$ and $\tilde{W}^K$ + +are shared across embeddings. However, $\pmb{x}_P$ and $\pmb{x}_A$ encode two kinds of information which are heterogeneous. Therefore, applying the same projection does not seem reasonable. To be precise, let us expand the first and last terms of Eq. 7: + +$$ +\begin{array}{l} \alpha_ {i j} ^ {\mathrm {L R}} = \frac {1}{\sqrt {d}} \left[ \left(\boldsymbol {x} _ {i P} W _ {P} ^ {Q}\right) \left(\boldsymbol {x} _ {j P} W _ {P} ^ {K}\right) ^ {T} + \left(\boldsymbol {x} _ {i P} W _ {P} ^ {Q}\right) \left(\boldsymbol {x} _ {j P} \Delta W ^ {K}\right) ^ {T} \right. \\ + (\boldsymbol {x} _ {i P} \Delta W ^ {Q}) (\boldsymbol {x} _ {j P} W _ {P} ^ {K}) ^ {T} + (\boldsymbol {x} _ {i P} \Delta W ^ {Q}) (\boldsymbol {x} _ {j P} \Delta W ^ {K}) ^ {T} \\ + \ldots + (\pmb {x} _ {i A} W _ {P} ^ {Q}) (\pmb {x} _ {j A} W _ {P} ^ {K}) ^ {T} + (\pmb {x} _ {i A} W _ {P} ^ {Q}) (\pmb {x} _ {j A} \Delta W ^ {K}) ^ {T} \\ \left. + \left(\boldsymbol {x} _ {i A} \Delta W ^ {Q}\right) \left(\boldsymbol {x} _ {j A} W _ {P} ^ {K}\right) ^ {T} + \left(\boldsymbol {x} _ {i A} \Delta W ^ {Q}\right) \left(\boldsymbol {x} _ {j A} \Delta W ^ {K}\right) ^ {T} \right] \tag {8} \\ \end{array} +$$ + +Eq. 8 shows that low-rank methods use pretrained parameters $W_{P}$ to indifferently process the embeddings $x_{P}$ and $x_{A}$ , although $x_{A}$ encodes spectral information that was not available during pretraining. Similarly, the new parameters $\Delta W$ handle both $x_{P}$ and $x_{A}$ , whereas we would expect the new parameters to be dedicated to handling $x_{A}$ . Thus, we argue that low-rank adaptation methods, due to the linear arithmetic of the self-attention module between $x_{P}$ and $x_{A}$ , may not fully leverage either the additional spectral information of multispectral images or the pretrained parameters of the GFM, which encode RGB information. + +# 4. Methodology + +This section describes DEFLECT, our parameter-efficient adaptation strategy, to adapt GFMs, pretrained on RGB satellite images, to multispectral satellite images. DEFLECT, illustrated in Fig. 2, is an additive technique that complements pretrained parameters with new parameters, in order to integrate the additional spectral information of multispectral images. It comprises three key elements: + +- An Untangled Patch Embedding Layer, called UPE, [section 4.1] that computes the patch embeddings $\mathbf{x}_P$ and $\mathbf{x}_A$ separately, +- A novel Untangled Attention Block, called uAtt, [section 4.2] that integrates the new spectral information, +- An Embedding Deflection Mechanism [section 4.3] that deflects the trajectory of patch embeddings $\boldsymbol{x}_P$ , transported by pretrained attention blocks, based on the untangled attention product. The embedding deflection aims to increase the representational power of the latent embeddings. + +# 4.1. Untangled Patch Embedding + +Appending multispectral channels to RGB images can be thought as adding color to grayscale images. New spectral channels provide informative radiometric information but we assume mostly redundant geometric information. Therefore, we focus on extracting discriminative spectral features from new multispectral channels, and rely on the pretrained model to extract geometric features (and RGB radiometric features). Our Untangled Patch Embedding is, thus, made of two parts: + +![](images/649bf7a0f79c8ec9512e3bcba30924ffb36bde4365e4442cc4dceb71ef396786.jpg) + +![](images/1b0a6875881df5acb9c4a175a41d0e31e899930d2ab6f3463325c7008fb0f990.jpg) + +![](images/baee62b24acce07a65af675f9943df09ce64bf5ac860e68267bddc96a900efa5.jpg) +Figure 2. Illustration of DEFLECT, our parameter-efficient adaptation technique. The upper-left block describes UPE, our untangled patch embedding layer, introduced in section 4.1. UPE computes the RGB embeddings $\pmb{x}_P$ and the auxiliary embeddings $\pmb{x}_A$ . The upper-right block illustrates uAtt, our untangled attention module, introduced in section 4.2. The middle part of the figure illustrates the first three attention layers of the GFM. In this example, first and third layers are adapted: the standard attention modules are replaced by uAtt. Adapted layer $l$ takes as input the concatenation of $\pmb{z}^{(l)}$ and $\pmb{x}_A$ . The additional radiometric information encoded into $\pmb{x}_A$ is leveraged by uAtt in order to deflect the trajectory of the embeddings. The displacement $\Delta_1\pmb{z}^{(l)}$ that the attention block with pretrained parameters would have computed is deflected, resulting in a new displacement $\tilde{\Delta}_1\pmb{z}^{(l)}$ . The norm of $\tilde{\Delta}_1\pmb{z}^{(l)}$ is constrained to be equal to the norm of $\Delta_1\pmb{z}^{(l)}$ , as illustrated in the bottom part of the figure. + +- Embedding of $x_P$ . We extract RGB channels from the multispectral image and compute $x_P$ with the pretrained patch embedding layer, from the pretrained GFM. +- **Embedding of $\pmb{x}_A$ .** As we are only interested in radiometric information, we compute $\pmb{x}_A$ with a pixel-set encoding technique [13]. First, we randomly sample a set of pixels (10% of pixels within a patch in our experiments). Second, we compute pixel-wise spectral indices (i.e. normalized linear combinations of spectral channels) such as NDVI [48] or NDTI [26], in order to extract spectral features without overloading the model with new parameters. Third, we compute and concatenate statistics of the spectral features (e.g. mean, standard deviation, first and last quartiles, minimum and maximum...). In this way, the dimension of $\pmb{x}_A$ is invariant to the size of the patch and the number of sampled pixels. Moreover, we can save memory and computation, without the need of introducing another learnable patch embedder. + +Our Untangled Patch Embedding is illustrated in the upper-left block of Fig. 2. + +# 4.2. Untangled Attention Block + +Inspired by [24], we introduce $uAtt$ , an untangled self-attention module that mitigates the effects of the linear arithmetic of self-attention. uAtt modules partially replace standard attention modules, for a subset of layers. At layer $l$ , uAtt leverages pretrained parameters $W_{lP}$ alongside new parameters $W_{lA}$ , in order to compute a modified displacement $\tilde{\Delta}_{1}$ , instead of $\Delta_{1}$ in eq. 2. Basically, parameters $W_{lP}$ and $W_{lA}$ are meant to process the untangled embeddings computed by our UPE layer: + +$$ +\tilde {\Delta} _ {1} \boldsymbol {z} _ {i} ^ {(l)} = \sum_ {j = 1} ^ {n} \frac {\exp (\tilde {\alpha} _ {i j})}{\sum_ {j ^ {\prime} = 1} ^ {n} \exp (\tilde {\alpha} _ {i j ^ {\prime}})} \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {l P} ^ {V} + \boldsymbol {x} _ {j A} W _ {l A} ^ {V}\right); \tag {9} +$$ + +$$ +\tilde {\alpha} _ {i j} = \frac {1}{\sqrt {d}} \left(\boldsymbol {z} _ {i} ^ {(l)} W _ {P} ^ {Q} + \boldsymbol {x} _ {i A} W _ {A} ^ {Q}\right) \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {P} ^ {K} + \boldsymbol {x} _ {j A} W _ {A} ^ {K}\right) ^ {T} \tag {10} +$$ + +At first layer, pretrained - and not updated during finetuning - parameters $W_{1P}$ process the embeddings $\pmb{x}_P = \pmb{z}^{(1)}$ . Then, + +at layer $l > 1$ , parameters $W_{lP}$ (not updated either) process the embeddings $z^{(l)}$ . Those operations result in usual RGB-to-RGB attention products, as in the pretrained GFM. In addition, new parameters $W_{lA}$ process the new spectral information encoded into $x_A$ , which is kept fixed along every layers. This yields extra RGB-to-spectral, spectral-to-RGB and spectral-to-spectral attention products: + +$$ +\begin{array}{l} \tilde {\alpha} _ {i j} = \frac {1}{\sqrt {d}} \left[ \overbrace {\left(\boldsymbol {z} _ {i} ^ {(l)} W _ {l P} ^ {Q}\right) \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {l P} ^ {K}\right) ^ {T}} ^ {\text {R G B - t o - R G B}} + \overbrace {\left(\boldsymbol {z} _ {i} ^ {(l)} W _ {l P} ^ {Q}\right) \left(\boldsymbol {x} _ {j A} W _ {l A} ^ {K}\right) ^ {T}} ^ {\text {R G B - t o - s p e c t r a l}} \right. \\ + \underbrace {\left(\boldsymbol {x} _ {i A} W _ {l A} ^ {Q}\right) \left(\boldsymbol {z} _ {j} ^ {(l)} W _ {l P} ^ {K}\right) ^ {T}} _ {\text {s p e c t r a l - t o - R G B}} + \underbrace {\left(\boldsymbol {x} _ {i A} W _ {l A} ^ {Q}\right) \left(\boldsymbol {x} _ {j A} W _ {l A} ^ {K}\right) ^ {T}} _ {\text {s p e c t r a l - t o - s p e c t r a l}} ] \tag {11} \\ \end{array} +$$ + +uAtt is illustrated in the upper-right of Fig. 2. The new parameters of the untangle attention module can, optionally, be re-parameterized in a low-rank fashion. + +# 4.3. Embedding Deflection + +In order to better separate ambiguous latent clusters, we aim to leverage the new radiometric information of multispectral images. To this end, we adapt a subset of the attention blocks, denoted as $\mathcal{K}$ , leading to few additional parameters. The attention module of adapted blocks is replaced by our uAtt module. Furthermore, we aim to preserve the structure of the pretrained GFM latent space, and thus the capacity of the GFM to process the geometric, textural, and contextual information of multispectral images. Therefore, we constrain the norm of the displacement computed by uAtt to match the norm of the displacement that the standard attention block would have computed. All in all, given a labeled training data set $\mathcal{D}_T$ , a classification or a semantic segmentation loss $\mathcal{L}$ , and a predictor head $p_{\phi}$ that maps the latent embeddings to the target classes, we define the adaptation problem as follows: + +$$ +\min _ {\theta_ {A}, \phi} \mathcal {L} \left(\theta_ {A}, \phi ; \theta_ {P}, \mathcal {D} _ {T}\right) \tag {12} +$$ + +subject to $\| \Delta_1\pmb {z}_i^{(k)}\| _2 = \| \tilde{\Delta}_1\pmb {z}_i^{(k)}\| _2$ , for all $k\in \mathcal{K}$ + +where $\theta_{P}$ is the set of all pretrained parameters, and $\theta_{A}$ is the set of new query, key, and value matrices. In practice, the hard constraints in Eq. 12 can be satisfied by tweaking the architecture of the untangle attention module, only at the cost of running the pretrained GFM on the RGB channels to compute the norm of $\Delta_1z$ . This principle of embedding deflection is illustrated in the bottom part of Fig. 2. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets To benchmark DEFLECT, we selected three classification datasets and two segmentation datasets (cf. Tab 1). + +Table 1. Overview of selected geospatial datasets used for classification and segmentation tasks. + +
DatasetTaskBandsPatch SizeSamples
Classification
So2SatUrban dynamics1032x3222,000
Brick KilnBrick kilns1364x6419,000
ForestNetForest monitoring12332x3328,000
Segmentation
MADOSMarine pollution13240x2403,000
BurnScarsBurn scars6512x5121,000
+ +All the datasets consist of satellite multispectral images with target data related to environmental sciences. Note that for the classification datasets, we adopted the GEO-Bench [27] preprocessing. + +Pretrained GFMs We evaluated the performance of DEFLECT on three GFMs, pretrained on RGB images, each selected for its distinct characteristics. The first model is Scale-MAE [46], a variant of MAE widely used for RS representation learning. The second model, DINO-MC [58], is a contrastive approach based on DINO. The third model, Cross-Scale MAE [52], was pretrained with a hybrid objective which combines both a MAE and a contrastive approach. + +Competing methods We compared the performance of DEFLECT against several competing PEFT techniques. The baseline uses a frozen encoder. The oracle represents the upper bound, where the entire model is finetuned end-to-end. Additionally, we evaluated DEFLECT against four widely used, open-source, both generalist and specialized PEFT approaches: LoRA [21], Scaled Low-Rank (SLR) [50], BitFit [62], and NormTuning [64]. + +DEFLECT implementation For DEFLECT training, the spectral patch embeddings were computed with the following statistics: mean, standard deviation, minimum, maximum, the first and third quartiles, as well as the 0.1/0.4/0.6/0.9-quantiles. In order to align the embedding dimension of the spectral encoder with that of the RGB feature extractor, we further projected the extracted feature with a linear layer. This layer was initialized with a Xavier initialization, followed by a Layer Normalization and a GELU activation function in a Transformer fashion. We replaced the traditional attention blocks with our uAtt in four layers, the ones used by UPerNet (i.e. 3, 5, 7, 11 for ViT Base; 7, 11, 15, 23 for ViT Large). The additional parameters of the uAtt blocks are low-rank (with a rank of 16). + +Evaluation protocol For the classification tasks, we used a linear layer and reported the mean F1-score. Models are trained for 60 epochs with a batch size of 24. For the segmentation tasks, we used a trainable UPerNet as the decoder and reported Intersection over Union (IoU) for 2-classes datasets and mean IoU (mIoU) otherwise. The segmentation models are finetuned for 120 epochs with a batch size of 8. In all + +Table 2. Comparison of F1-score (classification) and IoU (segmentation) results across downstream tasks for DEFLECT and competing PEFT methods on GFMs with different approaches, with standard deviation (across 3 runs). Each method is evaluated across diverse datasets representing geospatial challenges: So2Sat, Brick Kiln, ForestNet, Burn Scars, and MADOS. Average classification performance, average segmentation performance, and overall performance are also reported. DEFLECT consistently demonstrates robust performance with substantially fewer trainable parameters across self-supervised models and tasks, achieving top scores in multiple datasets and a good balance between efficiency and performance. The Oracle finetuning performance is included as a top reference. + +
MethodEncoder Tuned ParamsSo2Sat (mF1)Brick Kiln (mF1)ForestNet (mF1)Burn Scars (IoU)MADOS (mIoU)Avg. Class.Avg. Segm.Avg. Perf.
Scale-MAE [46]
Finetuning (oracle)100%52.7 ±0.196.6 ±2.144.9 ±0.278.6 ±1.246.2 ±2.564.862.463.8
Frozen0.0%32.1 ±0.694.3 ±0.241.3 ±0.575.3 ±2.236.3 ±0.755.955.855.9
Norm Tuning [64]0.03%45.5 ±6.697.0 ±0.541.8 ±0.870.7 ±3.830.6 ±21.161.450.657.1
BitFit [62]0.09%41.0 ±5.497.4 ±0.541.9 ±0.975.9 ±0.128.3 ±15.460.152.156.9
LoRA [21]2.1%54.7 ±0.297.4 ±0.139.4 ±3.278.8 ±2.245.2 ±0.563.862.063.1
SLR [50]2.2%52.0 ±0.596.4 ±1.943.0 ±1.080.3 ±0.745.5 ±2.263.862.963.4
DEFLECT (ours)0.2%52.7 ±0.597.6 ±0.243.2 ±0.977.0 ±1.250.5 ±0.264.563.764.2
DINO-MC [58]
Finetuning (oracle)100%48.3 ±0.598.3 ±0.541.8 ±2.476.8 ±0.960.3 ±1.7462.868.665.1
Frozen0.0%34.0 ±0.894.9 ±0.335.4 ±0.970.5 ±0.251.3 ±0.854.760.957.2
Norm Tuning [64]0.09%48.3 ±0.597.9 ±0.239.3 ±0.770.5 ±0.552.8 ±1.861.861.661.8
BitFit [62]0.2%49.6 ±0.598.1 ±0.245.9 ±0.270.0 ±0.452.3 ±2.064.561.163.2
LoRA [21]5.4%46.5 ±0.669.1 ±29.241.6 ±1.466.4 ±8.15.7 ±3.442.636.045.9
SLR [50]5.7%49.3 ±0.569.1 ±29.242.0 ±0.471.3 ±1.45.8 ±4.253.538.647.5
DEFLECT (ours)0.9%52.2 ±0.298.3 ±0.544.6 ±0.875.6 ±1.251.6 ±0.165.063.664.5
Cross-Scale MAE [52]
Finetuning (oracle)100%47.1 ±2.096.4 ±1.936.0 ±1.178.1 ±0.947.7 ±1.259.862.961.2
Frozen0.0%29.9 ±0.094.7 ±0.132.7 ±0.867.4 ±1.141.8 ±0.852.454.653.3
Norm Tuning [64]0.03%38.4 ±2.896.2 ±0.631.5 ±0.968.1 ±0.640.9 ±1.355.454.555.0
BitFit [62]0.09%39.2 ±1.095.3 ±0.336.1 ±2.867.9 ±0.240.6 ±0.756.954.355.8
LoRA [21]2.1%36.6 ±3.695.7 ±0.432.8 ±1.766.7 ±3.834.3 ±1.255.050.553.2
SLR [50]2.2%43.3 ±1.195.4 ±0.837.2 ±4.664.8 ±2.235.3 ±0.758.750.155.2
DEFLECT (ours)0.2%45.6 ±0.397.7 ±0.741.6 ±4.769.6 ±0.938.1 ±0.761.653.858.5
+ +experiments, all the images are $224 \times 224$ pixels to match the encoder input size (they are either upsampled or random cropped). The learning rate is set to 0.0001 and optimized using the AdamW optimizer, with a MultiStep scheduler that applies learning rate adjustments at steps 0.6 and 0.9 of the total number of epochs. The loss function used for both classification and segmentation tasks is the cross entropy loss. The code will be made available for reproducibility purposes. + +# 5.2. Experimental Results + +Table 2 presents the classification and segmentation performance of DEFLECT and competing methods. We report several key observations in the following. + +Stability across tasks, datasets and models We observe that every competing methods have an erratic performance across the tasks, datasets and models. For instance, Norm- + +Tuning reached on MADOS the best mIoU with DINO-MC (52.8 mIoU / +1.2 pt compared to DEFLECT) while it achieved the second worst with Scale-MAE (30.6 mIoU / -19.9 pt compared to DEFLECT) with a huge standard deviation across different runs. LoRA and SLR have also exhibited very large performance gaps, for instance on MADOS as well, on which their mIoU collapsed with DINO-MC. In contrast, DEFLECT demonstrated stable results across tasks, datasets and models, reaching the best performance in average (e.g. 64.2 mIoU with Scale-MAE), as well as for many configurations, with low standard deviations. In the Supplementary Material, we empirically study the link between performance consistency and embedding displacement. + +Parameter efficiency DEFLECT showcased a very good trade-off between the number of updated parameters and performance. As a matter of fact, DEFLECT is often in par, and sometimes better, than full finetuning (see Figure 1). For instance, DEFLECT outperformed full finetuning + +with Scale-MAE on MADOS by 4.3 pt and with Cross-Scale MAE on ForestNet by 5.6 pt. While the low-rank adaptation techniques, LoRA and SLR, have $2.1\%$ tunable parameters for Scale-MAE, DEFLECT only tunes $0.2\%$ of the model parameters for comparable or better performance. + +Overall, the performance of DEFLECT alongside its stability and parameter-efficiency support the potential of our embedding decomposition and embedding deflection technique. + +# 5.3. Ablation studies + +In the following, we conduct ablation studies about i) the best time to deflect the latent trajectories, and ii) about performance across different low-rank dimensions. In the Supplementary Material, we report additional ablations about the number of pixels sampled in UPE, about reproducing the features computed by UPE with a linear layer, and about the inconsistency of the parameters initialization strategies for competitive methods w.r.t DEFLECT. In addition, the Supplementary Material gives more details about the datasets and presents extensive results. + +Best time for embedding deflection? We argue that the embeddings can be deflected only a few times. In other words, only a few layers of the GFM have to be adapted. Experimental results, presented in Tab. 3, actually show that deviating embeddings at each time step (i.e. each layer), decreases the performance. On the contrary, only adapting the first layer leads to suboptimal performance. We argue that deflecting the embeddings at the first layer only is deflecting too little, not including enough spectral information in the embeddings, while deflecting the embeddings on every layer changes too much the trajectory of the embeddings. + +Table 3. Ablation study about the GFM layers to be adapted, for each model on MADOS / BurnScars (one run only). + +
ModelAdapted Layers
First LayerUPerNet LayersAll layers
Scale-MAE47.1 / 75.850.6 / 77.338.7 / 70.1
DINO-MC50.8 / 73.751.6 / 75.647.1 / 67.8
Cross-Scale MAE39.2 / 67.438.2 / 70.631.7 / 64.5
+ +Performance across low-rank dimensions Table 4 compares DEFLECT and LoRA across different models and low-rank dimensions. The results show that DEFLECT achieves competitive or superior performance while tuning significantly fewer parameters. For instance, in Scale-MAE with LR dim $= 32$ , DEFLECT attains $51.3 \mathrm{mIoU}$ (MADOS) and $77.3 \mathrm{IoU}$ (BurnScars) while tuning only $0.28\%$ of parameters, compared to $30.2 / 78.7$ with LoRA, which requires $4.1\%$ . Similar trends are observed for DINO-MC and Cross-Scale MAE. Besides, DEFLECT without low-rank adaptation is better than with low-rank adaptation. It confirms that DEFLECT is inherently independent of low-rank techniques and does not rely on low-rank adaptation to be effective. + +Table 4. Performance comparison of DEFLECT / LoRA for different models (#1 Scale-MAE, #2 DINO-MC, #3 Cross-Scale MAE) across varying low-rank dimensions (one run only). The results indicate minimal differences for MADOS and BurnScars, highlighting the potential for selecting a low-rank dimension that balances computational efficiency and performance. The superscript * indicates the default dimension used for the main experiments. + +DEFLECT / LoRA + +
ModelLR dimTuned params (%)MADOS (mIoU)BurnScars (IoU)
#180.15 / 1.150.7 / 47.077.4 / 79.3
16*0.20 / 2.150.6 / 45.077.3 / 79.5
320.28 / 4.151.3 / 30.277.3 / 78.7
None4.1 / N.A.51.4 / N.A.77.9 / N.A.
#280.51 / 2.950.9 / 4.075.5 / 72.7
16*0.9 / 5.451.6 / 6.375.6 / 65.5
321.2 / 10.052.3 / 7.674.3 / 26.4
None7.8 / N.A.52.9 / N.A.76.1 / N.A.
#380.15 / 1.1237.1 / 39.570.0 / 74.3
16*0.20 / 2.138.2 / 35.070.6 / 66.4
320.28 / 4.137.9 / 26.171.8 / 60.2
None4.1 / N.A.38.6 / N.A.72.1 / N.A.
+ +# 6. Conclusions and perspectives + +In this work, we introduced DEFLECT, a novel approach for adapting Geospatial Foundation Models to multispectral satellite images. In contrast to Low-Rank Adaptation techniques such as SLR [50], we leveraged inductive biases on the data and on the models, introducing an untangled patch embedding layer and an untangled attention module. Through a principle of embedding deflection, DEFLECT integrates the additional radiometric information of multispectral data, at the cost of very few parameters (but with higher FLOPs), in order to increase the expressiveness of the GFM latent space. Experiments across several tasks, datasets and models, demonstrated that DEFLECT reached high and consistent accuracy, compared with competing methods that performed erratically despite a larger number of parameters. Notably, DEFLECT achieved superior performance with 5-10x fewer parameters compared to low-rank-based PEFT methods. In future works, we would like to further experiment DEFLECT on hyperspectral and multi-temporal satellite images, whose spectral and temporal dimension provide rich information on the physical properties of the Earth's biosphere. Finally, we believe that DEFLECT could be applied with standard foundation models, for instance to integrate depth information for segmentation tasks. In conclusion, we see a huge potential for DEFLECT to adapt GFMs to multi-source satellite data and to environmental tasks. + +# Acknowledgment + +Authors would like to thank Julia Cohen and Adrien Dorise for fruitful discussions and valuable feedbacks. + +# References + +[1] Alan Ansell, Edoardo Ponti, Anna Korhonen, and Ivan Vulić. Composable sparse fine-tuning for cross-lingual transfer. 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Feng $^{3}$ , Sachin Shah $^{1}$ , Guan-Ming Su $^{2}$ , Christopher Metzler $^{1}$ $^{1}$ University of Maryland $^{2}$ Dolby Labs $^{3}$ MIT + +![](images/8cb2910862c507bd55ed8f7c744ab7c24cb764ffc2dd8b500bc3f94cfccdfc54.jpg) +Figure 1. Shadow manipulation on generated portrait images with diverse styles challenges existing editing methods. To address this limitation, we present Shadow Director, which enables intuitive and parametric shadow control during diffusion-based portrait generation, instead of post-processing, across diverse artistic styles. Top: Our method provides parametric control over (left) directional light position, (middle) progressive shadow strength, and (right) arbitrary shadow shapes, while maintaining identity and style consistency. Bottom: Comparison with baseline methods reveals their limitations: SwitchLight [24] and IC-Light [60] suffer from identity shifts or inaccurate lighting direction despite requiring substantial training resources, DiFaReli [35] fails at effectively providing strong variation in shadow strength. Prompt engineering results in unpredictable outcomes. + +# Abstract + +Text-to-image diffusion models excel at generating diverse portraits, but lack intuitive shadow control. Existing editing approaches, as post-processing, struggle to offer effective manipulation across diverse styles. Additionally, these methods either rely on expensive real-world light-stage data collection or require extensive computational resources for training. To address these limitations, we introduce Shadow Director, a method that extracts and manipulates hidden shadow attributes within well-trained diffusion models. Our approach uses a small estimation network that requires only a few thousand synthetic images and hours of training—no costly real-world light-stage data needed. Shadow Director enables parametric and intuitive control over shadow shape, placement, and intensity during portrait generation while preserving artistic integrity and identity across diverse styles. Despite training only on synthetic data built on real-world identities, it generalizes ef + +fectively to generated portraits with diverse styles, making it a more accessible and resource-friendly solution. Homepage: https://www.hm-cai.com/ShadowDirector/ + +# 1. Introduction + +Control over visual attributes in AI-generated imagery has advanced significantly [30, 58], yet shadow control for portraits remains unexplored in diffusion-based generation. While current diffusion models excel at generating portraits with consistent lighting based on text prompts, prompt engineering lacks intuitive controls for shadow effects, forcing digital artists to rely on time-consuming trial-and-error prompt engineering. + +# 1.1. Generated Portraits Challenge Editing Method + +Conventional editing-based methods struggle with shadow manipulation in generated images across diverse artistic styles. As shown in Figure 1, these methods not only fail + +to achieve effective shadow control but also struggle to preserve non-realistic artistic elements such as unique tones in stylized artwork, vibrant color palettes, and subject identity. + +This limitation partially arises from restricted diversity and quality in training data. Real-world OLAT (one-light-at-a-time) data by light stage system is prohibitively expensive to collect and inherently limited in diversity. Real-world OLAT datasets primarily capture a small group of real-world subjects, restricting variations in skin tones and facial features while lacking the necessary variety to handle artistic styles. Synthetic data, on the other hand, typically lacks the quality compared to real-world OLAT data. + +These limitations in training data have led researchers to incorporate diffusion models with their rich prior information, as seen in methods like DiFaReli [35] and IC-Light [60]. DiFaReli attempts to fine-tune diffusion models on synthetic data but fails to unlock the models' full capabilities for diverse artistic styles. IC-Light achieves better performance by scaling up to 10 million training examples (combining real and synthetic data), but struggles with identity preservation and requires substantial computational resources (8 H100 GPUs for a week), making its training pipeline impractical to many researchers. Table 1 summarizes the key aspects and computational resources required for these editing methods. + +These challenges motivate us to ask a question: Can we achieve effective shadow manipulation on generated portraits with diverse styles using few synthetic data and computational resources? Recent studies have found that well-trained diffusion models implicitly encode rich information about various visual attributes [12] like depth, normal [14], Shading [26], and human pose [30]. This suggests that shadow information for portraits might similarly be embedded within these models, raising a further question: is there an efficient way to access and utilize this shadow-related prior knowledge without extensive retraining? + +# 1.2. Key Technical Insight and Approach + +To address the question of efficiently accessing shadow information in diffusion models, we present Shadow Director: a method for extracting and manipulating shadow information embedded within diffusion models during generation. + +Our approach is based on the hypothesis that well-trained diffusion models already encode shadow information within their intermediate latent features. Although this information exists implicitly, we found that a trained shadow estimation network can effectively access it. Specifically, we train a small shadow estimation network that extracts shadow maps from the diffusion model's noisy intermediate features during denoising. Shadow control is implemented through an optimization process during image generation: we calculate the difference between the current estimated shadow (from noisy latent features) and our target shadow, then optimize + +
SwitchLight[24]IC-Light[60]DiFaReli[35]Ours
Typeeditingeditingeditingconditional generation
Philosophyneural renderingscaled datasetdiffusion modelattribute reveal
Synthetic Data involved✓✓✓✓
NO Real-world OLAT✓✓
Diffusion Model✓✓✓
Data Quantities (k)30+10,000+605.7
GPU32-A60008-H1001-V100s2-A6000
Training Time1 week140 hours8 days8 hours
+ +Table 1. Comparison with accessible shadow manipulation methods. Key advantages of our approach: (1) Better adaptation to generated images through conditional generation instead of postprocessing, (2) No real-world OLAT data required, and (3) Minimal data quantity needed (only 5.7k samples). Such resource-efficient design proves that our design based on attribute reveal is promising. It enables researchers with limited data and computing resources to more easily develop better shadow manipulation methods in the future. + +the latent features to achieve the desired shadow while preserving identity. + +Unlike editing methods that work as post-processing, Shadow Director enables parametric and intuitive shadow control directly during the portrait generation process, preserving artistic integrity across diverse styles. Our experiments show that Shadow Director effectively extracts shadow information from diffusion models while requiring only a few thousand synthetic examples of limited quality and just two A6000 GPUs with a few hours of training. This resource-efficient design philosophy demonstrates that leveraging information already present in diffusion models can significantly reduce dependence on expensive light-stage data collection, making it feasible for researchers with limited data and computing resources to develop better shadow manipulation methods. + +In summary, our contributions include: + +- We propose Shadow Director, a novel approach that accesses and manipulates implicit shadow information embedded in the latent space during diffusion model denoising, fundamentally different from editing methods. +- Our method achieves effective shadow control using only a small synthetic dataset and a few hours of training, demonstrating remarkable data efficiency without depending on costly light-stage data. +- Shadow Director enables intuitive and parametric control over multiple shadow attributes while preserving identity. Despite training only on synthetic data built on real-world identities, it generalizes to diverse artistic styles where editing methods fail. + +# 2. Related Work + +# 2.1. Portrait Relighting via Neural Networks + +Portrait relighting has been extensively explored in 2D [18, 19, 22, 24, 33, 34, 38, 41, 42, 51, 52, 56, 59, 61], and 3D [4, 5, 32, 37, 44, 46, 51, 62], often relying on inverse + +rendering [3, 39] or light-stage data [10]. Physics-based methods [24, 33] decompose albedo, normal, and shading but fail to capture complex effects like subsurface scattering [11, 25, 31]. Diffusion-based relighting approaches [6, 20, 22, 38, 56, 59] use HDR priors or synthetic datasets but remain constrained by domain gaps [42, 43, 55]. Models like DiffRelight [15] require per-subject fine-tuning for 3D. While SwitchLight [24], IC-Light [59], and Relightful Harmonization [38] mitigate gaps through real-image pretraining, pseudo-labeling, and large-scale augmentation. + +# 2.2. Diffusion Models for Lighting Manipulation + +With the rapid advancement of diffusion models, a wide range of image and video tasks have seen significant progress [8, 9, 17, 21, 40, 49, 50]. While primarily designed for generative tasks, diffusion models implicitly encode a wealth of structural and semantic information within their intermediate representations[29, 30, 47, 57], which can be leveraged for downstream applications. Moreover, numerous studies have shown that diffusion models exhibit strong capabilities in estimating and recovering intrinsic attributes such as depth [23], surface normals[14], and 3D structure[27], which are valuable for lighting manipulation. Recently, researchers have begun exploring how lighting-related information embedded within diffusion models can be utilized [2, 12]. Works such as [26, 53] have demonstrated the feasibility of training diffusion models for illumination manipulation in both indoor and outdoor scenes. These studies collectively suggest that well-trained diffusion models inherently encode shadow information. This raises the possibility of accessing and utilizing this hidden shadow information to enable shadow control for generated images across diverse artistic styles. + +# 3. Method + +The key challenge in our approach is accessing and manipulating shadow information embedded within diffusion models during the denoising process, while preserving identity and artistic style. Our solution, Shadow Director, extracts shadow information from UNet's features and enables intuitive user control through test-time optimization on diffusion model's latent feature maps. What distinguishes our approach is the ability to reveal and manipulate implicit shadow information during generation with minimal training resources. Sec. 3.1 details the design of Shadow Director for accessing latent shadow information. Sec. 3.2 explains our synthetic training dataset. + +# 3.1. Shadow Director + +Module Overview. As shown in Figure 2, Shadow Director comprises two key components: a Shadow-Depth (SD) Estimator and an Identity (ID) Estimator. Both operate on the same UNet's feature maps during denoising. The SD + +Estimator extracts 2D shadow and depth maps to enable shadow manipulation, while the ID Estimator produces feature embeddings (ID embeddings) to enable identity preservation. Both estimators are implemented as compact neural networks, with architecture details in Appendix B. + +Training of Shadow Director. Both estimators are trained independently on our synthetic dataset. For the SD Estimator, at each training iteration, we generate a noisy latent feature by adding random noise to the clean latent feature of a relit image. This noisy latent feature is fed into the UNet, and internal features are extracted for shadow and depth estimation. The SD Estimator is trained to minimize $\mathcal{L}_{\mathrm{SD}} = \mathcal{L}_{\mathrm{L1}}(S_{\mathrm{pred}}, S_{\mathrm{gt}}) + \mathcal{L}_{\mathrm{L1}}(D_{\mathrm{pred}}, D_{\mathrm{gt}})$ , where $S$ and $D$ represent shadow and depth maps respectively. For the ID Estimator, each training iteration requires three images: an original image with its original lighting, a same-identity image with different lighting, and a different-identity image. Similar to SD-Estimator training, we generate noisy latent features by adding random noise to the clean latent features of these three images. Their corresponding ID embeddings are then extracted independently by the ID-Estimator. We apply a triplet loss (details in Appendix Fig.13) [7, 13, 30] to enforce that embeddings of the same identity become closer while embeddings of different identities are pushed apart. This training approach enables the ID Estimator to maintain consistent identity representations despite lighting variations, ensuring our Shadow Director preserves the subject's identity. We train this ID-Estimator on our synthetic dataset. + +Enable Shadow Control. Shadow control is achieved through test-time optimization at a selected early denoising step. We pause denoising and optimize only the UNet's input tensor (noisy latent feature, fire icon in Fig. 2). Before optimization, a single forward pass extracts (i) reference identity embeddings $I_{\mathrm{ref}}$ . Also, (ii) the user-defined target shadow map $S_{\mathrm{target}}$ via a binary mask (Fig. 3a) or depth-based ray casting (Fig. 3b). Users can adjust three aspects of the shadow: intensity (via latent optimization strength), shape & placement (via mask), and light position (via ray casting). + +Optimization Details. During latent optimization, only the UNet's input tensor $x_{e}$ (noisy latent feature map) is estimizable; all network parameters remain frozen. At the selected early denoising step, we first extract the internal feature + +$$ +h = f e t c h (\mathrm {U N e t} (x _ {e})), +$$ + +and then obtain the shadow and identity estimates + +$$ +S = \operatorname {S D} (h), \quad I = \operatorname {I D} (h). +$$ + +![](images/d24d50643045f0944ce9589abb4e786fff7d835b8328074d1ce0a2621f3817c5.jpg) +Figure 2. Shadow control pipeline for image generation. Our approach consists of three main components: (1) User Interface (left), which provides intuitive controls for shadow strength, directional light position, and shadow shape; (2) Diffusion Model with Shadow Control (middle), where latent features are optimized at selected denoising steps; and (3) Shadow Director (right), which extracts shadow and identity attributes from UNet internal features using two estimators. Shadow Director is trained to infer these attributes from Unet's noisy feature maps. Shadow control is achieved through test-time optimization on the noisy latent features (the U-Net input marked with a fire symbol). By applying this optimization at an early denoising step, we gain greater freedom in manipulating shadows during image generation. Before latent optimization begins, both estimators perform an initial forward pass once (dashed lines) to obtain the user-defined target shadow and reference identity embedding. The shadow acquisition process is detailed in Figure 4. During latent optimization, the noisy latent features are guided to match the user-defined target shape while minimizing changes to the identity embeddings. Notably, the only estimable component in the pipeline is the noisy tent feature at the selected denoising step. Further architectural details of the estimators and feature extraction are provided in Appendix B. + +![](images/ba7f17169c7bb90e24bd1b0fedc1d27156015e67096a9ab6855a598a24db8e3a.jpg) +Figure 3. Two customization options for shadow maps, applied before latent optimization. (a) Shadow placement and shape: A user-defined binary mask is applied to the estimated shadow map. Masked regions become darker in the customized shadow, explicitly defining shadow areas. (b) Shadow synthesis through directional lighting: Using the estimated depth map and user-specified directional light position, we implement ray casting to generate geometrically consistent shadows. Users select only one of these two methods. Detail of ray casting is presented in Appendix C.1. + +We perform few iterations of gradient descent on $x_{e}$ : at each iteration, we compute + +$$ +\mathcal {L} _ {\text {s h a d o w}} = \| S - S _ {\text {t a r g e t}} \| _ {1}, \quad \mathcal {L} _ {\text {i d e n t i t y}} = 1 - \cos (I, I _ {\text {r e f}}), +$$ + +and update + +$$ +x _ {e} \leftarrow x _ {e} - \alpha \nabla_ {x _ {e}} \left(\lambda_ {\text {s h a d o w}} \mathcal {L} _ {\text {s h a d o w}} + \lambda_ {\text {i d e n t i t y}} \mathcal {L} _ {\text {i d e n t i t y}}\right). +$$ + +After latent optimization, we resume denoising to produce the final image with the desired shadow. Notably, we never decode or use intermediate noisy RGB images via the VAE; all optimization remains in the latent feature space. + +# 3.2. Synthetic Training Dataset + +As shown in Figure 4, our synthetic dataset makes Shadow Director a practical and accessible solution for broader researchers. We construct this dataset using the CelebA + +![](images/af2d3b274ad673aef492f2c1a3a33a87d20cbf0c6c49348b16784408082e3494.jpg) +Figure 4. Samples of Our Synthetic Dataset. Data pairs: relit images (top row), shadow maps (middle row), and depth maps (bottom row). Unlike IC-Light requiring 10 million samples, our approach needs only a few thousand paired synthetic examples. These are generated using GeomConsistentFR [19]. Despite limited photorealism in shadow, this dataset proves sufficient for accessing shadow information embedded within diffusion models. This demonstrates a promising research direction: reducing dependency on expensive light-stage data while focusing on revealing lighting information already hidden in diffusion models. + +dataset [28], generating six lighting variations per identity with GeomConsistentFR [19]. Specifically, for each subject, we randomly sample six light source positions within a circular frontal region of the face, with each light directed towards the facial center, and synthesize the corresponding relit images. This design enables training our ID-Estimator to focus solely on identity features while disregarding lighting variations. Since GeomConsistentFR itself is trained + +![](images/cb2948fffa324c2b891f818902c531e3558d6a4bc3c13b3ea3ac1932dda3784f.jpg) + +![](images/44885fcd85ceab1037f33466f02a4f11a6554af703dc63dc095594afe85cad62.jpg) +Figure 5. Shadow intensity control on generated portraits across diverse styles. The top two rows demonstrate gradual shadow intensity control, while the bottom four rows highlight strong and weak shadow variations for better visual comparison. Shadow Director enables parametric control over shadow strength, ranging from weak to strong, while preserving both identity and artistic integrity. + +on synthetic data, the generated relit images exhibit limited photorealism. However, our experiments show that this dataset is sufficient for Shadow Director to extract and utilize the rich shadow information already encoded in diffusion models. In this work, we focus on maximizing the potential of limited but accessible synthetic data in conjunction with a well-trained diffusion model. + +# 4. Experiment + +Additional qualitative results demonstrating Shadow Director's control are provided in Appendix D. Detailed implementation is provided in Appendix C. + +![](images/e13f7b5e204c869a4fb0d608fc203bc305a5d5e82f49cf52a1846e43289825e4.jpg) +Figure 6. Shadow shape control with user-defined masks on diverse portrait images. Shadow Director enables precise control over shadow shapes and placement using user-defined masks (shown as gray overlays). + +# 4.1. Settings of Training and Inference + +We implement our pipeline based on Stable Diffusion XL (SDXL) 1.0. For the synthetic dataset, we randomly select 1,000 identities from the CelebA dataset, rendering each with 6 different lighting conditions using GeomConstantFR. This generates a total of 6,000 synthetic images, which we split into 5,700 for training and 300 for validation to evaluate the SD Estimator's prediction accuracy. Both the SD Estimator and ID Estimator are trained on a single NVIDIA A6000 GPU, with each estimator taking approximately 8 hours to train. We use the Adam optimizer with a learning rate of 1e-4 and a batch size of 8. For inference-time shadow control, we begin latent feature optimization at denoising step 40 out of 100 (corresponding to $t = 0.6$ ). We use the Adam optimizer with a learning rate of 2e-4 for latent feature optimization. Our method adds only about 20 percent additional computation time compared to standard SDXL inference. + +# 4.2. Controlling Shadow Strength + +Our approach enables users to gradually adjust shadow intensity while preserving surrounding lighting conditions. Unlike text-prompt engineering, which lacks precise control over intensity changes, our provides fine-intuitive control over shadow strength. As shown in Fig.5, our method achieves modulation of shadow strength through latent optimization during inference time. Shadow intensity correlates + +![](images/e1f07fd330c4a4a8afb8e0f47964a8ad8e708fabb43e863f834386d8905f8248.jpg) +Figure 7. Shadow Synthesis by Controlling Lighting Direction: Comparison with Diffusion-Based Methods. Our approach (leftmost 5 columns) consistently preserves identity and artistic style while providing varied shadow control based on specified lighting positions. In contrast, diffusion-based editing methods IC-Light (columns 6-7) and DiFaRei (columns 8-9) show significant identity shifts and style inconsistencies compared to the original portraits (rightmost column). Results are shown across three different portrait styles: realistic (top row), super-realistic (middle row), and cartoon (bottom row). Our method maintains vibrant colors, facial features, and artistic elements while providing intuitive shadow control by directional lighting position. Please see Appendix D for more lighting positions. + +directly with the number of optimization iterations applied, allowing for gradual adjustments based on user preference. + +# 4.3. Controlling Shadow Placement and Shape + +Our method offers intuitive control over shadow placement and shape through user-defined shadow mask. In contrast to existing methods that generate unrealistic blended synthetic shadows, our approach ensures natural shadow placement and integration. Results in Fig.10 demonstrate controlled shadow placement using custom shadow masks. + +# 4.4. Controlling Directional Light Position + +Our method allows users to specify the 3D position of the directional light source for portrait relighting. As shown in Fig. 7, Shadow Director generates geometrically consistent shadows while preserving identity and artistic style. In contrast, other diffusion-based methods such as IC-Light and DiFaReli struggle with effective shadow control and often introduce identity shifts. + +To demonstrate our method's performance across a broad range of portraits, we randomly generate 800 portraits using text prompts (detailed in Appendix E) without specifying lighting conditions. For each portrait, all methods generate two relit images under left and right directional lighting correspondingly. + +For qualitative evaluation, we present results in Fig. 8. Comparisons are made against IC-Light [60], SwitchLight [24], Hou et al. [19], and DiFaReli [35]. For quantitative evaluation, we partially follow the protocols in [6] and [38], assessing both objective metrics (Table 2) and user studies (Table 3). Since ground-truth relit images are unavailable, non-reference image quality assessment + +methods are used to measure realism and image fidelity. CLIP-IQA+ [48], NIMA [45], and ARNIQA [1] assess image authenticity to ensure that shadow manipulation does not degrade perceptual quality. Following [6], CLIP Vision Score (CVS) is used to measure identity preservation through cosine similarity between the clip embedding [36] of source and relit images. CLIP Vision-Text Alignment (CVTA) evaluates how well relit images align with the augmented text prompts specifying "left light" or "right light." To further validate the results, we conduct user studies (Table 3) to assess shadow consistency and identity preservation through subjective evaluation. 40 users and 20 samples involved. For each sample, order of methods is random. + +# 4.5. Ablation Study + +We further investigate the necessity of each component in Shadow Director through a series of ablation studies. These studies are summarized in Table 4, with corresponding quantitative results presented in Table 5. + +Optimal Denoising Step for Shadow Control. We investigate whether shadow control is most effective during early/middle denoising steps, later steps, or only at the final step. Our experiments confirm that applying shadow control during early and middle denoising steps (t=0.5-0.7) provides the optimal balance between shadow manipulation flexibility and image quality preservation, outperforming later-stage or final-step interventions. + +Input of Shadow Estimator. We examine which feature source provides the most effective shadow information by comparing three options: UNet input, UNet internal features, and UNet output. Our experiments confirm that UNet + +![](images/dbde74ca9383be1f69ec973f349cdfef1519bb520e33e84f554103275f21bdc4.jpg) +Figure 8. Shadow Synthesis by Controlling Lighting Direction. Comparison of portrait relighting across different editing methods generated portrait. Each row corresponds to a different method, while each column maintains left lighting direction for easy comparison. + +Table 2. Quantitative results on 800 unseen portrait image generated from text prompts. + +
MetricOriHou 2022 [19]DiFaReLi [35]IC-Light [60]SwitchLight [24]Ours
CVTA ↑0.33070.26290.24660.26060.25200.2692
CVS ↑1.00000.93860.90490.91400.89450.9460
CLIPIQA+ ↑0.73660.37470.39060.41850.38760.4484
NIMA ↑6.37385.01955.23705.71935.32195.7735
ARNIQA ↑0.68950.46030.48310.52360.44420.5480
+ +Table 3. User study for preference. $2.44\%$ selected 'None' + +
OursIC-LightSwitchLightDiFaReliHou
Preference Rate45.69%27.44%20.46%1.86%2.09%
+ +internal features yield better performance due to their richer information. Consistent with findings in recent studies [30] + +Latent-space vs. Noisy RGB-space Estimation. This study compares our latent-space shadow estimation approach against an alternative RGB-space pipeline. The alternative first generates noisy RGB images from the UNet's output at early denoising steps, then applies an RGB-based + +shadow estimator (like our data generation method Geom-ConstantFR) to obtain noisy shadow and depth maps. After acquiring the user-defined shadow through a similar process, the loss between this target and the estimated noisy shadow in RGB space is backpropagated through both the RGB estimator and UNet to optimize the latent feature map. Although conceptually similar to our approach, this RGB-space alternative introduces reliability issues during latent optimization. Our experiments demonstrate that latent-space estimation achieves better shadow quality and identity preservation, confirming our design choice to operate directly on UNet's internal feature maps rather than noisy RGB outputs from denoising step. + +Necessity of ID Embedding for ID Preservation. We demonstrate why our dedicated ID embedding approach is superior to the simpler alternative of applying L1 loss directly on latent features. In this alternative approach, + +![](images/d9c5c12b1d18b5fb3c58e2320c3ed31db5772fddf95542e5e373b0bf905a3d74.jpg) + +Table 4. Necessity of Design in Shadow Director. + +
Feature Extraction LocationDenoising Step for Latent OptimConstraint Choice
Unet's InternalUnet's OutputEarly and MiddleLatterLast OneSDID
(a) Ours✓-✓--SD-EstimatorID-Estimator
Ablation Study 1: Optimal Denoising Step for Shadow Control
(b)✓--✓-SD-EstimatorID-Estimator
(c)✓---✓SD-EstimatorID-Estimator
Ablation Study 2: Input of Shadow Estimator
(d)-✓✓--SD-EstimatorID-Estimator
Ablation Study 3: Latent-space vs. Noisy RGB-space Estimation
(e)✓(for Ours-ID)✓(for RGB-SD)---RGB-EstimatorID-Estimator
Ablation Study 4: Necessity of ID Embedding for ID Preservation
(f)✓----SD-EstimatorL1 Loss
(g)✓(for Ours-SD)✓(for L1-ID)---SD-EstimatorL1 Loss
+ +Table 5. Necessity of Design in Shadow Director. + +
Metric(a) OursMethod (b)Method (c)Method (d)Method (e)Method (f)Method (g)
CVTA ↑0.26920.24100.23560.21970.19750.15560.1485
CVS ↑0.94600.93250.93200.89450.81730.76850.7679
CLIPIQA+ ↑0.44840.43250.43920.36390.32200.28730.2682
+ +the SD-Estimator remains, but identity preservation is attempted by constraining the optimized UNet input/output features to remain close to their original values via L1 distance. Unlike this direct feature constraint, our ID embedding network specifically captures meaningful identity characteristics while allowing shadow-relevant features to change. Our experiments confirm that specialized identity embeddings are essential for maintaining consistent identity during shadow manipulation, as direct feature constraints either limit shadow flexibility or fail to preserve key identity elements. + +Necessity of ID-Estimator. Without the ID Estimator to constrain latent optimization, the generated image tends to overemphasize shadow optimization, often resulting in unexpected textures and identity distortions. As shown in Fig.9, optimizing for strong shadows without identity preservation loss leads to significant unintended artifacts. + +# 5. Discussion + +Relation to Shadow Removal. Shadow Director does not perform shadow removal on the original image, as it does not reconstruct occluded details. Instead, it is a conditional generation framework that guides the diffusion model to generate or suppress shadows in specific region during synthesis. Unlike shadow removal methods that recover lost information, Shadow Director conditions the model to produce lighting-consistent images. For example, in the fifth column of Fig. 8, the left cheek shadow disappears not due to removal but because the model, conditioned on new lighting, generates an image where the shadow no longer forms. This distinction highlights Shadow Director's role in controlling shadow generation rather than removing it. + +Occlusion handling and object relighting? Yes. Our method handles occlusions (hair, hats, glasses) without retraining. It also generalizes to simple object relighting without retraining, though complex materials and geometry re + +![](images/5257ed7d934de1127bd1ac4b008c6c4aa343d073d782871a015560bc5afdfd8c.jpg) +Figure 9. Necessity of our ID-Estimator and failure of naive prompt engineering. The first row shows Prompt Engineering fails to produce desired shadows. The second row highlights artifacts and identity inconsistencies without our ID-Estimator. The third row (Ours) demonstrates that our full method achieves effective shadow manipulation while preserving identity and style. + +![](images/5fe1913cc64e0c9069ef6cc642682d8a09c86b326a07813dbb62f11e87a23085.jpg) +Figure 10. Limitations and Future Work. (a) Lighting effects in prompts (neon lighting) may override Shadow Director's control. (b) Training on CelebA, which consists mostly of simple, straight-on portraits, makes it difficult to preserve intricate clothing details in more complex outfits. (c) The model does not handle lighting temperature, which may lead to color tone inconsistencies. + +main challenging. For full details and results, please check Appendix D.1 and D.2. + +Limitation. Shadow Director is trained on CelebA, which mainly consists of close-up, straight-on portraits with simple clothing, making intricate garment preservation in full-body images challenging. Expanding dataset diversity or constraining latent optimization could help mitigate this. Additionally, strong lighting effects in text prompts, such as neon lighting, may override Shadow Director's control, which could be improved through refined hyperparameter tuning. The model also lacks explicit lighting temperature control, sometimes causing color tone inconsistencies. Despite these challenges, Shadow Director demonstrates that effective shadow control can be achieved with accessible training resources, paving the way for improvements with broader datasets and enhanced lighting models. + +# 6. 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Angelina Uy\*1 Donglai Xiang1 Hao Su4 + +Sanja Fidler1,2,3 Nicholas Sharp1 Jun Gao1,2,3 + +$^{1}$ NVIDIA $^{2}$ University of Toronto $^{3}$ Vector Institute $^{4}$ UCSD + +![](images/f450e2985291b869bc2cf17e4f0ebd643f69b23f54ba58177a10dcb66e0951c7.jpg) + +![](images/32354b5d9e673338e2c5c817f4c78724e792f439f4323b23c28130c0bbf3ad98.jpg) + +![](images/55ad139250eb7c58c275b35b72ca6ca85106f1a649ceab808fac0e202146580e.jpg) + +![](images/1e2ac7769c125c48ff22ec2c751952b50d4e59456f5a8694a84deb9ee047344b.jpg) + +![](images/fefc7f8cd2eaf6021877d9c9922fff62245959a8ccf0d030fcb01ba0bb42632b.jpg) + +![](images/69ed65a0331f686865b1aceef0ff5531048e4d0eced84442ddcaab64fa5c96a4.jpg) +AI Generated + +![](images/0c517ff8787c072e63688fcd12d14f9dbd8df06ac370ef09e193eb8e655ec4f8.jpg) +Input Modalities +Mechanical Parts + +![](images/f712c48db67e69daf8e2f2f4758b487973293b87778cb8941ba15813cca656ca.jpg) +3D Gaussian Splating + +![](images/f8ced3a935ef22c6b33786a8e815c281b5985af116c6bb4f5f50ce1446bb2cb9.jpg) + +![](images/5a5b1a8c45aba51d1ab6b8f72eb37eab966ae2c46db940f5580f61764cabbdab.jpg) +Cosegmentation + +![](images/3176e0d26af4b7f7bc983b42bb8a601cd021fb2debda7b22dc339b64f52ce358.jpg) +Downstream Applications +Interactive Selection +Figure 1. We propose PARTFIELD, a feedforward model that predicts part-based feature fields for 3D shapes. The learned features can be clustered to yield a high-quality part decomposition, and our method outperforms the latest open-world 3D part segmentation approaches in both quality and speed. PARTFIELD can be applied to a wide variety of inputs in terms of modality, semantic class, and style. The learned feature field exhibits consistency across shapes, enabling applications such as cosegmentation, interactive selection, and correspondence. + +![](images/615e346ed3dd52dbe866f52d3422d5376f3e63cdbe8679bcfe6001c1c668cf46.jpg) +Correspondence + +# Abstract + +We propose PartField, a feedforward approach for learning part-based 3D features, which captures the general concept of parts and their hierarchy without relying on predefined templates or text-based names, and can be applied to open-world 3D shapes across various modalities. PartField requires only a 3D feedforward pass at inference time, significantly improving runtime and robustness compared to prior approaches. Our model is trained by distilling 2D and 3D part proposals from a mix of labeled datasets and image segmentations on large unsupervised datasets, via a contrastive learning formulation. It produces a continuous feature field which can be clustered to yield a hierarchical part decomposition. Comparisons show that PartField is up to $20\%$ more accurate and often orders of magnitude faster than other recent class-agnostic part-segmentation methods. Beyond single-shape part decomposition, consistency in the + +learned field emerges across shapes, enabling tasks such as co-segmentation and correspondence, which we demonstrate in several applications of these general-purpose, hierarchical, and consistent 3D feature fields. Check our Webpage! https://research.nvidia.com/labs/toronto-ai/partfield-release/ + +# 1. Introduction + +Human visual perception parses 3D shapes into parts based on their geometric structure, semantics, mobility, or functionality, while generalizing easily to new shapes. Such part-level understanding is critical to many applications, including 3D shape editing, physical simulation, robotic manipulation, and geometry processing. To empower machines with similar capabilities, 3D part segmentation has been studied as a standard task in computer vision [46, 55, 61], yet it remains challenging. + +The first key challenge is data. Widely-adopted supervised learning-based methods [17, 46, 47, 55, 58, 61] are limited by the lack of scale and diversity in 3D part + +annotated datasets [38, 62], leading to poor generalization to unseen categories of shapes. Following the success of large 2D image-based foundation models such as Segment Anything [24, 28, 51], recent works have explored leveraging 2D priors to circumvent the reliance on 3D part annotations, and enabling open-world capability. However, most of these approaches [12, 21, 68] involve per-shape optimization. This requires a multi-step pipeline at inference time—rendering and segmenting multiple views, then fusing or distilling those segmentations into 3D—leading to lengthy runtimes (minutes to hours) and suffering from multi-view inconsistencies and noisy 2D predictions from 2D foundation models. In contrast, we aim to provide fast, direct predictions while generalizing across open-world shapes. + +Another fundamental challenge is the definition of a "part". For example, at what granularity should parts be defined? Is a whole hand a part, or is each finger a separate part? Many past approaches [46, 55, 61] including some recent open-world methods [31, 36] attempt to match predefined part templates or text prompts. However, committing to a predefined notion of parts impedes training at scale, as different data is inevitably inconsistent in part labels. Text prompts come with their own complications: a single part might be referred to in multiple ways, and geometric parts may have no obvious language description. Instead, we aim to learn from large-scale data without committing to any single notion of parts. We want our model to cover a wide range of possible parts and multi-level decompositions, allowing applications to define the desired granularity and semantics. + +This work proposes the PARTFIELD model for learning 3D parts and their hierarchy. Given a 3D shape as input, PARTFIELD predicts a continuous 3D feature field in a feedforward manner. Instead of relying on part templates or text, the distance among PARTFIELD features implies the notion of parts: points with similar features are more likely to belong to the same part. The learned features can be queried continuously at any location, and can then be clustered to yield a part-aware, hierarchical decomposition of the shape, or even used for other downstream applications. + +PARTFIELD is trained to match part proposals either predicted as image masks from existing 2D foundation models, or as explicit 3D supervision from existing datasets. There are no constraints on these part proposals; they can be defined based on semantic, geometric, or other criteria, and at any level of granularity. We leverage a carefully-chosen contrastive objective, encouraging samples from the same part to be more similar than samples for distinct parts — this sidesteps the challenges of varying part granularity and differing notions of parts, enabling training on large-scale open-world data. By fitting a 3D-native feedforward model, PARTFIELD not only achieves dramatically faster inference, but also gains robustness to inconsistent and noisy labels. While we have not explicitly incorporated cross-shape super + +![](images/95738d27e552e74e108d34139060f61aeda7bf7eb419c80b85eecb8a15360c3b.jpg) +Figure 2. PARTFIELD part segmentations across various 3D input modalities. + +vision, we observe that our model emerges a feature space that is consistent across shapes—a useful property for downstream applications. + +Our approach shares a similar philosophy—leveraging contrastive embedding learning and distilling image-space segmentations and features—with many recent or concurrent works on part segmentation [12, 21, 30, 68, 72], as well as numerous works on scene-level segmentation (see Section 2 for a full list). However, we show that adapting and extending these techniques into a feedforward model trained at scale in an open-world setting has significant benefits in quality, speed, and utility. We evaluate PARTFIELD against the latest baselines on the class-agnostic part segmentation task, showing performance improvements of more than $20\%$ while being an order of magnitude faster. As shown in Figure 1, this enables high-quality hierarchical part decomposition. The resulting model can be applied across modalities including in-the-wild meshes, point clouds, and 3D Gaussian splats (Figure 2). The cross-shape consistency in the feature field enables usages beyond part segmentation, such as co-segmentation, selection, and correspondence. The key advantages of PARTFIELD are summarized as: + +- We train a feedforward, 3D-native model that enables fast inference, robust performance, and large-scale priors. +- PARTFIELD learns a versatile concept of 3D parts, applicable to 3D shapes across modalities and sources. +- We utilize triplet-based contrastive learning to sidestep inconsistencies in the notion of parts, enabling training at scale from diverse 2D and 3D data. +- PARTFIELD features are consistent across shapes, yield promising cross-shape applications as a bonus, such as correspondence and co-segmentation. + +# 2. Related Work + +Traditional data-driven part segmentation approaches [17, 47, 58] typically predefine a part template, follow a super- + +vised learning pipeline, and suffer from the limited scale and diversity of 3D part-annotated datasets [38, 70]. Recently, open-world 3D segmentation has made significant progress, largely due to the success of 2D image foundation models [23, 29, 49, 50]. These methods can generally be divided into the following categories according to their tasks: + +Point-Prompt 3D Segmentation Inspired by 2D SAM [24], some methods [27, 78] train feedforward models that take 3D points as prompts to segment 3D parts. SAM2POINT [9] converts 3D input into videos and enables on-the-fly inference with SAM2 [51], which also supports point prompts. Our method addresses the more general problem of part-based feature learning and automatic hierarchical decomposition, and the learned field can also be applied to point-based interactive part selection. + +Text-Prompt 3D Segmentation To enable text-based 3D segmentation, many works [2, 22, 31] explore leveraging open-world 2D detectors by lifting and fusing predictions from multi-view rendering. Some works further explore combining both segmentation models and open-world detectors [1, 16, 56, 66, 75, 77]. Another strategy involves aligning the 3D feature space with the CLIP [49] text space, either through joint optimization with NeRF [20] or Gaussian Splatting [48]. Many works have also explored distilling text features into 3D networks for both scene segmentation [18, 44] and object segmentation [36, 57], applying lightweight fine-tuning on top of CLIP [74, 79], or using CLIP feature for retrieval [34, 53]. For 3D part segmentation, text prompts may not be ideal because many parts lack inherent semantic meaning. Instead, our work aims to learn from large-scale data what class-agnostic 3D parts could be, covering all possible parts—whether they are semantic or purely geometric. + +Class-Agnostic 3D Segmentation Many works leverage 2D SAM to achieve class-agnostic 3D segmentation. Instead of identifying and segmenting a single 3D part or object using a point prompt, they focus on segmenting or decomposing the entire input. For example, various methods have been developed to lift and merge multi-view 2D SAM prediction labels for both scene-level [8, 13, 40, 64, 65, 67, 71] and object-level [54] 3D segmentation. Some works attempt to train a feedforward scene segmentation model using SAM labels as pseudo-labels [15] or by distilling SAM features [45], but mainly focus on scene level segmentation. Other approaches explore marrying SAM with NeRF [3, 5, 7, 11, 21, 32, 72] or Gaussian Splatting [3, 14, 26, 52, 69, 76] by adding an additional feature field to distill features or masks from 2D SAM. A recent work, Part123 [30], integrates SAM into 3D reconstruction and enables part-aware single-image object generation. A line of traditional work also explores fine-grained 3D part segmentation models [35, 60, 73], but they are trained on closed-domain datasets and exhibit poor generalization to open-world scenarios. To the best of our + +knowledge, we are among the first to train a feedforward model that learns a feature field for open-world part decomposition. + +# 3. Method + +Given a 3D shape $S$ as input, PARTFIELD predicts a continuous 3D feature field that encodes the underlying structure of parts and their hierarchy, in a feedforward manner. As illustrated in Figure 3, this feature field maps any 3D point $\mathbf{p}$ to an $n$ -dimensional latent feature vector $f(\mathbf{p}; S): \mathbb{R}^3 \to \mathbb{R}^n$ . The concept of parts is modeled by the feature distance between any two points: if two points $\mathbf{p}_a$ and $\mathbf{p}_b$ belong to the same part, their features $f(\mathbf{p}_a; S)$ and $f(\mathbf{p}_b; S)$ should be close in the latent feature space. + +We first describe our data strategy, which involves collecting a diverse range of part proposals from multiple sources (Section 3.1). Next, we introduce our carefully chosen contrastive learning objective with hard negative mining, which captures multi-scale 3D parts and enhances training efficiency (Section 3.2). Finally, we present the architecture of our feedforward model (Section 3.3) and our inference strategy, which converts the learned part feature field into a hierarchical part decomposition (Section 3.4). + +# 3.1. Training Part Proposals and Point Triplets + +Part Proposals. We extract part proposals—which provide hints about which points should be grouped together to form a part—from both 2D and 3D data. Each part proposal $P$ labels a subset of the shape $P \subset S$ indicating that portion of the shape belongs to the same part. Note that we do not assume predefined part templates; therefore, the part proposals are not necessarily semantically associated. The proposals may come at any granularity and be defined by various criteria, such as geometry, semantics, or mobility. + +Specifically, for 2D proposals, we follow previous work to render multi-view RGB and normal images of 3D shapes from large-scale unlabeled datasets [6]. We then apply 2D foundation models (such as SAM2 [51]) to predict class-agnostic 2D masks, which are subsequently projected back onto the shape. We densely sample point prompts, and each mask generates a proposal. Note that proposals from multiple masks are likely to overlap, covering various levels of granularity. For 3D proposals, we leverage part annotations available in existing 3D datasets [39]. Again, proposals may overlap if the labels have a hierarchical structure. 2D and 3D proposals complement each other: 2D proposals from image foundation models enable training on large unlabeled datasets and equip our model with open-world capabilities, while 3D proposals offer complete supervision of interior structure and capture valuable human semantic annotations. + +3D Point Triplets. After obtaining part proposals, we sample triplets of 3D points from these proposals on the fly during training to apply a triplet-based contrastive loss. Specifically, for a given shape $S$ and part proposal $P$ on that shape, + +![](images/afe64bf5b4232eb9c5f34263565831ceaeb44bff09e266fd941a6a44d1940a5e.jpg) +Figure 3. We train a feedforward model that takes a point-sampled 3D shape as input (which could come from a mesh, Gaussian splats, or other representations) and predicts a feature field represented by a triplane. These features can then be clustered to generate parts at various scales. Our model is trained with a contrastive loss on both open-world data, distilled from image-space masks, which need not be consistent, and 3D supervision when available. + +![](images/1e7e25d216344fa8ae7392d2e2b669054eb0ec85a7143090e630f48ac84c6c16.jpg) +Figure 4. (Left) A point can belong to multiple parts at different scales. (Upper Right) Prior works [21, 68] utilize pull and push losses to directly minimize or maximize the feature distances between point pairs, requiring an additional scaling condition to learn point features at different scales. (Lower Right) Our method employs a triplet loss that only encourages the relative relations between points within a triplet, enabling self-contained features $(\mathrm{sim}(f(A), f(B)) > \mathrm{sim}(f(A), f(C)) > \mathrm{sim}(f(A), f(D)))$ that support multi-scale parts without need of scaling condition. + +we sample a collection of triples of 3D points $\{(\mathbf{p}_a, \mathbf{p}_b, \mathbf{p}_c)\}$ such that, within each triplet, points $\mathbf{p}_a$ and $\mathbf{p}_b$ come from the part proposal (i.e. $\mathbf{p}_a, \mathbf{p}_b \in P \subset S$ ), while $\mathbf{p}_c$ comes from outside the part proposal (i.e. $\mathbf{p}_c \in S \setminus P$ ). For 2D proposals, all points in the triplets are sampled from the visible 2D pixels of the shape in that view, then unprojected into 3D using the known camera pose and object depth. Note that this means a 2D mask only contributes supervision on the visible surface of a shape. For 3D proposals, points are sampled directly from the labeled 3D geometry, including the interior space of the shapes and parts. When forming triplets, the positive points $\mathbf{p}_a$ and $\mathbf{p}_b$ are uniformly sampled, while the negative points are selected using a mining strategy discussed later. + +# 3.2. Contrastive Learning with Negative Sampling + +The essential idea of a contrastive triplet loss is to encourage the positive triplet points $\mathbf{p}_a, \mathbf{p}_b$ within a part proposal to be close, while the negative point $\mathbf{p}_c$ should be distant. However, the hierarchical and scale-ambiguous nature of part labeling complicates the design and scaling of such a loss. Figure 4 illustrates how two equally valid part proposals can assign points either to the same part or to different parts, depending on their levels of granularity. Prior work has attempted to impose an explicit scale conditioning parameter on the space [21, 68], but setting this scale consistently across data and supervision sources can be challenging. + +Instead, we adopt a relative approach inspired by [4], + +which weakens the notion of supervision to simply encourage $\mathbf{p}_a$ to be closer to $\mathbf{p}_b$ than it is to $\mathbf{p}_c$ , and likewise for $\mathbf{p}_b$ . The contrastive loss becomes + +$$ +\begin{array}{l} \mathcal {L} = - \frac {1}{2} \left(\log \left(\frac {\operatorname {s i m} (f (\mathbf {p} _ {a}) , f (\mathbf {p} _ {b}))}{\operatorname {s i m} (f (\mathbf {p} _ {a}) , f (\mathbf {p} _ {b})) + \operatorname {s i m} (f (\mathbf {p} _ {a}) , f (\mathbf {p} _ {c}))}\right) + \right. \\ \left. \log \left(\frac {\operatorname {s i m} \left(f \left(\mathbf {p} _ {b}\right) , f \left(\mathbf {p} _ {a}\right)\right)}{\operatorname {s i m} \left(f \left(\mathbf {p} _ {b}\right) , f \left(\mathbf {p} _ {a}\right)\right) + \operatorname {s i m} \left(f \left(\mathbf {p} _ {b}\right) , f \left(\mathbf {p} _ {c}\right)\right)}\right)\right) \tag {1} \\ \end{array} +$$ + +where $\mathrm{sim}(f(\mathbf{p}_u), f(\mathbf{p}_v)) = \exp (\cos (f(\mathbf{p}_u), f(\mathbf{p}_v)) / \tau)$ represents the exponential of the cosine similarity between two point features, and $\tau$ is a learnable temperature. Related formulations have appeared in [12, 30, 72]. Unlike directly minimizing the feature distance, our approach avoids conflicts when handling multi-scale proposals, sidesteps the need for an explicit scaling condition, and enables training on large datasets from many sources. + +Hard Negative Sampling. In Section 3.1 we postponed the discussion of how to draw negative triplet samples $\mathbf{p}_c$ which do not belong to a particular part proposal. A naive approach is to uniformly draw samples from complement of the part proposal, but we find training efficiency is improved by instead sampling more challenging negative points near part boundaries. Precisely, we sample negative points using a mix of three strategies, all drawn from the complement of the part proposal, i.e. the unmasked visible surface in a 2D image view or the complement of a label in 3D. uniform negatives are uniformly sampled, 3D-hard prefers negatives closer to $\mathbf{p}_a$ in the Euclidean space, and feature-hard prefers negatives closer to $\mathbf{p}_a$ in feature space. For efficiency, we evaluate the contrastive loss in parallel over many negative samples $\mathbf{p}_c$ for each positive sample $\mathbf{p}_a$ , summing over the $\mathrm{sim}(\mathbf{p}_a,\mathbf{p}_c)$ term in the denominator of Equation 1. The combination of these samples improves accuracy, especially near part boundaries (see Table 3 and Figure 10). Please refer to the supplementary material for details of the sampling. + +# 3.3. Feedforward Model + +Unlike prior work [12, 21, 31, 68] that utilizes per-shape optimization to lift or distill 2D predictions or priors, we instead train a feedforward 3D model $f(\mathbf{p}, S)$ . This approach offers several benefits, including: (a) fast inference; (b) a consistent and complete 3D output feature field that smoothly extends + +![](images/5743424bb693c99c00af7ac77e862f5d5df96a740838fd2c69d8110ab06f0f18.jpg) +Figure 5. Qualitative comparison of class-agnostic segmentation on the PartObjaverse-Tiny dataset [68]. The baselines include Find3D [36], PartSLIP [31], Ultrametric Feature Field [12], SAMesh [54], and SAMpart3D [68]. Each color represents a different part. + +to the shape interior; (c) robustness against noisy and inconsistent part proposals, especially from 2D models; and (d) a unified feature space that naturally correlates across shapes, enabling additional downstream uses. + +Architecture. Figure 3 shows the architecture of our model. Input shapes, which may come as clean or in-the-wild meshes, point clouds, or even Gaussian particles [19] are sampled to a 3D point cloud. This point cloud is used as input to the model, which outputs a feature field encoded as a triplane that can be evaluated at any spatial location. The model consists of two main components. First, a PVCNN [33] encoder extracts per-point features, which are then orthogonally projected via mean-reduction onto three axis-aligned 2D planes as an initial triplane representation. These triplanes are then downsampled by a 2D CNN, flattened, passed to a transformer, then upsampled back to triplanes via a transposed 2D CNN. Finally, for any 3D query, we retrieve and sum its corresponding features from the triplanes to evaluate the feature field for that point. Additionally, we incorporate an SDF decoding branch. For any query point, the corresponding triplane features are passed through an MLP to decode the SDF value at that location. This branch is supervised using an L2 loss on the ground-truth SDF of the training shape. We find that this auxiliary reconstruction branch improves overall model performance. + +# 3.4. Inference and Clustering + +At inference, we apply the trained neural network once to generate the feature field triplanes, then sample part features as-desired, e.g. at each face of a potentially high-resolution + +input mesh or even on the interior of a shape. For mesh-based decomposition, we densely sample points from each face and use the average of these point features as the face feature. Although our network takes a 3D point cloud as input, we emphasize that it can also be applied to other 3D modalities (Figure 2). For example, the 3D points may originate from 3D Gaussians or be sampled from a mesh surface. + +We can then apply off-the-shelf clustering algorithms to obtain a part-aware decomposition of the 3D shape. Different settings may motivate different clustering strategies: $k$ -means clustering is simple and fast, but agglomerative clustering yields crisp results on mesh connectivity. Unless otherwise stated, we apply agglomerative clustering to mesh faces on the connectivity induced by face adjacency. The resulting hierarchical tree of parts can be leveraged in interactive applications, e.g. in manual shape editing or rigging where users can adaptively select the branches that require further decomposition. + +# 4. Experiments + +# 4.1. Implementation Details + +Training Datasets. We train our PARTFIELD on the Objaverse [6] and PartNet [39] datasets. For Objaverse, we filter out low-quality data (e.g., LiDAR scans) and use the remaining approximately 340k shapes. For each shape, we render RGB and normal maps from six randomly sampled viewpoints, and feed each image into SAM2 [51] for mask prediction. For each image, we densely sample a $32 \times 32$ grid of points as point prompts, generating 2D part proposals at various granularities. The PartNet dataset contains around + +Table 1. Quantitative evaluation of class-agnostic part segmentation on PartObjverse-Tiny [68] dataset. We use instance-level labels and report mean IoU. + +
MethodPropertyPer Caetgory mIoUAverageRuntime
feed-forwardmulti-scale feat fieldtext-input freeHuman-ShapeAnimalsDaily-UsedBuildings&OutdoorTranspor-tationsPlantsFoodElectronics
PartSLIP [31]×××30.8337.0932.0026.6028.1737.0331.5029.0931.54~4min
Find3D [36]✓××26.1723.9922.6716.0314.1121.7725.7119.8321.28~10s
Ultrametric [12]×✓✓43.5948.0546.1744.2945.2949.6044.9049.2546.39~1.5h
SAMesh [54]××✓66.0360.8956.5341.0346.8965.1260.5657.8156.86~7min
SAMPart3D [68]×✓✓55.0357.9849.1740.3647.3862.1464.5951.1553.47~15min
Ours✓✓✓80.8583.4377.8369.6673.8580.2185.2782.3079.18~10s
+ +Table 2. Quantitative evaluation of class-agnostic part segmentation on the PartNetE [31] test set. We use Instance-level labels and report mean IoU. Please refer to the supplementary material for the category group mapping. We do not report results from Ultrametric [12] because of the lengthy runtime on 1906 shapes. + +
PartSLIP [31]Find3D [36]SAMesh [54]SAMP3D [68]Ours
Electro. & Comput.20.7914.5823.9643.8643.70
Home Appliances36.3322.6626.7340.5752.37
Kitchen & Food40.7824.8931.5065.1869.85
Furnit. & Househo.37.4421.7222.8257.5060.22
Tools, Offi., & Misc.43.2429.1133.4965.8566.33
average34.9421.6926.6656.1759.10
runtime~4min~10s~7min~15min~10s
+ +30k shapes with hierarchical part labels. We use part labels from all levels as our 3D part proposals. To sample 3D point triplets within each part, we convert the surface mesh from PartNet into a tetrahedral mesh using Tetgen [10] and then take the vertices of tet mesh as sampled interior points. All shapes are normalized to $[-1,1]^3$ during training, and we uniformly sample 100,000 points per shape as input to the network. + +Training Details. Our feature field is 448-dimensional, the triplane spatial resolution is $512^2$ , with 128 channels, and the transformer consists of 6 layers. Before feeding the triplane into the transformer model, we first downsample it to a resolution of 128 and treat each pixel as a token. After the transformer, we convert it back to $512^2$ triplanes. We train our model on 8 A100 GPUs for 2 weeks with a batch size of 2 per GPU. + +# 4.2. Comparison of Class-Agnostic Segmentation + +Since PARTFIELD does not predict part semantics, we evaluate its performance on the class-agnostic segmentation task and compare to various latest baselines. + +Evaluation Datasets We evaluate on PartObjaverse-Tiny [68] and PartNetE [31] datasets, following previous work on open-world 3D part segmentation [31, 36, 68]. The PartObjaverse-Tiny dataset contains 200 shapes spanning a wide range of object categories with human-annotated part segmentation. The PartNetE test set contains 1,906 shapes and is adopted from the PartNetMobility [62] dataset, which covers 45 object categories with movable part annotations. + +Metric We evaluate the class-agnostic mean Intersection over Union (mIoU) metric, following previous work [59, 66, 68]. For each ground-truth part, we calculate the IoU + +with every predicted part and assign the maximum IoU as that part's IoU. We then compute the average IoU across all ground-truth parts. The IoU is computed between sets of mesh faces. + +Baselines We compare PARTFIELD with five latest baselines for open-world 3D part segmentation, four of which are recent works that just appeared in 2024. As shown in Table 1, PartSLIP [31] and Find3D [36] are text-input part segmentation methods, whereas the other three baselines generate text-agnostic part segmentation. Except for Find3D—which trains a feedforward model to match the 3D feature space with the text feature space—all the other baseline methods employ per-shape optimization to lift or distill the results and features from 2D foundation models and require significant time to infer a single 3D shape. Among them, Ultrametric Feature Fields [12] performs NeRF optimization and takes multi-view images as input. For comparison, we first render multi-view images from our 3D input mesh to serve as the input of Ultrametric. While SAMPart3D [68] uses 3D pretraining to distill multi-view DINOv2 [42] features into a 3D encoder, it still requires per-shape-based finetuning to distill from multi-view SAM predictions. SAMesh [54] leverages a well-designed community detection algorithm to lift the multi-view predictions to 3D. + +For all methods, we follow their released codes evaluate on two datasets. For text-based methods, we use the part label names provided in the datasets. For methods that produce multi-scale part segmentations (i.e., Ultrametric, SAMPart3D, and Ours), we generate 20 segmentation results across different scales or cluster counts and select the one with the highest mIoU, following previous work [68]. When computing metrics, as not all approaches directly predict labels on input mesh faces, we carefully align and transfer the predicted labels to the input mesh faces for consistency. Please refer to the supplementary material for more details. + +Results Table 1 presents the quantitative results on PartObjverse-Tiny, where PARTFIELD significantly outperforms the baselines by a large margin (improving by $22.3\%$ over the second-best method) and operates several orders of magnitude faster. While most baselines require several minutes—or even over one hour (in the case of Ultrametric [12])—to process a single 3D shape, PARTFIELD can predict the feature field for an input 3D shape in a single + +![](images/0e568bed4067de093a2cf6d72062a23b59cf096ae8431d5baff727c03abcd119.jpg) +Figure 6. Hierarchical decomposition from PARTFIELD. Each row from left to right reveals the structured decomposition at different levels of granularity. PARTFIELD effectively captures meaningful hierarchical part relationships. Notice that in the first row, the handlebars and wheel are initially grouped into a single part with the front of the moped before splitting into individual parts. + +feedforward pass, taking less than one second. We can then obtain the segmentation by applying the clustering algorithm to the features, which takes just a few seconds. Tables 2 report the results on PartNetE, where a similar outperforming phenomenon is observed. We observe that, in general, text-based methods perform worse than class-agnostic approaches, especially in more open-world scenarios (e.g., PartObjaverse-Tiny). This indicates that accurately detecting 3D parts using open-world semantics remains a challenging task. Instead, PARTFIELD learn general concepts of 3D parts from large-scale data, enabling more accurate and diverse part decomposition. + +Figure 5 provides the qualitative comparison. In addition to the underperforming text-based methods, we observe that many per-shape optimization methods yield noisy results. This is mainly because the multi-view 2D predictions for a single shape can be inconsistent and imperfect, and the optimization process is sensitive to such noise. In contrast, PARTFIELD trains a feedforward model on large-scale noisy data, enabling it to predict more consistent and robust part segmentations. Note that while SAMesh [54] produces decent results in many cases, it tends to generate overly fine-grained and sometimes over-segmented outputs (i.e. the temple roof). Furthermore, SAMesh is neither flexible nor efficient in adjusting part granularity, whereas PARTFIELD efficiently supports flexible and adaptive multi-scale part decomposition. + +# 4.3. Applications + +We evaluate the properties of the learned feature field in various applications, including hierarchical part decomposition, 3D shape co-segmentation and 3D shape correspondences, and feature field consistency. + +Hierarchical Part Decomposition PARTFIELD implicitly learns a hierarchy of multi-scale parts by contrastive learning at scale on a variety of 2D and 3D data. A discrete hierarchical decomposition can be explicitly extracted via agglomerative clustering. As shown in Figure 6 (with additional results provided in the supplement), PARTFIELD + +![](images/5861090bef1177e7f3726e9562f4d25d4dc32a60f771775aeb32579f5b24f28d.jpg) +Figure 7. Feature Exploration. When a user clicks a point (top row), we display the similarity between that point and other regions within the same shape (top row), as well as similarities with locations on a different shape (bottom row). + +effectively captures meaningful hierarchical relationships between parts, a capability which can be useful in many interactive applications. By exploring the hierarchical part tree, users can adaptively select which parts to decompose further. + +Feature Exploration While we do not explicitly incorporate any cross-shape supervision, we find that consistency surprisingly emerges in our learned features space across different shapes. We develop an interactive interface to explore this consistency, visualizing similarity across the field to a selected location. As shown in Figure 7, semantic consistency emerges across shapes with different topologies (characters with different poses), geometries (airplanes), or functionalities (knife and screwdriver). This emerging property arises from our feedforward model design, which enables training our PARTFIELD at scale. + +3D Shape Co-segmentation We further explore the consistency of feature fields across shapes through a co-segmentation task. Specifically, we first segment the source shape to obtain the mean feature for each part. To segment the target shape, we use the mean feature as initialization and perform KMeans clustering to obtain its segmentation. As shown in Figure 8, we successfully co-segment shapes with differing geometries and even establish correspondences on shapes with significant variations, such as an ogre and a + +![](images/7c9f30d5e685d7cec669ff5fa17756559c6f3a7a97e6b698945d0f1b01095889.jpg) +Figure 8. Quantitative results on co-segmentation. We co-segment the shapes from the top row with the corresponding one on the bottom row. The same color indicates the same part. + +![](images/a56c616133e943985741a9bb66f4db2137a30e2eab83fce724e66dbf2f1943b2.jpg) +Figure 9. Point-to-point correspondences obtained by Functional Maps [43] using our learned features as input. In each group, the color map defined on the source shape (left) is transferred to the target shape (right). On the top row, we compare with the features from SAMPart3D. + +bearded man. Furthermore, we compare our approach with SAMPart3D [68] using the same algorithm to obtain cosegmentation results. We observe that its performance is inferior, which may be attributed to its per-shape optimization training strategy. + +3D Shape Correspondences The cross-shape consistency from PARTFIELD allows it to serve as a large-scale prior for fine-grained point-to-point correspondence learning. We take Functional Maps [43] for a promising initial example, fitting correspondence between a source and target shape. We initialize correspondences between the shapes via nearest-neighbors in the PARTFIELD feature space, then refine these initial correspondences with Smooth Discrete Optimization [37], iteratively solves for functional maps in a coarse-to-fine manner to recover a smooth point-to-point map. Figure 9 shows results, including a comparison applying the same strategy to SAMPart3D [68] features. The feature field from PARTFIELD provides accurate correspondence even if the topology of two shapes is very different (such as chairs on the bottom left), or with different poses (such as animals on the left). + +# 4.4. Ablations and Analysis + +Hard Negative Mining and Training Triplet Source. We conduct an ablation study on our hard negative training strategy and the source of training triplets using the PartObjaverseTiny dataset [68]. As shown in Table 3, training on the large-scale, unlabeled 3D dataset Objaverse using only 2D part proposals already achieves quite decent results, demonstrating the effectiveness of this approach. Although additional 3D datasets are much smaller in scale (only $8\%$ of the Objaverse subset) and have limited diversity (only 24 cate + +Table 3. Quantative results for ablation study. We report mIoU scores on PartObjverse-Tiny dataset [68]. + +
Training TripletsObjverse (2D Proposals)✓✓✓✓
PartNet (3D Proposals)✓✓
Hard Negative Sampling✓✓
mIoU77.7077.9078.9079.20
without hard negativeswith hard negatives
+ +Figure 10. Ablating the hard negative sampling strategy. With hard negative mining, the part boundaries become much sharper. + +gories), they still provide a modest gain in the open-world setting, suggesting their potential. Note that their benefits for supervising interior structures have not yet been reflected in this surface-only metric. Hard negative mining further improves performance and enables us to learn a crisper part boundary, as shown in Figure 10 (see the chair's armrest). Incorporating both training triplets and the hard negative sampling strategy leads to the best overall performance. + +Robustness to Input Modality. Thanks to the feed-forward model that takes point clouds as input, PARTFIELD can theoretically be applied to 3D shapes with other representations as well. To examine the model's robustness to various input modalities, data sources, and input styles, we evaluate it using diverse inputs, including AI-generated assets from both open-source models (Trellis [63]) and closed-source models (Edify3D [41], accessed via their public link), real-world 3D Gaussian splattering [19] (see the corresponding reconstruction results in the supplementary material), and CAD models of mechanical parts from the ABC dataset [25]. The results are shown in Figure 2. While our method is trained mainly with point clouds from human-created meshes, we find it generalizes well to these various modalities, data sources, and input styles, suggesting that our method is widely generalizable and applicable. + +# 5. Limitations and Future Work + +Our PVCNN & triplane architecture enables fast inference, but is inherently extrinsic, and as such our feature space is weakly correlated with 3D position—fortunately part segmentation is agnostic to this correlation, but cross-shape applications (Section 4.3) do require the shapes to be consistently oriented. Current investigations explore our PART-FIELD at the object-scale only, future work may extend to large scenes. The cross-shape applications (Section 4.3) are small-scale, investigating a surprising emergent property of the method—we hope that they motivate ongoing research into part contrastive learning for foundational features in 3D shape analysis. + +Acknowledgements We would also like to thank Masha Shugrina, Vismay Modi, and their team for the 3D-scanned Gaussian splat assets and helpful discussions, as well as the Edify3D team for providing the Edify assets and insightful discussions. + +# References + +[1] Ahmed Abdelreehem, Abdelrahman Eldesokey, Maks Ovsjanikov, and Peter Wonka. Zero-shot 3d shape correspondence. In SIGGRAPH Asia 2023 Conference Papers, pages 1-11, 2023. 3 +[2] Ahmed Abdelreheem, Ivan Skorokhodov, Maks Ovsjanikov, and Peter Wonka. Satr: Zero-shot semantic segmentation of 3d shapes. 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Existing data pruning approaches aim to accelerate training by removing those less important samples. However, they often rely on gradients or proxy models, leading to prohibitive additional costs of gradient back-propagation and proxy model training. In this paper, we propose Partial Forward Blocking (PFB), a novel framework for lossless training acceleration. The efficiency of PFB stems from its unique adaptive pruning pipeline: sample importance is assessed based on features extracted from the shallow layers of the target model. Less important samples are then pruned, allowing only the retained ones to proceed with the subsequent forward pass and loss back-propagation. This mechanism significantly reduces the computational overhead of deep-layer forward passes and back-propagation for pruned samples, while also eliminating the need for auxiliary backward computations and proxy model training. Moreover, PFB introduces probability density as an indicator of sample importance. Combined with an adaptive distribution estimation module, our method dynamically prioritizes relatively rare samples, aligning with the constantly evolving training state. Extensive experiments demonstrate the significant superiority of PFB in performance and speed. On ImageNet, PFB achieves a $0.5\%$ accuracy improvement and $33\%$ training time reduction with $40\%$ data pruned. + +# 1. Introduction + +The availability of large-scale datasets[1, 4, 20, 29, 37] in recent years has propelled significant advancements in deep learning. Many powerful vision models[20, 34, 36] rely on vast amounts of training data to achieve robust generalization. However, behind the unprecedented generaliza + +![](images/33389fcc8d239d8b8b4f7f3fc4f53fd533dfb52ab4b2564b93c0ed408da823f9.jpg) +Figure 1. Computation cost comparison between Partial Forward Blocking (PFB) and existing approaches. The half blanks in Forward and Update indicate that only the selected samples participate in the network's forward inference, back-propagation, and updates. The proposed PFB strategy avoids the additional cost of gradient calculation and proxy model training by pruning based on features of the shallow network and blocking the subsequent deep network forward pass of the pruned samples. + +tion performance lies a critical challenge: the enormous volume of training samples substantially increases the computational cost of training. Thus, reducing the training cost has become a key and pressing concern. + +Replacing large datasets with a compact subset offers an intuitive and effective solution. Dataset distillation[3, 30, 45, 49, 50] aims to synthesize a small yet highly informative set of samples by leveraging information from the original dataset. However, the synthetic data often deviates significantly from real-world samples. In contrast, data pruning[8, 31, 42, 47] and online batch selection[15, 24, 26] directly selects a subset of real samples, ensuring authenticity. Yet, these existing methods typically rely on additional proxy models[8, 11, 26] or computationally expensive met + +rics, such as gradients[15, 31, 43, 47], to assess sample importance. The computational burden introduced by proxy models, along with the cost of computing losses and backpropagating gradients, becomes increasingly prohibitive as dataset size grows, thereby undermining their efficiency. + +This raises a critical question: Can we efficiently select training samples at a lower cost while preserving the strong generalization of target models? We believe an effective solution to this problem should possess the following characteristics: 1) Efficiency: Its computational overhead of importance evaluation should be minimal, making it feasible for large-scale datasets. 2) Diversity: The selected samples should span a broad and informative distribution to ensure a strong generalization and powerful performance. 3) Adaptability: The method should dynamically adjust to the evolving training state of the model. + +This paper proposes a novel paradigm that significantly reduces training costs while preserving model performance to achieve these goals. We introduce the Partial Forward Blocking (PFB) strategy, which prunes samples in a batchwise manner at the early stage of the forward pass to eliminate unnecessary computation as shown in Fig. 1. First, the target network is partitioned into a shallow sub-network and a deeper subsequent one. Importance scores are computed based on the features from the shallow sub-network. Samples with low importance are discarded immediately, blocking their forward pass through the deeper layers, thereby reducing computation costs. Meanwhile, the retained samples reuse their extracted features to continue forward propagation, further improving efficiency. Compared with gradient-based and proxy-based works, the PFB strategy avoids the substantial overhead of gradient back-propagation and proxy model training for importance scoring and significantly reduces the forward cost of the pruned samples. + +To ensure the diversity of retained samples, we introduce a new importance metric, which leverages probability density as an indicator of sample redundancy: samples with high probability density are common and less informative, making them less important, while those with low probability density are rare and valuable for generalization. This criterion ensures the diversity of the retained subset by prioritizing rare samples and preventing excessive concentration in densely populated feature regions. Additionally, an Adaptive Distribution Estimation (ADE) module continuously updates its estimated feature distribution based on retained samples, enabling PFB to dynamically adjust to the evolving training state. By adaptively favoring rare and informative samples, PFB ensures that the retained subset remains well-aligned with the model's learning needs. Extensive experiments demonstrate that PFB achieves superior training efficiency with minimal computational overhead while maintaining competitive performance. For example, PFB prunes $40\%$ training samples of ImageNet-1k + +but still achieve a $0.5\%$ accuracy improvement and $33.2\%$ training time reduction over the full data baseline. In summary, our contributions are as follows: + +1. We propose an efficient training acceleration pipeline that conducts pruning in a batch-wise manner at the early stage of forward and blocks the subsequent forward pass of pruned samples. +2. To ensure the diversity of selected samples, we propose utilizing the probability density of the feature distribution to measure importance. +3. We introduce a distribution estimation module that adaptively tracks the distribution shift during training. + +# 2. Related Work + +Extracting a small amount of valuable samples from large datasets is a common objective in many other tasks, such as active learning[2, 39], noisy learning[28], curriculum learning[48], and data distillation[30, 45]. Since our approach focuses on accelerating training using real data, we primarily introduce data pruning and online batch selection. + +# 2.1. Data Pruning + +Data Pruning aims at selecting a small subset of training samples that can achieve comparable results as the original dataset to accelerate model training. These methods can be divided into two types: static and dynamic data pruning. + +Static methods only prune the dataset once. Thus, the performance of target models trained on the pruned datasets demonstrates the effectiveness of static methods. The pioneering work Herding [7] tends to keep samples that are close to class centers. EL2N [31] quantifies the sample-wise learning difficulty by averaging the norm of error of a set of networks. Similarly, GraNd [31] adopts the expectation of the gradient norm as an importance indicator. Dataset Pruning [47] and MoSo [43] prune the samples which do the least damage to the empirical risk based on back-propagated gradients. SVP [8] and YOCO [14] both select samples according to the entropy and error of the prediction by pre-trained proxy models, respectively. On the other hand, Forgetting [44] measures the learning difficulty via the forgetting times during training, namely the change of prediction from correct to incorrect. + +Recently, dynamic pruning methods that periodically select samples during training have been proposed. Raju et al.[35] first introduced a strategy where the pruning decision for a given sample can change across different pruning cycles. Their proposed methods, UCB and $\epsilon$ -greedy, dynamically select different samples for training based on prediction uncertainty at each pruning stage. Subsequently, Dyn-Unc [13] adopts a similar pipeline and measures uncertainty in a sliding window of successive training epochs as a pruning metric. InfoBatch [33] mitigates distribution shifts by removing a proportion of low-loss samples while + +![](images/7e4db243353cdfeed2ecce030fb79d64ca9314af2739c4918f885326a56708a5.jpg) +Figure 2. Illustration of the proposed Partial Forward Blocking pipeline. The black and red arrows denote forward and backward procedures, respectively. We use A-H to denote individual samples. We adopt an online paradigm which prune samples and save the training cost by block the forward and backward pass of the pruned samples in a batch-wise manner. We introduce the Adaptive Distribution Estimation module to obtain probability density, based on which the Probability Density Importance is computed. + +assigning higher weights to the remaining ones in an epoch-wise manner. Despite their getting rid of the burden of both gradient calculation and proxy model training, they still require a full forward pass on all samples in the dataset for sample-wise importance assessment and pruning. + +# 2.2. Online Batch Selection + +Online batch selection [16, 24] can be regarded as a special type of data pruning, which is more flexible as it selects samples within each batch at every training iteration. Despite this flexibility, many methods still rely on additional surrogate models and expensive gradients, leading to limited efficiency. For example, RHO-Loss [26] requires training a surrogate model on a holdout dataset with a certain number of samples, while Deng et al. [11] use a pretrained zero-shot predictor as their surrogate model. On the other hand, while gradient-based online batch selection methods [15, 17] save the expense of proxy training, they incur additional computational costs due to the need for loss back-propagation to obtain gradients. + +# 2.3. Comparison with Existing Methods + +Compared to proxy-model-based methods, our approach eliminates the training cost associated with these models. Unlike gradient-based methods, our method avoids the costly and additional backward propagation for gradient calculation. Even compared to methods like SB[16], + +UCB[35] and InfoBatch[33] that mitigate both issues, our approach requires only a small portion of shallow network computations for pruned samples during the forward pass, saving the substantial computational cost in deeper layers. On the contrary, these methods still perform the full, expensive forward pass on pruned samples. + +# 3. Methodology + +# 3.1. Problem Definition + +Given a dataset $\varPsi$ , our task is to train a deep network $Net_{\theta}$ with parameters $\theta$ . At the $t$ -th iteration during training, a batch of samples $B^{t} = \{z_{i}^{t}\}_{i=1}^{N_{B}}$ is randomly sampled from $\varPsi$ . The samples with the least importance scores in the current $t$ -th batch $B^{t}$ are pruned with a prune ratio $p \in (0,1)$ which can be formulated as optimization problem: + +$$ +\min _ {m _ {i} ^ {t}} \sum_ {i = 1} ^ {N _ {B}} m _ {i} ^ {t} \mathcal {I} \left(z _ {i} ^ {t}\right), \quad s. t. \sum_ {i = 1} ^ {N _ {B}} m _ {i} ^ {t} = p N _ {B}, \tag {1} +$$ + +where $\mathcal{I}(z_i^t)$ denotes the importance score of $z_{i}^{t}$ , and $m_{i}^{t}\in$ $\{0,1\}$ signifies its pruning decision, where $m_{i}^{t} = 1$ indicates $z_{i}^{t}$ is pruned. Hence, by solving Eq. (1) we can get the pruning decisions $M^{t} = \{m_{i}^{t}\}_{i = 1}^{N_{B}}$ and conduct a subset batch $S^t = \{z_i^t|m_i^t = 0\}$ with a smaller size $|S^t | = (1 - p)N_B$ . For each training iteration, the target model is only trained on $S^t$ . Compared with the vanilla + +training procedure, the training cost on the subset of the pruned samples $B^{t} \backslash S^{t}$ is saved. Our goal is to maintain strong performance and speed up training simultaneously. + +# 3.2. Overall Pipeline of Partial Forward Blocking + +The training cost of pruning methods consists of three components: Forward, Backward & Parameter Update (B&PU), and Scoring. Since most methods perform B&PU only on retained samples, its cost can not be further reduced. Thus, how to effectively reduce the expense of Forward and Scoring is the key to training acceleration. + +Let us begin with analyzing the Forward and Scoring costs of existing methods. Gradient-based approaches rely on loss gradients to compute importance scores, requiring a full forward pass (for Forward) and loss backpropagation (for Scoring) on all samples before pruning. Some methods, such as InfoBatch [33], score samples directly based on loss values, reducing Forward and Scoring overhead to a single forward pass on all samples. However, they fail to save the substantial costs of forward pass on pruned samples. In contrast, proxy-based methods use lightweight models for early pruning, ensuring that only retained samples undergo a forward pass in the target model. However, these approaches require training proxy models for Scoring, which entails a computational cost comparable to training the target model itself, making them impractically expensive. + +To overcome these limitations, we propose Partial Forward Blocking (PFB), which computes importance scores and prunes samples in the early stage of forward propagation. Specifically, we derive importance scores from shallow network features, allowing retained samples to reuse these features for the remainder of their forward pass. By pruning early, our method eliminates unnecessary computation on pruned samples in deeper layers, significantly reducing Forward costs compared to gradient-based methods. Furthermore, for Scoring, we only incur the minor computational cost of shallow layers (e.g., stage-1) without requiring proxy model training. As a result, the total computational cost of Forward and Scoring is limited to a full forward pass on retained samples and a shallow forward pass on pruned ones. This makes our method significantly more efficient than prior approaches. The details are outlined in Algorithm 1. We use $\mathbb{1}[\cdot ]$ to denote the indicator function. + +# 3.3. Probability Density Importance Criterion + +It is commonly accepted that strong generalization requires diversified training samples. How, then, can we design a per-sample importance criterion to ensure that pruning retains this diversity? A natural approach is to eliminate highly redundant samples. If the entire dataset is available, redundancy can be estimated by exhaustively computing pairwise feature similarities. However, for ultra-large datasets, this brute-force method is impractical due to two + +Algorithm 1: Partial Forward Blocking Pipeline +1 Input: Target model $Net(\cdot)$ , which can be dived into shallow sub-model $Net^{sh}(\cdot)$ and a deep sub-model $Net^{dp}(\cdot)$ , its initial parameters $\theta^0$ , pruning ratio $p$ . +2 Output: The updated parameters $\theta^T$ . +3 for $t \in [1, T]$ do +4 $B^t \gets \text{Sampler}(\mathcal{D})$ + #Get feature map $\mathbf{f}_i^t \in \mathcal{R}^{H \times W \times D_{org}}$ +5 $F^t \gets \{\mathbf{f}_i^t = Net_{\theta^{t-1}}^{sh}(z_i^t) \mid z_i^t \in B^t\}$ + #Pooled representation $\mathbf{x}_i^t \in \mathcal{R}^{1 \times D}$ +6 $F_{rp}^t \gets \{\mathbf{x}_i^t = Pool(\mathbf{f}_i^t) \mid \mathbf{f}_i^t \in F^t\}$ +7 $I^t \gets \{\mathcal{I}(z_i^t) = Imp(\mathbf{x}_i^t) \mid \mathbf{x}_i^t \in F_{rp}^t\}$ + #Prune less important samples +8 $\tau \gets \text{Percentile}(I^t, p)$ + #Get threshold +9 $M^t \gets \{m_i^t = 11[\mathcal{I}(z_i^t) < \tau] \mid \mathcal{I}(z_i^t) \in I^t\}$ +10 $S^t \gets \{z_i^t | m_i^t = 0\}$ + #Block forward of the pruned ones +11 $L^t \gets \{Loss(\text{Net}_{\theta^{t-1}}^{dp}(\mathbf{f}_i^t)) \mid z_i^t \in S^t\}$ +12 $\theta^t \gets \text{Update}(\theta^{t-1}, L^t)$ +13 $t \gets t + 1$ +14 return $\theta^T$ + +major challenges. First, extracting and storing feature representations for all samples imposes significant storage overhead. Second, such a similarity calculation demands prohibitive time and computation. + +To tackle this problem, we first reframe it in terms of data distribution. Diversity can be preserved by maintaining a broad distribution and preventing excessive concentration of retained samples. In the feature distribution, samples in dense regions have many similar counterparts, making them highly redundant and less important. Even if a significant portion of these samples is removed, their retained counterparts can still preserve the essential information. Conversely, samples in sparse regions are relatively rare, and removing them would drastically reduce the likelihood of selecting similar samples, losing valuable learning opportunities. Thus, these samples exhibit low redundancy and high importance. Therefore, estimating the number or proportion of similar counterparts for each sample provides an indirect measure of its importance. + +Following this analysis, we propose leveraging the probability density of a sample's feature distribution as an importance metric. Probability density reflects the relative likelihood of a sample with a given feature representation occurring in the dataset. High probability density suggests a greater prevalence of similar samples, indicating substantial redundancy and diminished importance. Therefore, for a sample $z_{i}$ , its probability density importance $\mathcal{I}(z_i)$ is de + +fined as follows: + +$$ +\mathcal {I} \left(z _ {i} ^ {t}\right) = \frac {1}{f _ {\mathbf {X}} \left(\mathbf {x} _ {i} ^ {t}\right) + r}, \tag {2} +$$ + +where $\mathbf{X}$ denotes the vector-valued random variable (feature representation) that conforms to the probability distribution of training samples, $f_{\mathbf{X}}(\cdot)$ is the probability density function (PDF), and $r$ is set as follows: + +$$ +r = \alpha \cdot \max _ {z _ {i} \in B} f _ {\mathbf {X}} \left(\mathbf {x} _ {i} ^ {t}\right). \tag {3} +$$ + +where $\alpha \sim U(0,b)$ is randomly sampled from the uniform distribution, and the upper bound $b$ is set as 0.01. The ablation study of this random term can be found in Sec. 4.3. We add the this term $(r)$ in Eq. (2) to complement some randomness of the pruning process to further ensure the diversity of training data. + +# 3.4. Adaptive Distribution Estimation + +In Sec. 3.3, we propose to quantify the importance of all samples in each batch using their probability density. Nevertheless, how can we compute the PDF adaptively to track the distribution shift caused by parameter updating while maintaining a negligible computational cost? + +To address this challenge, we propose the Adaptive Distribution Estimation (ADE), which uses Kernel Density Estimation (KDE) to estimate the probability density. By clustering samples in each batch and updating centroids to represent previously retained samples, we reduce the number of kernels in KDE computation. We also track the number of samples each centroid represents and apply weight coefficients to balance kernel contributions. This approach enables efficient, adaptive distribution tracking with minimal computational overhead. + +Balanced Kernel Density Estimation. For each sample $z_{i}^{t}$ in the current batch $B^{t}$ of $t$ -th training iteration, we conduct spatial average pooling on its original feature map $\mathbf{F}_{i}^{t} \in \mathcal{R}^{H \times W \times D_{org}}$ to a $1 \times D_{org}$ vector, and then further down-sample on the channel dimension to a $1 \times D$ shaped vector $\mathbf{x}_{i}^{t}$ as the representation of $z_{i}^{t}$ , in order to improve the computation efficiency. Then, kernel functions are applied to the current set of centroids $C^{t} = \{\mathbf{c}_{j}^{t}\}_{j=1}^{N_{C}}$ to estimate the probability density of $z_{i}^{t}$ using its representation $\mathbf{x}_{i}^{t}$ : + +$$ +\hat {f} _ {\mathbf {X}} \left(\mathbf {x} _ {i} ^ {t}\right) = \sum_ {j = 1} ^ {N _ {C}} \frac {w _ {j} ^ {t}}{N _ {C}} K _ {\mathbf {H}} \left(\mathbf {x} _ {i} ^ {t} - \mathbf {c} _ {j} ^ {t}\right), \tag {4} +$$ + +where $\mathbf{c}_j^t\in \mathcal{R}^{1\times D}$ is the feature of the $j$ -th centroid among all $N_{C}$ ones, and $K_{\mathbf{H}}(\cdot)$ is the scaled kernel function. Please note that we introduce $w_{j}^{t}$ to balance different kernels, which will be explained later in Eq. (9). For simplicity, we use the standard multivariate normal kernel: + +$$ +K _ {\mathbf {H}} (\mathbf {x}) = \frac {1}{(2 \pi) ^ {d / 2} | \mathbf {H} | ^ {1 / 2}} e ^ {- \frac {1}{2} \mathbf {x} ^ {\top} \mathbf {H} ^ {- 1} \mathbf {x}}, \tag {5} +$$ + +where $\mathbf{H} \in \mathcal{R}^{D \times D}$ is the bandwidth serving as the covariance matrix and can be selected using various bandwidth selection methods [38, 41]. Following Silverman's rule of thumb[41], $\mathbf{H}$ is set as a diagonal matrix: + +$$ +\mathbf {H} = \operatorname {d i a g} \left(h _ {1}, h _ {2}, \dots , h _ {D}\right), +$$ + +$$ +\sqrt {h _ {d}} = \left(\frac {4}{(D + 2) N _ {C}}\right) ^ {\frac {1}{D + 4}} \sigma_ {d}, \tag {6} +$$ + +where the $\sigma_{d}$ is the standard deviation of all centroids along the $d$ -th dimension. Thanks to feature map pooling and the small number of centroids, the KDE process is efficient, as evidenced by results in Tab. 3. Based on Eqs. (4) and (5), we can compute $\mathcal{I}(z_i^t)$ for each $z_i^t$ according to Eq. (2). Following the objective in Eq. (1), we can conduct the small batch $S^t$ consisting of all the retained samples. + +# Clustering & Centroids Update. + +We update centroids and compute weights using only retained samples. Each sample is assigned to its most similar centroid via clustering, formulated as finding a partition $\mathcal{P}(S^t) = \{A_1^t,A_2^t,\ldots ,A_{N_C}^t\}$ of $S^t$ , where each $z_i^t\in S^t$ belongs to a cluster (subset) $A_j^t$ that minimizes the Euclidean distance to its centroid $\mathbf{c}_j^t$ .. + +$$ +\underset {\mathcal {P} \left(S ^ {t}\right)} {\arg \min } \sum_ {j = 1} ^ {N _ {C}} \sum_ {z _ {i} ^ {t} \in A _ {j} ^ {t}} \left| \left| \mathbf {x} _ {i} ^ {t} - \mathbf {c} _ {j} ^ {t} \right| \right| ^ {2}. \tag {7} +$$ + +Then, centroids are updated for KDE of the next iteration: + +$$ +\mathbf {c} _ {j} ^ {t + 1} = \frac {1}{n _ {j} ^ {t}} \left[ \beta n _ {j} ^ {t - 1} \cdot \mathbf {c} _ {j} ^ {t} + (1 - \beta) \sum_ {z _ {i} ^ {t} \in A _ {j} ^ {t}} \mathbf {x} _ {i} ^ {t} \right], \tag {8} +$$ + +$$ +n _ {j} ^ {t} = | A _ {j} ^ {t} | + n _ {j} ^ {t - 1} = \sum_ {i t e r = 1} ^ {t} | A _ {j} ^ {i t e r} |, +$$ + +where $\beta = 0.01$ is the coefficient of EMA, $n_j^{t - 1}$ and $n_j^t$ are the recorded number of all samples that were previously assigned to the $j$ -th centroid until the last and current training iteration, respectively. These continuously evolving centroids entitle our method with strong adaptability to the shifting distribution. Moreover, the number of samples previously assigned to each centroid is also used to construct the weight $w_{j}^{t}$ : + +$$ +w _ {j} ^ {t + 1} = \frac {n _ {j} ^ {t}}{t \cdot (1 - p) N _ {B}}. \tag {9} +$$ + +If many similar samples were retained in previous iterations, their assigned centroids gain higher weights, reducing the importance of future similar samples. With these weights, our method adaptively favors retaining rarer samples, preserving diversity in the selected subset. + +
DatasetCIFAR-10CIFAR-100
Pruning Ratio30%50%70%30%50%70%
Random94.693.390.273.872.169.7
Herding[7]92.288.080.173.171.869.6
Influence[21]93.191.388.374.472.068.9
K-Center[40]94.793.990.974.172.270.2
SVP[8]95.094.590.374.272.369.8
Craig[27]94.893.388.474.471.969.7
SB-12hours†[16]95.595.193.2---
GraNd[31]95.394.691.274.671.468.8
Glister[19]95.294.090.974.673.270.4
ε-greedy[35]95.294.994.176.474.8-
UCB[35]95.394.793.977.375.3-
Forgetting[44]94.794.191.775.373.169.9
EL2N[31]95.395.191.977.272.1-
Traning Loss[18]--94.6--72.6
AUM[32]95.195.391.476.967.430.6
Moderate[46]93.792.690.674.368.357.8
Grad Norm IS[17]--94.4--73.2
Dataset Pruning[47]94.993.890.877.273.1-
CCS[51]95.495.093.077.174.568.9
MoSo†[43]---76.772.365.8
InfoBatch*[33]95.695.194.778.278.176.5
DivBS†[15]95.495.295.178.578.277.2
PFB(Ours)95.995.595.279.178.877.9
↑0.3↓0.1↓0.4↑0.9↑0.6↓0.3
Full Data95.6±0.178.2±0.1
+ +Table 1. Comparison to state-of-the-art methods on CIFAR-10/100 using ResNet-18. The proposed PFB achieves performance improvements when $30\%$ samples are pruned. Under $50\%$ pruning ratio, PFB still achieves nearly lossless results. * denotes different prune ratio settings. † denotes our reproduction. + +# 4. Experiment + +# 4.1. Experimental Setup + +Datasets. Following the most common setting of the latest works[13, 15, 33], we conduct experiments to evaluate the performance of PFB on CIFAR-10[22], CIFAR-100[22], and ImageNet-1k[10] for image classification. CIFAR-10/100 datasets consist of $32 \times 32$ sized images that are divided into 10 and 100 classes, respectively. Each of them contains 50,000 images for training and 10,000 for testing. ImageNet-1k is a large-scale dataset containing 1,281,167 training images and 50,000 validation images that are categorized into 1,000 classes. We also evaluate the efficiency of PFB on the semantic segmentation datasets PASCAL VOC 2012 trainaug[6] and Cityscapes[9]. PASCAL VOC 2012 trainaug consists of 10,582 and 1,456 images for training and testing, respectively. The Cityscapes contains 2,975 fine annotated images with a resolution of $2,048 \times 1,024$ for training and another 500 images for validation. + +Implementation details. For image classification, we + +
ResNet-50Pruning Ratio30%50%70%
Random72.2↓4.269.1↓7.365.9↓10.5
Herding[7]73.5↓2.969.3↓7.165.1↓11.3
Forgetting[44]74.8↓1.672.0↓4.467.8↓8.6
EL2N[31]74.3↓2.168.5↓7.954.8↓21.6
Moderate[46]75.2↓1.272.2↓4.267.7↓8.7
MoSo†[43]76.5↑0.173.5↓2.970.0↓6.4
InfoBatch†[33]76.5↑0.175.8↓0.674.9↓1.5
PFB(Ours)77.0↑0.676.1↓0.375.3↓1.1
Full Data76.4±0.2
Swin-TPruning Ratio30%40%50%
Random77.2↓2.475.9↓3.774.5↓5.1
Forgetting[44]78.3↓1.377.6↓2.074.3↓5.3
EL2N[31]78.2↓1.475.9↓3.771.1↓8.5
SVP[8]76.6↓3.074.9↓4.772.7↓6.9
Moderate[46]77.1↓2.575.9↓3.775.0↓4.6
InfoBatch†[46]78.6↓1.078.2↓1.477.5↓2.1
Dyn-Unc[13]79.1↓0.578.5↓1.177.6↓2.0
PFB(Ours)79.6↑0.079.2↓0.478.2↓1.4
Full Data79.6±0.1
+ +Table 2. Performance Comparison on ImageNet-1k. ResNet-50 and Swin-T are trained from scratch for 90 and 300 epochs, respectively. The results demonstrate the effectiveness of PFB on both CNNs and Transformers. + +employ ResNet-18[12] as a backbone on CIFAR-10/100 trained for 200 epochs. The batch size is set as 128. On ImageNet-1k, we evaluate the performance of PFB using ResNet-50 and Swin-T[23] to evaluate the generalization across different network architectures. The batch size of both ResNet-50 and Swin-T is set as 1024. Other detailed settings can be found in our supplementary materials. + +# 4.2. Comparisons with SOTA Methods + +We compare our method with existing state-of-the-art data pruning and online batch selection methods on CIFAR10/100 and ImageNet-1k. We define the pruning $p$ as the proportion of pruned samples to all samples. For methods that prune the whole training dataset, like most data pruning methods[31, 33], the pruning ratio is set as $p = \frac{|\mathcal{D}|}{|\mathcal{D}_{\text{pruned}}|}$ . As for methods (including ours) that adopt batch-wise pruning paradigm[15, 16], the pruning ratio is set as $p = \frac{N_S}{N_B}$ . Note that InfoBatch[33] adopts a different pruning rate calculation strategy: it first selects only part of the samples with the lower loss as well-learned and applies pruning only within this subset, resulting in an actual pruning rate that is around only half of the reported value. To distinguish this, we denote the original InfoBatch with '\*' and our reproduction with ' $\dagger$ ', which considers $95\%$ of the samples as pruning candidates. We also introduce single-shot random + +
MethodYearPruning Freq.Top-1 Acc(%)Training(h)Overhead(h)Total(n*h)Reduction
Full Data--76.413.9-55.6-
EL2N†[31]2018Single-shot71.5↓4.910.1>14>96>72.7%↑
UCB†[35]2021Epoch75.8↓0.610.10.0840.826.7%↓
InfoBatch†[33]2023Epoch76.5↑0.110.10.0740.726.8%↓
DivBS†[15]2024Batch76.4↑0.011.20.7247.614.4%↓
PFB(ours)-Batch76.9↑0.59.20.0637.133.2%↓
+ +Table 3. Time cost comparison on ImageNet-1k using ResNet-50 under $40\%$ pruning ratio. PFB saves the overall cost by more than $30\%$ but still obtains a $0.5\%$ accuracy gain. Results are collected on a 4-RTX 4090 GPU server. Automatic Mixed Precision[25] is adopted during training for all methods. 'Training' and 'Overheads' denote the wall clock time spent on network training and the additional time brought in by pruning methods. 'Total(n*h)' is the total node hour with $n = 4$ . + +
DatasetMethodmIoUTime Saved
Cityscapes 30% PrunedFull Data80.4-
DivBS†79.0↓1.47.8%↓
InfoBatch†79.2↓1.215.8%↓
PFB(Ours)79.8↓0.624.1%↓
VOC 2012 70% PrunedFull Data77.9-
DivBS†72.7↓5.242.6%↓
InfoBatch†72.4↓5.549.1%↓
PFB(Ours)73.4↓4.556.7%↓
+ +Table 4. Results comparison with other pruning methods on Cityscapes and Pascal VOC 2012. PFB blocks the forward pass of pruned images at the third stage of the encoder. All methods adopt the same training settings. + +pruning (Random) as a baseline for comparison. Other reproduced results following the same experimental setup of PFB are also denoted with $\dagger$ . + +Performance Comparisons. Top-1 accuracy on CIFAR-10/100 and ImageNet-1K is reported in Tab. 1 and Tab. 2, respectively. The results demonstrate that PFB consistently outperforms existing methods across all three datasets and various pruning ratios. Notably, at a $30\%$ pruning ratio, PFB achieves better-than-lossless training, with ResNet models improving by $0.3\%$ , $0.9\%$ , and $0.6\%$ over full-data training on CIFAR-10, CIFAR-100, and ImageNet-1K, respectively. These results strongly validate the diversity of the retained training samples and the enhanced generalization of the trained models. We attribute this improvement to both the proposed importance criterion and the Adaptive Distribution Estimation module. + +Efficiency Comparisons on ImageNet-1k. The training efficiency of PFB is also compared with both classic methods (EL2N and UCB) and the latest methods (InfoBatch and DivBS). The time cost of ResNet-50 trained on ImageNet-1k for 90 epochs is reported in Tab. 3. EL2N and DivBS are representative proxy-based and gradient-based methods, respectively. As a result, they struggle to achieve satisfac + +tory speedup on large-scale datasets like ImageNet due to their inherent computational overhead. In contrast, UCB and InfoBatch rank sample importance based on prediction uncertainty and loss values, effectively mitigating the high cost associated with proxy models and backpropagation in the previous approaches. Despite this, our proposed PFB mechanism further reduces training overhead by additionally skipping part of the forward pass for pruned samples, leading to even greater efficiency gains. + +Efficiency Comparisons on Segmentation Datasets. To better demonstrate the acceleration advantage of PFB in skipping part of the forward pass, we further conduct experiments on a more computationally intensive semantic segmentation task, with results presented in Tab. 4. We apply InfoBatch, DivBS, and PFB to DeepLabV3-ResNet50[5], ensuring all methods undergo the same number of training iterations. Since semantic segmentation is a dense prediction task that requires per-pixel supervision, its forward inference and loss computation demand significantly more computational resources and time compared to classification tasks. Consequently, PFB achieves a more pronounced efficiency gain over InfoBatch and DivBS by skipping the forward pass through deep layers. Furthermore, as PFB does not rely on gradient-based importance estimation, it exhibits a greater advantage over DivBS on Cityscapes than VOC, where images are larger and computational demands are higher. Experimental results show that with the PFB mechanism, PFB achieves a threefold reduction in training time compared to DivBS on Cityscapes. + +# 4.3. Ablation Study + +Location to Block. We first investigate the impact of the blocking location on performance. The results in Fig. 3(a) show that For both ResNet-50 and Swin-T, PFB performs well when blocking after stage-1 layers. When PFB is applied directly at the stem layers (stage-0) of ResNet-50, using the corresponding features as sample representations, we observe a significant drop in performance. We conjecture that this is due to the relatively noisy and less informative nature of shallow features in ResNet, which may not + +![](images/c1fc1169b3a9c875fcb70eb1df4f202b722715c13e904a59bbc03d0d5650e4bb.jpg) + +![](images/f969af69a61e10013bd1698c9c213d9886db51eedad340d26120350985a05df7.jpg) + +![](images/2361b1f799f995a7548692791b11f2e39e6220006c2d13acb7d6de87d2567d54.jpg) + +![](images/2274d40e7bf98f130d6d8b3ce4421c3a34175ff0304267465c470aad2d9f8eca.jpg) +(a) Location to Block +(d) Different Batch Size +Figure 3. Ablation studies of PFB on (a) the blocking location of PFB strategy on ImageNet-1k, (b) the upper bound of the uniformly sampled coefficient of the random term, (c) the number of centroids for KDE, (d) the size of batch on ImageNet-1k, (e) performance under large pruning ratios, and (f) the channel number of feature representation. We use the shading to show the maximum and minimum of five independent runs. Unless otherwise specified, experiments are conducted on CIFAR-100. + +![](images/6e97b297fa82849e03894df2242dd431296f22e7e3757e4cab4f08c70686adf9.jpg) +(b) Scale of Random Term +(e) Large Pruning Ratios + +![](images/3148fc42471d292abe6fb58c13e9b73b7386c2a1039eaa41b49747e41aaffa8c.jpg) +(c) Number of Centroids +(f) Representation Dimension + +sufficiently capture the semantic distinctions and relationships between samples. To balance performance and efficiency, we therefore apply PFB at stage-2 for ResNet and stage-1 for Swin. + +Batch Size. As the recorded centroids and the number of samples assigned to it is related to the number of samples in the batch, we conduct experiments to verify the robustness of PFB to different batch size settings on ImageNet-1k. Results in Fig. 3(d) reveal that the trend of PFB is consistent with that of full-data training. This phenomenon demonstrates that PFB is not sensitive to various batch sizes. + +Random Term of Importance. The random term $r$ in our proposed importance metric (Eq. (2)) enhances the diversity of retained samples, ensuring those with plenty of similar counterparts can sometimes be retained as well. We conducted five repeated experiments on the upper bound $b$ , which controls the scale of $r$ on CIFAR-100. We report the results in Fig. 3(b) with blue shading indicating the range between the maximum and minimum values. The results demonstrate that the accuracy remains stable when the upper bound $b$ of random coefficient $\alpha$ is within [0.001, 1]. However, when $\alpha$ is excessively large, the random term dominates probability density in (Eq. (2)), leading to an excessive retention of randomly selected samples. Thus, the performance drops significantly with large fluctuations when $b$ is set as 10. + +Effectiveness on High Pruning Ratio. To explore the effectiveness under extreme conditions, we conduct ablation studies on CIFAR-100 with very large pruning ratios(0.7-0.9). As shown in Fig. 3(e), PFB still outperforms other powerful methods, including both gradient-based ones[15, + +17] and those relying on proxy-models[8]. + +Coefficients in Adaptive Distribution Estimation. To find the best coefficients for probability density estimation, we compare the accuracy and the fluctuation under different settings in Fig. 3(c) and (f). The results show that our method is robust to variations in the number of centroids $N_{C}$ and feature dimensions $D$ within a normal range. Moreover, a larger $N_{C}$ and a lower $D$ help to reduce performance fluctuations. This aligns with intuition: increasing the kernel number within a reasonable range improves KDE estimation accuracy, while a higher dimension increases the complexity and difficulty. We set $N_{C} = 64$ and $D = 128$ . + +# 5. Conclusion + +In this paper, we introduce Partial Forward Blocking (PFB), a novel training data compression paradigm designed to accelerate deep model training. Unlike existing dataset pruning methods that rely on computationally expensive gradient-based importance evaluation or additional proxy models, PFB efficiently selects samples by leveraging a lightweight probability density estimation mechanism without compromising model generalization. Furthermore, we propose a Partial Forward Blocking (PFB) strategy, which skips deep-layer computations for pruned samples, significantly reducing training costs. Extensive experiments demonstrate that PFB achieves superior training efficiency while outperforming state-of-the-art data pruning and online batch selection methods on both classification and segmentation datasets. Our approach provides a scalable and adaptive solution for large-scale dataset training, paving the way for more efficient deep learning models. + +# 6. Acknowledgement + +This work was supported by the National Natural Science Foundation of China No.62176097, and the Hubei Provincial Natural Science Foundation of China No.2022CFA055. Some of the computational work presented in this paper was completed in the HPC Platform of Huazhong University of Science and Technology. + +# References + +[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. arXiv preprint arXiv:1609.08675, 2016. 1 +[2] Antoine Bordes, Seyda Ertekin, Jason Weston, and Léon Bottou. Fast kernel classifiers with online and active learning. Journal of machine learning research, 6(Sep):1579-1619, 2005. 2 +[3] George Cazenavette, Tongzhou Wang, Antonio Torralba, Alexei A Efros, and Jun-Yan Zhu. Dataset distillation by matching training trajectories. 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Existing coarse-to-fine frameworks assume that each query text precisely corresponds to the center area of a submap, limiting their applicability in real-world scenarios. This work redefines the task under a more realistic assumption, relaxing the one-to-one retrieval constraint by allowing partially matching query text and submap pairs. To address this challenge, we augment datasets with partially matching submaps and introduce an uncertainty-aware framework. Specifically, we model cross-modal ambiguity in fine-grained location regression by integrating uncertainty scores, represented as 2D Gaussian distributions, to mitigate the impact of challenging samples. Additionally, we propose an uncertainty-aware similarity metric that enhances similarity assessment between query text and submaps by propagating uncertainty into coarse place recognition, enabling the model to learn discriminative features, effectively handle partially matching samples and improve task synergy. Extensive experiments on KITTI360Pose and CityRefer demonstrate that our method achieves state-of-the-art performance across both stages. Our code is available at https://github.com/Afoolbird/PMSH + +# 1. Introduction + +Understanding natural language instructions in city-scale 3D environments is critical to enable collaboration in applications such as autonomous systems and intelligent logistics [21, 37, 40]. Conventional visual place recognition (VPR) methods, which rely on unimodal sensor data (e.g., cameras or radar) to extract 2D image or point cloud features for database matching, exhibit two key limitations: inefficiency in interactive scenarios and degraded accuracy under seasonal or viewpoint variations [25, 35]. By contrast, text to city-scale point cloud localization circumvents + +![](images/f2235b6b397867f7ec54855fd26f3a7b77b4ddf7caa38cda1b7b899adb92961f.jpg) +Figure 1. Query text retrieves partially matching submaps, causing cross-modal ambiguity when only a few hints align with scene instances, degrading performances in the coarse-to-fine framework. Our method mitigates this, enhancing across stages' accuracy. + +these issues, achieving precise geolocation without requiring physical user proximity [23, 43]. + +To date, few methods have addressed the language based localization task in large-scale 3D city maps [40]. Text2Pose [21] pioneers this task by partitioning the proposed KITTI360Pose city-scale point cloud into submaps and aligning textual descriptions with corresponding instances through a coarse-to-fine approach. In coarse stage, it employs cross-modal text-to-submap retrieval to identify potential submaps. The fine stage then refines localization using a text-instance matching module. Building on this framework, RET [37], Text2Loc [40], and IFRP-T2P [38] enhance contextual and relative position modeling, improving localization accuracy. However, existing methods and datasets simply assume each query text has one corresponding submap whose center area fully matches the location of the query text. This assumption is not practical for real-world applications [4], as query texts may appear anywhere within an area of interest, while submaps are captured beforehand [5, 44]. Consequently, multiple submaps may partially overlap with the same query, disrupting the strict one-to-one correspondence. As shown in Fig. 1, the query text is not positioned at the center area of the retrieved partially matching submap, only three hints align with instances, the remaining three fail to establish a match. + +Partially matching samples exacerbate semantic gaps and increase cross-modal ambiguity during training, de + +grading both retrieval based coarse place recognition and fine-grained localization regression. This occurs because query texts describe only a subset of instances in partially matching submaps, making their feature embeddings less similar to the query text than fully matching samples. While Text2Loc [40] introduces a prototype-based map cloning module to generate submap variants, it overlooks cross-modal ambiguities caused by minimal instance overlap. However, efficiently handling partially matching submaps presents two challenges: 1) In fine-grained localization, their partial alignment with query text complicates regression training. Treating them as fully matching submaps without adjustment risks overfitting and reduced accuracy. 2) In coarse place recognition, contrastive learning is undermined as their similarity to the query text lies between fully matching positives and mismatched negatives, rather than fitting either category. Addressing these challenges in both stages is crucial for robust localization. + +To address this issue, we account for cross-modal ambiguity between the query text and instances of partially matching submaps in fine-grained localization and quantify it through uncertainty modeling. Specifically, we represent the predicted fine-grained location and its uncertainty as a 2D Gaussian distribution, jointly optimizing both via a Gaussian log-likelihood loss. We apply the negative log-likelihood to mitigate the impact of high uncertainty on the regression loss, improving localization performance. In coarse place recognition, we introduce an uncertainty-aware similarity metric to assess query text and submap alignment while accounting for cross-modal ambiguity. By propagating uncertainty scores into retrieval, this metric enhances focus on reliable partially matching submaps, enabling the model to learn discriminative features. By integrating this, the model effectively learns useful information from partially matching samples, promoting adaptive learning and reducing the adverse effects of partially matching samples for practical scenarios. Our main contributions are: 1) We augment datasets by incorporating partially matching submaps for text to point cloud task under a more realistic and practical setting and develop an uncertainty modeling and propagation strategy to enhance cross-modal localization performance. 2) We address cross-modal ambiguity in fine-grained location regression through uncertainty modeling, reducing the impact of challenging samples on accuracy. 3) We integrate uncertainty propagation into contrastive learning for partially matching samples, proposing an uncertainty-aware similarity metric to learn discriminative features and improve task synergy. Extensive experiments on KITTI360Pose and CityRefer datasets demonstrate the superiority of our method, improving both tasks. + +# 2. Related Work + +Visual Localization. Visual localization estimates a query image's pose using environmental data, such as images and + +point clouds, and follows two main paradigms: image-based and 3D structure-based localization. Image-based methods [8, 20, 28] treat localization as an image retrieval task, first retrieving relevant images [2, 3, 16, 36] and then establishing pixel correspondences for precise pose estimation [7, 39]. NetVLAD [2] achieves state-of-the-art performance via weakly supervised contrastive learning, while MapLocNet [39] integrates BEV and navigation map features for real-time, high-precision localization without HD maps. In contrast, 3D structure-based methods align 2D keypoints from the query image with 3D keypoints in a prebuilt model [27, 31, 32]. HF-Net [31] improves efficiency and accuracy by combining local features with global descriptors for 6-DoF pose estimation. + +Language-based 3D Localization. Language-based 3D localization determines a 3D point cloud's spatial position using natural language descriptions. ScanRefer [6] and Referit3D [1] introduce indoor datasets for 3D visual grounding with free-form object annotations on ScanNet [9]. Later methods [11, 14, 15, 17, 18, 30, 34, 41] localize 3D objects in raw point clouds based on textual queries. While these approaches focus on indoor scene localization, 3D visual grounding in open outdoor environments remains underexplored. Text2Pose [21] introduced largescale city scene localization by partitioning maps into discrete submaps, establishing the KITTI360Pose dataset. It first identifies coarse locations before refining location estimation but overlooks associations between textual prompts and point cloud instances. RET [37] addresses this by employing a Transformer-based approach to enhance representation discriminability. Building on this, Text2Loc [40] eliminates text-instance matching via contrastive learning with a more efficient strategy, improving localization accuracy. IFRP-T2P [38] proposes a two-stage localization method without real instance input, achieving competitive results. GOTLoc [19] reduces storage and computation by constructing a compact scene graph [13]. However, existing coarse-to-fine frameworks assume that each query text precisely corresponds to the center of a submap, limiting their applicability in real-world scenarios. + +# 3. Partially Matching Sample Augmentation + +Partially Matching Samples Definition. The large-scale 3D map $\mathcal{M} = \{S_i : i = 1, \dots, n\}$ is a collection of semantic submaps $S_i$ . Each submap $S_i = \{p_i : i = 1, \dots, m\}$ includes a set of 3D object instances $p_i$ . Let $T$ represent the query text, which comprises a set of spatial hints $t_i$ , each describing the spatial relationship between the position and instances of submap. The KITTI360Pose [21] consists of a series of overlapping square submaps, as illustrated in Fig. 2. Each submap spans $30m$ , and the query text in each text-position pair is generated based on instances of submap within a $15m$ radius of the ground truth posi + +![](images/4412ae2a5076db32fa923b9ee8f27301f48f1ff22c818e2f7f9a09d7eb0dfb6f.jpg) +Figure 2. The sampling strategy and IOU definition. Red star: ground truth position; green dot: center of fully matching submap; yellow dot: center of partially matching submap. + +![](images/ce483f56df8d8003e2186aed1e21e3561e32e2a03053c21fb515813ab0e21dae.jpg) + +tion (the red star), forming a reference area (the red circle). Each position is uniquely associated with a fully matching submap (the submap centered at the green point), denoted as $S_{f}$ , which contains all the referenced instances of submap in the query text. As shown in Fig. 2, due to the spatial overlap between submaps, there exist partially matching submaps (submaps centered at yellow point), denoted as $S_{p}$ which contain only a subset of the referenced instances in the submap. + +Collection. In the training set, we filter partially matching submaps based on the submap around each true location. After excluding fully matching submaps, we further discard submaps without any point cloud-instance text match pairs, resulting in all partially matching submaps. Each ground truth position is typically associated with multiple partially matching submaps, with the highest number of submaps having three point cloud instance and text match pairs, followed by two and four. We prioritize selecting the submap with three match pairs as the partially matching submap for a true position. If such a submap is unavailable, we randomly select from submaps with other match pair counts, ensuring that the selected partially matching submap contains at least two point cloud instances relevant to the query text. We exclude fully matching samples without any partially matching submaps, which account for only $1\%$ of the total dataset. Note that information from partially matching samples is utilized only in the training set to improve overall task performance. Evaluation on the validation and test sets follows prior works to ensure fair comparison with only fully matching samples. + +Distance and IOU. After obtaining the partially matching submap, its semantic consistency with the query text differs from that of the fully matching submap. To effectively leverage the information contained in partially matching submaps, we require a metric to quantify their discrepancy. A straightforward approach is to measure the L2 distance between the position and the submap center. Let the L2 distance between the centers of $S_{f} / S_{p}$ and the position be denoted as $D_{f}$ and $D_{p}$ , respectively. Both are less than $15m$ but $D_{f} < D_{p}$ . The second intuitive method is the Intersection Over Union (IOU) between the circle of position and the submap center circle. As illustrated in Fig. 2, we cal + +culcate the IOU between the circle of position with a radius of $15m$ and the center circle of $S_{f} / S_{p}$ , denoting the IOU as $O_{f}$ and $O_{p}$ , respectively. Empirical analysis shows that $O_{f}$ consistently exceeds 0.54, while $O_{p}$ typically falls within the range [0.10, 0.54]. + +# 4. Methodology + +Preliminaries. Following prior work, we adopt a hierarchical coarse-to-fine strategy for text to point cloud localization. In the coarse place recognition stage, the objective is to identify the most relevant submap corresponding to the query text. Text2Loc encodes the query text $T$ and the instances in the fully matching submap $S_f$ , extracting their respective global feature representations $F^T$ and $F^S$ . These features are then optimized via cross-modal contrastive learning, ensuring their proximity in a shared embedding space. For a given batch of $N$ semantic submap descriptors $\{F_i^S\}_{i=1}^N$ and corresponding query text descriptors $\{F_i^T\}_{i=1}^N$ , the contrastive loss $\mathcal{L}_{\mathrm{con}}$ for each pair is computed as follows: + +$$ +\mathcal {L} _ {\text {c o n}} = - \log \frac {\exp \left(F _ {i} ^ {T} \cdot F _ {i} ^ {S} / \tau\right)}{\sum_ {j \in N} \exp \left(F _ {i} ^ {T} \cdot F _ {j} ^ {S} / \tau\right)} - \log \frac {\exp \left(F _ {i} ^ {S} \cdot F _ {i} ^ {T} / \tau\right)}{\sum_ {j \in N} \exp \left(F _ {i} ^ {S} \cdot F _ {j} ^ {T} / \tau\right)}, \tag {1} +$$ + +where $\tau$ is the temperature coefficient, similar to CLIP [29]. + +In the Fine-grained Location stage, the goal is to localize the ground-truth position within the submap. Text2Loc extracts and fuses features from the hints in the query text and the fully matching submap to predict the position via regression. The model is trained with mean squared error loss $\mathcal{L}_{\mathrm{reg}}$ for supervision. + +$$ +\mathcal {L} _ {\text {r e g}} = \left\| L _ {g t} - L _ {p r e d} \right\| _ {2}, \tag {2} +$$ + +where $L_{pred} = (x, y)$ is the predicted position, and $L_{gt}$ is the ground truth position. + +In contrast, our approach integrates the informative content of partially matching samples throughout the entire localization pipeline to enhance both stages' performance. The overall pipeline is shown in Fig. 3. + +# 4.1. Cross-Modal Partial Matching Localization + +In the fine-grained localization stage, the misalignment between point cloud instances in partially matching submaps and the query text poses additional challenges to accurate localization. As a result, treating a partially matching submap $S_{p}$ equivalently to a fully matching submap $S_{f}$ and applying direct regression-based localization introduces overfitting, ultimately compromising the model's localization performance (see ablation study for details). To mitigate this, we utilize uncertainty to quantify the degree of cross-modal ambiguity between the query text and the semantic submap. This allows the network to adaptively adjust its optimization strategy based on varying levels of uncertainty [12, 22]. + +![](images/6de3c90aa088fedd8e0a8604005cb3468fd417854e6abc24016d92400f1154f8.jpg) +Figure 3. Framework overview. We first propose the uncertainty based cross-modal ambiguity modeling module to improve fine-grained location prediction accuracy. The uncertainty-aware similarity metric is then proposed to enhance retrieval performance by propagation uncertainty and learning discriminative features. + +We denote the fused feature obtained in the fine-grained localization stage as $f_{c}$ , which is then passed through a simple MLP to predict the position. Since the predicted position within the submap is distributed around the ground truth position, we model the predicted position as a Gaussian distribution [42]. Specifically, we represent the predicted coordinates as the mean $\mu$ of the Gaussian distribution, while the uncertainty of the predicted position is captured by its covariance matrix $\sigma$ , which serves as a measure of cross-modal ambiguity. The matrix $\sigma$ is a symmetric positive-definite matrix of size $2 \times 2$ , which has three degrees of freedom. To model this, we pass the fused feature $f_{c}$ through an additional MLP that decomposes $\sigma$ into its lower triangular matrix $L$ , such that $LL^{T} = \sigma$ . The MLP consists of two fully connected layers, which derive the three variables that determine $L$ , with the Exponential Linear Unit (ELU) activation function applied to ensure that the diagonal elements of $L$ are positive. By learning $\sigma$ from the cross-modal fusion features, we effectively capture the discrepancies between the text and point cloud modalities. These discrepancies help us address cross-modal ambiguity with uncertainty. + +Given the predicted Gaussian distribution for each sample pair, the likelihood of the predicted position at the ground truth position $L_{gt}$ is formulated as follows: + +$$ +P \left(L _ {g t} \mid \mu \left(f _ {c}\right), \sigma \left(f _ {c}\right)\right) = \frac {\exp \left(- \frac {1}{2} \left(L _ {g t} - \mu\right) ^ {T} \sigma^ {- 1} \left(L _ {g t} - \mu\right)\right)}{2 \pi \sqrt {| \sigma |}} \tag {3} +$$ + +where $||$ denotes determinant and $\mu(f_c)$ represents the predicted location $L_{pred}$ . The model represents the predicted position as a 2D Gaussian distribution, parameterized by $\mu$ and $\sigma$ . The objective is to train the network to establish a mapping from fused features $f_c$ to the parameters of the Gaussian distribution. Since maximizing the likelihood function (Eq. 3) is mathematically equivalent to minimizing the negative log-likelihood, we adopt negative log + +likelihood as our new loss function $\mathcal{L}_{reg}^{\prime}$ + +$$ +\begin{array}{l} \mathcal {L} _ {r e g} ^ {\prime} = - \ln P \left(L _ {g t} \mid \mu \left(f _ {c}\right), \sigma \left(f _ {c}\right)\right) \\ = \frac {1}{2} \left(L _ {g t} - \mu\right) ^ {T} \sigma^ {- 1} \left(L _ {g t} - \mu\right) + \frac {1}{2} \ln | \sigma | + \ln 2 \pi , \tag {4} \\ \end{array} +$$ + +The first component penalizes the discrepancy between the predicted and ground truth position, while the second component regularizes high uncertainty. + +Guided by Eq. 4, the model utilizes uncertainty estimates to dynamically adjust its optimization based on sample characteristics. When predicting the position for challenging partially matching samples, the network allows a larger covariance $\sigma$ , signaling high uncertainty to moderate the severe residuals $(L_{gt} - \mu (f_c))$ . As a result, the influence of these challenging partially matching samples is reduced during training. This mechanism acts as a strategy for loss attenuation [24], enabling the model to effectively learn from partially matching samples while preserving information from fully matching samples, ultimately enhancing localization accuracy. + +# 4.2. Uncertainty-Aware Place Recognition + +During the coarse place recognition stage, the valid information from partially matching submaps also contributes to enhanced retrieval performance. However, directly incorporating these submaps into cross-modal contrastive learning is inappropriate, not only due to the differences between $S_{f}$ and $S_{p}$ , but also because of their overlapping regions. Consequently, their similarity to the query text should be closer than that of mismatched pairs in contrastive learning, but not as close as matched pairs. Thus, a new approach is required to effectively leverage the information from partially matching samples. Since the point cloud instances in partially matching submaps only partially align with the query text, their similarity in the feature embedding space should be lower than that of fully matching pairs. As explained above, we assign embedding similarity based on the IOU + +or L2 distance between the ground truth position and the submap. The corresponding loss functions for these assignments are defined as follows: + +$$ +\mathcal {L} _ {\mathrm {d i s}} = \left(\frac {D _ {f}}{D _ {p}} - \frac {C _ {p}}{C _ {f}}\right) ^ {2}, \mathcal {L} _ {\mathrm {i o u}} = \left(\frac {O _ {p}}{O _ {f}} - \frac {C _ {p}}{C _ {f}}\right) ^ {2}, \tag {5} +$$ + +where $C_p$ and $C_f$ denote the cosine similarities between the query text and the partially matching and fully matching submaps, respectively. This loss forces the ratio of the similarities in the embedding space to be close to the ratio of L2 distance/IOU. As $\mathcal{L}_{\mathrm{iou}}$ exhibited superior performance during training, we adopt IOU as our method for addressing partially matching samples. Further details are provided in the ablation study. We observe that $\mathcal{L}_{\mathrm{iou}}$ exhibits instability during training. This is primarily because, in some partially matching submaps, the IOU value fails to accurately reflect the correspondence between point cloud instances and the query text. Specifically, instances occur where the IOU value is high despite the actual number of matched point cloud instances being low. A comparable issue arises when employing $\mathcal{L}_{\mathrm{dis}}$ . Furthermore, certain partially matching samples exhibit challenges in identification. It is necessary to further optimize assignment loss. + +Accurately predicting the positions of these challenging partially matching samples is also difficult due to inherent ambiguities in their alignment with the query text, a challenge analogous to those encountered in fine-grained localization. Therefore, we propagate the uncertainty estimated during fine-grained localization into $\mathcal{L}_{\mathrm{iou}}$ . To prevent the model from excessively optimizing on challenging samples, we modulate the cosine similarity based on the degree of cross-modal ambiguity. Based on the cosine similarity $C$ (include $C_p$ and $C_f$ ), we define an uncertainty-aware similarity metric $S(C,\sigma)$ , which is adaptively adjusted using the uncertainty $\sigma$ . Leveraging this metric, we propose a novel assignment loss function. + +$$ +\mathcal {L} _ {\mathrm {i o u}} ^ {\prime} = \left(\frac {O _ {p}}{O _ {f}} - \frac {S (C _ {p} , \sigma_ {p})}{S (C _ {f} , \sigma_ {f})}\right) ^ {2}, +$$ + +$$ +S (C, \sigma) = 1 - (1 - C) \phi (\sigma), \quad \phi (\sigma) = \frac {1}{1 + \alpha e ^ {\beta (| \sigma | - \gamma)}}, \tag {6} +$$ + +where $\phi (\sigma)$ is a decaying exponential function [22] with three positive parameters: $\alpha$ , $\beta$ , and $\gamma$ . When the uncertainty $\sigma$ is low, the similarity metric $S(C,\sigma)$ closely approximates the original cosine similarity $C$ . As uncertainty $\sigma$ approaches zero, the function $\phi (\sigma)$ converges to 1, resulting in $S(C,\sigma) = C$ , then the original assignment loss is applied for contrastive learning. Conversely, when the uncertainty $\sigma$ is high, $\phi (\sigma)$ approaches 0, and $S(C,\sigma)$ takes a value close to 1, effectively excluding the challenging sample from optimization. This mechanism filters out challenging partially matching samples, reducing their impact on + +training. By focusing on samples with lower cross-modal ambiguity, the network can extract more reliable information, thereby enhancing retrieval performance. + +As fully matching submaps typically exhibit strong certainty and high similarity with text queries, the network focuses on enhancing the embedding similarity for partially matching submaps. Through gradient analysis, we demonstrate how the uncertainty measure $S(C,\sigma)$ contributes to discriminative learning in the embedding space. By replacing the similarity measure in the assignment loss function $\mathcal{L}_{\mathrm{iou}}$ with $S(C,\sigma)$ , we derive the relationship $\frac{\partial\mathcal{L}_{\mathrm{iou}}}{\partial C} = \frac{\partial\mathcal{L}_{\mathrm{iou}}^{\prime}}{\partial S}$ , which is influenced by the specific form of the loss function. Let the network parameters and feature embeddings be denoted as $\theta$ and $f$ , respectively; the gradient of the loss with respect to parameter $\frac{\partial\mathcal{L}_{\mathrm{iou}}^{\prime}}{\partial\theta}$ can be expressed as: + +$$ +\begin{array}{l} \frac {\partial \mathcal {L} _ {\mathrm {i o u}} ^ {\prime}}{\partial \theta} = \frac {\partial \mathcal {L} _ {\mathrm {i o u}} ^ {\prime}}{\partial S} \frac {\partial S}{\partial C} \frac {\partial C}{\partial f} \frac {\partial f}{\partial \theta} = \frac {\partial \mathcal {L} _ {\mathrm {i o u}}}{\partial C} \frac {\partial S}{\partial C} \frac {\partial C}{\partial f} \frac {\partial f}{\partial \theta} \tag {7} \\ = \frac {\partial \mathcal {L} _ {\mathrm {i o u}}}{\partial \theta} \frac {\partial S}{\partial C} = \frac {\partial \mathcal {L} _ {\mathrm {i o u}}}{\partial \theta} \phi (\sigma), \\ \end{array} +$$ + +We observe that $\frac{\partial\mathcal{L}_{\mathrm{iou}}}{\partial\theta}$ is modulated by the decay function $\phi (\sigma)$ , meaning that, compared to the original gradient $\frac{\partial\mathcal{L}_{\mathrm{iou}}}{\partial\theta}$ , higher uncertainty results in a smaller gradient. Additionally, the design of $S(C,\sigma)$ enables the model to focus on specific partially matching submaps, providing more informative feature embeddings for the coarse place recognition task. This approach not only mitigates the issue of cross-modal ambiguity but also ensures proper gradient alignment during training [33], which aids in achieving more effective optimization for the coarse place recognition task. + +# 5. Experiments + +Datasets. Our experiments are primarily conducted on the KITTI360Pose [21] dataset. Through our data augmentation strategy, we train the model with both partially matching and fully matching submaps corresponding to the query texts. We also use the text to point cloud dataset CityRefer [26] to evaluate the generalization of the method. Following [21], we also segment the large-scale 3D city maps into comparable semantic submaps. Further details can be found in the Appendix. + +Evaluation Metrics. Following [40], we adopt top-k retrieval recall ( $k \in \{1,3,5\}$ ) for text-to-submap retrieval evaluation in coarse place recognition. To evaluate fine-grained localization, we assess performance based on the top-k retrieved candidates and report localization recall, where $k$ is set to 1, 5, and 10. Localization recall is defined as the fraction of queries that are successfully localized when their localization error falls below certain thresholds, specifically $\epsilon < 5/10/15m$ by default. Additionally, we further evaluate the normalized Euclidean distance error between the ground truth and predicted positions. + +
MethodsReferenceLocalization Recall (ε < 5/10/15m) ↑
Validation SetTest Set
k=1k=5k=10k=1k=5k=10
Text2Pos [21]CVPR'220.14/0.25/0.310.36/0.55/0.610.48/0.68/0.740.13/0.21/0.250.33/0.48/0.520.43/0.61/0.65
RET [37]AAAI'230.19/0.30/0.370.44/0.62/0.670.52/0.72/0.780.16/0.25/0.290.35/0.51/0.560.46/0.65/0.71
Text2Loc [40]CVPR'240.37/0.57/0.630.68/0.85/0.870.77/0.91/0.930.33/0.48/0.520.61/0.75/0.780.71/0.84/0.86
IFRP-T2P [38]ACM MM'240.23/0.45/0.530.53/0.70/0.810.64/0.86/0.890.22/0.40/0.460.47/0.68/0.730.58/0.78/0.82
Ours-0.42/0.62/0.680.75/0.89/0.900.83/0.94/0.950.39/0.55/0.590.68/0.81/0.830.78/0.89/0.90
+ +Table 1. Performance comparison on the KITTI360Pose. Both Validation and test sets are used for fair comparison with SOTA. + +
MethodsValidation Error ↓Test Error ↓
Text2Pos [21]0.1200.127
Text2Loc [40]0.0910.090
IFRP-T2P [38]0.1180.119
Ours0.0850.081
+ +Table 2. Fine-grained localization comparison on KITTI360Pose. + +
MethodsSubmap Retrieval Recall ↑
Validation SetTest Set
k=1k=3k=5k=1k=3k=5
Text2Pos [21]0.140.280.370.120.250.33
RET [37]0.180.340.44---
Text2Loc [40]0.320.560.670.280.490.58
IFRP-T2P [38]0.240.460.570.230.390.48
GOTLoc [19]0.360.580.670.300.490.57
Ours0.370.630.730.340.560.65
+ +Table 3. Coarse place recognition comparison on KITTI360Pose. + +# 5.1. Comparison with State-of-the-Art + +We compare our method with state-of-the-art methods [19, 21, 37, 38, 40] across both stages. + +Fine-grained localization. Tab. 1 presents the top- $k$ recall rates ( $k = 1/5/10$ ) under different localization error thresholds ( $\epsilon < 5/10/15m$ ). IFRP-T2P [38] eliminates the reliance on ground truth semantic submaps by leveraging its own semantic segmentation approach [10], but lacks open-source code; thus, we conduct direct comparisons under different settings. To ensure consistency, we use the semantic submap input provided by the original dataset, similar to other methods. However, unlike previous approaches that trained solely on fully matching samples, our method leverages both partially and fully matching samples (all tabulated data are sourced from the original papers). Our approach surpasses all existing methods across all recall levels, outperforming the previous state-of-the-art, Text2Loc [40], by $14\%$ and $18\%$ in top-1 recall on the validation and test sets, respectively. Moreover, our method consistently demonstrates superior performance as the threshold or $k$ increases. These results validate the effectiveness of our uncertainty modeling and propagation in leveraging partially matching samples throughout the coarse-to-fine framework, enhancing overall localization accuracy. Additionally, we analyze the impact of integrating partially matching samples into the open-source method Text2Loc [40] in Tab. 4 as part of our + +ablation study. + +To independently assess our fine-grained location stage, we evaluate the trained model using only fully matching samples for a consistent and fair comparison with others. Normalized Euclidean distance serves as the evaluation metric. As shown in Tab. 2, our method reduces error by $7\%$ and $10\%$ on the validation and test sets, respectively, compared to Text2Loc [40]. These results validate the effectiveness of our uncertainty modeling in leveraging both partially and fully matching samples during training, enhancing fine-grained localization accuracy. + +Coarse place recognition. In the coarse place recognition stage, we evaluated top-1/3/5 recall rates, with our method surpassing the SOTA Text2Loc by $16\% / 13\% / 9\%$ (Tab.3), showing similar gains on the test set. It also outperforms the retrieval-only method GOTLoc[19] (arXiv 2025). These results highlight the importance of partially matching samples in enhancing retrieval and validate the effectiveness of our proposed IOU and uncertainty propagation approach. + +Qualitative Analysis. We provide a qualitative comparison of coarse-to-fine localization between Text2Loc and our method, as shown in Fig. 4. Given a query text, we visualize the ground truth, top-3 retrieved submaps, and top-1 fine-grained localization result. Each submap spans $30m$ ; thus, in coarse place recognition, a retrieved submap is classified as a partially matching submap if its center distance is within $15m$ of the ground truth and it is not a fully matching submap. In coarse place recognition, both Text2Loc and our method retrieve fully or partially matching submaps near the position. However, our method is more likely to retrieve a fully matching submap under stricter metrics, such as top-1. As shown in the first column, while Text2Loc retrieves only a partially matching submap at top-2, our method achieves a fully matching submap at top-1. This demonstrates that our uncertainty-aware assignment loss $\mathcal{L}_{\mathrm{iou}}'$ in the coarse stage helps distinguish fully and partially matching samples, improving retrieval performance. The second column highlights a key challenge for Text2Loc: despite failing to retrieve the correct fully matching submap at top-3, the retrieved submaps contain similar object instances, indicating difficulty in resolving inter-submap ambiguities. In contrast, our method retrieves the fully matching submap at top-1, followed by a partially matching submap. This + +![](images/eb2d9257fc7ea909871c8b01adf3f90a3b7b74c50e0de3f78580854abb4f45b6.jpg) +Figure 4. Qualitative comparisons on KITTI360Pose: In coarse place recognition, the numbers in top-3 retrieved submaps show their center to ground truth distances. Green boxes denote fully matching submaps containing the position, while red indicates retrieval failures. In fine-grained localization, red and yellow dots mark the ground truth and predicted locations, with red numbers showing their distances. + +
MethodsLocalization Recall (ε < 5m) ↑
Validation SetTest Set
k=1k=5k=10k=1k=5k=10
Text2Loc0.370.680.770.330.610.71
Text2Loc*0.400.710.800.360.650.74
w/o L'reg0.250.430.510.210.380.47
Ours0.420.750.830.390.680.78
+ +Table 4. Ablation study on fine localization (KITTI360Pose). * denotes the Text2Loc fine localization network with submaps retrieved by our coarse recognition. 'w/o $\mathcal{L}_{\mathrm{reg}}^{\prime}$ indicates training with $\mathcal{L}_{\mathrm{reg}}$ using partially matching submaps. + +demonstrates that integrating $\mathcal{L}_{\mathrm{con}}$ with $\mathcal{L}_{\mathrm{iou}}^{\prime}$ helps the model focus on distinctive features of fully and partially matching submaps, enhancing its ability to differentiate from other semantically similar submaps. The top-1 fine-grained localization results in Fig. 4 confirm our method's ability to refine predictions using the retrieved fully matching submap. Additional visualizations are provided in the Appendix. + +# 5.2. Ablation Study + +Fine-grained localization. To further assess our method's effectiveness in fine-grained localization, we present a quantitative analysis in Tab. 4. For fair comparison, all methods use the same submaps retrieved by our coarse place recognition. Text2Loc* significantly outperforms the original Text2Loc, demonstrating the benefits of our coarse place recognition. However, incorporating partially matching submaps into Text2Loc's training degrades performance, consistent with our earlier analysis (see Sec. 5.1). By introducing uncertainty modeling as a loss function to handle partially matching samples, our method achieves a + +![](images/ecc2489652042f9eed3aaecd15b369b94f9cbe289df12066cc8f1388f08ecfe5.jpg) +Figure 5. Visualization of cross-modal ambiguity modeling. Estimated uncertainty is shown as yellow circles, while the orange dashed line links the text query to its corresponding point cloud instance in the submap. + +top-1 accuracy of 0.39 on the test set at $\epsilon < 5m$ , an $8\%$ improvement over Text2Loc. These results confirm that our framework effectively models cross-modal ambiguity, enhancing the model's ability to distinguish fully from partially matching samples and improving text to submap localization accuracy. + +To further validate this finding, we visualize predicted location, uncertainty scores, and prediction errors. As shown in Fig. 5(a), higher uncertainty scores correspond to fewer matched text-point cloud instances and larger prediction errors, indicating that uncertainty reflects cross-modal ambiguity arising from imperfect text-point cloud alignment. Moreover, Fig. 5(b) and (c) reveal that as the number of matched instances increases, both uncertainty and prediction errors decrease, demonstrating the model's ability to learn discriminative feature representations for improved localization accuracy. + +We further analyze the results by binning test samples based on uncertainty values using histogram binning and computing mean and median localization errors within each + +![](images/67923f314afd696645fd21532ccbf2fd747661c4be71100ebdb876a114a36eed.jpg) +Figure 6. The mean and median errors of fine-grained predictions are evaluated across uncertainty intervals, with the range [0.01, 0.06] divided into 10 segments, corresponding to bins $B_{i}$ . + +
MethodsSubmap Retrieval Recall ↑
Validation SetTest Set
k=1k=3k=5k=1k=3k=15
Text2Loc0.320.560.670.280.490.58
Text2Loc*0.190.280.410.160.250.37
w/ Ldis0.330.590.690.310.500.61
w/ Liou0.350.600.710.320.530.63
Our0.370.630.730.340.560.65
+ +bin (Fig. 6). Lower uncertainty corresponds to smaller errors, while higher uncertainty correlates with increased errors, confirming its positive relationship with localization accuracy. These findings validate the effectiveness of our uncertainty modeling in capturing cross-modal ambiguity and serving as a reliable indicator of localization accuracy. + +Coarse place recognition. To evaluate the effectiveness of our method in coarse place recognition, we compare strategies for handling partially matching samples (Tab. 5). Consistent with fine-grained localization, naively incorporating partially matching samples into contrastive learning reduces retrieval performance. Based on this, we explore alternative approaches using $\mathcal{L}_{\mathrm{iou}}$ , $\mathcal{L}_{\mathrm{dis}}$ , and our final proposed $\mathcal{L}_{\mathrm{iou}}'$ . The results show that both $\mathcal{L}_{\mathrm{iou}}$ and $\mathcal{L}_{\mathrm{dis}}$ outperform the baseline, with IOU-based similarity surpassing L2 distance. The IOU ratio more effectively distinguishes between partially and fully matching samples. Our final approach achieves the best performance, demonstrating that the uncertainty-aware similarity loss filters out hard samples, allowing the model to better utilize informative partially matching samples and enhance retrieval accuracy. + +Further Training Analysis. We analyze the training process, as shown in Fig. 7. The left panel displays loss curves for the coarse place recognition stage with $\mathcal{L}_{\mathrm{iou}}$ and $\mathcal{L}_{\mathrm{iou}}^{\prime}$ . Propagating uncertainty guidance improves stability and accelerates convergence, suggesting that $\mathcal{L}_{\mathrm{iou}}^{\prime}$ allows + +![](images/7cf6e05b2160f0e3b4d8de927a231c215e06c3fa0948e51cd6f21367772bc8b1.jpg) +Figure 7. $\mathcal{L}_{\mathrm{iou}}$ and $\mathcal{L}_{\mathrm{iou}}^{\prime}$ loss curves (left), the Normalized Euclidean distances when utilize $\mathcal{L}_{\mathrm{reg}}$ or $\mathcal{L}_{\mathrm{reg}}^{\prime}$ loss (right). + +![](images/a4032bd91a38559cd103855123a708b6e592101c1e715a6a10d801203662a190.jpg) + +Table 5. Ablation study of coarse stage on KITTI360Pose. * denotes training with partially matching submaps using $\mathcal{L}_{\mathrm{con}}$ . 'w/ $\mathcal{L}_{\mathrm{dis}}$ denotes training both partially and fully matching samples using $\mathcal{L}_{\mathrm{con}}$ and $\mathcal{L}_{\mathrm{dis}}$ , 'w/ $\mathcal{L}_{\mathrm{iou}}$ follows a similar strategy. + +
MethodsLocalization Recall(ε < 10m) ↑
Validation SetTest Set
k=1k=5k=10k=1k=5k=10
Text2Pos0.130.320.550.100.280.47
Text2Loc0.250.460.690.190.380.57
Ours0.290.540.780.240.470.66
+ +Table 6. Performance comparison on the CityRefer. + +dynamic adjustment, mitigating the impact of hard samples within partially matched pairs and enhancing training efficiency. The right panel shows the normalized Euclidean distance error curve in the fine-grained localization stage. Using $\mathcal{L}_{\mathrm{reg}}^{\prime}$ improves convergence, indicating that uncertainty based cross-modal ambiguity modeling effectively utilizes discriminative features from partially matching samples, boosting accuracy for fully matching samples. + +Details in Appendix: The hyperparameter ablation in Eq. 6 and its impact on model performance. The effectiveness of our method in structuring the embedding space and refining spatial retrieval. + +# 5.3. Generalization to CityRefer dataset + +We evaluate our method against new CityRefer dataset and report the fine-grained localization performance in Tab. 6. We implement the open-source methods on CityRefer with the same settings as KITTI360Pose. Due to the increased linguistic variability of CityRefer compared to the fixed templates in KITTI360Pose, existing methods show degraded performance. In contrast, our method maintains a significant advantage and outperforms Text2Loc by $16\%$ and $26\%$ in top-1 recall on the validation and test sets, respectively, highlighting its robustness in handling diverse query text and improving localization accuracy. + +# 6. Conclusion + +In this paper, we pioneered a more realistic setting for text to large-scale point cloud task by relaxing the one-to-one retrieval constraint by allowing partially matching submap and query text pairs. To address the associated challenges, we first modeled cross-modal ambiguity in fine-grained location regression by integrating uncertainty scores and then proposed an uncertainty-aware similarity metric to propagate uncertainty into coarse place recognition. Experiments show our method's superiority. In the future, we will design more efficient similarity metrics with the modeled uncertainty for overall performance improvement. + +# Acknowledgments + +This work was supported in part by Science and Technology Project of Jiangxi province (20232ACC01007), in part by Ji'an Science and Technology Project (20233TGV06020), in part by the National Natural Science Foundation of China under Grant (62373293, 62463020, 62403189), in part by Jiangxi Provincial Natural Science Foundation (20242BAB20050), in part by Ji'an Science and Technology Plan Natural Science Foundation (20244018591). + +# References + +[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. Referit3d: Neural listeners for fine-grained 3d object identification in real-world scenes. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part I 16, pages 422-440. 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Beyond standard spatial and visual question-answering (QA) tasks on current autonomous driving benchmarks, driving knowledge tests require a complete understanding of all traffic rules, signage, and right-of-way principles. To pass this test, human drivers must discern various edge cases that rarely appear in real-world datasets. In this work, we present DriveQA, an extensive open-source text and vision-based benchmark that exhaustively covers traffic regulations and scenarios. Through our experiments using DriveQA, we show that (1) state-of-the-art LLMs and Multimodal LLMs (MLLMs) perform well on basic traffic rules but exhibit significant weaknesses in numerical reasoning and complex right-of-way scenarios, traffic sign variations, and spatial layouts, (2) fine-tuning on DriveQA improves accuracy across multiple categories, particularly in regulatory sign recognition and intersection decision-making, (3) controlled variations in DriveQA-V provide insights into model sensitivity to environmental factors such as lighting, perspective, distance, and weather conditions, and (4) pretraining on DriveQA enhances downstream driving task performance, leading to improved results on real-world datasets such as nuScenes and BDD, while also demonstrating that models can internalize text and synthetic traffic knowledge to generalize effectively across downstream QA tasks. + +# 1. Introduction + +Safe navigation in traffic requires not only recognizing and interpreting visual information but also reasoning over traffic rules and making decisions that align with regulations. To ensure drivers develop these critical skills, before receiving their license they must first pass a written knowledge test—a structured (multiple choice questions) assessment designed to evaluate precise understanding of traffic laws, right-of-way rules, and complex driving scenarios [32, 56]. + +Driving tests are not merely procedural; they assess a driver's ability to apply reasoning across a wide range + +![](images/69213569699773d82a9ed41ba52f0cc9102594cd1b440669df134f95f9706131.jpg) +Figure 1. Can LLMs Pass a Driving Knowledge Test? We introduce a comprehensive multimodal dataset to evaluate the traffic rule-following capabilities of MLLMs. While most question answering (QA) benchmarks in autonomous driving focus on spatial understanding and common planning tasks, our DriveQA dataset assesses broad driving knowledge. The challenging benchmark comprises text-based questions derived from various U.S. state driving manuals, as well as visual tasks for traffic sign recognition and right-of-way judgment. We evaluate both text-only and image-text QA using synthetic images (varying perspectives, weather, time of day, and sign types) while showing transferability and generalization to downstream real-world driving tasks. This figure shows one example for a right-of-way question, a category where models frequently struggle. Incorrect responses are highlighted in red and correct answers in green. + +of traffic conditions. While primarily textual, these tests may also include graphical illustrations to ground questions in real-world scenarios. Recent advances in Multimodal Large Language Models (MLLMs) [3, 26, 47, 75, 97] as general-purpose reasoning models provide an opportunity to explore a key question: how well do current vision-and-language models perform when faced with the same driving knowledge assessments? Even without targeted fine-tuning, MLLMs may inherit some traffic rule knowledge from their pretraining data (however, our findings indicate that both such knowledge and associated reasoning capabilities remain limited). + +Researchers have been increasingly integrating MLLMs into autonomous driving systems [11, 14, 28, 39, 42, 51, 53, 54, 70, 77, 84, 89, 95, 98]. However, while these models are often tested on perception-focused benchmarks that em + +Table 1. A Multimodal Dataset Emphasizing Traffic Rules. The table compares existing benchmarks in terms of: the total number of images (#Images), the number of QA pairs (#QA Pairs), the method of annotation (Annotations, A+M means semi-automatic labeling), environment settings (Settings, including camera perspective of forward-Fwd, oblique-Obl, and top-down-Top views, weather, and time of day conditions), explanations for each question's answer (Explanations), and traffic rule reasoning (Traffic Rules), which is our focus. + +
BenchmarksImage Source#Images#QA PairsAnnotationsSettingsExplanationsTraffic Rules
PerspectiveWeatherTime of Day
EQA-v1 [19]House3D [85]7675,281AFwd, OblXXXX
OpenEQA [52]OpenEQA1801,600MFwd, OblXXXX
SpatialVLM [9]Internet10M2BAFwd, OblXXXX
NuScenes-QA [63]nuScenes [6]34K450KAFwd✓✓XX
DriveLM-nuScenes [72]nuScenes [6]4,871443KA+MFwd✓✓XX
DriveLM-CARLA [72]CARLA [22]64,2851,566KAFwd✓✓XX
DriveBench [86]nuScenes [6]19,20020,498A+MFwd✓✓XX
LingoQA [55]LingoQA28k419.9KA+MFwd✓✓XX
DriveQA-V (ours)CARLA [22], Mapillary [57]68K448KA+MFwd, Obl, Top✓✓✓✓
DriveQA-T (ours)--26KA+M-✓✓✓✓
+ +phasize spatial awareness and standard planning tasks (e.g., lane keeping, collision avoidance [44, 78, 87]), they are rarely evaluated for their ability to understand and comply with diverse traffic regulations, such as reasoning about traffic rules, reacting safely to no-entry signs, or maintaining speed limit. While most existing datasets narrowly focus on perception and basic trajectory planning, driving knowledge tests are designed to assess a broad spectrum of all regulations, including rare traffic signs, difficult right-of-way cases, and edge-case rules that are essential for safe navigation but seldom appear in collected driving data. This highlights a critical gap in evaluating AI systems: while they may perform well in current benchmarks, their ability to reason over long-tail traffic rules and regulatory compliance remains understudied. There is also substantial anecdotal evidence suggesting that current commercial systems, e.g., Tesla's Full Self-Driving [24, 25, 36, 79], often struggle with interpreting traffic rules. + +To address this gap and enhance the evaluation of reasoning capabilities in both LLMs and MLLMs, we introduce a novel driving knowledge benchmark, DriveQA. Our dataset includes both text-only question-answers (QA) and aligned image-text (VQA) pairs. Thus, we enable the first thorough evaluation of vision-and-language model performance across broad driving tasks, from basic regulatory questions and signs to complex multimodal reasoning tasks. Our contributions are summarized as follows: + +- We introduce DriveQA, a large-scale benchmark featuring both text-based (DriveQA-T) and vision-based (DriveQA-V) driving knowledge assessments. To ensure broad coverage of traffic regulations, right-of-way rules, and rare driving scenarios, we leverage synthetic procedural data generation with comprehensive traffic reasoning, controlled variations (e.g., sign placement and weather), and new 3D sign assets integrated into CARLA [21], as well as manually annotated real-world data from Mapillary [57]. DriveQA covers 19 question categories, 220 traffic signs, and 474K samples. + +- We benchmark state-of-the-art LLMs and MLLMs on DriveQA to uncover that while these models perform well on basic traffic rules, they struggle with numerical precision, right-of-way reasoning, spatial awareness, and environmental sensitivity (e.g., time-of-day, perspective, and geometric layouts). Our findings suggest that MLLMs inherit limited traffic knowledge from pretraining and require fine-tuning for our task. +- We demonstrate the effectiveness of DriveQA pretraining; models trained on our text and purely synthetic data demonstrate improved performance across various real-world driving tasks [87, 88]. We show that pretraining on DriveQA improves the performance on both trajectory prediction and driving action reasoning tasks. This highlights its role in evaluating and enhancing multimodal reasoning, and as a step toward bridging theory and practice in embodied AI systems that can learn to make decisions in the real-world based on text or synthetic data. + +# 2. Related Work + +Based on our survey of MLLM-based studies and VQA benchmarks for autonomous driving below, we find prior work rarely addressed traffic rules, signage, and right-of-way principles within their driving knowledge assessments. Relevant related benchmarks are compared in Table 1. + +Multimodal Large Language Models: Our study diagnoses multimodal reasoning capabilities in MLLMs [2, 17, 38, 61, 78, 80, 95, 97]. A typical MLLM architecture comprises three main modules: a pre-trained modality encoder, a pre-trained language model, and a modality projector that aligns them. The modality encoder processes non-textual inputs, such as images, transforming them into representations compatible with the language models. Vision Transformer (ViT) [23] is widely used to extract image features. For example, CLIP [65] leverages ViT as its visual encoder to transform images into feature representations that align with text through extensive pre-training on large-scale + +![](images/1a05a3f911055cfe3f84faf8dededf546d5a1622865cb95c14b216bb7c6b17e4.jpg) +Figure 2. Example Questions and Answers of DriveQA Dataset. We introduce a text and vision-based benchmark for extensively validating driving knowledge with question type categorization, answer explanation, and environmental information ground truth (GT). + +![](images/076730b4cba0915c126a3aab82fe0c112010c4ad24d9d5f58cd242dc53b4a8b3.jpg) + +![](images/2b5e637e62197fc52e8cd1bbd411a829c99896866ef24b9c1a16ad6a2089db29.jpg) + +![](images/55d36f57b5669cbb3e3d40c016bddd873671099ebd020dd07d0f1582e0ca552c.jpg) + +image-text pairs. The modality projector aligns encoder outputs with the language model, enabling integration of modality data with text. A common approach is to use a set of learnable query tokens to extract information in a query-driven manner [7], which has been employed by a variety of models [10, 13, 18, 40, 43, 90–92]. Additionally, methods may design MLPs to transform the high-dimensional input features into a unified representation [2, 50, 62, 73]. Our systematic study controlling for variations in QA category and image factors reveals limitations of current alignment mechanisms in supporting multimodal or spatial reasoning. + +MLLM-based Driving Agents: While recent advancements have applied MLLMs to autonomous driving tasks, most focus on leveraging reasoning and language understanding capabilities to improve driving decisions in narrow tasks [12, 15, 16, 28, 53, 70, 82, 89, 98]. For instance, several vision-and-language agents for motion planning and decision-making have been proposed and evaluated on datasets such as nuScenes [4, 6, 28, 42, 51, 53, 54, 67, 78, 89]. The key hypothesis in such studies is that MLLMs can inherit general-purpose reasoning and knowledge from their pretraining; however, our findings suggest that while they may grasp basic traffic concepts, their ability to apply traffic reasoning in driving-specific scenarios remains limited. Moreover, these works have not explicitly addressed MLLMs' ability to comprehend diverse traffic rules and regulations-a critical requirement for safe driving. + +Datasets for Autonomous Driving: Several real-world, synthetic, and VQA benchmarks for autonomous driving are currently being used to evaluate driving models, including KITTI [30, 45], Waymo Open [74], Argoverse [8, 83], and nuScenes [6]. However, few incorporate more than a + +handful of traffic rules, e.g., researchers may evaluate collision on nuScenes [6, 20, 34, 78, 93, 94, 99], yet lack coverage and exclude explicitly evaluating for traffic signs or right-of-way reasoning. Crowdsourced benchmarks such as Mapillary [57], which we augment with VQA annotations, are broad but still lack in long-tail events, motivating the use of synthetic benchmarks. Yet, prior simulation-based studies (e.g., [1, 21, 27, 35, 66, 68, 71, 96]) have only accounted for a handful of potential regulatory and safety violations. For instance, while CARLA [21] enables controllable and diverse data generation (e.g., perspectives, scenarios, weather), most traffic signs are missing in CARLA, a limitation addressed by our work. The development of MLLMs and their applications in autonomous driving lead to the emergence of driving vision-language datasets [5, 55, 64, 69, 72, 78, 80] specifically designed to support vision understanding and reasoning in complex driving scenarios. However, here as well existing efforts focus on scene understanding, perception and basic planning (i.e., collision avoidance, intersection boundary [44]), neglecting reasoning about traffic rules and regulations (i.e., reacting safely to no-entry signs, maintaining speed limit, etc.) which is a foundational driving test for humans. + +# 3. A Multimodal Driver Knowledge Test + +In this section, we outline our scalable data collection and annotation process. Our dataset consists of QA pairs that cover essential aspects of real-world driving knowledge. As illustrated in Fig. 2, our dataset comprises two tasks: DriveQA-T, which consists of text-based QA pairs on general driving rules, and DriveQA-V, focusing on visual (image-based) QA related to traffic sign comprehension and right-of-way scenarios. We adhere as closely as possible to standard driving knowledge tests to ensure meaningful + +![](images/726f70807bada81194cd606db20d82acc95faaef4570e8371502b1ca5ecb8b83.jpg) +Figure 3. Distribution of Question Type in DriveQA-T. The benchmark covers five key domains and 19 sub-class types. + +comparisons to human performance on these assessments, and generate a diverse set of multiple-choice questions. We note that there are commercial driver knowledge tests available [56, 76], however these are closed-source. To ensure in-depth analysis, we further provide reasoning for ground-truth answers on both tasks. This design is intended to provide a holistic and systematic analysis of both LLMs and MLLMs in decision-oriented tasks. Ultimately, our overarching goal is to enable novel mechanisms to teach MLLMs real-world tasks, e.g., through text descriptions or synthetic examples. + +Text-based QA Dataset—DriveQA-T: Our DriveQA-T dataset contains a total of 26K QA pairs covering different general driving topics, including traffic lights, traffic signs, parking, regulation, and symbols (see our supplementary for full details on the categories). Each QA pair contains an explanation for the correct answer, which can be used to evaluate the reasoning capabilities of LLMs. To curate the QA pairs, we first gathered 51 official driver's handbooks from all 50 US states plus DC. Although our data set is US-centric, it can inform the construction of additional international datasets in the future. We build DriveQA-T in three steps. First, we generate questions automatically by prompting GPT-4o [59, 98] with the driver's handbooks as context, and then conduct manual quality verification based on the driver's handbooks. Quality checks were performed in rounds, where each verifier went through questions, and then ambiguous or inconsistent cases were discarded. Additional details about this process can be found in the supplementary. We note that humans, once trained, can obtain $100\%$ on our benchmark. We categorized the text data into 19 classes, grouped into five main categories, as shown in Fig. 3. A summarized description of the dataset is depicted + +![](images/37967e04d4a6bc757b4bfb8973a784505b773690bff7a3f37c4ae38e1b5b7818.jpg) +Figure 4. Word Cloud of Questions in DriveQA. The figure statistically summarizes the language terms in the introduced DriveQA benchmark. + +in Fig. 4, showing a focus on traffic participants and intersections (e.g., right-of-way, yielding behaviors). + +Multimodal Extension With DriveQA-V: Driver knowledge tests [56, 76] are primarily text-based, e.g., with a full description of objects and spatial layout information in text. However, certain questions particularly related to traffic signs and right-of-way, test understanding through graphical illustrations accompanying text information. DriveQA-V focuses on these two types of questions. To ensure comprehensive coverage through procedural variations (e.g., camera perspectives, time of day, weather, distance), images are collected with the open-source Unreal Engine-based CARLA simulator [21]. However, since CARLA was not originally designed with extensive traffic rule knowledge, e.g., traffic signs, we augment the simulation with additional 3D assets and automatic traffic rule scripts. Due to procedural and synthetic generation, in addition to aligned text-image VQA pairs, we are able to collect full state information, such as camera perspective, distance from ego-vehicle, and sign type. Specifically, we insert 220 US-based traffic sign models into the map, simulator, and spawn an ego vehicle to collect sensor readings. For right-of-way questions, we identify intersections in the CARLA maps and randomly spawn vehicles on each side of the intersection. Each vehicle varies in color to facilitate identification in the questions. + +# 4. Method + +In this section, we describe our approach to evaluating models on our proposed dataset. The methodology includes question-type classification, model evaluation using Chain of Thought (CoT) [81] reasoning, Retrieval-Augmented Generation (RAG) [41] techniques, and model fine-tuning on the benchmark. + +Question-Type Classification: To precisely assess model performance across specific traffic rule categories, we di + +vide the DriveQA-T dataset questions into types. This enables us to assess performance on specific traffic rule categories, thereby providing a nuanced understanding of how well they generalize across various traffic contexts. Specifically, we apply hierarchical clustering [58] to organize questions into semantically coherent groups, ensuring that similar questions are grouped together based on their thematic content. We begin by generating embeddings for each question using BERT [37], which effectively captures the semantic nuances of each question and represents them in a high-dimensional embedding space. By applying hierarchical clustering to these embeddings, we identify clusters that correspond to distinct traffic rule topics, such as traffic signals, speed limits, parking regulations, etc. To interpret and label each cluster, we use KeyBERT [31] to extract semantic keywords for each group, combined with sample questions from each cluster, finally we assign descriptive types to the clusters. In DriveQA-V, we assign types manually (see supplementary for more details). + +Fine-Tuning: Off-the-Shelf models were trained on open web data, thus having potential access to driver handbooks and tests. To further investigate the role of training data for our task, we also fine-tune models on our dataset. We find this to enhance, but not fully address, models' ability to handle the specific complexities of traffic scenarios. We employ LoRA [33], which reduces the number of trainable parameters by introducing low-rank updates to the weight matrices in transformer layers, allowing efficient fine-tuning without requiring extensive computational resources. + +CoT and RAG: We employ CoT reasoning and RAG-based context in our evaluation. CoT reasoning guides the LLMs and MLLMs through each reasoning step in a logical progression, which allows us to test their capacity for logical consistency, especially in multi-vehicle or rule-based scenarios. We also evaluate the produced reasoning, e.g., to ensure correct answers are selected for the correct reasons. For RAG, we construct a retrieval corpus derived from the official driver's handbooks of all 50 U.S. states and DC. This corpus serves as a reliable, contextually relevant reference to provide the models with related context when answering questions. By retrieving it for each question, RAG-based context grounds the model's responses in actual regulations, aiming to enhance both the accuracy and contextual relevance of answers. + +# 5. Experiments + +# 5.1. Setup + +We evaluate our dataset on various MLLMs. For each model type, we consider both open-source and closed-source variants, applying CoT and RAG strategies to structure the input prompts. Our evaluation is based not only on testing the original capabilities of each off-the-shelf model + +but also on a comprehensive analysis of their performance after fine-tuning the open-source checkpoint on our dataset. + +Prompt Structure: We designed four prompt structures to explore model performance under varying levels of reasoning and contextual support. Beginning with a basic prompt, we tested standard question-answering without additional guidance. Building on this, we introduced a CoT prompt to encourage step-by-step reasoning, aiming to enhance answer consistency in complex scenarios. To further improve contextual relevance, we combined CoT with RAG-based context by retrieving pertinent information from drivers' handbooks, thereby grounding the responses in real-world regulations. Finally, we assessed the impact of RAG-based context alone, where we provided retrieved contextual information without step-by-step reasoning. These four prompts allowed us to examine the models' capabilities in integrating both reasoning and factual support effectively. + +Metrics: To comprehensively evaluate our model's performance on both the DriveQA-T and DriveQA-V datasets, we use accuracy as the primary metric, reflecting the model's ability to correctly answer a wide range of driving-related questions across textual and visual domains. For the DriveQA-T dataset, we place an additional emphasis on reasoning capability, as each question includes an accompanying explanation. To measure the relevance of the model's reasoning, we employ BLEU-4 [60] and ROUGE-L [46], providing insights into the model's ability to generate responses that are not only accurate but also demonstrate high-quality reasoning aligned with expected standards. + +# 5.2. Results + +Performance of LLMs on DriveQA-T: Table 2 presents the performance of various models on our DriveQA-T dataset. Phi-3.5-mini and Gemma-2 (9B) generally perform better across most categories than other models, demonstrating their ability to comprehend driving rules. Observably, models with CoT reasoning and RAG-based context tend to achieve higher accuracy, suggesting that these enhancements contribute to performance improvements. This trend highlights the importance of advanced reasoning and contextual retrieval for complex, rule-based tasks. While certain models show promising results in accurately interpreting and following traffic regulations, consistent performance across diverse driving-related categories may still require further refinement. + +As shown in Table 2, all models exhibit a significant improvement in overall accuracy after fine-tuning. However, they still struggle with numerical questions, such as those in the "Limits" and "Alcohol" categories. This difficulty suggests that models may lack the precise numerical reasoning capabilities needed to respond accurately to questions involving specific values or quantitative thresh + +Table 2. Challenging Categories on DriveQA-T. We show the results of most difficult 3 types: Limits: Speed and Distance Limits, Parking: Parking and Wheel Positioning, Intersection: Right-of-Way and Lane Selection. The Average is the summary based on all 19 types of questions. We denote with green the top method, and light green second best. + +
ModelsSizeCoTRAGFinetuneLimitsParkingIntersectionAverage
Gemma-2 [75]2B42.1535.6427.8844.15
✓42.9842.5734.5152.77
✓✓58.6847.5255.7556.62
✓✓✓62.4061.3985.8472.01
Gemma-2 [75]9B57.8554.4658.4171.00
✓59.5058.4262.8372.20
✓✓64.8868.3277.8876.91
✓✓✓72.3188.1291.1587.28
Llama-3.1 [26]8B53.7237.6248.2355.89
✓55.3738.6165.9356.22
✓✓55.3746.5368.5860.79
✓✓✓72.7386.1491.5987.62
Llama-3.2 [26]3B36.7835.6442.9250.93
✓48.3526.7349.5648.92
✓✓61.1653.4761.5064.19
✓✓✓69.4275.2585.8482.82
Phi-3.5-mini [3]3.8B49.1748.5179.6569.79
✓55.7945.5479.6571.14
✓✓63.2262.3884.9677.30
✓✓✓66.9465.3587.1781.08
GPT-4o [59]-✓✓76.7293.7597.2791.96
+ +Table 3. Performance of CoT Reasoning on DriveQA-T. The evaluation includes both off-the-shelf and fine-tuned models under two settings of with and without RAG. + +
ModelsSizeBLEU-4ROUGE-L
w/o RAGw/ RAGw/o RAGw/ RAG
Off-The-Shelf Models
Gemma-2 [75]2B0.10980.17040.29200.3387
Gemma-2 [75]9B0.32340.31160.42950.4276
Llama-3.1 [26]8B0.25730.26190.32700.3317
Llama-3.2 [26]3B0.22580.31400.33480.4024
Phi-3.5-mini [3]3.8B0.24370.25740.36160.3996
GPT-4o [59]-0.39050.39890.53540.5393
Finetuned Models
Gemma-2 [75]2B0.36230.29340.50580.4458
Gemma-2 [75]9B0.41120.41050.54200.5528
Llama-3.1 [26]8B0.30420.29460.47490.4750
Llama-3.2 [26]3B0.21310.19160.38530.3570
Phi-3.5-mini [3]3.8B0.23620.18910.40730.3476
+ +olds, which are critical in understanding speed limits, alcohol levels, and other regulatory metrics. Furthermore, for certain decision-making-focused categories, including "Passing", "Signs" and "Turning", most models achieve only slightly above accuracy of $80\%$ . These categories are crucial for safe driving in practical conditions, highlighting the models' continuous shortcomings in handling nuanced, context-dependent traffic rules despite fine-tuning improvements. + +CoT Reasoning of LLMs on DriveQA-T: Table 3 shows the evaluation results of CoT reasoning on the DriveQA-T dataset. Most models show improvements when using RAG-based context. Specifically, GPT-4o achieves the highest BLEU-4 and ROUGE-L scores among the off-the + +shelf models, reaching a BLEU-4 score of 0.3989 and a ROUGE-L score of 0.5393 with RAG-based context. After fine-tuning, Gemma-2 (9B) surpasses GPT-4o in both BLEU-4 and ROUGE-L scores, demonstrating the effectiveness of fine-tuning in adapting the model specifically to traffic rules and enabling it to provide more accurate, context-specific explanations. However, these scores still fall short of what would be considered high-quality for generating fully robust and exhaustive explanations, indicating that the models are not yet capable of consistently producing complete and nuanced responses. Furthermore, the lower scores of Llama-3.2 and Phi-3.5-mini after fine-tuning suggest potential issues. One possible reason for this decline is overfitting the fine-tuning dataset, which may cause the models to become too specialized and lose some of their generalization capabilities. This overfitting can result in explanations that are overly tailored to specific training examples, reducing the models' ability to produce flexible, broadly applicable responses. Additionally, fine-tuning may interfere with the effectiveness of RAG-based retrieval, leading to less relevant contextual information and, consequently, lower alignment with ground-truth explanations. These factors highlight the challenges of balancing specificity and generalization in fine-tuning for complex, rule-based tasks. + +Performance of MLLMs on DriveQA-V: Table 4 presents the accuracy of MLLM models on DriveQA-V, which assesses model performance across intersection types and traffic sign categories. The dataset divides intersections into 4 different categories based on the intersection types and camera perspective, and 4 different categories of signs based on most states' driver handbooks. Among the off-the-shelf models, GPT-4o achieves the highest accuracy in all intersection and sign categories, with a particularly strong performance in the sign types (around $94\%$ ). This suggests that GPT-4o possesses a deep understanding of signs. However, for intersection-based categories, the performance remains relatively low, with the highest off-the-shelf accuracy of $60.36\%$ in the "T-Top" category. Most models except GPT-4o perform below random guess level ( $25\%$ ) in several categories due to bias [2]. This indicates that off-the-shelf models struggle to fully understand and apply traffic rules in intersection scenarios, which often require more complex visual-spatial reasoning. Additionally, Finetuning significantly enhances model performance across all categories. All models achieve notable improvements after fine-tuning, which demonstrates that fine-tuning effectively adapts MLLMs to handle the visual-spatial and contextual nuances for the accurate understanding of both right-of-way rules and traffic signs. + +Despite these gains, there remain limitations. Both LLaVA-1.5 and VILA-1.5, even after fine-tuning, achieve only moderate accuracy in intersection categories, with par + +Table 4. Summarized Results on DriveQA-V. We show model performance (accuracy %) for VQA. The dataset is divided into two main categories: intersections and signs (categorized into camera perspective and type). + +
ModelsSizeDriveQA-V (Inters.)DriveQA-V (Signs)Average
T-FrontT-TopCross-FrontCross-TopRegulatoryWarningGuideTemporary Control
Off-The-Shelf Models
Mini-InternVL [29]2B27.8324.8326.0025.6564.0655.3465.8245.0441.82
LLaVA-1.5 [48]7B23.3023.1024.9623.2423.5126.6122.3121.1023.52
LLaVA-1.6-mistral [49]7B18.7719.6630.9930.4742.5843.0152.7537.5034.47
VILA-1.5 [47]8B15.5316.8615.6920.3525.3223.3327.7821.4620.79
GPT-4o [59]-55.0960.3650.5259.1493.7594.0295.1194.3575.29
Finetuned Models
Mini-InternVL [29]2B86.7382.0774.3376.0193.7992.1991.0896.5186.59
LLAVA-1.5 [48]7B64.1870.5754.7756.5272.2273.0076.8289.2769.67
LLaVA-1.6-mistral [49]7B86.0885.5274.3874.5382.0584.1088.1194.4983.66
VILA-1.5 [47]8B47.6752.2755.6057.2687.1083.1491.4695.3371.23
+ +Table 5. 10 Most Difficult Sign Types in DriveQA-V. We calculate the lowest accuracy over all the models' performance based on different sign types. Most challenging cases belong to regulatory and warning signs. + +
ModelSizePlaygroundTrauma CenterGolf CartsGround ClearanceNo StoppingNo ParkingPush ButtonWeekday OnlyFire TruckTractor Crossing
Off-The-Shelf Models
Mini-InternVL [29]2B0.0027.7814.8115.0042.1048.140.008.700.0020.00
LLaVA-1.5 [48]7B5.262.385.4311.7616.3010.4212.5020.8320.4521.59
LLaVA-1.6-mistral [49]7B0.0016.6725.9325.005.0022.2248.0017.390.0024.00
VILA-1.5 [47]8B1.322.380.008.828.705.212.7819.793.4131.82
Finetuned Models
Mini-InternVL [29]2B88.4694.4488.8895.00100.0090.9196.00100.0092.8680.00
LLaVA-1.5 [48]7B73.6885.7161.9664.7165.2261.4675.0037.5059.0957.95
LLaVA-1.6-mistral [49]7B80.7783.3374.0785.0085.1977.2792.00100.0092.8692.00
VILA-1.5 [47]8B68.4259.5283.7066.1865.2279.1766.6780.2180.6852.27
+ +ticularly lower performance on first-person perspective images. This suggests that the models still struggle with complex, multi-vehicle intersection scenarios, where perspective and spatial relationships are critical. For the traffic signs recognition task, We can observe the best training performance in the Guide Signs and Temporary Traffic Control categories. This is because guide signs typically feature simpler images with blue backgrounds, while temporary traffic control signs have distinct orange backgrounds and normally larger sign sizes, making them easier for the model to learn and generalize. However, many critical traffic signs fall under the Regulatory and Warning categories, including speed limit, no entry, etc. As shown in Table 5, among the ten worst-performing sign types, only "Trauma Center" belongs to the Guide Signs category, with the most challenging signs coming from the Regulatory and Warning categories. This highlights significant room for improvement in the current visual model. While fine-tuned models perform well on "Guide" and "Temporary Control" signs, their performance does not consistently exceed $90\%$ . Based on both Table 2 and Table 4 and shown in categories' accuracy, the zero-shot performance on DriveQA-V is much lower than on DriveQA-T. This indicates that cur + +rent MLLMs' fine-grained perception and visual reasoning capabilities are nascent, exhibiting systematic shortcomings due to CLIP's failures. + +Role of Difficulty and Distractors: To further increase the evaluation difficulty, we adopt a negative sampling strategy to construct more challenging distractors. Specifically, for DriveQA-T, we construct a difficult question set containing 1249 questions. For DriveQA-V (Signs), we leverage metadata, i.e., the ground-truth traffic sign artifact categories to ensure that distractors belong to the same category as the correct answer. For numeric signs, all candidates are constrained to numerical values to further increase ambiguity. Evaluation results on GPT-4o and a representative open-source baseline are summarized in Table 6. + +Sim-to-Real Transferability: We evaluate our models finetuned on DriveQA on a curated dataset by us from Mapillary [57] (1303 annotated images, including 166 sign types), as shown in Table 7. Additionally, results in Table 8 show the downstream trajectory planning task with OpenEMMA [87] on nuScenes dataset, where our task-agnostic QA model is intentionally only fine-tuned on DriveQA but tested zero-shot in waypoint prediction to measure general + +Table 6. Role of Difficult Questions and Distractors. The accuracy degradation on a hard subset of DriveQA-T and on a challenging set of DriveQA-V with negative sampling shows the limitations of current models, including GPT-4o, in accurately understanding complex traffic rules and signs. + +
Test SetModelsSizeNeg. SamplingDegradation
BeforeAfter
DriveQA-TLlama-3.1 [26]8B55.8939.8728.66%
GPT-4o [59]-91.9678.9114.19%
DriveQA-V (Signs)LLaVA-1.5 [48]13B11.929.8217.62%
GPT-4o [59]-94.1079.4015.62%
+ +Table 7. Sim-to-Real Generalization. We pre-train on synthetic DriveQA (DQA) and evaluate on real-world Mapillary images. The Mapillary dataset comprises challenging scenarios with various traffic sign placements, occlusion, and illumination. + +
Test SetModelsSizeAccuracy
Off-The-ShelfDQA-Finetuned
Real-World Mapillary [57]Mini-InternVL [29]2B57.2568.61
LLaVA-1.5 [48]7B40.6852.34
LLaVA-1.6-mistral [49]7B53.1857.71
VILA-1.5 [47]8B34.3860.86
GPT-4o [59]-84.73-
+ +Table 8. End-to-End Trajectory Planning Results on nuScenes. We compute the L2 error at different prediction horizons (1s, 2s, and 3s). Lower L2 error shows our DriveQA (DQA) dataset can transfer from simulation to real-world driving tasks. + +
ModelPretrained on DQAL2(m)↓
1s2s3sAvg.
LLaVA-1.6-mistral [49] (OpenEMMA [87])1.493.384.092.98
LLaVA-1.6-mistral [49]✓1.303.463.982.91
InternVL-2.5-8B1.663.364.153.06
✓1.303.083.732.71
+ +Table 9. Evaluation on BDD-OIA Dataset [88]. We report mean F1 score (mF1) and overall F1 score $(\mathrm{F1_{all}})$ for both action and explanation tasks. The results show that fine-tuning on DriveQA improves performance on both tasks. + +
ModelFinetuneActionExplanation
DQABDD-OIAmF1↑F1all ↑mF1↑F1all ↑
InternVL-2.5-8B✓0.29510.5540.06240.2223
0.22260.41030.15490.1850
✓0.49110.70720.28720.5015
✓✓0.52850.73340.31020.5448
+ +ization. Reduced L2 errors show the transferability of our dataset. However, nuScenes lacks diversity and is generally uneventful (e.g., minimal signage), while our benchmark exhaustively covers all traffic rules and scenarios. We therefore also make evaluations on the more diverse datasets of BDD-OIA [88] as shown in Table 9. After fine-tuning on DriveQA, the models achieve better performance in cross-domain real-world driving tasks, demonstrating the effectiveness of our data in improving the understanding of traffic rules and real-world generalizability. We provide additional analysis in the supplementary. + +Limitation: While our benchmark, models, and analysis provide insights into the performance of models in understanding diverse traffic rules for autonomous driving, there + +are several limitations, which we plan to address in future work. First, the benchmark primarily evaluates static, structured knowledge of traffic rules. While this is aligned with standard driving knowledge tasks, there is an opportunity to leverage video-based models in the future (e.g., using our augmented CARLA simulation). Our analysis demonstrates that incorporating knowledge from text does indeed transfer to dynamic settings in nuScenes, yet vision-based reasoning remains nascent in MLLMs (or even spatial reasoning [2]). Moreover, our study highlights weaknesses in numerical reasoning and spatial awareness yet does not explore potential mitigation strategies beyond fine-tuning. The reliance on synthetic data also raises concerns about domain adaptation. Nonetheless, simulation data is crucial for scalability, as we are able to control for various variations, including occlusions and ambiguous signage, which may be rare in real-world benchmarks. Finally, while the dataset includes controlled variations in environmental factors like lighting and weather, it does not extensively cover edge cases such as emergency vehicle interactions (only covered in DriveQA-T) or pedestrian intent recognition. The models also exhibit biases towards frequently seen traffic patterns, which may result in poor generalization to geographically diverse driving environments with different road layouts and regulations. + +# 6. Conclusion + +In this paper, we introduce DriveQA, a novel benchmark for autonomous driving that evaluates models through text-based (DriveQA-T) and visual-text (DriveQA-V) question-answering, focusing on general traffic rules, traffic signs, and complex right-of-way scenarios. Our evaluation of state-of-the-art models reveals critical limitations: even fine-tuned models struggle with nuanced right-of-way scenarios, falling short of the reasoning needed for safe driving guidance. Our work deliberately focuses on static visual and textual inputs, i.e., to align with real-world driver knowledge tests. While video-based learning is not required to adhere to these standards, future research could explore hybrid frameworks incorporating video to address time-dependent scenarios. Ultimately, while humans can learn traffic rules through textual instruction and contextual practice, current models remain overly reliant on observational training data. Models thus lack the ability to internalize explicit textual knowledge and apply it effectively in decision-making. This suggests that learning traffic rules from text remains an underexplored paradigm, highlighting the need for methods that better integrate language understanding with spatial reasoning. + +Acknowledgments: We thank the National Science Foundation (award IIS-2152077) and Red Hat Collaboratory (award #2024-01-RH02) for supporting this research. + +# References + +[1] Carla autonomous driving leaderboard. https://leaderboard.carla.org/, 2022.3 +[2] Eyes wide shut? exploring the visual shortcomings of multimodal llms. In CVPR, 2024. 2, 3, 6, 8 +[3] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. Phi-3 technical report: A highly capable language model locally on your phone. arXiv:2404.14219, 2024. 1, 6 +[4] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florecia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Recent efforts have explored reasonable acceleration schemes by reducing the number of sampling steps. However, these approaches treat all regions of the image equally, overlooking the fact that regions with varying levels of reconstruction difficulty require different sampling steps. To address this limitation, we propose PatchScaler, an efficient patch-independent diffusion pipeline for single image super-resolution. Specifically, PatchScaler introduces a Patch-adaptive Group Sampling (PGS) strategy that groups feature patches by quantifying their reconstruction difficulty and establishes shortcut paths with different sampling configurations for each group. To further optimize the patch-level reconstruction process of PGS, we propose a texture prompt that provides rich texture conditional information to the diffusion model. The texture prompt adaptively retrieves texture priors for the target patch from a common reference texture memory. Extensive experiments show that our PatchScaler achieves favorable performance while significantly speeding up inference. Project page: https://github.com/yongliuy/PatchScaler. + +# 1. Introduction + +Single image super-resolution (SISR) aims to reconstruct a high-resolution (HR) image from its low-resolution (LR) observation, a highly ill-posed problem due to the unknown degradation processes in real-world scenarios. As two predominant approaches, deep convolutional neural + +![](images/c668a283b67b5e95f23076a19cea7acd0c2fde61367f1f116f609e55bbb7544d.jpg) +(a) Unified sampling vs. adaptive sampling + +![](images/6905f43743a37ec22036ba1e604fb9a5fcc6c24cf5021d6b69737d0c2dda977b.jpg) +(b) Quantitative evaluation +Figure 1. (a) Analysis of unified sampling and adaptive sampling. (b) Quantitative comparison on the RealSR [6] dataset. + +network (CNN)-based [25, 51, 66, 70] and Transformer-based [27, 29, 56, 67] SISR methods have made significant progress in the past decade. However, most of them are optimized primarily for the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM), which are less effective in restoring realistic image details. + +Diffusion models [13, 44], with their powerful ability to model data distributions from noise, have offered immense potential for conditional generation tasks, such as image synthesis [10, 41, 57], image editing [5, 18, 55], and image super-resolution [28, 48, 60]. Although diffusion models have achieved significant success in the field of image superresolution (SR), their inference process remains inefficient due to the large number of iterative sampling steps required for high-quality image reconstruction. + +Recent methods have attempted to accelerate diffusion-based SR models by introducing conditional distillation [34, 52] or redefining the diffusion process [62, 63]. However, these approaches tend to treat all regions of an image equally and indiscriminately reduce the number of sampling steps, which inevitably compromises the quality of the super-resolved images. Furthermore, when dealing with high-resolution images, these approaches continue to incur substantial computational costs. + +In this paper, we observe that a unified sampling process is suboptimal for all patches of an image. As illustrated in Fig. 1 (a), patches with fewer structural details can be effectively reconstructed with fewer sampling steps, whereas patches rich in textural information require more sampling steps. This observation motivates us to develop a patch-adaptive accelerated diffusion model for SISR. + +Based on this insight, we propose PatchScaler, an efficient diffusion-based SR method that dynamically accelerates the inference process through a patch-independent diffusion pipeline. Specifically, we first employ a global restoration module to generate a coarse HR feature along with a confidence map that reflects the reconstruction difficulty across different regions. We then introduce Patch-adaptive Group Sampling (PGS), which divides the coarse HR features into patches and groups them according to quantified reconstruction difficulty. PGS identifies an optimal shortcut point and sampling configurations for each group, enabling a shortcut path from coarse HR patches to the ground truths. Finally, we introduce a Patch-wise Diffusion Transformer (PatchDiT) as the backbone of PatchScaler to refine the fine textures from the coarse HR patches. Since the reconstruction of local image textures plays a more critical role for SISR than the Text2Image task, Patch-DiT is naturally well-suited for restoring lost details. + +To further improve the patch-level reconstruction quality of PGS, we propose a texture prompt that supplies rich conditional information to Patch-DiT by retrieving high-quality texture priors for the target patch from a universal reference texture memory. The texture prompt is effective for reconstructing local details and addressing the misalignment issue between image and text prompts in diffusion models [7]. Experiments show that our PatchScaler significantly accelerates inference speed (e.g., only $0.23 \times$ the runtime of ResShift [63] on the 512→2048 SR task), while still maintaining superior performance, as shown in Fig. 1(b). We summarize our main contributions as follows: + +- We propose PatchScaler, a novel patch-independent SR pipeline that employs patch-adaptive group sampling to dynamically accelerate the sampling process, enabling efficient restoration of high-resolution images. +- We present an effective texture prompt for the Patch-wise Diffusion Transformer (Patch-DiT) in PatchScaler to provide rich texture priors and improve reconstruction quality. +- Experiments show that PatchScaler achieves favorable performance on several datasets against state-of-the-art SR methods and is much more efficient than previous diffusion-based SR methods. + +# 2. Related Work + +Single Image Super-Resolution. Over the past decade, a series of deep networks [15, 23, 29, 36, 45, 70, 71] have been proposed to address SISR challenges. For real-world + +degradation scenarios, Ji et al. [15] proposed RealSR that learns the specific degradation of blurry and noisy images by estimating the kernel and noise. By incorporating GANs [11, 43, 50] into the SISR task, Zhang et al. [64] presented BSRGAN, a practical degradation model that synthesizes realistic degradations via a random shuffling strategy. Wang et al. [51] proposed Real-ESRGAN that employs a high-order degradation process to simulate practical degradations and incorporates sinc filters to replicate common ringing and overshoot artifacts. Liang et al. [27] introduced SwinIRGAN based on the Swin Transformer [30], to achieve competitive image restoration performance. Nevertheless, these approaches often struggle to generate realistic fine details. + +Diffusion Model. Recently, diffusion models have brought significant gains to SISR task [28, 48, 52, 60, 63] due to their ability to effectively model complex distributions. For instance, Wang et al. [48] presented StableSR, integrating LR images into the diffusion model via a time-aware encoder to reconstruct high-quality HR images. Lin et al. [28] proposed a unified image restoration framework, DiffBIR, which sequentially uses two stages of restoration and generation to ensure fidelity and realism. Yue et al. [63] introduced ResShift, utilizing an iterative sampling approach from LR to HR images by shifting residuals. However, these methods treat all regions of the image equally and apply the uniform sampling indiscriminately to different regions, which is suboptimal. To this end, we propose an efficient patch-independent diffusion pipeline, namely PatchScaler, which achieves superior results with faster inference speed. + +# 3. PatchScaler + +# 3.1. Overall Architecture + +The overall architecture of PatchScaler is illustrated in Fig. 2. Given an LR image $I_{\mathrm{LR}}$ , we first encode it using the frozen encoder [41] and obtain the latent LR feature $y_{\mathrm{LR}}$ . Then, to remove the possible degradations (e.g., noise and artifacts) from $y_{\mathrm{LR}}$ and assess the reconstruction difficulty of different feature regions, we develop a simple yet effective Global Restoration Module (GRM), which generates the coarse high-resolution (HR) feature $y_{\mathrm{HR}}$ and a confidence map $C$ , simultaneously. Next, to achieve dynamic sampling for different feature regions, we introduce a Patch-adaptive Group Sampling (PGS), which partitions $y_{\mathrm{HR}}$ into the coarse HR patches and derives the quantified confidence map $Qmap$ by averaging the confidence map $C$ within the patch. Based on the $Qmap$ , the coarse HR patches are divided into groups with different sampling configurations. Patch-DiT restores the fine details of the coarse HR patches of different groups using the given sampling configurations and obtains the corresponding HR patches. Finally, these patches are reshaped into $\hat{x}_{\mathrm{HR}}$ and decoded to produce the HR output $\hat{I}_{\mathrm{HR}}$ . + +![](images/93fcd0e2961b335c6788d093ac4d2b9a931d3298a65c4495d65d1ca9cf9a7e78.jpg) + +![](images/7f69c40ddf19874f93e9eacfd711bac810b80fd197750015f8d729608b2d2cbc.jpg) +Figure 2. Overview of the proposed PatchScaler. PGS dynamically assigns feature patches into groups with different sampling configuration based on quantified confidence map. Moreover, the texture prompt provides rich conditional information for Patch-DiT by retrieving high-quality texture priors from universal RTM. + +# 3.2. Global Restoration Module + +To preliminarily remove the degradation of $y_{\mathrm{LR}}$ and obtain the reconstruction difficulty corresponding to different feature regions, we introduce a Global Restoration Module (GRM) for PatchScaler. + +Specifically, GRM consists of a series of residual blocks and downsampling convolutions followed by a stack of residual blocks with upsampling convolutions and skip connections. Different from the previous models, our GRM has two output branches at the last scale. One branch generates coarse HR feature $\mathbf{y}_{\mathrm{HR}}$ through the normalization-SiLU-conv layers; the other branch generates confidence map $C$ through the conv-SiLU-conv-sigmoid layers. $C$ is designed to estimate the reconstruction difficulty of different regions of the coarse HR feature $\mathbf{y}_{\mathrm{HR}}$ by predicting the distance between $\mathbf{y}_{\mathrm{HR}}$ and ground truth $x_{\mathrm{HR}}$ . The detailed architecture of GRM is illustrated in Fig. 9(a) in the appendix. + +# 3.3. Patch-adaptive Group Sampling + +To achieve adaptive sampling of different regions of the image based on the reconstruction difficulty, we propose a patch-adaptive group sampling strategy for PatchScaler, as illustrated in Fig. 2 (b). + +Denoising Diffusion Probabilistic Models (DDPM) [13, 44] assume a forward diffusion trajectory where Gaussian noise is gradually applied to real data $\boldsymbol{x}_0$ . This process can be expressed in a closed form as: + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {0}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t}; \sqrt {\bar {\alpha} _ {t}} \boldsymbol {x} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {1} +$$ + +where $\bar{\alpha}_t\coloneqq \prod_{i = 0}^t\alpha_i$ . $\pmb {x}_t$ can be sampled by $\pmb {x}_t =$ $\sqrt{\overline{\alpha}_t}\pmb {x}_0 + \sqrt{(1 - \bar{\alpha}_t)}\epsilon$ for $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ . In the reverse pro + +![](images/0e00706b018bcd4e53ca8e301ef470d4432285300a28ad5126496ae14b545658.jpg) +Figure 3. Illustration of the proposed PGS, which establishes a shortcut path between $\pmb{x}_0$ and $\pmb{y}_0$ . PGS treats different patches discriminatively and dynamically assigns different sampling configurations. Here, $\pmb{y}_0$ and $\pmb{x}_0$ denote the coarse HR patch and ground truth, respectively. $f_{\theta}$ denotes the diffusion model Patch-DiT. + +cess, denoising models $\pmb{f}_{\theta}(\pmb{x}_t,t)$ are trained to map any point at any time step on the diffusion trajectory to $\pmb{x}_0$ . + +For the SISR task, since there is a deviation between the LR image and the ground truth, previous approaches either apply a large noise strength (i.e., $t = T$ ) to the LR image, approximating the endpoint $x_{T}$ of diffusion trajectory, or sample $x_{T}$ directly from a Gaussian noise $\mathcal{N}(0,\mathbf{I})$ . Subsequently, the HR result is reconstructed step by step from $x_{T}$ with a unified global sampling that treats all regions of the image equally. However, we argue that it is redundant because simple patches can be reconstructed with fewer iterations than hard patches, as illustrated in Fig. 1(a). To enable dynamic acceleration of the denoising process, we propose Patch-adaptive Group Sampling (PGS), which establishes a shortcut path between HR patch $x_{0}$ and coarse HR patch $y_{0}$ as shown in Fig. 3. Here, $y_{0}$ is taken from the patch set. + +Specifically, let $\pmb{x}_0 = \pmb{y}_0 + \triangle \pmb{x}_0$ , then Eq. (1) can be reformulated as: + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {y} _ {0}, \triangle \boldsymbol {x} _ {0}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t}; \sqrt {\bar {\alpha} _ {t}} \left(\boldsymbol {y} _ {0} + \triangle \boldsymbol {x} _ {0}\right), (1 - \bar {\alpha} _ {t}) \mathbf {I}\right). \tag {2} +$$ + +![](images/d4677eaec2529cfc1a52c22ba352b002224f2bd36899e892bfcd100a4bdbd080.jpg) +Figure 4. Examples of coarse HR images and $Qmap$ . + +The goal of PGS is to identify an appropriate shortcut point $\tau \in [1, T]$ along the diffusion trajectory for each patch such that $\sqrt{\bar{\alpha}_{\tau}} \triangle x_0 \to 0$ . For a small $\triangle x_0$ , $\tau$ can be small enough, while for a large $\triangle x_0$ , a larger $\tau$ is required to ensure that $\bar{\alpha}_{\tau}$ is sufficiently small. In this way, the original diffusion trajectory at time step $\tau$ is approximated as: + +$$ +q \left(\boldsymbol {x} _ {\tau} \mid \boldsymbol {y} _ {0}\right) \approx \mathcal {N} \left(\boldsymbol {x} _ {\tau}; \sqrt {\bar {\alpha} _ {\tau}} \boldsymbol {y} _ {0}, (1 - \bar {\alpha} _ {\tau}) \mathbf {I}\right). \tag {3} +$$ + +This finding encourages us to introduce a new forward diffusion trajectory for the coarse HR patch $\mathbf{y}_0$ with truncated forward diffusion time steps: + +$$ +q \left(\boldsymbol {y} _ {t} \mid \boldsymbol {y} _ {0}\right) = \mathcal {N} \left(\boldsymbol {y} _ {t}; \sqrt {\bar {\alpha} _ {t}} \boldsymbol {y} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {4} +$$ + +where $t = 1, \dots, \tau$ . As a result, the reverse process can start from a shortcut point $t = \tau$ , thus significantly reducing the required number of sampling steps $N$ . + +In practice, to obtain a preliminary smaller $\triangle x_0$ , we first preliminarily remove the degradations from $y_{LR}$ using GRM and obtain the coarse HR feature $y_{HR}$ . Meanwhile, the reconstruction difficulty in the different regions of $y_{HR}$ is estimated by the confidence map $C$ , which predicts the distance between the coarse HR feature $y_{HR}$ and ground truth $x_{HR}$ . To facilitate parallel computing and improve efficiency, we derive the quantified confidence map $Qmap$ from $C$ by averaging the confidence map $C$ within the patch: + +$$ +Q m a p \left(\boldsymbol {y} _ {0}\right) := \left\{ \begin{array}{l l} \text {S i m p l e}, & A v g (C \langle \boldsymbol {y} _ {0} \rangle) \in (\gamma_ {1}, 1 ], \\ \text {M e d i u m}, & A v g (C \langle \boldsymbol {y} _ {0} \rangle) \in (\gamma_ {2}, \gamma_ {1} ], \\ \text {H a r d}, & A v g (C \langle \boldsymbol {y} _ {0} \rangle) \in [ 0, \gamma_ {2} ] \end{array} \right. \tag {5} +$$ + +where $Avg(C\langle \pmb{y}_0\rangle)$ represents the average confidence value over the patch, $\gamma_{1}$ and $\gamma_{2}$ are the confidence thresholds. Based on the Qmap, PGS classifies the patches into three groups. Fig. 4 presents two examples of coarse HR images generated by GRM along with the corresponding quantified confidence maps Qmap. It can be seen that our method accurately quantifies the reconstruction difficulty of different regions within the image. We analyze the impact of different numbers of groups on model performance in Sec. 4.3.2. + +# 3.4. Texture Prompt + +To address the misalignment problem between image and text prompt in the diffusion model, we introduce a novel + +texture prompt for PatchScaler that can greatly improve the patch-level reconstruction quality of PGS, as illustrated in Fig. 2 (c). + +# Algorithm 1 The Construction Process of RTM. + +Input: $\mathcal{E}$ ; $\mathcal{T}$ ; High-quality image set. + +$\triangleright \mathcal{E}$ is the encoder; $\mathcal{T}$ is the feature extraction module of Texture Classifier. + +1: Extract image patch set $X_{\mathrm{patch}}$ by random cropping from high-quality image set; +2: Obtain initial latent feature patch set: RTM-value $^{\mathrm{init}} = \mathcal{E}(X_{\mathrm{patch}})$ ; +3: Obtain corresponding semantic feature vector: RTM-key $\mathrm{init} = \mathcal{T}$ (RTM-value $\mathrm{init}$ ); +4: Use FPS algorithm to cluster RTM-key $^{\text{init}}$ and get the most representative subset RTM-key; +5: Obtain corresponding RTM-value based on RTM-key: + +Output: RTM-key; RTM-value. + +Reference Texture Memory. Our RTM serves as a universal repository for storing diverse and high-quality texture feature patches (denoted as RTM-value), along with their corresponding semantic feature vectors (denoted as RTM-key). The construction process is shown in Algorithm 1. We first extract 20,000 initial latent texture patches (i.e., RTM-value $^{\text{init}}$ ) from the high-quality image datasets DIV2K [1], OutdoorSceneTraining [49], and Manga109 [33], which contain a wide variety of categories, such as animal, sky, cartoon, building, mountain, and plant. Subsequently, we introduce a pre-trained texture classifier to extract deep semantic representation (i.e., RTM-key $^{\text{init}}$ ) from the RTM-value $^{\text{init}}$ . To accelerate the feature retrieval process, we employ the farthest point sampling algorithm (FPS) [39] on RTM-key $^{\text{init}}$ to sample 2,000 representative pairs as our final RTM. It is important to note that all of these operations are performed offline, thus incurring no additional inference cost. + +Retrieval of Texture Priors. Our objective is to retrieve high-quality texture priors from RTM for the target feature patch $\mathbf{y}_0$ and transfer them into Patch-DiT. The retrieval process is shown in Algorithm 2. We first use the texture classifier to project $\mathbf{y}_0$ into a semantic feature vector, denoted as $\mathbf{y}_0$ -query. We then calculate the similarity scores between $\mathbf{y}_0$ -query and RTM-key using normalized inner products [68]. By ranking these similarity scores, we retrieve the top- $K$ matches, denoted as $d^k$ , along with corresponding texture prior $tp^k$ , for $\mathbf{y}_0$ -query across the entire RTM-key. We then introduce a similarity-aware texture encoder attached to Patch-DiT to encode these texture priors. + +Patch-DiT. Since previous diffusion models [35, 41, 42] produce inferior results in low-resolution patches [69], we propose Patch-DiT upon DiTs [37]. We explore the following modifications: (1) concatenating $\mathbf{y}_0$ with the noisy latent $\mathbf{y}_{\tau}$ as the input of Patch-DiT to generate content-consistent results; (2) adding a cross-attention layer in each base block to + +incorporate the texture prompt; (3) removing the class label embedding and learnable covariance. In addition, we copy the first half of the Patch-DiT and trim it as the similarity-aware texture encoder. Features of the similarity-aware texture encoder and Patch-DiT are combined through trainable cross-attention layers [46]. Notably, our similarity-aware texture encoder is time-independent, so it does not need to be recalculated for each iteration, significantly accelerating the inference process. The detailed architecture of Patch-DiT is illustrated in Fig. 9(b) in the appendix. + +# 3.5. Training Strategy + +For the training of GRM, we incorporate the confidence-driven loss [36], which has been demonstrated to be effective in the low-level tasks [8, 32, 54], as a constraint, and the training objective is: + +$$ +L (\theta) := \left\| \boldsymbol {y} _ {\mathrm {H R}} - \boldsymbol {x} _ {\mathrm {H R}} \right\| _ {1} + \lambda \left(C \left\| \boldsymbol {y} _ {\mathrm {H R}} - \boldsymbol {x} _ {\mathrm {H R}} \right\| _ {2} ^ {2} - \eta \log (C)\right), \tag {6} +$$ + +where $\lambda$ and $\eta$ are the coefficients, and $\log (C)$ represents the logarithm of $C$ . When the regions of coarse HR are far from the ground truth, the term $C\| y_{\mathrm{HR}} - x_{\mathrm{HR}}\| _2^2$ is dominant, encouraging $C$ to decrease. Conversely, the term $-\log (C)$ becomes dominant, encouraging $C$ to approach 1. + +For the training of Patch-DiT, we optimize the reweighted variational lower bound at the patch level: + +$$ +L (\theta) := \mathbb {E} _ {\boldsymbol {x} _ {0}, t, \epsilon} \left[ \left\| \boldsymbol {\epsilon} - f _ {\theta} \left(\boldsymbol {x} _ {t}, t, \boldsymbol {y} _ {0}, t p ^ {k}, s ^ {k}\right) \right\| _ {2} ^ {2} \right], \tag {7} +$$ + +where $\mathbf{x}_0$ is the patch from the ground truth $\mathbf{x}_{HR}$ , $\mathbf{y}_0$ is the coarse HR patch, $tp^k$ denotes the retrieved texture priors, and $s^k$ denotes the corresponding top-K similarities. + +# Algorithm 2 Retrieval Texture Priors from RTM. + +Input: $\mathcal{T}$ ; RTM-key; RTM-value; coarse HR patch $y_0$ $\triangleright$ $\mathcal{T}$ represents the feature extraction module of Texture Classifier; RTM-key=Normalize( $\mathcal{T}$ (RTM-value)). +1: Obtain corresponding semantic feature vector from $\mathbf{y}_0$ : $\mathbf{y}$ -query $= \mathcal{T}(\mathbf{y}_0)$ ; +2: Calculate normalized inner products between $\mathbf{y}_0$ -query and RTM-keyi: $s_i = \langle \mathrm{RTM - key}_i, \mathrm{Normalize}(\mathbf{y}_0 \text{-query}) \rangle$ ; +3: Ranking $s_i$ and determine top-K indices $d^k$ and top-K similarities $s^k$ ; +4: Retrieve corresponding texture prior $tp^k$ from RTM-value based on top-K indices $d^{k}$ + +Output: Texture prior $tp^k$ ; top-K similarities $s^k$ . + +# 4. Experiments + +# 4.1. Experimental Settings + +Training. We train our PatchScaler based on the LSDIR [26] and HQ-50K [58] datasets, which consist of large-scale high-resolution images for image restoration. During training, the + +LR images are synthesized using the degradation pipeline of Real-ESRGAN [51]. The patch size $V$ is set to 16. We utilize the Adam optimizer [20] with a batch size of 6, and the learning rate is fixed as 5e-5. $\lambda$ and $\eta$ are set to 0.3 and 0.2, respectively. Our PatchScaler is trained for 700K iterations using the Adam optimizer [20] with a batch size of 6, while GRM only participates in the training for the first 100K iterations based on Eq. (8). The training process takes 10 days using eight NVIDIA Tesla V100 GPUs. + +Evaluation. We evaluate our PatchScaler on both synthetic and real-world datasets. For synthetic data, we generate LR-HR pairs based on randomly selected 2000 test images from LSDIR [26], referred to as LSDIR-Test, following the degradation method used in ResShift [63]. We also evaluate our model on two real-world datasets: RealSR [6] and RealSet110. As the degradation in RealSR is monotonic and lacks common SR scenes such as animals and illustrations, we collect an extended dataset named RealSet110. It is worth noting that 98 of the LR images collected from previous works [3, 17, 28, 31, 58, 63, 64], with the remaining images were collected from online sources. To evaluate the performance of our PatchScaler at both patch and image scales, the resolution of the LR images in LSDIR-Test and RealSR datasets is fixed at $128 \times 128$ , while the images in the RealSet110 dataset have arbitrary resolutions. + +# 4.2. Comparisons with State-of-the-Art Methods + +To verify the effectiveness of our PatchScaler, we conduct a series of quantitative and qualitative experiments with the following state-of-the-art SR methods: (1) classic CNN-based and Transformer-based SR methods: RealSR-JPEG [15], BSRGAN [64], RealESRGAN [51], and SwinIR [27]; (2) representative diffusion-based multi-step SR methods: LDM [41], StableSR [48], ResShift [63], DiffBIR [28], and PASD [60]; (3) the latest diffusion-based one-step SR methods: SinSR [52] and OSEDiff [53]. Following the default settings, the sampling step of ResShift [63] is set to 15. For other multi-step methods, it is set to 20. We also compare with SUPIR [61] in Sec. B of the appendix. + +Evaluations on Synthetic Data. We first evaluate our PatchScaler on the synthetic LSDIR-TEST dataset. The quantitative results are presented in Tab. 10. It can be seen that our method outperforms all others in the non-reference metrics, i.e., ManIQA [59], CLIPIQA [47], and MUSIQ [19]. ManIQA [59] utilizes a multi-dimensional attention network for perceptual assessment, CLIPIQA [47] leverages rich visual language priors from CLIP to evaluate both the perceptual quality and perceptual abstraction, and MUSIQ [19] captures image quality at different granularities using a multiscale image quality Transformer. The consistent improvements across these metrics highlight PatchScaler's superior ability to restore fine texture detail and achieve high perceptual quality. In addition, the full-reference metrics (i.e., + +
MethodsLSDIR-TESTRealSRRealSet110
PSNRSSIMLPIPSManIQACLIPiQAMUSIQManIQACLIPiQAMUSIQManIQACLIPiQAMUSIQ
RealSR-JPEG [15]22.090.48190.39820.36470.646662.470.17100.526733.690.30300.758854.03
BSRGAN [64]23.740.57480.33360.40690.685369.090.37870.551263.200.38700.791867.13
Real-ESRGAN [51]23.080.57580.32340.43350.681069.910.38110.549260.560.37790.784465.05
SwinIR-GAN [27]23.050.56980.32620.41950.683368.720.35830.566959.230.35980.800963.92
LDM [41]24.140.56300.33230.34660.673561.830.26310.561747.720.28340.762855.01
StableSR [48]23.090.56640.31700.47720.673969.910.39920.535061.330.38560.785162.08
ResShift [63]23.750.56860.31020.51410.691969.620.38210.569458.810.40110.758462.07
PASD [60]21.020.49400.36510.51770.684771.910.46560.560767.440.43780.760866.03
DiffBIR [28]23.330.53050.34690.54060.672669.780.45460.576262.750.49330.775666.75
SinSR [52]23.520.55770.31700.48660.696069.730.39980.577060.750.42500.673855.24
OSEDiff [53]22.500.53570.31030.46840.707072.160.47440.589069.120.46790.794970.26
PatchScaler22.600.52970.35200.62610.714573.230.52250.583969.500.54420.821370.97
+ +Table 1. Quantitative comparison with state-of-the-art SR methods on both synthetic and real-world datasets. The best and second best results are highlighted and underlined, respectively. PSNR/SSIM on Y channel are reported on each dataset. We calculate ManIQA metric based on the official ManIQA-KONIQ pre-trained model. + +![](images/0332a7fdaf8fe8bba264b360580bc0257bac5a313b6ea2d269de3e8325b35cdf.jpg) + +![](images/39ae085f43203012da84af01f0a5e80ac280a9f8d9e8880367e2b363be2fe36c.jpg) + +![](images/56c94a6683e6868190c203bdfa67002239287d590829b6912990f628d19b1535.jpg) + +![](images/e1d5987b4d246cf7a6c2046b616267531e90cc33fddb4357260bca1655ebaf3e.jpg) + +![](images/a06a69eed6888b391c3fd5b2e64872f6f609f1c7102beb7591e39c0ebb1023f3.jpg) +(a) LR image + +![](images/58339fda8d1f4f93d35dda0d884a460c8909b3aed9de9477a3136587977de95e.jpg) + +![](images/856b0c9a29dbf89904a3a9318d7969b2624363536632ed2b854b4b31154b1c22.jpg) + +![](images/30e2cc2c3304fa43829a49946f9546fc8b2366c5d8b0a0addce43cce033506de.jpg) + +![](images/b0fbe34255365ee29244d184ec57a23f1aff798f83ae1d4e62e6df90e5cf8952.jpg) + +![](images/c34f4126581cdae1280d2bfb7e1a9e1fd6ee571331574ecb9cbefc6e33727703.jpg) +(b) StableSR + +![](images/0d94c2bf0ab90461249a6c551097c192fe1cbde0bba8b2dd324d1346c7b1bd32.jpg) + +![](images/73f208e5e83ff224cfc3af292271a5ae372b3b8f1416a3202a21fe79cb54fd08.jpg) + +![](images/b36d85cb64b3dd1bf008173331d5f4c4cb8369ee84c9ad6e40732e746013be41.jpg) + +![](images/fdcdd870112497e63c38c1c8853d8cc1bf3589f6236372de27b21ed0a496b108.jpg) + +![](images/f992a7502841e14e0271a50e27ba14e2d60fc4913a1a86b8b720b9003e474933.jpg) +(c) ResShift + +![](images/fbe9bb7df63698af97497442a97d1cebe5bd99a4c45a9e31b3e76898d6772e94.jpg) + +![](images/089c0d0bee958bde3992cb242f665c3d13c8eb01e0c270fc387ece741dd5ae3e.jpg) + +![](images/19ff898f2e06401ed904b8f13d0c25ba358e86311ddc71967d9298bba2c5b97f.jpg) + +![](images/56fbbcca54b090e03af93a923d9f4a2be4121efc70a03548c9a277b4aacf77e1.jpg) + +![](images/087b06de11722b3bdbdda444207405e25ced3039406e0f685692134cb1a6ef63.jpg) +(d) DiffBIR + +![](images/b75817f7aa22ff5c0591909b30b1fd5dd8b48c61bc80d89e792d6ed6c0704fc0.jpg) + +![](images/be67d64ad487186b7f1649aec37fcfc58c8758557a846266839407b3c9d15dba.jpg) + +![](images/8bc3e8ec94d3c0d31ebdcdc154d1e657239d84a8e66d0fc677350780ef521911.jpg) + +![](images/7bde47e219df5ce771b83778697e0070596f600f96060a5f1dbfad5f558d1440.jpg) + +![](images/0ab49f9f881c9caf7a0057c60d8e76293a36296a2615ad1ef202e036a0db50b5.jpg) +(e) OSEDiff +Figure 5. Visual comparisons of state-of-the-art SR methods on real-world low-resolution images. + +![](images/19aee774fb7271c078d2982974329568ed7555e8fe1ef1ab31f6ed648a75de35.jpg) + +![](images/ff0fba01daf116d257e176f846ad67018f60bbaf73fc82fced68458fd4f7ed04.jpg) + +![](images/0b3c3c15b910f2ef29024189d71b59108d1b764b43e6945cbfb31c67e64c3e7e.jpg) + +![](images/e359a7d694000df6ca3a3f358ff9f280fc7605625a458053217d39c788befc00.jpg) + +![](images/444c905e0acf2167b699398d847fdb9c8563e75e76361a454c0af01c75c7f3a1.jpg) +(f) Ours + +PSNR, SSIM, and LPIPS [65]) are also given in Tab. 10 as a reference. However, it should be noted that these metrics only reflect certain aspects of performance and poorly respond to realistic visuals[4, 12, 16, 22, 61], which cannot reliably evaluate the performance of diffusion-based SR models. As the generative capabilities of models improve, it becomes increasingly necessary to reexamine these full-reference metrics and consider more effective evaluation methods for diffusion-based SR models. + +Evaluations on Real-World Data. As shown in Tab. 10, we further evaluate PatchScaler on two real-world datasets. + +It can be seen that our method surpasses others in both ManIQA [59] and MUSIQ [19] metrics, indicating the excellent performance of our approach. Moreover, PatchScaler also demonstrates competitive performance in CLIPIQA [47] metric, with an improvement of $+0.0204$ over the second-best results on the RealSet110 dataset. We also provide qualitative comparisons with other diffusion-based SR methods on four LR images in Fig. 5. It can be observed that other diffusion-based SR methods struggle to reconstruct realistic textures. StableSR [48] tends to produce highly blurred (e.g., Real02-illustration) results with unclear texture details. The + +
MethodsSwinIR-GAN [27]LDM [41]StableSR [48]ResShift [63]DiffBIR [28]PASD [60]SinSR [52]OSEDiff [53]PatchScaler
Runtime (s)1.5525.8235.2214.8978.1259.03-30.353.41 (2.26)
+ +![](images/0929c31ab16167d6651b491e8cc3eba093bcac05b096e7f10c10097bca1a4d22.jpg) +Figure 6. Performance analysis of PatchScaler on RealSet10 dataset under different configurations. Our PatchScaler achieves a better tradeoff between metrics and runtime at the intersection of two red dashed lines. + +results of ResShift [63] and DiffBIR [28] contain inaccurate generation, which negatively impacts visual perception. In addition, OSEDiff [53] employs a uniform one-step strategy to minimize sampling steps indiscriminately across all image regions, resulting in unsatisfactory reconstruction results in regions with complex textures (e.g., Real03-other). In contrast, our PatchScaler succeeds in producing realistic results at both the patch and global levels, with much better perceptual quality and richer fine details. More visual comparisons can be found in Fig. 13 of the appendix. + +Efficiency Evaluations. To assess the efficiency of PatchScaler, we compare its runtime against other diffusion-based SR methods on the $\times 4$ ( $512 \rightarrow 2048$ ) SR task, as shown in Tab. 2. Due to the lack of optimization for high-resolution inputs, the inference time of OSEDiff [53] is quite long. Moreover, SinSR [52] suffers from an out-of-memory problem at this scale. In contrast, PatchScaler achieves the fastest inference time among the diffusion-based methods, just $0.23 \times$ that of the second fastest ResShift [63]. In addition, we highlight that PGS also allows the use of multiple GPUs to process patches from different groups separately. To demonstrate this, we re-evaluate our PatchScaler using two NVIDIA Tesla A100 GPUs. By assigning one GPU to handle patches from the hard group and another to handle patches from the simple and medium groups, our PatchScaler achieves an additional $33.7\%$ inference speedup. We also provide the runtime and memory usage of each component of PatchScaler, as well as the FLOPs and parameters of different methods in the appendix for reference. + +# 4.3. Configuration Analysis + +# 4.3.1. Analysis of GRM + +The contribution of GRM. Our GRM aims to remove the degradations and capture long-range dependencies within images. It generates the confidence map $C$ and the coarse HR feature $y_{HR}$ , respectively. To verify its effectiveness, we replaced the coarse HR feature with the LR feature in + +Table 2. Running time comparisons of the proposed PatchScaler to other methods on the $\times 4$ (512 → 2048) SR task. Note that SinSR [52] suffers from an out-of-memory problem at this scale. The highlighted result is evaluated using dual-GPU parallel computing. + +
SettingManIQACLIPIQAMUSIQ
Replace coarse HR to LR0.51290.809469.07
Ours0.54420.821370.97
+ +Table 3. Ablation studies of GRM. The best results are highlighted. + +
γ1γ2ManIQACLIPIQAMUSIQRuntime (s)
0.850.600.51190.804668.962.98
0.950.750.54420.821370.973.41
1.000.850.54700.814271.153.58
+ +Table 4. Ablation studies under different confidence threshold $\gamma$ . + +the subsequent process and got a reduced performance (as shown in Tab. 3). + +Determine confidence threshold $\gamma$ . Tab. 4 shows quantitative evaluations under different confidence thresholds. It can be seen that PatchScaler achieves a trade-off between model performance and inference time with $\gamma_{1} = 0.95$ and $\gamma_{2} = 0.75$ . Classifying patches further into more difficult groups will not significantly improve performance and will take longer. As shown in Fig. 4, this setting can accurately quantify the reconstruction difficulty across different image regions. + +# 4.3.2. Analysis of PGS + +Determine shortcut point $\tau$ . As shown in Fig. 6, we provide an intuitive analysis (metrics against runtime) of PatchScaler under different sampling configurations. It can be found that when reducing the shortcut points $T_{1}, T_{2}$ , and $T_{3}$ of simple, medium, and hard patches from [1000, 1000, 1000] to [400, 700, 1000], PatchScaler consistently achieves competitive performance. This is because simple patches have higher confidence and a smaller distance $\triangle x_{0}$ , allowing a larger $\sqrt{\bar{\alpha}_{\tau}}$ (i.e., a smaller $\tau$ ) to satisfy Eq. (3), and vice versa. Further reducing them significantly deteriorates performance. Thus, we set $T_{1} = 400$ , $T_{2} = 700$ , and $T_{3} = 1000$ . + +Determine sampling step $N$ . When we continue to reduce $N_{1}$ , $N_{2}$ , and $N_{3}$ from [20, 20, 20] to [8, 14, 20] under the above configuration, it can be observed that the performance of the model can be well maintained. This is because a large number of sampling steps is redundant for a small $\tau$ . Further reducing the sampling steps significantly decreases the performance scores of the three metrics. To this end, we set $N_{1} = 8$ , $N_{2} = 14$ , and $N_{3} = 20$ . + +How many groups are appropriate to divide patches into? We provide an intuitive experiment analysis (metrics against runtime) of PatchScaler under different numbers of groups (ranging from 2 to 6) in Fig. 12 of the appendix. To be fair, we fix the max/min values of $\tau$ and $N$ , and obtain the middle values by equal division. It can be seen that our method strikes a balance between quality and efficiency with three groups. Further increasing the number of groups will reduce + +
MethodsManIQACLIPIQAMUSIQRuntime (s)
StableSR0.38560.785162.0835.22
StableSR+PGS0.50350.780965.548.53
+ +Table 5. Quantitative comparison of StableSR and StableSR+PGS. The best results are highlighted. The runtime is measured on the $\times 4$ (512 →2048) SR task using an NVIDIA Tesla A100 GPU. + +
Prompt typeManIQACLIPIQAMUSIQ
Text prompt0.48490.789066.79
Texture prompt0.54420.821370.97
+ +the distinction between patches of different groups, which will not only fail to bring performance gain but also increase the inference complexity. + +Advantages over previous grouping schemes. Our grouping scheme differs from previous methods, e.g., ClassSR [21] and PCSR [14], in both model design and optimization strategy. Previous methods that use classification modules and handcrafted classification losses to predict the categories of patch or pixel, while we introduce a confidence-driven module GRM that generates a coarse HR and a confidence map $C$ simultaneously. $C$ predicts the distance between coarse HR and ground truth, and the grouping scheme is determined by quantizing $C$ . Restoring features through GRM effectively aids in estimating the confidence map. As shown in Fig. 7, our confidence map accurately reflects the reconstruction difficulty of different regions and Qmap achieves more accurate grouping, resulting in better performance. + +Is there a potential boundary effect between the patches? To ensure pixel consistency between different groups and eliminate potential boundary effects within patches, we decompose the coarse HR feature into overlapping patches, which is commonly used in leading diffusion-based methods [2, 48]. In addition, we also apply wavelet-based color normalization [48] on the super-resolved image to align its low-frequency features with those of the LR input. + +Extension of PGS. Our PGS scheme can be seamlessly extended to other architectures and tasks as a plug-and-play component. As an example, we applied PGS and GRM to StableSR [48] in a trainable-free manner. Since its backbone, Stable Diffusion [41], performs best with a latent feature size of 64, we set the patch size $V$ to 64. The results are presented in Tab. 5 and Fig. 8, which show that our PGS achieves significant gains in both quantitative (ManIQA: +0.1179; MUSIQ: +3.46) and qualitative comparisons, and accelerates the inference (only $0.24 \times$ ) of StableSR. + +# 4.3.3. Analysis of Texture Prompt + +Text prompt vs. texture prompt. To verify the effectiveness of the proposed texture prompt, we evaluate the text prompt and the texture prompt on the RealSet110 dataset, respectively. We utilize the pre-trained BLIP-2 model [24] to generate the text from the LR image and then obtain the + +![](images/e011c4cd8039734e0ec50b7576aba7fa0a1d4d9168999c9d6a7588e214c87e0e.jpg) +Figure 7. Evaluation of different grouping schemes. + +![](images/9f12629af71a7d5d9a8e6036cbaba60ce32213f1d9a1853f326839cf1c2ff73d.jpg) +Figure 8. Visual comparison of StableSR and StableSR+PGS. + +text embedding based on the pre-trained CLIP model [40]. The quantitative results are presented in Tab. 6. It can be seen that the model with the texture prompt achieves higher values than the model with the text prompt. We provide further analysis and visual comparison in the appendix. + +The effect of the size of RTM. Our final RTM contains 2k texture patch pairs, which takes up 16.4M memory. As shown in Tab. 7, increasing the RTM size to 20k significantly increases the memory usage but only brings a very small performance gain (ManIQA: +0.0034, CLIPIQA: +0.0079, MUSIQ: +0.05), as the 2k selected pairs already contain the most representative textures. + +Table 6. Ablation studies of different prompt in our method. The best results are highlighted. + +
Size of RTMManIQACLIPIQAMUSIQMemory (M)
2k0.54420.821370.9716.4
20k0.54760.829271.02164
+ +Table 7. Ablation studies of the RTM size. + +# 4.4. Limitation and Future Work + +Our PatchScaler achieves a significant improvement in computational efficiency than previous diffusion-based SR methods and rivals state-of-the-art GAN-based models. Nevertheless, real-time inference remains challenging for all diffusion-based SR methods, due to the large number of model parameters. In the future, we will explore integration options with sampling distillation solutions and improve the deployment efficiency through engineering solutions. + +# 5. Conclusion + +We have presented PatchScaler, motivated by the observation that unified sampling across image regions with varying reconstruction difficulties is suboptimal. Specifically, we developed a PGS strategy to adaptively assign sampling configurations for each patch so that the high-resolution images can be efficiently recovered. 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Diagnostic text reports provide high-level semantic descriptions, and masks offer fine-grained spatial structures essential for representing distinct morphological regions. However, public datasets lack paired text and mask data for the same histopathological images, limiting their joint use in image generation. This constraint restricts the ability to fully exploit the benefits of combining both modalities for enhanced control over semantics and spatial details. To overcome this, we propose PathDiff, a diffusion framework that effectively learns from unpaired mask-text data by integrating both modalities into a unified conditioning space. PathDiff allows precise control over structural and contextual features, generating high-quality, semantically accurate images. PathDiff also improves image fidelity, text-image alignment, and faithfulness, enhancing data augmentation for downstream tasks like nuclei segmentation and classification. Extensive experiments demonstrate its superiority over existing methods. Our code is published at https://github.com/bhosalems/PathDiff. + +# 1. Introduction + +The recent advancements in computational pathology, driven by deep learning, are revolutionizing the field of histopathology by addressing critical challenges in tasks such as nuclei classification and segmentation [39], survival prediction [41], multi-instance learning [10], and transfer learning [39]. Despite these successes, a significant obstacle persists: the substantial volume of annotated data necessary to effectively train deep learning models. Moreover, the high costs and domain expertise required to annotate such data further ag- + +![](images/d7b2a0a76eaea869a6c5c3563a1b6521dcf6f722d135dad557fff1e3d10df92b.jpg) +Figure 1. PathDiff is trained on unpaired datasets, integrating two conditional modalities — Text and Mask—to enable versatile image generation. Unlike unimodal conditional models, PathDiff can generate images conditioned on Text, Mask, or both, allowing greater control and adaptability in image synthesis. + +gravate this problem. Pathologists must start with low magnification to assess tissue architecture and cellular arrangement, then shift to higher magnification to evaluate finer details such as cell morphology, nucleoli appearance, and chromatin density. Annotating these intricate features is both time-consuming and labor-intensive. For instance, fully annotating the 1k whole slide images from the TCGA dataset [8] would require approximately 40k pathologist hours [15]. Overcoming these limitations is essential to fully unlock the potential of deep learning in histopathology [42]. + +Generative models in histology [7, 30] have thus emerged as a valuable tool to complement existing datasets, extending beyond traditional data augmentation [9, 27]. More recently, owing to the superior generation quality of diffusion models [5, 18], they are widely used for histological image synthesis, either conditioned on diagnostic text reports [15, 45] or spatial labels such as cell nuclei [32, 33] or regions of interest [1]. However, these existing approaches rely solely + +![](images/9362383b69669cfc3086a36c2dd8845ad08b0942fd3daa0945193a87d60b74d5.jpg) +Figure 2. (a) PathDiff Training Framework: A training sample is drawn from either the Mask-to-Image (M2I) or the Text-to-Image (T2I) dataset, determined by the probability $p_{\mathrm{split}}$ , which controls the connection of the Switch. The missing condition in each case is set to $\varnothing$ . When the Switch selects a sample from the M2I dataset, the Mask-to-Image loss $L_{\mathrm{M2I}}$ is applied; when it selects from the T2I dataset, the Text-to-Image loss $L_{\mathrm{T2I}}$ is used. This approach enables joint training of a single diffusion model on both datasets. (b) Image Generation: During generation, both conditions, $c_m$ (mask) and $c_t$ (text), are applied to produce samples that unify both conditions. + +on a single modality for conditioning, which limits both the quality of control and the amount of data that can be used. + +We recognize the importance of considering text and masks, as they provide complementary information. The text offers contextual knowledge, which varies across cancer types, grades, disease stages, or tissue abnormalities, enabling high-level semantic control over the generation process. In contrast, spatial masks capture local structural details, such as cell shapes and types, providing critical spatial information. Intuitively, simultaneous control of both contextual and spatial information enhances generation. However, no publicly available datasets include open-world text and spatial mask annotations alongside images. + +We propose PathDiff, a diffusion framework that unifies text and mask conditions to address the above-mentioned challenges. As shown in Fig. 2, it learns jointly from two independent datasets: one containing image-text pairs and the other containing image-mask pairs. By integrating unpaired text and mask into a single latent space, our model maximizes the use of complementary data and effectively enables generation conditioned on paired text and mask. The main contributions can be summarized as follows: + +- To address the data scarcity issue in histology image analysis, we propose a novel diffusion-based framework that unifies unpaired text and masks conditions within a single latent space for complementary knowledge exploration. +- Our pipeline enables joint learning from independent text-image and mask-image datasets, allowing image generation conditioned on both during inference. +- Experiments and qualitative results showcase that our pro + +posed model can effectively integrate the guidance from paired text and mask modalities while the model is trained on unpaired mask and text modalities. + +- Owing to the robust and rich joint latent space, empirical evaluations demonstrate that our model outperforms existing approaches across various evaluations, including image fidelity, image-text/mask alignment, and downstream classification and segmentation tasks when conditioned on individual modalities. + +# 2. Related Work + +Generative adversarial networks [12] have become popular for medical image synthesis [3, 4, 36]; however, they frequently introduce artifacts, particularly in histopathology images [31]. In contrast, diffusion-based methods [18] have demonstrated enhanced image quality in both natural and medical images [31]. Building on this, Classifier Guidance [6] was introduced to condition image generation on specific classes, followed by Classifier-Free Guidance (CFG) [17], which eliminates the need for an auxiliary classifier. Latent Diffusion Models (LDMs) [37] further enhance the computational efficiency, while ControlNet [47] utilizes CFG to introduce multiple spatial controls in Text-to-Image LDMs [37]. Recent approaches for conditional histopathology image generation emphasize text- and mask-based conditioning, which we briefly review in the following sections. + +# 2.1. Text to Histopathology Image Synthesis + +The application of diffusion models in text-conditioned histopathology image generation remains limited. Summarized reports from the Large text-image histopathology dataset TCGA-BRCA [8] were used for text-conditioned image generation in [45] in conjunction with text annotated Tumor-Infiltrating Lymphocyte (TIL) and Tumor probabilities from off-the-shelf classifiers. Genome sequencing data from the TCGA-BRCA dataset was used in [30], where heavier weights were assigned to earlier steps and lower weights to later steps in the diffusion process to focus on morphological features. Authors in [15] train diffusion model conditioned on Self Supervised Learned (SSL) embeddings. An auxiliary diffusion model is trained on SSL embedding paired with Quilt [24] image embeddings. At the time of inference, text embeddings are used as proxies for image embeddings, allowing for Text-to-Image synthesis. However, note that none of these methods use mask conditions in conjunction with text. + +# 2.2. Mask to Histopathology Image Synthesis + +The authors of [1] propose a hierarchical diffusion model to generate large whole-slide images (WSIs) conditioned on synthesized regions of interest. But, this approach does not incorporate fine-grained, cell-level masks. In [33], a text-driven approach is used first to generate cell masks, which, along with their distance maps, are then used to condition histopathology image synthesis. However, this method does not allow for fine-grained control over the spatial placement of the masks. In [46], the diffusion model is trained to synthesize nuclei structures as pixel-level semantic and distance-transform maps, which are then post-processed into instance maps. This is followed by a conditional diffusion model to generate histopathology images. Similarly, [29] introduces a cell-point map to synthesize cell-type masks and images jointly. To tackle class imbalance, [32] employs a Semantic-Diffusion-Model (SDM) [44] for data synthesis, effectively balancing class variance in nuclei datasets. + +In contrast, PathDiff uniquely generates histopathology images by unifying mask and text conditions from unpaired datasets, which is beyond the scope of the works discussed above. + +# 3. Method + +# 3.1. Background + +Diffusion models. Diffusion Models [18] are generative models that gradually add noise to data through a forward diffusion process, followed by a reverse denoising process that reconstructs the original sample. The forward process corrupts the data sample $x_0$ through iterative noise addition controlled by a schedule $\alpha_t$ : + +$$ +q \left(x _ {t} \mid x _ {t - 1}\right) = \mathcal {N} \left(x _ {t}; \sqrt {1 - \alpha_ {t}} x _ {t - 1}, \alpha_ {t} I\right), \tag {1} +$$ + +where $\alpha_{t}$ is a predefined noise schedule. The noisy sample $x_{t}$ can be computed by $x_{t} = \sqrt{\bar{\alpha}_{t}} x_{0} + \sqrt{1 - \bar{\alpha}_{t}\epsilon}$ , where $\bar{\alpha}_{t} = \prod_{i=1}^{t}(1 - \alpha_{i})$ and $\epsilon \in \mathcal{N}(0,1)$ is a random Gaussian noise. + +The reverse process, parameterized by a neural network $p_{\theta}$ , learns a time-conditioned model to remove the noise added at each step. + +Latent Diffusion Models (LDMs) work in a compressed latent space $z_{t}$ rather than the high-dimensional data space [37], where the data $x_0$ is encoded as $z_0$ through an encoder. LDMs learn to minimize the objective, + +$$ +L = \mathbb {E} _ {z _ {0}, t, \epsilon \sim \mathcal {N} (0, 1)} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t\right) \| _ {2} ^ {2} \right], \tag {2} +$$ + +where $\epsilon_{\theta}$ is the model's predicted noise at time $t$ . Owing to the relevance to score-based generation models, the model estimates the log density of the distribution $z_{t}$ , i.e., $\epsilon_{\theta}(z_t,t)\approx -\nabla_{z_t}\log p(z_t)$ . + +Classifier-free guidance. In the denoising process, different conditional inputs $c$ (text, image, depth, mask, etc.) can be added to control the generation, so the denoising model predicts $\epsilon_{\theta}(z_t,t,c)$ . In classifier-free guidance [17], a single neural network is used to parameterize both the unconditional denoising diffusion model $p_{\theta}(z)$ and conditional denoising diffusion model $p_{\theta}(z|c)$ . While training, with some probability $p_{\mathrm{uncond}}$ , the unconditional model receives a null token, $\varnothing$ as $c$ . $p_{\mathrm{uncond}}$ is set as a hyperparameter. While sampling, a linear combination of conditional and unconditional score estimates is used: + +$$ +\tilde {\epsilon} _ {\theta} \left(z _ {t}, t, c\right) = (1 + w) \epsilon_ {\theta} \left(z _ {t}, t, c\right) - w \epsilon_ {\theta} \left(z _ {t}, t\right). \tag {3} +$$ + +# 3.2. PathDiff + +Histopathology image synthesis requires both high-level semantic guidance and precise structural fidelity. Existing methods [47] often require paired text and mask data, limiting their practicality due to the scarcity of such paired datasets in the histopathology domain. To address these challenges, we propose a unified framework, PathDiff, that leverages unpaired text and mask conditions, enabling fine-grained control over semantic and spatial features. This approach eliminates the need for paired data, supporting flexible and realistic image generation for downstream tasks. + +Formally, let $D_{\mathrm{T2I}} = \{(x_t, c_t)_i\}$ and $D_{\mathrm{M2I}} = \{(x_m, c_m)_i\}$ represent two unpaired datasets, where $D_{\mathrm{T2I}}$ consists of image-text pairs and $D_{\mathrm{M2I}}$ contains image-mask pairs, with no overlapping images between the two datasets. We aim to learn a latent denoising diffusion model $p_\theta(z_t|t, c_t, c_m)$ . At the inference time, $p_\theta$ can generate image samples conditioned on text $c_t$ and mask $c_m$ . + +Joint training on unpaired datasets. The training pipeline, illustrated in Fig. 2 (a) and detailed in Algorithm 1, takes as input triplets of noisy latent, conditional mask, and conditional text, $(x_{t},c_{m},c_{t})$ . We adopt a sampling strategy alternating between T2I and M2I datasets, allowing + +the model to learn from both sources and effectively integrate text and mask conditions. Specifically, we jointly train PathDiff by sampling data from the T2I dataset with probability $p_{\mathrm{split}}$ and from the M2I dataset with probability $1 - p_{\mathrm{split}}$ . When sampling from $D_{\mathrm{T2I}}$ dataset, we set $c_m = \varnothing_m$ , leading to a training triplet of $(x_t, \varnothing_m, c_t)$ . Similarly, when sampling from $D_{\mathrm{M2I}}$ , we set $c_t = \varnothing_t$ , resulting in a training sample of $(x_m, c_m, \varnothing_t)$ . Following existing methods [37], we set $\varnothing_t$ as an empty string. For $\varnothing_m$ , while previous works [32, 33, 44] use a zero vector, we instead use a mask filled with an invalid label, as zero in our dataset indicates a background mask. Additionally, for robustness, we apply unconditional training by setting both $c_t = \varnothing_t$ and $c_m = \varnothing_m$ with a small probability $p_{\mathrm{uncond}}$ , as suggested in [47]. This training pipeline effectively allows PathDiff to learn from both unpaired conditions, enhancing its ability to generate realistic images conditioned on both modalities. + +Following ControlNet [47] to add spatial control over image generation, we duplicate parts of the U-Net's down-sampling and middle layers, adding zero convolution layers to these duplicates. Outputs from these layers are integrated into the original U-Net's skip connections. U-Net was pretrained on the T2I histopathology dataset before duplicating. The conditional mask is embedded with shallow CNN before being added as input to the U-Net encoder, while text embeddings are extracted from PLIP: pathology CLIP [20] and cross-attended with U-Net layers. We use VAE from [45] trained on the TCGA-BRCA [8] histopathology dataset to encode and decode images. However, as noted by [45], reconstruction loss significantly affects the generation quality; therefore, we study its effect in supplementary material. As shown in Fig. 2, all models are frozen except the copied U-Net encoder and shallow mask embedder. + +We employ a latent diffusion pipeline [37] to train PathDiff. A shared VAE encoder-decoder is used for both datasets, resulting in a unified latent representation $z$ . This approach assumes that the VAE can compress and reconstruct images from both datasets without significant loss, maintaining a consistent latent representation across domains. + +Optimization loss. PathDiff jointly optimizes the diffusion model $p_{\theta}$ to predict the noise added at every step $t$ of the noising process. When the training sample is sampled from $D_{\mathrm{T2I}}$ it minimizes loss with respect to sample $x_{t} \in D_{\mathrm{T2I}}$ , + +$$ +L _ {\mathrm {T} 2 \mathrm {I}} = \mathbb {E} _ {z _ {0}, t, \epsilon \sim \mathcal {N} (0, 1)} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, \varnothing_ {m}, c _ {t}\right) \| _ {2} ^ {2} \right] \tag {4} +$$ + +similarly, for training samples from $D_{M2I}$ it minimizes the loss with respect to sample $x_{m} \in D_{M2I}$ , + +$$ +L _ {\mathrm {M} 2 \mathrm {I}} = \mathbb {E} _ {z _ {0}, t, \epsilon \sim \mathcal {N} (0, 1)} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, c _ {m}, \varnothing_ {t}\right) \| _ {2} ^ {2} \right] \tag {5} +$$ + +Unified conditional sampling. Since PathDiff is jointly trained on both $D_{\mathrm{T2I}}$ and $D_{\mathrm{M2I}}$ datasets, it can be queried to sample images conditioned on both $c_t$ and $c_m$ , effectively unifying these conditions as guidance, as illustrated + +Algorithm 1 Joint Training on Unpaired Datasets +Require: $p_{\text{uncond}}$ : probability of unconditional training, Text-to-Image dataset $\mathbf{D}_{\mathbf{T2I}}$ , Mask-to-Image dataset $\mathbf{M}_{\mathbf{T2I}}$ , $p_{\text{split}}$ : probability of sampling from $\mathbf{D}_{\mathbf{T2I}}$ +1: repeat +2: if $\mathbf{u} \sim \text{Uniform}[\mathbf{0}, \mathbf{1}] \geq \mathbf{p}_{\text{split}}$ then +3: $(\mathbf{z}_0, \mathbf{c_m} = \varnothing_{\mathbf{m}}, \mathbf{c_t}) \sim \mathbf{p_1}(\mathbf{z}_0, \mathbf{c_t})$ ▷ Sample data from $D_{T2I}$ +4: $\mathbf{c_t} \gets \varnothing_{\mathbf{t}}$ with probability $\mathbf{p_{\text{uncond}}}$ ▷ Randomly discard text +5: else +6: $(\mathbf{z}_0, \mathbf{c_m}, \mathbf{c_t} = \varnothing_{\mathbf{t}}) \sim \mathbf{p_2}(\mathbf{z}_0, \mathbf{c_m})$ ▷ Sample data from $D_{M2I}$ +7: $\mathbf{c_m} \gets \varnothing_{\mathbf{m}}$ with probability $\mathbf{p_{\text{uncond}}}$ ▷ Randomly discard mask +8: $\mathbf{t} \sim \text{Uniform}\{\mathbf{1},.., \mathbf{T}\}$ ▷ Sample timestep +9: $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ ▷ Sample noise +10: $\mathbf{z_t} = \sqrt{\bar{\alpha_t}} \mathbf{z_0} + \sqrt{\mathbf{1} - \bar{\alpha_t}} \epsilon$ ▷ Corrupt data +11: Take gradient step on: + $\| \epsilon - \epsilon_\theta (\mathbf{z_t}, \mathbf{t}, \mathbf{c_m}, \mathbf{c_t}) \|^2$ with respect to $\nabla_\theta$ ▷ Optimizing PathDiff +12: until converged + +in Fig. 4 (c) and Fig. 5. The image generation process is illustrated in Fig. 2 (b). For completeness, we include a sampling algorithm in the supplementary. During inference, we generate images using classifier-free guidance [17], updating the predicted noise with the model using Eq. (3). The conditioning variable $c$ can take values from $\mathbf{c} \in \{(\varnothing_{\mathbf{m}}, \mathbf{c}_{\mathbf{t}}), (\mathbf{c}_{\mathbf{m}}, \varnothing_{\mathbf{t}}), (\mathbf{c}_{\mathbf{m}}, \mathbf{c}_{\mathbf{t}})\}$ . We can selectively generate images from either distribution by setting one of the conditions to $\varnothing$ . Specifically, + +$$ +z _ {t} \sim \left\{ \begin{array}{l l} p _ {\theta} (z _ {t} | t, c _ {t}) & \text {i f} c = (\varnothing_ {m}, c _ {t}), \\ p _ {\theta} (z _ {t} | t, c _ {m}) & \text {i f} c = (c _ {m}, \varnothing_ {t}), \\ p _ {\theta} (z _ {t} | t, c _ {m}, c _ {t}) & \text {i f} c = (c _ {m}, c _ {t}). \end{array} \right. +$$ + +Images generated according to the conditions are illustrated in Fig. 3 and Fig. 4 (b) and Fig. 5. We present extensive experiments on images drawn from each variation of conditions in Sec. 4. + +# 4. Experiments + +We evaluate our method in two main aspects: the quality of the generated images and the effectiveness of using synthetic images as additional training data for downstream task. We evaluate image generation quality in Sec. 4.3, focusing on image fidelity, image-mask faithfulness, and alignment quality between images and text. Additionally, the utility of the synthetic images in downstream segmentation tasks is detailed in Sec. 4.4. We also discuss the domain experts' survey results in the supplementary. PathDiff was jointly trained on M2I and T2I datasets; however, we can generate images conditioned on text, mask, or both. Each of these variants is evaluated separately. ControlNet [47] uses SD [37] backbone pre-trained on the T2I dataset for further finetuning on the M2I dataset. Therefore, ControlNet is also evaluated in two variants for a fair and inclusive comparison. + +![](images/3b8c617c2d54fb9ef3a6451ec90895f747036a90b0b880ecb6829b3f74af4acb.jpg) +(a) PanNuke + +![](images/92d5ce268649101c47ea1e61c16064f18e0d62b51925cb2e4e94525b4ff45b52.jpg) +(b) CoNIC + +![](images/2d2e67cb3bb96decb46ea0750b65b8fd9a793d56176f89670d36ca396d6f4c56.jpg) +(c) MoNuSAC +Figure 3. Synthetic images generated by PathDiff on Mask to Image datasets (a) PanNuke [11], (b) CoNIC [14], (c) MoNuSAC [43]. PathDiff closely follows the spatial structures defined by the cell type label map, producing synthetic images that closely resemble the spatial arrangement of real images. + +
MethodCondition ModalityPanNukeCoNICMoNuSAC
TrainTestTrainTestTrainTest
(Train, Sample)FID ↓ KID ↓FID ↓ KID ↓FID ↓ KID ↓FID ↓ KID ↓FID ↓ KID ↓FID ↓ KID ↓
Diffmix [32](Mask, Mask)7.280.04928.320.05368.090.09668.580.09379.250.103616.780.35
SDM [44](Mask, Mask)7.140.11477.130.11498.270.07099.800.07377.460.12789.440.1340
ControlNet [47](Mask+Text, Mask)16.440.070515.360.77226.760.07906.790.069520.060.105020.560.1068
PathDiff(Mask+Text, Mask)6.940.03897.210.04155.640.05245.540.04886.710.06166.990.0758
+ +Table 1. Comparison of CLIP-FID and KID across training and test splits for PanNuke [11], CoNIC [14], and MoNuSAC [43]. PathDiff is trained jointly with T2I dataset: PathCap [40]. ControlNet [47] uses SD [37] backbone trained on the PathCap dataset. The best results are in bold and the second best is underlined. + +# 4.1. Datasets + +We use three mask-image histopathology datasets (PanNuke [11], CoNIC [14], and MoNuSAC [43]) and one text-image dataset (PathCap [40]) to conduct a comparative analysis across multiple metrics, evaluating various diffusion methods and their related downstream tasks. + +The PanNuke dataset [11] provides annotated histopathology images across 19 tissue types with 189,744 annotated nuclei in five classes (neoplastic, inflammatory, connective, dead, and epithelial). The dataset is highly imbalanced [22] and one of the most challenging to perform the segmentation task [25]. + +CoNIC dataset [14] is one of the most extensive publicly available histopathology datasets, containing approximately + +535,000 labeled colon nuclei across six cell types: epithelial, lymphocytes, plasma cells, eosinophils, neutrophils, and connective tissue cells. + +MoNuSAC [43] spans four organs (lung, prostate, kidney, and breast) and includes over 46,000 annotated nuclear boundaries collected from diverse sources for four cell types: epithelial cells, lymphocytes, macrophages, and neutrophils. + +PathCap [40] includes 207K pathology image-caption pairs, 197K from PubMed and guidelines, and 10K annotated by expert cytologists in liquid-based cytology (LBC). PathCap has diverse Pan-Cancer image-text pairs spanning multiple organs, making it suitable for joint training. We used a 100K subset of PathCap containing only H&E-stained histology images to ensure consistency with the three mask + +
MethodPanNukeCoNICMoNuSAC
FS1 ↑FS2 ↑FS1 ↑FS2 ↑FS1 ↑FS2 ↑
Diffmix [32]0.74190.69640.75970.71630.64880.6182
SDM [44]0.70250.68260.74330.73760.63770.6104
ControlNet [47]0.69900.68210.76290.75370.63170.6081
PathDiff0.74370.74060.78730.76320.65190.6308
+ +Table 2. Faithfulness scores for the PanNuke [11], CoNIC [14], and MoNuSAC [43] datasets. FS1 measures the adherence of synthetic images to the spatial structure of real masks by computing $\mathrm{DICE}(M_{syn}^{pred}, M_{real})$ . At the same time, FS2 assesses the similarity between synthetic and real images for potential downstream tasks, calculated as $\mathrm{DICE}(M_{syn}^{pred}, M_{real}^{pred})$ . + +image datasets, which are also H&E-stained. + +Data splits: All datasets use an 80:20 train/test split, applied consistently to both generation and downstream evaluations. Synthetic examples for downstream task are drawn only from the conditions training split and added during model training to ensure fair comparisons. + +# 4.2. Implementation Details + +PathDiff is trained on $256 \times 256$ image patches. We resize patches for the MoNuSAC [43] and PathCap [40] datasets by taking crops of size $256 \times 256$ from WSIs. PanNuke [11] and CoNIC [14] datasets originally have images with size $256 \times 256$ . Our model is trained for 60 epochs on 4 NVIDIA A6000 GPUs with a batch size of 72 and a learning rate of $3.75 \times 10^{-5}$ with 1000 warmup steps. We use DDIM sampling [38] with 200 steps and a classifier-free guidance scale set to 1.75 for image generation. We train CellViT on a single NVIDIA RTX A6000 for 130 epochs (with the first 30 epochs frozen), using a batch size of 16 and a learning rate of 0.001, retaining all other training parameters from the original work [22]. + +# 4.3. Image Generation Quality + +Image Generation Fidelity: To evaluate the quality of generated images, we use CLIP-FID following [15, 35]. We additionally report Kernel Inception Distance (KID) [2] to provide an unbiased estimate. As shown in Tab. 1, PathDiff achieves the best generation quality in terms of FID and KID compared against the existing Mask-to-Image generation methods: Diffmix [32], SDM [44] and ControlNet [47]. Fig. 3 presents qualitative examples generated with the guidance of mask conditions. + +Mask-to-Image Faithfulness: To evaluate whether the generated images adhere to the spatial guidance provided by the masks, we use the evaluation protocol of SPADE [34], also termed as Faithfulness Score (FS) [26]. Auxiliary segmentation model [22] $S$ is trained on a train split of mask-image datasets. Real images $I_{real}$ from test split $(I_{real},M_{real})$ are passed through $S$ to get predicted segmentation masks $M_{real}^{pred}$ . Synthetic images generated by + +our model conditioned on masks $M_{real}$ are passed through $S$ to get predicted segmentation masks $M_{syn}^{pred}$ . FS1 calculates $\mathrm{DICE}(M_{syn}^{pred}, M_{real})$ , FS2 on the other hand calculates $\mathrm{DICE}(M_{syn}^{pred}, M_{real}^{pred})$ . As shown in Tab. 2, we attain the best FS1 and FS2 among methods, indicating that the synthetic images closely align with the real masks and reach similarity to real images, enhancing their utility for downstream segmentation tasks. Notably, compared with the counterparts [32, 44, 47], which also sample from the single mask condition, the joint training strategy demonstrates a superior ability to learn from the limited data. + +Text-to-Image Alignment: Fig. 4(b) presents qualitative samples generated by our model conditioned only on text; images generated replicate visual attributes about the text as observed in real images. Tab. 3 presents FID and KID scores compared to ControlNet [47] conditioned only on text. We also use metric - PLIP [20] cosine similarity to evaluate the consistency between image and text embeddings. High PLIP image similarity scores indicate better alignment between text and images. PathDiff has the highest PLIP score of $\geq$ 24.66, indicating good alignment between texts and generated images. Our model performs better than ControlNet on FID [16] and KID [2] across all M2I constituent datasets, indicating large T2I datasets can be jointly trained with a wide range of M2I datasets. + +Unified Sampling Evaluation: No public dataset currently provides (text, mask, image) triplets, which complicates the evaluation of unified conditional sampling. In medical imaging, silver-standard masks [28] often replace human (gold standard) annotations when such labels are unavailable. We use DeepCMorph [23]—an encoder-decoder model extensively trained on heterogeneous data—to generate silver-standard masks for PathCap. These masks, combined with PathCap text, form triplets for inference and evaluation. Because CONIC [14] covers all nuclei types targeted by DeepCMorph, we employ its checkpoints for these experiments. To check whether the masks generated by DeepCMorph are reasonable, we randomly pair the text in PathCap with masks in the CONIC dataset and use this pairing as conditions for a generation, as indicated by PathDiff-R. + +In Tab. 4, PathDiff and ControlNet rely on silver-standard masks from PathCap. Even with random pairing, PathDiff-R surpasses ControlNet in FID while maintaining a similar PLIP score. PathDiff attains the best FID and PLIP results, indicating a meaningful pairing of silver-standard masks with text. Furthermore, comparing PathDiff's FID on CONIC in Tab. 3 to the metrics in Tab. 4 shows that a joint conditioning space yields richer images with improved FID values while preserving text-image similarity, as reflected by a comparable PLIP score. The approach still yields a performance boost even with these silver-standard masks. Note that the models have never seen silver standard masks of the PathCap dataset in the training process. Fig. 5 shows + +![](images/a4eb24cbfe690fcc80d91fb8901daf3ced3804dbe8f7f019ed9d7595ba36d2f4.jpg) +Figure 4. Qualitative examples demonstrate the effectiveness of unifying guidance from random pairings of text and mask conditions. (a) Real images are shown with their respective text-based descriptions. (b) PathDiff generated images conditioned solely on text replicate the visual attributes observed in real images, with the mask condition set to $\varnothing_{m}$ . (c) PathDiff-generated images conditioned on the same text $c_{t}$ and an additional mask $c_{m}$ accurately incorporate the visual features of the real images and adhere to the specified cell mask structure. + +
MethodCondition ModalityM2I Dataset: PanNukeM2I Dataset: CoNICM2I Dataset: MoNuSAC
TrainTestTrainTestTrainTest
(Train,Sample)FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP ↑FID ↓ KID ↓ PLIP↑FID ↓ KID ↓ PLIP ↑
ControlNet [47](Mask+Text,Text)45.390.087223.2745.040.088622.9526.320.127521.9725.100.126921.98
PathDiff(Mask+Text,Text)18.520.061924.1819.600.064424.0518.970.064024.0319.960.065524.17
13.720.053824.17
+ +Table 3. Comparison of CLIP-FID, KID, and PLIP similarity scores for training and test splits for text-image dataset: PathCap. PathDiff is jointly trained with three M2I datasets: PanNuke [11], CoNIC [14], and MoNuSAC [43]. PLIP similarity scores on real PathCap [40] train and test splits are 26.34 and 26.56, respectively, as a reference for the comparison. + +
Data DomainCondition ModalityFID ↓ KID ↓ PLIP ↑
ControlNet(Mask+Text, Mask+Text)15.720.0699 22.03
PathDiff-R(Mask+Text, Mask+Text)11.120.1059 22.09
PathDiff(Mask+Text, Mask+Text)10.540.0766 24.02
+ +Table 4. Comparison of CLIP-FID, KID, and PLIP scores using text-silver standard mask pairs versus random text-mask pairs. Text is drawn from PathCap [40], with masks predicted by DeepCMorph [23]. Random pairings use masks from CONIC [14] and texts from PathCap. Both ControlNet [47] and PathDiff rely on silver standard masks, whereas PathDiff-R uses random pairings. + +faithful image generation with silver standard masks and texts. + +# 4.4. Downstream tasks + +To evaluate the utility of the generated images, we use them as additional training data for the segmentation model. CellViT [19] (SAM-B variant) backbone with HoVer-Net [13] as decoder. Tab. 5 compares segmentation and classification performance in multiple metrics, including Dice, Jaccard, AJI (Aggregated Jaccard Index), HD95 [21] (95th percentile Hausdorff Distance), F1 score, precision and recall. We note that our proposed method consistently improves the performance across various metrics on all three datasets. In segmentation tasks on PanNuke, PathDiff trained on real and synthetic data achieves the highest Dice score (0.8164) and performs well across other metrics like Jaccard (0.7122) and AJI (0.7117). Similarly, in classification tasks on PanNuke, PathDiff achieves a strong F1 score of 0.8161 with balanced precision and recall. On the CoNIC dataset, PathDiff again + +![](images/222d484a60981a9196fc687dd1f6877c190b1444efc1327fd75be15b8d176108.jpg) +Figure 5. Qualitative examples demonstrate the effectiveness of unifying guidance from paired text and silver standard masks generated by [23] from PathCap dataset [40] (a) Real images and Text with silver masks (b) PathDiff generated images (c) ControlNet generated images. + +
DatasetMethodTrain DataSegmentationClassification
Dice ↑Jaccard ↑AJI ↑HD (95) ↓F1 ↑Precision ↑Recall ↑
PanNukeBaselineReal0.78340.69510.69046.810.78260.74720.8215
w/ SDMReal+Synth0.78910.68160.67296.260.77920.80140.7581
w/ ControlNet [47]Real+Synth0.80930.69790.69545.870.81340.83540.7925
w/ PathDiffSynth0.73110.65380.65397.730.71400.70390.7244
w/ PathDiffReal+Synth0.81640.71220.71175.120.81610.78270.8524
CoNICBaselineReal0.79270.69780.69174.380.76140.71530.8138
w/ SDMReal+Synth0.80070.68460.68464.500.78830.76200.8164
w/ ControlNet [47]Real+Synth0.80760.69990.69503.160.80000.83440.7683
w/ PathDiffSynth0.76120.64800.64736.370.74490.77830.8107
w/ PathDiffReal+Synth0.83560.71950.71412.970.80530.77900.8328
MoNuSACBaselineReal0.70890.61310.60976.770.66520.63830.6944
w/ SDMReal+Synth0.67830.57440.57316.490.66850.69400.6448
w/ ControlNet [47]Real + Synth0.69400.58520.58006.540.68430.65330.7183
w/ PathDiffSynth0.66710.58940.58947.070.68510.63450.7445
w/ PathDiffReal+Synth0.72210.61970.61925.880.71150.69510.7286
+ +Table 5. Comparison of segmentation and classification metrics across different datasets and methods on the CellViT model. The Baseline is trained with real data, and the rest of the methods have synthetic data added in equal proportion to the train set. + +leads in segmentation with a Dice score of 0.8356 and performs well in classification with an F1 score of 0.8053. On MoNuSAC, where performance is generally lower across all methods, PathDiff still outperforms others in segmentation with a Dice score of 0.7221 and achieves an F1 score of 0.7115 for classification. Importantly, training solely with synthetic images still achieves performance comparable to the baseline. This outcome suggests that the synthetic images are robust and simulate the original data effectively. It is pertinent to mention that when evaluating the classification and segmentation performance, the split used included only real test data. + +# 5. 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We propose PathFinder, a system capable of navigating image patches in a whole slide image, describe each patch to collect evidence, and produce a diagnosis. Pathfinder's process is interpretable and reminiscent of pathologists. Our system consists of multiple steps carried out by multi-modal agents: 1) Initial Assessment by Triage Agent; 2) Evidence Collection by Navigation and Description Agents; and 3) Integrated Diagnosis by Diagnosis Agent. + +![](images/cadc9b11f405b8262fa740528691e25e2de8e17f2d452c91cf3c9a08162daf76.jpg) + +![](images/e685684f8f3afecffcac5df45479d6ae9c8ebf12ff5a60d9afa98821cfb1ce20.jpg) + +# Abstract + +Diagnosing diseases through histopathology whole slide images (WSIs) is fundamental in modern pathology but is challenged by the gigapixel scale and complexity of WSIs. Trained histopathologists overcome this challenge by navigating the WSI, looking for relevant patches, taking notes, and compiling them to produce a final holistic diagnostic. Traditional AI approaches, such as multiple instance learning and transformer-based models, fail short of such a holistic, iterative, multi-scale diagnostic procedure, limiting their adoption in the real-world. We introduce PathFinder, a multi-modal, multi-agent framework that emulates the decision-making process of expert pathologists. PathFinder integrates four AI agents—the Triage Agent, Navigation Agent, Description Agent, and Diagnosis Agent—that collaboratively navigate WSIs, gather evidence, and provide comprehensive diagnoses with natural language explanations. The Triage Agent classifies the WSI as benign or risky; if risky, the Navigation and Descrip + +tion Agents iteratively focus on significant regions, generating importance maps and descriptive insights of sampled patches. Finally, the Diagnosis Agent synthesizes the findings to determine the patient's diagnostic classification. Our Experiments show that PathFinder outperforms state-of-the-art methods in skin melanoma diagnosis by $8\%$ while offering inherent explainability through natural language descriptions of diagnostically relevant patches. Qualitative analysis by pathologists shows that the Description Agent's outputs are of high quality and comparable to GPT4o. PathFinder is also the first AI-based system to surpass the average performance of pathologists in this challenging melanoma classification task by $9\%$ , setting a new record for efficient, accurate, and interpretable AI-assisted diagnostics in pathology. Data, code and models are available at https://pathfinder-dx.github.io/. + +# 1. Introduction + +Medical diagnosis of histopathology through the examination of whole slide images (WSIs) is a cornerstone of mod + +ern pathology. WSIs are high-resolution, digitally scanned histopathology cases, providing an extensive view of tissue architecture and cellular detail. Pathologists navigate these gigapixel-scale images to identify morphological features and spatial relationships critical for accurate diagnoses. They start with a low magnification to identify suspicious regions and then zoom in for detailed examination [11, 32]. They gather evidence across patches and accumulate them together to make a final holistic diagnosis. This process is the gold standard. However, it is labor-intensive and requires significant expertise to interpret complex visual data effectively. It is becoming increasingly unsustainable due to the rising number of cancer cases globally. + +The shift towards more efficient diagnostic methods in medical imaging is essential, yet must maintain accuracy. Recent advancements in deep learning report achieving expert-level performance, promising such a scalable approach [47]. However, current methods typically divide WSIs into smaller patches for independent analysis, making diagnoses without the holistic context [1, 13, 23, 26, 44, 46, 53, 54, 56]. Transformer-based models attempt to capture both local and global patterns but are not scalable with the high-resolution demands of WSI [3, 14, 45, 52, 55]. + +In contrast, we propose PathFinder, a multi-modal and multi-agent system designed to mimic the decision-making process of expert pathologists by integrating four AI agents: Triage, Navigation, Description, and Diagnosis. The system begins with the Triage Agent, classifying the WSI as benign or risky; if risky, the Navigation and Description Agents iteratively examine patches, generating natural language descriptions and refining their focus with each cycle. Finally, these detailed insights are integrated by the Diagnosis Agent to produce an accurate and holistic diagnostic classification. Figure 1 shows PathFinder's pipeline. + +Our experiments demonstrate that the proposed agentic system significantly outperforms prior state-of-the-art (SOTA) methods on WSI skin melanoma grading, achieving an accuracy of $74\%$ on the M-Path Skin Biopsy dataset [9]. This marks an $8\%$ improvement over the best baseline with accuracy of $66\%$ and a $9\%$ improvement over the $65\%$ average performance of pathologists [9]. Our proposed system is fully explainable from the patches visited to the description of the patches and the final diagnoses, which takes into consideration all the patch-wise information. To the best of our knowledge, PathFinder is the first AI-based system capable of surpassing the average performance of pathologists on this challenging melanoma classification task. + +# 2. Related Work + +Multi-modal Histopathology Models. There have been a series of studies in histopathology that leverage WSI-level and pachth-level images to train unimodal classifiers based on multiple instance modeling leveraging pretrained feature + +extractors [35, 45, 51]. More recently unimodal foundational models trained on varying self-supervised objectives have achieved significant improvements on performance downstream [4, 22, 49, 53]. With the introduction of large-scale multi-modal datasets in histopathology, we have seen significant advancements, with the emergence of large language models and vision-language models for histopathology. For instance, studies like Quilt-1M [23] and PathGen-1.6M [46] curate large histopathology image-text paired dataset and train CLIP-based models to learn joint vision-language representations, significantly enhancing clinical histology downstream tasks on patch-level. On the WSI-level, PathAlign [1] aligns diagnostic texts from pathology reports with corresponding WSIs, facilitating applications such as automatic report generation and case/patient-level visual question answering, moving towards a more clinically integrated and holistic diagnostic process. While many other studies like Quilt-LLaVA [44], SlideChat [5], and PathChat [34] train histopathology Multi-modal Large Language models (MLLM) and improve on diagnostic reasoning tasks, none of these models effectively automatically navigate the giga-pixel scale WSIs towards a diagnosis. + +The role of Navigation in Histopathology Diagnosis. Computational pathology studies have tried to capture and analyze the navigation patterns of pathologists when reviewing digital slide images [11, 36, 37, 41] specifically characterizing mouse patterns, zooming in/out, and panning the field of view to piece out morphological clues towards a diagnosis. Often, these studies juxtapose the navigation patterns of junior and senior-level pathologists. NaviPath [13], presents a human-AI collaborative navigation system designed to integrate into pathologists' workflows, considering the domain knowledge and navigation strategies required for effective examination of pathology scans. + +Multi-agent Systems. The concept of multi-agent systems has gained traction in AI research, particularly for tasks requiring dynamic behavior and contextual understanding. Recent research has demonstrated the potential of large foundation models in creating interactive agent-based AI systems including interactions between robots, environments, and humans in the field of robotics [8, 15, 50]. These systems can perform complex tasks by leveraging the strengths of individual agents utilizing collaboration and coordination. The potential of multi-agent systems in handling real-world scenarios has been demonstrated in recent studies including but not limited to role-playing [29], reasoning [6], gaming [19] and software engineering [16]. In the medical domain some studies have explored roleplaying providers (clinicians) treating patients and accumulating proficiency with increasing interactions [10, 30]. These studies are centered around multiple providers; however, in medical image analysis, multi-agent systems can simulate the collaborative nature of different sub-tasks + +![](images/ed2b7535b732513f884309b3910542e1b2a95a4a9b241dea85b139f290903ac8.jpg) +Figure 2. The left panel illustrates the Navigation Agent, as outlined in Section 4.2. The right panel presents the iterative trajectory generation process, which employs both the Navigation Agent and Description Agent, as described in Section 4.4. + +![](images/a89ba654f0876f00a8f3a4d612c8e48d2cbebc860eb6bf60f8b2a46688fb2baf.jpg) + +within the human-expert decision-making processes, including navigation, understanding and holistic diagnosis. + +# 3. Datasets + +To lay the groundwork for describing our agents, we first introduce the data used for training and evaluating PathFinder. M-Path Skin Biopsy WSIs. The WSIs in this dataset are from M-Path study [2, 9, 38], consisting of 238 melanocytic lesions stained with Hematoxylin and eosin (H&E). A consensus panel of three dermatopathologists, each with internationally recognized expertise, independently interpreted all 238 cases and established a consensus diagnosis for each case. There are 4 diagnostic classes in M-Path: class 1 with 35 cases (mild and moderate dysplastic nevi); class 2 with 86 cases (severe dysplasia/melanoma in situ); class 3 with 70 cases (invasive melanoma stage pT1a); and class 4 with 47 cases (advanced invasive melanoma stage pT1b or more). For model development, the dataset is divided into training, validation, and test sets with a 168/35/35 case split + +with same class distribution across the sets. + +M-Path Pathologists' Viewport Data. The M-Path study conducted viewpoint data collection, recruiting 87 pathologists from 10 U.S. states. Eligibility criteria included completion of residency and/or fellowship training and recent experience interpreting skin specimens in clinical practice. Pathologists' worldview data was gathered through an online digital slide viewer developed using Microsoft's open-source Silverlight-based HD View SL, a gigapixel image viewer. This viewer enabled pathologists to navigate each image by panning and zooming up to $60\mathrm{x}$ magnification. During interpretation, the web-based viewer automatically logged viewpoint tracking data, capturing a rectangular image area displayed on the pathologist's screen at any given moment. For each interpretation (unique pathologist-case pair), the system recorded a list of viewpoint coordinates, magnification levels, and timestamps. Data from the pathologists who completed the M-Path study (32 out of 87) were included in the current study. Detailed methodology of the + +M-Path study is available in [38]. + +# 4. PathFinder + +The multi-agent multimodal framework proposed in this study includes four agents: 1) Triage ; 2) Navigation ; 3) Description ; and 4) Diagnosis. The details of training data and model architectures are described below. Figure 1 demonstrates how the four agents interact with each other towards the final goal which is diagnosing a WSI. + +# 4.1. Triage Agent + +The Triage Agent is an image-only transformer-based model for separating class 1 (mild and moderate dysplastic nevia) from the rest in the M-Path dataset (Refer to section 3 for M-Path class definitions). We describe the data preparation, model architecture, and training details below. + +Data Generation. Each WSI is divided into non-overlapping $512 \times 512$ patches at $10 \times$ magnification. Background patches (saturation less than 15) are discarded. If fewer than 150 patches remain, we randomly select additional patches from the WSI, apply the saturation filter again, and include the ones that pass. These additional patches may overlap with existing patches but ensure that each WSI contains sufficient information. All patches are then rearranged based on their spatial coordinates to approximate spatial structure which allows conv. layers and positional encodings to capture meaningful local context. The patches are embedded using the Quilt-Net image encoder [23], resulting in a feature vector of shape $(N,768)$ per WSI, where $N$ is the total number of patches in a WSI. + +Model Architecture. The Triage Agent includes several sequential stages (See Fig 5 in the Appendix): The feature vector is initially projected from $(N,768)$ to $(N, dim)$ using a linear layer to align with the model's embedding dimension $dim$ . For compatibility with 2D processing, the vector is reshaped into a square grid through padding to dimensions $H \times H$ , where $H$ is the smallest integer satisfying $H \times H \geq N$ , with padding achieved by repeating the first $M = H^2 - N$ features. The padded vector is then processed through a transformer block, followed by positional encoding via the Pyramid Position Encoding Generator (PPEG) [45], and an additional transformer block, where each transformer block contains a single self-attention layer. Subsequently, multi-scale convolutional layers and a squeeze-and-excitation (SE) block [18] refine the vector, capturing spatial patterns across scales and emphasizing key features. The output is then flattened and transformed back to the embedding dimension. A learnable class token is appended to capture global context, and the modified vector is passed through another transformer block, positional encoding, and a final transformer block. Finally, the class token is pooled and passed through an MLP head to produce the model's output. + +Training Details. We used BCE loss for the classification task. The embedding dimension $dim$ is 512. Training hyperparameters are as follows: a batch size of 1, learning rate of $2 \times 10^{-4}$ , weight decay of $1 \times 10^{-5}$ , and gradient accumulation over 32 steps. Training is conducted for up to 100 epochs, with early stopping after 30 epochs without improvement to prevent overfitting. Our approach achieved higher F1 and accuracy compared to other methods that are directly comparable for this task (See Table 2 in the App.). + +# 4.2. Navigation Agent + +The Navigation Agent is designed to mimic a pathologist's methodical approach to identifying regions of interest (ROIs) in WSIs. Unlike traditional systems that scan the entire WSI in a single, mechanistic sweep, our Navigation Agent adopts a more human-like, iterative process collaborating with the Description Agent. It begins by pinpointing an initial ROI from an importnace map, much as a pathologist would focus on one area at a time. This selected ROI is then relayed to the Description Agent, which provides a natural-language description of the area back to the Navigation Agent to select the next ROI. Figure 2 illustrates the workflow of the Navigation Agent in the left panel. + +In our initial attempt, we designed the Navigation Agent using a multi-modal architecture inspired by LLaVA [31], integrating an image encoder and a large language model (LLM). The image encoder extracted features from a low-resolution version of the WSI, and the LLM processed these features along with previous text descriptions to predict the next ROI. Specifically, the WSI was divided into a grid of patches, and the LLM would output the grid coordinates of the most relevant patch based on both visual and textual inputs. However, this approach faced significant challenges due to the limited size of our training dataset. The model tended to overfit, frequently selecting central patches regardless of the input (see Appendix 8 for details). This limitation prompted the exploration of more data-efficient methods that could better generalize from limited samples. + +To overcome these challenges, we restructured the Navigation Agent to directly generate an importance map over the WSI, conditioned on textual descriptions from previous observations. This approach removes the dependency on LLM for spatial selection and leverages a feedback mechanism between image and text modalities. Let $I^{(t)}$ be the input WSI at iteration $t$ , with previously selected patches masked out (replaced by the background color) to avoid resampling and $D^{(1:t)} = \{D^{(1)}, D^{(2)}, \ldots, D^{(t)}\}$ be the set of textual descriptions up to iteration $t$ . At each iteration $t$ , the Navigation Agent processes the masked WSI $I^{(t)}$ to predict an importance map $M^{(t)}$ , indicating the likelihood of each region being the next ROI. The importance map is conditioned on the aggregated textual information from previous descriptions. We define the importance map generation as + +$M^{(t)} = f_{\mathrm{Nav}}\left(I^{(t)},E^{(t - 1)}\right)$ where, $f_{\mathrm{Nav}}$ is the Navigation Agent's function (implemented as a U-Net [42]) that has four layers in both encoder and decoder and is conditioned with text embeddings of descriptions, as well as the masked version of the WSI that masks the earlier predicted ROIs, and $E^{(t - 1)}$ is the aggregated text embedding up to iteration $t - 1$ . $E^{(t - 1)}$ is computed by encoding each description $D^{(k)}$ using a pre-trained Text-to-Text-Transfer-Transformer (T5) text encoder [40] and averaging the embeddings: + +$$ +E ^ {(t - 1)} = \frac {1}{t - 1} \sum_ {k = 1} ^ {t - 1} \mathrm {T} 5 _ {\text {t e x t}} (D ^ {(k)}) \tag {1} +$$ + +At the first iteration $(t = 1)$ , since there are no prior descriptions, the importance map is generated solely from the unmasked WSI $M^{(1)} = f_{\mathrm{Nav}}\left(I^{(1)}\right)$ . From the importance map $M^{(t)}$ , we then statistically sample the next patch to analyze. The probability $p_{(i,j)}^{(t)}$ of selecting a location $(i,j)$ is proportional to its importance score: + +$$ +p _ {(i, j)} ^ {(t)} = \frac {M _ {(i , j)} ^ {(t)}}{\sum_ {\left(i ^ {\prime} , j ^ {\prime}\right)} M _ {\left(i ^ {\prime} , j ^ {\prime}\right)} ^ {(t)}} \tag {2} +$$ + +We then sample the patch coordinates $(i^{*},j^{*})$ based on this probability distribution: $(i^{*},j^{*})\sim p_{(i,j)}^{(t)}$ . The selected high-resolution patch corresponding to $(i^{*},j^{*})$ is sent to the Description Agent, which generates a new textual description $D^{(t)}$ . The new description $D^{(t)}$ is encoded and incorporated into the aggregated text embedding $E^{(t)}$ : + +$$ +E ^ {(t)} = \frac {1}{t} \sum_ {k = 1} ^ {t} \mathrm {T 5} _ {\text {t e x t}} (D ^ {(k)}) \tag {3} +$$ + +This updated embedding $E^{(t)}$ is then used to condition the Navigation Agent in the next iteration, enabling the model to refine its importance map $M^{(t + 1)}$ based on both the visual information from $I^{(t + 1)}$ and the accumulated textual insights. Therefore, we refer to it as the Text-conditioned Visual Navigator. + +Training details. To train the Navigation Agent, we constructed a dataset from M-Path [38] consisting of WSIs and sequences of textual descriptions for the most important patches. Each training sample includes: The WSI and the corresponding masked versions, the set of descriptions $D^{(1:t)}$ for each iteration generated by Quilt-LLAVA [44] and the ground truth importance maps derived from pathologist viewpoint data in M-Path. We minimized the binary cross-entropy loss between the predicted importance maps $M^{(t)}$ and the ground truth maps $\hat{M}^{(t)}$ . Finally, to prevent overfitting, we paraphrased each description multiple times while preserving the semantic meaning, augmenting the textual data available for training. + +# 4.3.Description Agent + +We utilize Quilt-LLaVA [44], a multi-modal large language model capable of describing individual histopathology patches, as our Description Agent. While the original Quilt-LLaVA generates highly detailed findings, in this work, we instruction-tuned the model to produce more concise summaries, optimizing for computational efficiency. Using captions from the Quilt-1M dataset [21], we prompted GPT-4 to generate a list of findings as concise as possible. This process yielded 102,000 instruction-tuning samples. Figure 6 in the Appendix presents our prompt and a sample data entry generated for tuning the Description Agent. The Quilt-LLaVA 7B model was instruction-tuned for one epoch to obtain the Description Agent. + +# 4.4. Diagnosis Agent + +The Diagnosis Agent is a language-only model that analyzes all the text descriptions of histopathological findings produced by the Description Agent over all the patches identified by the Navigation Agent, to classify them into three categories (classes 2, 3, and 4). + +Data Generation. To train the Diagnosis Agent, we generated diagnostic trajectories—sequences of patch descriptions that simulated how a pathologist examined a WSI. Using our Navigation Agent, we proceeded as follows. + +We first obtained a heatmap for a sub-sampled WSI $(512 \times 512$ pixels) using a text-conditioned U-Net model, which highlighted regions of diagnostic significance. The WSI was divided into a $16 \times 16$ grid, creating 256 patches of $32 \times 32$ pixels each. Each patch received an importance score based on the mean intensity of the heatmap over the patch, indicating its diagnostic relevance. These scores were normalized across all patches. + +To generate a single trajectory, we iterated the following steps ten times, yielding ten patches per case. At each iteration, a patch was selected using weighted probabilistic sampling based on the normalized importance scores, introducing variability and ensuring different patches were chosen across iterations. The selected patch was then cropped from the high-resolution $10 \times$ WSI, and a description was generated by the Description Agent. Selected patches were masked on the WSI to prevent reselection, and all descriptions generated thus far were combined into a single text input for the next iteration. The generation of a single trajectory is presented in the right panel of Figure 2. + +For each WSI in the training and validation sets, we generated five $(n = 5)$ different trajectories, each containing ten patch descriptions, to capture various examination patterns. For the test set, we extracted additional trajectories $(n = 20)$ to assess the effect of trajectory number on diagnosis results. To add variability, we used LLaMA 3.1 Instruct [7] at each iteration to rephrase descriptions, simulating how pathologists examine cases with different patterns + +Figure 3. Ablation results. We ran 10 experiments, and plotted both the mean and standard deviation. +![](images/c5d4c996dd934dd6a8afe6799979aa60b35d49f582929ec79180272b9cf029c3.jpg) +(a) Majority voting accuracy for 1-20 trajectories. Each trajectory contains 10 patches visited by the navigator. + +![](images/181981bedfb965f76d3a4d7c5498e607d147fc32633ec9fd3b2bdf8b7533740b.jpg) +(b) Majority voting accuracy for 5 trajectories with 1-10 patches per trajectory. + +when seeking diagnostic regions. + +Training Details. The Diagnosis Agent consists of a large language model (LLM) with a classification head on top. The classification head maps the LLM's output (vocabulary size) to the number of classes, producing the final classification probabilities using a single linear layer. Due to resource constraints and the limited size of the dataset, we selected GPT-2 [39] as the base pre-trained LLM. Please see Section 10 in the Appendix for training details. + +# 5. Experiments and Results + +This section outlines the experimental setup and evaluates the performance of the proposed PathFinder framework. First, we conduct a qualitative assessment of the descriptions generated by the Description Agent, comparing them to two vision-language models (VLMs). Next, we evaluate PathFinder on the M-Path dataset for melanoma diagnosis (see Section 3), benchmarking it against state-of-the-art transformer-based and MIL-based baselines, as well as public and private large language models (LLMs) using prompting without additional training. Finally, we analyze PathFinder's performance under various configurations, altering the Triage, Navigation, and Description Agents. Detailed evaluations are provided in the following subsections. + +# 5.1. Pathologist Evaluation of Description Quality + +To assess the quality of descriptions generated by our Description Agent, we conducted a survey in which two expert pathologists rated descriptions produced by our Description agent in comparison to those generated by GPT4-o [20] and LLaVA-Med [28]. We selected 25 cases from the M-Path dataset, sampling across the four diagnostic classes. For each case, we cropped the consensus region of interest, manually labeled by a panel of expert dermatopathologists as the area most representative of the diagnosis. Using this region, we prompted our Description Agent, LLaVA-Med and GPT4-o to generate concise descriptions of each histopathology patch. These descriptions were then presented to two expert pathologists in a randomized, double + +blind format. Each pathologist was asked to respond to two questions for each case to indicate their preferred description and the reason for their preference. Refer to Appendix 11 for a detailed explanation of this assessment. The results shown in Figure 4 indicate that, PathFinder's Description agent achieves comparable performance to GPT-4o while being significantly more cost-effective, operating with just 7B parameters - a fraction of GPT-4o's size. + +![](images/c4903468bdf84b4b465473c64d4ad60136ff4413241b0beab754cd18733aee34.jpg) +Figure 4. Expert human pathologist preferences for each model in assessing description quality, evaluated in a double-blind survey. + +For evaluating PathFinder, we utilize the M-Path dataset which contains histopathology WSIs of melanocytic skin tissue. As outlined in 4.4, multiple trajectories are generated per case to simulate the variability in diagnostic patterns observed among pathologists, who may assess a single case with diverse visual strategies to identify diagnostically significant regions. To mitigate randomness in our results, we evaluated PathFinder 10 times on the test set, each time using a different random subset of 5 trajectories selected from the total of 20. For each WSI, majority voting is performed on the predictions from the 5 selected trajectories to produce the final result. The overall performance is then reported in Table 1 as the mean of the results across the 10 runs. We balanced the testing dataset to ensure that each diagnostic class is represented by an equal number of samples. Consequently, the micro-averaged F1 score, precision, and recall are equivalent to the accuracy reported in the table. We used micro-averaged metrics as they appropriately balance the importance of different skin cancer stages, crucial for assessing diagnostic reliability. + +We compared Pathfinder to four state-of-the-art baseline + +
MethodsAccuracyF-1 score
Baselines
Human Experts [9]0.650.65
ScAtNet [52]0.620.62
ScAtNet + ROI Heatmap [12]0.630.63
ScAtNet + SAG [32]0.600.60
ABMIL [24]*0.460.47
ABMIL w/ CONCH [33]*0.660.60
ABMIL w/ UNI2-h [4]*0.660.66
ABMIL w/ QuiltNet [23]*0.610.63
LLM Prompt Baselines
BioMistral-7B0.430.43
Mistral-Nemo-Instruct-24070.410.41
GPT-4o0.490.49
Meta-Llama-3-8B-Instruct0.310.31
LLaVA-Med-v1.5-Mistral-7b0.430.43
Quilt-LLaVA-v1.5-7b0.290.29
Ours
PathFinder + ABMIL w/ UNI2-h Attention-Based Top Patches0.460.46
PathFinder + ABMIL w/ QuiltNet Attention-Based Top Patches0.460.46
PathFinder + ABMIL w/ CONCH Attention-Based Top Patches0.540.54
PathFinder + T5-Based Text-Conditioned Visual Navigator + No Triage Agent0.580.58
PathFinder + T5-Based Text-Conditioned Visual Navigator + LLaVA-Med Descriptions0.560.56
PathFinder + CLIP-Based Text-Conditioned Visual Navigator + LLaVA-Med Descriptions0.600.60
PathFinder + Standalone Triage-only Full Classifier0.600.60
PathFinder + Imitated Sampling0.630.63
PathFinder + Vision-Only Navigator0.640.64
PathFinder + CLIP-Based Text-Conditioned Visual Navigator0.620.62
PathFinder + Exhaustive search0.680.68
PathFinder + T5-Based Text-Conditioned Visual Navigator0.740.74
+ +* ABMIL result is based on a single run and does not use majority voting + +Table 1. Majority voting performance for whole slide image (WSI) diagnosis on the M-Path dataset. Accuracy is reported, and the F-1 score is identical due to the balanced testing set. Finally, coverage here is the percent of patches used across all trajectories. All experiments are conducted using the same split of the M-Path dataset, as detailed in Section 3. + +models: 1) three transformer-based models all utilizing the ScAtNet architecture [12, 32, 52] and 2) four MIL-based model, using ABMIL [24] with different backbones. ScAtNet utilizes a MobileNetV2 backbone [43] to extract multiscale features from images at $7.5\mathrm{x}$ , $10\mathrm{x}$ , and $12.5\mathrm{x}$ magnification. For the first baseline model, these feature vectors are subsequently fed into ScAtNet which aggregates information of the three scales to perform the diagnostic task using Transformer blocks. The second approach [12] augments the WSI with ROI heatmaps generated by the U-Net model, appending these maps as a fourth input channel and using ScAtNet for classification. The third baseline model, SAG [32], converts diagnostically relevant entities into attention signals, integrating these with ScAtNet and employing an attention-guiding loss function that combines heuristic guidance (HG) and tissue guidance (TG) based on disease-specific prior knowledge such as tissue, structure, + +and cellular information. In addition to the original AB-MIL model [24], we extended our evaluation by incorporating three additional ABMIL variants, each using a different pathology-specific foundation model as a backbone: CONCH [33], UNI2-h [4], and QuiltNet [23]. ABMIL aggregates information across instances using an attention mechanism that assigns weights to each instance, allowing the model to capture its contribution to the final bag label in a permutation-invariant manner. Then, we conducted comprehensive experiments to evaluate PathFinder by examining different architectures for each agent component, achieving $74\%$ accuracy that surpasses both human experts $(65\%)$ and previous state of the art $(66\%$ best). Our evaluation focused on three main aspects: + +Navigator Architectures. First, to quantify the importance of Description Agent feedback, we tested a Visual-Only Navigator that employs weighted probabilistic sampling for + +patch selection without iterative feedback in a single pass of the WSI. Additionally, we implemented Imitated Sampling (see App. 12), which statistically selects WSI patches based on pathologists' viewing patterns from M-Path dataset. Regions observed longer had higher sampling probabilities. Both Imitated Sampling and Vision-Only Navigator performed similarly (64% and 63% respectively), indicating that both pure statistical and learned "sampling", regardless of source, has limited effectiveness. To assess the necessity of our iterative navigation approach, we added a non-iterative baseline, selecting the top 10 patches from AB-MIL attention scores using three pathology-specific foundation model backbones. The best model with CONCH [33] backbone performed substantially lower than our best navigation-based approach (74% vs 54%). This confirms that a purely image-based, non-iterative selection approach is insufficient, as it lacks the ability to iteratively refine patch selection based on textual descriptions. Furthermore, we evaluated text-conditioned visual navigators using either CLIP-based or T5-based text encoders. The T5-based navigator significantly outperformed its CLIP-based counterpart (74% vs 62%), suggesting CLIP's 77-token limit constrains its ability to effectively process multiple descriptions (we truncate descriptions exceeding 77 tokens, then average if a description is long). Finally, our navigation-based approach (74%) outperformed exhaustive search (68%), which uses all tissue patches of the WSI, suggesting that selective patch sampling helps avoid confusion from irrelevant regions. + +Description Agents. We compared a fine-tuned version of Quilt-LLaVA against off-the-shelf LLaVA-Med. Ours showed superior performance (74% vs 56%), demonstrating better guidance for the navigator. Notably, when paired with LLaVA-Med descriptions, the T5-based Navigator showed no advantage over the CLIP-based version (56% vs 60%). This suggests that a more powerful text encoder like T5 can actually be detrimental when processing lower-quality descriptions, potentially steering the Navigator toward irrelevant regions. This finding emphasizes the importance of high-quality descriptions for effective navigation. + +Diagnosis Agents. We evaluated various public and private LLMs as baselines for our Diagnosis Agent(detailed in Table 1 under LLM Prompting Baselines). Specifically, we used PathFinder with T5-Based Text-Conditioned Visual Navigator and Quilt-LLaVA Description Agent to generate multiple descriptions for each WSI and prompted LLMs to make the classification given the descriptions. To view our prompt, please see Section 11.2 in Appendix. + +The evaluation of the baseline models are similarly done using the majority voting over 10 runs. PathFinder achieves $8\%$ improvement compared to the best baseline approaches, ABMIL with CONCH [33] and UNI2-h [4] backbones. Considering that GPT-2 is a relatively small LLM compared to the current state-of-the-art, we believe that uti + +lizing larger LLMs could improve performance. Also, note that without the Triage Agent, the performance of the best Pathfinder-variant dropped below baselines, likely due to Quilt-LLaVA's train dataset's bias toward malignant cases. Finally, we trained a standalone Triage-only classifier across all four classes, which achieved $60\%$ accuracy on the test set. This highlights the importance of incorporating the other agents in the PathFinder pipeline. + +Lastly, to investigate the impact of the number of trajectories on model performance, we evaluated the model using between 1 and 20 trajectories for majority voting, as well as the effect of varying trajectory lengths. Figure 3 illustrates this, indicating optimal performance with 5 trajectories and 10 patches per trajectory. We run every experiment for 10 rounds and report the mean and standard deviation. + +# 6. Discussion + +This study presents PathFinder, a multi-modal, multi-agent AI framework designed to emulate the multi-scale, iterative diagnostic approach of pathologists for histopathology whole slide images. By integrating Triage, Navigation, Description, and Diagnosis Agents, PathFinder collaboratively gathers evidence to deliver accurate, interpretable diagnoses with natural language explanations. Notably, it surpasses state-of-the-art methods and the average performance of human experts in melanoma diagnosis, setting a new benchmark in AI-driven pathology. While it was trained on skin cancer, one of the most challenging histopathology types, its strong performance demonstrates its effectiveness, and its Description Agent, trained on Quilt-1M covering 12 tissue types, enables adaptation to other cancers. + +PathFinder has the potential to accelerate diagnostic workflows, reducing the reliance on manual examination and enabling timely patient care in clinical settings. Its natural language descriptions provide interpretability, facilitating the validation of AI-generated diagnoses by pathologists. Moreover, its integration of vision-language models and large language models highlights the promise of multimodal AI in delivering scalable, specialized diagnostic tools that could improve access to pathology expertise. + +Despite its strengths, PathFinder has limitations. Acquiring large-scale data that capture pathologists' viewing behavior is challenging due to privacy, ethical, and logistical constraints, restricting our evaluation (App. 13). Also, the Navigation Agent's decision-making process and the Description Agent's occasional inaccuracies may impact diagnostic consistency. Future work should focus on expanding dataset diversity and refining patch selection strategies to enhance PathFinder's reliability in AI-assisted pathology. + +# Acknowledgments + +Research reported in this study was supported by the National Cancer Institute under Awards No. R01 CA15130, R01 CA225585, and R01 CA201376, and by the Office of the Assistant Secretary of Defense for Health Affairs through the Melanoma Research Program under Awards No. W81XWH-20-1-0797 and W81XWH-20-1-0798. 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However, a common limitation in these models is the incomplete display of objects, where fragments or missing parts undermine the model's performance in downstream applications. In this study, we conduct an in-depth analysis of the incompleteness issue and reveal that the primary factor behind incomplete object generation is the usage of RandomCrop during model training. This widely used data augmentation method, though enhances model generalization ability, disrupts object continuity during training. To address this, we propose a training-free solution that penalizes activation values at image boundaries during the early denoising steps. Our method is easily applicable to pretrained Stable Diffusion models with minimal modifications and negligible computational overhead. Extensive experiments demonstrate the effectiveness of our method, showing substantial improvements in object integrity and image quality. Code is available at https://github.com/HaoyXu7/Object_Completeness. + +# 1. Introduction + +Diffusion models excel in text-to-image (T2I) generation by producing high-quality, diverse outputs [15, 33, 37, 41, 47, 52], with broad applications in areas like dataset synthesis and video generation [9, 18, 24, 26, 40, 53]. However, the generated images often contain incomplete targets – fragmented or missing object parts as shown in Fig. 1. Such object incompleteness issues not only undermine the reliability of diffusion models but also adversely affect the per + +![](images/c8a641bc9179e62aebae6cd686777721cb875e987055768891da152f0b33a502.jpg) +SDv2.1 + +![](images/d4f5ba121f800c1a93b2eff4c53762749781e5c2e4fbc674a1ddee0ee1737470.jpg) +A bed + +![](images/937a5d2c88473861cb889b79c8953e68689a429f8308b3a3909eda3e60ea63ea.jpg) +A red car +A complete bathhtub +A cap in the middle + +![](images/769387668985d1d543ab4eb6dbb28d89bd1d0f86d71287f973c58b288b633736.jpg) + +![](images/a60136ec9cfbcc9b17d27a4f93d94bb661119febb8e5153b71d3db87523c5f03.jpg) +SDv1.5 + +![](images/23780a7bcb10ef410a6ae344fc55e7e47b5201d999d8b32c9d860215a4682670.jpg) +Figure 1. Incomplete objects generated by different Stable Diffusion models with varying prompts, even with modifiers indicating completeness (e.g. "complete", "in the middle"). + +![](images/058d748ab2bc0931108af9c7f034cdfff4a60871b1d97bc482d304f0d270853f.jpg) + +![](images/63ec4ad4da1ae571e776128f04745fa4dfd31f275f37e298a6fe7bfca8bb2539.jpg) + +formance of downstream tasks dependent on the generated data. + +However, this issue has largely been overlooked in existing studies [23, 27, 36, 45]. Some studies [14, 35, 48] dismiss these minor imperfections as inherent randomness in the generation process, while others [6, 21, 25, 57] categorize them as generation failures without delving into the underlying causes. The layout generation methods [6, 21, 64] benefit from planning the placement of objects to address the object incompleteness issue. These methods either produce objects that overflow the layout due to insufficient constraints or apply overly strict constraints, causing distortion. SDXL [31] recognizes this issue and attempts to mitigate it by incorporating the coordinates of the cropped operation during training. While the method does not eliminate the issue and carries the risk of introducing errors, such as the unnatural clustering of multiple objects at the center of the image. Despite these efforts, there has been little in-depth exploration of the underlying causes of the incompleteness problem or further advances in solutions. + +To better understand the issue, we conducted an in-depth investigation into the phenomenon of generative incom + +
ModelDALL-E 2 [8]SDv2 [37]SDv3 [37]SDXL [31]
HOIR47.3%45.5%30.1%18.0%
+ +pleteness and its causes. We manually check that the incompleteness issue persists universally across various diffusion models, as shown in Tab. 1, with the highest object incompleteness rate (from DALL-E 2) reaching $47.3\%$ . Even SDXL, which is specifically trained to address this issue, still exhibits an incompleteness rate of $18\%$ . We attempt to adjust prompts by adding adjectives to specify object completeness. However, as shown in the left two columns of Tab. 2, this does not resolve the issue, highlighting that the issue lies beyond prompt engineering. Based on the findings above, we propose two primary hypotheses: the issue might stem from inherent incompleteness in the object characteristics present in the training dataset or from biases introduced by the training strategy. We design experiments to establish that the usage of RandomCrop as a data augmentation method is the primary factor contributing to this issue. More details of the discussions of the two hypotheses are illustrated in Sec. 3.2. + +Despite its drawbacks, RandomCrop remains an indispensable component of diffusion model training, as it significantly enhances the model's diversity and generalization capabilities. Moreover, addressing the incompleteness issue by fine-tuning diffusion models without RandomCrop would be prohibitively expensive due to the high costs involved in training. Thus we propose a training-free solution to achieve object completeness in generic generation scenarios. To achieve this, we implicitly guide the subject toward the central region by reducing the probability of generating objects near the image edges. Specifically, we first utilize cross-attention maps to identify corresponding self-attention maps. These features are then integrated to penalize activation values at image boundaries during the early stages of the denoising process. This way, we can facilitate the generation of complete objects during model inference without requiring additional model training or external spatial signals, offering a lightweight and efficient solution. Our approach is inherently orthogonal to SDXL's training methodology while resolving its potential layout challenges and can be easily applied to existing diffusion models with minimal modifications and computational overhead. + +In summary, our contributions are threefold: + +- We identify and validate the cause of incomplete object generation in diffusion models, attributing it primarily to the use of RandomCrop during model training. +- We propose a training-free method that improves object completeness in diffusion-generated images by re + +Table 1. Statistics on the incompleteness of objects of different T2I models using datasets constructed from benchmarks in Tab. 2. HOIR is the abbreviation for human-evaluated object incompleteness rate. + +
Prompt TypeHOIRPrompt SourceHOIR
a [CLASS]45.7%COCO Caption38.5%
a complete [CLASS]43.2%Flickr30k40.3%
a [CLASS] in the middle44.3%DrawBench22.5%
+ +Table 2. Statistics on the incompleteness rate of the images generated by SDv2.1 across different prompts. We evaluate both manually constructed prompts and public datasets. HOIR is the human-evaluated abbreviation for object incompleteness rate. + +ducing the probability of generating objects near the image edges, easily applicable to pretrained diffusion models with minimal additional cost. + +- Experimental results validate the effectiveness of our method. Our method reduces the object incompleteness rate of SDv2.1 to $17.3\%$ with a negligible computation cost, demonstrating substantial improvements in image quality and object completeness, making diffusion models more reliable for applications. + +# 2. Related Work + +# 2.1. Controlled Generation in Diffusion + +Many studies [12, 13, 28, 34, 51, 61] aim to enable diffusion models to generate high-quality results under more precise control. Among these, controlled generation [16, 17, 30, 50, 59, 63] is frequently used to modify the attributes and details of images, while maintaining the model's generative capabilities. These methods leverage the attention mechanism in the generation process [38]. Some studies [5, 14] incrementally updates the activation levels of specific words corresponding to objects in $A$ to control the expression intensity of the prompt. Others [35, 48] uses cross-attention maps to bind entities and attributes, thereby ensuring the generated results more accurately align with the prompt. + +Additionally, with the release of pre-trained models like Stable Diffusion [37], many tasks find it more appropriate to transfer the prior knowledge of these models rather than training the network [3, 29, 39]. FastComposer [56] introduces cross-attention maps for the localization of multiple specific subjects in the generation, ensuring that the attention on reference subjects is precisely focused on the corresponding regions of the target image. MasaCtrl [4] obtains the object mask from the cross-attention map and applies it in the proposed mutual self-attention strategy to control the generation results. + +# 2.2. Seed Select in Latent Space + +The Gaussian noise as the starting point of the diffusion denoising process may differ. As a result, even with the same prompt, the generated outcome can vary [15, 42, 46]. SeedSelect [43] solves the problem of difficulty in generating specific objects by selecting suitable seeds in the noise + +space. Mao et al. [25] discovered that certain pixel blocks in the initial latent image have a tendency to generate specific content. They modify these blocks to gain precise control over specific regions of the image. S2ST [11] inverses the original image into a noise seed and matches the target scene through seed translation and trajectory optimization to control the style and layout of the result. Consequently, they achieved a relatively controllable generation process by attempting to select seeds in the seed space that better aligned with their objectives. + +# 2.3. Layout Control in Image Generation + +The prompt exhibits ambiguity in guiding the image layout. Layout generation attempts to specify the generation regions of objects through additional positional information (such as box, keypoints, depth map, semantic map, etc.). GLIGEN [21] incorporates new conditional information into the generation process through a gated self-attention layer. LayoutDiffusion [64] integrates the bounding box conditions of multiple objects into the proposed layout fusion module and then combines it with cross-attention to precisely control spatial information. Chen et al. [6] use cross-attention maps to update the current step latent and participate in the next iteration. Some studies [2, 57] directly increase the probability of specific objects in the attention map with masks to achieve layout arrangement. Although layout generation attempts to address the completeness of object generation from a different angle, it sometimes places objects in physically unrealistic poses and still fails to address object incompleteness. Our method avoids such placement errors by adhering to the diffusion setup and effectively addresses incompleteness. + +# 3. Object Incompleteness + +This section analyzes persistent object incompleteness in diffusion models (Sec. 3.1). We further investigate the causes, focusing on the dataset characteristics and data augmentation techniques (Sec. 3.2). + +# 3.1. Issue Statement + +To investigate the issue, we test prompts containing a single object (such as a backpack, a car, etc.), along with various T2I model benchmarks, obtaining the corresponding image. Fig. 1 illustrates some cases, where the generated images only display a part of the object (e.g. the rear half of the car is missing, the bathtub and cap are missing their right halves). The situation remains the same when we use prompts with spatial descriptions. + +To further investigate the occurrence of this issue, we randomly select 1,200 object categories (including animals, furniture, tools, clothing, vehicles, etc.), and generate corresponding prompts for each category. At the same time, + +![](images/be4a610c2e56225f27c0a9552696ea5fe7280de8a5e98a6617462f6f70b838a5.jpg) +Figure 2. The trend of the rate of object incompleteness in images generated by diffusion models fine-tuned in different ways. Here, "Seen Class" and "Unseen Class" indicate whether the category of the object generated by the fine-tuned diffusion model is seen in the fine-tuning data. + +we also prompt SDv2.1 with a randomly sampled subset of 1,200 images from each of COCO Caption [7] and Flickr30k [62], as well as the full DrawBench [41]. For all results, we manually evaluate an image complete if its subject is mostly intact. As shown in Tab. 2, the probability of the object incompleteness issue occurring is surprisingly $45.7\%$ when the given prompt type is "a [CLASS]". Even after adding adjectives indicating completeness to the prompt, the probability only slightly decreased to $43\%$ . Using DrawBench as the prompt source yields the lowest HOIR of $22.5\%$ , but with only 200 prompts, the results may be unstable. + +# 3.2. Cause Analysis + +Regarding the underlying causes, we posit that images generated by diffusion models exhibit statistical distribution alignment with the input tensors during training. Therefore, the issue of object incompleteness likely exists in the training input. This issue may arise from two main factors: 1) the dataset, and 2) data augmentation. Below we discuss the potential causes of this issue from these two perspectives. + +The dataset. We select a collection of datasets employed in training diffusion models, including the aesthetic subset of LAION-5B [44], and then we manually calculate the incompleteness rate of 1,200 randomly sampled images from these datasets to estimate the overall incompleteness rate of the entire dataset. However, we find it to be only $4\%$ , much lower than the probability observed in the images generated by the diffusion model. This suggests that the primary cause of the issue does not stem from the dataset itself. + +Data augmentation. The images in the dataset undergo data augmentation to increase diversity before being input + +into the diffusion model in the training process. We that the data augmentation technique RandomCrop, v is widely used in various diffusion models for train may contribute to incomplete objects. To validate the pact of RandomCrop on this issue, we separately fine SDv2.1 on 10,000 images selected from the aesthetic set of the LAION-5B dataset, using the original image their RandomCrop-augmented versions. + +As shown in Fig. 2, RandomCrop significantly incr the probability of object incompleteness in images g ated by the fine-tuned model. Moreover, as the tra epochs increase, the incompleteness rate exhibits a n tonically increasing trend and stabilizes around epoch contrast, the incompleteness rate of the fine-tuned n with original images monotonically decreases with more fine-tuning epochs. To demonstrate that this tendency toward incompleteness or completeness is not caused by the content of the images that we select, we divide the objects in the generated images into two categories based on whether they appeared in the fine-tuning dataset and calculate the probability of incompleteness for each category. As shown in the Fig. 2, the trends and values of the dashed line (representing unseen categories) and the solid line (representing seen categories) are largely consistent. This indicates RandomCrop is a primary cause of the incompleteness issue. + +# 4. Penalizing Boundary Activation + +According to the analysis in Sec. 3, the issue of object incompleteness in images generated by diffusion models stems from the use of RandomCrop. However, RandomCrop plays a crucial role in improving the model's generalization ability and enhancing the diversity of its generated images, making it indispensable. Furthermore, existing pre-trained diffusion models, such as Stable Diffusion 2.1, require substantial computational resources, making it impractical to fine-tune solely to address this issue. + +To address the incompleteness issue, we propose a training-free method that implicitly guides the subject toward the central region by reducing the probability of generating objects near the image edges. And our method can be applied to all existing diffusion models with minimal modifications and negligible additional computational cost. + +The overview of the method is shown in Fig. 3. Our method leverages cross-attention maps to identify corresponding self-attention maps. These attention maps are integrated to construct the dispelling constraint to optimize the diffusion latent during the early denoising stage, effectively driving objects away from boundaries. Sec. 4.1 introduces our proposed unified dispelling constraint and Sec. 4.2 details the optimization strategy. + +![](images/f76ce365b8c388c241d5877f427750ce27051d8e63f93842de479f6f50aedf10.jpg) +Figure 3. An overview of our method with cross-attention constraint and self-attention constraint. The cross-attention maps, which encode semantic information, are initially extracted and subsequently processed using a clustering algorithm to identify the corresponding self-attention maps that represent spatial information. These two are then integrated via the dispelling constraint during the early denoising stage, effectively driving objects away from boundaries. + +# 4.1. Dispelling Constraint + +Our method aims to reduce the probability of generating objects near the image edges. Therefore, we utilize cross-attention maps to suppress semantic expression at the boundaries while leveraging self-attention to adjust spatial layout. According to our findings, when we focus on only one of these two attention mechanisms, the image modification progresses insufficiently in the desired direction and requires more iterations to optimize, leading to a decline in image quality. When constrained solely by $M^{\text{cross}}$ , the results still struggle to capture the spatial structure accurately and remain incomplete. Conversely, when only $M^{\text{self}}$ is employed, the generated images tend to lack fine-grained details and exhibit deficiencies in semantic consistency. So we combine both attention maps to drive objects away from the boundaries. And our approach facilitates efficient control of object completeness during the critical initial steps, which are pivotal for shaping the coarse structure [51]. + +Extracting Cross-Attention Maps. Cross-attention maps are used to model the interactions between the prompt and the image. So we first extract the cross-attention maps $M^{\mathrm{cross}}$ corresponding to the objects $X$ in the prompt, which represents the semantic imprint of $X$ within the image. In other words, it reflects the intensity of the location in the $M^{\mathrm{cross}}$ associated with the object $X$ . + +Searching Self-Attention Maps. Although the attention $M^{\text{cross}}$ is effective in capturing the object contours, it focuses more on the semantic information of the image rather than spatial information. Therefore, to better ensure the + +Algorithm 1: Pseudocode of our method +Input: An object category $X$ and corresponding text prompt $\mathcal{P}$ , a timestep $t$ , time thresholds $T_{1}$ , hyperparameter $\alpha_{t}$ , $K$ , and a pre-trained Stable Diffusion model $SD$ . Output: Latent representation $z_{t-1}$ for the next timestep +1. $M^{cross}$ , $M^{self} \gets SD(z_{t}, \mathcal{P}, t)$ ; +2. $x \gets \text{get_index}(X, \mathcal{P})$ ; +3. $\mathcal{L}^{cross} \gets M_{x}^{cross}$ ; +4. $(p_{1}, p_{2}, \ldots, p_{K}) \gets \text{topk}(M_{x}^{cross}, K)$ ; +5. $M_{avg}^{self} \gets \frac{1}{K} \sum_{k=1}^{K} M_{pk}^{self}$ ; +6. $\mathcal{L}^{self} \gets M_{avg}^{self}$ ; +7. if $t > T_{1}$ then +8. $\mathcal{L}^{all} \gets \mathcal{L}^{cross} + \mathcal{L}^{self}$ ; +9. end +10. $z_{t}' \gets z_{t} - \alpha_{t} \cdot \nabla_{z_{t}} \mathcal{L}^{all}$ ; +11. $z_{t-1}, -, - \gets SD(z_{t}', \mathcal{P}, t)$ ; +12. return $z_{t-1}$ ; + +completeness of objects in the image, we introduce the self-attention maps $M^{\mathrm{self}}$ that encode spatial reference information of the image. When capturing self-attention maps, we apply Gaussian smoothing to $M^{\mathrm{cross}}$ to avoid noise caused by extremum Point, making the variation of local values in object $X$ relatively uniform. Subsequently, we use a clustering algorithm to identify $K$ key points to guide self-attention, ensuring that the selected points are well distributed. The $K$ key points are selected as the top $K$ (indexed by $p_1, p_2, \ldots, p_K$ ) cluster centers after clustering. Afterward, we find the corresponding self-attention maps $M^{\mathrm{self}}$ for these points $M_{p_k}^{\mathrm{self}}$ and compute their average to obtain the final self-attention map. + +Dispelling Loss. The core of our constraint is to implicitly guide the subject toward the central region by reducing the probability of generating objects near the image edges. Specifically, we design a loss function on the attention maps, where the activation values of a randomly selected internal region $A_{inter}$ are subtracted from those of the surrounding region $A_{sur}$ . $\mathcal{L}$ is computed as follows: + +$$ +\mathcal {L} = \alpha \cdot A _ {\text {s u r}} - \beta \cdot A _ {\text {i n t e r}}, \tag {1} +$$ + +where $\alpha$ and $\beta$ are hyperparameters. In summary, our method integrates both types of guidance. A detailed visual comparison and analysis are provided in the Sec. 5.6. + +# 4.2. Latent Representation Optimization + +We have computed two distinct losses, $\mathcal{L}^{\mathrm{cross}}$ and $\mathcal{L}^{\mathrm{self}}$ through Eq. (1), based on the dispelling constraints. Since we aim to improve the completeness of objects, we optimize the latent representation $z_{t}$ through gradient backpropagation + +tion to minimize both losses: + +$$ +z _ {t} ^ {\prime} = z _ {t} - \alpha_ {t} \cdot \nabla_ {z _ {t}} \left(\mathcal {L} ^ {\text {c r o s s}} + \mathcal {L} ^ {\text {s e l f}}\right), \tag {2} +$$ + +where $\nabla_{z_t}$ denotes the magnitude of the gradient updates, which gradually decreases over time. + +Specifically, we set an early timestep $T_{1}$ ( $T > T_{1} > 0$ ) ( $T_{1} = 45$ when $T = 50$ ) and apply the unified dispelling constraint for timesteps $t$ ( $T \geq t > T_{1}$ ). All module parameters are fixed, and we adapt the diffusion latent only during inference time. + +The pseudocode of our method is shown in Algorithm 1. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. For this study, we construct two prompt datasets. One dataset consists of 1,200 prompts from various categories, carefully selected to represent medium to small-sized physical objects. These objects were sourced from the "lists of lists" on Wikipedia and include categories such as animals, stationery, household items, furniture, vehicles, clothing, and fruits and vegetables. The other dataset consists of 30,000 prompts randomly selected from COCO Caption [7], Flickr30k [62] and Drawbench [41], and excludes prompts containing more than five objects. + +Implementation details. In our experiment, unless otherwise specified, the reported results are obtained by applying our method to SDv2.1 and SDv1.5. During the forward process, we perform a total of 50 diffusion steps, but our method is applied only to the first 5 steps. For the parameters, we set $\alpha = 1.2$ , $\alpha = 0.4$ We extract attention maps using $16 \times 16$ attention units, as previous work [14] has shown that this configuration captures the most semantic information. To select activation values from the cross-attention maps, we set $K = 10$ , which typically ensures that the object's spatial information is fully captured. Regarding the matrices $W^{\text{cross}}$ and $W^{\text{self}}$ , which match the size of the extracted attention maps, we modify specific areas. + +# 5.2. Evaluation Metrics + +Object Incompleteness Rate. We have human evaluation and large multimodal models (LMM) evaluation to determine whether one image is complete or not. We calculate the proportion of generated images in which the object is identified as incomplete through human evaluation, referred to as the Human-Evaluated Object Incompleteness Rate (HOIR). Similar to HOIR, LMM-Evaluated Object Incompleteness Rate (LOIR) leverages LMMs to assess the incompleteness rate on a large scale, primarily using GPT-4 [1] and LLaVA-v1.5-13B [22] to replace human. The images that are inputted into the LMM are processed with SAM [19] to remove background pixels, improving the reliability of the LOIR. + +
MethodLLM-basedHOIR ↓LOIR ↓Time Cost (s) ↓CLIP-IQA ↑PickScore ↑Hpsv2 ↑ImageReward ↑
Stable Diffusion [37]×45.7 %32.0 %5.510.71420.0325.200.221
GLIGEN [21]×34.2 %27.9 %8.740.67220.5924.730.177
Layout Guidance [6]×42.1 %35.7 %24.020.65422.8124.18-0.222
Boxdiff [57]×39.1 %29.8 %7.180.67420.2123.14-0.134
LayoutLLM [32]✓32.7 %28.6 %10.440.59422.4624.980.109
RPG [60]✓35.4 %30.5 %8.540.65322.5725.150.240
LayoutGPT [10]✓30.3 %31.5 %14.360.63121.9424.830.175
SLD [54]✓27.1 %23.1 %9.540.69423.0725.170.253
Ours×17.3 %11.7 %5.750.70323.4125.660.327
+ +Table 3. Quantitative comparison between the layout-based methods and our method across different metrics, where H (L)OIR is the abbreviation for Human (LMM)-Evaluated object incompleteness rate. All methods are conducted using Stable Diffusion version 2.1. In the Time Cost metric, the overhead induced by the Large Language Model (LLM) is excluded. + +
A backpackA carA bathtub
Stable DiffusionGLIGENLayout Guidance
RPG
Ours
+ +Figure 4. Visualization comparison between the layout-based methods and our method. For methods that require additional layout information, the bounding box positions are marked on the result images. Our method does not require any additional input. + +LMM-Evaluated Completeness Preference Rate (LCPR) The LCPR metric is derived through a systematic comparison of two images assessed by the LMM: one synthesized using our method and another generated through the baseline approach. We concatenate them and prompt the LMM to determine which appears more complete. + +Time Cost. To assess the computational cost of different methods, we use each model to generate 100 images and calculate the average generation time per image. + +Evaluation with Human Preferences. PickScore [20], HPSv2 [55] and ImageReward [58] all serve as evaluation metrics designed to align generated images with human + +preferences. They assess image quality based on perceptual realism, aesthetic appeal, and alignment with text. + +CLIP-IQA [49] quantifies perceptual fidelity through CLIP-encoded feature analysis, evaluating synthesized images across critical dimensions including realism, clarity, and structural coherence. + +# 5.3.Quantitative Comparison + +In this section, we present a quantitative comparison between our proposed method and several layout-based text-to-image generation methods, including GLIGEN [21], Layout Guidance [6], Boxdiff [57] and four methods [10, + +![](images/f4799ad12e10c7ecd1a838d95de2f5609f0af7addbf095a8be6a2cdc46bf8cd1.jpg) +Figure 5. Visualization of our ablation study. + +# 32, 54, 60] incorporating LLM. + +Object completeness. As shown in Tab. 3, our method achieves best overall performance, with the lowest HOIR and LOIR of $17.3\%$ and $11.7\%$ , significantly lower than the baseline Stable Diffusion's $45.57\%$ and $32.0\%$ , demonstrating its effectiveness in improving object completeness. Compared to other layout-based methods without LLM, such as GLIGEN [21] and Layout Guidance [6], the best HOIR still reaches as high as $34.2\%$ , with the corresponding LOIR at $27.9\%$ . Among LLM-based methods, approaches such as SLG [54] and RPG [60] achieve the best results of only $27.1\%$ and $23.1\%$ respectively. As shown in Tab. 4, different LMMs consistently assess our method's results as more complete, achieving over $81\%$ on SDv1.5 and SDv2. Since SDXL produces relatively more complete results, LMMs still favor our method in $71\%$ and $68\%$ of cases. As a result, our method still outperforms them in HOIR, LOIR and LCPR. + +Time cost. Our method exhibits a slight increase compared to Stable Diffusion (5.75s vs. 5.51s), but it is still more efficient than other layout-based methods such as Layout Guidance [6] (24.02s) and RPG [60] (8.54s). This demonstrates that our method significantly enhances image completeness, while the additional computational overhead is negligible. + +Image quality and human preference, measured by CLIP-IQA [49], our method achieves a score of 0.703, which is the closest to Stable Diffusion's score of 0.714, suggesting that the improvements in object completeness do not severely degrade image quality. In layout generation, conflicts between object placement and the initial layout during denoising may lead to the generation of physically implausible objects, such as the floating backpack in Fig. 4, resulting in degraded image quality. + +When assessing image quality with human preference, our method achieves a significant lead — PickScore [20] (23.41 vs. the second-best 23.07), HPSv2 [55] (25.66 vs. 25.17), and ImageReward [58] (0.327 vs. 0.253). These re + +
ModelHOIR ↓LCPR (GPT4) ↑LCPR (LLaVA) ↑
SD1.543.7 %--
SD1.5 + Ours18.7 %81 %88 %
SD245.5 %--
SD2 + Ours17.3 %85 %81 %
SDXL18.3 %--
SDXL + Ours7.1 %71 %68 %
+ +Table 4. Comparison of incompleteness rates across different models with our method applied. In this experiment, we tested 1,200 prompts. 360 prompts contain descriptions of 2 to 5 objects, while the remaining 840 include only a single object. The higher the LCPR, the more broadly and effectively our method enhances image completeness. + +sults suggest that human preference favors complete object representations, demonstrating our method's effectiveness. + +# 5.4. Visualization Comparison + +We present a visualization comparison between our method with the layout-based methods in Fig. 4. + +Object completeness. Our results clearly show complete details of the object as described in the prompt, such as details like the straps of a backpack or the rear end of a car. As shown in Fig. 4, for the compared layout-to-image methods, objects in the generated images often exceed the given box boundaries (such as the car in the fifth column of GLIGEN, in the fourth column of Layout Guidance, etc.). The analysis in Sec. 5.3 and the complete objects shown in Fig. 4 demonstrate the feasibility of our method. + +Image realism and quality. Our method yields peak performance in image realism and quality due to the preservation of fine, complete details and the natural placement of objects in appropriate positions. As shown in Fig. 4, for the comparison methods, generated objects often appear unrealistic despite being complete, such as the floating backpack in the second row. This aligns with CLIP-IQA results and human preference. Other issues include distorted objects, anomalous textures (e.g., the third row's first backpack), and inconsistent regional styles (e.g., the third row's second backpack with mismatched upper and lower halves). + +In summary, while layout-guidance can address the problem of object incompleteness from another perspective, some of its results come at the cost of image realism and quality. Our method seldom produces results where the objects are in extreme discord with the background. + +# 5.5. Comparison Analysis of SDXL + +SDXL addresses incompleteness issue by incorporating the coordinates of the cropped operation during training. In contrast, our method can be summarized in the following three aspects. 1) Orthogonal approach. Our approach is orthogonal to the training method proposed by SDXL + +
MethodHOIR ↓LOIR ↓CLIP-IQA ↑
Ours w/o Cross Constraint38.7 %24.5%0.643
Ours w/o Self Constraint34.7 %26.9%0.681
Ours17.3 %11.7%0.700
+ +Table 5. Ablation study on whether to use the cross-attention constraint and self-attention constraint of our method. + +![](images/576be4bbf17e77d1f59b7fe075ab816271b1f86a244461de6eeb45c54eb24baf.jpg) +SDXL + +![](images/e9025f07f1ff8f70c76ea8d11509f4b18c7ea51a6e3316fd7997ca855f0876e7.jpg) +Ours + +and can be easily integrated into SDXL. In fact, training or fine-tuning is prohibitively expensive, whereas our approach serves as an effective remedy for widely deployed pretrained models. 2) Further progress. As shown in Tab. 4, SDXL exhibits the HOIR of $18.0\%$ . However, after incorporating our method, the HOIR is reduced to $7.1\%$ , demonstrating the effectiveness of our approach in further addressing the incompleteness issue. 3) Avoiding minor shortcomings in SDXL. The method proposed by SDXL addresses the incompleteness issue by incorporating the top-left crop coordinates during training. This seems to cause the model to forcibly center objects. For a single object, it is guided to an appropriate position, but for multiple objects, it rigidly adheres to the placement of a single object's coordinates. As shown in the left two columns of Fig. 6, the guitar and player, as well as the dog and ball, become entangled. In contrast, our method pushes objects away from the boundaries, ensuring consistent effectiveness for both single and multiple objects. + +# 5.6. Ablation Study + +Impact of the cross-attention constraint. We conduct experiments under the same parameter settings without the cross-attention constraint. As shown in the first row of Tab. 5, with the absence of $\mathcal{L}^{\mathrm{cross}}$ , the rate of incomplete results increased by $21.4\%$ . The results in the first row of Fig. 5 show that without cross-attention constraint, the objects still appear incomplete in the generated images. Such as the car in results lost its front part. It proves that relying solely on self-attention guidance is inadequate for accurately associating the object's generated position with + +![](images/5ff03cab5c9035c7b632bf40da85e30fed3f9b94c0d145ad1ef3c3349b52d526.jpg) +Figure 6. Visualization of SDXL generation results. SDXL sometimes enforces object centering. +Figure 7. Ablation study on the variation of attention maps across time steps. + +its semantic expressions. This conclusion is consistent with the greater decline in CLIP-IQA metrics in Tab. 5. + +Impact of the self-attention constraint. When using only cross-attention guidance, as shown in Tab. 5, the incompleteness rate increases by $17.4\%$ . In the second row of Fig. 5, objects like the bathtub and hat persist at image boundaries, indicating self-attention's critical role in position refinement. + +These findings validate that both cross-attention and self-attention constraints complement each other, with self-attention improving the localization and structure of objects, while cross-attention focuses on enhancing object completeness and detail. As evidenced by the attention map changes in Fig. 7, the combined guidance of both can efficiently correct the tendency for incomplete generation. + +# 6. Conclusion + +In this study, we identified a significant issue in diffusion models: the incomplete display of objects in generated images. Through our in-depth analysis, we found that using RandomCrop during training is a major contributor to this issue. To address this, we proposed a training-free method that can be easily applied to pre-trained models like Stable Diffusion. Our method enhances object completeness and improves the overall quality of generated images with minimal computational cost. Extensive experiments demonstrated the effectiveness of our method, showing significant improvements in object completeness and image realism. This work not only provides a practical solution for improving the performance of diffusion models but also contributes to the development of more reliable and accurate text-to-image generation techniques for real-world applications. + +# Acknowledgements + +This work was supported in part by the National Natural Science Foundation of China under grant 62471344, in part by the Key Research and Development Program of Yunnan Province under Grant No. 202403AA080002, and in part by the National Key Research and Development Program of China under grant 2023YFC2705700. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. 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Existing methods focus on the integration of diverse generative information into controlling inputs, utilizing frameworks such as GLIGEN or ControlNet, to produce commendable outcomes in controllable generation. However, such approaches intrinsically restrict generation performance to the learning capacities of predefined network architectures. In this paper, we explore the innovative integration of controlling information and introduce PerLDiff (Perspective-Layout Diffusion Models), a novel method for effective street view image generation that fully leverages perspective 3D geometric information. Our PerLDiff employs 3D geometric priors to guide the generation of street view images with precise object-level control within the network learning process, resulting in a more robust and controllable output. Moreover, it demonstrates superior controllability compared to alternative layout control methods. Empirical results justify that our PerLDiff markedly enhances the precision of controllable generation on the NuScenes and KITTI datasets. + +# 1. Introduction + +The advancement of secure autonomous driving systems is fundamentally dependent on the accurate perception of the vehicle's environment. Recently, perception utilizing Bird's Eye View (BEV) has seen rapid progress, markedly pushing forward areas such as 3D object detection [13, 15] and BEV segmentation [37]. Nonetheless, these systems necessitate extensive datasets with high-quality 3D annotations, + +![](images/87e72f4408d8c9549322cbd2fbc401a70917ac873d3d594b03b407d2b32ec8a5.jpg) + +![](images/e9bd967de39ec696f42a880ad4290414547a1aa718865497bc115400384da9dd.jpg) +MagicDrive + +![](images/0cb69e475ac6414a6fd2a9687696b8d271209657f51105e2ba03f35697b2f909.jpg) +(a) Object Controllability (rotate $+90^{\circ}$ ) +BEVControl* + +![](images/71b3876f7562f2e352d1e644c82e50f91c554c2a097d3b49fc1f636cb219b08d.jpg) +PerLDiff (Ours) + +![](images/04f6dc872bbe18bda8489e941040c74c4c8ca0cc832647eb88ec29b6b7b833b1.jpg) +(b) Scene Controllability + +![](images/5319157c2c36a4a6e9e091b3fea5f231677389f26c4c34b525bcd636c64b330b.jpg) +MagicDrive + +![](images/1098ddc01d313c8a517a9752f5488931f5fdd8ff8572ccf42c6d3960a265c567.jpg) +BEVControl* +Figure 1. PerLDiff enhances controllability over BEVControl* and MagicDrive using geometric priors. Top: Demonstrates object controllability by adjusting the 3D annotation yaw by 90 degrees. Bottom: Shows scene controllability through the alignment of the street map with the generated image. Regions highlighted by rectangles indicate areas where the generated images fail to achieve control and alignment with ground truth conditions. + +![](images/57fc9541b4fa3c3fa29e29bfa7c8b92adc54023da01838aa34e379eeb0db3d1c.jpg) +PerLDiff (Ours) + +the acquisition of which typically involves two consecutive steps: data scene collection and subsequent labeling. Each of these steps incurs significant expenses and presents considerable challenges in terms of data acquisition. + +To mitigate issue of data scarcity, the adoption of generative technologies [5, 9, 29] has proven practical for reversing the order of data annotation. The paradigm of this approach is to use the collected annotation as controlling information to generate the corresponding lifelike images depicting urban street scenes. By implementing this strategy, it is possible to dramatically lower the costs associ- + +ated with data annotation while also facilitating the generation of extensive long-tail datasets, subsequently leading to improvements in the perception model's performance. Pioneering research, exemplified by BEVGen [27], harnesses the capabilities of autoregressive transformers [5, 29] to render detailed visualizations of street scenes. Additionally, subsequent studies such as BEVControl [34] and MagicDrive [6] employ diffusion-based techniques, including GLIGEN [12] and ControlNet [35], to integrate controlling information through a basic cross-attention mechanism. However, these methods simply extract integrated conditional features from controlling information to adjust the generation process and are limited in making full use of detailed geometric layout information for accurate attention map manipulation. While these techniques make strides towards meeting the requirements toward generating data from 3D annotations, Fig. 1 demonstrates that there remains significant potential for improvement in scene and object controllability. + +To this end, in this paper, we introduce the perspectivelayout diffusion models (PerLDiff), a novel method specifically designed to enable precise control over street view image generation at the object level. In addition to extracting integrated conditional features from controlling condition information, i.e. 3D annotations, our PerLDiff explicitly renders perspective layout masking maps as geometric priors. Subsequently, a PerL-based controlling module (PerLCM) is proposed to leverage the geometric priors, i.e. perspective layout masking maps. Within PerL-CM, an innovative PerL-based cross-attention mechanism is utilized to accurately guide the generation of each object with their corresponding condition information. We integrate PerL-CM into the pre-trained Stable Diffusion model [22] and fine-tune it on our training dataset. Consequently, our PerLDiff incorporates the formidable generative capabilities of Stable Diffusion with the finely detailed geometric priors of perspective layouts, effectively harnessing their respective strengths for precise object-level image synthesis. Overall, our PerLDiff is capable of generating precise, controllable street view images while also maintaining high fidelity (see Section 3 for details). + +The main contributions of this paper are summarized as following three-folds: + +- We present PerLDiff, a newly developed framework crafted to synthesize street view images from user-defined 3D annotations. Our PerLDiff carefully orchestrates the image generation process at the object level by leveraging perspective layout masks as geometric priors. +- We propose a PerL-based cross-attention mechanism that utilizes perspective layout masking maps from 3D annotations to enhance the underlying cross-attention mechanism within PerL-CM. This method enables precise control over the street view image generation process by in + +tegrating road geometry and object-specific information derived from 3D annotations. + +- Our PerLDiff method attains state-of-the-art performance on the NuScenes [1] and KITTI [7] dataset compared to existing methods, markedly enhancing detection and segmentation outcomes for synthetic street view images. Furthermore, it holds the potential to function as a robust traffic simulator in the future. + +# 2. Related Work + +Diffusion-based Generative Models in Image Synthesis. Initially developed as a method for modeling data distributions through a sequence of Markov chain diffusion steps [24-26], diffusion models have undergone rapid advancement. Ho et al. [9] introduced denoising diffusion probabilistic models (DDPMs), which have established new benchmarks in the quality of image synthesis. Following efforts have aimed to enhance the efficiency and output diversity of these models by investigating various conditioning strategies [2, 4], architectural adjustments, and training methodologies to refine the image synthesis process [10]. Nichol and Dhariwal [4] proved that diffusion models can be text-conditioned to produce coherent images that are contextually appropriate. Furthermore, advances such as multimodal-conditioned diffusion models have effectively utilized layout images [12, 20, 22, 35], semantic segmentation maps [12, 35], object sketches [12, 17, 30, 35], and depth maps [12, 17, 35] to inform the generative process. These methods enable more targeted manipulation of the imagery, thus yielding complex scenes characterized by enhanced structural integrity and contextual pertinence. + +Data Generation for Autonomous Driving. BEVGen [27] represents the pioneering endeavor to harness an autoregressive Transformer [5, 29] for synthesizing multi-view images pertinent to autonomous driving. Building upon this, BEVControl [34] introduces a novel method that incorporates a diffusion model [9] for street view image generation, and integrates cross-view attention mechanisms to maintain spatial coherence across neighboring camera views. Subsequently, MagicDrive [6] propels the field forward by refining the method for controlling input conditions, drawing insights from ControlNet [35]. DrivingDiffusion [11] further augments the framework by introducing a consistency loss designed to achieve the perceptual uniformity requisite for high precision in the generation of video from autonomous driving. Panacea [32] broadens the capabilities of the model by tackling the challenge of ensuring temporal consistency in video. In contrast to the above approaches, which primarily utilize controlling input conditions to steer the image generation process, our PerLDiff exploits detailed geometric layout information from the input to directly guide object generation with higher precision. + +Geometric Constraints in Image Generation. Incorpo + +![](images/4ba8bdd34151d67d407ecaa8689385002004c669b163fed02ba8e20e1bd4c0c0.jpg) +Figure 2. Overview of PerLDiff framework for multi-view street image generation (multi-view dimension omitted for simplicity). PerLDiff utilizes perspective layout masking maps derived from 3D annotations to integrate scene information and object bounding boxes. PerLCM is responsible for integrating control information through employing PerL-based cross-attention (Scene & Object) mechanism, using PerL masking map (road & box) as geometric priors to guide object-level image generation with high precision. View cross-attention ensures consistency across multiple views, while Text cross-attention integrates textual scene descriptions to facilitate further adjustments. + +rating geometric priors into image synthesis has been explored to a lesser extent. Work on 3D-aware image generation [18, 19] suggests the feasibility of integrating geometric information into generative processes to improve spatial coherence. Nevertheless, these methods often rely on complex 3D representations and may not be directly applied to diffusion model frameworks. Recently, BoxDiff [33] reveals a spatial correspondence between the attention map produced by the diffusion model and the corresponding generated image. During the testing phase, the geometric configuration of the attention map's response values is adjusted to yield a more precise image generation. ZestGuide [3] introduces a loss function that enforces a geometric projection onto the attention map, further refining the shape of the attention map's response values to closely approximate the geometric projection of the control information during the inference stage. However, utilizing text prompts to facilitate the generation of complex urban environment layouts poses inherent challenges, owing to the need for crafting intricate prompts to accurately depict urban environments. Furthermore, modifying the cross-attention map to impose strict constraints during the denoising phase of inference can disrupt the intrinsic relationships, leading to a suboptimal approach to synthesizing controllable images. In contrast, PerLDiff incorporates geometric prerequisites as training priors to guide the generation of street view images, offering a more effective solution. + +# 3. Controllable Street View Generation Based on Perspective Layout + +In this paper, we introduce PerLDiff, depicted in the Fig. 2, which is designed to enable controllable multi-view street scene image generation using 3D annotations. Specifically, our PerLDiff leverages perspective projection information from 3D annotations as controlling condition within the training regimen and utilizes perspective layout masks as geometric priors, enabling accurate guidance in object generation. In the following sections, we delineate the process of encoding the controlling condition information from the 3D annotations in the Section 3.1. Additionally, we explain how incorporating the perspective layout knowledge to ensure scene and object controllability in street view image generation in the Section 3.2. + +# 3.1. Controlling Conditions Encoding + +Given 3D annotations of a street scene, our goal is to generate multi-view street images. To be more specific, for controllable street view image generation, we extract not only scene information (i.e., textual scene descriptions $\mathbf{S}_d$ and street maps $\mathbf{M}$ revealing features such as road markings and obstacles) but also object information (i.e., bounding box parameters $\mathbf{P}$ and the associated object category $\mathbf{Y}$ ) from 3D annotations as controlling conditions. These controlling conditions encompass rich semantic and geometric information, so establishing a robust encoding method + +to utilize this information is essential for generating street view images. Hereafter, we present our controlling condition encoding approach. For simplicity, we omit the details of multi-view perspectives. + +PerL Scene Information encompasses perspective scene images and supplemental data specific for the whole scene. Typically, the selected scene for annotation is coupled with a street map of the driving environment, which visually differentiates between the road and other background elements using distinct colors. In addition, a generic textual description of the scene is customizable to align with particular scenarios. We employ ConvNext [14] and the CLIP text encoder [21] to encode the perspective road map, denoted as $\mathbf{S}_m$ , derived from the projection of the street map and the textual scene description $\mathbf{S}_d$ , respectively. This approach results in the generation of encoded scene features $\mathbf{H}_m \in \mathbb{R}^{1 \times C}$ for the road map and $\mathbf{H}_d \in \mathbb{R}^{1 \times C}$ for the textual scene description: + +$$ +\mathbf {H} _ {m} = \operatorname {C o n v N e x t} (\mathbf {S} _ {m}), \quad \mathbf {H} _ {d} = \varphi (\mathbf {S} _ {d}). \tag {1} +$$ + +PerL Object Information encapsulates perspective geometric data alongside object category information, which stems from the projections of annotated 3D boxes. Through projecting 3D annotations onto their corresponding perspective images, we ascertain eight 2D corner points for each bounding box within a single image, denoted as $\mathbf{P}_g\in$ $\mathbb{R}^{M\times 2\times 8}$ , where $M$ represents the maximum number of bounding boxes and eight corresponds to the number of corners per bounding box. In conjunction with the object's categorical text $\mathbf{P}_c = \{\mathbf{P}_{c_i}\}_{i = 1}^M$ , we derive the encoded box geometric features $\mathbf{H}_g\in \mathbb{R}^{M\times C}$ and the box categorical features $\mathbf{H}_c\in \mathbb{R}^{M\times C}$ , which are illustrated as follows: + +$$ +\mathbf {H} _ {g} = \mathcal {F} \left(\mathbf {P} _ {g}\right), \quad \mathbf {H} _ {c} = \varphi \left(\mathbf {P} _ {c}\right), \tag {2} +$$ + +where $\mathcal{F}(\cdot)$ is the Fourier embedding function [16], $\varphi (\cdot)$ represents the pre-trained text embedding encoder of CLIP [21] and $C$ representing the dimension of features. Furthermore, we concatenate the encoded geometric features $\mathbf{H}_g$ and categorical features $\mathbf{H}_c$ and subsequently pass the concatenated vector through a Multilayer Perceptron (MLP) [28] $\mathbf{F}$ , to achieve feature fusion $\mathbf{H}_b\in \mathbb{R}^{M\times C}$ . The resulting fused box feature representation is given by: + +$$ +\mathbf {H} _ {b} = \mathbf {F} \left(\left[ \mathbf {H} _ {g}, \mathbf {H} _ {c} \right]\right). \tag {3} +$$ + +We subsequently input the encoded conditions into the denoising diffusion model to guide the generation process. This is achieved utilizing PerL-based cross-attention that incorporates PerL masking maps, as detailed below. + +# 3.2. Object Controllability via PerL-based Controlling Module + +PerL-based Controlling Module (PerL-CM) is responsible for integrating controlling condition information, which encompasses both the PerL scene and object information, + +into the latent feature maps of noisy street view images. This integration is primarily achieved via the scene and object PerL-based cross-attention mechanism. Initially, this mechanism assigns initial values to the attention maps, under the guidance of road and box PerL masking maps. Throughout the training of the network, these values are optimized to ensure that the response of the attention map accurately corresponds to the regions where the objects are located. Subsequently, the information from both the road map and the bounding box are sequentially integrated into the noise street view image. To more effectively integrate PerL scene and object information, a gating operation similar to GLIGEN [12] is used, which dynamically adjusts the contribution of condition information according to the adaptive process. To ensure multi-view consistency, View Cross-attention leverages information from the immediate left and right views for uniformity across various perspectives. Additionally, Text Cross-attention manipulates the weather and lighting conditions of street scenes using textual scene description. The details of the PerL-CM process are delineated in the Appendix. + +PerL Masking Map (road & box) is comprised of PerL road masking map $\mathcal{M}_s\in \mathbb{R}^{HW\times 1}$ and PerL box masking map $\mathcal{M}_b\in \mathbb{R}^{HW\times M}$ , where $H$ and $W$ represent the height and width dimensions of the image, respectively. These masking maps are articulated as follows: + +$$ +\mathcal {M} _ {s} = \Upsilon (\mathbf {S} _ {m}), \quad \mathcal {M} _ {b} = \Phi (\mathbf {P} _ {g}), \tag {4} +$$ + +where $\Upsilon (\cdot)$ generates the masking map for the non-empty regions of the projected road maps. Meanwhile, $\Phi (\cdot)$ produces the masking map corresponding to the inner region of each projected 3D bounding box for every perspective image, enabling precise control at the object level. + +PerL-based Cross-attention (Scene & Object) leverages the prior masking maps to enhance the learning of cross-attention between the input controlling conditions and the noisy street view images. As depicted in Fig. 3, the cross-attention map exhibits perceptual equivalence with the generated street view image. However, this correspondence is imprecise and lacks the necessary alignment during the training stage. To this end, our approach utilizes a PerL-based cross-attention mechanism that incorporates geometric knowledge derived from both the scene context and the bounding box into the computation of the cross-attention map. In PerLDiff, the road map and object bounding box data are seamlessly merged with the noisy street view images throughout each stage of the denoising process. For the sake of notational simplicity, the linear embeddings and normalization steps typically involved in the attention mechanism have been omitted. + +$$ +\mathcal {A} _ {s} = \operatorname {s o f t m a x} \left(\lambda_ {s} \cdot \mathcal {M} _ {s} + \mathbf {Z H} _ {m} ^ {T} / \sqrt {d}\right), \tag {5} +$$ + +$$ +\mathcal {A} _ {b} = \operatorname {s o f t m a x} \left(\lambda_ {b} \cdot \mathcal {M} _ {b} + \mathbf {Z} _ {\mathbf {s}} \mathbf {H} _ {b} ^ {T} / \sqrt {d}\right), \tag {6} +$$ + +![](images/bf7be2e1a4f3b5377243433f65bb2f0a7d5739b9e19b044fd99342cbfb1e7b66.jpg) +Figure 3. Visualization of cross-attention maps reveals perceptual congruency with the generated image. BEVControl* produces disorganized and vague attention maps, which result in inferior image quality. Conversely, our PerLDiff method fine-tunes the response within the attention maps, resulting in more accurate control information at the object level and improved image quality. Please see more qualitative examples in the Appendix. + +where $\lambda_{s}$ and $\lambda_{b}$ are weight parameters that control the influence of the masking map, $d$ denotes the dimensionality, and $\mathbf{Z},\mathbf{Z}_b,\mathbf{Z}_s\in \mathbb{R}^{HW\times C}$ represent different noisy street view images. Here, $\mathcal{A}_s\in \mathbb{R}^{HW\times 1}$ characterizes the association between the road map and the noisy image, while $\mathcal{A}_b\in \mathbb{R}^{HW\times M}$ clarifies the relationship between the conditions of the object bounding box and the noisy image. For visualization purposes, as shown in Fig. 3, we average $\mathcal{A}_b$ along the second dimension and merge all object attention maps into one representation at step 50 of the DDIM process in the last block of U-Net. The final noisy street view image is synthesized through an attention-based aggregation mechanism enhanced by a residual connection, which can be expressed as: + +$$ +\mathbf {Z} _ {\mathbf {s}} = \gamma_ {s} \cdot \mathcal {A} _ {s} \mathbf {H} _ {m} + \mathbf {Z}, \quad \mathbf {Z} _ {\mathbf {b}} = \gamma_ {b} \cdot \mathcal {A} _ {b} \mathbf {H} _ {b} + \mathbf {Z} _ {\mathbf {s}}, \tag {7} +$$ + +where $\gamma_{s}$ and $\gamma_{b}$ represent learnable parameters modulating the influence of respective conditions. + +View Cross-attention is corroborated by preliminary works such as BEVControl [34], MagicDrive [6], DrivingDiffusion [11], and Panacea [32], plays an instrumental role in facilitating the synthesis of images that maintain visual consistency across varying camera perspectives. For additional information, please see the Appendix. + +Text Cross-attention enhances Stable Diffusion [22] model's ability to modulate street scenes through textual scene description. This capability is crucial for dynamically adapting the rendering of street scenes to accommodate various lighting and weather conditions. By integrating detailed textual scene description, PerLDiff can alter visual elements such as illumination and atmospheric effects, ensuring that the generated images reflect the specified conditions. For qualitative examples, see the Appendix. + +# 3.3. Discussion + +In contrast to previous approaches for autonomous driving such as BEVControl [34], MagicDrive [6], DrivingDiffusion [11], and Panacea [32], which employ a basic cross-attention mechanism to integrate controlling condition in + +formation, our PerLDiff leverages geometric priors via PerL masking map. This approach directs the generation of each object with its respective control information during the training phase, effectively countering the common misalignment between the attention map and condition information that often results in compromised image controllability. For instance, the attention map of BEVControl [34], illustrated in Fig. 3, demonstrates disorganized patterns and lacks precision. Conversely, our PerLDiff markedly enhances the accuracy of generated images and the granularity of condition information at the object level by ensuring meticulous guidance within the attention map. For more qualitative results, please see the Appendix. + +# 4. Experiments + +We assess PerLDiff's ability to control quality across multiple benchmarks, including multi-view 3D object detection [13, 15, 31, 36], BEV segmentation [37] and monocular 3D object detection [36]. Subsequently, we conduct ablation studies to ascertain the contribution of each component within our proposed methodology. + +# 4.1. Datasets + +NuScenes dataset comprises 1,000 urban street scenes, traditionally segmented into 700 for training, 150 for validation, and 150 for testing. Each scene features six high-resolution images $(900 \times 1600)$ , which together provide a complete 360-degree panoramic view of the surroundings. Additionally, NuScenes includes comprehensive road maps of the driving environment, featuring details such as lane markings and obstacles. We extend the class and road type annotations similar to MagicDrive [6] and NuScenes, incorporating ten object classes and eight road types for map rendering. To address the resolution limitations of the U-Net architecture in Stable Diffusion [23], we adopt image resolutions of $256 \times 384$ as in BEVFformer [13], and $256 \times 704$ following BEVFusion (Camera-Only) [15]. + +KITTI dataset contains 3,712 images for training and 3,769 images for validation. KITTI has only one perspective im + +
MethodDetectorFID↓mAP↑NDS↑mAOE↓
OracleBEVFormer-27.0641.890.54
OracleBEVFusion-35.5441.200.56
MagicDrive [6]BEVFusion16.2012.3023.32-
MagicDrive*BEVFusion15.9210.2720.420.78
BEVControl*BEVFusion13.059.9819.610.94
PerLDiff (Ours)BEVFusion13.3615.2424.050.78
BEVGen [27]-25.54---
BEVControl [34]BEVFormer24.8519.6428.680.78
BEVControl*BEVFormer13.0516.4828.080.88
MagicDrive*BEVFormer15.9215.2128.790.81
PerLDiff (Ours)BEVFormer13.3625.1036.240.72
+ +Table 1. Comparison of the controllability on NuScenes validation set. BEVControl*, serving as the baseline, employs standard cross-attention mechanisms contrary to PerL-based cross-attention utilized in PerLDiff. MagicDrive* represents our replication using the official configuration. **Bold** indicates the best result. + +age and does not have road map information. Given the varied image resolutions in KITTI (approximately $375 \times 1242$ ), we pad them to $384 \times 1280$ for generative learning. + +# 4.2. Main Results + +In this subsection, we assess PerLDiff's generative quality through the perception results of several pre-trained methods: BEVFformer [13], BEVFusion (Camera-Only) [15], and StreamPETR [31] for multi-view 3D detection; CVT [37] for BEV segmentation; and MonoFlex [36] for monocular 3D detection trained on the KITTI. Additionally, we leverage synthesized dataset to enhance the performance of various 3D detection models (i.e., BEVFformer and StreamPETR) on the NuScenes test, validating the effectiveness of our PerLDiff. + +# 4.2.1. Controllable Generation on NuScenes + +To evaluate the effectiveness of PerLDiff, we trained the model on the NuScenes train set and subsequently generated a synthetic validation set using the provided road maps and 3D annotations. The controllability of PerLDiff was examined by applying perception models, originally trained on the real train set, to our synthetic validation set. As summarized in Tab. 1, PerLDiff outperforms competing methods across most metrics, as tested with BEVFormer [13] and BEVFusion [15]. In a rigorous comparison, we replicated BEVControl [34] using identical settings, with the exception of our innovative element: the PerL-based cross-attention mechanism. PerLDiff demonstrates notable improvements, with increases of $8.62\%$ , $8.16\%$ , and $0.16\%$ in mean Average Precision (mAP), NuScenes Detection Score (NDS), and mean Average Orientation Error (mAOE), respectively, compared to BEVControl* when using BEVFormer. With BEVFusion, it achieves gains of $5.26\%$ , $4.44\%$ , and $0.16\%$ in these metrics against BEVControl*, confirming its effectiveness at a resolution of $256 \times 384$ . + +
MethodOracleBEVGenBEVControlBEVControl*MagicDrive*PerLDiff (Ours)
Road mIoU↑70.3550.2060.8060.7455.5661.26
Vehicle mIoU↑33.365.8926.8622.4724.8127.13
+ +Table 2. Comparison of the controllability performance on the NuScenes validation set using BEV segmentation metrics in CVT [37]. Bold indicates the best result. + +
MethodKITTINuScenes → KITTI
Easy↑Mod.↑Hard↑FID↓Easy↑Mod.↑Hard↑FID↓
Oracle22.2915.5413.38-22.2915.5413.38-
BEVControl*0.330.290.3939.471.321.511.6432.96
PerLDiff (Ours)11.047.446.0339.0313.129.247.5931.70
+ +Table 3. Controllability comparison on KITTI [7] validation set, showcasing vehicle mAP obtained by MonoFlex [36] using data generated by PerLDiff and the baseline BEVControl*. “NuScenes $\rightarrow$ KITTI” denotes initial training on NuScenes train set followed by fine-tuning on KITTI train set. Bold indicates the best result. + +The superiority of PerLDiff is further affirmed by BEV segmentation metrics [37] presented in Tab. 2. It significantly outperforms BEVControl* with a $0.52\%$ increase in Road mIoU and a $4.66\%$ increase in Vehicle mIoU, validating the efficacy of the PerL-based cross-attention mechanism in enhancing scene controllability. Regarding the Fréchet Inception Distance (FID) [8] metric, our results are comparable to those of BEVControl*. While PerLDiff incorporates prior constraints to ensure accuracy in object detection, this may adversely affect the details in the background of the images. As illustrated in the Appendix, PerLDiff produces background details that do not align with those of real images. + +Compared to the state-of-the-art MagicDrive [6], our method demonstrates superior performance across all metrics, particularly in the FID metric, reflecting an improvement of $2.84\%$ . Additionally, we achieve a $2.94\%$ improvement in mAP and a $0.73\%$ increase in NDS. These results substantiate the strengths of PerLDiff in terms of both generation quality and controllability. + +# 4.2.2. Controllable Generation on KITTI + +The scarcity of training data in the KITTI dataset [7] often limits a generative model's ability to understand the relationship between control information and image synthesis. To address this challenge, we implement two distinct strategies for generating images within the KITTI framework: one strategy involves direct training using the KITTI train set, while the other entails initial training on the NuScenes train set followed by fine-tuning on the KITTI train set. In Tab. 3, we present the results of monocular 3D object detection on the KITTI validation set, utilizing a pretrained MonoFlex [36] detector. As illustrated in Fig. 4, the naive approach results in significant misalignment between the labels and the corresponding generated images, leading to a considerable performance gap: 11.04 vs. 0.33 for one metric and 13.12 vs. 1.32 for another. There are two main + +
TrainingDetectormAP↑NDS↑mATE↓mASE↓mAOE↓
trainBEVFormer28.9742.5272.9028.1556.34
train + Real val32.2045.4469.4327.4052.88
train + Syn. val*29.92 (-2.28%)43.20 (-2.24%)70.76 (+1.33%)27.69 (+0.29%)57.57 (+4.69%)
train + Syn. val (Ours)31.66 (-0.54%)44.91 (-0.53%)70.09 (+0.66%)27.56 (+0.16%)55.05 (+2.17%)
trainStreamPETR47.8456.6655.9125.8147.40
train + Real val50.9258.6854.3625.1245.36
train + Syn. val*47.37 (-3.55%)56.40 (-2.28%)56.99 (+2.63%)25.58 (+0.46%)47.69 (+2.33%)
train + Syn. val (Ours)49.07 (-1.85%)57.92 (-0.76%)55.71 (+1.35%)25.57 (+0.45%)47.08 (+1.72%)
+ +Table 4. Performance comparison for the boosting performance of 3D detection models using synthesized dataset on NuScenes [1] test set using BEVFormer [13] and StreamPETR [31]. The "train + Real val" configuration serves as a benchmark, representing the ideal upper performance limit achievable. "Syn. val*" represents the synthetic validation set generated by BEVControl. The numbers in parentheses indicate the performance disparity relative to the "train + Real val" configuration. Bold indicates the best result. + +![](images/adcddb791ed11c2fdbcf228fff19ebabf1c5fea882097e6b9635dffddb5f15a3.jpg) +Figure 4. Qualitative visualization comparison on KITTI [7] dataset. Yellow markers denote instances where BEVControl* inaccurately generates output compared to PerLDiff. + +reasons for the observed differences. First, the limited size of the KITTI dataset, which contains just 3,712 training images, impedes the learning process of traditional methods that do not utilize PerL masking map. Second, monocular 3D object detection is highly sensitive to accurate depth prediction. Depth is derived from the 2D projected size and the estimated 3D size through perspective projection. Our method produces more precise object sizing, thereby enhancing detection performance. More visual results on KITTI can be found in the Appendix. + +# 4.2.3. Boosting Perception Models Using Synthesized Dataset + +Generative models have become widely acknowledged as effective tools for data augmentation, thereby improving the generalization capabilities of perception models. To evaluate this, we leverage synthesized image dataset to improve the performance of various detection models on NuScenes test set. The gains presented in the second row of Tab. 4 + +confirm that augmenting with data annotated optimally (i.e., using the combined real NuScenes train + Real val set) is beneficial. The performance of BEVFormer [13] and StreamPETR [31] improved significantly after the dataset was augmented with real validation set. The most notable gains for BEVFormer were observed in the mAP and NDS metrics, which increased by $3.23\%$ and $2.92\%$ , respectively. Similarly, for StreamPETR, increases in mAP and NDS were recorded at $3.08\%$ and $2.02\%$ , respectively. + +Furthermore, augmentations using synthetic validation set yielded competitive improvements that almost matched the performance gains observed with real validation set. The gaps in performance metrics, such as mAP, NDS, and mAOE, were minimal, thus solidifying the value of synthetic augmentation compared to the train-only baseline. Specifically, BEVFormer and StreamPETR exhibited only slight gaps in mAP (0.54% and 1.85%), NDS (0.53% and 0.76%) and mAOE (2.17% and 1.72%), respectively. In addition, these discrepancies were even less pronounced compared to BEVControl*, highlighting the effectiveness of the PerL-based cross-attention mechanism. + +# 4.3. Ablation Study + +To determine the effectiveness of the key components within PerLDiff, we perform ablation studies concentrated on key elements: PerL-based cross-attention. Additionally, we provide more qualitative results in the Appendix to further demonstrate the efficacy of PerLDiff compared to the baseline approaches, BEVControl* and MagicDrive. + +# 4.3.1. Effectiveness of PerL-based Cross-attention + +To illustrate the impact of PerL-based cross-attention, we devised a comprehensive comparative experiment, the results of which are presented in Tab. 5. Method (a) employs road map and 3D box as conditions, which are integrated into the model using standard cross-attention [6, 34] with the configuration mirroring that of BEVControl*. "Box Mask" and "Road Mask" denote the process wherein the control information is merged with the model through PerL + +
MethodRoad MaskBox MaskFID↓mAP↑NDS↑mAOE↓Road mIoU↑Vehicle mIoU↑
Oracle-27.0641.890.5470.3533.36
(a)13.0516.4828.080.8860.7422.47
(b)✓13.2016.2728.400.8661.1823.14
(c)✓13.5426.0736.070.7461.2126.27
(d)✓✓13.3625.10 (+8.62%)36.24 (+8.16%)0.72 (-0.16%)61.26 (+0.52%)27.13 (+4.66%)
+ +Table 5. Ablation of the PerL-based cross-attention, reporting 3D object detection improvements using BEVFormer and BEV segmentation enhancements using CVT. Numbers in parentheses indicate performance gains over the baseline. Bold indicates the best result. + +
MethodλsλbFID↓mAP↑NDS↑mAOE↓Road mIoU↑Vehicle mIoU↑
Oracle--27.0641.890.5470.3533.36
(a)1.0 1.012.8722.3034.080.7361.3125.03
(b)3.0 3.014.0324.4135.750.7460.5826.82
(c)5.0 5.013.3625.1036.240.7261.2627.13
(d)10.0 10.014.2424.9835.520.7661.7526.62
+ +based cross-attention. Method (a) $\rightarrow$ (b) signifies the adoption of PerL-based cross-attention for the road map, leading to improvements of $0.44\%$ in Road mIoU and $0.32\%$ in NDS. These gains underscore the augmented controllability achieved by combining the road map with PerL-based cross-attention and its efficacy in aligning generated data with real observations. Additionally, Method (a) $\rightarrow$ (c) results in marked improvements of $9.59\%$ in mAP, $7.99\%$ in NDS, $0.14\%$ in mAOE and $3.80\%$ in Vehicle mIoU, strongly supporting the utility of PerL-based cross-attention in producing accurate data-annotation alignments for objects. To optimally regulate elements of the background and foreground, Method (c), in contrast to baseline Method (a), indicates increases of $8.62\%$ in mAP, $8.16\%$ in NDS, $0.16\%$ in mAOE, $0.52\%$ in Road mIoU and $4.66\%$ in Vehicle mIoU. These results validate the efficiency of PerL-based cross-attention in enhancing image controllability. + +# 4.3.2. Effectiveness of Masking Map Weight Coefficients + +Tab. 6 examines the effects of varying the masking map weight coefficients $\lambda_{s}$ and $\lambda_{b}$ , where higher values indicate a greater integration of PerL knowledge into network learning. The table demonstrates that detection metrics improve with increasing values of $\lambda_{s}$ and $\lambda_{b}$ within a certain range. However, the FID score also increases, underscoring the significant role of PerL knowledge in the controllable learning process. For optimal controllability, we set the default values of $\lambda_{s}$ and $\lambda_{b}$ to 5.0 in the main text. + +Table 6. Ablation of different values of masking map weight coefficients $\lambda_{s}$ and $\lambda_{b}$ in PerL-based cross-attention. We report the 3D object detection results based on BEVFormer and BEV Segmentation results based on CVT. Bold indicates the best result. + +
MethodDetectorParameter (M)FID↓mAP↑NDS↑mAOE↓
CLIP encoderBEVFormer303.9712.7725.4136.260.73
ConvNext encoder27.8213.3625.1036.240.72
CLIP encoderBEVFusion303.9712.7715.8024.450.81
ConvNext encoder27.8213.3615.2424.050.78
+ +Table 7. Ablation study comparing different road map encoders with frozen weights. We present 3D object detection results based on BEVFformer and BEVFusion. Bold indicates the best result. + +# 4.3.3. Effectiveness of Different Road Map Encoders + +In Tab. 7, we present an ablation study comparing different road map encoders, replacing ConvNext [14] with alternatives such as the CLIP image encoder. ConvNext was initially chosen for its ability to effectively extract image features while maintaining a relatively low parameter count (27.82M). Additionally, it has demonstrated strong performance in downstream segmentation tasks, particularly in capturing edge information [14]. As shown in Tab. 7, the results indicate that the choice of feature extraction network has minimal impact on PerLDiff, with only a $\pm 0.02$ NDS difference between the CLIP and ConvNext encoders. Therefore, we adopt ConvNext as the road map encoder and freeze its weights in the main results. + +# 5. Conclusion + +In conclusion, PerLDiff introduces a streamlined framework that adeptly merges geometric constraints with synthetic street view image generation, harnessing diffusion models' power for high-fidelity visuals. The architecture boasts a PerL-based controlling module (PerL-CM), through training, becomes seamlessly integrated with Stable Diffusion. Meanwhile, a cutting-edge PerL-based cross-attention mechanism guarantees meticulous feature guidance at the object level for precise control. Experiments on NuScenes and KITTI datasets confirm PerLDiff's enhanced performance in image synthesis and downstream tasks like 3D object detection and segmentation. Flexible yet precise, PerLDiff's method of PerL-based cross-attention with geometric perspective projections during training finely balances image realism with accurate condition alignment. + +# Acknowledgement + +This work was supported by National Natural Science Foundation of China (No. 62476051, No. 62176047) and Sichuan Natural Science Foundation (No. 2024NS-FTD0041). + +# References + +[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11621-11631, 2020. 2, 7 +[2] Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. 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However, these methods tend to generate inaccurate and unnatural reconstructions in complex and/or heavily degraded scenes, primarily due to their limited perception and understanding capability of the input low-quality image. To address these limitations, we propose, for the first time to our knowledge, to adapt the pre-trained autoregressive multimodal model such as Lumina-mGPT into a robust Real-ISR model, namely PURE, which Perceives and Understands the input low-quality image, then REstores its high-quality counterpart. Specifically, we implement instruction tuning on Lumina-mGPT to perceive degradation levels and inter-token dependencies, understand content via semantic description generation, and ultimately restore the image by generating high-quality image tokens autoregressively with the collected information. In addition, we reveal that the image token entropy reflects the image structure and present a entropy-based Top-k sampling strategy to optimize the local structure of the image during inference. Experimental results demonstrate that PURE preserves image content while generating realistic details, especially in complex scenes with multiple objects, showcasing the potential of autoregressive multimodal generative models for robust Real-ISR. The model and code are available at https://github.com/nonwhy/PURE. + +# 1. Introduction + +Real-world image super-resolution (Real-ISR) is a challenging task in computer vision, aiming to reconstruct high-quality (HQ) images from low-quality (LQ) inputs degraded by complex combinations of factors such as blur, + +noise, downsampling, etc. Traditional discriminative image restoration methods [6, 8, 17, 18, 55] are typically designed for optimizing image fidelity using $L_{1}$ or $L_{2}$ losses, tending to produce over-smoothed results. While generative adversarial network (GAN [10])-based approaches [14, 37] can generate more visually appealing details, they suffer from unstable training and unnatural visual artifacts. + +The recently developed large-scale pre-trained text-to-image (T2I) generation models, such as Stable Diffusion (SD) [1], have enabled more effective modeling of the complex distribution of natural images, and researchers have proposed to leverage the powerful T2I generative priors to achieve more perceptually realistic Real-ISR outcomes. Many SD-based methods [26] adopt a ControlNet [53] architecture, extracting features from the LQ image as control signals to guide the generation of HQ image from random noise. Meanwhile, methods have also been proposed to extract semantic information, such as tags [45], short captions [49] and long descriptions [50], from the LQ image to help the SD model synthesizing more visual details. One-step diffusion-based Real-ISR methods [4, 29, 44] have also been proposed, which directly take the LQ image as input and finetune the SD model using LoRA [11] techniques. + +Despite the significant progress achieved in SD-based Real-ISR, the existing models exhibit certain limitations, particularly in handling complex scenes with multiple objects or severe degradation. First, they may lack global understanding of the image content, leading to the generation of semantically inaccurate details. As shown in Fig. 1a, the state-of-the-art models SeeSR [45] and OSEDiff [44] misidentify buildings as cliffs, leading to incorrect restoration of the scene. Second, existing models lack strong perception of the local structural relationships in natural images, leading to semantically coherent but physically unnatural appearance. As shown in Fig. 1b, SeeSR and OSEDiff erroneously synthesize the lion's tongue with fur. These limitations highlight the need for a new Real-ISR model, which can simultaneously perceive, understand and restore the image with complex contents. + +The recent advances in autoregressive multimodal large + +![](images/2aad89633a13bdf5d5114c2f33e066df83c9993ecca5613bfa8ef9daa2f65387.jpg) +(a) Incorrect content restoration + +![](images/9b2dd36cb44744c66a7829d36731e5ae0cc49c3c4ce1943b8443059a1116affa.jpg) +(b) Physically unnatural restoration +Figure 1. Examples of (a) inaccurate and (b) unnatural restoration of current SD-based Real-ISR methods, such as SeeSR[45] and OSEDiff [44], in complex and heavily degraded scenes. + +language models (MLLMs) [20, 21, 32, 46, 57] may offer a promising solution to the above-mentioned problem. Leveraging the large-capacity network trained on extensive multimodal datasets, these models excel at modeling the joint distribution of texts and images, integrating image understanding and generation within a unified framework, while the autoregressive generation process can model the image local structure relationships, providing a strong prior for local structure perception. Based on these facts, we present a framework, namely PURE, to Perceive, Understand, and REstore the HQ image from its LQ observation by fin-tuning a pre-trained MLLM. Specifically, by taking the LQ image as input, we implement instruction tuning on the Lumina-mGPT [20] to predict image degradation characteristics, semantic descriptions, and consequently the HQ output within a single model. On the one hand, our model can effectively utilize the perceived image degradation and semantic understanding features during the image generation process. On the other hand, the autoregressive generation process explicitly considers the relationships between generated and upcoming image tokens, mitigating physically unnatural artifacts. Furthermore, we propose a entropy-based Top- $k$ sampling strategy, which adaptively chooses the optimal Top- $k$ value based on the entropy during inference, further optimizing the local structure preservation. + +Our contributions are summarized as follows. First, we propose, for the first time to our best knowledge, an autoregressive multimodal learning framework, which integrates global understanding and local perception, for robust Real-ISR. Second, we develop an entropy-based Top- $k$ sampling strategy during inference to better preserve image structures while generating realistic details. Finally, our experimental results demonstrate the potential of PURE for Real-ISR tasks, particularly in complex scenarios. + +# 2. Related Work + +Real-World Image Super-Resolution. Traditional RealISR methods [6, 8, 17, 18, 55] typically adopt discriminative networks trained with pixel-wise $L_{1}$ or $L_{2}$ losses to recover high-frequency details, but often produce oversmoothed results. To improve perceptual quality, GAN-based approaches [14, 37] leverage adversarial losses to synthesize realistic textures, albeit at the cost of unstable training and artifacts. Recent advances focus on exploiting pre-trained text-to-image (T2I) diffusion models, such as SD [1], as generative priors. Some methods employ a ControlNet-based architecture [53] to guide SD generation using LQ image features as conditional signals, while some other methods enhance semantic alignment by extracting text descriptions [49, 50] or tags [45] from LQ inputs. One-step diffusion variants [4, 29, 44] further accelerate inference by directly mapping LQ to HQ images through LoRAfinetuned SD-UNet. Despite improved perceptual quality, these methods struggle with semantic inaccuracies and unnatural local structures in complex scenes due to limited global understanding and local relationship modeling. + +Multimodal Large Language Models. Recent advancements in MLLMs [20, 21, 32, 46, 57] and deep learning[22, 31, 39, 42, 43, 47, 56, 58, 59] have expanded the capabilities of traditional language models to process and generate cross-modal content. Early works, such as LLaVA [21] and BLIP [15], focused on enhancing multimodal understanding by aligning pretrained vision encoders (e.g., CLIP [24]) with LLMs like LLaMA [33], enabling tasks such as visual question answering and image captioning. However, these models primarily emphasized perception, lacking native generative abilities for visual content. To address multimodal generation, approaches like Show-o [46] and Transfusion [57] integrate autoregressive text modeling with diffusion-based image decoders, where the LLM predicts text tokens and relies on external diffusion models to synthesize images. Although effective, this hybrid paradigm introduces dependency on separate generative frameworks, leading to inconsistent outputs and limited end-to-end learning. In contrast, unified understanding and generation is pioneered by multimodal models such as Chameleon [32], Lumina-mGPT [20] and Emu3 [38], which treat images as discrete tokens within an autoregressive framework, enabling seamless multimodal sequence modeling for text and images. In this work, we employ Lumina-mGPT as the MLLM for Real-ISR tasks. + +# 3. Method + +# 3.1. Preliminaries + +Chameleon [32] is a representative MLLM, which uses next-token prediction in a discrete space to handle texts and images. Lumina-mGPT [20] further enhances Chameleon + +by enabling photorealistic text-to-image generation through supervised fine-tuning. In our work, we leverage LuminamGPT as the base model for Real-ISR, leveraging its strong image synthesis and understanding priors. + +Vision Tokenizer. Lumina-MGPT [20] unifies vision-language understanding and generation through a VQGAN-based [9] tokenizer, which converts continuous images into symbolic sequences. It integrates three functional components: an encoder compressing visual inputs with down-sampling factor $f$ , a quantizer discretizing latent vectors by nearest-codebook matching with size $N$ , and a decoder reconstructing images from token-codebook mappings. In Real-ISR, the tokenizer will directly impact reconstruction quality: lower $f$ preserves spatial details by reducing compression, while larger $N$ enhances feature expressiveness through fine-grained codebook representations. + +Training. Multimodal large language models process concatenated text-image token sequences through autoregressive learning. The objective maximizes the likelihood of target sequence $\mathbf{y} = \{y_1, \dots, y_T\}$ via conditional probability factorization $P(\mathbf{y}|\mathbf{x}) = \prod_{t=1}^{T} P(y_t|\mathbf{c}_{TokenizersOST-ValRealSRDrealSRVAE25.0024.4336.20VQGAN24.29 (-0.71)23.53 (-0.90)33.59 (-2.61) + +PSNR and SSIM [40] computed on the Y channel in YCbCr color space. Perceptual similarity is evaluated using LPIPS [54] and DISTS [7], which compare deep feature representations between restored and GT images. FID quantifies the statistical distribution alignment between restored and reference images. For blind quality assessment without reference images, we incorporate NIQE [52], MANIQA [48], MUSIQ [13], CLIPIQA [34] and TOPIQ [5] to evaluate image naturalness and structural integrity. + +Implementation Details. We train PURE using the AdamW optimizer with an initial learning rate of $4 \times 10^{-4}$ , following a cosine decay schedule during training. The model is trained on the entire dataset for 2 epochs with a batch size of 128, including a warmup phase spanning the first 0.5 epochs to stabilize early-stage optimization. Training is conducted on $512 \times 512$ resolution images with 32 NVIDIA A800 GPUs. During the inference process, the dynamic Top- $k$ sampling parameters for image token generation are configured as $k_{\mathrm{min}} = 1$ , $k_{\mathrm{max}} = 2000$ with $\mu = 5$ , while a conservative Top- $k = 1$ strategy is implemented for text token generation to ensure optimal textual accuracy. We maintained the inference parameters used in LuminamGPT, setting CFG [20] to 0.8 and temperature to 0.9. + +# 4.2. Comparison with State-of-the-Arts + +Quantitative Comparisons. In all of our competing methods, the variational auto-encoder (VAE) [25] is used to convert the input image into latent space for diffusion, while in our PURE, a VQGAN is used to convert images into discrete tokens for processing. Both VAE and VQGAN will lose image details, but VAE is more advantageous for its continuous representation. Tab. 1 quantify the fidelity (in terms of as PSNR) of GT images on the three test sets, which is actually the PSNR upper bounds of Real-ISR performance. Taking DrealSR as an example, VAE outperforms VQGAN by 2.61 dB. Taking this fact into account, we investigate whether PURE, which relies on VQGAN for autoregressive token generation, can overcome this deficiency and show competitive Real-ISR performance. + +Tabs. 2 and 3 presents a comprehensive quantitative comparison between PURE and state-of-the-art diffusion-based approaches on the four test datasets. (Note that RealLQ250 does not have GTs so that we can only compute the no-reference metrics.) Although PURE, as expected, + +Table 2. Quantitative comparison between PURE and state-of-the-art diffusion-based methods. The best and second best results of each metric are highlighted in red and blue, respectively. + +
DatasetsMethodsPSNR↑SSIM↑LPIPS↓DISTS↓FID↓NIQE↓MUSIQ↑MANIQA↑CLIPQA↑TOPIQ↑
OST-ValStableSR19.970.46380.33670.200751.113.766974.380.60090.71940.7789
DiffBIR20.470.46940.36220.205961.284.547773.980.63770.73780.7983
SeeSR20.710.50040.32740.193556.323.939974.030.59200.69000.7945
PASD20.950.50530.41210.219066.924.830569.770.42890.51410.6307
OSEDiff20.590.49540.31330.192652.113.894774.300.61020.67090.7755
PURE18.520.41810.38630.205255.194.797774.810.64240.75810.8148
RealSRStableSR24.640.70790.30040.2141128.665.882372.190.40540.62340.6809
DiffBIR24.820.64950.36560.2400131.015.847772.500.47290.70590.7313
SeeSR25.140.72100.30080.2224125.615.391372.610.42030.67050.7354
PASD26.630.76600.28700.2034125.265.989270.010.33820.48690.5988
OSEDiff25.150.73410.29200.2127123.735.644272.950.45070.66860.7106
PURE22.830.60790.38210.2458188.335.409072.370.45270.68170.7165
DrealSRStableSR25.860.73800.28750.195195.715.903373.550.43990.70210.7408
DiffBIR26.820.70350.33890.217980.115.697773.230.50070.72250.7608
SeeSR27.710.76760.27680.203393.805.444073.450.48080.70460.7673
PASD29.730.83260.20990.164367.165.689972.400.42040.62680.6979
OSEDiff26.600.76930.26330.188294.595.772473.980.49780.71140.7345
PURE24.730.64590.34520.207679.415.484673.280.52510.72590.7560
+ +Table 3. Quantitative results on the RealLQ250 dataset. The best and second best results of each metric are highlighted in red and blue, respectively. + +
MethodsNIQE↓MUSIQ↑MANIQA↑CLIPIQA↑TOPIQ↑
StableSR5.912273.750.50750.72730.7431
DiffBIR4.754773.680.59710.76690.7629
SeeSR4.209473.910.52410.72370.7621
PASD4.323872.140.43880.62000.6578
OSEDiff4.149174.210.52630.71010.7285
PURE4.505474.100.54090.77110.7751
+ +Table 4. Complexity comparison among different methods. All methods are tested with an input image of size $512 \times 512$ , and the inference time is measured on an A100 GPU. + +
StableSRDiffBIRSeeSRPASDOSEDiffPURE
Inference Time (s)11.502.724.302.800.35256.87
Total Param (M)141017172524190017757080
+ +show inferior results in full-reference based metrics such as PSNR, SSIM, etc., it demonstrates highly competitive performance across no-reference metrics. This substantiates that PURE, via effective perception and understanding of the input LQ image, can exhibit robust image restoration capability and produce HQ images aligning with human visual preferences. We argue that this achievement is non-trivial considering the significant loss of details in the discrete tokenization process. On the other hand, such results imply the significant potentials of autoregressive multimodal generative models in real-world image restoration tasks. + +Qualitative Comparison. We present qualitative comparisons with other Real-ISR methods in Fig. 4. As shown in + +the first case, our PURE approach successfully recovers the most authentic and accurate details, while the other methods yield either over-smoothed or incorrect textures. Similar observation can be found in the second case, where our approach generates more natural results with significantly reduced artifacts compared to the competing methods. For the remaining cases, PURE also shows advantages in terms of visual quality, producing more realistic texture details while maintaining better overall image fidelity. More visual results are provided in the Supplementary Material. + +User Study. To further evaluate the performance of competing methods, we conduct a user study. We randomly select 50 real-world LQ images from RealSR, DrealSR and RealLQ250, then employ PURE and five state-of-the-art diffusion-based Real-ISR approaches (StableSR, PASD, DiffBIR, SeeSR and OSEDiff) to enhance them. These Real-ISR results, together with the LQ images, are presented to volunteers, who are asked to select the best restoration output based on two key criteria: 1) content consistency with the LQ input (including color fidelity, structural preservation, and texture accuracy); and 2) visual perceptual quality (encompassing natural appearance and richness of plausible details). Fifteen volunteers are invited to participate in the study, each making 50 pairwise comparisons over different methods. As demonstrated in Fig. 5, our PURE method achieves significantly better preference than diffusion-based methods, with a selection rate of $38.9\%$ . This result demonstrates the great potential for autoregressive multi-modal models in solving real-world image restoration tasks. + +Complexity Analysis. We then make a complexity com + +![](images/2526f6f5236ff3c743a11799f56798b644bf5936702302888d034f3ed4c6267f.jpg) +Figure 4. Qualitative comparisons of different Real-ISR methods. Please zoom in for a better view. + +parison between PURE and the competing methods. As shown in Tab. 4, it is not a surprise that PURE, as an autoregressive multimodal generative model-based method, has much more parameters and significantly longer inference time than those SD-based methods. Specifically, the large amount of parameters are inherited from the Lumina-mGPT model, while the slower inference speed results from the sequential next-token prediction in autoregressive models. In contrast, the SD-based approaches can perform diffusion denoising in parallel. However, it is worth mentioning our work presents, to our knowledge, the first successful application of an autoregressive multimodal model to Real-ISR, with demonstrated effectiveness. + +# 4.3. Ablation Study + +We perform ablation studies on our proposed perception-understanding strategy and the entropy-based Top- $k$ sampling strategy. The visual comparisons for the ablation study are presented in the Supplementary Material. + +Perception-Understanding Guidance. To validate the effectiveness of our sequential perception-understanding-restoration paradigm, we systematically ablate the contribution of each text-guided component on DrealSR. The Full Guidance strategy strictly follows our paradigm, sequentially producing degradation scores, semantic descriptions, and restored images. Perception Guidance omits semantic captioning but retains degradation estimation, while Understanding Guidance removes degradation analysis to focus + +Table 5. Ablation study on perception-understanding guidance mechanisms. The best results of each metric are marked in bold. + +
StrategyPSNR↑SSIM↑LPIPS↓DISTS↓FID↓NIQE↓MUSIQ↑MANIQA↑CLIPQA↑TOPIQ↑
No Guidance23.430.55880.44520.2409191.215.972273.230.49500.72020.7601
Perception Guidance24.480.65100.34710.210683.205.557373.150.51890.71660.7410
Understanding Guidance24.230.62820.39370.2244141.055.689873.030.49550.71680.7493
Full Guidance24.730.64590.34520.207679.415.484673.280.52510.72590.7560
+ +Table 6. Ablation study on sampling strategies. The best results of each metric are marked in bold. + +
StrategyPSNR↑SSIM↑LPIPS↓DISTS↓FID↓NIQE↓MUSIQ↑MANIQA↑CLIPQA↑TOPIQ↑
Top-127.590.79450.25070.2173115.397.930871.820.37790.52910.6313
Top-200024.560.63790.36190.210780.545.615973.380.51800.71690.7471
Dynamic Top-k24.730.64590.34520.207679.415.484673.280.52510.72590.7560
+ +![](images/eaab325e357c57aa6e1550c261929877d3511b24dc38dffe9b25beedc5d2f27c.jpg) +Figure 5. User study results on PURE and five state-of-the-art diffusion-based Real-ISR methods (StableSR, PASD, DiffBIR, SeeSR, OSEDiff) with 50 real-world images. + +solely on semantic understanding. No Guidance bypasses all textual intermediates, directly mapping low-quality inputs to restored outputs. The results are shown in Tab. 5, from which we can have the following observations. + +First, the No Guidance method under-performs on most metrics, particularly on reference-based metrics. In comparison, the Perception Guidance method shows significant improvements on reference-based metrics, especially PSNR (with a 1.05 dB increase), demonstrating the effectiveness of adaptive degradation perception for restoration. Meanwhile, Understanding Guidance significantly outperforms No Guidance on reference-based metrics and some no-reference metrics (NIQE and MANIQA), proving that semantic understanding aids realistic detail generation aligning with the original image's semantics better. Finally, Full Guidance attains the best performance across most metrics. This hierarchy confirms that explicit degradation modeling enhances structural fidelity, semantic understanding drives realistic detail generation, and Full Guidance well balances physical accuracy and perceptual authenticity. + +Entropy-based Top- $k$ Sampling. We evaluate the proposed entropy-based dynamic Top- $k$ sampling strategy against fixed Top- $k$ baselines on DrealSR: 1) Top-1: Deterministic sampling ( $k = 1$ ); 2) Top-2000: Maximal stochasticity ( $k = 2000$ ). As quantified in Tab. 6, Top-1 strategy achieves the best PSNR/SSIM metrics as it consistently se + +lects the token with the highest probability, ensuring strong fidelity. However, it performs poorly on most other metrics due to the lack of diversity in generation. In contrast, the Top-2000 strategy exhibits the worst PSNR/SSIM scores but outperforms Top-1 on other metrics, benefiting from its diversity. The proposed Dynamic Top- $k$ strategy effectively balances these two extremes. While achieving good PSNR and SSIM scores, it achieves the best performance on perceptual metrics (DISTS, FID) and no-reference metrics (NIQE, MUSIQ, MANIQA). This demonstrates that our dynamic Top- $k$ sampling approach successfully navigates the trade-off between fidelity and perceptual quality, leveraging adaptive stochasticity to enhance the realism and naturalness without compromising much structural accuracy. + +# 5. Conclusion and Limitation + +We proposed PURE, a robust Real-ISR framework that integrated perception, understanding and restoration through instruction-tuning of the autoregressive multimodal generative model Lumina-mGPT. By jointly perceiving degradation strength, generating semantic descriptions, and restoring high-quality image tokens autoregressively, PURE addressed effectively the limitations of existing diffusion-based methods for handling complex scenes with semantic ambiguity and restoring unnatural local structures. The proposed entropy-based Top-k sampling strategy further improved local structure by adaptively adjusting token generation. Experiments showed that PURE effectively preserved both global semantics and local details in challenging real-world scenarios, showcasing the potential of autoregressive multimodal paradigms for low-level vision tasks. + +Limitations. Due to the large parameter size of multimodal LLM and the slow inference caused by autoregressive token prediction, PURE faces deployment challenges on resource-constrained devices. Additionally, VQGAN as the vision decoder has lower reconstruction accuracy than diffusion model VAEs. In future, we plan to develop distillation techniques and explore parallel decoding to improve computational efficiency, and investigate more effective vision encoders compatible with autoregressive models. + +# Acknowledgment + +# References + +[1] Stability.ai. https://stability.ai/stable-diffusion.1,2 +[2] Yang Ai, Xiaoqiang Zhou, Huaibo Huang, Xiaotian Han, Zhengyu Chen, Quanzeng You, and Hongxia Yang. Dreamclear: High-capacity real-world image restoration with privacy-safe dataset curation. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. 5 +[3] Jianrui Cai, Hui Zeng, Hongwei Yong, Zisheng Cao, and Lei Zhang. Toward real-world single image super-resolution: A new benchmark and a new model. In ICCV, pages 3086-3095, 2019. 5 +[4] Bin Chen, Gehui Li, Rongyuan Wu, Xindong Zhang, Jie Chen, Jian Zhang, and Lei Zhang. 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First-Person_ A Dataset and Benchmark for Egocentric Human-Object-Human Interactions/full.md b/ICCV/2025/Perceiving and Acting in First-Person_ A Dataset and Benchmark for Egocentric Human-Object-Human Interactions/full.md new file mode 100644 index 0000000000000000000000000000000000000000..62aebb9f95e9d93e75620efffac2a4c448c7708f --- /dev/null +++ b/ICCV/2025/Perceiving and Acting in First-Person_ A Dataset and Benchmark for Egocentric Human-Object-Human Interactions/full.md @@ -0,0 +1,418 @@ +# Perceiving and Acting in First-Person: A Dataset and Benchmark for Egocentric Human-Object-Human Interactions + +Liang Xu $^{1,2,3}$ Chengqun Yang $^{1}$ Zili Lin $^{1,2,3}$ Fei Xu $^{1}$ Yifan Liu $^{1}$ Congsheng Xu $^{1}$ Yiyi Zhang $^{4}$ Jie Qin $^{5}$ Xingdong Sheng $^{6}$ Yunhui Liu $^{6}$ Xin Jin $^{2,3}$ Yichao Yan $^{1*}$ Wenjun Zeng $^{2,3}$ Xiaokang Yang $^{1}$ + +1Moe Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University +$^{2}$ Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo, China +3Ningbo Key Laboratory of Spatial Intelligence and Digital Derivative, Ningbo, China +$^{4}$ MoE Key Lab of AI, School of Computer Science, Shanghai Jiao Tong University $^{5}$ Nanjing University of Aeronautics and Astronautics $^{6}$ Lenovo + +https://liangxuy.github.io/InterVLA/ + +![](images/5b1e8c692c1737cb1e0eb29b5c3a38c029b747793e3b461b4632c3d509aebf44.jpg) + +![](images/acd341e15c99227f8634e3ed4adcee0c8c1beebbe8debdee99c7535c19996aa9.jpg) +Figure 1. InterVLA features a large-scale human-object-human interaction dataset in a vision-language-action scheme, where an assistant provides services to an instructor based on egocentric perception and verbal commands. This comprehensive dataset comprises 3.9K sequences, totaling 11.4 hours and 1.2M frames of multimodal interaction data, including egocentric and exocentric RGB videos, language commands and high-precision human/object motions, promoting the development of general-purpose intelligent AI assistants. + +# Abstract + +Learning action models from real-world human-centric interaction datasets is important towards building general-purpose intelligent assistants with efficiency. However, most existing datasets only offer specialist interaction category and ignore that AI assistants perceive and act based on first-person acquisition. We urge that both the generalist interaction knowledge and egocentric modality are indispensable. In this paper, we embed the manual-assisted task into a vision-language-action framework, where the assistant provides services to the instructor following egocentric vision and commands. With our hybrid RGB-MoCap system, pairs of assistants and instructors engage with multi- + +ple objects and the scene following GPT-generated scripts. Under this setting, we accomplish InterVLA, the first largescale human-object-human interaction dataset with 11.4 hours and 1.2M frames of multimodal data, spanning 2 egocentric and 5 exocentric videos, accurate human/object motions and verbal commands. Furthermore, we establish novel benchmarks on egocentric human motion estimation, interaction synthesis, and interaction prediction with comprehensive analysis. We believe that our InterVLA testbed and the benchmarks will foster future works on building AI agents in the physical world. + +# 1. Introduction + +Learning generalist interaction knowledge is indispensable towards general-purpose intelligent agents to assist humans in the physical world. To avoid expensive robot data col + +lection, learning from human-centric interactive datasets is more efficient [8, 77, 80, 97]. Existing datasets on human-human interactions contribute to human-robot interactions [14, 56, 81, 93], teleoperation [44, 45, 100]; human-object interactions promote human-to-robot handover [17, 18, 115, 116], human-robot collaboration [20, 98, 134] and human-scene interactions advance navigation [118, 136, 139]. + +Despite the rapid development of magnitude and richness in human-centric datasets and benchmarks, they still face some limitations in building intelligent assistants. Imagining the most basic capabilities for home robots, perceiving and comprehending the instructor's commands, navigating smoothly, and manipulating objects are required. However, most datasets only offer specialist interaction category [37, 66, 76, 86, 116, 122, 130, 134] rather than a generic scenario composed of diverse human-human, object and scene interactions. Besides, existing datasets [37, 66, 76, 116, 122, 130, 137] ignore the fact that AI assistants always perceive and then react based on their first-person acquisition [112, 134]. The absence of egocentric perspective could hinder the physical deployment of AI assistants. + +To address these limitations and foster the development of general human-centric interactions and versatile AI assistants, a comprehensive dataset encompassing diverse interaction patterns and stable egocentric perception is pivotal. In this paper, we focus on the common daily scenarios of manual-assisted tasks with the majority being human-object-human interactions where an assistant providing services to an instructor following the egocentric vision and verbal commands, such as "Pass me the cup on the table", where the human-human, object, scene interactions are naturally integrated. To simulate real-world robotic assistance scenarios, we randomly arrange various pieces of furniture and additional operable objects to establish the scene. The instructor gives verbal commands accompanied by body gestures while the assistant comprehends the intention and then responds accordingly. + +Inspired by the vision-language-action (VLA) paradigm emerged for instruction-following robots, we formulate our data collection setup within the VLA framework and introduce InterVLA, the first large-scale egocentric human-object-human interaction dataset with various interaction categories as depicted in Fig. 1. For the vision modality, we capture two egocentric videos from the instructor's perspective and five exocentric videos covering the full scene. The language component consists of 100 meticulously crafted scripts featuring various scene arrangements, versatile interaction types, multi-object interactions and navigation tasks. To acquire action data, we attach reflective markers to the human and object surfaces, enabling high-precision motion tracking while preserving RGB data fidelity. We recruit 47 participants to form 27 unique instructor-assistant pairs en + +
DatasetModalityScale
HHIHOIHSIMulti-ObjEgoExo#Seqs#Objs#Hours
You2Me [86]✓✗✗✗✓✗42-1.4
ExPI [37]✓✗✗✗✗✓115-0.3
Hi4D [130]✓✗✗✗✗✓100--
InterHuman [66]✓✗✗✗✗✓6.0K-6.6
Inter-X [122]✓✗✗✗✗✗11.4K-18.8
HIMO [76]✗✓✗✓✗✗3.4K539.4
HOH [116]✗✓✗✗✗✓2.7K136-
CORE4D [134]✓✓✗✗✓✓1.0K37-
HOI-M3 [137]✓✓✓✓✗✓1999020
InterVLA✓✓✓✓✓✓3.9K5011.2
+ +Table 1. Dataset comparison. We compare InterVLA with existing human-centric interactive datasets. Modality measures the human-human, human-object, human-scene interactions, multi-object interactions, egocentric and exocentric views. Scale measures the number of sequences, objects and hours. + +gaging with 50 household objects, yielding 3.9K sequences of 11.4 hours and 1.2M frames of interaction data in total. All the captured data are well-calibrated and temporally synchronized. A comparison with existing human-centric interactive datasets is summarized in Tab. 1. + +With our proposed InterVLA dataset, we introduce novel tasks and benchmarks on how AI assistants better perceive the surroundings and then generate appropriate responses. We formulate four downstream tasks of 1) Egocentric human motion estimation to extract the global body motion of the instructor based on the first-person perspective of the assistant, 2) Interaction synthesis to generate plausible human-object-human sequences given the textual descriptions and the initial states of the human and objects, 3) Motion-based interaction prediction to anticipate the future human/object motions conditioned on the previous motion frames and 4) Vision-language based interaction prediction to forecast the future human motions from the historical first-person videos and the verbal instruction. We establish comprehensive benchmarks for these tasks, providing baseline models, quantitative and qualitative evaluations, and in-depth analysis. The results highlight the challenges posed by rapid camera movement, limited visibility, occlusions, and multi-object interactions within InterVLA. Additionally, we emphasize the dataset's potential applications in tasks such as sparse-view 4D scene reconstruction, handobject interaction, and motion reconstruction from sparse signals. Our contributions can be summarized as: + +- We collect the first large-scale human-object-human interaction dataset called InterVLA with diverse generalist interaction categories and egocentric perspectives. +- Our proposed benchmark with thorough analysis on egocentric human motion estimation, interaction synthesis and interaction prediction will stimulate future works on building intelligent AI assistants. We will release all the datasets, code and models for further exploration. + +# 2. Related Work + +Egocentric Vision. Increasing attention is attached to egocentric vision with datasets [6, 22, 23, 32, 34, 35, 41, 62, 64, + +![](images/852319e0c53c108d04ab4e50212de0b22c04e552e7be9f40588a120bb3f371a8.jpg) +(a) Human Setup + +![](images/0572d44f3f57f54dea1422bd9ccf49cb17dd5580190c3f5bd2f0d4d9959b9712.jpg) +(b) Object-Scene Setup + +![](images/6382db08cfda05e07e3f88853a115f45ab9ae080d98518a36e9c71094b2b6e91.jpg) +(c) Hybrid RGB-MoCap System +Figure 2. InterVLA capturing system. (a). We attach 41 reflective markers to the subject's body with strong medical glue to track the human body motion. The assistant wears two GoPro cameras to capture the egocentric data. (b). Reflective markers are positioned on the surface of real objects to track the precise object trajectories. We also collect the precise 3D object scans with a KSCAN Magic Scanner. (c). Our hybrid RGB-MoCap system with two egocentric RGB cameras, five exocentric RGB cameras, and an OptiTrack MoCap system. + +85, 112], spurred by applications like robotics, AR and VR. The unique dynamics and perspective of egocentric vision present new challenges and opportunities for various tasks, including wearer pose estimation [3, 53, 62, 75, 82, 110, 111], activity recognition [35, 57, 65, 141], human-object interaction (HOI) [15, 21, 61, 77, 84], robotic active perception [4, 58, 107, 126], and interactive assistants [112]. InterVLA captures the egocentric data via two GoPro cameras showing in Fig. 2, together with accurate humans and objects motions obtained by the OptiTrack MoCap system. Compared to most video datasets such as Ego-Exo4D [35], InterVLA provides ground-truth 4D human and object motions captured by an optical MoCap system. + +Human-Human Interactions. Besides numerous single-human motion datasets [36, 50, 67, 69, 91, 96, 113, 121, 143], several human-human datasets [33, 37, 66, 69, 86, 108, 122, 130, 133] have also been constructed for interaction synthesis [28, 66, 120, 122], human reaction generation [122, 123]. [14, 44, 56, 92, 93] also verifies that the learned interaction knowledge can be applied to humanrobot interactions. InterVLA is essentially a human-human interaction dataset composed by an instructor and an assistant interacting with objects. + +Human-Object Interactions. Recent efforts have expanded the boundaries of HOI datasets from hands-interactions [11, 39, 40, 51, 72, 73] and full-body interactions [29, 48, 105, 125] with single object to full-body interactions with multiple objects [76, 79]. In contrast to previous datasets focusing on individual HOI episode without context, InterVLA captures a series of coherent and consecutive HOI episodes for each GPT-generated script. + +Human-Scene Interactions. Human-scene interactions incorporate comprehensive aspects ranging from navigation and collision avoidance to interaction with objects in the scene with various applications like embodied AI and + +VR. Real-world datasets [9, 38, 42, 43, 54, 83, 99, 138] face limitations such as static scenes [38, 43], single objects [9, 54, 138], or noisy 3D pose estimated from image [42, 83, 99]. Synthetic datasets [5, 10, 16, 55] resolve these issues yet suffer from appearance reality and physical plausibility. We build simple scenes with random furniture arrangements, offering comprehensive navigation and interaction data in real-world dynamic scenes. + +Human-Object-Human Interactions. HOH interactions are common in cooperative tasks and settings. Several datasets [17, 18, 27, 60, 116] focusing on handover are limited by fixed scene and body position settings, lack of egocentric RGB data, and absence of either natural human appearance or 3D human pose data. While CORE4D [134] provides egocentric HOH interaction data, it focuses exclusively on a single interaction type of two person collaboratively rearranging objects. InterVLA addresses those limitations to involve diverse HOH interaction types, flexible scene settings and multi-object interactions. + +Vision-Language-Action Models. VLA models integrate vision and language as multi-modal inputs and generate actions for agents to accomplish tasks. The last few years have witnessed many great works [12, 13, 25, 47, 59, 78, 87, 140] propelling the advancement of VLA models with the support of large pre-trained models. HumanVLA [126] pioneeringly simulated humanoid VLA using simulator-style images as vision input. We anticipate InterVLA with real-world egocentric RGB data, language instructions, human response motion and object trajectories, could accelerate the practical humanoid VLA in real-world applications. + +# 3. The InterVLA dataset + +# 3.1. Overview + +InterVLA is a large-scale human-object-human interaction dataset collected in a vision-language-action scheme, which + +![](images/30ff7e8553d39db45c992c32bed907ab40ba9283fcae852af11d8f410d33142a.jpg) +(a) Egocentric Videos + +![](images/f7460d2c8a849806c7f2b0eaf32c0506e155e1a8b78cac3c48aa8435876a8bf8.jpg) +(b) Exocentric Videos + +1. Open the beer bottle and pour some beer out into the teapot. +2. Put the beer bottle back on the edge of the table. +3. Pass me the fruit knife. I need the fruit knife to cut something. +4. Put the fruit knife back on the table. +5. Pass me the teapot again. +6. Pass me the spoon to stir the teapot. +7. Pass me the mouse. I will use it. +8. Put the mouse back on the table. + +![](images/cccca1ba58fb7bb17eef54098ff3fbbd5bc78a88a0d8d0118e477900ce2ebbdf.jpg) +(c) Instructions + +![](images/5e3cac11e587208fec8c7021bffec4ed2e2864a95b31221c6b76c7fbf127619f.jpg) +(d) Human & Object Motions +Figure 3. Components of the InterVLA dataset. For the vision modality, we capture (a) two egocentric and (b) five exocentric RGB videos; For the language modality, we comprehensively supply the (c) GPT-generated commands; For the action modality, we provide the high-precision (d) human and object motions during the interactions. + +features an assistant providing diverse services to the instructor in daily scenarios. We believe that our two-person and multi-object setting integrates several specialist humancentric interactions and will facilitate further research on robot-centric interactions. Besides, our InterVLA dataset also emphasizes the utility of egocentric perception and the assistant's action based on it. As depicted in Fig. 1, each scene comprises randomly arranged furniture with two persons interacting with several daily objects. The assistant performs a series of consecutive actions following the language commands of the instructor, such as "Give me the mug on the table". We provide multi-view exocentric (third-person) viewpoints and two egocentric (first-person) perspectives from the assistant. The human and object motions are obtained by the optical motion capture (MoCap) system. Next, we will describe the vision-language-action data collection scheme and pipeline in Sec. 3.2 and dataset post-processing, components, and statistics in Sec. 3.3. + +# 3.2. Vision-Language-Action Capturing + +The concept of vision-language-action (VLA) emerges with the rise of instruction-following robotics. Inspired by it, we embed the manual-assisted task into the VLA framework where the assistant performs diverse services to the instructor such as picking up, retrieval, handover, and rearrangements of multiple objects. The hybrid RGB-MoCap capturing system of InterVLA is elaborately illustrated in Fig. 2. + +Capturing Pipeline. We recruit 46 participants to form 27 unique instructor-assistant pairs for data collection. For the object and scene setup, we primarily select 50 common household objects of various sizes, including small objects such as fruit, mug, knife, and large objects such as suitcases, floor hangers, and besom. Note that we adopt real objects rather than 3D printed objects as [76, 105] for the fidelity of the RGB modality. The details of the object list are provided in the supplementary material. To align with real-world intelligent robotic assistance and enrich the interaction categories, we meticulously develop the following + +data-capturing pipeline. We first randomly arrange some furniture of tables or chairs in the MoCap venue with several operable objects positioned in the scene. During collection, the instructor first communicates with the assistant using verbal commands along with complementary body gestures, while the assistant should interpret the instructor's intention and react appropriately. For each recording, a sequence of atomic interactions is performed to preserve long-duration interactions and maintain continuity. + +Vision. Two egocentric GoPro cameras are mounted tightly on the forehead and chest of the assistant, respectively, to capture first-person RGB videos with a high resolution of $5312 \times 2988$ at 30 fps. The camera intrinsics are obtained following [1]. The camera positions and orientations are carefully adjusted based on the height of the participants to maximize the valid shooting area of the scene, the other person, and the interactions. Besides, we also integrate five well-calibrated RGB cameras to compensate for the multiview exocentric viewpoints with a resolution of $1920 \times 1080$ at 30 fps. The egocentric and exocentric cameras are all temporally synchronized by millisecond-level timestamps. To protect the privacy of participants, we mask the faces of all the exocentric and egocentric RGB videos with [2]. + +Language. Commands of the instructor serve as the starting point, trigger, and bridge for the following interactions. Given the household objects and furniture library, we employ large language models, i.e., ChatGPT [88] to select the scenes and objects setup, determine their placement, and then generate a script of instructor-assistant interaction sequences within the scene based on the object affordance. With the majority of interactions focusing on human-object-human interactions such as handover and collaborative rearrangement, we also include some pure human-human interactions such as supporting or massaging. Furthermore, we encourage multi-object interactions with object-object interactions such as "Slicing the apple with a knife" and simultaneous manipulation such as "Tidying up the objects + +on the table". Additionally, moving around and navigating within the scene are also supported. Ultimately, we produce 100 scripts, each involving an average of 2-3 furniture, 5 household objects, and 8 consecutive atomic commands. Each script is manually reviewed to ensure validity. + +Action. For robotic arms, action can be defined as the rotations and translations of the robot joints. Similarly, motion is a compact representation for modeling human actions and object movements. To acquire high-quality human and object motions, we establish a MoCap system of $8.5 \times 5.4$ meters with 20 infrared cameras. For the human motions, we discard the tight MoCap suits but instead directly attach the reflective markers on the skin or clothes surface by strong medical glue as [29, 49] to preserve the fidelity of the RGB modality. The relative displacement between skin and clothing is eliminated by glue to ensure robust and precise MoCap results. The objects are treated as rigid bodies with at least four reflective markers placed on the surfaces for optical tracking. In our setting, we adopt the $12.5\mathrm{mm}$ diameter reflective spheres for both humans and objects to achieve the best tracking results. All the assets are well-created and calibrated before recording. We also equip the MoCap system with timecodes for the temporal alignment with the ego-exo RGB videos. + +# 3.3. Dataset Components + +Human Parametric Model. SMPL parametric model [74] is widely adopted in human-centric interaction datasets, which formulates the human mesh as the body pose $\theta \in \mathbb{R}^{23\times 3}$ , global orientation $q_{i}\in \mathbb{R}^{3}$ , root translation $\gamma_{i}\in \mathbb{R}^{3}$ and the body shape parameters $\beta \in \mathbb{R}^{10}$ , which are determined based on the height, weight and gender of the participant as [76, 94, 122]. We fit the BVH-format human skeleton captured from the MoCap data to the SMPL parameters with the following optimization objective as: + +$$ +\mathcal {L} = \lambda_ {j} \mathcal {L} _ {j} + \lambda_ {s} \mathcal {L} _ {s} + \lambda_ {r e g} \mathcal {L} _ {r e g}, \tag {1} +$$ + +where $\mathcal{L}_j$ measures the difference between the raw MoCap joint position and the optimized result, $\mathcal{L}_s$ smoothes the inter-frame motion transitions and mitigates pose jittering, $\mathcal{L}_{reg}$ regularizes the optimized poses from deviating and $\lambda_{j} = 1$ , $\lambda_{s} = 0.1$ , $\lambda_{reg} = 0.01$ are loss weights. We give further details of each optimization term in supplementary. + +Object Meshes and Tracking. To render accurate human-object interactions, we scan all 50 objects and obtain the precise object surface geometries with a KSCAN Magic Scanner. Each object is then attached by more than 3 reflective markers and tracked by the optical MoCap system. We further scan the objects together with the attached markers and align the new scans with the previous results to eliminate the offsets between the two centroids. The object motion can be represented as the translation $t^o \in \mathbb{R}^3$ and rotation $r^o \in \mathbb{R}^6$ of the 6D rotation representation [142]. + +Alignment and Segmentation. We standardize all the video data to a resolution of $1920 \times 1080$ at 30 fps and downsample the MoCap data to the same fps for consistency. The exocentric videos, egocentric videos and motion data are well synchronized with millisecond-level timestamps. To facilitate training for downstream tasks, we render the interaction results and then manually split the long-duration script into short clips by the atomic commands while retaining the temporal continuity across the clips. The RGB videos are also segmented in the same way. + +InterVLA Statistics. As aforementioned, we recruit 47 participants forming 27 unique instructor-assistant pairs for the data collection, spanning 519 valid long-duration interaction recordings with different GPT-generated scripts and scene arrangements. We ensure that each object appears in at least five scenarios. After the alignment, segmentation and thorough manual refinement of the motion data, we obtain 3,906 interaction sequences with 11.4 hours and 1.2M frames of four-tuple data composed by the egocentric videos, exocentric videos, instructions and human/object motions. We showcase an example of the dataset in Fig. 3 for a better illustration and more video examples will be provided in the supplementary materials. + +# 4. Tasks, Benchmarks and Experiments + +We define new tasks and benchmarks of egocentric human motion estimation, interaction synthesis and interaction prediction as presented in Fig. 4 and potential downstream tasks based on InterVLA, oriented towards general-purpose AI agents. We also provide the evaluation results for the proposed benchmarks with detailed analysis. + +# 4.1. Preliminary Formulation + +Egocentric videos exhibit the active perspective that shows the superiority of capturing the details of the close-by interactions and the first-person intentions. However, they also suffer from the constrained camera field of view without global perception, rapid viewpoint changes of objects exiting and re-entering the field of the frame. + +We formulate our multimodal data as $[V, T, H, O, l]$ for each sequence, where $V = \{v_h, v_c\}$ are the head-mounted and chest-mounted egocentric videos respectively, $T = \{t_i\}_{i=0}^{N_t}$ are the exocentric videos and $N_t = 5$ indicates the video number. The human motions are denoted as $H = \{h_I, h_A\}$ for the Instructor and Assistant respectively, where $h_I / h_A$ can be detailed as $\{\theta \in \mathbb{R}^{23 \times 6}, q \in \mathbb{R}^6, \gamma \in \mathbb{R}^3, \beta \in \mathbb{R}^{10}\}$ for the body pose, global orientation, root translation and the body shape parameters, respectively. The object motions can be represented as $O = \{o_i\}_{i=0}^{N_o}$ , where $o_i = \{r_i^o \in \mathbb{R}^6, t_i^o \in \mathbb{R}^3\}$ for the rotation and translation of the object, respectively. $N_o$ means the number of objects. The geometries of all involved objects are precisely scanned denoted as $G = \{g_i\}_{i=0}^{N_o}$ . Here + +![](images/319fa5681a44600c1ba8dfce880c7fd4d672858729307f336501a15f27a9e2d3.jpg) +(A) Egocentric Human Motion Estimation +(B) Text-driven Interaction Synthesis + +![](images/e8cde8fc4d727274e8c9bdb3a88e5969b7b80ba703aa38046af559fcc15c0b64.jpg) +Figure 4. Task Formulation of InterVLA. We establish multiple downstream tasks on egocentric human motion estimation, text-driven interaction synthesis, motion-based interaction prediction and vision-language based interaction prediction. All these benchmarks showcase the great challenges of our InterVLA dataset and will benefit practical, intelligent AI assistants. + +![](images/1093600c14d3d82b261de0b3a0bd9b268b78772520431b4d25469efe81227f9f.jpg) +(C-1) Motion-based Interaction Prediction +(C-2) Vision-Language Based Interaction Prediction + +![](images/0974624abecd69668c002510d0840237fe4d5b9471e5066c8aff6b2976e762a7.jpg) + +we adopt the 6D rotational representation [142] for humans and objects as in previous works [36, 90]. $l$ refers to the language commands. We split the dataset into training, testing and validation sets with the ratio of 0.8, 0.15 and 0.05 for all downstream tasks. Note that we adopt only the head-mounted camera $v_{h}$ for all the video-based experiments. + +# 4.2. Egocentric Human Motion Estimation + +Task Formulation. Egocentric perception and comprehension of the instructor's intention are fundamental as the first step of AI assistants. As depicted in Fig. 4 (A), we aim to reconstruct the world-grounded human motion sequences given the egocentric RGB videos as + +$$ +F _ {M E} \left(\boldsymbol {v} _ {h}\right) \mapsto \hat {\boldsymbol {h}} _ {I}, \tag {2} +$$ + +where $\hat{h_I}$ denotes the estimated instructor motion. Note that it is quite challenging to maintain accurate body pose estimation and keep the consistent global coordinate system. The rapid movement of egocentric cameras, occlusion and limited visibility raise substantial challenges for this task. + +Experiment Settings. We evaluate four state-of-the-art global human motion estimation methods, TRACE [104], GLAMR [132], TRAM [114], and WHAM [103] on all the head-mounted camera sequences of the InterVLA dataset for an intuitive understanding. + +Evaluation Metrics. Following previous works [103, 114], We compute Mean Per Joint Position Error (MPJPE), Procrustes-aligned MPJPE (PA-MPJPE) and Per Vertex Error (PVE) to evaluate the 3D human pose and body shape estimation performance, and Acceleration error (Accel) for the inter-frame motion smoothness. More specifically, MPJPE calculates the average of the Euclidean distances between the predicted and ground truth joint positions. PA-MPJPE is the MPJPE calculated after Procrustes analysis that aligns the predicted poses to the ground truth through translation, rotation, and scaling. PVE measures the average distance between predicted and ground truth positions of the 6,890 vertices derived from the SMPL parametric + +model. Accel calculates the average difference in acceleration between the predicted and ground-truth coordinates. + +Results and Analysis. We present the visualization results comparison in Fig. 5 with the raw egocentric frames, the ground truth motion captured by the MoCap system and the baseline results. Note that we manually add a horizontal offset to avoid the motion entanglement, yet we place the anchor points on the floor to refer the global translation of the motion. The results show that even the best-performing algorithms obtain unsatisfactory results. For the three samples, the assistant turns head to locate scene objects slightly (first-row) or rapidly (third-row), causing the instructor to move out of the camera's field of view. The red red dashed boxes show that GLAMR and WHAM fail to track the correct global orientation and keep the correct coordinate system. The green dashed boxes show that TRACE misses many frames. Besides, we also provide the quantitative results comparisons in Tab. 2, where WHAM [103] show remarkable superiority over other methods across all metrics except PA-MPJPE. However, there remains a significant gap between its performance and the ground truth. This discrepancy can be attributed to several challenges inherent in our dataset, such as occlusions, rapid camera motion movements, the incomplete capture of human bodies, and frequent occurrences of subjects entering and exiting the frame (re-entering). + +# 4.3. Interaction Synthesis + +Task Formulation. Following existing text-driven HOI synthesis methods [24, 76, 89, 137], we define the task as multiple humans and objects motion generation as shown in Fig. 4 (B). We formulate this task as + +$$ +F _ {I S} \left(\boldsymbol {H} ^ {0}, \boldsymbol {O} ^ {0}, \boldsymbol {G}, l\right) \mapsto \{\hat {\boldsymbol {H}}, \hat {\boldsymbol {O}} \}, \tag {3} +$$ + +where $H^0$ and $O^0$ represent the initial pose of the humans and objects respectively, and $\hat{H}$ and $\hat{O}$ are the generated human and object motions. Compared with previous HOI datasets such as BEHAV [9], our InterVLA dataset con + +![](images/4fb0820474cebbb30ab466ad30d60abf4ee41d3f56ca4edeb4e4fbd3507fe434.jpg) +Figure 5. Visualization result comparison of the egocentric world-grounded human motion estimation results on the InterVLA dataset. For each sequence, we provide the original RGB frames along with the ground truth motion obtained by the MoCap system and four baseline models. Higher opacity indicates later frames of the sequence. Please zoom in for a more detailed view. + +
MethodPA-MPJPE↓MPJPE↓PVE↓Accel↓
TRACE [104]91.2720.1761.331.0
GLAMR [132]134.8589.9596.724.9
TRAM [114]102.7684.1718.727.5
WHAM [103]103.2333.6359.78.7
+ +tains multiple humans and objects and multi-object manipulations, which introduces greater challenges. + +Experiment Settings. Text-driven human motion generation methods MDM [106], priorMDM [101] and HIMO [76] are re-implemented to support the condition input of object meshes and the initial states of two persons and multiple objects. Further details regarding these methods can be found in the supplementary materials. + +Evaluation Metrics. We train the text feature extractor and human-object motion feature extractor first via contrastive learning as [36, 76]. The generation quality is evaluated by the following metrics: R Precision to evaluate the top-3 accuracy in retrieving the ground-truth description, Frechet Inception Distance (FID) [46] to measure the latent space divergence between authentic and synthetic samples, MultiModal distance (MM Dist) to determine the latent space distance between generated motions and input texts, Diversity to gauge the variance within the latent space, multimodality (MModality) to quantify the diversity of outputs + +Table 2. Quantitative results of egocentric global human motion estimation on the InterVLA dataset. Bold for the best results. + +
MethodsR Precision (Top 3) ↑FID ↓MM Dist ↓Diversity →MModality ↑
Real0.7592±0.00260.0203±0.00183.8718±0.00649.0164±0.0831-
MDM [106]0.4897±0.00672.8039±0.07275.4879±0.02127.7260±0.06331.9888±0.0694
priorMDM [101]0.5250±0.00686.2766±0.07775.5129±0.01888.9414±0.08882.1227±0.0993
HIMO [76]0.5707±0.00290.6805±0.01364.9609±0.01628.9849±0.05541.1478±0.0658
+ +Table 3. Quantitative results of human-object-human interaction synthesis on the InterVLA dataset, where $\pm$ indicates $95\%$ confidence interval and $\rightarrow$ means the closer the better. Bold highlights the best results. + +generated from the same textual input. + +Results and Analysis. The quantitative results presented in Tab. 3 demonstrate that HIMO [76] surpasses other methods across all metrics except for MModality, with a particularly impressive performance on FID. All these methods achieve a higher FID than the real interaction data, which shows that there remains ample opportunity for future endeavors to enhance the naturalness of the generated interaction results. + +# 4.4. Interaction Prediction + +Task Formulation. We propose two types of interaction prediction tasks of motion-based and vision-language based as demonstrated in Fig. 4 (C1) and (C2). For the motion-based interaction prediction, the model predicts the subsequent HOI sequences for the following frames given the adjacent past few frames of HOI sequences as + +$$ +F _ {M - I P} \left(\boldsymbol {H} ^ {t _ {I}: t - 1}, \boldsymbol {O} ^ {t _ {I}: t - 1}, \boldsymbol {G}\right) \mapsto \left\{\hat {\boldsymbol {H}} ^ {t: t _ {E}}, \hat {\boldsymbol {O}} ^ {t: t _ {E}} \right\}, \tag {4} +$$ + +
MethodsHumanObjectContact
Je(mm, ↓)Tc(mm, ↓)Re(°, ↓)Cacc(%, ↑)Pr(%, ↓)
MDM [106]175.3 (± 0.8)140.2 (± 0.7)11.0 (± 0.2)85.5 (± 0.3)0.4 (± 0.0)
InterDiff [124]175.3 (± 0.8)138.7 (± 0.6)10.8 (± 0.1)86.0 (± 0.2)0.4 (± 0.0)
CAHMP [19]172.5 (± 0.4)115.6 (± 0.5)9.5 (± 0.1)--
+ +where $t_I(t_E)$ denotes the initial (ending) frame of the sequence, $\hat{H}^{t:t_E}$ and $\hat{O}^{t:t_E}$ are the predicted future motions. In the experiments, we set $t_I = 0$ , $t = 15$ and $t_E = 30$ to predict the poses in the subsequent 15 frames given the previous 15 frames. While for the vision-language based interaction prediction, the model manages to anticipate the future human motions from the historical egocentric videos and the verbal instruction as + +$$ +F _ {V L - I P} \left(\boldsymbol {v} _ {h} ^ {t _ {I}: t - 1}, \boldsymbol {h} _ {A} ^ {t _ {I}: t - 1}, \boldsymbol {l}\right) \mapsto \left\{\hat {\boldsymbol {h}} _ {A} ^ {t: t _ {E}} \right\}, \tag {5} +$$ + +where $\hat{h_A}^{t:t_E}$ means the predicted motion of the assistant. + +Experiment Settings. We evaluate three state-of-the-art methods CAHMP [19], MDM [106] and InterDiff [124] for motion-based interaction prediction. For vision-language guided interaction prediction, we re-implement the existing hand trajectory prediction models FHOI [70], OCT [71], and USST [7] with integrated language embeddings to predict the motion of the assistant. + +Evaluation Metrics. For motion-based interaction prediction, we follow [134] to apply the evaluation metrics of human joint position error $(J_{e})$ to measure the Mean Per Joint Position Error (MPJPE) for two individuals; object translation error $(T_{e})$ representing the average $L2$ differences between predicted and real object translations; object rotation error $(R_{e})$ , indicating the average geodesic differences between predicted and actual object rotations; human-object contact accuracy $(C_{acc})$ to assess the average error rate in contact detection with a 5cm threshold to detect hand contacts; and penetration rate $(P_{r})$ calculating the percentage of object vertices penetrating human meshes. For vision-language guided interaction prediction, we adopt the average displacement error as the average $L2$ distance between the predicted and ground truth trajectories, and the final displacement error as the $L2$ distance between the two final predicted and ground truth locations following FHOI [70]. + +Results and Analysis. We provide the quantitative results of three state-of-the-art models for motion-based interaction prediction in Tab. 4. From the results, we can derive that CAHMP [19] achieves the best performance over the other baseline methods for both the human joint position error and the object translation and rotation error, thanks to the semantic-graph model to learn the relationship between human and context objects. From the quantitative comparisons of the vision-language based interaction prediction in Tab. 5, we can derive that USST [7] achieves the + +Table 4. Quantitative results of motion-based interaction prediction on the InterVLA dataset. + +
MethodAvg. Disp. Error ↓Final Disp. Error ↓
FHOI [70]0.290.38
OCT [71]0.280.36
USST [7]0.240.32
+ +Table 5. Quantitative results of vision-language based interaction prediction on the InterVLA dataset. + +best performance for the two metrics due to the proposed uncertainty-aware state space Transformer. However, we find that existing state-of-the-art methods have not achieved satisfactory performance on these two tasks. Significant errors remain in the predicted human motion, object translation & rotation and human-object contact for these two tasks, which indicates that our dataset presents significant challenges for subsequent optimization. + +# 4.5. Potential Downstream Tasks + +Sparse-view 4D Scene Reconstruction. Multi-view exocentric videos are synergistic with the egocentric viewpoint for global awareness of the scene. Existing works [63, 109, 119, 131, 135] are dedicated to reconstructing static scenes from sparse-view images with 3D representations like meshes, neural radiance fields, and 3D Gaussian splating while the majority of existing 4D reconstruction efforts [68, 95, 102, 117] are confined to dense perspective input. Our dataset comprising five exocentric-view videos, is anticipated to assist in downstream tasks of 4D scene reconstruction through additional supervisory signals, such as poses and meshes of people and objects. + +Hand-object Interaction Reconstruction. Similar to [30, 31, 127, 128] that jointly estimate the poses of both hands and the interacting objects, our InterVLA dataset with egocentric viewpoints and multi-object manipulation can also empower this task with substantial challenges. + +Motion Reconstruction from Sparse Signals. This task aims to reconstruct one's own whole-body motion of the assistant given the sparse signals of the egocentric captured low body or arms as in previous works [26, 52, 129]. + +# 5. Conclusion + +In this paper, we introduce a large-scale egocentric human-object-human interaction dataset called InterVLA. By embedding the manual-assisted tasks into a vision-language-action scheme, we formulate vision as the egocentric perspective, language as the instructor's verbal commands and action as the human and object motions, and demonstrate the indispensability of both generalist interaction knowledge and egocentric perception for building physical-world AI assistants. Through our extensive dataset and novel benchmarks for egocentric motion estimation, interaction synthesis and interaction prediction, we provide valuable tools that will drive further research and development in the field of real-world AI-assisted applications. + +# Acknowledgements + +This work was supported in part by NSFC (62201342), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), Grants of NSFC 62302246, ZJNSFC LQ23F010008, Ningbo 2023Z237 & 2024Z284 & 2024Z289 & 2023CX050011 & 2025Z038, and supported by High Performance Computing Center at Eastern Institute of Technology and Ningbo Institute of Digital Twin. 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b/ICCV/2025/Perception-as-Control_ Fine-grained Controllable Image Animation with 3D-aware Motion Representation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d888897b27848a1a16bf55a588c7b315862c2986 --- /dev/null +++ b/ICCV/2025/Perception-as-Control_ Fine-grained Controllable Image Animation with 3D-aware Motion Representation/full.md @@ -0,0 +1,318 @@ +# Perception-as-Control: Fine-grained Controllable Image Animation with 3D-aware Motion Representation + +Yingjie Chen, Yifang Men, Yuan Yao, Miaomiao Cui, Liefeng Bo Tongyi Lab, Alibaba Group + +{chenyingjie.cyj, myf272609, ryan.yy, miaomiao.cmm, liefeng.bo}@alibaba-inc.com + +# Motion Generation + +![](images/6f35573b285ed40b2f85938397cafa0754f33962ad8b887ac30b1b54cf1afcc9.jpg) + +![](images/5579c21880a684f401e86d11318a82da31f7541886e4cf0a645c2095b7f22d90.jpg) + +![](images/cf5c209f2a3360dba819525be4cd8148aea886f0eebd1f03041014062bfdffab.jpg) + +![](images/aa08182d0746182813d73bb771f2458521f2770349db2a300c35448f0aa75672.jpg) + +![](images/bdbc1f4e4dafbc2209ef24b2604b9fab4e9d92208d6b84f5e3d931b80e49eb87.jpg) + +# Motion Clone + +![](images/a903f8ef44371f47d3f96355ac9bd182e4250f71eb3f46aa945732571b3b602a.jpg) + +![](images/d1d496a6d8b3ef257cff7abd11654156f15d594fa33e7f4e52b73094765c226e.jpg) + +![](images/785bd6131fb02409612269076917b68c342ff0b85010300a02acb0b837de4546.jpg) + +![](images/923e615b63c5c381e0d023660394891685ccd39a0e16facef9e48a1a30063190.jpg) + +![](images/7a5fda605babe83d900e0da7c4af739f72eda8a3c810d2a0d01ad70d9a4c3425.jpg) + +# Motion Transfer + +![](images/2083019ad057951695ffd93b7d44f72b3ed4adaf8549e9dd307d3e95185056e4.jpg) + +![](images/bb2b5d30779fbc04c02d8b00542520246bab2a1eb57da25f3e135c6b69a91332.jpg) + +![](images/9f713523e59cf6a91528162064b05b6e5c73de3bc76eccf0b40ddd053e44c51f.jpg) +rrespondence + +![](images/82873e86b7cce07ffd8193ba0267f46e0361bb67def73624c6f6d5d12e7898d2.jpg) + +![](images/447c7b87a031af2677ab33d095ee8d960a9c017cdf52d214aa6d348a8fac8430.jpg) + +![](images/c9c509e357faffda9f19a780327ef1264410bf5ddbe495ad55ed48e1f34d1887.jpg) + +# Motion Editing + +![](images/cedfc4249a43f95d4568205d9a28490aae769b18358b7782565e3926aa36585e.jpg) +Figure 1. Potential applications for Perception-as-Control. By constructing 3D-aware motion representation based on user intentions and utilizing the perception results as motion control signals, the proposed fine-grained motion-controllable image animation framework can be applied to various motion-related video synthesis tasks, such as image-based motion generation (animate image according to user instructions), and video-based motion clone (mimic the entire motions), motion transfer (relocate and rescale local motions based on semantic correspondence), local motion editing (edit fine-grained scene and object motions in user-specified regions). + +![](images/4eed32780b379d9ea944984be0cf0470a9b7de085db6ed48651db639672e0516.jpg) + +![](images/3b789f9792202d9e155a94e24cdc61b1afb6d39d5f3558053042de3170d6fa9d.jpg) +Edit the Motion Outside Seg Mask + +![](images/aeda413801c4d2c367abd52e70351809d6852854b50cae2307c7448755acea0a.jpg) + +![](images/8211b182f8b74db7cb253f5a76664c310322d6bdba1495a920d330c1dcc82511.jpg) + +![](images/843015db5ae096eadc869ca6049422e1916e89d97e2b2b0e55f6517f5d2e6ef5.jpg) + +![](images/4872947e79649a6d7de204c176d32cfbd1257b783c26a1d2322ff732f6bc7639.jpg) + +# Abstract + +Motion-controllable image animation is a fundamental task with a wide range of potential applications. Recent works have made progress in controlling camera or object motion via various motion representations, while they still struggle to support collaborative camera and object motion control with adaptive control granularity. To this end, we introduce 3D-aware motion representation and propose an image animation framework, called Perception-as-Control, to achieve fine-grained collaborative motion control. Specifically, we construct 3D-aware motion representation from a reference image, manipulate it based on interpreted user instructions, and perceive it from different viewpoints. In this way, cam + +era and object motions are transformed into intuitive and consistent visual changes. Then, our framework leverages the perception results as motion control signals, enabling it to support various motion-related video synthesis tasks in a unified and flexible way. Experiments demonstrate the superiority of the proposed approach. For more details and qualitative results, please refer to our anonymous project webpage: Perception-as-Control. + +# 1. Introduction + +With the proliferation of generative AI, image animation as a fundamental task is undergoing rapid progress [2, 8, 18, 22, 25, 29, 35, 44]. Various potential application scenarios + +put forward higher demands for this task, i.e., particularly in achieving precise motion-controllable image animation based on user intentions. Motion-controllable image animation usually takes a reference image and motion control signals derived from motion representation as input, aiming to generate videos with the expected motions while maintaining the specific appearance. Since the reference image already includes rich appearance information, the key is to design better motion representations and effectively guide the motion content generation process. + +Motion in videos can be decomposed into camera motion and object motion. Object motion refers to dynamic movements relative to the world coordinate system, while camera motion arises from viewpoint changes. Although researchers have made great progress in designing various motion representations to obtain control signals for camera or object, achieving collaborative camera and object motion control with fine control granularity remains nontrivial. For camera motion control, some methods directly use camera intrinsic and extrinsic parameters [37] or convert them into Plücker embeddings [9, 41, 51] as high-level control signals, while others reconstruct point cloud to render incomplete frames [3, 11, 47] or use dense optical flow [17, 25] as more concrete control signals. For object motion control, recent works usually follow an interactive setting that allows users to draw point trajectories on the reference frame. These methods convert sparse point trajectories into optical flow [17, 18, 25, 37, 49] or reorganize point embeddings [4, 5, 29, 38] as control signals. Nevertheless, works [4, 5, 17, 37] focusing on collaborative motion control still suffer from conflict control issues and insufficient control granularity. + +The key observations of this paper are three-fold: 1) Motion representations based on pixel offsets such as optical flow are flexible for in-the-plane motions, while the lack of 3D awareness leads to conflict control issues with simultaneous camera and object motions. 2) Reconstruction-based motion representations such as point clouds show better spatial consistency, making them effective for camera motion control but inflexible to support fine-grained object motion control. 3) For controllable visual content generation tasks that maintain basic spatial structures, spatially aligned control signals are easier for alignment than high-level ones. Based on these observations, an effective motion representation for fine-grained collaborative motion control should have the following properties. First, the motion representation is equipped with 3D awareness to disentangle local components from the reference image. Second, the motion representation is spatially consistent for stable camera motion control and flexible enough for fine-grained object motion control. Third, the motion control signals derived from the motion representation are spatially aligned with the generated frames to enhance their connections. + +![](images/9580440c208d5413d1a0a0bc6ca43e493edd6f04af21f163338d03cf94ff388d.jpg) +Figure 2. 3D-aware motion representation for simplifying the 3D scene corresponding to the reference image, which consists of several unit spheres denoting key object parts and a world envelope accommodating them. We manipulate those spheres and observe the scene based on user intentions to transform camera and object motions into unified and consistent visual changes. + +To this end, we introduce 3D-aware motion representation. In controllable image animation applications, users generally have clear intentions about how objects move and how to observe the scene. The intuitive approach is to reconstruct the 3D scene based on the reference image, drive objects according to user intentions, and render the scene from the expected viewpoints. Considering the significant effort required to reconstruct everything in the scene, we notice that human visual attention is predominantly drawn to moving parts, while the remaining parts are generally perceived as a whole [6]. Therefore, as shown in Fig. 2, we simplify and summarize the 3D scene as a combination of several unit spheres representing key object parts (most moving parts and a few static parts) and a vast world envelope akin to The Truman Show accommodating them to demonstrate how the scene evolves as the observer's viewpoint changes. We then render the instantiated 3D scene to obtain perception results that reflect camera and object motions and necessary spatial relations. + +Based on 3D-aware motion representation, we propose an image animation framework to achieve fine-grained collaborative motion control. The framework takes a reference image and the perception results of the corresponding 3D-aware motion representation as motion control signals, which are spatially aligned with the generated frames. Specifically, we apply two lightweight encoders to encode camera and object control signals separately to avoid RGB-level interference, and then merge them to form the final + +motion control signals. We employ a U-Net-based diffusion model and inject both the reference image and motion control signals, enabling motion-controllable image animation. A data curation pipeline is introduced to construct 3D-aware motion representations from in-the-wild videos. Moreover, we propose a three-stage training strategy to balance camera and object motion control during training. + +Our contributions are three-fold: + +- We introduce 3D-aware motion representation to facilitate flexible and fine-grained collaborative motion control, which transforms camera and object motions into unified and consistent visual changes and is orthogonal to specific base model architectures. +- We propose an image animation framework to incorporate 3D-aware motion representation as spatially aligned motion control signals, which achieve collaborative motion control precisely and harmoniously. +- The proposed approach can support various motion-related applications via translating user intentions, such as motion generation, motion clone, motion transfer, and motion editing. + +# 2. Related Work + +Motion-controllable image animation has made significant progress recently. Since reference images have greatly limited the degree of freedom in generating contents, achieving fine-grained collaborative motion control is even harder for image animation than text-based video generation. + +Camera Motion Control. Works for camera motion control [3, 8, 9, 31, 37, 41, 47, 51] aim to generate novel view images with spatial consistency. In computer graphics, camera information is typically represented using a set of intrinsic and extrinsic parameters. Methods like MotionCtrl [37] directly repeat these flattened camera parameters to image size as control signals. CameraCtrl [9] and CamCo [41] transform the camera parameters into Plücker coordinates as pixel-wise embeddings, which is more discriminative. ViewCrafter [47] and I2V-Camera [3] lift the reference image to 3D and render the point cloud to generate incomplete frames. SparseCtrl [8] and DimensionX [31] generate a specific set of training data for each type of camera motion and train individual LoRA models [12] tailored for each camera motion pattern. Concurrent work TrajectoryAttention [40] uses dense pixel trajectories to enhance temporal consistency, which is effective for camera motion control but hard to further support object motion control. Compared to high-level camera motion representations, our 3D-aware motion representation embodies camera motion information via visual changes of the world envelope, which is more intuitive and effective. + +Object Motion Control. Previous works usually follow the drag-based interaction setting for object motion control [18, 25, 29, 38, 46, 49], which conveys user inten + +tions via sparse point trajectories. Methods such as DragNUWA [46], ImageConductor [18], Motion-I2V [29] and MOFA-Video [25] employ optical flow as an intermediate motion representation. The former two methods transform point trajectories into sparse optical flow as control signals, while the latter two methods transform sparse point trajectories into dense optical flows via off-the-shelf or pretrained sparse-to-dense flow generation models. Tora [49] enhances point trajectories into a trajectory map and employs 3D VAE to encode it. DragAnything [38] obtains features for each pixel via DDIM inversion [30] and reorganizes those features according to segmentation masks and point trajectories while being less effective in handling motions containing shape variations. Although the above methods support camera control using point trajectories, they suffer from conflict control issues in local regions with simultaneous camera and object motions. Instead of modifying 2D motion representation, we employ a simplified 3D scene and use its inherent perception results as control signals to avoid control conflicts. Due to this design, diffusion models can handle both local object motion and global camera motion simultaneously. + +Collaborative Motion Control. Only a few concurrent works [4, 5, 17] support collaborative motion control. ImagineAnything [17] applies two-stage generation, one for transforming camera and object control into optical flow representation, the other for generating videos based on that. However, they represent camera motion as Plücker embeddings, which is heterogeneous to optical flow and may lead to imprecise control. MotionPrompting [5] employs dense point embeddings constructed from 2D point tracking results as motion control signals, while such representation is not friendly enough for complicated motion control. I2VControl [4] also employs dense point embeddings constructed via point transform and projection, while the granularity of object motion control is limited to object segmentation masks. In contrast, we propose Perception-as-Control, which takes motion control signals derived from efficiently constructed 3D-aware motion representation and achieves fine-grained collaborative motion control. + +# 3. Perception-as-Control + +As shown in Fig. 3, our approach consists of three primary parts: a data curation pipeline for constructing 3D-aware motion representation from in-the-wild videos, an image animation framework for motion-controllable video generation, and a three-stage training strategy to facilitate fine-grained collaborative motion control. + +# 3.1. Preliminaries + +Video Diffusion Model (VDM) [2, 7, 44] adopts the foundational principles of image diffusion probabilistic models and models the temporal dependencies between frames, re + +![](images/5dcf7ea51e5118e07c40ccf8e7d942552e58d3f6afa5c9e8d800503efdbd4eb0.jpg) + +![](images/efa9da131a1d2a5412ab8469349d2ab6858c8fd40fac3d0fbca8e30ede0b8b4c.jpg) +Figure 3. Overview. In our data curation pipeline, an in-the-wild video is taken as input, and off-the-shelf algorithms are applied to obtain camera poses and 3D point locations. Based on the results, 3D-aware motion representation can be constructed and rendered to derive camera and object control signals. During training, those control signals are fed into separate encoders to avoid RGB-level interference and merged afterward. A three-stage training strategy is introduced to achieve fine-grained collaborative motion control. During inference, user intentions are first interpreted as 3D-aware motion representation, enabling our framework to support various motion-related applications. + +![](images/3961505b3753c5cd9e1113ea9b82d4faae361b0766595a4f6803c5ea51d13629.jpg) + +sulting in videos with consistent visual content and coherent motion. Let $x_0 \in \mathbb{R}^{L \times H \times W \times C}$ denote the initial video latent, where $L$ is the number of frames. The forward process is defined as a chain that progressively adds Gaussian noise to the original video, as shown in Eq. 1: + +$$ +x _ {t} = \sqrt {\hat {\alpha_ {t}} x _ {t - 1}} + \sqrt {1 - \hat {\alpha_ {t}} \epsilon}, \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), \tag {1} +$$ + +where $t \in \{1, \dots, T\}$ denotes diffusion timestep, $\hat{\alpha}_t$ regulates the intensity of noise added at each $t$ , and $\epsilon$ is drawn from standard Gaussian noise. The optimization objective is to predict the probability distribution $p(x_{t-1} | x_t)$ using a parameterized network $\theta$ . The loss function is in Eq. 2: + +$$ +\mathcal {L} _ {\theta} = \mathbb {E} _ {x _ {0}, \epsilon , \mathcal {C}, t} [ \| \epsilon - \hat {\epsilon} _ {\theta} (x _ {t}, \mathcal {C}, t) \| _ {2} ^ {2} ], \tag {2} +$$ + +where $\mathcal{C}$ is an optional parameter denoting the conditions, such as reference images and motion control signals. + +# 3.2. 3D-aware Motion Representation + +For training purposes, pairs of video clip and the corresponding 3D-aware motion representation are required. Unfortunately, commonly used large-scale video datasets predominantly consist of in-the-wild videos lacking camera settings and scene information. Reconstructing a delicate 3D scene is computationally expensive and the scale ambiguity issue leads to non-negligible reconstruction errors. + +Alternatively, constructing the simplified 3D scene directly via appropriate approximations can bypass these problems and is readily achievable even for in-the-wild videos. Thus, we introduce our data curation pipeline, using off-the-shelf algorithms to construct 3D-aware motion representation for any collectible video. + +SceneCut Detection and Motion Filtering. First, we apply common preprocessing steps to extract video clips containing continuous visual contents. We employ PySceneDetect [33] to split videos into video clips. Then, we use RAFT [32] to estimate optical flow for each video clip and use the Frobenius norm as a motion score to filter out video clips with non-obvious motion (motion scores lower than $30^{\text{th}}$ percentile), the same as previous methods [18]. + +3D Point Tracking for Local Object Motion. Key object parts refer to not only moving object parts but also stationary ones, which are critical for revealing spatial relations. They are simplified as unit spheres in the 3D scene, and the number of these spheres is defined according to the control granularity flexibly. We require 3D locations of key object parts at each moment to set these spheres initially and manipulate their movements. Therefore, we employ SpaTracker [39] to achieve 3D point tracking in each video clip. Note that combining algorithms of 2D point tracking [15] and depth estimation [26, 42, 43] also helps. In our implementation, we track $25 \times 25$ grid points + +for each video clip, resulting in 3D point tracking results $\mathbf{P} = [\mathbf{P}^{\mathrm{x}},\mathbf{P}^{\mathrm{y}},\mathbf{P}^{\mathrm{z}}]^{\top}\in \mathbb{R}^{L\times N\times 3}$ ( $L$ is the number of frames and $N$ is the number of tracked points). + +Camera Pose Estimation for Global Camera Motion. We employ a world envelope to mark the remaining parts, which is stationary relative to the world coordinate system. To transform global camera motion into visual changes, we can use off-the-shelf algorithms [36, 50] to recover camera trajectories from a sequence of continuous frames and render the world envelope. Despite the scale ambiguity problem, our world envelope, which serves as a scene marker, only requires coarse camera poses instead of extremely precise ones. In our implementation, we employ TartanVO [36] for this purpose, since it is fast and generalizes well across various cameras. Camera intrinsic parameters are set to $\mathbf{K} = [W,0,W / / 2;0,H,H / / 2;0,0,1]$ , where $W$ and $H$ are the width and height of the first frame. For each video clip, we obtain the estimated camera poses $\mathbf{E} = \{\mathbf{E}_l|l\in \{1,2\dots ,L\}\}$ , where $L$ is the number of frames, $\mathbf{E}_l = [\mathbf{R}\in \mathbb{R}^{3\times 3},\mathbf{t}\in \mathbb{R}^{1\times 3}]$ are camera extrinsic parameters at frame $l$ . + +Perceptual 3D Scene Rendering. Once we have obtained the 3D point tracking results $P$ and the estimated camera poses $E$ , we construct our 3D-aware motion representation and render it as motion control signals. + +First, we set $N$ unit spheres with different colors representing key object parts. These spheres are rendered on the pixel plane according to a specific camera pose and appear as circles that are larger near and smaller far away in the rendering images under perspective projection. Since the estimated depth is not precise enough in some cases, we normalize point depths $\mathbf{P}^{\mathrm{z}}$ as $\mathbf{P}^{\mathrm{d}}$ for each video clip to only focus on their relative distance. After that, we set the projected circle radius of the $n^{\mathrm{th}}$ sphere to $1 - \mathbf{P}_{l,n}^{\mathrm{d}}$ ( $\mathbf{P}_{l,n}^{\mathrm{d}}$ is the normalized depth of the $n^{\mathrm{th}}$ sphere at frame $l$ ). For convenience, we generate a continuous color map where each pixel has a distinct color. We then set the color of each sphere to the corresponding color of its projection center in the first frame. Finally, these spheres are projected and rendered as colorful circles with varying radii. + +Then, we construct a cube centered at the origin with the side length of $z_{\mathrm{far}}$ ( $z_{\mathrm{far}}$ is the far clipping plane of a viewing frustum) as an implementation of our world envelope. We apply checkerboard textures to increase the recognizability of the world envelope, which helps demonstrate how the scene evolves as the viewpoint changes. We align the camera coordinate system to the world coordinate system for the first frame and render the subsequent frames according to the relative camera pose sequence $E$ , without loss of generality. Note that the implementation of the world envelope is not limited to a cube, and its textures can vary beyond the checkerboard style. To avoid RGB-level interference, we render unit spheres and world envelope separately as two + +spatial layers, acting as object and camera control signals respectively. + +# 3.3. Network Architecture + +We propose an image animation framework to incorporate our 3D-aware motion representation, which takes a reference image and a sequence of spatially aligned motion control signals as input and generates a video as output. + +As shown in Fig. 3, our framework is based on a denoising U-Net architecture, with extra motion modules [7] for modeling temporal information. Under the image animation setting, it is essential to preserve the appearance information contained in the reference image (image control signals) and follow the motion information contained in motion control signals. Previous methods inject control signals by directly adding them to the input noise [21, 24] or integrating them into denoising U-Net through auxiliary architectures [9, 13, 23, 25, 37, 45, 48]. Given that the motion control signals are already spatially aligned, in our framework, we inject motion control signals by adding them to the noise and inject the reference image via ReferenceNet [13] for better appearance preservation. Specifically, we use two lightweight encoders to encode camera and object control signals separately, avoiding RGB-level interference, and then use a fusion module to merge them as the final motion control signals. We implement the fusion module empirically as a convolution block. + +During training, training data are prepared through our data curation pipeline, and a three-stage training strategy is applied for balancing camera and object motion control. During inference, user intentions conveyed in various forms are transformed into motion control signals via 3D-aware motion representation, as the input of our framework. + +# 3.4. Training Strategy + +Although both camera and object motions can be transformed into unified and consistent visual changes through 3D-aware motion representation, video clips with entangled motions increase the difficulty of training. + +Stage 1: Camera Motion Control Training. In the first stage, we use video clips from RealEstate-10K[52] with camera motion only to train our camera encoder. We temporarily exclude object encoder and fusion module from the framework. Since pure viewpoint changes bring about coherent and consistent overall scene movements, we train motion modules together to capture the correspondence between changes of the world envelope and scene contents. Thus, we optimize camera encoder, motion modules, and ReferenceNet in this stage. + +Stage 2: Collaborative Motion Control Training. In the second stage, we add video clips from WebVid-10M[1] that contain both camera and object motions for training. We add object encoder and fusion module back for collabor + +![](images/5381180c20996a73bb174737343c28be827eec933d52fb0a3270029c15ee6da6.jpg) +Figure 4. Results of fine-grained collaborative motion control. + +rative motion control. Motion modules are optimized to align each rendered unit sphere with its corresponding object parts, since the initial location of each unit sphere is not restricted. To speed up the alignment between unit spheres and object parts, we use dense unit spheres in this stage. We fix camera encoder and optimize object encoder, fusion module, motion modules, and ReferenceNet. Moreover, to preserve the effectiveness of both control signals, especially in conflict cases, we randomly drop one type of control signal at a fixed rate for RealEstate10K video clips. + +Stage 3: Dense-to-Sparse Fine-tuning. This stage aims to achieve fine-grained motion control with our world envelope and sparse unit spheres, which requires the model to determine each sphere's control range adaptively. Considering that object motion tends to occur on salient objects, we employ an off-the-shelf segmentation algorithm [19] to obtain salient objects in the reference image and select unit spheres inside their mask as Set1. Then we calculate the trajectory length of each unit sphere and select those with a trajectory length higher than the $80^{\mathrm{th}}$ percentile as Set2. By combining Set1 and Set2, we obtain the dense sphere set and randomly sample $N \in \{1, 2, \dots, 16\}$ spheres from it per iteration. In this stage, we fix all components except fusion module and motion modules during training. + +For all stages, the loss function is in Eq. 3: + +$$ +\mathcal {L} = \mathbb {E} _ {x _ {0}, c _ {\mathrm {i m g}}, c _ {\mathrm {c a m}}, c _ {\mathrm {o b j}}, t} [ | | \epsilon - \epsilon_ {\theta} (x _ {t}, c _ {\mathrm {i m g}}, c _ {\mathrm {c a m}}, c _ {\mathrm {o b j}}, t) | | ^ {\frac {2}{2}} ], \tag {3} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ is drawn from standard Gaussian noise, $t\in \{1,\dots ,T\}$ denotes the diffusion timestep, and $c_{\mathrm{img}}$ , $c_{\mathrm{cam}}$ , $c_{\mathrm{obj}}$ are the reference image, camera motion control signals and object motion control signals, respectively. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. We use video datasets RealEstate-10K [52] and WebVid-10M [1] for training. RealEstate-10K contains + +
FID↓FVD↓RotErr↓TransErr↓
CameraCtrl14.538178.4970.6480.203
Ours1411.79573.4490.6410.199
MotionCtrl17.081122.5700.9570.278
CameraCtrl*14.942136.6020.8370.257
MotionCtrl++16.327104.0200.9060.265
CameraCtrl*++12.923113.1650.7610.291
Ours9.67552.4210.7570.235
+ +Table 1. Comparison on RealEstate test set for camera motion control. CameraCtrl* denotes the 16-frame version we reproduced. + +
FID↓FVD↓ObjMC↓SubCon↑
Motion-I2V60.643367.52434.520.845
MOFA-Video26.895175.70130.260.944
MotionCtrl++32.528208.38728.570.959
CameraCtrl*++28.393164.65425.720.963
Ours16.465161.07623.320.968
+ +videos with pure camera motion, and each video is annotated with ground-truth camera parameters. WebVid-10M is a large-scale dataset containing in-the-wild videos with both camera and object motions. For our experiments, the training data contains around 61K video clips from RealEstate and 352K from WebVid. + +Metrics. We adopt Frechet Video Distance (FVD) [34], Frechet Inception Distance (FID) [10] to measure visual quality. ObjMC [37] and Subject Consistency (SubCon) in VBench [14] are used to measure object motion controllability and average rotation error (RotErr) and translation error (TransErr) [9] are used to measure camera motion controllability. We select 1K clips from RealEstate test set and 1K from WebVid test set for quantitative evaluation. + +Implementation Details. We adopt Stable Diffusion 1.5 (SD1.5) [28] as our base model, and initialize both denoising U-Net and ReferenceNet [13] using its pretrained weights. We add motion modules as in previous works [2, 7] with random initialization. During training, CLIP [27] image encoder and VAE [16] encoder and decoder remain frozen. The model generates videos with 16 frames at a resolution of $768 \times 512$ . We use AdamW [20] as optimizer. We conduct the training on 4 NVIDIA A100 GPU. We train around 20k iterations for both stage 1 and stage 2 with learning rate of 1e-5, and 50k for stage 3 with learning rate of 1e-6, with a batch size of 4 for convergence. + +Table 2. Comparison on WebVid test set for object motion control. + +
FID↓FVD↓ObjMC↓SubCon↑
2D point offset26.823254.90753.280.967
2D point position16.520177.71030.610.968
Sph (3D)16.458176.98929.470.968
Env + Sph (Ours)16.465161.07623.320.969
+ +Table 3. Ablation study on 3D-aware motion representation. Env denotes our world envelope and $Sph$ denotes 3D unit spheres. + +![](images/27da9893000e275324177f75366441d2bc4ffb9c6b746bfc2f285fdc2035c461.jpg) +Figure 5. Qualitative comparison with state-of-the-art methods regarding camera motion control. Reference images are generated by reconstructing point clouds based on the reference image and rendering them according to camera parameters. + +![](images/cc728bd5183e8ba614c99b72a7470ca2778ae7cfd8647b77409060f56bf76833.jpg) +Figure 6. Qualitative comparison with state-of-the-art methods regarding object motion control and simple collaborative motion control. + +
FID↓FVD↓ObjMC↓SubCon↑
One-stage59.040318.94136.720.959
Two-stage26.823254.90731.290.966
Three-stage (Ours)16.465161.07623.320.969
+ +Table 4. Ablation study on the proposed training strategy. + +# 4.2. Comparison with State-of-the-Art Methods + +We compare our approach with state-of-the-art methods in Tab. 1 and Tab. 2. We use the SVD version of MotionCtrl [37] and CameraCtrl [9] for image-based generation. MotionCtrl directly takes camera extrinsic parameters as control signals, and CameraCtrl uses Plücker embeddings. Motion-I2V [29] and MOFA-Video [25] employ dense optical flow as the final control signals. Since the proposed 3D-aware motion representation is orthogonal to specific base models, we also incorporate our representation into + +![](images/ffada782dffffaf586f64b7ad871fc8aede1e5efa8c5dd07ec73cc62ee53f6b9.jpg) +Figure 7. Qualitative evidence for ablation study. + +![](images/b5027382a7ddce5d0c4c91393d3d470d74b410392b0bd1e80014577e292cb7c6.jpg) + +CameraCtrl and MotionCtrl and train them following our training strategy to empower them with fine-grained collaborative motion control capability, denoted as CameraCtrl++ and MotionCtrl++, respectively (see Sec. B in Supp.). By incorporating our 3D-aware motion representation in CameraCtrl and MotionCtrl, their ++ versions perform better on camera motion control and are capable of collaborative motion control. Moreover, ours outperforms their ++ versions, which shows the superiority of our framework. + +Our approach achieves the best performance in terms of both camera and object motion control, as further evidenced in Fig. 5 and Fig. 6. In Fig. 5, we notice that CameraCtrl degrades on out-of-distribution camera trajectories such as large arbitrary ones and tends to lose details in later frames, and MotionCtrl fails to adhere to the designated camera trajectories strictly and causes image blurring under large camera motions. In contrast, our approach generalizes well and achieves precise camera motion control. From Fig. 6 we can observe that optical flow-based methods face conflict control issues in collaborative motion control and struggle to maintain object appearance under large motions. + +# 4.3. Ablation Study + +We conduct ablation studies to demonstrate the effectiveness of 3D-aware motion representation and validate the + +![](images/2c5ff3e415ad4486e27acfcdb31489c600ee7b2fde00443d8543c7a90ffbfceb.jpg) +Figure 8. Results on four kinds of motion-related applications. More details and results please refer to Supplementary Materials. + +necessity of our three-stage training strategy. In Tab. 3, $2D$ point offset refers to motion representations in previous works [18, 37], and $2D$ point position is similar to visualizing the projection of unit sphere centroids with a fixed radius. We have these observations: 1) $2D$ point offset underperforms others, and we argue that this form is neither as complete as dense optical flow nor visually aligned as point positions, making it hard to associate points with object parts in the reference image. 2) The lack of depth information in $2D$ point position makes the spatial relations less clear and harms performance (Fig. 7a). 3) Only using $3D$ unit spheres may cause the ambiguity problem (Fig. 7b). + +In Tab. 4. One-stage refers to directly optimizing all the modules mentioned using mixed data and Two-stage refers to merging the last two stages into one. The results show that our carefully designed training strategy is essential in reducing training difficulty and achieving harmonious collaborative motion control (See Sec. C in Supp.). + +# 4.4. Fine-grained Collaborative Motion Control + +Fig. 4 shows the superiority of Perception-as-Control on fine-grained collaborative motion control. For clarity, we project unit sphere centroids onto the reference image to visualize how they change over time (colors represent movement direction). In the first row, we set object motions for several hot air balloons, and the result precisely reflects each one. In the second row, when setting several unit spheres to the bamboo simultaneously, our approach adaptively determines the control range for each one. In the last two rows, we set both camera and object motions, the results adhere to the camera motion and present the adapted object motions (see Sec. A in Supp.). + +# 4.5. Applications + +As illustrated in Fig. 1, our approach has the potential to support various motion-related applications. More results + +are given in Fig. 8. For motion generation, we construct 3D-aware motion representation based on the reference image and manipulate it according to user-provided 2D/3D trajectories. Our approach handles motions including natural swaying, shape changes, intersections, and large displacements. For motion clone, we construct 3D-aware motion representation from the source video as motion control signals, and edit the first frame as the reference image. The results exactly mimic the entire motions (camera and object) in the source video. For motion transfer, we extract 3D trajectories of unit spheres corresponding to semantic points and relocate them to match those in the reference image. The results show that local motions from the source video are successfully transferred to objects that differ in scale and location. For motion editing, we partially manipulate the 3D-aware motion representation based on user-specified regions, e.g., reset unit sphere trajectories or viewpoint changes. 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In this paper, we make the observation that a defocused image can be viewed as a blend of illuminated blobs based on fundamental imaging principles, and the defocus blur in the defocused image is caused by large illuminated blobs intermingling with each other. Thus, from a novel perspective, we perform SIDD by adjusting the shape and opacity of the illuminated blobs that compose the defocused image. With this aim, we adopt a novel 2D Gaussian blob representation for illuminated blobs and a differentiable rasterization method to obtain the parameters of the 2D Gaussian blobs that compose the defocused image. Additionally, we propose a blob deblurrer to adjust the parameters of the 2D Gaussian blobs corresponding to the defocused image, thereby obtaining a sharp image. We also explore incorporating prior depth information via our depth-based regularization loss to regularize the size of Gaussian blobs, further improving the performance of our method. Extensive experiments on five widely-used datasets validate the effectiveness of our proposed method. + +# 1. Introduction + +Single image defocus deblurring (SIDD) aims to reconstruct an all-in-focus image from a single defocused and blurry input. SIDD is essential for removing unwanted blur from captured images, which often contain defocus blur resulting from photographing scenes with varying depths. Deblurring images through SIDD can also significantly enhance the performance of downstream machine vision tasks (e.g., object detection [6, 9] and semantic segmentation [34, 53]) for important practical applications. Existing SIDD works can be broadly divided into two approaches: i) Conventional SIDD approaches typically employ a two-step process involving defocus map estimation [8, 11, 16, 18, 28, 60] followed by deconvolution meth + +![](images/22dbbf0531a2fc5ef65d55da8c9a7c3213eb4a2707adef010a976814d9da2f6b.jpg) +Figure 1. Due to the varying distances between objects and the lens, the sizes of the illuminated blobs formed on the film plane differ, resulting in some objects appearing sharp while others appear blurred (i.e., with larger illuminated blobs). + +ods [3, 12, 21] using the estimated defocus maps for defocus deblurring. ii) Recently, end-to-end deep learning-based approaches [2, 24, 36-38, 45, 49] have been introduced for SIDD, where a deep neural network (DNN) is trained to map defocused images to their sharp counterparts. Existing state-of-the-art (SOTA) methods [37-39] are mostly based on deep learning, and typically focus on learning the defocus kernel or its inverse, employing intricately designed networks that utilize the learned defocus kernels or inverse kernels for SIDD. Despite recent progress in SIDD, the task remains challenging, particularly in scenarios involving defocus blur with large blur areas [38, 49], severely blurred regions [36], and irregularly shaped blurs [24, 45]. There are also challenges in terms of the model's ability to generalize across different datasets [37]. + +To better address the challenging SIDD task, it is crucial to review how the phenomenon of defocus blur is formed from fundamental imaging principles. As shown in Fig. 1, defocus blur is a common "degradation" in optical systems caused by variations in scene depth during image capture. Within an optical system (e.g., camera), lenses are employed to refract incoming light, directing the light rays to converge at the apex of a conical path. When an object is positioned such that the apex of this cone aligns precisely with the film plane, the light rays form small illuminated blobs on the film plane, rendering the object in sharp focus. This specific distance where objects appear sharp and clear is known as the focal plane. Objects positioned away from the + +focal plane cause the light rays to diverge, forming larger illuminated blobs on the film plane that intermingle with other blobs, thus producing a blurry appearance in the captured image [45, 49]. Hence, due to the inherent physical properties of the camera and its lenses, defocused images can be interpreted as being composed from numerous illuminated blobs of varying sizes, where the larger illuminated blobs lead to defocus blur in the resulting images. It is worth noting that the illuminated blobs here are not necessarily perfectly circular; they match the shape of the aperture and can also be oval, polygonal, or other shapes [42, 54]. + +In this work, based on the insights from defocused photography discussed above, we approach SIDD from a novel perspective, by modeling the formation process of defocused images. Then, by leveraging the modeled formation process, we can effectively perform deblurring on the defocused images to obtain sharp images. However, it is very challenging to model the formation process of a defocused image, since it is an inherently ill-posed problem. This difficulty arises because we often lack crucial information, e.g., the camera's focal length and aperture size, making it difficult to directly apply optical principles to compute the resulting defocus blur. Consequently, a key question naturally emerges: how do we tackle SIDD according to the fundamental optical imaging principles of photography, despite its challenges and ill-posed nature? + +To address the above question and effectively model the formation process of defocused images, we draw inspiration from 3D Gaussian Splatting (3D GS) [19], a method for 3D scene representation that has gained significant attention in the areas of 3D scene deblurring [22], single-view reconstruction [27, 46, 50, 56, 68], novel view synthesis [4, 5, 10, 33, 67], 3D generation [51], and image compression [63]. Specifically, inspired by Deblurring 3D GS [22] and GaussianImage [63], we propose a novel approach that represents defocused images as stacks of 2D Gaussian blobs, i.e., via 2D Gaussian blob representation [63]. Intuitively, by representing the defocused images with a set of 2D Gaussian blobs, we encourage each 2D Gaussian blob to model an illuminated blob that contributes to the defocused image, which allows us to better model the formation process of the defocus blur. Our method involves several key designs: First, to represent the defocused image via the 2D Gaussian blob representation, we design a rasterization method to facilitate optimization in an end-to-end differentiable manner. Next, after modeling the formation of the defocused image via our 2D Gaussian blob representation, we introduce a blob deblurrer that adjusts the shape and opacity of each 2D Gaussian blob to perform the deblurring. The adjustment by the blob deblurrer reduces the blur on defocused images by decreasing the size of the 2D Gaussian blobs (i.e., illuminated blobs) and reducing their intermingling. Finally, to further improve the + +quality of the conversion process between the defocused images to 2D Gaussian blobs, we enhance our method with a depth-based regularization loss using pre-trained depth estimators, which leads to further performance gains. + +By taking a different approach as compared to previous methods, our proposed method holds a few advantages. To be specific, traditional two-stage SIDD methods typically rely on manually defined kernels to estimate the defocus blur, but the blurring patterns in real-world defocused images can be quite complex and may not conform to these manually defined kernels. Thus, trying to model the complex blurs with manually defined kernels may impede accurate defocus map estimation and successful defocus deblurring [45, 49]. Our method does not employ defocus map estimation and does not rely on any such kernels, thus we avoid facing such errors. On the other hand, current SOTA end-to-end DNN-based SIDD approaches [37-39] often operate under the assumption that the blurring in an image can be modeled by blurring kernels which are applied in a convolutional manner to the original sharp image. Through this modelling, they attempt to learn the inverse kernels (deconvolutional kernels) to effectively deblur the images. However, these works make the assumption that the blurring in the image is the result of a (convolutional) kernel, which might not hold well in real-world scenarios. Therefore, since our method does not rely on such assumptions, we avoid such issues that may affect our performance. Overall, our approach achieves more effective deblurring and demonstrates strong generalizability, as shown by our extensive experiments. + +In summary, our contributions are as follows: (i) We tackle SIDD from a novel perspective, by viewing defocused images as blended illuminated blobs based on fundamental imaging principles. (ii) We propose a deblurring framework for performing SIDD on defocused images represented by 2D Gaussian blobs, that adjusts the size, shape and opacity of the 2D Gaussian blobs to achieve deblurring. (iii) To further improve performance, we introduce a depth-based regularization loss to regularize the Gaussian blob optimization process, regularizing the sizes of Gaussian blobs based on prior depth information. (iv) We conduct extensive experiments to assess the performance of our proposed framework, where we demonstrate SOTA performance across multiple benchmarks. + +# 2. Related work + +Two-stage SIDD. Conventional SIDD typically employs a two-stage approach: estimating a defocus map [3, 8, 11, 16, 18, 23, 28, 35, 48, 55, 60, 64, 65] from the input defocused image, followed by applying the non-blind deblurring methods [12, 21, 25, 28, 31, 41, 58] using the defocus kernels derived from the defocus map. The majority of two-stage approaches for the SIDD focus predominantly on the initial + +![](images/0dbaaba3dbb655e666a375435309520f515f3b8f2b9d8210fa67557935ad38e5.jpg) +Figure 2. Illustration of our proposed SIDD pipeline. We first represent the defocused image using illuminated blobs (2D Gaussian blobs) through a rasterization method. Then, we adjust the size, shape, and opacity of the 2D Gaussian blobs with a blob deblurrer to minimize the intermingling between the blobs, thereby enhancing the clarity of the resulting image. + +stage—defocus map estimation. The subsequent stage typically involves implementing existing non-blind deconvolution techniques [12, 21, 25]. Significant effort [16, 35, 48] has been dedicated to enhancing the accuracy of defocus map estimation, as it substantially influences the performance of deblurring processes. Despite significant efforts by researchers, the two-stage approaches for the SIDD still exhibit limitations. First, blur kernel estimation is typically based on manually defined kernels and may lack precision. Second, even with an accurately estimated blur kernel, deconvolution can introduce ringing artifacts along edges due to the Gibbs phenomenon [57]. Unlike traditional two-stage SIDD methods, which typically rely on manually defined kernels for defocus map estimation and subsequently deblurring defocused images, our method takes a novel perspective to SIDD. We represent defocused images using 2D Gaussian blobs and perform deblurring by adjusting the shape and opacity of these blobs. + +End-to-end DNN-based SIDD. Recently, deep end-to-end learning has emerged as a promising approach for SIDD, with researchers increasingly adopting end-to-end DNN to directly restore sharp images from defocused images. The seminal work [1] involves training an encoder-decoder CNN that maps a defocused image to its in-focus counterpart, achieving significant performance gains over traditional two-stage methods. Deep end-to-end learning-based SIDD methods [2, 7, 17, 24, 26, 29, 32, 36-38, 44, 45, 49, 61, 66] generally surpass conventional two-step approaches in both performance and efficiency. However, current SOTA deep end-to-end learning approaches [37-39] for SIDD assume that the defocus blurring in the image can be modeled by a convolutional kernel, an assumption that may not be valid in real-world scenarios. Different from current SOTA deep end-to-end learning SIDD methods [37-39], our approach does not assume that the blur in defocused images is caused by specific blur kernels. We approach SIDD from a novel perspective by modeling the formation of defocused images based on fundamental imaging principles, specifically modeling how such defocused images result from the blending of various illuminated blobs. After representing the image with 2D Gaussian blobs, we adjust the size, shape and opacity of the blobs to reduce the intermingling between pixels, thereby yielding sharper images. + +3D Gaussian Splatting (3D GS). 3D GS [19] represents + +a significant advancement in 3D scene representations, enabling high-quality real-time rendering, and has been applied across various domains, including 3D scene deblurring [22], single-view reconstruction [27, 46, 50, 56, 68], novel view synthesis [4, 5, 10, 33, 67], 3D generation [13, 15, 51], and image compression [63]. Since 3D GS is an efficient representation [19, 63], its applications have led to significant advancements within each respective domain. In this paper, we adopt a novel perspective to model the fundamental principles underlying defocus deblurring. Inspired by [22, 63], we represent the defocused image using blended 2D Gaussians blobs, and adopt a rasterization method to facilitate the optimization. Our proposed approach effectively models the blur of the defocused image from the standpoint of imaging principles, leading to improved SIDD performance. + +# 3. Method + +Defocus blur is a degradation phenomenon in optical systems when capturing images of scenes with varying depths. Objects that are out of the focal plane have their light rays diverge, forming large illuminated blobs on the film plane that overlap with others, causing the objects to appear blurry in the captured image. To recover an all-in-focus image with sharp and clear details from a defocused image, our key insight is that we can represent the defocused image in terms of "illuminated blobs", and then we can adjust the size, shape, and opacity of the illuminated blobs in defocused images to minimize the intermingling between them, thereby enhancing the clarity of the resulting image. The overall pipeline of our method is depicted in Fig. 2. + +Specifically, from a new perspective, we propose using 2D Gaussian blobs to represent illuminated blobs in defocused images. To render images from 2D Gaussian blobs, we adopt a differentiable rasterization method (Sec. 3.1). Then, we introduce a blob deblurrer (Sec. 3.2) to adjust the size, shape and opacity of each 2D Gaussian blob, thereby performing the deblurring. Additionally, to improve the fitting of the defocused image to our 2D Gaussian blob representation, we design a depth-based regularization loss (Sec. 3.3), which regularizes the sizes of 2D Gaussian blobs based on their depths, since the size of illuminated blobs is often highly correlated with depth. Finally, we detail the + +training and testing processes of our method (Sec. 3.4). + +# 3.1. Fitting to our 2D Gaussian blob representation + +To represent the illuminated blobs that comprise defocused images, inspired by [22, 63], we adopt a 2D Gaussian blob representation. Specifically, given an input defocused image, we first fit it with the 2D Gaussian blob representation, where the image is represented with $N$ Gaussian blobs. Intuitively, by representing the defocused image with a set of 2D Gaussian blobs, we encourage each 2D Gaussian blob to model an illuminated blob of the defocused image, thereby allowing us to model the formation process of the defocused image. Next, to obtain the defocused image from the 2D Gaussian blob representation, we develop an efficient rasterization method to render the image formed by these 2D Gaussian blobs, which facilitates the optimization process of representing the input image with 2D Gaussian blobs. In this subsection, we first describe our 2D Gaussian blob representation, followed by the rasterization method used for rendering these 2D Gaussian blobs. + +2D Gaussian blob representation. Defocused images consist of a stack of illuminated blobs that are blended together, and our goal is to model these illuminated blobs, thereby modeling the formation process of the defocused images. Yet, this can be challenging, since illuminated blobs can take various shapes (e.g., oval, polygonal, etc) based on the shape of the aperture [42, 54], as well as various sizes and colors. To address this challenge, we represent the defocused image with $N$ 2D Gaussian blobs [63], where each Gaussian blob contains a set of attributes (i.e., parameters) representing the location ( $u$ ), size and shape ( $\Sigma$ ), color ( $c$ ), and opacity ( $o$ ). These parameters enable our Gaussian blobs to effectively model and approximate circular/polygonal/oval shapes of various sizes, while also accounting for individual color and opacity. Below, we detail each attribute and how they are encoded. + +Specifically, the distribution represented by each $i$ -th Gaussian blob $G_{i}(x)$ can be defined as: + +$$ +G _ {i} (x) = \exp \left(- \frac {1}{2} \left(x - u _ {i}\right) ^ {\top} \Sigma_ {i} ^ {- 1} \left(x - u _ {i}\right)\right), \tag {1} +$$ + +where $u_{i}\in \mathbb{R}^{2}$ encodes the position of the $i$ -th 2D Gaussian blob, i.e., the coordinates of the central point, $\Sigma_{i}\in \mathbb{R}^{2\times 2}$ is the covariance matrix that determines the shape and size of the Gaussian blob, while $x\in \mathbb{R}^2$ is the variable encoding the location of the queried point on the image. In particular, the covariance matrix $\Sigma_{i}$ encodes the rotation and scaling of the Gaussian blob, and needs to remain positive semi-definite during parameter updates to maintain a feasible shape. Therefore, to naturally enforce this constraint during parameter updates, we follow [63] by further decomposing the covariance matrix $\Sigma_{i}$ and optimizing the decomposed form instead. The covariance matrix $\Sigma_{i}$ is decom + +posed as follows: + +$$ +\Sigma_ {i} = R _ {i} S _ {i} S _ {i} ^ {\top} R _ {i} ^ {\top}, \text {w h e r e} +$$ + +$$ +R _ {i} = \left[ \begin{array}{c c} \cos (\theta_ {i}) & - \sin (\theta_ {i}) \\ \sin (\theta_ {i}) & \cos (\theta_ {i}) \end{array} \right], \quad S _ {i} = \left[ \begin{array}{c c} s _ {1, i} & 0 \\ 0 & s _ {2, i} \end{array} \right]. \tag {2} +$$ + +Here, $\theta_{i}$ represents the rotation angle, and $s_{1,i}$ and $s_{2,i}$ are scaling factors along the directions of each eigenvector. Importantly, with this decomposition, we can freely update the parameters $\theta_{i}, s_{1,i}, s_{2,i}$ while naturally constraining $\Sigma_{i}$ to be positive semi-definite. This is because $\Sigma_{i}$ is the result of multiplying matrix $R_{i}S_{i}$ with itself, thus ensuring that the resulting $\Sigma_{i}$ is positive semi-definite. + +Additionally, each $i$ -th 2D Gaussian blob has color parameters $c_{i} \in \mathbb{R}^{3}$ which are normalized RGB values, where the color of the Gaussian blob at each point $x$ is given by: + +$$ +c _ {i} (x) = c _ {i} \cdot \exp \left(- \frac {1}{2} (x - u _ {i}) ^ {\top} \Sigma_ {i} ^ {- 1} (x - u _ {i})\right). \quad (3) +$$ + +Note that each blob also has an opacity value $o_i \in \mathbb{R}$ , which is only applied during rasterization, as discussed below. + +Rasterization. Next, we need a way to convert input defocused images to the 2D Gaussian blob representation discussed above. One promising way is to randomly initialize a set of 2D Gaussian blobs, then follow the 3D GS [19] approach to optimize the Gaussian blob parameters to fit the input defocused image. Yet, this approach requires a rasterization technique to render images from the 2D Gaussian blob representation, which should also ideally be differentiable to facilitate convenient end-to-end optimization. To address these issues, we modify the tile rasterizer [19] to develop a differentiable and efficient rasterization method tailored to the 2D Gaussian blobs. We also note that 3D GS involves 3D to 2D projection with EWA [69] estimation, but, as we can directly represent 2D Gaussian blobs efficiently with no projection required, we can achieve much faster rasterization. + +Specifically, following the intuition that each defocused image can be seen as being composed of a stack of overlapping illuminated blobs, our rasterization method also regards the rendered image as a blend of layers, with each layer being a 2D Gaussian blob. Therefore, during rasterization, for each pixel in the rendered image, we compute the color of the pixel by blending the effects from all 2D Gaussian blobs, where the color $C(x)$ at a pixel location $x$ of the rendered image is computed as the cumulative sum of these 2D Gaussian blobs' colors weighted by their opacities: + +$$ +C (x) = \sum_ {i = 1} ^ {N} c _ {i} (x) \cdot o _ {i}, \tag {4} +$$ + +where $c_{i}(x)$ represents the color of the $i$ -th Gaussian blob at pixel location $x$ (calculated using Eq. (3)), and $o_{i}$ represents + +the opacity of the $i$ -th Gaussian blob. With this formulation, the rasterization process only uses differentiable operations, and is thus fully differentiable. Besides, our rasterization method is implemented in CUDA to make parallel calculations of pixel colors, thus making it efficient. + +2D Gaussian blob initializer. Yet, obtaining a good-quality Gaussian blob representation of the defocused image necessitates multiple rounds of rasterization and optimization, which can be time-consuming and may hinder the efficiency of our method in practical applications. To address this issue, inspired by previous works [50, 51], we design an efficient 2D Gaussian blob initializer which adopts a fully convolutional U-Net architecture [43]. The initializer is crafted to perform the transformation from an input defocused image to a high-quality initialization of its 2D Gaussian representation in a single step. + +# 3.2. Deblurring by adjusting Gaussians' attributes + +In the previous subsection, we discuss how to represent defocused images using 2D Gaussian blobs. Here, we explore how to effectively deblur these defocused images represented by 2D Gaussian blobs, by adjusting the size, shape and opacity of the 2D Gaussian blobs with our blob deblurrer. + +As discussed in Sec. 1, fundamental imaging principles suggest that defocus blur is caused by large illuminated blobs (see Fig. 1). Hence, to deblur defocused images, we need to adjust the size of these large illuminated blobs appropriately. To achieve this, we draw inspiration from [22] and design a blob deblurrer. As shown in Fig. 2, our proposed blob deblurrer takes the stack of 2D Gaussian blobs and their parameters as input, and modifies their covariance and opacity parameters. Modifying the covariance parameters reduces the size of the large Gaussian blobs (large illuminated blobs), removing the blurriness caused by the divergence of light rays that come from outside the focal plane (see Fig. 1). At the same time, because the luminous flux on the downscaled illuminated blobs should still remain consistent compared to their previous larger size, their brightness will also need to be adjusted. Hence, to allow for these adjustments, our blob deblurrer also adjusts the opacity of the 2D Gaussian blobs. Below, we explain our blob deblurrer in more detail. + +Blob deblurrer. Our blob deblurrer, denoted as $f_{bd}$ , is a Transformer model that takes as input the parameters of all $N$ 2D Gaussian blobs, where each $i$ -th Gaussian blob includes the parameters: central points $u_i$ , rotation matrix $R_i$ , scaling matrix $S_i$ , color $c_i$ , and opacity $o_i$ . + +Specifically, given the all $N$ Gaussian blobs as input, our deblurrer $f_{bd}$ performs a one-time forward pass to produce four outputs $(\Delta \theta_{i},\Delta s_{1,i},\Delta s_{2,i},\Delta o_{i})$ for each of the $N$ Gaussian blobs. Then, these outputs are used to update the Gaussian parameters, as follows: + +$$ +\Delta \phi_ {i} = \operatorname {c l a m p} \left(\Delta \theta_ {i}, \min = 0, \max = \pi\right), \tag {5} +$$ + +$$ +R _ {i} ^ {\prime} = \left[ \begin{array}{c c} \cos (\theta_ {i} + \Delta \phi_ {i}) & - \sin (\theta_ {i} + \Delta \phi_ {i}) \\ \sin (\theta_ {i} + \Delta \phi_ {i}) & \cos (\theta_ {i} + \Delta \phi_ {i}) \end{array} \right], \tag {6} +$$ + +$$ +S _ {i} ^ {\prime} = \left[ \begin{array}{c c} s _ {1, i} ^ {\prime} & 0 \\ 0 & s _ {2, i} ^ {\prime} \end{array} \right] \tag {7} +$$ + +where $\begin{cases} s_{1,i}' = \min \left(s_{1,i} - \mathrm{ReLU}(\Delta s_{1,i}), 0.1\right), \\ s_{2,i}' = \min \left(s_{2,i} - \mathrm{ReLU}(\Delta s_{2,i}), 0.1\right), \end{cases}$ + +$$ +o _ {i} ^ {\prime} = \operatorname {c l a m p} \left(\left(o _ {i} + \Delta o _ {i}\right), \min = 0, \max = 1\right). \tag {8} +$$ + +Here, the outputs $R_{i}^{\prime}, S_{i}^{\prime}$ , and $o_{i}^{\prime}$ represent the attributes of the modified 2D Gaussian blobs. Since our aim is to perform deblurring by reducing the size of the Gaussian blobs, we ensure that the scaling factors $s_{1,i}$ and $s_{2,i}$ are decreased by subtracting the non-negative values $\mathrm{ReLU}(\Delta s_{1,i})$ and $\mathrm{ReLU}(\Delta s_{2,i})$ respectively (see Eq. (7)). For improved training stability, we enforce lower bounds on $s_{1,i} - \mathrm{ReLU}(\Delta s_{1,i})$ and $s_{2,i} - \mathrm{ReLU}(\Delta s_{2,i})$ , ensuring they are clamped to values no less than 0.1. We also constrain the value range of the predicted $\Delta \theta_{i}$ based on the symmetric nature of the elliptical shape (see Eq. (5)), transforming it to $\Delta \phi_{i} \in [0,\pi]$ before applying $\Delta \phi_{i}$ to adjust the rotation matrix (see Eq. (6)). Besides, the term $o_{i} + \Delta o_{i}$ in Eq. (8) is clamped to the range [0, 1]. + +# 3.3. Depth-based regularization loss + +As discussed in Secs. 3.1 and 3.2, through our novel perspective, we are able to perform deblurring according to fundamental imaging principles by representing defocused images using 2D Gaussian blobs. However, the conversion of images to 2D Gaussian blobs may not always be so clear cut and can be quite ambiguous, with many different combinations to optimize the 2D Gaussian blobs. For instance, ambiguous areas of the image may be modeled with fewer but bigger blobs, or with more but smaller blobs. In these ambiguous cases, the optimization may depend on the initial placement of the Gaussian blobs, where if an area starts with fewer Gaussian blobs, it may tend to continue to use fewer blobs. The ambiguity and inconsistency of the Gaussian blob sizes in such situations may affect the effectiveness of our blob deblurrer in deblurring the images. + +To address this issue, we revisit the formation process of the illuminated blobs and observe that the size of each blob is often influenced by the relative distance between the corresponding object (point light source) and the focal plane, i.e., the depth difference between them. Thus, to resolve the ambiguity, we propose to leverage depth priors from a pre-trained depth estimator to regularize the Gaussian blob sizes. Below, we first introduce the relationship between the blob sizes and the depth differences, and then explain how to integrate depth priors into our framework. + +![](images/518e8ad37193a54fbc42aa04fa6543bc4cab4f8f1231d235dc4dd092259cd28d.jpg) +Figure 3. Visualizing the parameters of the imaging process. + +It is well known that, the diameter $D$ of the illuminated blob on the film plane caused by a point light source $p$ located outside of the focal plane, is calculated as follows [14]: + +$$ +D = \frac {f \cdot A}{d _ {2}} \cdot \left| \frac {d _ {2} - d _ {1}}{d _ {1} - f} \right| = \frac {f \cdot A}{\left| d _ {1} - f \right|} \cdot \left| 1 - \frac {d _ {1}}{d _ {2}} \right|, \tag {9} +$$ + +where $f$ is the lens' focal length, $A$ represents the diameter of the lens' aperture, $d_{1}$ and $d_{2}$ represent the distances from the focal plane and the point light source $p$ to the lens, respectively. See Fig. 3 for a visualization of these parameters. Since the values of $A$ , $f$ , and $d_{1}$ are constant for each defocused image, Eq. (9) can be rewritten as: + +$$ +D \propto \left| 1 - \frac {d _ {1}}{d _ {2}} \right|. \tag {10} +$$ + +As shown in Eq. (10), a linear relationship can be observed between the diameter $D$ of the illuminated blob and a function of the relative depths $|1 - \frac{d_1}{d_2}|$ . Next, guided by this relationship, we incorporate depth priors into our proposed framework to regularize the size of the Gaussian blobs. + +It is worth noting that our 2D Gaussian blob is represented as an ellipse, not a circle. Therefore, we denote its diameter $D$ using the area-equivalent diameter, which can be interpreted as the diameter of a circle with the same area as the ellipse. Thus, + +$$ +D = 2 \sqrt {D _ {\text {m a j o r}} \cdot D _ {\text {m i n o r}}}, \tag {11} +$$ + +where $D_{\text{major}}$ and $D_{\text{minor}}$ denote the lengths of the major and minor axes, respectively. In our method, the lengths of the major and minor axes, $D_{\text{major}}$ and $D_{\text{minor}}$ , are determined by the scaling factors $s_1$ and $s_2$ in the scaling matrix $S$ (see Eq. (2)). Hence, following Eq. (10), we can establish the relationship between scaling matrix parameters ( $s_1$ and $s_2$ ) and depth ( $d_1$ and $d_2$ ) as: + +$$ +\sqrt {s _ {1} s _ {2}} = K \left| 1 - \frac {d _ {1}}{d _ {2}} \right|. \tag {12} +$$ + +Then, reorganizing this expression leads us to the following equation: + +$$ +\frac {1}{K ^ {2}} s _ {1} s _ {2} d _ {2} ^ {2} + 2 d _ {1} d _ {2} - d _ {1} ^ {2} = d _ {2} ^ {2}. \tag {13} +$$ + +We note that in Eq. (13), the right side $(d_2^2)$ can be directly computed with the help of a depth estimator. Consequently, after we obtain the depth prior $d_{2}$ , they can act as guidance signals for the optimization of the left hand side, which consists of learnable parameters (i.e., $s_1, s_2, d_1, K$ ) to be optimized. Thus, the regularization loss $L_{\mathrm{reg}}$ can be defined as: + +$$ +L _ {\text {r e g}} = \left(d _ {2} ^ {2} - \left[ \frac {1}{K ^ {2}} s _ {1} s _ {2} d _ {2} ^ {2} + 2 d _ {1} d _ {2} - d _ {1} ^ {2} \right]\right) ^ {2} \tag {14} +$$ + +By applying $L_{\mathrm{reg}}$ to the Gaussians and using the depth values $(d_2)$ at their central points as guidance, we can regularize their sizes (i.e., the scaling matrix parameters $s_1$ and $s_2$ ) based on the depth information. We also note that, while $s_1$ and $s_2$ are parameters specific to individual Gaussian blobs, $d_1$ and $K$ are image-level parameters that remain fixed for a single image, meaning they are shared across all Gaussian blobs. As such, we treat $d_1$ and $K$ as learnable image-level parameters to be updated during training. Overall, by applying this depth-based regularization loss during the Gaussian blob optimization phase, we can regularize the size of Gaussian blobs according to their corresponding depths, which can improve the consistency of their sizes and facilitates better performance by the blob deblurrer. + +# 3.4. Training and testing procedures + +Training. Given the input defocused image $I_{d}$ , we first compute its depth map via a pre-trained depth estimator [40], and then generate the predicted deblurred image $I_{p}$ through the following steps: (i) We input the defocused image $I_{d}$ along with its depth map into the initializer (described at the end of Sec. 3.1) to obtain an initial 2D Gaussian blob representation $\Phi$ (Sec. 3.1). (ii) We optimize the image-level parameters $(d_{1}, K)$ and $\Phi$ to bring the rendering $I_{r}$ of $\Phi$ - which is rendered using rasterization (Eq. (4)) - closer to the input defocused image $I_{d}$ . For the optimization, we apply the loss $L$ , where + +$$ +L = \operatorname {M S E} \left(I _ {r}, I _ {d}\right) + \lambda_ {r} \cdot \operatorname {S S I M} \left(I _ {r}, I _ {d}\right) + \lambda_ {r e g} L _ {r e g}, \tag {15} +$$ + +and $\lambda_r, \lambda_{reg}$ are hyperparameters. (iii) The obtained 2D Gaussian blob representation $\Phi$ , its depth information $d_2$ , and the optimized image-level parameters $(d_1, K)$ are passed through the blob deblurrer (Sec. 3.2) in a one-time forward pass to perform deblurring and obtain the adjusted 2D Gaussian blob parameters $\Phi_a$ (Eqs. (6) to (8)). (iv) We render the image through rasterization (Eq. (4)) from $\Phi_a$ to get the deblurred image $I_p$ as our output. + +Testing. During testing, we are initially given an input defocused image $I_{d}$ . Then, we follow the steps (i, ii, iii, iv) discussed above to obtain the deblurred image $I_{p}$ . + +Table 1. Quantitative comparisons on DPDD and LFDOF datasets. Best and Second Best results are highlighted. + +
ModelDPDDLFOF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
DPDNet [1]24.3480.7470.277---
AIFNet [44]24.2130.7420.30929.6770.8840.202
IFANet [24]25.3660.7890.21729.7870.8720.156
KPAC [49]25.2210.7740.22628.9420.8570.174
GKMNet [36]25.4680.7890.21929.0810.8670.171
MDP [2]25.3470.7630.26828.0690.8340.185
DRBNet [45]25.4850.7920.25430.2530.8830.147
MPRNet [30]25.7300.7920.232---
Restormer [59]25.9800.8110.178---
INIKNet [38]26.0550.8030.18530.2930.8860.132
NRKNet [37]26.1090.8100.21030.4810.8840.147
GGKMNet [39]26.2720.8100.21530.5520.8860.154
Ours (w/o depth)26.4310.8270.17130.6600.8890.129
Ours26.6510.8350.16830.8850.8920.123
+ +# 4. Experiments + +# 4.1. Experiment setup + +Evaluation datasets and metrics. Following previous works [1, 38, 44], we train our models on two widely-used datasets, DPDD [1] and LFDOF [44]. To evaluate the generalization performance of our method, we also test our method on three additional datasets, RTF [11], RealDOF [24], and CUHK [47]. Since CUHK dataset [47] lacks ground truths, it is only used for qualitative evaluation. + +Evaluation metrics. Following previous works [38], we employ three metrics for quantitative evaluation: i) Peak Signal to Noise Ratio (PSNR); ii) Structural SIMilarity index (SSIM); iii) Learned Perceptual Image Patch Similarity (LPIPS) [62] assesses perceptual similarity between images using deep learning features, leveraging pre-trained neural networks to compare image patches, with lower values indicating higher perceptual similarity. + +Baselines. We select 12 representative NN-based SIDD methods for comparison, including DPDNet [1], AIFNet [44], IFANet [24], KPAC [49], GKMNet [36], MDP [2], DRBNet [45], Restormer [59], INIKNet [38], NRKNet [37], MPRNet [30], and GGKMNet [39]. We report experiment results for these baselines by referring to their published papers if they are available, otherwise we report the results using their released pretrained models and code. + +Implementation details. After obtaining the predicted 2D Gaussian blob parameters by the initializer, we optimize the defocused image's Gaussian parameters with the Adam optimizer [20] for 600 iterations. For all our experiments, we set $\lambda_r$ and $\lambda_{reg}$ to 0.3 and 0.2, respectively. We initialize $d_1$ as the average depth value from the predicted depth map corresponding to the defocused image, and set the initial value of $K$ to 0.05. Our initializer is an U-Net [43]. Note that the number of Gaussians $(N)$ for each image varies according to the initializer. Following previous SIDD meth + +Table 2. Quantitative comparisons on RealDOF and RTF datasets, with models trained on DPDD and LFDOF. Best and Second Best results are highlighted. + +
ModelRealDOFRTF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Trained on DPDDDPDNet [1]22.8700.6700.42523.6080.5910.296
AIFNet [44]23.0930.6800.41324.0410.7580.289
MDP [2]23.5000.6810.44424.0120.7380.312
KPAC [49]23.9750.7620.33824.6180.7770.236
IFANet [24]24.7120.7480.30624.9240.8010.227
GKMNet [36]24.2540.7320.39224.9700.7890.261
DRBNet [45]24.8840.7510.37624.4630.7730.311
MPRNet [30]24.5410.7360.33924.5880.7880.304
Restormer [59]25.0910.7620.28524.2120.8210.224
NRKNet [37]25.1480.7680.33825.9310.8290.215
INIKNet [38]25.2310.7650.28725.4500.8340.215
GGKMNet [39]25.3550.7700.32026.0120.8460.210
Ours (w/o depth)25.5670.7720.28126.1140.8550.207
Ours25.7930.7780.27826.2800.8640.204
ModelRealDOFRTF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Trained on LFOFIFANet [24]22.5040.6690.48326.4370.8380.238
KPAC [49]22.5500.6710.45725.9590.8030.230
AIFNet [44]22.6230.6670.46127.5520.8820.176
GKMNet [36]23.6090.7210.40826.9850.8560.246
MDP [2]22.7260.6800.45325.5800.8090.228
DRBNet [45]22.9100.6910.43726.7170.8530.200
NRKNet [37]23.5280.7160.43128.0470.8890.145
INIKNet [38]23.8100.7240.35627.4010.8850.179
GGKMNet [39]24.1080.7350.38528.3080.9050.140
Ours (w/o depth)24.2190.7500.36228.4510.9090.136
Ours24.4250.7620.35528.5850.9130.132
+ +ods [37, 38], we augment training images by applying random flipping, rotation, and cropping. Tile size for the rasterization is set to 16, which is also used as the block width in CUDA. Our blob deblurrer is a Transformer [52] that is composed of 3 blocks, each containing a feedforward network and a self-attention layer. We train the deblurrer for 20K iterations using the AdamW optimizer [20], starting with an initial learning rate of $5 \times 10^{-2}$ , which is gradually reduced to $2 \times 10^{-3}$ . In our work, we employ DPT [40] as the depth estimator, which is a vision transformer that performs full-resolution predictions at different stages of the model, providing fine-grained and globally coherent depth predictions. Notably, we observe that DPT often produces decent depth estimation results even in defocused regions (see Fig. 5 in the main paper and Fig. 1 in the supplementary material). + +# 4.2. Quantitative results + +DPDD and LFDOF datasets. In Tab. 1, we present the quantitative results on the DPDD and LFDOF datasets. Besides our full method (Ours), we also run experiments without using the depth information (i.e., the depth-based regularization loss in Sec. 3.3), and report the results as (Ours w/o depth). Even without using depth information, our method already consistently surpasses existing baselines across all metrics on both DPDD and LFDOF datasets. Moreover, when the depth-based regularization + +![](images/4b17abe39d73e90764d5fb6c7561f2e35816bd52425834c63c4ccf2d8e65dd77.jpg) +Figure 4. Qualitative comparison using models trained on the DPDD dataset. The visualization results are from the CUHK dataset. Note that CUHK does not provide ground truths. + +![](images/afe44bf7e46faf0c4fad413014919d9d1241fcad4c605d9bba5cc86bd0a534a6.jpg) + +![](images/0632607f40a59a6d7f19db24ba7a8b19234ef45dd07c2f32ef139cfd51e72eb0.jpg) + +![](images/8adcbdc0fb2bf371a436d246422fa1e39c6473602a5bfbd222b3b13160f61e4d.jpg) + +![](images/1a2d01edd37448a37f9160deeda4f6bc8cfb6b45f200de2c82eda7ec0ffcb3d1.jpg) + +![](images/d1e73c8762379420490aaaaf6844aafda717627b7462c36267894446f916bea8.jpg) + +![](images/46335882f6c2fc7af509e0e76e71b06cddbdc784d329b3927ab0d0e287f7c3a5.jpg) + +![](images/cf33da3c50411f2f41bad75f673c1083e5ed98f25fca3bc2a413589b8871ad8f.jpg) + +![](images/4b8262396c0c3eb078482bd121226161936329e768dc13f69b0ca2972696bdca.jpg) + +![](images/994740f9862366733f884d72f138496bebc5113bfabfe494e7c3afa97939bf61.jpg) + +![](images/e6c8457644157fbd876d70dfff19c8b6a916e8abba126ceb66355786c4db526a.jpg) + +![](images/cc102976dc550d7867bfa176bf601638e08b4a1071d3a621fef115b00dc694be.jpg) + +![](images/b3d2d51b812cb9ecb594ddcf492db93eb664a789af688f751070e3eb21874e8a.jpg) + +![](images/88d32ce1fef9a05757c4a597a468c271b8ca674ae1fe1b0955ea57888d9b8938.jpg) +Defocused image + +![](images/1b148a8ee71a7e69333db5bc019a4ae991504dda8444371301d372e861a04ebe.jpg) +ge Depth + +![](images/c1482eed4f86f78b5f045a06f44f8ce425c3fb34a6d74c4a1f54d5fe053d7c69.jpg) +Defocused image + +![](images/3c82b4a186cf72b6cb7bb01b1619b3c4a58a2ae0e8f9fc879eef3e59d7868755.jpg) +e Depth + +![](images/3521490f6840fa9246e8257ba2d44fe599b4e172facb24b6ebbb0ec4771bb7ad.jpg) +Figure 5. Defocused images from DPDD and CUHK datasets, with their corresponding estimated depth maps. + +![](images/67f9caee3bc36fb48533cffb7e5571692623c86f618d631d083054b8c6644566.jpg) +Defocused image +Depth +Defocused image + +![](images/4ce47490cb571db3a95d3663653b318418c4b0d38e0facce92ed6b3c98e8e473.jpg) + +![](images/370cc24f4ee9824a35268b7e0cd3df83683c870be477086301e5141aa522f380.jpg) +je Depth + +loss is added, our performance improves even further across all metrics, showing its efficacy. These results demonstrate the efficacy of our novel approach to SIDD, hinting at its huge potential. + +RealDOF and RTF datasets. The models trained on DPDD and LfDOF datasets are then evaluated on RealDOF and RTF datasets; results are reported in Tab. 2. We observe that, even without depth information, our method already attains SOTA performance across almost all metrics on both RealDOF and RTF. This demonstrates the strong generalization capabilities of our approach. Moreover, using the depth-based regularization loss (Sec. 3.3) leads to even better performance across all metrics. These results show the superior generalizability of our method compared to existing baselines. + +# 4.3. Qualitative results + +Qualitative comparison on CUHK dataset. In Fig. 4, we compare the visualization results of our method with the SOTA SIDD methods [36-39, 45] on CUHK dataset. In the second column we present the outputs of our method, and we observe that our method consistently produces clearer and sharper images compared to existing methods, achieving superior visual quality. For instance, compared to existing methods (columns 3-6), our method better recovers image structures and details, restores clearer text, and produces fewer artifacts. + +Visualization of the predicted depth map. We provide visualizations to demonstrate the quality of the depth maps generated by the pretrained depth estimation model DPT in Fig. 5. Note that, we perform this evaluation qualitatively since all datasets used in our experiments do not offer ground-truth depth information. From these visualizations, + +it can be observed that the depth maps produced by DPT often exhibit good quality, which can provide useful information for our depth-based regularization loss. + +# 4.4. More Experiments + +Analysis on adjustment of Gaussian blob size. To verify the efficacy of our method, we further investigate the impact of adjustments to the Gaussian blob size. As the scaling factors $s_1$ and $s_2$ in the Gaussian blob representation (Eq. (2)) determine the blob sizes, we first compute the average adjustments in the mean values of $s_1$ and $s_2$ before and after applying our method on the DPDD dataset. Specifically, on average across all test images in the DPDD dataset, the values of $s_1$ and $s_2$ decrease on average by $21.1\%$ and $18.9\%$ respectively after applying our method for deblurring. + +# 5. Conclusion + +In this paper, from a novel perspective, we perform Single image defocus deblurring (SIDD) by adjusting the illuminated blobs that comprise the defocused image. To this end, we adopt a novel 2D Gaussian blob representation and a differentiable rasterization method to obtain the corresponding 2D Gaussian blob parameters of the defocused image. Besides, we also introduce a blob deblurrer to perform defocus deblurring by modifying the size, shape and opacity of the 2D Gaussian blobs in our work. Moreover, we explore a depth-based regularization loss to further enhance the performance of our method. With the proposed framework, our method achieves good results on five widely-used datasets. + +# References + +[1] Abdullah Abuolaim and Michael S Brown. Defocus deblurring using dual-pixel data. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part X 16, pages 111-126. 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Existing 3D HPE approaches often use the cropped image alone as input for their models. However, the relative depths of joints cannot be accurately estimated from cropped images without the corresponding camera intrinsics, which determine the perspective relationship between 3D objects and the cropped images. In this work, we introduce Perspective Encoding (PE) to encode the camera intrinsics of the cropped images. Moreover, since the human subject can appear anywhere within the original image, the perspective relationship between the 3D scene and the cropped image differs significantly, which complicates model fitting. Additionally, the further the human subject deviates from the image center, the greater the perspective distortions in the cropped image. To address these issues, we propose Perspective Rotation (PR), a transformation applied to the original image that centers the human subject, thereby reducing perspective distortions and alleviating the difficulty of model fitting. By incorporating PE and PR, we propose a novel 3D HPE framework, PersPose. Experimental results demonstrate that PersPose achieves state-of-the-art (SOTA) performance on the 3DPW, MPIINF-3DHP, and Human3.6M datasets. For example, on the in-the-wild dataset 3DPW, PersPose achieves an MPJPE of $60.1\mathrm{mm}$ , $7.54\%$ lower than the previous SOTA approach. Code is available at: https://github.com/KenAdamsJoseph/PersPose. + +# 1. Introduction + +Estimating 3D human pose from a single image is a crucial task in computer vision, with numerous practical applications such as AR/VR and human-computer interaction. The objective of 3D human pose estimation (HPE) is to recover + +![](images/11c4bdad002c68248686effa726d9f6c5fabea78e6bf170ea0ca86fe3fff9442.jpg) +Figure 1. Comparison of previous 3D HPE frameworks and ours. + +the 3D coordinates of human joints from images, whereas 3D human pose and shape estimation (HPS) aims to predict the 3D coordinates of human mesh vertices. Some 3D HPS methods [4, 16, 24, 29, 42] treat 3D HPE as a sub-task, first estimating the 3D positions of the joints (or a larger set of mesh vertices) and then reconstructing the human mesh. + +Existing 3D HPE methods [15, 23, 28, 32, 36] and 3D HPS methods [4, 16, 17, 24, 29, 42] typically use cropped images as input to estimate 3D joint positions, meaning that the region corresponding to the human bounding box is cropped from the original image, as illustrated in Figure 1. However, the CLIFF method [18] demonstrates that using cropped images alone cannot accurately estimate global rotation (i.e., the orientation of the human in the camera coordinate system), thus it employs both bounding box information and the cropped images as inputs to the neural network. In this paper, we demonstrate through the example in Figure 2 that when only the cropped image is provided as input, the relative depths of joints cannot be accurately estimated either. Additionally, the example in Figure 3 reveals that even when the full image is used, the absence of field of view angle (FOV) information results in an inaccurate estimation of the joints' relative depths. Moreover, cropping can be con + +sidered as a modification of the camera intrinsics and sensor resolution; in this context, the camera intrinsics corresponding to the cropped image effectively encapsulate both the cropping and FOV information. We refer to the camera intrinsics corresponding to the cropped image as cropped intrinsics, denoted as $K^{\mathrm{crop}}$ , which include the focal length $f^{\mathrm{crop}}$ and the principal point coordinates $c_x^{\mathrm{crop}}$ and $c_y^{\mathrm{crop}}$ . We propose a Perspective Encoding (PE) module that encodes the cropped intrinsics as a 2D PE map, which is then jointly fed into the CNN with the cropped image. + +Since a person can appear at any location within an image, the principal points of the cropped intrinsics $c_x^{\mathrm{crop}}$ and $c_y^{\mathrm{crop}}$ vary significantly across different samples. This reflects substantial changes in the perspective relationship between the 3D scene and the cropped image. Additionally, the further the human subject deviates from the image center, the more pronounced the perspective distortions of the cropped image become. These factors increase the difficulty of model fitting. To mitigate these issues, we propose a Perspective Rotation (PR) module, which centers the human subject and generates a centered image from the original image, thereby ensuring that $c_x^{\mathrm{crop}}$ and $c_y^{\mathrm{crop}}$ remain fixed across samples while also reducing perspective distortions. + +In this study, we propose a 3D HPE framework, PersPose, which incorporates the proposed PE and PR modules, as illustrated in Figure 1. First, the original image undergoes the PR module, yielding a centered image (see Section 4.2 for details), which is then cropped from the center. Subsequently, the cropped intrinsics $K^{\mathrm{crop}}$ , calculated using Eq. 4, are encoded by the PE module to form a PE map, as detailed in Section 4.1. The PE map and the cropped image are then fed into a CNN backbone, and then a decoder is used to predict the 3D Pose $P_{\mathrm{XYZ}}$ . The contributions of this paper can be summarized as follows: + +- Without camera intrinsics information, the relative depths of joints cannot be accurately estimated. To mitigate this previously overlooked limitation, we propose an innovative PE module that encodes the cropped intrinsics as a 2D PE map, which is then jointly fed into the CNN with the cropped image. +- Due to the variation in a person's location within the original images, the perspective relationships between the 3D scene and the cropped image vary significantly, which complicates model fitting. To address this, we propose a novel PR module that centers the human subject, thereby reducing perspective distortions and alleviating the difficulty of model fitting. +- We propose a 3D HPE framework, PersPose, incorporating our PE and PR modules. To evaluate our framework, we conduct comprehensive experiments on 3DPW [33], Human3.6M [7], and MPI-INF-3DHP [25] datasets. Experimental results show that our framework outperforms existing state-of-the-art (SOTA) methods. Ablation stud + +ies further validate the effectiveness of the proposed PE and PR modules. + +# 2. Related Work + +Some 3D HPE methods [15, 23, 28, 32] directly estimate 3D joint coordinates. Pavlakos et al. [28] proposed to voxelize the 3D space into a 3D probabilistic heatmap. Sun et al. [32] proposed a differentiable soft-argmax operation to derive joint coordinates from estimated heatmaps. Ma et al. [23] proposed an attention-based context modeling framework that propagates structural cues across joints and effectively suppresses absurd 3D pose estimates. Li et al. [15] designed RLE from a maximum-likelihood perspective to learn flexible output distributions for joint positions, thereby facilitating the training process. + +Other methods [16, 24, 29, 36], including ours, first estimate 2D pixel coordinates and relative depths of joints, and then convert these into 3D joint coordinates based on camera intrinsics. This approach facilitates joint training with 2D keypoint datasets. The principal point is usually near the image center. As for focal length, some studies assume it to be unknown. Some methods [8, 12] employ a weak perspective model, which effectively corresponds to using a large fixed focal length. Kissos et al. [10] proposed estimating a rough focal length using image resolution. The SPEC method [13] incorporates a camera calibration sub-network to estimate the focal length directly from images, while the Zolly method [35] estimates the human-to-camera distance and scale from images to derive the focal length. However, the focal length of a camera is usually obtainable (e.g., through device APIs/SDKs) and is essential for estimating the relative depths of joints, as illustrated in Figure 3. + +The CLIFF method [18] demonstrates that global rotation, i.e., the orientation of the human in the camera coordinate system, cannot be accurately inferred from cropped images alone. Their work underscores the necessity of incorporating bounding box information. To address the adverse effects of cropping on global orientation, Yao et al. [39] proposed applying a compensatory rotation within their self-supervised 3D HPE framework to correct the global orientation of the estimated 3D skeleton. + +Furthermore, some 3D HPE methods utilize 2D keypoint sequences as input. The recent Ray3D method [41] leverages camera intrinsics to convert 2D keypoints into 3D rays, and subsequently employs a temporal network to recover the 3D pose sequence from the 3D ray sequence. Additionally, methods like ElePose [34] and EPOCH [5] estimate camera pose within unsupervised 3D HPE frameworks. + +# 3. Importance of Camera Infrinics in 3D HPE + +In the following, we first introduce camera intrinsics and FOV. Then, we demonstrate the limitation of using cropped + +images alone for 3D HPE. Finally, we discuss the importance of FOV for 3D HPE when images are not cropped. Since the cropping operation can be considered as a modification of the camera intrinsics and resolution, the cropped intrinsics are inherently linked to the cropping operation and FOV; this underscores the significance of camera intrinsics in 3D HPE. + +Camera Intrinsics and FOV. Camera intrinsics are used to map 3D coordinates onto 2D image coordinates, playing a pivotal role in 3D HPE. The intrinsic matrix $K$ is a $3 \times 3$ matrix: + +$$ +K = \left[ \begin{array}{c c c} f & 0 & c _ {x} \\ 0 & f & c _ {y} \\ 0 & 0 & 1 \end{array} \right], \tag {1} +$$ + +where $f$ denotes the effective focal length in pixel units. If the virtual sensor* moves along the $z$ -axis, $f$ scales accordingly. The coordinates $(c_x, c_y)$ represent the principal point, which is typically located near the image center. Adjusting $(c_x, c_y)$ is equivalent to moving the virtual sensor within the $x-y$ plane. + +The FOV quantifies the extent of the observable world through a camera. FOV is determined by the effective focal length $f$ and the image size: + +$$ +\mathrm {F O V} _ {x} = 2 \arctan \left(\frac {w}{2 f}\right), \mathrm {F O V} _ {y} = 2 \arctan \left(\frac {h}{2 f}\right), (2) +$$ + +where $\mathrm{FOV}_x$ and $\mathrm{FOV}_y$ are the horizontal and vertical fields of view, respectively. $h$ and $w$ represent the height and width of the captured image in pixels. + +Limitation of Depth Estimation from Cropped Images. In the preprocessing stage of existing 3D HPE methods [15, 23, 32, 36] and 3D HPS methods [4, 16, 24, 29, 42], original images are typically cropped based on the bounding boxes of human subjects. However, using only cropped images for 3D HPE introduces significant difficulty due to the lack of important information about the position of the human subject within the camera's view frustum. This information directly relates to how human subjects are projected onto images from the camera's perspective. + +Figure 2 gives visual examples demonstrating the limitation of using only cropped images for 3D HPE. A camera captures three human subjects. The original image is displayed in the upper right, while the lower right shows three cropped images corresponding to the three human subjects. For subjects (a) and (b), their cropped images are very similar despite having different relative depth labels. Similarly, + +![](images/43527461739541d538eaa42c686a44c2bc2aeec80bea60a5f950f9793860d088.jpg) +Figure 2. Examples that illustrate the limitation of depth estimation using cropped images alone. A single camera captures three human subjects with the identical body shape, and the resulting images are subsequently cropped. The blue lines denote the relative depths (i.e., to the pelvis) of a particular joint, while the red lines measure the arm lengths. In addition, the red lines for (a) and (c) are parallel. For cropped images, two key observations are noted: 1) subjects (a) and (b), despite having different relative depths, yield the same cropped images; 2) subjects (a) and (c), which share the same relative depths, produce distinct cropped images. + +![](images/f6348699bce1e419d2b4f35dce4cec667953937ce488e683b3ecbf488ccc57c6.jpg) +Figure 3. Examples that illustrate the importance of FOV to depth estimation. Two cameras at varying distances from a human subject capture images, resulting in images (a) and (b). Both cameras have the same optical axes but different FOV. Although there are significant visual differences between the two images, they share identical relative depth labels. + +the cropped images of subjects (a) and (c) are quite different, even though they share the same relative depth labels. + +Furthermore, cropping an image is equivalent to capturing a photo using another camera with the same camera extrinsic but with different camera intrinsics and resolution. The same camera extrinsic mean keeping the position of the pinhole and the camera's orientation fixed in the world coordinate system, and the modification of the camera intrinsic from $K$ to $K^{\mathrm{crop}}$ can be geometrically viewed as a translation of the virtual sensor. Specifically, $K^{\mathrm{crop}}$ is calculated by: $K^{\mathrm{crop}} = AK$ , where $A$ is the affine transformation + +matrix corresponding to the cropping operation. The matrix $A$ is defined as + +$$ +A = \left[ \begin{array}{c c c} s & 0 & t _ {u} \\ 0 & s & t _ {v} \\ 0 & 0 & 1 \end{array} \right], \tag {3} +$$ + +where $s = w^{\mathrm{bbox}} / w^{\mathrm{crop}}$ (or $s = h^{\mathrm{bbox}} / h^{\mathrm{crop}}$ ), $t_u = w^{\mathrm{crop}} / 2 - s c_u^{\mathrm{bbox}}$ , $t_v = h^{\mathrm{crop}} / 2 - s c_v^{\mathrm{bbox}}$ . Here, $w^{\mathrm{crop}}$ and $h^{\mathrm{crop}}$ denote the resolution of the cropped image, $w^{\mathrm{bbox}}$ and $h^{\mathrm{bbox}}$ represent the bounding box resolution, and $c_u^{\mathrm{bbox}}$ and $c_v^{\mathrm{bbox}}$ are the center coordinates of the bounding box. Given the original camera intrinsics in Eq. 1, the cropped intrinsics $K^{\mathrm{crop}}$ become + +$$ +K ^ {\text {c r o p}} = A K = \left[ \begin{array}{c c c} f ^ {\text {c r o p}} & 0 & c _ {x} ^ {\text {c r o p}} \\ 0 & f ^ {\text {c r o p}} & c _ {y} ^ {\text {c r o p}} \\ 0 & 0 & 1 \end{array} \right], \tag {4} +$$ + +where $f^{\mathrm{crop}} = sf$ , $c_x^{\mathrm{crop}} = sc_x + t_u$ , and $c_y^{\mathrm{crop}} = sc_y + t_v$ . + +Consequently, the cropped intrinsics $K^{\mathrm{crop}}$ can be utilized to map 3D coordinates onto the 2D coordinate system of the cropped image. + +Importance of FOV to Depth Estimation. In Figure 3, two cameras with the same optical axis capture the same human subject. The left camera has a larger field of view angle, i.e., $FOV_{a} > FOV_{b}$ , and it is closer to the human subject compared to the right camera. These two cameras produce images (a) and (b). Note that (a) and (b) look quite different: for image (a), the depth of the right wrist relative to the pelvis seems larger than in image (b). However, images (a) and (b) actually have the same relative depth labels. This example demonstrates that the FOV must also be considered to infer relative depths accurately. + +# 4. Method + +In this section, we detail the proposed PersPose, illustrated in Figure 4. First, the original image $I$ undergoes the PR process, during which a rotation matrix $R$ is applied to center the human subject, yielding a centered image $I^{\prime}$ (see Section 4.2 for details). Then, the image $I^{\prime}$ is cropped from the center, resulting in the cropped image $I^{\mathrm{crop}}$ . Subsequently, the cropped intrinsics $K^{\mathrm{crop}}$ , calculated using Eq. 4, is encoded to form a 2D map $M^{xy}$ using PE, as detailed in Section 4.1. This PE map $M^{xy}$ and the cropped image $I^{\mathrm{crop}}$ are separately processed through distinct convolutional layers before being element-wise added. The fused features are further passed through a backbone network, and then a decoder is used to predict 2D joint coordinates and relative depths of joints $P_{\mathrm{UVD}}$ , as well as a scale factor $\hat{s} = d_0^{\mathrm{abs}} / f^{\mathrm{crop}}$ . Here, $d_0^{\mathrm{abs}}$ is the absolute depth of the pelvis joint in the camera coordinate system, and scale factor $\hat{s}$ is expressed in mm/pixel. These outputs are then used to compute the rotated 3D pose $P_{\mathrm{XYZ}}^{\prime}$ . For a joint + +index by $i$ , the calculation from $P_{\mathrm{UVD},i} = [u_i,v_i,d_i]^\top$ to $P_{\mathrm{XYZ},i}' = [x_i',y_i',z_i']^\top$ is given by + +$$ +\left[ \begin{array}{l} x _ {i} ^ {\prime} \\ y _ {i} ^ {\prime} \\ z _ {i} ^ {\prime} \end{array} \right] = d _ {i} ^ {\text {a b s}} \left(K ^ {\text {c r o p}}\right) ^ {- 1} \left[ \begin{array}{l} u _ {i} \\ v _ {i} \\ 1 \end{array} \right], \tag {5} +$$ + +where $d_i^{\mathrm{abs}} = d_i + \hat{s} f^{\mathrm{crop}}$ . Finally, the inverse rotation $R^{\top}$ is applied to $P_{\mathrm{XYZ}}'$ to derive $P_{\mathrm{XYZ}}$ , the 3D pose for the original image $I$ . + +$$ +P _ {\mathrm {X Y Z}} = R ^ {\top} P _ {\mathrm {X Y Z}} ^ {\prime}. \tag {6} +$$ + +# 4.1. Perspective Encoding + +We propose PE to encode cropped intrinsics. As illustrated in Figure 5, three virtual sensors have different cropped intrinsics $K_{\text{red}}^{\text{crop}}$ , $K_{\text{green}}^{\text{crop}}$ and $K_{\text{blue}}^{\text{crop}}$ . The red virtual sensor has a larger focal length compared to the green and blue virtual sensors. Additionally, the red and green virtual sensors are aligned along the optical axis, while the blue virtual sensor is placed off-axis, which is common for cropped images. In this setup, the principal points of $K_{\text{red}}^{\text{crop}}$ and $K_{\text{green}}^{\text{crop}}$ are located at the image center, while the principal point of $K_{\text{blue}}^{\text{crop}}$ is not. We project virtual sensors at different positions onto a fixed reference plane at $z = 1$ . The red virtual sensor has a larger focal length than the other two virtual sensors, thus its corresponding projected region is smaller. Similarly, the principal point of the blue virtual sensor deviates from the optical axis, and its corresponding projected region also shifts away from the axis. In other words, for each sensor, the corresponding projected area geometrically represents the unique view frustum determined by its cropped intrinsics. Consequently, we employ this projected area as the encoded representation of the cropped intrinsics. + +Specifically, we construct the PE map $M^{xy}$ by projecting each pixel coordinates $(u_i, v_i)$ of the cropped image onto the plane at $z = 1$ , as shown in Figure 5, and the projected coordinates are computed as: + +$$ +\left[ \begin{array}{l} x _ {i} \\ y _ {i} \\ 1 \end{array} \right] = \left(K ^ {\text {c r o p}}\right) ^ {- 1} \left[ \begin{array}{l} u _ {i} \\ v _ {i} \\ 1 \end{array} \right]. \tag {7} +$$ + +Consequently, the pixel coordinate map $M^{uv}$ , defined as + +$$ +M ^ {u v} = \left[ \begin{array}{c c c c} (1, 1) & (1, 2) & \dots & (1, w) \\ (2, 1) & (2, 2) & \dots & (2, w) \\ \vdots & \vdots & \ddots & \vdots \\ (h, 1) & (h, 2) & \dots & (h, w) \end{array} \right], \tag {8} +$$ + +is transformed into the PE map $M^{xy}$ : + +$$ +M ^ {x y} = \left[ \begin{array}{c c c c} \left(x _ {1}, y _ {1}\right) & \left(x _ {1}, y _ {2}\right) & \dots & \left(x _ {1}, y _ {w}\right) \\ \left(x _ {2}, y _ {1}\right) & \left(x _ {2}, y _ {2}\right) & \dots & \left(x _ {2}, y _ {w}\right) \\ \vdots & \vdots & \ddots & \vdots \\ \left(x _ {h}, y _ {1}\right) & \left(x _ {h}, y _ {2}\right) & \dots & \left(x _ {h}, y _ {w}\right) \end{array} \right]. \tag {9} +$$ + +![](images/3ec2e40c0385853a4417c4cc50a8242d5ea4b45229aaf9ebadb2a5e74f95158e.jpg) +Figure 4. Overview of the PersPose. PersPose introduces two key components: 1) PE, which encodes the cropped intrinsics as a 2D map $M^{xy}$ ; and 2) PR, which centers the human subject in the image, reducing the difficulty of model fitting. + +![](images/5b6524272c97264a5de632df070bddb4ea2d5754f2f1c5e3415269d3fc2c5cf4.jpg) +Figure 5. Perspective Encoding. The grey region denotes the plane at $z = 1$ in the camera coordinate system. The red, green, and blue virtual sensors, corresponding to different cropped intrinsics, are placed on the planes at $z = f_{1}$ and $z = f_{2}$ . The focal lengths $f_{1}$ and $f_{2}$ , measured in meters, correspond to two effective focal lengths measured in pixel units. The projected areas of these three virtual sensors on the plane at $z = 1$ are also denoted in red, green, and blue. $(u_{i}, v_{i})$ denotes a pixel coordinate on the virtual sensor, and the corresponding 3D point projected onto the $z = 1$ plane is $(x_{i}, y_{i}, 1)$ . For each virtual sensor, the corresponding projected area on the plane at $z = 1$ geometrically encodes its unique view frustum. Consequently, we use the projected area as the encoding result of the cropped intrinsics. + +The PE map $M^{xy}$ encodes the view frustum and is subsequently fed into the 3D HPE model, enabling the model to capture the perspective variations induced by different cropped intrinsics. + +# 4.2. Perspective Rotation + +In Section 3, we explain the importance of camera intrinsics in 3D HPE. Then, we introduce PE to encode cropped intrinsics $K^{\mathrm{crop}}$ as part of model input in Section 4.1. Given a + +![](images/6565b5515f536263e149bc846017802ed4b7588c7e6d072c9b5edff427475b05.jpg) +Figure 6. Perspective Rotation. In Figure (a), a virtual sensor captures an image $I$ that is marked with the human bounding box center $(u_c, v_c)$ . An upscaled image $U$ is added to the scene, placed on the plane at $z = 1$ , and the human bounding box center $(x_c, y_c, 1)$ on $U$ is also marked. Additionally, a 3D human skeleton $P_{XYZ}$ is added to the scene. The scene, including the 3D skeleton $P_{XYZ}$ and the upscaled image $U$ , is rotated around the optical center $O$ from the setting in (a) to the setting in (b), so that the optical axis points to the human subject. After applying this rotation, the upscaled image $U'$ in (b) is then reprojected onto the virtual sensor in (b), and the centered image $I'$ in Figure 4 is obtained. + +![](images/2b6258215905d335348effd5fdf1ada78a03f701333ee38de0d7614e112814f0.jpg) + +cropped image $I^{\mathrm{crop}}$ and the corresponding cropped intrinsics $K^{\mathrm{crop}}$ (composed of $f^{\mathrm{crop}}$ , $c_x^{\mathrm{crop}}$ , and $c_y^{\mathrm{crop}}$ ), a 3D HPE model, parameterized by $\theta$ , aims to learn the following mapping function: + +$$ +f _ {\theta}: \left(I ^ {\text {c r o p}}, f ^ {\text {c r o p}}, c _ {x} ^ {\text {c r o p}}, c _ {y} ^ {\text {c r o p}}\right)\rightarrow P _ {\mathrm {X Y Z}}. \tag {10} +$$ + +Notably, the principal point $(c_x^{\mathrm{crop}}, c_y^{\mathrm{crop}})$ may exhibit considerable variance across different images, as the human subject can appear at any region within the original image. This substantially increases the difficulty of model fitting. To mitigate this challenge, we introduce PR to center the + +human subject, as shown in Figure 4. This ensures that the cropped principal point $(c_x^{\mathrm{crop}}, c_y^{\mathrm{crop}})$ is fixed to the center of the cropped image across different images. Therefore, the mapping function changes from Eq. 10 to + +$$ +\tilde {f} _ {\theta}: \left(I ^ {\text {c r o p}}, f ^ {\text {c r o p}}\right)\rightarrow P _ {\mathrm {X Y Z}}, \tag {11} +$$ + +thus reducing the model's fitting difficulty. + +In the following, we describe the process of PR. As illustrated in Figure 4, through PR, the human subject in the original image $I$ is reprojected to the center in the image $I'$ . The reprojection process of this example is shown in Figure 6. + +In Figure 6(a), the virtual sensor, the upscaled image $U$ and the 3D skeleton $P_{\mathrm{XYZ}}$ form a perspective relationship: if a ray is projected from a particular joint of the $P_{\mathrm{XYZ}}$ towards the optical center $O$ , this ray passes through the corresponding joint in the original image $I$ on the sensor, and also through the corresponding joint in the upscaled image $U$ . + +The coordinates $(u_c, v_c)$ and $(x_c, y_c, 1)$ in Figure 6(a) denote the center of the human bounding box on the sensor and on the upscaled image $U$ , respectively. Here, $(x_c, y_c, 1)$ is calculated as + +$$ +\left[ \begin{array}{l} x _ {c} \\ y _ {c} \\ 1 \end{array} \right] = K ^ {- 1} \left[ \begin{array}{l} u _ {c} \\ v _ {c} \\ 1 \end{array} \right], \tag {12} +$$ + +where $K$ is the camera intrinsic of the original image $I$ . + +The goal of PR is to center the bounding box in the centered image $I^{\prime}$ . To achieve this, we rotate the $U$ around the optical center such that the bounding box center $(x_{c},y_{c},1)$ is brought onto the $z$ -axis at $(0,0,d)$ , where $d = \| (x_c,y_c,1)\| _2$ , as shown in Figure 6(b). Therefore, the rotation axis $\mathbf{n}$ and rotation angle $\phi$ can be computed as follows: + +$$ +\mathbf {n} = \frac {\left(x _ {c} , y _ {c} , 1\right) \times (0 , 0 , d) ^ {\top}}{\| \left(x _ {c} , y _ {c} , 1\right) \times (0 , 0 , d) ^ {\top} \|}, \tag {13} +$$ + +$$ +\phi = \operatorname {a r c c o s} \left(\frac {\left(x _ {c} , y _ {c} , 1\right) \cdot (0 , 0 , d)}{\| \left(x _ {c} , y _ {c} , 1\right) \| \| (0 , 0 , d) \|}\right), \tag {14} +$$ + +where $\times$ denotes the cross product, and $\cdot$ represents the dot product. Applying Rodrigues' rotation formula, the rotation matrix is: + +$$ +R = \text {R o d r i g u e s} (\mathbf {n}, \phi) \tag {15} +$$ + +This rotation $R$ is first applied to the upscaled image $U$ in Figure 6(a) and obtain $U'$ in Figure 6(b). $U'$ is then reprojected onto the virtual sensor in (b) and the centered image $I'$ is obtained, with the bounding box center located at image center $\left(\frac{w}{2},\frac{h}{2}\right)$ . + +The 3D pose corresponding to the centered image $I^{\prime}$ can be derived by applying the same rotation $R$ to $P_{\mathrm{XYZ}}$ : + +$$ +P _ {\mathrm {X Y Z}} ^ {\prime} = R P _ {\mathrm {X Y Z}}. \tag {16} +$$ + +Since both $U$ and $P_{\mathrm{XYZ}}$ undergo the same 3D rotation about the optical center, the perspective relationship of the centered image $I^{\prime}$ , the rotated upscaled image $U^{\prime}$ , and the rotated 3D skeleton $P_{\mathrm{XYZ}}^{\prime}$ is maintained, as illustrated in Figure 6(b). Consequently, the rotated 3D skeleton $P_{\mathrm{XYZ}}^{\prime}$ maintains geometric consistency with the new image $I^{\prime}$ . + +Finally, the perspective transformation matrix $M$ used to warp the original image $I$ into the centered image $I'$ is computed as follows: + +$$ +M = K R K ^ {- 1}, \tag {17} +$$ + +where $K$ is the camera intrinsic of the original image $I$ . + +# 5. Experiments + +# 5.1. Experimental setup + +We set the resolution of the cropped images to $256 \times 256$ . The HRNet-W48 [31] is used as the backbone, which outputs a feature map of dimensions $64 \times 64 \times 48$ and a global feature vector of length 2048. The Perspose decoder comprises one convolutional layer and two linear layers. The convolutional layer processes the feature map to produce a 2D heatmap, from which the 2D pose is obtained using the soft-argmax operation. Simultaneously, the two linear layers take the global feature vector as input to predict the relative depths of joints and the scale factor $\hat{s}$ , respectively. Additionally, the element-wise addition in Figure 4 is performed before the second stage of HRNet. + +To compare with HPS methods, we additionally add two linear layers into the Perspose decoder to estimate human shape and twist, and the analytical IK algorithm in HybrIK [16] is used to derive SMPL parameters prediction. + +The loss function is defined as + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\mathrm {u v d}} + \lambda_ {2} \mathcal {L} _ {\hat {s}} + \lambda_ {3} \mathcal {L} _ {\mathrm {b e t a}} + \lambda_ {4} \mathcal {L} _ {\mathrm {t w}}, \tag {18} +$$ + +where $\mathcal{L}_{\mathrm{uvd}}$ is the L1 loss for the $P_{\mathrm{UVD}}$ predictions, $\mathcal{L}_{\hat{s}}$ is the L1 loss for the estimated scale factor $\hat{s}$ , $\mathcal{L}_{\mathrm{beta}}$ is the L1 loss for the estimated human shape parameters, $\mathcal{L}_{\mathrm{tw}}$ is the L2 loss for the twist predictions, and $\lambda_1$ , $\lambda_2$ , $\lambda_3$ and $\lambda_4$ are weight hyperparameters, set to 1.0, 0.5, 0.01 and 0.1 respectively. + +The batch size is set to 96. The AdamW [22] optimizer is used with an initial learning rate of 3e-4. The training lasts for 70 epochs, and the learning rate is reduced by a factor of 0.75 every 6 epochs. This process utilizes one NVIDIA 3090 GPU and is completed in around 60 hours. + +To evaluate the estimated 3D pose, we report Mean Per Joint Position Error (MPJPE), Procrustes Aligned MPJPE (PA-MPJPE), Percentage of Correct Keypoints (PCK), and Area Under Curve (AUC). Additionally, Per Vertex Error (PVE) is computed to evaluate all vertices on the human mesh. Furthermore, we report on the depth error in our ablation experiments to evaluate the estimated relative depths. + +
3DPWHuman3.6MMPI-INF-3DPH
PA-MPJPE↓MPJPE↓PVE↓PA-MPJPE↓MPJPE↓PVE↓PCK↑AUC↑MPJPE↓
HMR [8]†CVPR'1881.3130.0152.756.888.096.172.936.5124.2
SPIN [14]†ICCV'1959.296.9116.441.1--76.437.1105.2
I2L-MeshNet [26]†ECCV'2057.793.2110.141.155.765.1---
Pose2Mesh [3]†ECCV'2058.388.9106.346.364.985.3---
Mesh Graphormer [19]ICCV'2145.674.787.734.551.2----
HybrIK [16]‡CVPR'2145.074.186.534.554.465.787.546.993.9
CLIFF [18]ECCV'2243.069.081.232.747.1----
FastMETRO [2]ECCV'2244.673.584.133.752.2----
IKOL [42]‡AAAI'2345.573.386.4---87.948.188.8
VirtualMarker [24]‡CVPR'2341.367.577.932.047.358.0---
ProPose [4]‡CVPR'2340.668.379.429.145.7----
PLIKS [29]‡CVPR'2342.866.982.634.749.3-91.852.372.3
Zolly [35]ICCV'2339.865.076.332.349.4----
Gwon et al. [6]CVPR'2444.373.280.3------
GLNet-W48 [37]ECCV'2439.566.977.929.448.8----
PostoMETRO [38]WACV'2539.867.776.8------
PersPose‡39.160.172.428.343.052.794.055.272.1
+ +Table 1. Comparison between our method and SOTA HPS methods. ↓ indicate that lower values are better, while ↑ indicate that higher values are better. † denotes that 3DPW training split is not used. ‡ denotes methods that estimate UVD coordinates as an intermediate representation prior to obtaining 3D XYZ positions. + +The depth error is defined as the mean absolute difference between the estimated and ground-truth relative depths of joints. Following [16, 24], We evaluate 14 joints on 3DPW and Human3.6M datasets and 17 joints on MPI-INF-3DHP dataset. For MPJPE, PA-MPJPE, PCK, and AUC, the joints regressed from the human mesh are evaluated, while the relative depths predicted by the PersPose decoder is used to compute depth error. + +Our experiments employ the following 3D datasets: 1) 3DPW [33], an in-the-wild dataset annotated with SMPL parameters, which can be used to derive 3D pose labels. 2) Human3.6M [7], which was captured in a controlled environment. We use the SMPL parameters derived from Mosh [21]. Following [9, 11], we use 5 subjects (S1, S5, S6, S7, S8) for training, and 2 subjects (S9, S11) for evaluation. 3) BEDLAM [1], a large and realistic synthetic dataset annotated with accurate SMPL parameters. 4) MPIINF-3DHP [25], a 3D human pose dataset that includes both controlled indoor settings and complex outdoor scenes. + +# 5.2. Comparison with the State-of-the-art + +Table 1 presents a comparison between our method and SOTA HPS methods on 3DPW, Human3.6M, and MPIINF-3DHP datasets. In this study, we employ HRNet-W48 [31] as the backbone, and results utilizing the same backbone from other works will be preferred when available. The results for the proposed PersPose in Table 1 were obtained by training on a combination of datasets, including 3DPW [33], Human3.6M [7], MPI-INF-3DHP [25], and + +COCO [20]. Note that while some methods may have incorporated additional 2D keypoint datasets during training, none of the results in Table 1 were derived using synthetic 3D datasets. + +PersPose outperforms other methods across all three datasets. On MPI-INF-3DHP benchmark, PersPose surpasses the second-best approach by 2.2 on PCK and 2.9 on AUC. Furthermore, on 3DPW dataset, PersPose outperforms the second-best approach by $4.9\mathrm{mm}$ $(7.54\%)$ in MPJPE. The test splits of MPI-INF-3DHP and 3DPW datasets both contain complex outdoor scenes, demonstrating the robustness of the proposed PersPose under challenging real-world conditions. + +# 5.3. Ablation Study + +Experimental Setup. To evaluate the effectiveness of our PE and PR modules, we conduct ablation studies comprising the following configurations: 1) our framework without PE and PR, 2) our framework without PR, and 3) our framework with both PE and PR. + +For evaluation metrics, we employ PA-MPJPE and MPJPE to assess the accuracy of 3D pose estimation. In addition, Section 3 highlights the importance of camera intrinsics for relative depth estimation with two examples (Figure 2 and Figure 3). Section 4.1 introduces PE to transfer camera intrinsics to the neural model. Section 4.2 proposes PR to reduce the difficulty of model fitting. To evaluate the effectiveness of our proposed PE and PR in estimating relative depths, we additionally report on the depth error. + +
PRPEDataset3DPWMPI-INF-3DHP
Depth error↓PA-MPJPE↓MPJPE↓Depth error↓PA-MPJPE↓MPJPE↓
--R45.139.862.457.357.380.1
-✓44.539.762.253.756.376.6
✓✓43.839.160.151.054.471.9
--R+B41.537.858.454.255.576.8
-✓41.237.858.151.055.173.4
✓✓40.037.357.248.653.770.2
+ +Table 2. Ablation experiments on 3DPW [33] and MPI-INF-3DHP [25]. R denotes the use of real datasets, and B denotes BEDLAM. + +![](images/b4d8fea95306020c631c4ce929a65850d96228c91aac2292a8f60930914dad74.jpg) +Figure 7. Distribution of PR rotation angle $\phi$ . We analyze the distribution of $\phi$ (measured in degrees) across various datasets. A broader spread in $\phi$ reflects greater variability in the centre of the bounding box's coordinates $(u_c, v_c)$ . The values of $\phi$ for 3DPW and Human3.6M concentrate around $5^\circ$ . In contrast, BEDLAM and MPI-INF-3DHP exhibit a wider spread, suggesting these datasets feature more diversity and complexity. + +Prior work has demonstrated that training on synthetic data improves accuracy [1, 29, 30]. In this study, we further investigate the impact of incorporating synthetic data into the training phase. Specifically, in Table 2, "R" represents training on real-image datasets (3DPW, Human3.6M, MPI-INF-3DHP, and COCO), while "B" denotes training on BEDLAM synthetic dataset. + +Ablation Study Results. Table 2 displays the results of our experiments. The addition of PE or PR consistently leads to performance improvements across both datasets, regardless of whether the additional synthetic dataset is used for training, indicating the effectiveness of the proposed PE and PR in relative depth estimation and 3D pose estimation. + +On MPI-INF-3DHP dataset, the addition of PE or PR results in a considerable reduction in depth error. Specifically, PE reduces depth error by $3.6\mathrm{mm}$ and $3.2\mathrm{mm}$ for training settings "R" and $\mathrm{R + B}$ , respectively. Similarly, PR achieves reductions in depth error of $2.7\mathrm{mm}$ and $2.4\mathrm{mm}$ for "R" and $\mathrm{R + B}$ , respectively. + +On 3DPW dataset, incorporating PE or PR leads to a relatively modest performance improvement compared to MPI-INF-3DHP dataset. To investigate this effect, we analyzed the distribution of the rotation angle $\phi$ in PR across different datasets. + +Distribution of the rotation angle $\phi$ across datasets. Figure 7 displays the distribution of $\phi$ , using kernel density estimation to estimate the density curve. The rotation angle $\phi$ for MPI-INF-3DHP spans a broader range than 3DPW. This distribution quantifies the variability in the person's position within the dataset's images: a wider spread in $\phi$ indicates greater variation in the center of the human bounding box $(u_c, v_c)$ , reflecting significant changes in the perspective relationship between the 3D scene and the cropped image; in such cases, the benefits of PE and PR become even more pronounced. + +Effect of Synthetic Training Data. Comparing the training settings “R+B” and “R” across various model configurations, we observe that the model trained with “R+B” consistently outperforms the one trained with “R” under identical model configurations. For instance, by incorporating additional synthetic training data, the MPJPE of our framework with PE and PR decreases from $60.1\mathrm{mm}$ to $57.2\mathrm{mm}$ on 3DPW dataset and from $71.9\mathrm{mm}$ to $70.2\mathrm{mm}$ on MPI-INF-3DHP dataset. This underscores the beneficial impact of incorporating additional synthetic datasets during training. + +# 6. Conclusion + +In this paper, we propose a novel 3D HPE framework, PersPose, integrating PE and PR. We first underscore the necessity of camera intrinsics for accurately inferring the relative depths of joints in 3D HPE and then introduce the PE module to encode camera intrinsics as a 2D map, which is jointly fed into the CNN alongside the cropped image. Considering that the human subject may appear anywhere in an image, we propose the PR module to center the human subject, thereby reducing perspective distortion and the difficulty of model fitting. Experimental results on the multiple datasets demonstrate that PersPose achieves considerable improvement over existing SOTA methods. Ablation studies confirm the effectiveness of PE and PR and demonstrate that the performance enhancements provided by these modules become more pronounced when perspective relationships are more variable. + +# References + +[1] Michael J Black, Priyanka Patel, Joachim Tesch, and Jinlong Yang. Bedlam: A synthetic dataset of bodies exhibiting detailed lifelike animated motion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8726-8737, 2023. 7, 8 +[2] Junhyeong Cho, Kim Youwang, and Tae-Hyun Oh. Cross-attention of disentangled modalities for 3d human mesh recovery with transformers. In European Conference on Computer Vision, pages 342–359. Springer, 2022. 7 +[3] Hongsuk Choi, Gyeongsik Moon, and Kyoung Mu Lee. Pose2mesh: Graph convolutional network for 3d human pose and mesh recovery from a 2d human pose. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part VII 16, pages 769-787. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 574-584, 2023. 1, 2, 3, 7, 8 +[30] Soyong Shin, Juyong Kim, Eni Halilaj, and Michael J. Black. Wham: Reconstructing world-grounded humans with accurate 3d motion. In Computer Vision and Pattern Recognition (CVPR), 2024. 8 +[31] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5693-5703, 2019. 6, 7 +[32] Xiao Sun, Bin Xiao, Fangyin Wei, Shuang Liang, and Yichen Wei. Integral human pose regression. In Proceedings of the European conference on computer vision (ECCV), pages 529-545, 2018. 1, 2, 3 +[33] Timo Von Marcard, Roberto Henschel, Michael J Black, Bodo Rosenhahn, and Gerard Pons-Moll. Recovering accurate 3d human pose in the wild using imus and a moving camera. 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Ray3d: ray-based 3d human pose estimation for monocular absolute 3d localization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13116-13125, 2022. 2 +[42] Juze Zhang, Ye Shi, Yuexin Ma, Lan Xu, Jingyi Yu, and Jingya Wang. Ikol: Inverse kinematics optimization layer for 3d human pose and shape estimation via gauss-newton differentiation. 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a/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/full.md b/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4bd01135d17bdc5d90f97d0e015b7b6f6568c174 --- /dev/null +++ b/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/full.md @@ -0,0 +1,464 @@ +# PersonaCraft: Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion + +Gwanghyun Kim $^{1*}$ , Suh Yoon Jeon $^{1*}$ , Seunggyu Lee $^{1}$ , Se Young Chun $^{1,2\dagger}$ + +$^{1}$ Dept. of Electrical and Computer Engineering, $^{2}$ INMC & IPAI Seoul National University, Republic of Korea + +{gwang.kim, euniejeon, leeseunggyu, sychun}@snu.ac.kr + +![](images/f84efcf5b4b6ce0a9c3d500dc709524be5f4c145add6f7fe6d16cea14bbf45e0.jpg) +Full-body Ref. Images +"A man hugging a woman by the shore." + +![](images/7b82397c1c25c614201cb3e0970593c3e351dd89a41e66879bea286770191c3c.jpg) +"Three women at the red carpet." + +![](images/5e6d603c145add8d03a948c303a69504704f4bcfa1c20320831f285e30ce787c.jpg) +"Four women in sports uniform, cheerleading pose." + +![](images/0c41150aee531a63584251498db0f7eaaf79a284e87081354edde6217feeb49c.jpg) +Pose Input + +![](images/e142c94d6154a3b39648e279f9d67762800a86c27ba20b9d6c9327453680cbcb.jpg) + +![](images/0bb47acf2943a2cb6672f196d9fff45babe1a17c4ae2fd981e19306ac96dffc8.jpg) +Figure 1. PersonaCraft generates realistic, personalized images of multiple individuals with complex occlusions, preserving facial identity and body shape using occlusion-aware 3D pose and shape conditioned diffusion. PersonaCraft outperforms baselines in body shape personalization (blue arrows indicate failures) and naturalness (yellow arrows highlight artifacts, with zoomed-in views in yellow boxes). + +![](images/2b3ae814970761617122260ce4b6455b69f62de12e48b6df79285ed854418987.jpg) +DreamBooth + +![](images/bb26901ba2cf0cd2529e89ac94a0091d13d8448534d8e2a97043e659e0653fb5.jpg) + +![](images/e7bb4cd632903c0c6665bc61ea162e019bb24e8bb3e88d929b12ab2536861847.jpg) + +![](images/bc27d6cf542eb690e1a806827f1e6671fa70ca2e8eba30a46ad6343be8bc850a.jpg) +InstantID + OMG +IPAdapter + OMG + +![](images/de658e3cdfd8af43a2dc44dd302015fea4d7a57d4953a7c7a167d9a0e12b22c8.jpg) + +![](images/7ff2b6543df3c5a893a1a5fb3930dc3b1f0e658897208c8e4385a3c5e375d8ec.jpg) + +![](images/eb39db88b6a6163416da5fcdab4a13963e1a09c41ccafc7d2a687c088d04290b.jpg) +PersonaCraft (Ours) + +![](images/4dce2b4bb3082f0942124213ea62601a6929537dea89d9e97e0fbcfa79d42c88.jpg) + +![](images/c479281faedb3e0f4b2814d65abe4ad9f5d2cb7bd23a95eb027d57cc5a5c157c.jpg) + +# Abstract + +We present PersonaCraft, a framework for controllable and occlusion-robust full-body personalized image synthesis of multiple individuals in complex scenes. Current methods struggle with occlusion-heavy scenarios and complete body personalization, as 2D pose conditioning lacks 3D geometry, often leading to ambiguous occlusions and anatomical distortions, and many approaches focus solely on facial identity. In contrast, our PersonaCraft integrates diffusion models with 3D human modeling, employing SMPLx-ControlNet, to utilize 3D geometry like depth and normal maps for robust 3D-aware pose conditioning and enhanced anatomical coherence. To handle fine-grained occlusions, we propose Occlusion Boundary Enhancer Network that exploits depth + +edge signals with occlusion-focused training, and Occlusion-Aware Classifier-Free Guidance strategy that selectively reinforces conditioning in occluded regions without affecting unoccluded areas. PersonaCraft can seamlessly be combined with Face Identity ControlNet, achieving full-body multi-human personalization and thus marking a significant advancement beyond prior approaches that concentrate only on facial identity. Our dual-pathway body shape representation with SMPLx-based shape parameters and textual refinement, enables precise full-body personalization and flexible user-defined body shape adjustments. Extensive quantitative experiments and user studies demonstrate that PersonaCraft significantly outperforms existing methods in generating high-quality, multi-person images with accurate personalization and robust occlusion handling. + +![](images/5b89ab0ff3842ced84bd318c0a7e57e05d9cd6e022db671a8d3eed7ecb86a97f.jpg) +Figure 2. SMPLx-ControlNet (SCNet) with SMPLx depth and normal improves occlusion handling in pose generation compared to 2D OpenPose, though fine-grained occlusions remain challenging. Using our occlusion-focused methods, OccNet and OccCFG, we achieve superior pose consistency and anatomical coherence. + +![](images/d6b7e62d2d1971e70ea9ed149f445d1a2dbda8b67d0de543f238710cb08ecf07.jpg) + +![](images/81fd5ae6ffbdcb81dbfc195ea063cb45a68cf6e22c4f4f9b59ee98ff7c9d8f1b.jpg) + +# 1. Introduction + +Recent advances in personalized image generation [2, 4, 13-19, 24, 26, 43, 47, 50, 56, 57, 63, 63, 64, 67, 68, 70, 73, 76, 78, 80, 82-84] and controllable image generation [11, 22, 31, 44, 69, 79, 86], powered by diffusion models [9, 27, 33-36, 59, 65, 83], have paved the way for synthesizing multi-human scenes with explicitly defined poses. Despite these breakthroughs, generating images with multiple individuals in complex, occlusion-heavy environments remains a formidable challenge. Conventional approaches that rely on 2D skeleton-based conditioning lack the depth cues necessary to capture overlapping body parts and intricate inter-person interactions, often resulting in ambiguous occlusions and anatomical distortions. Although recent works [11, 48, 86] have begun exploring the use of 3D pose information, they are limited to single-person scenarios, thereby restricting their applicability to multi-person scenes. + +Furthermore, achieving full-body personalization remains a significant challenge. Most existing methods prioritize facial identity, often overlooking the distinct characteristics of body shape. Although several approaches [78, 85] have enabled full-body personalization using general image encoders [55], they often struggle to disentangle intrinsic body shape from clothing attributes. + +To address these challenges, we propose PersonaCraft, a framework for controllable and occlusion-robust full-body personalized image synthesis of multiple individuals in complex scenes. Firstly, our approach integrates diffusion models with 3D human modeling, employing SMPLx-ControlNet (SCNet), to utilize critical 3D geometric information to overcome the limitations of conventional 2D pose conditioning. Through careful exploration of 3D pose representations, we found that combining SMPLx depth and normal maps offers the most robust conditioning, ensuring high pose consistency and anatomical naturalness. However, despite the benefits of 3D-aware conditioning, handling complex, fine-grained occlusions still remains challenging, as shown in Fig. 2. Secondly, we propose the Occlusion Boundary Enhancer Network (OccNet), which explicitly enhances occluded regions at a finer level by leveraging depth edge signals that high + +light occlusion boundaries. Complemented by our Occlusion-Aware Classifier-Free Guidance (OccCFG) strategy, our OccNet adaptively reinforces conditioning in occlusion-heavy areas without compromising contrast in unoccluded regions. Together, these components ensure robust anatomical coherence, even in complex multi-human interactions with significant occlusions, as presented in Fig. 2. + +Another key advantage of our 3D-aware pose conditioning, beyond enhancing pose accuracy with improved occlusion handling and anatomical coherence, is its ability to encode body shape through SMPLx body shape coefficients. Our method can seamlessly be combined with Face Identity ControlNet [70] to achieve full-body multi-human personalization, representing a significant advancement beyond prior methods focused solely on facial identity [25, 37, 70, 74, 78, 81, 85]. Moreover, to overcome the limitations of SMPLx-based body representation, especially in challenging cases where body shape characteristics conflict, we introduce a dual-pathway approach where an optional textual pathway refines body shape. PersonaCraft enables fine-scale, user-defined body shape control through reference-based and interpolation/extrapolation-based adjustments. + +Through extensive quantitative and qualitative evaluations, including user studies, our PersonaCraft shows significant improvements in occlusion handling, pose consistency, setting a new benchmark for anatomically precise controllable and personalized multi-human image synthesis. + +# 2. Related Works + +Single-Concept Personalization. Text-to-image (T2I) diffusion models and applications [9, 27, 33-36, 59, 65, 83] enable single-concept personalization, adapting pretrained models for individual subjects. Early methods used optimization-based techniques [13, 16, 24, 26, 56, 57, 64] or textual embeddings [2, 17, 50, 67, 68, 80, 82]. LoRA methods [28, 66] reduced the need for many trainable parameters. Recent works [4, 14, 15, 18, 19, 43, 47, 63, 63, 70, 73, 76, 78, 83, 84] like IP-Adapter [78] and InstantID [70] adopt modular designs for fast personalization from a single reference image and human-centric modules. However, these methods face challenges in handling complex human poses, neglect body shape preservation, or fail to disentangle identity from clothing in personalized human image synthesis. + +Multi-Concept Personalization. Recent multi-concept personalization methods [5, 20, 23, 45] use cross-attention to prevent concept entanglement. Custom Diffusion [39] integrates models via joint training or constrained optimization. Mix-of-Show [21] employs gradient fusion for identity preservation and regional sampling for attribute binding. Modular Customization [53] isolates concepts via orthog + +![](images/769045775829ea15eba321d76dd6a4f3ead972c7c09241f7f169ca7c45bd45ab.jpg) +Figure 3. Overview of our occlusion-aware 3D pose and shape conditioning. We generate SMPLx renderings for SMPLx-ControlNet (SCNet) and derive occlusion masks for the Occlusion Boundary Enhancer Network (OccNet) by counting intersected faces and masking depth edges. Combining SCNet and OccNet residuals with occlusion masks enables the base U-Net to handle occlusion-aware 3D pose and shape conditioning. Occlusion-aware classifier-free guidance (OccCFG) further improves anatomical coherence in occluded regions. + +onal directions. FastComposer [74] enhances training-free personalization. OMG [37] propose 2-stage multi-concept personalization without training. StoryMaker [85] ensures multi-character consistency via segmentation-constrained cross-attention. UniPortrait [25] proposes ID embeddings and routing modules for high fidelity and editability. ID-Patch [81] mitigates ID leakage and ensures precise identity-position association introducing ID patches. However, existing methods still exhibit limitations in maintaining occlusion robustness and precise control over body shapes. + +Controllable Human Generation. Recent works, such as ControlNet [79] and HyperHuman [44], integrate T2I diffusion with 2D skeletons for controllable human synthesis. HumanSD [31] enhances skeleton-based generation with heatmap-guided denoising, while Stable-Pose [69] improves pose alignment using attention masking. DWpose [77] refines OpenPose [12] for better skeleton accuracy, and Dense-Pose [22] maps RGB images to 3D surfaces. However, lacking depth cues, these methods struggle with occlusions in multi-human or complex pose scenarios. PODIA-3D [35] incorporates depth for pose guidance but not image synthesis. The SMPL [46] (Skinned Multi-Person Linear Model) and SMPLx [51] are parametric human body models that provide realistic 3D representations of human pose and shape. SMPL models the body using shape parameters and pose parameters with a differentiable blend skinning function, making it widely used in vision and graphics applications. SMPLx extends this by incorporating expressive facial and hand articulation, enabling more detailed human motion modeling. Recent works leverage SMPL for generative tasks: Champ [86] applies SMPL for single-human video synthesis, while HumanLDM [11] integrates SMPL with Control + +Net for stable pose-conditioned human generation. However, these methods focus solely on single-human cases and do not address complex occlusions in multi-human scenarios. + +# 3. Proposed Method: PersonaCraft + +We propose PersonaCraft, a framework for controllable and occlusion-robust full-body personalized image synthesis of multiple individuals in complex scenes. PersonaCraft integrates diffusion models with 3D human modeling, leveraging SMPLx-ControlNet (SCNet) to incorporate 3D geometry, including depth and normal maps, for robust 3D-aware pose conditioning and enhanced anatomical coherence (Sec. 3.1). To handle fine-grained occlusions, we introduce the Occlusion Boundary Enhancer Network (OccNet), which exploits depth edge signals through occlusion-focused training, and the Occlusion-Aware Classifier-Free Guidance (OccCFG) strategy, which selectively reinforces conditioning in occluded regions without affecting unoccluded areas (Sec. 3.2). Furthermore, PersonaCraft seamlessly integrates with Face Identity ControlNet, enabling full-body multi-human personalization and surpassing prior approaches that focus solely on facial identity. Our dual-pathway body shape representation, combining SMPLx-based shape parameters with textual refinement, ensures precise full-body personalization and flexible user-defined body shape adjustments (Sec. 3.3). + +Existing methods rely on 2D skeleton-based Control-Nets [79], which lack depth cues and fail to capture identity-specific body shapes. We propose a 3D-aware pose conditioning, SMPLx-ControlNet (SCNet), that leverages SMPLx [51] to incorporate depth information, enabling occlusion-aware conditioning and body shape control. + +![](images/f21c7940f04675f095288e28be923d153914f4650cfdf9e086e8234d07165ac8.jpg) +Figure 4. Full pipeline of PersonaCraft for multi-human full-body personalization. By integrating our method with face embeddings from InsightFace [1] and Face Identity ControlNet [70], we advance toward full-body multi-human personalization. + +# 3.1. 3D-Aware Pose and Shape Conditioning for Multi-Human Generation + +Existing methods rely on 2D skeleton-based ControlNets [79], which lack depth cues and fail to capture identity-specific body shapes in multi-human scenes. We propose a 3D-aware pose conditioning technique using SMPLx-ControlNet (SCNet). By leveraging SMPLx [51], we represent pose with depth information, enabling occlusion and controlling body shape. As shown in Fig. 3, given 3D poses $\{\pmb{p}^{(i)}\}_{i = 1}^{N_{\mathrm{human}}}$ , body shape parameters $\{\beta^{(i)}\}_{i = 1}^{N_{\mathrm{human}}}$ , and camera parameters $c$ , we construct a 3D human scene of $N_{\mathrm{human}}$ individuals with occlusions using SMPLx meshes. SMPLx renderings, like depth $d_{\mathrm{SMPLx}}$ , serve as conditioning signals for the diffusion model, enabling high-fidelity image generation with improved identity preservation and occlusion handling. + +We train SCNet $\mathcal{E}_{\phi}^{\mathrm{SC}}$ by leveraging the pretrained ControlNet [79] framework, with the following objective: + +$$ +\mathbb {E} _ {\boldsymbol {x} _ {0}, t, y, \boldsymbol {d} _ {\mathrm {S M P L} x}, \epsilon} \left[ \left\| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t}, t, y, \mathcal {E} _ {\phi} ^ {\mathrm {S C}} (\boldsymbol {d} _ {\mathrm {S M P L} x})\right) \right\| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(0,1)$ , $\epsilon_{\theta}$ is a base text-to-image diffusion model, $t$ is the diffusion timestep, $y$ is the text prompt, $x_{t}$ is the noisy latent representation of the image at timestep $t$ , and it gets progressively refined during the denoising process. We evaluate different SMPLx renderings—depth, normal, and RGB—for conditioning and find that combining depth SCNet (SCNet-D, $\mathcal{E}_{\phi_D}^{\mathrm{SC}}$ , for occlusion cues) and normal SCNet (SCNet-N, $\mathcal{E}_{\phi_N}^{\mathrm{SC}}$ , for surface orientation) by integrating the residuals from each SCNet provides the most robust pose consistency and anatomical coherence (see Tab. 5). Therefore, we adopt depth-normal as the default 3D representation for SCNet. + +# 3.2. Occlusion-Focused Generation + +Although 3D-aware pose conditioning improves handling occluded regions, generating small, detailed occlusions remains difficult due to inter-person contact and self-occlusion, + +which cause anatomical distortions. To address this, we introduce occlusion masks from SMPLx-rendered 3D scenes, marking pixels as occluded if covered by multiple surfaces, as shown in Fig. 3 (right). For each pixel $(i,j)$ , we count the number of faces $n_{\mathrm{faces}}(i,j)$ that a projected ray passes through. A pixel is considered occluded if the ray intersects more than two surfaces. The occlusion mask $M_{\mathrm{occ}}$ is defined as: + +$$ +M _ {\text {o c c}} (i, j) = \left\{ \begin{array}{l l} 1, & \text {i f} n _ {\text {f a c e s}} (i, j) > 2 \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +To reduce subtle occlusions and prevent overfitting, we filter small occlusions and refine the boundaries by dilating the mask's edges. This improves the representation of occluded regions, especially in poses with inter-person contact and self-occlusion. + +Occlusion Boundary Enhancer Network. Using this occlusion mask, we introduce an Occlusion Boundary Enhancer Network (OccNet) by training the model to generate images based solely on SMPLx depth edges within the occlusion mask. The SMPLx depth edges, defined as $e_{\mathrm{SMPLx}} = \left|\frac{\partial d_{\mathrm{SMPLx}}}{\partial x}\right| + \left|\frac{\partial d_{\mathrm{SMPLx}}}{\partial y}\right| > \tau$ , where $\tau$ is the edge threshold, highlight occlusion boundaries where depth changes abruptly. Although this information is limited due to the loss of 3D information inside the occluded regions, it serves as a crucial signal by highlighting the occlusion boundaries. + +As shown in Fig. 3, we only provide the depth edges within the occluded region and train the model to generate images based on this sparse signal, which enables the model to focus more on generating the occluded region while preserving its boundaries, compared to training with the full conditioning. We train OccNet $\mathcal{E}_{\omega}^{\mathrm{Occ}}$ using the following objective: + +$$ +\mathbb {E} _ {\boldsymbol {x} _ {0}, t, y, e _ {\mathrm {S M P L} x}, M _ {\mathrm {o c c}}, \epsilon} \left[ \left\| \boldsymbol {\epsilon} - \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, y, \mathcal {E} _ {\omega} ^ {\text {O c c}} \left(e _ {\mathrm {S M P L} x} \odot M _ {\mathrm {o c c}}\right)\right) \right\| _ {2} ^ {2} \right]. \tag {3} +$$ + +Occlusion-Aware Classifier-Free Guidance. We observe that increasing classifier-free guidance (CFG) in occluded regions enhances anatomical consistency by strengthening 3D pose information, resolving local ambiguities. However, a uniformly high CFG strength induce over-saturation in non-occluded areas, as noted in prior works [40, 58, 59]. This highlights the need for a spatially adaptive guidance strategy [62] tailored for occlusion in human scene scenarios. To this end, we introduce Occlusion-Aware Classifier-Free Guidance (OccCFG) as shown in Fig. 3: + +$$ +\hat {\epsilon} = \epsilon_ {\text {u n c o n d}} + \left(k _ {\text {o c c}} M _ {\text {o c c}} + k _ {\text {b a s e}} \left(1 - M _ {\text {o c c}}\right)\right) \left(\epsilon_ {\text {c o n d}} - \epsilon_ {\text {u n c o n d}}\right) \tag {4} +$$ + +where $k_{\mathrm{occ}}$ and $k_{\mathrm{base}}$ are CFG scales for occluded and non-occluded regions, respectively, $M_{\mathrm{occ}}$ is the occlusion mask, $\epsilon_{\mathrm{uncond}}$ is the unconditional noise prediction, and $\epsilon_{\mathrm{cond}}$ is the conditional noise prediction. + +![](images/fbb099e926d373d43aaea2074e836972b37ba82b3eeabc4a25401598235a39ed.jpg) +Full-body Ref. Images + +![](images/67e3afb7afd02861b8b12edff8e4f74fe97d1e212299a96235a19f600896d795.jpg) +Two men shaking hands at a diplomatic summit. +"Three women standing next to each other at home." + +![](images/9a57741f3096f88044b7d2f384a2f27fdaf938ea0d2ac42dafec846dffc42398.jpg) +Pose Input + +![](images/274d55931ba2f23685ceaf1cad30e33430b755c15ad32c425e27a6b917cd2244.jpg) + +![](images/5af9a476f28c86d00b2944889e670001ddc9dbd79a0460a15fbd36cf2d60157f.jpg) +DreamBooth + +![](images/65e5d63f26e5e7dc337b7425f82b196a7ff34068edbdd2e2e374305aac2ff91c.jpg) + +![](images/c7401236a275b084c71cc4dcdbb3ab79f259596bddef2666a8d74ea3ad20d7a0.jpg) +InstantID + OMG + +![](images/fdb271bb470f78bb2d291498354c036a2048958411fb59f5ea758d28a35c3428.jpg) + +![](images/19a03953c37e8ccf17eb8595157f980a15fef6e0f75003f59dea62ea2996b86b.jpg) +IPAdapter + OMG + +![](images/aa8a53584850fdd749b00d55cd03f036714bad66812374569de0605cc9822960.jpg) + +![](images/87fb4d807eb77aac5573260c829c768f59e40a4fc545a46683726088ce764585.jpg) +PersonaCraft (Ours) + +![](images/eb1ff704a891f65197618bafff9d82f34dc8327d1020a8921fbd9dd22ca15442.jpg) + +![](images/46b566b2c0779633429f68136fac5afa386488dc9ddf51fbb011903409ad4ed2.jpg) +"Five men cutting a cake at a casual party." + +![](images/faaaa53ba50dec64f4deec3fc9063ce06011e49b54b45bba6a1e0f5a850b4a48.jpg) +Figure 5. Qualitative comparison of personalized multi-human scene generation. Blue arrows indicate failures in body shape personalization, while yellow arrows highlight unnatural anatomical structures, with yellow boxes providing zoomed-in views. + +![](images/0c0eee58704443d80bcbff273ddb97de9ca51d64a4861ff6696507eb0ab8fd72.jpg) + +![](images/66f9870cb67a8c2f2e2c8945833dca5bd1eba03fcf4c3c8b54e1814d0d1e6152.jpg) + +![](images/242dabd06376f30532e6a8342fe5a7604c1a4a4d18918a9d8cbe20b97e426acd.jpg) + +Table 1. Quantitative evaluation of multi-human personalization across face identity, body shape preservation, pose accuracy, text alignment, and image quality. 'Single' denotes personalization for a single individual, while 'Multi' refers to cases with multiple identities (2-5), with 'Total' representing the averaged results. + +
Multi-Human PersonalizationFace ID preservation↑Body shape preservation↑PoseTextImage quality
SingleMultiTotalSingleMultiTotalMPJPE (3D)↓AP-0.5 (2D)↑CLIP sim ↑IS ↑KID ↓
InstantID + OMG0.3690.1990.2270.5200.3450.374112.60.2580.2673.9230.101
IPAdapter+ OMG0.2280.1290.1420.5650.3760.401116.30.2440.2664.1330.102
IPA-Face + OMG0.3100.1660.1880.5150.3410.367115.40.2490.2674.0210.102
Ours0.4210.2980.3170.6300.5480.56060.650.5060.2734.2370.093
+ +Table 2. Top-1 preference rates from the user study on naturalness, face identity, body shape, and text-image correspondence in personalized multi-human scene generation. + +
Top 1 (%)Natural.↑Face ID↑Body shape↑Text corr.↑
Textual Inversion9.7711.4610.298.41
DreamBooth15.411.1313.3313.01
InstantID + OMG10.7411.6511.5912.62
IPAdapter + OMG12.7511.7812.6214.3
IPA-Face + OMG10.879.5110.6810.74
Ours40.4544.4741.4940.91
+ +# 3.3. Full-Body Personalized Generation + +Beyond robust pose, SMPLx's key advantage is encoding body shape with coefficients, enabling full-body multi-human personalization. Unlike prior methods that only focus on facial identity and struggle to disentangle garments from body shape, our approach explicitly isolates body shape as the true identity. + +The overall process of full-body personalized image synthesis is illustrated in Fig. 4. Given full-body reference images $\{I_{\mathrm{ref}}^{(i)}\}_{i = 1}^{N_{\mathrm{human}}}$ of $N_{\mathrm{human}}$ individuals, target poses $\{\pmb {p}^{(i)}\}_{i = 1}^{N_{\mathrm{human}}}$ , and a text prompt $y$ , our goal is to generate a + +personalized image $I_P$ that faithfully preserves both face and body identities while ensuring pose consistency. To achieve this, we use MultiHMR [8] to estimate SMPLx body shape parameters $\beta^{(i)}$ and InsightFace [1] to extract face embeddings $\pmb{f}^{(i)}$ . + +We then leverage our depth-normal SCNet $\mathcal{E}_{\phi_D}^{\mathrm{SC}} - \mathcal{E}_{\phi_N}^{\mathrm{SC}}$ , OcNet $\mathcal{E}_{\omega}^{\mathrm{Occ}}$ , and face ControlNet IdentityNet [71] $\mathcal{E}_{\psi}^{\mathrm{ID}}$ . Let $F_{\theta}^{(k)}(\cdot)$ denote the $k$ -th neural block and $s^{(k)}$ the corresponding input feature map. When $R_{\mathrm{sc}} = \mathcal{E}_{\phi_D}^{\mathrm{SC}}(d_{\mathrm{SMPLx}}) + \mathcal{E}_{\phi_N}^{\mathrm{SC}}(n_{\mathrm{SMPLx}})$ , $R_{\mathrm{occ}} = \mathcal{E}_{\omega}^{\mathrm{Occ}}(d_{\mathrm{SMPLx}})$ , and $R_{\mathrm{id}}^{(i)} = \mathcal{E}_{\psi}^{\mathrm{ID}}(f^{(i)}, p_{\mathrm{face}}^{(i)})$ are the residual features from each model, the next feature map $s^{(k+1)}$ is obtained by adding these residual features to the neural block output $F_{\theta}^{(k)}(s^{(k)})$ , scaled by their conditioning weights $\alpha_{\mathrm{sc}}, \alpha_{\mathrm{occ}},$ and $\alpha_{\mathrm{id}}$ , and modulated by the face masks $M_{\mathrm{face}}^{(i)}$ and occlusion mask $M_{\mathrm{occ}}$ : + +$$ +\begin{array}{l} \boldsymbol {s} ^ {(k + 1)} = F _ {\theta} ^ {(k)} (\boldsymbol {s} ^ {(k)}) + \alpha_ {\mathrm {s c}} (1 - M _ {\mathrm {o c c}}) R _ {\mathrm {s c}} \\ + \alpha_ {\text {o c c}} M _ {\text {o c c}} R _ {\text {o c c}} + \alpha_ {\mathrm {i d}} \sum_ {i = 1} ^ {N _ {\text {h u m a n}}} M _ {\text {f a c e}} ^ {(i)} * R _ {\mathrm {i d}} ^ {(i)}. \tag {5} \\ \end{array} +$$ + +Dual-Pathway Body Shape Personalization. We intro + +![](images/da0611900ea3c532e269a6365aa6e86cd9e554bcda67062ba96b011093ac2982.jpg) +Full-body Ref. Images +"Four people standing in a TV show." + +![](images/e674d8df6eb1b892713c7af5bec2f3dc525b5f9c2d19be851492bbb4fb007134.jpg) +Pose Input +Figure 6. Comparison of personalized multi-human scene generation with the methods which are not direct baselines. Yellow arrows highlight anatomical inconsistencies in poses and occlusions, while Pink arrows indicate identity mixing or duplication in the baselines. + +![](images/062e780cf80ef7b6bf28b1dbb3d20f2570e276e670912c065d22af2ec431a5fa.jpg) +UniPortrait + +![](images/a4e312cb7689f775d8847b4b9f8cc13cba4a2416a419e0d516e1fad254a017f3.jpg) +MS-Diffusion + +![](images/468b946288eb697f3f1ef726589659fc8b4ee4f847b97e729536c30bf72e2201.jpg) +FastComposer + +![](images/b70a18ac8945928bc1366e530a069661137f91377970ea8dd79ec7d73e0f67b4.jpg) +Ours + +![](images/282e5f960817d32cb5bae2abd39e134dc3b38a25f668db0e8ef9c00a85908790.jpg) +Pose Input +"A woman doing yoga on the grass." + +![](images/23477d310c3848883f5d17d12e3b5b3f5b5ade2b0816c306f84c6e6271107ea6.jpg) +T2IApapter-SDXL + +![](images/daa47b6006af9c7f9668f6a1110e788a84901c6b5b090cb7bd6857ec0c150e3b.jpg) +ControlNet-SDXL + +![](images/2cb8accb640136b0eedf368f5edfa15596ddce0f47f14fb72c0aeb537fd9ff35.jpg) +ControlNet-Flux cond(scale 0.8) + +![](images/d3d5f0435532ba5d8dad02dd9b4d4db2ce246d678fa13ee3b03780d61051a595.jpg) +ControlNet-Flux (cond.shape 1.0) + +![](images/33812a6933a57367aea12b5438e200f641802ccdc37e09050465a85f718b7c43.jpg) +HumanSD + +![](images/d8733b3515dc7554e468af56aa573bdfa08b8f51766c26fb26f248d4e1735b0a.jpg) +PersonaCraft (Ours) + +![](images/291dfd7460765a9aa8c76a07301d7ef4913687d562adaa0419dfc02acb03a779.jpg) +"A man hugging a woman in a wedding garden." + +![](images/ea727df9793f39f45a4659b98d9666deb7f434b8d5c613a360f59d9a82171b3b.jpg) +"Three women." + +![](images/c086121827154189f48236f96c7a10e1c591dc1b0c315d96881a2756374b2dd4.jpg) + +![](images/221b7116568ce329d3f77a24c39177bcbde008285cd9b9c13aa5b511f44dd090.jpg) +Figure 7. Qualitative comparison of pose-controlled multi-human generation. yellow arrows highlight unnatural anatomical structures, with yellow boxes providing zoomed-in views. + +![](images/5afa6129e2bc0427a39b2c0aa71fc3a15d2a9b15520cdc60c5f837f84e33da56.jpg) + +![](images/846c1d1ec01df7b58260b92d6b4d42da930b5309221d92e5202c826bc7a5b0c2.jpg) + +![](images/fe260e8927bbcfac9cd09ea650058e19a15fe9b0a703e4b18308eee2d224820e.jpg) + +![](images/37d1fbbe559988dba0eb4c6e033de8916a2eb2e153d3feb627759d4e2d4ebd4e.jpg) + +![](images/815697be2cdf6061d6049b0141e9e4b74d88dfed64b318e71a208f05b55ab9b8.jpg) + +![](images/782f628943ede0a9c410a0807520bef6e9327c802b7e68ed590487a38d002de4.jpg) + +![](images/909ab6d4eeb45b066c58ff5654b529539709ebe5ea3aed140d2c19918d076491.jpg) + +![](images/d39d35691a51d94a9cda97242422e6479c0c7d2ea41d6b4aea3122265e6622ca.jpg) + +![](images/b5c7e641c2f7ac88cb2cbcf12a3e0039fdbc10808d93aa909f865d8dd45587ce.jpg) + +![](images/e5abca85e80fde9268dc8ec952f14a07c33fbd421ea1bdee0e8bf381bdfaa023.jpg) + +Table 3. Quantitative evaluation of pose-controlled human generation across pose accuracy, text alignment, and image quality. + +
Pose-Controlled Human GenerationPoseTextImage quality
MPIJPE (3D) ↓AP-0.5 (2D) ↑CLIP sim ↑IS ↑KID ↓
T2I Adpater-SDXL198.140.3230.2693.7400.129
ControlNet-SDXL114.930.2910.2853.0620.138
ControlNet-Flux102.640.3930.2183.6510.107
HumanSD-SD2103.620.3570.2613.6100.082
Ours62.6470.4950.2744.1130.091
+ +Table 4. Top-1 preference rates from the user study on naturalness, pose consistency, and text-image correspondence in pose-controlled multi-human scene generation. + +
Top 1 (%)Natural.↑Pose consistency↑Text corr.↑
T2I Adpater-SDXL9.537.318.19
ControlNet-SDXL17.7218.1919.36
Ours72.7574.5072.46
+ +duce a dual-pathway approach for body shape personalization, leveraging both SMPLx-based and text-based representations. Compared to textual descriptions of body shape, SMPLx-based representations provide more spatially fine-grained encoding of the identity. However, they are limited in accurately conveying body composition details, such as fat and muscle distribution [52]. In challenging cases where body shape characteristics conflict (e.g., a muscular + +physique with high body fat), our method optionally incorporates a textual pathway to enhance body shape representation. Specifically, a CLIP-based classifier [55] extracts body shape attributes in text, which are applied using regional prompting [6] and integrated with SCNet. Further details are provided in the supplementary material. + +# 4. Experiments + +Implementation Details. PersonaCraft is built on Stable Diffusion XL (SDXL) [54]. We extend the MPII dataset [3] with textual descriptions [32] and 3D human reconstructions from MultiHMR [8] using SMPLx [51]. SCNet and OccNet were fine-tuned on ControlNet [79] with a learning rate of 1e-5, Adam optimizer, batch size of 2, for 50,000 iterations on an NVIDIA A100 GPU. We use 30 denoising steps. We set the base CFG scale to 3 ( $k_{\mathrm{base}} = 3$ ) and increased the scale for occluded regions to 5 ( $k_{\mathrm{occ}} = 5$ ) to enhance occlusion handling. We set all conditioning scales ( $\alpha_{\mathrm{sc}}$ , $\alpha_{\mathrm{occ}}$ , and $\alpha_{\mathrm{id}}$ ) to 0.8 across all cases. + +Metrics. For personalized multi-human scene generation, face identity preservation is measured using FaceNet [61], following FastComposer [74]. Body shape preservation is + +![](images/c193c2d9fb446beacafb0c960ea3b00772500381a77c77d4c717edb5978ab37d.jpg) +Figure 8. Effect of our occlusion-aware 3D pose & shape conditioning components. D and N denote the conditioning types of SCNet: depth, normal. + +![](images/3f59b8684caf55e17d627fcc68df705e27e007ae3b21126757d8db2076ae0d6b.jpg) +Figure 9. Effectiveness of dual-pathway body shape personalization in challenging cases where body shape characteristics conflict (e.g., a muscular physique with high body fat). + +Table 5. Ablation study on SCNet, OccNet, and OccCFG for pose consistency. D, N, and R denote the conditioning types of SCNet: depth, normal, and RGB representations, respectively. + +
Ablation StudyPose
MPJPE (3D)↓AP-0.5 (2D)↑
SCNet-D71.200.423
SCNet-N79.300.398
SCNet-R82.520.394
SCNet-D + SCNet-N63.160.494
SCNet-D + SCNet-N + OccNet62.920.499
SCNet-D + SCNet-N + OccNet + OccCFG62.640.495
+ +evaluated via cosine similarity of SMPLx body shape parameters $\beta$ . Pose consistency is assessed using MPJPE (3D) [29], while 2D pose estimation is evaluated with AP-0.5 (2D) by comparing the target pose to the estimated pose from generated images. Text-image alignment is measured via CLIP-L/14 similarity. Image quality is quantified using Inception Score (IS) [60] and Kernel Inception Distance (KID) [10]. A user study evaluates perceptual quality. + +For pose-controlled multi-human scene generation, the same key metrics are applied: MPJPE (3D) and AP-0.5 (2D) for pose accuracy, CLIP similarity for text-image alignment, and IS/KID for image quality. + +Test Dataset. We test on the COCO-WholeBody dataset [30], containing $1\sim 5$ people per image. A total of 1,000 images were selected (200 per group). Text prompts were extracted via BLIP [42]. MultiHMR [7] provided poses and 3D conditioning. + +Additional details on experiments, results (including qualitative results), stylized artwork, PersonaCraft with LoRA and other face control modules, as well as ablation studies, are provided in the supplementary material. + +# 4.1. Personalized Multi-Human Scene Generation + +Baselines. We mainly compared PersonaCraft with baseline methods for single-shot, multi-identity, and + +pose-controllable synthesis, all implemented using SDXL [54]. Key baselines include OMG [37] with InstantID/IPAdapter/IPAdapter-Face (IPA-Face) [70, 78], and 2D pose ControlNet [79]. We also evaluated optimization-based methods like DreamBooth [56] and Texture Inversion [17]. Both qualitative and quantitative comparisons, as well as a user study, were conducted. Additionally, qualitative comparisons were made with Uni-Portrait [25], MS-Diffusion [72], and FastComposer [75]. + +Qualitative Results. As shown in Fig. 5, PersonaCraft surpasses baselines in multi-identity scene generation, particularly in identity preservation and occlusion handling. Our 3D-aware conditioning and occlusion-focused generation enhance the preservation of body shapes and identity features, and ensure pose fidelity, producing realistic generations with fewer artifacts. Baseline methods struggle with occlusion and body shape accuracy, often leading to distorted identities and unrealistic compositions, especially in multi-subject scenes. PersonaCraft excels in occlusion-aware full-body personalization, maintaining consistent identities across varying poses. + +Quantitative Results. We evaluate PersonaCraft on face ID preservation, body shape, pose accuracy, text-image alignment, and image quality. As shown in Tab. 1, our method consistently outperforms baselines in identity and body shape preservation. It achieves the lowest MPJPE (3D) and highest AP (2D), indicating superior alignment with input poses. In terms of text-image alignment, ours also achieves the highest CLIP score. Furthermore, PersonaCraft outperforms baselines in IS and KID, producing perceptually aligned generations. + +User Study. We conducted a user study evaluating naturalness, face identity, body shape, and text-image correspondence across baselines and our method. With 18,540 responses from 103 participants, Tab. 2 shows our method achieved the highest Top-1 preference across all metrics, demonstrating superior perceptual quality in personalized multi-human scene generation. + +# 4.2. Pose-Controlled Multi-Human Scene Generation + +Baselines. Key baselines include ControlNet-SDXL [54, 79], T2I Adapter-SDXL [49], ControlNet-Flux [41, 79], and HumanSD [41]. Both qualitative and quantitative comparisons were conducted for all baselines. Additionally, a user study was performed specifically for SDXL-based baselines, including ControlNet-SDXL and T2I Adapter-SDXL. + +Qualitative Results. We evaluate pose-controlled multi-human scene generation by comparing PersonaCraft with existing methods in both single-human and multi-human settings (Fig. 7). Our method achieves superior pose alignment compared to baseline methods. Baselines relying on 2D pose conditioning (e.g., T2IAp dter-SDXL [49], ControlNet + +![](images/167774d3fe1b7343b2690c77a4329724c9e26bde284e348418c63691ca38d39d.jpg) +(a) Reference based user-defined body shape control + +![](images/5f8acfb24436c0f26bd36b1b6e6c4ad6c5bb22282fd9aa187bb2833b5e924ff0.jpg) +(b) Interpolation based user-defined body shape control +Figure 10. Result of PersonaCraft's user-defined body shape control. (a) Reference-based body shape control. (b) Interpolation and extrapolation-based control, where $\gamma$ controls the interpolation or extrapolation between the reference body shapes. + +SDXL [54, 79]) struggle with occlusion handling, leading to misaligned poses and distorted structures. ControlNet-Flux [41, 79] exhibits instability: at a lower conditioning scale (0.8), it fails to maintain anatomical coherence, while at a higher scale (1.0), it improves pose accuracy but reduces image fidelity. HumanSD [31] lacks precise pose control, producing unrealistic compositions. In contrast, PersonaCraft balances pose accuracy, anatomical coherence, and image fidelity, demonstrating the efficacy of our 3D-aware pose conditioning. + +Quantitative Results. We evaluate pose-controlled multi-human scene generation in terms of pose accuracy, text-image correspondence, and image quality. As shown in Tab. 3, PersonaCraft achieves the lowest MPJPE (3D) and highest AP-0.5 (2D), demonstrating precise pose alignment and keypoint localization. Compared to ControlNet-based baselines, which suffer from structural inconsistencies and occlusion issues, our method maintains accurate pose fidelity. PersonaCraft also achieves the highest IS and lowest KID, indicating superior perceptual realism. While text-image correspondence scores are comparable across methods, prior studies [36, 38] highlight CLIP's limitations in evaluating complex multi-human scenes. A user study further analyzes perceptual quality. + +User Study. We conducted a user study to assess naturalness, pose consistency, and text-image correspondence. Participants ranked their top three preferences among T2I Adapter-SDXL, ControlNet-SDXL, and PersonaCraft, collecting 15,390 responses from 114 participants. As shown in Tab. 4, PersonaCraft achieved the highest Top-1 preference across all metrics, excelling in naturalness (72.75%), pose consistency (74.50%), and text alignment (72.46%). These + +results confirm that our occlusion-aware 3D pose conditioning significantly improves perceptual quality, producing well-posed, visually coherent multi-human scenes. + +# 4.3. Ablation Studies and Analysis + +Comparison of 3D Pose Representations for SCNet. In Tab. 5, we evaluate different SMPLx renderings—depth, normal, and RGB—as conditioning inputs for SCNet. We find that depth yields the best pose consistency among these representations. Additionally, combining the depth and normal representations achieves the best performance. Therefore, we adopt this combination as the base conditioning for SCNet. + +Effectiveness of OccNet and OccCFG. In Tab. 5, we also evaluate the effectiveness of OccNet and OccCFG. We found that OccNet and OccCFG improve pose consistency. Also, as analyzed in Fig. 8, we observe the effect of our Occlusion-aware 3D pose & shape conditioning components. Using only 2D pose leads to front-back ambiguities and structural inconsistencies, while relying solely on 3D pose (SCNet) struggles with fine-grained occluded regions. Using only OccNet improves occluded region synthesis but fails to maintain overall pose alignment. Our full model (SCNet + OccNet + OccCFG) effectively preserves pose structure while handling occlusions. + +Dual-Pathway Body Personalization. As shown in Fig. 9, the SMPLx-based pathway captures fine-grained identity features but struggles with detailed body composition (e.g., muscle vs. fat distribution). The text-based pathway refines body shape using semantic attributes. Our approach combines both for more accurate and realistic personalization. + +# 4.4. User-Defined Body Shape Control + +A key feature of PersonaCraft is its user-defined body shape control, as shown in Fig. 10. Users can select a reference to adapt body characteristics for personalized images. The system also allows body proportions to be adjusted through interpolation or extrapolation between references, offering enhanced customization for precise body shape control. + +# 5. Conclusion + +We present PersonaCraft, a framework for occlusion-robust, full-body personalized image synthesis in complex multi-human scenes. PersonaCraft integrates diffusion models with 3D human modeling, using SMPLx-ControlNet for enhanced pose conditioning. To address occlusions at a fine level, we introduce Occlusion Boundary Enhancer and Occlusion-Aware Classifier-Free Guidance strategy, improving conditioning in occluded areas. Seamlessly combined with Face Identity ControlNet, our approach enables full-body personalization beyond facial identity. Extensive experiments show PersonaCraft outperforms prior arts in personalization accuracy and occlusion robustness in complex scenes. + +# Acknowledgement + +This work was supported in part by Samsung Electronics MX Division and by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)]. Also, the authors acknowledged the financial support from the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University. + +# References + +[1] Insightface: 2d and 3d face analysis project. Github, https://github.com/deepinsight/insightface.4,5 +[2] Yuval Alaluf, Elad Richardson, Gal Metzer, and Daniel Cohen-Or. A neural space-time representation for text-to-image personalization. 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Champ: Controllable and consistent human image animation with 3d parametric guidance. arXiv preprint arXiv:2403.14781, 2024. 2, 3 \ No newline at end of file diff --git a/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/images.zip b/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..54a60bf09fb668c0eed6d14fee1c0c8e51f1f175 --- /dev/null +++ b/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene Generation Using Occlusion-Aware 3D-Conditioned Diffusion/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:98fe506138a07c31a4ec84632ee919cdc47d92aff13df6030c3a3b2e0de5c0fd +size 901447 diff --git a/ICCV/2025/PersonaCraft_ Personalized and Controllable Full-Body Multi-Human Scene 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High ID-Fidelity Video Customization without Dynamic and Semantic Degradation/full.md b/ICCV/2025/PersonalVideo_ High ID-Fidelity Video Customization without Dynamic and Semantic Degradation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c036e0e6655c5fde1131b074374e3a31b4e5e686 --- /dev/null +++ b/ICCV/2025/PersonalVideo_ High ID-Fidelity Video Customization without Dynamic and Semantic Degradation/full.md @@ -0,0 +1,319 @@ +# PersonalVideo: High ID-Fidelity Video Customization without Dynamic and Semantic Degradation + +Hengjia Li $^{1}$ , Haonan Qiu $^{2}$ , Shiwei Zhang $^{3,*}$ , Xiang Wang $^{3,4}$ , Yujie Wei $^{3}$ , Zekun Li $^{3}$ , Yingya Zhang $^{3}$ , Boxi Wu $^{1,\dagger}$ , Deng Cai $^{1}$ + +1Zhejiang University + +$^{2}$ Nanyang Technological University + +3Alibaba Tongyi + +$^{4}$ HUST + +lhjzju@zju.edu.cn, zhangjin.zsw@alibaba-inc.com + +Project page: https://personalvideo.github.io/ + +![](images/f8296cb496d5b5d970e51fb78ad2b41b5492f72311f28b27806b0bbe7706d043.jpg) +Reference + +![](images/a84ee71d23794a9070b5f24cd0dc21c13bbf4d5af7d656a1f63773553942c5c9.jpg) +"A $< v>$ woman in a sparkly, magical dress, casting spells with her hands as glowing lights swirl around her. Her face is visible with a mischievous grin, surrounded by floating mystical symbols." + +![](images/5c84b7bdbbd94e7988fca3f845c4c642d162f4136909e3e6baf0d6c7fc7c0e7a.jpg) +Reference + +![](images/769e6ad82fb1d79e7d5c2e7cbdbb4cb3fe6d7fad72af9290ad071250811ad752.jpg) +"A $< v>$ musician man sitting on a stool, strumming an acoustic guitar with a serene expression. He wears a casual button-down shirt and jeans, lost in the melody." + +![](images/7412f4c11917f91bcbc638cb8750912b2c1b1ff656b91423bbf72cb8d9c80093.jpg) +Reference + +![](images/1bae6012089d14540edff601a17987e432dfe4c5299b81fc7da0dc3475411fa3.jpg) +"A $< v>$ woman dressed as a warrior princess, holding a glowing sword as she stands in a field of wildflowers. Her face is visible, showing determination as she prepares to protect her kingdom." + +![](images/ab3d5693f7891c5a5ec9204dc7d17542abc716a3e8ae49b0cc61f5c499f29e6d.jpg) +Reference + +Figure 1. Results of PersonalVideo. Given the reference images of a specific identity, PersonalVideo can generate high ID-fidelity videos with promising motion dynamics and prompt following. +![](images/7c3f9cd59e3acb9c4f4a3568f6678ab02bb1db66820b8e6df9f9b1fd97a363ab.jpg) +"A $< v>$ man in a black suit, paired with a white shirt and a dark tie, is walking along a busy city street. He is carrying a steaming cup of coffee in one hand. The street is lined with tall buildings and bustling with people." + +# Abstract + +The current text-to-video (T2V) generation has made significant progress in synthesizing realistic general videos, but it is still under-explored in identity-specific human video generation with customized ID images. The key challenge lies in maintaining high ID fidelity consistently while preserving the original motion dynamic and semantic following after the identity injection. Current video identity customization methods mainly rely on reconstructing given identity images + +on text-to-image models, which have a divergent distribution with the T2V model. This process introduces a tuning-inference gap, leading to dynamic and semantic degradation. To tackle this problem, we propose a novel framework, dubbed PersonalVideo, that applies a mixture of reward supervision on synthesized videos instead of the simple reconstruction objective on images. Specifically, we first incorporate identity consistency reward to effectively inject the reference's identity without the tuning-inference gap. Then we propose a novel semantic consistency reward to align the semantic distribution of the generated videos with the original T2V model, which preserves its dynamic and semantic + +![](images/141a764f57dfe443612d2b1be872cbfa7d1b0798099b28b13b5e922a87d79b6a.jpg) +Figure 2. Analysis of the tuning-inference gap. Previous T2V customization supervises the tuning process via reconstructing images on T2I models, suffering from a tuning-inference gap. Differently, we aim to directly apply the supervision on generated videos, which aligns with inference and bridges the gap. + +following capability during the identity injection. With the non-reconstructive reward training, we further employ simulated prompt augmentation to reduce overfitting by supervising generated results in more semantic scenarios, gaining good robustness even with only a single reference image. Extensive experiments demonstrate our method's superiority in delivering high identity faithfulness while preserving the inherent video generation qualities of the original T2V model, outshining prior methods. + +# 1. Introduction + +Recently, there has been considerable scholarly interest in text-to-video (T2V) generation [7, 10, 14, 40], which allows for the production of videos from user-defined textual descriptions. However, the identity-specific customization of high-fidelity human videos has not been fully explored. It aims to customize a wide variety of engaging videos using a few users' photos, allowing for personalized content creation that features them in different actions, scenes, or styles while maintaining high ID fidelity. Without the need for complex scene construction and tedious post-production special effects, this convenient way of video creation also has great potential in the film and television industry. + +Identity customization has achieved significant advancements in the field of text-to-image (T2I) [12, 15, 30, 36, 41, 50]. Typically, these methods use a reconstructive approach on provided reference images to inject the identity into the pre-trained T2I model during the customization. However, directly employing this strategy in video customization [32, 44] will lead to unsatisfied results due to two notable challenges: + +(1) Preserving inherent motion dynamics and semantic following. Existing video customization methods [32, 44] naively use image reconstruction supervision during tuning to model a customized T2I prior, which is then injected into the T2V model to generate identity-specific videos during inference. However, the distribution of the pre-trained T2V model often deviates from that of the pretrained T2I model, which brings a tuning-inference gap as shown in Fig. 2. Since tuning on limited static images will significantly shift the video prior of the pre-trained T2V model, it leads to a dynamic and semantic degradation, making the generated videos tend to appear static and fail to follow the given prompts. +(2) Inserting consistent identity with high fidelity. For reconstruction-based video customization, the tuning-inference gap also brings challenges for ID-fidelity. As humans are sensitive to facial features, higher fidelity, and consistent identity are required in customized videos. To achieve identity consistency while preserving the model's dynamics and semantics, traditional reconstructive video customization methods [9, 19, 44] often require more images, even additional video input, to inject identity without overfitting, which brings great inconvenient for users. + +To address these challenges, we propose a novel framework, dubbed PersonalVideo, for ID-specific video generation that can achieve high ID fidelity and maintain original motion dynamics and semantic following with only a few images of an identity given. Different from previous methods with a reconstructing objective on T2I models, our core insight is applying the direct reward to videos generated by the T2V model thus bridging the tuning-inference gap as shown in Fig. 2. Specifically, we integrate feedback from a + +mixture of differentiable reward models to inject an identity consistent with the reference while preserving the original model's dynamic and semantic following capability. + +Inspired by the successful experience of the identity supervision [35, 42] in encoder-based T2I customization [13, 15], we propose to apply Identity Consistency Reward (ICR) to a randomly selected frame in the generated video, leveraging the similarity feedback from an identity recognition model to consistently inject the reference's identity without the tuning-inference gap. However, applying only ID reward still suffers from degraded dynamic and semantic following capabilities, which is caused by the inherent distribution shift introduced by the limited number of static images during ID injection. To address this shift, we further propose a Semantic Consistency Reward (SCR) to preserve the original model's semantic distribution, thereby mitigating the degradation of dynamic and semantic following capabilities. Leveraging the semantic reward model, we can evaluate the image-text correspondence of the sampled video frames and then align the score distribution between the original video and the target video, thus effectively preserving the dynamics and semantics of the original generator without affecting the injection of the identity. + +With the non-reconstructive reward supervision, we also employ simulated prompt augmentation, which is independent of provided reference images and supervises generated results in more semantic scenarios. Unlike the reconstructive training method, they do not correspond to each reference nor are they limited by the number of reference images, effectively mitigating overfitting and demonstrating strong robustness, even when only a single reference image is available. + +To achieve the identity injection with preserved motion dynamics and semantic following, it is also essential to design the learnable modules. Based on the observations for the denoising steps, we further propose an Isolated Identity Adapter injected in the only later denoising step, which minimizes the impact on the original video's dynamic. Qualitative and quantitative experiments demonstrate that our PersonalVideo achieves high ID fidelity and effectively preserves the original T2V model's capabilities. Benefiting from the scalability of T2V models, it also supports any style-specific fine-tuned model, which offer valuable flexibility for abundant creation in the AIGC community. Our contributions are summarized as follows: + +- We introduce a novel framework, dubbed PersonalVideo, for video personalization with static images. To bridge the tuning-inference gap, we propose to apply the direct reward feedback to generated videos, achieving high ID-fidelity without dynamic and semantic degradation. +- We propose a novel semantic consistency reward to effectively preserve the original model's semantic distribution without affecting the injection of the identity. + +- With the non-reconstructive supervision, we introduce simulated prompt augmentation which is independent of the reference images and robustly improves ID-fidelity, even for just a single image. + +# 2. Related Work + +Text-to-Video Generation. The topic of T2V generation has attracted considerable interest among researchers for a long time. Recently, the utilization of diffusion models has become predominant in the realm of T2V tasks. VDM [21] stands as the pioneer that first leverages a diffusion model for T2V generation. Subsequently, Make-A-Video [37] and Imagen Video [20] were proposed to generate high-resolution videos in pixel space. To save computational resources, various frameworks have been developed to perform a latent denoising process [6, 18, 40, 43, 52–55]. Although these methods can produce high-quality generic videos by pre-training on large-scale text-video pair datasets, it remains challenging to synthesize id-specific videos. + +Text-to-Image Customization. In the field of T2I, a lot of approaches [12, 13, 26-28, 30, 31, 34, 38, 49] have emerged for ID customization. As a seminal work, Textual Inversion [12] represents the user-provided identity with a specific token embedding of a frozen T2I model. For better ID fidelity, DreamBooth [36] optimizes the original model, where efficient fine-tuning techniques such as LoRA [22] can also be applied. On the other hand, encoder-based methods aims to directly inject ID into the generation process. IP-Adapter [50] and InstantID [41] focus on adapting encoders that extract ID-relevant information. PuLID [15] suggests optimizing an ID loss between the generated and reference images in a more accurate setting. + +Text-to-Video Customization. The T2V customization presents further challenges compared to the T2I customization due to the temporal motion dynamics involved in videos. Currently, only limited works [17, 23, 29, 32, 44–47, 51] have undertaken early investigations into this area. MagicMe [32] adopts an ID module based on extended Textual Inversion. However, training under T2I reconstruction supervision deviates from the T2V inference, leading to inferior ID fidelity and model degradation. DreamVideo [44] customizes the identity given a few images, but the inconvenience lies in the fact that it necessitates additional videos to provide motion patterns. ID-Animator [17] proposes to encode ID-relevant information with a face adapter, which requires thousands of high-quality human videos for fine-tuning, thereby incurring significant costs associated with dataset construction and model training. + +# 3. Preliminaries + +Text-to-video diffusion models (T2V) [6, 14, 25, 39, 40] are tailored for generating videos by adapting image diffu + +![](images/ce0855ce52b472658b13d2421b3ba44e478f1322721e70552e6045b3cd605e5a.jpg) +Figure 3. Overview of the framework of PersonalVideo. To bridge the tuning-inference gap, we directly apply reward supervision on generated videos starting from pure noises, including identity consistency reward with the reference and semantic consistency reward with the original video. During the optimization, we adopt simulated prompt sampled from the Large Language Model to supervise generated results in more semantic scenarios. + +sion models to handle video data. Specifically, the diffusion model $\epsilon_{\theta}$ aims to predict the added noise $\epsilon$ at each timestep $t$ based on text condition $c$ , where $t \in \mathcal{U}(0,1)$ is normalized. The training objective can be simplified as a noise-prediction loss: + +$$ +\mathcal {L} _ {\text {d i f f}} = \mathbb {E} _ {z, c, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, \tau_ {\theta} (c), t\right) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $z \in \mathbb{R}^{B \times F \times H \times W \times C}$ is the latent code of video data with $B, F, H, W, C$ being batch size, frame, height, width, and channel, respectively. $\tau_{\theta}$ presents a pre-trained text encoder. A noise-corrupted latent code $z_{t}$ from the groundtruth $z_{0}$ is formulated as $z_{t} = \alpha_{t} z_{0} + \sigma_{t} \epsilon$ , where $\alpha_{t}$ and $\sigma_{t}$ are hyperparameters to control the diffusion process. + +# 4. Methodology + +# 4.1. Non-Reconstructive Reward Framework + +Current T2V customization typically adopts a reconstruction approach to train a customized T2I prior on provided images and inject it into the pre-trained T2V models to generate identity-specific videos. However, it leads to a tuning-inference gap due to the misaligned distribution between reference images during tuning and generated videos in inference time, which brings inferior ID fidelity and degradation of inherent motion dynamics and semantic following. + +To bridge the gap, as shown in Fig. 3, we propose a nonreconstructive framework to directly apply reward on the generated videos for high ID fidelity without dynamic and semantic degradation. Inspired by the successful experience of the identity supervision [35, 42] in encoder-based T2I customization [13, 15], we propose to apply Identity Consistency Reward (ICR) to the generated video. During the tuning time, we start from pure noise instead of noised + +references in the previous reconstructive methods. Then we directly supervise the a randomly selected frame from the generated video to mimic the identity in the generated videos with that in references using ID similarity reward, which closely aligns with human perception and the distribution of the real world. + +Specifically, we use pre-trained ID recognition model [11] $\mathcal{R}_{id}$ to precisely extract the ID embeddings of the references and the random $i$ -th frame of the generated video. Then we minimize the cosine similarity of them to align the identity effectively and directly. Here we crop the faces and adopt image augmentation techniques like color jitter to make it more robust for limited references. Formally, our training objective is: + +$$ +\mathcal {L} _ {\mathrm {I C R}} = \mathbb {E} _ {i, c \sim p (c)} [ \operatorname {C o s S i m} (\mathcal {R} _ {i d} (I _ {r e f}), \mathcal {R} _ {i d} (G _ {\mathcal {T}} (z _ {T}, c, i))) ], \tag {2} +$$ + +where $I_{ref}$ are the reference images, $G_{\mathcal{T}}$ is the target trained diffusion model with the VAE decoder, and $c$ is the text prompt with the specific keyword. + +# 4.2. Semantic Consistency Reward + +While the non-reconstructive ICR addresses the tuning-inference gap in existing methods, the distribution gap introduced by the limited static references still remains, which makes it challenging to preserve the original dynamics and semantics. To address this issue, we further introduce a novel Semantic Consistency Reward (SCR) to maintain the original model's semantic distribution, effectively alleviating the decline in dynamic and semantic following. Specifically, we randomly sample a batch of $M$ frames from the video generated by original and target model. Then we leverage the semantic reward model $\mathcal{R}_{sem}$ to evaluate the + +![](images/7bc2ebae1e3196a2b4d944b4a3dc2c46eb941c14339663055db96a48d4a7eec8.jpg) +Figure 4. Visualization of the video denoising steps. The motion of the person, e.g., his hand, is formed in early stages of the denoising process. The later steps focus on the recovering of the detailed appearance. + +image-text correspondence of the sampled video frames + +$$ +V _ {c} ^ {\mathcal {S}} = \operatorname {S o f t m a x} \left(\left\{\mathcal {R} _ {s e m} \left(G _ {\mathcal {S}} \left(z _ {T}, c, i\right) \right\} _ {i = 1} ^ {M}\right)\right), \tag {3} +$$ + +$$ +V _ {c} ^ {\mathcal {T}} = \operatorname {S o f t m a x} \left(\left\{\mathcal {R} _ {s e m} \left(G _ {\mathcal {T}} \left(z _ {T}, c, i\right) \right\} _ {i = 1} ^ {M}\right)\right), +$$ + +where $G_{S}$ is the frozen original diffusion model with the VAE decoder. Finally, we align the score distribution between the original and the target video with KL divergence, + +$$ +\mathcal {L} _ {\mathrm {S C R}} = \mathbb {E} _ {c \sim p (c)} D _ {K L} \left(V _ {c} ^ {T} \| V _ {c} ^ {S}\right). \tag {4} +$$ + +Through the distribution alignment with the original generator, we can effectively preserve its dynamics and semantics without affecting the injection of the identity. + +Thus, the full learning objective is defined as: + +$$ +\mathcal {L} _ {\text {t r a i n}} = \mathcal {L} _ {\text {I C R}} + \mathcal {L} _ {\text {S C R}}. \tag {5} +$$ + +# 4.3. Simulated Prompt Augmentation + +To further enhance the robustness of the customization, we introduce simulated prompt augmentation. During the customization process, traditional reconstruction frameworks can only utilize prompts that describe the reference image, which limits the model's generalization capabilities. Benefiting from the non-reconstructive framework, we can incorporate numerous reference-irrelevant prompts during the optimization, e.g., 'V' playing the violin and 'V' smiling on the beach. Specifically, we leverage the Large Language Model to create 50 prompts as our simulated prompts with various motion, appearance, and backgrounds and randomly select the prompts during the customization. They align well with actual test scenarios to mitigate overfitting with strong robustness, even when only a single reference image is available. + +# 4.4. Isolated Identity Adapter + +To achieve the identity injection with preserved motion dynamics and semantic following, it is also essential to design the learnable modules. Based on the observations for the denoising steps shown in Fig. 4, we find that the motion of the person is typically formed in the early denoising step. During these steps, the model tends to restore the layout [8] and motion. In contrast, the later steps focus on recovering of the detailed appearance of the objects [33]. Therefore, we propose to isolatedly inject the identity only in the later denoising steps during training and inference time, to reduce the influence on the motion generation and mitigate the distribution shift caused by static reference images. Formally, it adopts the residual path of two low-rank matrices including a down block $A^{\mathrm{down}} \in \mathbb{R}^{d \times r}$ and up block $A^{\mathrm{up}} \in \mathbb{R}^{r \times k}$ . Formally, the updated parameter matrices are + +$$ +\tilde {W} = W + \Delta W = W + A ^ {\mathrm {d o w n}} A ^ {\mathrm {u p}}, \tag {6} +$$ + +for all $W$ in the layers of query, key, and value. + +# 5. Experiments + +# 5.1. Experimental Settings + +To demonstrate the effectiveness of our method, we utilize a DiT-based model, HunyuanVideo [25], and a UNet-based modelAnimateDiff as our T2V generation models. We use ResNet-100 [16] backbone pre-trained on Glint360K [5] dataset as the identity reward model and HPSv2 [48] as the semantic reward model. To demonstrate the superiority of PersonalVideo, we compare it with MagicMe [32], a recent identity-specific T2V customization method, as well as Dreambooth with LoRA [22, 36]. Additionally, we compare the results with encoder-based methods like IDAnimator [17] and ConsisID [51]. We present the details of baselines and training process in Appendix. + +# 5.2. Qualitative Results + +We provide a qualitative comparison between PersonalVideo and baselines. As shown in Fig. 5, both Dreambooth and MagicMe suffer from inferior ID fidelity, due to the tuning-inference gap. In contrast, our PersonalVideo achieves high ID fidelity and preserves the original motion dynamics and semantic following. To verify the robustness of our method, we also conduct the experiments for only a single image reference and compare with encoder-based methods. As shown in Fig. 6, they not only demonstrate suboptimal identity fidelity but also suffer from compromised dynamic motions and insufficient video quality. The results further underscore the superiority of PersonalVideo, with promising robustness to achieve high ID fidelity and preserve motion dynamics and semantic following. To demonstrate the generalization of our method, we + +![](images/b9d0abaa65bb401a896525e230cc95c56cc7c8dbedbf4f4ae3f4e9d96d8fa205.jpg) +Figure 5. Qualitative comparison for a few references. As observed, both Dreambooth and MagicMe suffer from inferior ID fidelity. In contrast, our PersonalVideo maintains high ID fidelity and preserve the original motion dynamics and semantic following, significantly surpassing others. + +
MethodFace Sim. (↑)Dyna. Deg. (↑)FVD (↓)T. Cons. (↑)CLIP-T (↑)CLIP-I (↑)
DreamBooth42.6213.861325.890.991926.2644.27
MagicMe50.5111.881336.730.992825.4873.03
IDAnimator43.8814.331538.440.991224.3350.23
ConsisID53.2215.221622.210.992325.3974.58
PersonalVideo62.3517.801272.320.993526.3076.48
+ +Table 1. Quantitative comparison. The metrics cover the ability to achieve high ID fidelity (i.e., Face Similarity and CLIP-I), dynamic degree, text alignment (i.e., CLIP-T), distribution distance (i.e., FVD), and temporal consistency. + +also conduct the experiments on a UNet-based model, Animatediff, in the appendix. + +# 5.3. Quantitative Results + +We present the quantitative results in Tab. 1 and evaluate 1000 generated videos for 20 identities with 50 prompts from these perspectives: (1) Face Similarity: the ID cosine similarity to evaluate ID fidelity, with ID embeddings extracted using Antelopev2 [11], which is different from the face recognition models in our framework. (2) Dynamic Degree: we use VBenchmark [24], an effective benchmark to compute video dynamics. Besides, we use well-known metrics for video evaluation. As observed, DreamBooth suffers + +from inferior face similarity due to the tuning-inference gap. MagicMe gets better face similarity yet degraded dynamics and text alignment. In contrast, our PersonalVideo significantly surpasses previous methods, especially for face similarity and dynamic degree. It achieves high ID fidelity and effectively preserves the ability of the original T2V model, which is consistent with the qualitative results. + +# 5.4. User Study + +To further assess the effectiveness of our approach, we perform a human evaluation comparing our method with existing T2V identity customization techniques. We invite 15 people to review 50 sets of generated video results. For each + +![](images/abf4f5b9927d7b1ea1d3aa57d36c127fd42ce6ad02a16a1b97447b50c527b023.jpg) + +![](images/2484db39a48568c60fde3b7d300f0f19d08f52fcc8bc225a515aba7ef0235eef.jpg) +"A woman in a +sparkly, magical dress, +casting spells with her +hands as glowing lights +swit around her. Her face is +visible with a mischievous +grin, surrounded by +floating mystical symbols." +JIOIOWAIAI DIISUO +sunO + +![](images/e9c1a90cd61f7381979b76ccc530b626ab7316eb355c8e9ae350dcfff7e389fe.jpg) +"A $< V>$ man standing on a quiet street at night, hands in his pockets, gazing up at the stars with a thoughtful expression. Then he turns and looks the other way, wearing a leather jacket and jeans." + +![](images/f7c15f67f4aa505945ca05c1e94d11723a6b55c73a599bffec990c011acc1ed7.jpg) +Figure 6. Qualitative comparison for a single reference. As observed, the baseline methods not only demonstrate suboptimal identity fidelity but also suffer from compromised dynamic motions and insufficient video quality. In comparison, our PersonalVideo maintains higher ID fidelity without dynamic and semantic degradation, which is consistent with Fig. 5. + +![](images/15f7ce6bcf983a4cbda4320db4006d683c8c09c25dc161e2e6dbbdadef252468.jpg) +Figure 7. User study. Our PersonalVideo achieves the best human preference compared with DreamBooth and MagicMe. + +set, we provide reference images alongside videos created using the same seed and text prompt across different methods. We evaluate the quality of the generated videos on four criteria: Identity Fidelity (the resemblance of the generated object to the reference image), Text Alignment (how well the video corresponds to the text prompt), Dynamic Degree (the dynamic degree of motion in the video), and Overall Quality (the overall satisfaction of users with the video quality). As illustrated in Fig. 7, our PersonalVideo receives significantly higher user preference across all evaluation metrics, demonstrating its effectiveness. + +# 5.5. Compatibility with LoRAs + +We also showcase that our framework demonstrates excellent compatibility with existing fine-grained condition modules, such as style LoRAs. As shown in Fig. 8, We use the + +Civitai community models to show that it operates effectively with these weights, even though it was not specifically trained on them. The first row displays the results from the RCNZ Cartoon 3D model [2], while the second row and the third row highlight the outcomes from the GuoFeng RealMix [1] and GuoFeng model [4]. Our approach consistently delivers reliable facial preservation and effective motion generation, which has great compatibility with these customized style LoRAs. + +# 5.6. Ablation Study + +Non-Reconstructive Training. To validate the impact of proposed non-reconstructive training, we conduct a detailed ablation study in Fig. 9 and Tab. 2 in Appendix. They show the comparison between our PersonalVideo trained on the T2I model or T2V model, including with and without Prompt Augmentation. As observed, tuning on the T2I Model gets inferior ID fidelity due to the tuning-inference gap, which also exacerbates the distribution shift which leads to the blurred background. In contrast, tuning on the T2V model bridges the gap to achieve better ID fidelity with the preserved ability of semantic following. On the other hand, tuning without simulated prompt augmentation overfits the reference images and disrupts the original capability of the semantic following, which manifests as an inability to precisely modify the background with reduced CLIP score. With the introduction of simulated prompt augmentation, this overfitting can be significantly reduced. + +![](images/dcbf78054242efd45a3dc36d3fabdece0bce3295a07a6fb748c179ae215ecd36.jpg) +Figure 8. Compatibility with customized style LoRAs, i.e., RCNZ Cartoon 3D, GuoFengRealMix, and GuoFeng. + +![](images/0fc85970f08fb58e59d2dcc80a62043f65a2a5f3e3edcddcd1cf6388414fa470.jpg) + +![](images/019792b09e7fd4e05b26b2cb91db0edad22280aa56225ee2fa1964715f2a76e6.jpg) + +![](images/8e09dd23c15c1c5a28533c13204b6ffb8d37ce6df67ea80bf726def64b6e6b1b.jpg) +Figure 9. Ablation study for the non-reconstructive training and simulated prompt augmentation. As observed, tuning on the T2I model suffers from inferior ID fidelity and blurred background. Besides, tuning without prompt augmentation degrades the semantic following, i.e., the wine rack. + +![](images/cebbe4454561abf494774338389e1e6619704808e18faddf225531630085c81b.jpg) +Figure 10. Ablation study for the Semantic Consistency Reward. As observed, tuning without SCR suffers from the dynamic degradation and the inferior semantic following, i.e., by the lake. + +Semantic Consistency Reward. To demonstrate the effectiveness of our SCR loss, we conduct the experiments in Fig. 10 and Tab. 3. As observed, the results of tuning without SCR loss suffer from the dynamic degradation in the first example, which exhibits less movements. Besides, the results has inferior semantic following in the second example, i.e., by the lake. They verify that our proposed SCR + +![](images/fabbc6895cb772229ffc4e08ff1d8b8ba5ecca1f946456593ad8efaf4c375dbb.jpg) +Figure 11. Ablation for different steps to inject the identity. As the denoising steps for injecting identity become more later, the motion dynamics of the generated videos improve accordingly. + +effectively preserve the desired dynamics and semantics. + +Different Steps to Inject the Identity. We also conduct the ablation studies in Fig. 11 and Tab. 4a in Appendix, which illustrate the improvement in motion dynamics of our Isolated Identity Adapter to inject the identity only in the last quarter of denoising steps. As the denoising steps for injecting identity become more concentrated in the later stages, the motion dynamics of the generated videos improve accordingly. This aligns with our observations and validates the effectiveness of our design. + +# 6. Conclusion + +In conclusion, we present PersonalVideo, a novel framework designed for identity-specific video generation, achieving high identity fidelity while preserving the motion dynamics and semantic following of the original T2V model. By applying direct reward supervision on generated videos, we successfully bridge the tuning-inference gap, mitigating the degradation. Furthermore, the simulated prompts augmentation enhances robustness, allowing for high-quality results even with minimal reference. Our method demonstrates superior performance over prior approaches, offering a flexible, efficient, and scalable solution for video personalization within the AIGC community. + +# 7. Acknowledgments + +This research was supported by The National Nature Science Foundation of China (Grant Nos: 62402417, 62273302, 62036009, 61936006), in part by the Key R&D Program of Ningbo (Grant No.2024Z115), in part by Yongjiang Talent Introduction Programme (Grant No: 2023A-197-G). + +# References + +[1] Guofeng v3. https://civitai.com/models/10415/3-guofeng3, 2023.7 +[2] Rcnz cartoon 3d v1.0. https://civitai.com/models/66347?modelVersionId=71009, 2023.7 +[3] Realistic vision v5.1. https://civitai.com/models/4201/realistic-vision-v51, 2023.12 +[4] Guofeng realmix. https://civitai.com/models/77650/guofengrealmix, 2023.7 +[5] Xiang An, Xuhan Zhu, Yuan Gao, Yang Xiao, Yongle Zhao, Ziyong Feng, Lan Wu, Bin Qin, Ming Zhang, Debing Zhang, et al. Partial fc: Training 10 million identities on a single machine. 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Personalized federated learning (pFL) has been shown to be an effective approach to addressing data heterogeneity in federated learning. However, many existing pFL studies rely on directly using the global model for local training without fully assessing its impact on the performance of the local model, resulting in a potential conflict between personalization and generalization. To address this issue, we propose a parallel structure of a local supervisor and an inter-learning model for the local model and introduce a novel pFL method called federated learning by considering data similarity across clients assisted by a local supervisor (FedSimSup). Specifically, FedSimSup maintains an inter-learning model for each client and refines the inter-learning model using a local supervisor for each client. The local supervisor monitors the aggregated global information and ensures that the interlearning model aligns with the local heterogeneous data to enhance local model performance. Additionally, the similarity between clients is measured based on differences in local data distributions, and this similarity is used to adjust the weights of the inter-learning models. Experimental results show that FedSimSup outperforms eight state-of-the-art federated learning methods in handling heterogeneous data. Additionally, it supports different model architectures across clients, providing greater flexibility when computational resources vary among them. Our code can be found at https://github.com/jqLi1626/FedSimSup. + +# 1. Introduction + +With the increasing importance of data privacy in the digital era, federated learning (FL) has emerged as a response to the growing need for data in artificial intelligence [9]. FL aims to maximize the use of local data while maintaining privacy and minimizing communication costs by training a global machine learning model. Despite its widespread use, the traditional federated learning method FedAvg [33] often suffers from performance degradation and slow convergence due to data heterogeneity [18, 34]. This issue is prevalent in real-world applications, where data gathered from different sources, such as users, devices, and organizations, typically exhibit distributional shifts (Non-IID data). + +Personalized federated learning (pFL) [43] has emerged as an effective solution for handling Non-IID data. Mainstream pFL methods can be broadly divided into two groups, one focusing on training a global model that generalizes well across all clients, while the other on training personalized models for each client to better address data heterogeneity. For instance, the algorithms reported in [2, 10, 30] construct client-specific models by dividing the model for each client into a feature extractor (the backbone) and a classifier. The backbone serves as the shared component to capture generalization information across clients, while the classifier focuses on learning personalized information. Motivated by the observation that the decoupling approach, which extracts information from model parameters, may not fully exploit all the potential of the data, Zhang et al. [51] propose generating a conditional policy for each sample to separate global and personalized information in its characteristics. Furthermore, it has been found that retaining all layers sensitive to Non-IID data for extracting personalization information can degrade the collaborative effect. To address this, Wu et al. [47] propose a sensitivity- + +based quantitative metric to assess each parameter and identify those most sensitive for personalization. Recently, Yang et al. [50] tackle the inter-client and intra-client inconsistency between personalized and shared components by introducing a federated parameter-alignment and client-synchronization method, which shows promising results. + +The aforementioned parameter decoupling method all adopt a serial structure, where information of the backbone and classifier is processed sequentially. However, the two modules are often dependent on each other's performance. If the backbone is suboptimal, it can significantly affect the classifier's ability to function well. Additionally, a serial structure often requires a unified model to handle data heterogeneity, which, however, may lead to suboptimal results when the data distributions are highly different. More importantly, information is processed step-by-step in serial structures. Thus, there is a potential for information loss or degradation, especially when one component (like the backbone) overshadows or fails to convey crucial details that would benefit the classifier. + +Therefore, we propose setting up a parallel structure of a supervisor and an inter-learning model for personalization and generalization, respectively. Our proposed algorithm is termed FedSimSup (Federated learning by considering Similarity across clients under a local Supervisor). The contributions of our work are summarized as follows. + +- We propose a novel supervisor-assisted pFL framework. Each client is assigned a local unique supervisor to monitor the information contained in the aggregated interlearning model received from the server. By utilizing a parallel structure, each part of the model is better able to preserve the original input data. The two branches ensure that distinct features or characteristics of the data are captured independently, thereby minimizing the risk of inaccurate final predictions that can arise from inconsistencies between different components, as seen in a serial structure. +- We propose leveraging the local data distribution of each client to enhance model training. By evaluating the similarity based on the differences in local data distribution between clients, each client can selectively learn from others. Specifically, we maintain an inter-learning model on the server for each client. If a client does not participate in a particular round of communication, we aggregate the inter-learning models of that client and others, using similarity values to update the client's inter-learning model. +- We conduct experiments by adopting different supervisor architectures across various clients. Compared to the serial structure, the parallel architecture of our FedSimSup enables clients to build supervisor architectures tailored to their specific needs and computational capabilities, offering greater flexibility when computational resources vary + +across clients. + +# 2. Related Work + +Personalized Federated Learning is an effective way to address data heterogeneous settings. Existing methods can generally be categorized into several types. First, data augmentation [13, 20, 40] aims to reduce data heterogeneity, enabling the use of standard FL to address the problem. Following this, regularization [1, 16, 26, 42] prevents client overfitting and accelerates global convergence, enhancing the overall robustness of the model. Additionally, meta learning [14, 21, 38] enables the global model to achieve personalization more quickly on the client side. Furthermore, multi-task learning [19, 41] treats each client as a different task and leverages relationships between them to handle heterogeneous settings. Moreover, clustering [3, 15, 37] divides clients into different homogeneous groups, within which FL is performed more effectively. Knowledge distillation [22, 25, 45, 48] transfers knowledge from the server or other clients to a specific client, ensuring that each client benefits from shared insights. Model interpolation learns personalized models by combining local models with the global model, thus balancing the model's generalization and personalization capabilities. Along this line, Hanzely et al. [16] design a new objective function that incorporates a penalty term with a coefficient. Deng et al. [12] propose a method to find an optimal combination of local and global models, aiming to enhance model performance under diverse client data distributions. Chen et al. [6] propose elastic aggregation, which performs adaptive interpolation based on the sensitivity of the model parameters, allowing for dynamic adjustments according to the specific needs of each client. + +Parameter decoupling refers to separating the model's parameters and implementing stepwise training, with one set of parameters being globally shared and another set trained locally, thereby enhancing the personalization capability. There are several main decoupling methods. The first method divides the network into base layers and personalized layers [2, 31, 49], with the base layers being globally shared to obtain the generalized feature information, while the personalized layers are trained only locally to allow different clients to process the features in their own ways. The second method uses embeddings from each client as personalization layers [4, 30], aiming to extract unique features to be processed by the global model. Other methods, like [28], propose FedRAP, which learns a global view and a personalized view locally on each client to achieve personalization. Parameter decoupling reduces the amount of transmitted parameters, thereby decreasing communication overhead to some extent. Although parameter decoupling has demonstrated its effectiveness in multiple aspects, it still faces challenges in handling scenarios with extreme + +![](images/49990ebafb3dffc3987d554f0337632c1ca41d2a9452225a7784908a701153c7.jpg) +Figure 1. The main framework of FedSimSup. During each communication round, the server distributes the corresponding inter-learning models to the participating clients. These clients train their inter-learning models under the supervision of the local supervisor. Once the communication concludes, the inter-learning models are uploaded to the server, while the non-participating clients aggregate their inter-learning model with the trained inter-learning model based on similarity information. + +data heterogeneity. Future research could explore more efficient decoupling strategies to optimize the performance of federated learning. + +As mentioned above, due to data heterogeneity, each client's model is complemented by the data of other clients with different weights. As a subfield of pFL, there is also a line of research that manages to address potential conflicts of interest between competitive clients when FL is adopted to provide personalized models to clients [7, 8, 29, 44, 46, 52]. + +# 3. Method + +# 3.1. Problem Formulation + +In this work, we assume supervised federated learning with a total of $n$ clients, each having its own Non-IID distributed dataset $D_{i} = \{(x_{1}^{i},y_{1}^{i}),(x_{2}^{i},y_{2}^{i}),\ldots ,(x_{m_{i}}^{i},y_{m_{i}}^{i})\} \subset \mathcal{X}\times \mathcal{Y}$ , for $i\in \{1,2,\dots ,n\}$ , where $m_{i}$ is the amount of data for client $i$ . We specifically focus on statistical heterogeneity, i.e., the differences in data distributions across clients in this work. To model this, we use Dirichlet [17] and Pathological distributions [33], which are commonly + +employed to simulate Non-IID data scenarios (detailed partitioning methods are provided in Sec. 7.2 in the Appendix). + +The model of each client $q_{\theta_i}:\mathcal{X}\to \mathcal{Y}$ maps the input $x_j^i\in \mathcal{X}$ to predict the label $q_{\theta_i}(x_j^i)\in \mathcal{V}$ , which is compared to the true label corresponding to $y_j^i\in \mathcal{V}$ . The local models $q_{\theta_i}$ are the same in standard FL, but differ in pFL. $\theta_{i}\in \Theta$ represents the model parameters. The parameters of each client's model $\theta_{i}$ are trained based on its local dataset by minimizing the following objective function: + +$$ +\min _ {\theta_ {i} \in \Theta} L \left(D _ {i}, \theta_ {i}\right) = \frac {1}{m _ {i}} \sum_ {j = 1} ^ {m _ {i}} \ell \left(q _ {\theta_ {i}} \left(x _ {j} ^ {i}\right), y _ {j} ^ {i}\right), \tag {1} +$$ + +where $\ell : \mathcal{Y} \times \mathcal{Y} \to \mathbb{R}_+$ is the loss function that measures the degree of inconsistency between the predicted labels $q_{\theta_i}(x_j^i)$ and the true labels $y_j^i$ . + +The server distributes the model to clients, who then train the model locally using the local objective function Eq. (1). After training, the clients upload their models to the server for aggregation [33]: + +$$ +\theta^ {t + 1} = \frac {\sum_ {i \in \mathcal {N} (t)} m _ {i} \theta_ {i} ^ {t}}{\sum_ {i \in \mathcal {N} (t)} m _ {i}}, \tag {2} +$$ + +where $\theta_i^t$ is the model of client $i$ after completing local training in the $t$ -th communication round, and $\mathcal{N}(t)$ denotes the set of clients participating in the $t$ -th communication round. + +Standard FL struggles with slow convergence and suboptimal model performance when dealing with Non-IID data across clients. Given that pFL has proven effective in addressing this challenge by learning personalized models for each client, we build upon the pFL framework and present a new, highly effective solution for handling statistically heterogeneous data, called FedSimSup. The details of our approach are outlined in the following sections. + +# 3.2. Learning under Supervisor + +In this work, instead of using a serial model as in existing pFL approaches, we divide the model into two parallel parts. The first part is the supervisor, which is trained locally but not uploaded. The second part is the interlearning model, which is uploaded and aggregated. The role of the supervisor is to guide the local model during training by providing oversight based on the previously learned local data. It helps prevent the model from deviating too much from its fit to the local data while still incorporating beneficial global updates. The supervisor ensures that the inter-learning model maintains a balance between leveraging global information and staying aligned with the local distribution. + +The local objective function also changes from Eq. (1) to + +$$ +\begin{array}{l} \min _ {s _ {i} \in \mathcal {S}, \theta_ {i} \in \Theta} L \left(D _ {i}, s _ {i}, \theta_ {i}\right) \\ = \frac {1}{m _ {i}} \sum_ {j = 1} ^ {m _ {i}} \ell \left(q _ {\theta_ {i}} \left(x _ {j} ^ {i}\right) + q _ {s _ {i}} \left(x _ {j} ^ {i}\right), y _ {j} ^ {i}\right), \tag {3} \\ \end{array} +$$ + +where $s_i \in S$ is the parameters of supervisor and $\theta_i \in \Theta$ is the parameters of inter-learning model. Here, we simply sum the results of the two models. The training process of our model is divided into two parts: + +$$ +\min _ {s _ {i} \in S} L \left(D _ {i}, s _ {i}, \theta_ {i}\right), \tag {4} +$$ + +$$ +\min _ {\theta_ {i} \in \Theta} L \left(D _ {i}, s _ {i}, \theta_ {i}\right). \tag {5} +$$ + +The purpose of Eq. (4) is that if the global model contains more beneficial information, the supervisor will undergo a significant update to better assist the training process. However, if the global model is not beneficial to the local data, the supervisor has already been fitted to the local data, we hypothesize that it will undergo only minor updates or remain unchanged. The purpose of Eq. (5) is to train the model under the supervision of the supervisor, ensuring that after acquiring global information, it becomes more fitted to the local data. + +For demonstration purposes, we directly scale down the inter-learning model proportionally to create the supervisor, + +which then assists the inter-learning model in its usage. In practice, the architecture of the supervisor does not need to be the same for every client. Each client can independently design their own supervisor architecture according to their specific needs and capabilities. The server only needs to manage the inter-learning model but not the whole local model. This approach significantly enhances the personalization capability of the model while simplifying management. We demonstrate the performance results when clients adopt different supervisor structures in Sec. 5.2. The effect of the supervisor is verified in Sec. 7.5. + +# 3.3. Utilization of Similarity Information + +We establish an inter-learning model for each client based on their local data distribution. At the end of a local training round, we perform the following operations on all clients' inter-learning models (the following operations are performed on the inter-learning model, unrelated to the supervisor). + +If a client $i$ participates in this round of communication, then the inter-learning model $\theta_{i}^{t + 1}$ of the $i$ -th client at $t + 1$ round is set to the updated $\theta_{i}^{t}$ after training without aggregating information from other clients + +$$ +\theta_ {i} ^ {t + 1} = \theta_ {i} ^ {t}, \quad \text {i f} i \in \mathcal {N} (t). \tag {6} +$$ + +If the client $i$ does not participate in this round of communication, then $\theta_i^{t + 1}$ of the $i$ -th client is updated as follows. + +$$ +\theta_ {i} ^ {t + 1} = \left(1 - \alpha_ {i} ^ {t}\right) \theta_ {i} ^ {t} + \alpha_ {i} ^ {t} \sum_ {j \in \mathcal {N} (t)} \frac {s _ {i j}}{\sum_ {j \in \mathcal {N} (t)} s _ {i j}} \theta_ {j} ^ {t}, \text {i f} i \notin \mathcal {N} (t), \tag {7} +$$ + +$$ +\alpha_ {i} ^ {t} = \lambda_ {i} ^ {t} \beta^ {t}, \tag {8} +$$ + +$$ +\lambda_ {i} ^ {t} = \frac {\sum_ {j \in \mathcal {N} (t)} m _ {j}}{\sum_ {j \in \mathcal {N} (t)} m _ {j} + K \cdot m _ {i}}, \tag {9} +$$ + +$$ +\beta^ {t} = \left\{ \begin{array}{l l} 1, & t < C T ^ {\gamma} \\ \left(\frac {C T ^ {\gamma}}{t}\right) ^ {2}, & t \geq C T ^ {\gamma}, \end{array} \right. \tag {10} +$$ + +where $\alpha_{i}^{t}$ is a parameter that represents how much the current client is to learn from the clients participating in the $t$ -th communication. It is related to the volume of data and the number of communication rounds. $\lambda_{i}^{t}$ measures the amount of data, calculated based on the ratio of the amount of local data to the total amount of data of clients participating in the $t$ -th communication, which aligns with the original standard FL concept. $K$ is the number of clients participating in communication in each round. $\beta^{t}$ is influenced by the current number of communications rounds. In the initial stages, it is set to 1, in which case $\alpha_{i}^{t}$ will only be affected by the amount of data. In later stages, to ensure convergence, $\beta^{t}$ gradually decreases under the control of parameters $C$ + +# Algorithm 1 FedSimSup + +Input: Dataset distributed across $n$ clients $D = \{D_{1},D_{2}\dots D_{n}\}$ , client participating rate $r$ , the global communication rounds $T$ , inter-learning model epochs $\tau_{\theta}$ , supervisor epochs $\tau_{s}$ + +1: Initialize $\theta_1^0, \theta_2^0 \dots \theta_n^0, s_1^0, s_2^0 \dots s_n^0$ +2: for $t = 1,2\dots T$ do +3: $\mathcal{N}(t) \gets$ Server randomly samples max(1, nr) clients +4: for Each client $i\in \mathcal{N}(t)$ do +5: Client $i$ initializes $s_i^{t,0} \gets s_i^{t - 1,\tau_s}$ +6: Server sends $\theta_i^{t - 1,\tau_\theta}$ to client $i$ as $\theta_i^{t,0}$ +7: $s_i^{t,\tau_s},\theta_i^{t,\tau_\theta}\gets \mathbf{LocalUpdate}(s_i^{t,0},\theta_i^{t,0},f_i,D_i)$ +8: Client $i$ sends updated inter-learning model $\theta_{i}^{t,end}$ to server +9: end for +10: for Each client $i \notin \mathcal{N}(t)$ do +11: Set $s_i^{t,\tau_s} \gets s_i^{t - 1,\tau_s}$ +12: Aggregate $\theta_i^{t,\tau_0}$ by Eq. (7) +13: end for +14: end for +15: +16: LocalUpdate $(s^0,\theta^0,f,D)$ +17: for $j = 1,2\cdot \cdot \cdot \tau_{s}$ do +18: $s^j \gets SGD\left(f(s^{j-1}, \theta^0), s^{j-1}\right)$ +19: end for +20: for $j = 1,2\cdot \cdot \cdot \tau_{\theta}$ do +21: $\theta^j\gets SGD\left(f(s^{\tau_s},\theta^{j - 1}),\theta^{j - 1}\right)$ +22: end for +23: return $s^{\tau_s}$ , $\theta^{T\theta}$ + +and $\gamma$ , where $C$ and $\gamma$ are constant values and $T$ denotes global communication rounds. $s_{ij} \in [0,1]$ is the value that measures the similarity between the client $i$ and the client $j$ . A higher value of $s_{ij}$ indicates a greater similarity between client $i$ and $j$ . In Eq. (7), we aggregate the inter-learning models of clients who do not participate in communication, based on the volume of data, the similarity to the clients participating in communication, and the current number of rounds of communication. By doing this, we can ensure that clients who do not participate in the training in each round can still benefit from the clients who participate in the training, thereby promoting effective global information aggregation. In this work, the similarity information is represented by the cosine similarity between the proportions of each client's data-label distribution, which we believe better reflects the intrinsic similarity between clients. This requires us to collect the proportions of the label of the clients at the beginning of the entire task and to compute the similarity between each client on the server, as shown in Fig. 1. + +# 3.4. FedSimSup Algorithm + +We provide the pseudocode for FedSimSup in Algorithm 1, and below we will explain it in detail. + +Local Update. In each communication round, clients are randomly selected to participate based on a fixed participation rate $r$ and receive the inter-learning model $\theta$ sent by the server. Client $i$ participates in the $t$ -th round, receives the inter-learning model $\theta_i^t$ , and has a supervisor $s_i^t$ stored locally. The local supervisor is updated for $\tau_s$ epochs. + +$$ +s _ {i} ^ {t, j} \leftarrow S G D \left(f \left(s _ {i} ^ {t, j - 1}, \theta_ {i} ^ {t, 0}\right), s _ {i} ^ {t, j - 1}\right), \tag {11} +$$ + +where $j \in (1,2,\dots \tau_s)$ , and $\theta_i^{t,0}$ denotes the inter-learning model of client $i$ that has not been updated. We use Stochastic Gradient Descent (SGD) [36] to update $s_i^{t,j}$ based on the gradient of $s_i^{t,j}$ . Then, the inter-learning model is updated within round $\tau_{\theta}$ : + +$$ +\theta_ {i} ^ {t, j} \leftarrow S G D \left(f \left(s _ {i} ^ {t, \tau_ {s}}, \theta_ {i} ^ {t, j - 1}\right), \theta_ {i} ^ {t, j - 1}\right), \tag {12} +$$ + +where $j \in (1,2,\dots \tau_{\theta})$ . After completing these two processes locally, the client $i$ saves the supervisor $s_i^{t,\tau_s}$ and uploads the inter-learning model $\theta_i^{t,\tau_\theta}$ for aggregation of other clients. + +Server Update The server receives the inter-learning models uploaded from client set $\mathcal{N}(t)$ , without modifying them. For clients who did not participate in the communication, it aggregates their models based on Eq. (2), leveraging similarity information to learn from the clients that have participated in this round of training. + +# 4. Convergence Analysis of FedSimSup + +# 4.1. Assumptions + +We make the following standard assumptions that are widely used in convergence analysis in federated learning [14, 16, 26, 27, 35]. + +Assumption 1 (Bounded Loss). There exists constant $F^{*} \in \mathbb{R}$ such that for any client $i \in \{1, \dots, n\}$ , $f_{i}$ is bounded from below by $F^{*}$ , $f_{i}(s, \theta) > F^{*}$ , $\forall s, \theta$ . + +Assumption 2 (Smoothness). There exists $L > 0$ such that for any client $i \in \{1, \dots, n\}$ , $\nabla_{s} f_{i}(\cdot, \theta)$ , $\nabla_{s} f_{i}(s, \cdot)$ , $\nabla_{\theta} f_{i}(\cdot, \theta)$ and $\nabla_{\theta} f_{i}(s, \cdot)$ are $L$ -Lipschitz. + +Assumption 3 (Bounded Gradient). For all $i \in \{1, \dots, n\}$ , the gradient of loss function $f_{i}$ is bounded. There exists $G > 0$ such that + +$$ +\left\| \nabla_ {s} f _ {i} (s, \theta) \right\| \leq G, \quad \left\| \nabla_ {\theta} f _ {i} (s, \theta) \right\| \leq G, \quad \forall s, \theta . \tag {13} +$$ + +Assumption 4 (Unbiasedness). SGD estimator is unbiased. There exists $\sigma >0$ such that for any client $i\in \{1,\dots ,n\}$ + +$$ +\begin{array}{l} \mathbb {E} [ S G D (f _ {i} (s, \theta), s) ] = \nabla_ {s} f _ {i} (s, \theta), \quad \forall s, \theta , \\ \mathbb {E} [ S G D (f (s, 0), 0) ] = \overline {{\mathbf {\Pi}}} _ {s} f (s, 0), \quad \forall s, 0 \end{array} \tag {14} +$$ + +$$ +\mathbb {E} [ S G D (f _ {i} (s, \theta), \theta) ] = \nabla_ {\theta} f _ {i} (s, \theta), \quad \forall s, \theta . +$$ + +Assumption 5 (Bounded Variance). The variance of SGD estimator is bounded. That is, for any client $i \in \{1, \dots, n\}$ , + +$$ +\mathbb {E} \left[ \| S G D (f _ {i} (s, \theta), s) - \nabla_ {s} f _ {i} (s, \theta) \| ^ {2} \right] \leq \sigma^ {2}, \forall s, \theta . \tag {15} +$$ + +$$ +\mathbb {E} \left[ \| S G D \left(f _ {i} (s, \theta), \theta\right) - \nabla_ {\theta} f _ {i} (s, \theta) \| ^ {2} \right] \leq \sigma^ {2}, \forall s, \theta . \tag {16} +$$ + +# 4.2. Main Theorem + +With the above assumptions in Sec. 4.1, we present the convergence of the proposed FedSimSup. The proof of the theorem is given in Sec. 8. + +Theorem 1 (Convergence of FedSimSup). Suppose Assumptions 1 to 5 hold, and the learning rates in FedSimSup are chosen as + +$$ +\eta_ {s} ^ {t} = \eta / \sqrt {T} L \tau_ {s}, \quad \eta_ {\theta} ^ {t} = \eta / \sqrt {T} L \tau_ {\theta} \tag {17} +$$ + +with $\eta < 1$ . The hyperparameters of FedSimSup are chosen as $\gamma \in (0,1/2)$ and $C > 0$ . Then we have the following bound for all client $i$ . + +$$ +\begin{array}{l} \frac {1}{T} \sum_ {i = 0} ^ {T - 1} \left[ \left\| \nabla_ {s} f _ {i} \left(s _ {i} ^ {t, 0}, \theta_ {i} ^ {t, 0}\right) \right\| ^ {2} + 2 \left\| \nabla_ {\theta} f _ {i} \left(s _ {i} ^ {t, 0}, \theta_ {i} ^ {t, 0}\right) \right\| ^ {2} \right] \\ \leq \frac {L}{2 T ^ {1 / 2} r \eta} (f _ {i} (s _ {i} ^ {0, 0}, \theta_ {i} ^ {0, 0}) - F ^ {*}) + \frac {3 \eta^ {2} G ^ {2}}{2 T} + \frac {\eta \sigma^ {2}}{T ^ {1 / 2} \bar {\tau}} \\ + \frac {(1 - r) \lambda_ {i} G ^ {2}}{2 r} \left(- C ^ {2} (1 - 2 \gamma) T ^ {2 \gamma - 1} \ln T \right. \\ \left. + C ^ {2} \left(1 + 2 \ln C\right) T ^ {2 \gamma - 1} + 3 C T ^ {\gamma - 1} + 1 / T - C ^ {2} T ^ {2 \gamma - 2}\right) \\ + \frac {(1 - r) \lambda_ {i} ^ {2} \eta^ {2} G ^ {2}}{2 r L} \left(3 C T ^ {3 \gamma - 3 / 2} + 9 C ^ {2} T ^ {2 \gamma - 3 / 2} \right. \\ \left. + 3 C T ^ {\gamma - 3 / 2} - 3 C ^ {4} T ^ {4 \gamma - 9 / 2}\right). \tag {18} \\ \end{array} +$$ + +Here, $\bar{\tau} = 2 / (1 / \tau_s + 1 / \tau_\theta)$ and $\lambda_{i}$ = $\max_{|\mathcal{N}|\subset \{1,\ldots ,n\}}(\sum_{j\in \mathcal{N}}m_j) / (\sum_{j\in \mathcal{N}}m_j + Km_i).$ + +The left-hand side of Eq. (18) is the average over time of a weighted sum of the gradient norm. Convergence is measured in the rate at which this quantity decays to zero. We note that Theorem 1 and Fig. 2 together demonstrate a trade-off between generalization and convergence speed. As shown in Fig. 9 in the Appendix, larger values of $C$ and $\gamma$ encourage inter-learning models to incorporate more global information, enhancing their generalization performance. In contrast, smaller values of $C$ and $\gamma$ direct the local models to prioritize private data, leading to faster convergence. This highlights the need for careful hyperparameter selection. Additionally, clients with more private data (smaller $\lambda_{i}$ ) require less global information and therefore achieve faster convergence. + +# 5. Experiments + +# 5.1. Experimental Settings + +Datasets. We evaluate FedSimSup on classification tasks using CIFAR10, CIFAR100 [23], FEMNIST [5], and IMAGENET [11]. For CIFAR10 and CIFAR100, we simulate a Non-IID setting by partitioning data based on a Dirichlet distribution with $\alpha = 0.1$ and $\alpha = 0.5$ , where a lower $\alpha$ indicates a greater heterogeneity. FEMNIST and IMAGENET are partitioned using a Dirichlet distribution with $\alpha = 0.1$ . To our knowledge, this is the first evaluation of pFLs on IMAGENET. We compare the performance of FedSimSup and competing algorithms on CIFAR10, CIFAR100, and IMAGENET under the Dirichlet distribution, as well as under the Pathological distribution for CIFAR10 and CIFAR100. Further details on data partitioning and the datasets are provided in Sec. 7.1 and Sec. 7.2 in the Appendix. + +Baselines. We compare FedSimSup with eight state-of-the-art methods, including FedAvg [33], FedProx [26], Per-FedAvg [14], FedRep [10], FedProto [45], FedPac [48], pFedFda [32] and FedAs [50]. Additionally, we also compare our FedSimSup with the performance of conducting local training separately on each client. Introduction of the baselines, experimental settings of baseline, and training details are provided in Sec. 7.3. + +Model. Like most pFL approaches, FedSimSup uses LeNet-5 [24] as the local model for each client, considering the communication cost. LeNet-5 consists of two convolutional layers and two linear layers. In fairness, we use LeNet-5 as the model for all the algorithms in this work. Since our FedSimSup includes both a supervisor and an inter-learning model in each client. Thus, to ensure that the number of parameters of FedSimSup is almost the same as that of competing algorithms, we proportionally reduce the size of LeNet-5 to approximately one-sixth of that of the inter-learning model. + +# 5.2. Experimental Results + +Performance comparison. On the FEMNIST and IMA-GENET datasets under a Dirichlet distribution, as shown in Tab. 1, FedSimSup consistently outperforms all other methods on both datasets. We observe that FedAvg performs surprisingly well on the FEMNIST dataset, likely because, despite the non-IID nature of the data, clients share common visual patterns such as digits and letters. Tab. 2 and Tab. 3 show the performance comparison in the CIFAR10 and CIFAR100 datasets under the Dirichlet distribution and the Pathological distribution, respectively. In the Dirichlet distribution, our FedSimSup method consistently outperforms all other methods across both the CIFAR10 and CIFAR100 datasets, achieving the highest accuracy in all cases. In the Pathological distribution, although the accuracy of all meth + +
LocalFedAvgFedProxPer-FedAvgFedRepFedProtoFedPacpFedFdaFedAsFedSimSup
FEMNIST.660(.003).797(.023).742(.017).025(.04).812(.027).099(.06).782(.014).773(.004).764(.006).843(.006)
IMAGENET.133(.002).094(.033).089(.024).013(.005).209(.007).127(.013).132(.004).212(.005).211(.003).224(.008)
+ +Table 1. Accuracy comparison on FEMNIST and IMAGENET under Dirichlet distribution with $\alpha = {0.1}$ (best valued per setup in bold). + +
No. of Clients (Dir)CIFAR10CIFAR100
100 (0.1)50 (0.1)100 (0.5)50 (0.5)100 (0.1)50 (0.1)100 (0.5)50 (0.5)
Local.863(.001).853(.030).588(.004).611(.003).399(.002).415(.006).175(.003).209(.002)
FedAvg (2017).276(.026).341(.058).484(.015).506(.028).191(.006).189(.009).224(.005).252(.010)
FedProx (2020).275(.023).317(.039).488(.011).509(.028).184(.006).184(.008).210(.007).244(.008)
Per-FedAvg (2020).774(.005).750(.024).368(.006).464(.015).038(.001).103(.002).016(.001).003(.001)
FedRep (2021).875(.009).840(.053).706(.011).718(.015).454(.008).497(.020).245(.009).312(.011)
FedProto (2022).865(.001).828(.030).592(.004).612(.002).407(.002).424(.003).173(.002).213(.002)
FedPac (2023).839(.014).787(.047).599(.017).603(.033).348(.006).398(.023).178(.008).230(.006)
pFedFda (2025).878(.006).867(.005).703(.009).714(.005).463(.008).509(.005).307(.006).332(.009)
FedAs (2024).874(.003).865(.006).712(.004).720(.004).467(.005).512(.004).316(.005).342(.008)
FedSimSup (Ours).892(.002).882(.004).725(.005).736(.006).503(.004).546(.003).331(.006).385(.005)
+ +Table 2. Accuracy comparison on CIFAR10 and CIFAR 100 under Dirichlet distribution (best valued per setup in bold). + +ods is generally lower compared to the Dirichlet case, our FedSimSup still leads the performance. Methods like FedRep and FedProto show moderate performance, but are still outperformed by newer methods like FedAs (2024) and pFedFda (2025) in some cases. These results underscore the superior effectiveness of FedSimSup in federated learning tasks, particularly in the Dirichlet distribution setup. + +We also compare the convergence speeds of different methods. In Fig. 2, we present the accuracy changes of various methods under Non-IID distributions for CIFAR10 and CIFAR100, using the Dir (0.1) setting over 1000 communication rounds. On the CIFAR10 dataset, all methods exhibit faster convergence, except for FedAvg and FedProx. Notably, our proposed FedSimSup achieves the best performance. In the more challenging CIFAR100 task, which + +![](images/8d35627cd3c3d7a6def2c861cd6678dba8de53cdbc373ee5f3e4e30cb9edda8d.jpg) + +![](images/0c4864c20dae58f67fbdfbbf7f5e06ded05975f114dc5dc148dd07415171723e.jpg) +(c) Accuracy curve on IMAGENET +Figure 2. Accuracy curve along global training rounds. + +![](images/8dd46d0180161966c7f4f450edbea3879a9b8200c6e4e34bb2cfdff89d625bc4.jpg) + +![](images/3e71fe9f6c0186b0d0aeb9b52b2a1f1c46599868d09db230a4af52641b4828c1.jpg) +(d) Accuracy curve on FEMNIST + +involves a larger number of categories, FedSimSup shows a slower initial improvement compared to other methods. However, it eventually catches up and surpasses the others, highlighting its robust learning capabilities, particularly in settings with a higher number of categories. We provide the accuracy curves on CIFAR10 and CIFAR 100 under all Non-IID settings in Fig. 7 and Fig. 8 in the Appendix. + +Different Supervisor Architectures. To demonstrate the performance of FedSimSup with different supervisor architectures across various clients, we allow each client to randomly select one of three supervisor architectures: a Transformer, a CNN, or LeNet-5. This variant of FedSimSup, where clients use different supervisor architectures, is termed FedSimSup-TCL. We refer to the average accuracy achieved by the subset of clients using the Transformer, CNN, and LeNet-5 as FedSimSup-T, FedSimSup-C, and FedSimSup-L, respectively. + +Tab. 4 presents a performance comparison between FedSimSup and FedSimSup-TCL. We use a pre-trained Transformer, which explains the competitive performance of FedSimSup-T. We also note that the overall performance of FedSimSup-TCL is slightly lower than that of FedSimSup, which is an inevitable consequence of model heterogeneity. However, the performance gap is not substantial, and some clients achieved better results by selecting models better suited to their individual needs. Therefore, we conclude that our proposed FedSimSup is flexible enough to accommodate different model architectures for different clients based on their computational resources and requirements, enabling them to achieve improved performance and faster inference. + +Ablation Studies. To demonstrate that similarity-based model aggregation can accelerate the convergence speed, we replace Eq. (7) with a direct model average as in Fe- + +
No. of Clients (Shard)CIFAR10CIFAR100
100 (2)50 (2)100 (5)50 (5)100 (5)50 (5)100 (20)50 (20)
Local.859(.001).881(.001).646(.004).681(.002).664(.002).647(.003).275(.002).340(.006)
FedAvg (2017).348(.024).312(.038).484(.021).478(.033).119(.007).124(.012).192(.006).294(.011)
FedProx (2020).340(.021).295(.032).483(.019).481(.031).111(.008).117(.011).184(.007).184(.012)
Per-FedAvg (2020).515(.001).675(.012).290(.001).476(.050).107(.001).242(.023).064(.001).069(.002)
FedRep (2021).858(.004).871(.009).735(.008).759(.010).614(.010).657(.016).380(.007).450(.010)
FedProto (2022).858(.001).876(.001).638(.002).668(.001).652(.003).642(.003).276(.003).328(.002)
FedPac (2023).839(.016).857(.015).648(.014).658(.002).513(.014).572(.018).201(.004).330(.009)
pFedFda (2025).862(.007).871(.009).746(.003).763(.005).642(.007).683(.002).443(.003).440(.005)
FedAs (2024).853(.004).881(.007).742(.002).760(.006).630(.002).643(.005).427(.005).442(.004)
FedSimSup (Ours).866(.006).877(.008).757(.005).757(.002).637(.005).652(.004).464(.006).480(.007)
+ +Table 3. Accuracy on CIFAR10 and CIFAR 100 under Pathological distribution (best valued per setup in bold). + +
clients num (Dir)CIFAR10CIFAR100
100 (0.1)50 (0.1)100 (0.5)50 (0.5)100 (0.1)50 (0.1)100 (0.5)50 (0.5)
FedSimSup-T.898(.006).908(.003).693(.008).721(.007).504(.003).548(.004).293(.007).354(.005)
FedSimSup-C.835(.004).864(.005).680(.008).707(.006).432(.005).437(.004).244(.008).296(.003)
FedSimSup-L.851(.007).843(.004).664(.012).693(.004).445(.003).465(.007).227(.003).320(.001)
FedSimSup-TCL.861(.005).871(.005).679(.009).707(.005).460(.003).482(.006).254(.007).323(.004)
FedSimSup.892(.002).882(.004).725(.005).736(.006).503(.004).546(.003).331(.006).385(.005)
+ +Table 4. Experiments of using different supervisor architectures. + +![](images/a5e38444cadbca6d5f4e5eb75569a36d08f4225b7f64489007669736fdc30a58.jpg) +Figure 3. The accuracy with and without similarity information on CIFAR10 + +![](images/d4855cdc2ccef950a010bb3e7c66f27a2224f448b7ac32eedc33a2bcfdf9b686.jpg) +Figure 4. The accuracy with and without parallel architecture on CIFAR100 + +dAvg. In Fig. 3, we compare the impact of using similarity information versus not using it on the convergence speed. The experiment is carried out on CIFAR10 in Dirichlet distribution with $\alpha = 0.1$ , and we display the results for the first 100 epochs. The results show that the use of similarity information accelerates the convergence speed, demonstrating the effectiveness of our proposed similarity measurement and aggregation strategy. Furthermore, to demonstrate the effectiveness of the parallel structure in FedSimSup, we replace the parallel structure with a serial model, as in FedRep [10]. Specifically, we adopt the inter-learning model on each client and increase the number of parameters to ensure fairness. Only the backbone of the model is transmitted between the server and the clients. We conduct experiments + +on CIFAR100 under Dirichlet distribution with $\alpha = 0.1$ . As shown in Fig. 4, the performance was subpar, demonstrating the effectiveness of our parallel architecture. More detailed ablation experiments are provided in Sec. 7.4 in the Appendix. + +Parameter Sensitivity Analyses. In the model aggregation process of FedSimSup (see Eq. (7)), two critical parameters, $C$ and $\gamma$ , are involved. These parameters work together to control $\alpha_{i}^{t}$ in Eq. (7), which determines how much the current client $i$ learns from other clients. To analyze their impact on performance, we evaluate four pairs of $C$ and $\gamma$ . Specifically, we set $C$ and $\gamma$ to (10, 1/3), (20, 2/5), (40, 2/5), and (40, 3/7). The results on CIFAR10 and CIFAR100, shown in Fig. 9 in the Appendix, demonstrate that setting $C$ and $\gamma$ to 40 and 3/7 yields the best performance. + +# 6. Conclusion + +Our proposed FedSimSup allows each client to employ their own supervisor with flexible architectures to assist local training, preventing the model from deviating too much from the local data. Additionally, we utilize the similarity information to standardize the way of clients learning from other clients' information. Overall, FedSimSup provides better performance in handling Non-IID scenarios, while allowing clients to customize their model architectures. + +# Acknowledgments + +# References + +[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263, 2021. 2 +[2] Manoj Ghuhan Arivazhagan, Vinay Aggarwal, Aaditya Kumar Singh, and Sunav Choudhary. 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Lee1 Jihyeon Je2 Chanho Park1 Mikaela Angelina Uy3 Leonidas Guibas2 Minhyuk Sung1 +1KAIST 2Stanford University 3NVIDIA + +![](images/f7f13ab830846437b2abab9173a3ceb40785b36ae93f81ac69aa3b641a9c111f.jpg) +Figure 1. We introduce Abstract Perspective Change (APC), a framework that empowers VLMs to adopt arbitrary perspectives for spatial reasoning. As demonstrated by the examples above, APC significantly enhances VLM's ability to imagine a scene from alternative viewpoints, overcoming the inherent egocentric bias that constrains the spatial reasoning of existing VLMs to the camera's viewpoint. + +# Abstract + +We present a framework for perspective-aware reasoning in vision-language models (VLMs) through mental imagery simulation. Perspective-taking—the ability to perceive an environment or situation from an alternative viewpoint—is a key benchmark for human-level visual understanding, essential for environmental interaction and collaboration with autonomous agents. Despite advancements in spatial reasoning within VLMs, recent research has shown that modern VLMs significantly lack perspective-aware reasoning capabilities and exhibit a strong bias toward egocentric interpretations. To bridge the gap between VLMs and human perception, we focus on the role of mental imagery, where humans perceive the world through abstracted representations that facilitate perspective shifts. Motivated by this, we propose a framework for perspective-aware reasoning, + +named Abstract Perspective Change (APC), that effectively leverages vision foundation models, such as object detection, segmentation, and orientation estimation, to construct scene abstractions and enable perspective changes. Our experiments on synthetic and real-image benchmarks, compared with various VLMs, demonstrate significant improvements in perspective-aware reasoning with our framework, further outperforming fine-tuned spatial reasoning models and novel-view-synthesis-based approaches. Our project page is at https://apc-vlm.github.io/. + +# 1. Introduction + +Vision-language models (VLMs) have made remarkable progress, positioning themselves as a crucial backbone for general-purpose physical AI agents. The growing research efforts to improve VLMs' spatial reasoning capabilities [8, 10, 45, 64] reflect this potential. Early VLMs were limited to basic tasks such as visual question answering (VQA) and image captioning [1, 34, 35]. How- + +ever, recent advancements have enabled them to perform complex visual reasoning [2, 14, 23, 24, 40, 63] and extract spatial properties, including spatial relationships, relative sizes, and distances [31, 64]. Further techniques such as instruction-tuning and vision-centric adapters, have expanded their capabilities, allowing depth-aware [6, 8] and region-aware [10, 21] spatial reasoning. + +Despite these advances, progress remains largely confined to egocentric spatial reasoning, and even the latest VLMs struggle with allocentric reasoning—answering questions from perspectives other than the camera's (Fig. 2). Allocentric reasoning is crucial for high-level planning, environmental interaction, and collaboration with autonomous agents [16, 70, 74]. Moreover, it serves as a key benchmark for human-level spatial understanding. However, as analyzed by Zhang et al. [78], most VLMs exhibit a strong bias toward an egocentric perspective. Even when explicitly prompted to adopt an allocentric viewpoint, VLMs often revert to egocentric interpretations [19, 37, 77, 78]. Recent efforts to enhance spatial reasoning remain focused on improving egocentric reasoning [8, 10, 45], leaving allocentric reasoning largely unaddressed. + +To bridge the gap between VLMs and human perspective reasoning, we ask: What cognitive process allows humans to effortlessly shift perspectives? Unlike current VLMs, humans seamlessly form internal representations of the physical world, making perspective reasoning an intuitive and natural process. The mechanism of creating internal representations, known as mental imagery [17, 29, 48, 49, 57], plays a fundamental role in cognition, enabling us to simulate visual, spatial, and conceptual scenarios. This ability allows for abstraction beyond immediate perception, facilitating sophisticated spatial reasoning tasks such as mentally rotating objects, inferring occlusions, and envisioning alternative viewpoints [5, 12, 15]. + +A key aspect of mental imagery is that it is not simply the process of visualizing a clear image from different perspectives; rather, it involves forming an abstract representation of a scene that encodes essential spatial information and can be reinterpreted from a new perspective. From a computational standpoint, such an abstract representation is particularly advantageous, as equipping VLMs with the imaginative capability to generate novel views remains extremely challenging. In contrast, constructing an abstract representation requires significantly less computation and can be achieved procedurally. + +Inspired by this, we introduce a novel framework for adapting perspectives in VLMs by simulating the mental imagery process and modifying the perspective in the given prompt. Our goal is to leverage the strengths of both VLMs and recent vision foundation models, such as object detection [7, 43, 81], image segmentation [27, 52], and orientation estimation [66]. The proposed framework takes an im + +![](images/24061a7fdeb196267779df9dd94678edbcbf9daaf9586ae2caa4e3f65ef76b38.jpg) + +Question: Given the image, consider the real-world 3D locations and orientations of the objects. If you stand at the camera's position facing where it is facing, Is the cat on the left or right of the dog? + +# Answer: + +Human: "on the right" +VLM: "on the right" + +![](images/818a20bd177aaaf303ef78ceec827d267e31df94ea7d4ac8874cc250d6de04b7.jpg) +Figure 2. Egocentric vs. Allocentric. While VLMs perform well when questions are asked from an egocentric (i.e. camera's) perspective, they struggle when the same questions are posed from an allocentric perspective, showing a strong bias toward egocentric reasoning. + +# Question: + +Given the image, consider the real-world 3D locations and orientations of the objects. If you stand at the man's position facing where he's facing, Is the dog on the left or right of the man? + +# Answer: + +Human: "on the right" +VLM: "on the left" + +age and a perspective-based question as input and operates through three key stages. First, by simulating the mental imagery process, it builds an abstract representation of the scene in the input image. The VLM parses the prompt to identify objects in the image, while vision foundation models extract the center and orientation information of each object in 3D space. Second, the VLM analyzes the prompt to determine the reference object from whose perspective the question is asked, and transforms the abstraction to be aligned with that perspective. Finally, a new prompt is generated by reinterpreting the scene from the reference object's perspective. We explore different formats for rendering the scene abstraction: (1) a text-based representation, where objects are described using numerical 3D coordinates, and (2) an image-based representation, where objects are visualized as colored boxes corresponding to the original image. The newly generated prompt is fed to the VLM to obtain the final answer. Note that our framework is not designed for a specific type of allocentric question. We leverage the egocentric reasoning capabilities of VLMs by performing allocentric-to-egocentric prompt conversion through scene abstraction, removing the perspective-related barrier in the question while preserving its original intent in the new prompt. + +In our experiments on COMFORT++ [78] and 3DSR-Bench [46], our method achieves robust spatial reasoning across a variety of tasks and perspectives. In constraint, baseline VLMs and previous frameworks for spatial reasoning often struggle with even simple viewpoint shifts, reconfirming a notable bias toward the camera's perspective. These results highlight how our abstraction-based representation significantly enhances the spatial reasoning capabilities of VLMs beyond their default egocentric perspectives. + +# 2. Related Work + +# 2.1. Spatial Reasoning with VLMs + +Building on the remarkable advancements of vision-language models (VLMs) [2, 14, 31, 40, 41], recent studies have adapted VLMs for real-world spatial reasoning. Numerous evaluations revealed that VLMs struggle on even elementary spatial-perception tasks [18, 50, 51, 62, 65] and higher-level spatial reasoning based on images or videos [26, 32, 39, 58, 60, 72]. SpatialVLM [8] tackles this issue with a data-synthesis pipeline that injects rich spatial cues, while Cambrian-1 [64] introduces an architecture purposely for improved spatial reasoning. Another line of work allows VLMs to utilize richer vision-centric data such as points, depth maps or segmentation masks through finetuning [6, 44, 60, 76] or employing auxiliary encoders [10]. Taking a different approach, other works exploit the planning and programming abilities of language models, building LLM/VLM-in-the-loop systems that call external vision modules as needed [20, 47, 61]. Notably, SpatialPIN [45] extracts dense visual priors from multiple vision foundation models [25, 42] and uses a VLM [24] to combine and interpret this information. + +# 2.2. Visual Perspective-Taking + +Visual perspective-taking (VPT) is the ability to imagine an alternative viewpoint, whether from another person's perspective or a different camera angle. This ability is essential for fundamental human skills such as navigation, spatial awareness, and social interaction [3, 11, 17, 55]. To be regarded as a general vision agent capable of human-like reasoning, a VLM should possess robust perspectivetaking abilities. However, recent analyses reveal that current VLMs fail to shift to allocentric perspectives, showing a strong bias toward the egocentric viewpoint of a given image [19, 37, 46, 77, 78]. Zhang et al. [78] propose a synthetic evaluation protocol to assess whether VLMs can adopt different frames of reference (i.e. perspective). Likewise, 3DSRBench [46] includes real image-question pairs asked from an object's viewpoint, and finds that recent VLMs still demonstrate near chance level on perspectivel-related tasks. These findings suggest that while VLMs are rapidly improving in both complex visual reasoning [2, 14, 24, 40, 63] and basic spatial reasoning [6, 8, 10, 21, 31, 64], their abilities remain confined to the egocentric viewpoint, posing a significant barrier to human-like reasoning. Recently, SAT [53] proposed to improve VLMs' allocentric reasoning through instruction-tuning, yet it remains restricted to left/right relations with the need for annotations. In this work, we empower VLMs to reason from arbitrary perspectives, by reformulating any spatial reasoning task into their default egocentric viewpoint, resulting in a generalizable framework. + +# 2.3. Visual Prompting + +Visual prompting frames an input image as an instruction for a VLM, functioning similarly to how text prompts guide language models [30, 38, 59, 67, 69, 73, 80]. Numerous studies have demonstrated its effectiveness by exploiting the inherent image comprehension capabilities of VLMs. Set-of-Marks [71] augments each object in an image with its corresponding segmentation mask for more fine-grained visual grounding. Visual Sketchpad [22] provides tool-based framework for VLMs to utilize drawing tools to annotate images for complex tasks such as math problem solving and visual search. Recent research further proposes visual chain-of-thought (CoT) pipelines [9, 33, 54, 56, 68, 79, 80] that visualize intermediate reasoning steps as images and feed them back to the model as auxiliary inputs. This visual feedback loop has proven effective for spatial tasks, as it anchors textual reasoning to concrete visual cues [33, 68]. Building on this idea, we propose to transform an abstraction of a given scene and feed it back to a VLM in the form of a visual prompt, offering a new way for the model to reason from arbitrary viewpoints. + +# 3. Method: Abstract Perspective Change + +Our goal is to enable VLMs to solve spatial reasoning tasks from any given perspective (Fig. 2). Let us call the entity of the target perspective as the reference viewer. Since VLMs inherently approach spatial reasoning from an egocentric perspective [78], we propose to reformulate perspective-specific questions to align with the reference viewer's egocentric perspective. Inspired by theories in mental imagery [17, 48, 57], we begin by explicitly building an abstraction of the scene and use it as a foundation for shifting perspectives (Fig. 3). + +Overview of APC. We call our approach Abstract Perspective Change (APC), which consists of three main stages. + +![](images/32f39661f886ca7c7061baba1cd9cb24b9fdff1c1a1f0c513e5570dde6802ef9.jpg) +Figure 3. Mental Imagery Simulation. Inspired by how humans employ mental imagery to reason from across different perspectives (left), we propose a similar process for VLMs, by constructing an explicit abstraction of the input scene and using it as a foundation for perspective changes (right). + +![](images/02775c675c2440cea7b5f51319f45df65951022d6d9ca6c08ef758fbb08ba626.jpg) +Figure 4. Pipeline Overview of APC. Our proposed framework consists of three stages. 1) Scene Abstraction (Sec. 3.1): APC first detects the objects of interest and build a coarse 3D abstraction of the scene using off-the-shelf vision foundation models. 2) Perspective Change (Sec. 3.2): Then, a reference perspective is set and the abstraction is transformed into the reference viewer's egocentric coordinate frame. 3) Perspective Prompting (Sec. 3.3): Finally, APC passes the transformed scene to the VLM by producing (1) a numerical (textual) prompt or (2) an abstract visual prompt, and poses the question of interest from the reference perspective. + +(1) First, APC constructs a coarse 3D abstraction of the scene from the input image by selecting and extracting objects of interest using off-the-shelf vision modules (Sec. 3.1), drawing inspiration from human mental imagery [17]. (2) Next, APC selects a reference viewer for the spatial reasoning task among the objects of interests in the constructed scene abstraction. This determines "where to look from". Such a formulation allows the conversion of the allocentric reasoning problem to an egocentric spatial reasoning task by performing a perspective change that transforms the base coordinate system of the abstraction from the original camera view to that of the reference viewer (Sec. 3.2). (3) Finally, the transformed abstracted scene, which can now be posed as an egocentric problem, is fed back into the VLM for spatial reasoning (Sec. 3.3). We explore two alternative representations when providing the VLM with transformed abstract scene information: 1) directly feeding numerical 3D coordinates of each object as a text prompt (numerical prompt), and 2) generating an abstract rendering of the scene as viewed by the reference perspective (visual prompt). An illustration of our APC pipeline is shown in Fig. 4, and we detail each step as follows. + +# 3.1. Scene Abstraction + +APC begins by building a coarse 3D abstraction of the scene. Given an image $I$ and a spatial reasoning question $Q$ , we define the abstraction of a scene as the set $S_{E} \coloneqq \{O_{i}\}_{i=1}^{n}$ composed of objects of interest from the question $Q$ . Here, $E$ denotes that the abstraction is defined in the camera's egocentric coordinate system, and the number of objects of interest $n$ is determined by the VLM based on $Q$ . Each $O_{i}$ corresponds to an object of interest in the image and is represented as a tuple $(t_{i}, c_{i}, p_{i})$ , where $t_{i}$ is the object's description, $c_{i} \in \mathbb{R}^{3}$ is its 3D position, and $p_{i} \in \mathbb{S}^{3}$ + +is a unit vector that indicates its orientation. Additionally, the camera is also included as an object of interest. This abstraction provides a minimal yet sufficient information in order to perform perspective changes, and mirrors how humans draw and rotate mental images when reasoning with perspectives [17, 57]. It allows for our APC to convert an allocentric problem to an egocentric spatial reasoning task, which VLMs can better solve [78]. More details are described below. + +Extracting Objects of Interest. To determine which objects in the image should be included in the scene abstraction $S_{E}$ , we provide the image $I$ and the question $Q$ to the VLM and instruct it to identify the list of objects necessary for answering the question. The VLM then returns the list of objects of interest, specified by their name, which we denote as $t_{i}$ . The detailed instruction prompts are included in the Appendix (Sec. E). + +Building Object Abstractions. Given the list of objects of interest, we complete our abstracted scene representation by extracting the position and orientation of each object $O_{i}$ using off-the-shelf vision foundation models. To obtain the 3D position of $O_{i}$ , we first query GroundingDINO [43] with image $I$ and the object description $t_i$ and obtain its 2D bounding box $b_{i}$ . We then crop $I$ with $b_{i}$ , and utilize SAM [28] to obtain a precise segmentation mask for $O_{i}$ . Next, we extract the metric depth map of $I$ using DepthPro [4] and unproject the pixels within the segmentation mask to 3D. Subsequently, the position $c_{i}$ is obtained by taking the median coordinate of this 3D point cloud. For further implementation details, please refer to the Appendix (Sec. C). Estimating the orientation $p_i$ for each object $O_{i}$ is also necessary to perform the desired perspective transformation. We utilize OrientAnything [66], which returns the object's frontal orientation within the camera co + +![](images/54492bf6dbf22a295edcbf475e841866fcf45946a7d7e69dc2aa752372083ccc.jpg) +Q: From the woman's perspective, which object located on the left side, the snowman or the horse? +A: snowman +Figure 5. Perspective Prompt Samples. We explore two variations of perspective prompting, numerical (left) and visual (right). Numerical (textual) prompt is generated by directly utilizing the 3D coordinate and orientation information. To generate the Visual prompt, we first place a colored cube at each object's identified 3D position then render the scene at the reference viewpoint, which results in an egocentric depiction of the scene. In addition, we construct an abstract question along with object-color mapping to ground the abstracted view. + +# Numerical Prompt + +Imagine that you are at the woman's position and facing where she is facing. We have the coordinates of different objects in the woman's coordinate system. + +# Coordinate System + +The origin is at the woman's position. +- The woman's facing direction is $[0, 0, 1]$ , which is aligned with the z-axis. +- The x-axis is to the right, the y-axis is up, and the z-axis is forward. + +# # Object Coordinates + +woman : [0, 0, 0] +- snowman: [-1.741, -0.707, 1.611] +- horse: [0.746, 0.187, 1.08] + +# Task + +Given the above woman's coordinate system and the object coordinates, please answer the following question: + +{Question} + +# Visual Prompt + +![](images/3cb310c3f49efdb7b6f6d0f8771b028f50ad9fa04f7d2ccd627c33b483772ac7.jpg) + +# Abstract Question + +Which object is located on the left side, the blue cube or the red cube? +: The blue cube is located on the left side of the red cube + +# # Object Abstraction + +We provide a color-object map that maps each colored box to an object: + +# Color-Object Map + +- blue cube $\rightarrow$ snowman +red cube $\rightarrow$ horse + +Given the color-object map above, change all the colored boxes in the below response into their respective objects. + +[Original Response]: The blue cube is located on the left side of the red cube. +: The snowman is located on the left side of the horse. + +Based on the previous response, answer the question: {Question} + +ordinate system. For this, we crop the image with $b_{i}$ and feed the cropped image to OrientAnything to obtain $O_{i}$ 's orientation, hence completing our scene abstraction representation. + +# 3.2. Perspective Change + +With egocentric scene abstraction $S_{E}$ for a given image $I$ and question $Q$ , APC then determines the reference viewer and performs perspective change to obtain a transformed scene abstraction from the reference viewer's perspective. This effectively converts an allocentric problem into an egocentric task, which VLMs find easier to handle. + +Setting a Reference Perspective. APC first determines "where to look from" by selecting a reference viewer from the set of objects of interest. For this, we provide the spatial reasoning question $Q$ to the VLM and instruct it to identify the reference perspective from which the question should be answered. We denote the extracted reference perspective as $A$ , and provide the complete instruction for perspective extraction in the Appendix (Sec. E). + +Transforming Scene Abstraction. After identifying the reference viewer, we then transform the original camera-based scene abstraction $S_{E}$ into the reference viewer's egocentric coordinate system. Specifically, we apply coordinate transformation from the camera's frame to that of the reference viewer $A$ . In the resulting abstraction $S_{A}$ , the reference viewer $A$ is placed at the origin, and its orientation is aligned with the $z$ -axis. This step supports APC's main objective of reframing a general perspective question—typically an allocentric problem—into the reference viewer's egocentric viewpoint, making it an egocentric task. Finally, we provide $S_{A}$ to the VLM so it can answer the question $Q$ from $A$ 's perspective. We describe this stage more in depth below. + +# 3.3. Perspective Prompting + +The final step of APC involves generating a prompt from the transformed scene abstraction $S_{A}$ to feed as input for the VLM. That is, how is the VLM asked with the transformed, now egocentric spatial reasoning task? We refer to our generated prompt as the perspective prompt for image $I$ and question $Q$ . Since VLMs can take images and text inputs, we explore two choices for the representation of this prompt: numerical (textual) and visual. + +Numerical (Textual) Prompt. Recall that an object abstraction in the transformed scene abstraction $S_A$ consists of the object's textual description, its corresponding 3D position, and its orientation, i.e. $O_i' = (t_i, c_i', p_i')$ . Hence, a straightforward approach is to directly feed this information into the VLM. Specifically, we include the 3D position $c_i'$ in a predefined instruction template and instruct the VLM to directly solve the question $Q$ . The full instruction template is provided in the Appendix (Sec. E). + +Visual Prompt. Our goal is to let VLMs "view the scene from $A$ 's perspective"; thus an alternative choice for the perspective prompt is a visualization of our abstraction $S_A$ . We begin by assigning each object an equal-sized cube, with each cube's position matching the objects' positions $c_i'$ . We then render these cubes from the reference viewer $A$ 's vantage point, generating an egocentric depiction of the scene abstraction. To distinguish between objects, each cube is assigned a unique color. When providing this information to the VLM, we modify the original question $Q$ to reflect the abstract visual representation. Specifically, we replace object names (e.g. "dog") with their corresponding colored cubes (e.g. "red box"), forming an abstract question $Q^*$ . Refer to Fig. 5 for an example of an obtained abstraction question. Putting it all together, the VLM receives as a prompt both the abstract rendered image—showing colored + +cubes—and the reformulated question $Q^{*}$ . This allows it to answer spatial reasoning questions originally posed from arbitrary perspectives by reasoning with this abstract, egocentric visual prompt. More details on the visual prompting process are presented in the Appendix (Sec. C.3). + +# 4. Results + +In this section, we present the experimental results of our APC across a range of spatial reasoning tasks that include specified reference perspectives. We compare APC to multiple baseline methods and show how our abstraction-based allocentric-to-egocentric reasoning framework enables the VLM to handle alternative perspectives. We use Qwen2.5-VL [2] as our backbone VLM. + +# 4.1. Evaluation Settings + +**Benchmarks.** We validate our APC on both synthetic [78] and real-world [46] benchmarks in which the spatial reasoning requires perspective changes. Sample image-question pairs from each benchmark are shown in Fig. 6. + +- COMFORT++: Zhang et al. [78] introduce COMFORT, a benchmark synthesis protocol designed to evaluate VLMs on perspective-aware spatial reasoning. It employs a simple Blender [13] rendering pipeline to place multiple objects in a synthetic scene with one reference viewer and various other objects. Each scene poses a spatial reasoning question from the reference viewer's perspective. Building on COMFORT, we construct four types of spa + +![](images/fe3b044f3b32cd693b59556a4adafab069bcc97f73f63ad69815057132f714c0.jpg) +Spatial Relationship (L/R) +Q: If I stand at the fridge's position facing where it is facing, is the microwave on the left or right of me? A: Right + +![](images/e23e5e111fd6698f7ee9ae3965d528e2d1f4440835b2e112a7a75a10ff2154c6.jpg) +Real - 3DSRBench +Visibility +Q: If I stand at the teddy bear's position facing where it is facing, is the kid visible or not? A: Yes + +![](images/60a1e117cbee351bb41d364079113e77ac9395c7114751da5089bfbb8e05f8bc.jpg) +Facing Direction +Q: Which object is the man in blue t-shirt facing towards, the frisbee or the bench? A: Frisbee + +![](images/4f130087e4b354540cc629163e02522e3c5214bd53542cf10eadb1f183b8c8e7.jpg) +Spatial Relationship (L/R) +Q: From the horse's perspective, which object is located closer to the viewer, the duck or the basketball? A: Duck +Figure 6. Benchmark Visualization. Example image-question pairs from 3DSRBench [46] and COMFORT++ [78] benchmarks. The tasks probe spatial reasoning across left-right relations, object visibility, closss, and the facing direction of objects. + +![](images/aa0986cc4a07a52fb769818e3dcadc3fa1d0905a3e65c2ebe76663c1407d1783.jpg) +Synthetic-COMFORT++ +Closer +Q: From the refrigerator's perspective, which object is located closer to the viewer the laptop or the camel? A:Laptop + +![](images/482de34832abee706da694782b850195122228721790064830520174e501015e.jpg) +Facing Direction (U/B) +Q: From the cat's perspective, which object between dog, snowman is visible? A: Snowman + +tial reasoning tasks that require a reference viewer different from the camera: left/right, closer/further, visibility, and facing. + +- 3DSRBench: Ma et al. [46] introduce a 3D spatial reasoning benchmark based on MS-COCO images [36]. We focus on three categories that require an allocentric viewpoint: left/right, visibility, and facing. Note that we recast the original front/behind question in 3DSRBench into a visibility question using the same images. We provide further discussion on the dataset and the evaluation protocol in the Appendix (Sec. D). + +Baselines: VLMs. We benchmark our APC against multiple state-of-the-art VLMs, including both open-source and proprietary models. For open-source, we include LLaVA-NeXT [41], LLaVA-OneVision [31], Molmo [14], and Qwen2.5-VL [2]. We also include proprietary models: GPT-4o [24] and Gemini-2.0-Flash [63]. We refer to these as pure VLMs. Additionally, we compare against grounded VLMs, which include models explicitly tuned for spatial reasoning, such as SpatialVLM [8] and SpatialRGPT [10]. We also include SpatialPIN [45], which leverages interactions between VLMs and vision foundation models for complex spatial reasoning. + +Baselines: Dense Reconstruction. To compare APC with standard dense reconstruction techniques for novel view synthesis, we introduce two baselines. First, we extend SpatialPIN [45] to include our perspective change phase (Sec. 3.2). We use the generated meshes from its original pipeline and render the meshes from the reference perspective, and denote this extension as SpatialPIN*. Refer to the Appendix (Sec. B) for more details. Second, we adopt ViewCrafter [75], a novel view synthesis method designed for single-image inputs. For both baselines, we synthesize a novel view according to the reference perspective's relative pose, and feed the resulting image to the VLM for spatial reasoning. + +# 4.2. Evaluation on COMFORT++ [78] + +Tab. 1 (cols 2-5) provides quantitative comparisons on COMFORT++. Here, APC-Vis refers to our visual prompt, and APC-Num corresponds to the numerical prompt. Even though the benchmark consists of objects rendered in a simple, synthetic scene (see Fig. 6), we find that most pure VLMs (rows 3-9) struggle with the left/right task, hovering around chance level with the best performing model LLaVA-OneVision scoring only $55.33\%$ . This confirms earlier observations [78] that VLMs fail to adopt alternative perspectives. Even specialist VLMs designed for spatial reasoning perform poorly, with SpatialVLM at $46.0\%$ and both SpatialRGPT and SpatialPIN also exhibiting low accuracy. We observed that SpatialRGPT often generates hallucinated responses unrelated to the instruction, + +
MethodCOMFORT++ [78]3DSRBench [46]
left/rightcloservisibilityfacingleft/rightvisibilityfacing
Random50.0050.0050.0050.0050.0050.0050.00
LLaVA-NeXT [41]48.0047.3340.0039.0034.1041.5750.29
LLaVA-OneVision [31]55.3379.0050.9438.3332.0946.5160.12
Molmo [14]36.3335.6731.8829.0019.7722.9732.08
Qwen2.5-VL [2]43.3374.3351.2543.0034.9645.0653.47
Cambrian-1 [64]52.0079.0057.5041.0040.9749.7165.03
GPT-4o [24]41.0061.3353.7538.672.0140.1247.70
Gemini-2.0-Flash [63]43.6726.0040.3113.0024.9357.6555.20
SpatialVLM [8]46.0041.6742.8129.3322.3546.5147.11
SpatialRGPT [10]27.0833.9029.251.3325.9827.1942.55
SpatialPIN [45]19.6223.9648.4343.9111.1042.4011.66
SpatialPIN* [45]59.8070.4549.8450.5150.1052.3028.86
ViewCrafter [75]32.3353.0038.7537.4628.4122.4718.31
APC-Num (Ours)88.6796.0071.2562.0071.9262.7960.98
APC-Vis (Ours)89.6794.3390.0088.3372.7867.4466.47
+ +Table 1. Quantitative Comparisons. Purple ( ) represents pure VLMs, green ( ) represents grounded VLMs, and red ( ) represents dense reconstruction-based frameworks. Gray ( ) corresponds to our APC. Bold and underline indicate the best and the second-best result for each column, respectively. APC-Num and APC-Vis refer to our method employing numerical prompt and visual prompt, respectively. + +thereby resulting in low accuracy. While SpatialPIN*—employing perspective change—shows better performance, low-quality meshes often bottleneck further improvements (refer to Sec. B for more discussions). In contrast, our APC significantly outperforms these baselines, achieving $89.67\%$ accuracy with a visual prompt and $88.67\%$ with a numerical (textual) prompt. + +For the closer task, some VLMs show relatively high accuracy (79.00% for both LLaVA-OneVision and Cambrian-1), likely since they can also solve the question by comparing object distances directly from the egocentric viewpoint. Even in this case, APC achieves higher accuracy, attaining 96% when using a numerical prompt. Moreover, for visibility and facing categories, the baseline models perform at near-chance levels, failing to take the reference perspectives into account. Notably, APC exhibits a performance gap between visual and numerical prompts, with the visual prompt outperforming the numerical one by +18.75% and +26.33%, respectively. We attribute this difference to trivial logical errors that VLMs often make when relying on numerical coordinates. In contrast, for these two tasks the visual prompt requires only simple visual perception, mitigating such logical errors and achieving more accurate results. + +# 4.3. Evaluation on 3DSRBench [46] + +Tab. 1 (cols 6-8) presents quantitative comparisons on 3DSRBench, which includes real images. Compared to + +the synthetic environment in COMFORT++, using real images introduces additional noise into both the VLMs' visual reasoning and our APC's scene abstraction phase. For the left/right task, baseline VLMs consistently fall under $50\%$ accuracy, including the grounded VLMs. Even SpatialPIN* with perspective change only reaches $50.10\%$ , at near chance-level. We find that using ViewCrafter to generate a novel view from the reference perspective yields $28.41\%$ accuracy, due to the noise and hallucinations during generation. We provide visualizations of the rendered views from both SpatialPIN* [45] and ViewCrafter [75] in the Appendix (Sec. B), along with more discussions on the different between our abstraction-based approach and the dense reconstruction-based approaches. Compared to other baselines, APC consistently achieves accuracies above $60\%$ both with visual and numerical prompts, showing that our framework is robust to real images. + +For visibility task, while our method outperforms the baselines, the accuracy appears lower than previous tasks— $67.44\%$ with the visual prompt and $62.79\%$ with the numerical prompt. We attribute this decline to the noise in the scene abstraction phase, particularly errors in detected orientations or centroids. This issue is evident when compared to the visibility task in COMFORT++, which employs the same question format but with a simpler scene. Lastly, for the facing task, Cambrian-1 achieves $64.03\%$ , yet our APC with a visual prompt still leads at $66.47\%$ . Qualitative examples on 3DSRBench are shown in Fig. 7. + +![](images/168264f61e158cf3b1e79520ce3464e856053086e768689f43f16a65ff541123.jpg) +Q: From the woman's perspective, which object between penguin, duck is visible? +Figure 7. Spatial Reasoning with Perspective Change. Recent VLMs such as Qwen2.5-VL [2] and Cambrian-1 [64] often struggle with spatial reasoning tasks that require a shift to a specific reference viewpoint. In constraint, our APC effectively handles such perspective changes by constructing a scene abstraction and delivering the transformed view through a simple prompting technique. + +# 4.4. Probing the Perspective-Awareness of VLMs + +Finally, we analyze the perspective-awareness of each method by assessing spatial reasoning accuracy across different viewpoints. Specifically, we select two tasks—left/right and closer—and construct 60 scenes similar following our setting in COMFORT++. Each scene is rendered from 20 evenly spaced azimuth angles. We define $\theta$ as the angular offset between the camera's orientation and the reference viewer's orientation. Here, for $\theta = 0^{\circ}$ the camera is aligned with the reference perspective, while $\theta = 180^{\circ}$ indicates that the reference viewer is facing towards the camera. + +![](images/435eec4c0f5459202848f69fd35613c380540e248e3c7ed765d1beff5e1d3a75.jpg) +Figure 8. Perspective Awareness. Each plot shows accuracy versus the angular offset $\theta$ between the camera and the reference viewpoint. While baselines show clear degradation at certain ranges of $\theta$ , APC retains robust accuracy across all angles, demonstrating strong perspective-aware reasoning. + +The results are shown in Fig. 8. For the left/right task (left), the baselines exhibit clear bell-shaped curves, achieving near perfect accuracy when $\theta$ is close to $0^{\circ}$ (egocentric) but rapidly declining as the magnitude of $\theta$ increases (allocentric). In contrast, APC maintains consistently high accuracy across all angles, demonstrating strong perspective-aware reasoning. For the closer task (right), baseline models also show noticeable accuracy drops, especially near the leftmost and rightmost $\theta$ ranges. APC consistently achieves over $80\%$ accuracy, robustly handling viewpoints regardless of their deviation from the egocentric perspective. + +# 5. Conclusion + +In this work, we introduced APC, a framework empowering VLMs with the capability of perspective-aware reasoning. Our key idea is to simulate the mental imagery process of humans, abstracting the scene in an image to facilitate allocentric-to-egocentric perspective shifts, and in turn convey the transformed view to the VLM in the form of a prompt. The scene abstraction is constructed using vision foundation models for object detection, segmentation, and orientation estimation. The reframed prompt from the new perspective, either in text or image form, is then processed by VLMs, leveraging their egocentric reasoning capabilities. As shown by our experiment on both synthetic and real spatial reasoning benchmarks, APC enables robust accuracy across diverse perspectives, thereby opening new possibilities of VLMs on real-world spatial tasks. + +# Acknowledgements + +This work was supported by the NRF of Korea grant (RS-2023-00209723); IITP grants (RS-2019-II190075, RS-2022-II220594, RS-2022-00156435, RS-2023-00227592, RS-2024-00399817, RS-2025-25443318); and the Technology Innovation Program (RS-2025-02317326), all funded by the Korean government (MSIT and MOTIE), as well as grants from the DRB-KAIST SketchTheFuture Research Center. L. Guibas acknowledges the ARL grant (W911NF-21-2-0104) and a Vannevar Bush Faculty Fellowship. + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. 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Prior KD techniques typically assume homogeneity between the teacher and student models. However, as technology advances, a wide variety of architectures have emerged, ranging from initial Convolutional Neural Networks (CNNs) to Vision Transformers (ViTs), and Multi-Level Perceptrons (MLPs). Consequently, developing a universal KD framework compatible with any architecture has become an important research topic. In this paper, we introduce a perspective-aware teaching (PAT) KD framework to enable feature distillation across diverse architectures. Our framework comprises two key components. First, we design prompt tuning blocks that incorporate student feedback, allowing teacher features to adapt to the student model's learning process. Second, we propose region-aware attention to mitigate the view mismatch problem between heterogeneous architectures. By leveraging these two modules, effective distillation of intermediate features can be achieved across heterogeneous architectures. Extensive experiments on CIFAR, ImageNet, and COCO demonstrate the superiority of the proposed method. Our code is available at https://github.com/jimmylin0979/PAT.git. + +# 1. Introduction + +Knowledge distillation (KD) has received increasing attention from both academic and industrial researchers in recent years. The goal is to develop a lightweight and efficient student model by transferring knowledge from an already trained, larger teacher model. This knowledge may come in the form of predictions [17, 37], or intermediate features + +![](images/979cd1aecd6ab0938d5528ab9b57cc92caf793a5f809852c11d6b19597de741e.jpg) +View Mismatch Related (Red) --Teacher Unawareness Related (Brown Dashed) +Figure 1. High-level comparison between former state-of-the-art OFA and our method PAT. Due to the view mismatch (red lines) and teacher unawareness (brown dashed lines) problems, OFA can only use final logits to supervise student intermediate features (black solid lines), thereby restricting its utility in downstream tasks. In contrast, PAT enables feature imitation by solving these two issues with RAA and AFP modules respectively. + +[2, 3, 12], from the cumbersome pre-trained teacher model. Despite the significant progress in KD, there remains a gap in addressing cross-architecture distillation comprehensively. Existing KD approaches have predominantly focused on distillation between teacher and student models with homogeneous architectures, particularly feature-based approaches, leaving cross-architecture distillation relatively unexplored. For example, FitNet [30] achieves good results in CNN-to-CNN format but performs poorly when distilling in a heterogeneous CNN-to-ViT scenario, only getting $24.06\%$ on CIFAR-100 with ConvNeXt-T teacher and Swin-P student model pair, which is lower than the basic logit-based method KD [10] by more than $50\%$ . + +Heterogeneous KD, however, offers numerous advantages. First, it helps overcome architecture-specific limitations, allowing the student model to mitigate weaknesses inherent to individual architectures and achieve a better performance than learning from a homogeneous teacher model. For instance, CNNs can assimilate a more comprehensive understanding from ViTs, conversely, ViTs can augment + +their capacity for local feature extraction by leveraging insights from CNNs. Second, it enhances the robustness, as the student model learns from the varied error patterns and inductive biases of the teacher models, leading to better performance across different tasks and datasets. While a few studies have delved into the realm of heterogeneous architectures [20, 29, 38], it is noteworthy that these architectures often exhibit limitations in accommodating specific teacher-student pairings. As a result, a thorough restructuring of the link between the teacher and student models is essential whenever a new architecture is introduced into the system. + +To overcome the existing limitations, OFA-KD [8] is the first to propose a generic framework for heterogeneous KD by projecting the intermediate student features into the logits space and subsequently aligning them with the final predictions of the teacher model. The projection into a latent space with reduced architecture-specific details allows the distillation process to concentrate on high-semantic information, thereby enhancing distillation performance across different architectures. However, this projection results in a loss of spatial information that is crucial for downstream tasks. Furthermore, distilling based on the final high-semantic output of the teacher model may not fully exploit the valuable intermediate features. + +To effectively leverage the richly informative intermediate layer features and facilitate distillation across diverse architectures, we revisit the fundamental feature-based distillation pipeline to identify the potential issues. As illustrated in Fig. 1, apart from the different perspectives inherent in different architectural biases, which we refer to as the view mismatch problem, teacher unawareness is a notable concern, whereby the teacher model fails to adjust based on the student's learning progress. Hence, a novel perspective-aware teaching (PAT) KD framework is proposed for distillation between heterogeneous architectures to tackle these issues. To address the view mismatch problem, a region-aware attention (RAA) module is proposed to let the student model learn how to reblend features from different patches and stages to achieve a similar perspective with the corresponding teacher features via the attention mechanism. Since the perspective is now similar, traditional stage-wise feature alignment across different architectures can be applied normally. For the teacher unawareness problem, an adaptive feedback prompt (AFP) module is introduced. The AFP module employs prompt tuning [24] to generate distillation-friendly teacher features with additional branches. Moreover, the difference of the feature map between the student and teacher model, referred to as feedback, is integrated as extra input to the prompt tuning blocks, enabling the teacher model to dynamically adapt its features in response to the student model's learning trajectory. + +Our contributions are summarized as follows: + +- To address the view mismatch issue, we propose region-aware attention (RAA) to reblend student features to have a similar perspective with the teacher model. +- To address the teacher unawareness problem, we propose an adaptive feedback prompt (AFP) that enables the teacher model to dynamically adapt its features in response to the student model's feedback. +- Extensive experiments manifest that PAT improves student model performance with gains of up to $16.94\%$ on CIFAR-100 and $3.35\%$ on ImageNet-1K and $3.50\%$ performance gain on COCO. + +# 2. Related Works + +# 2.1. Homogeneous Knowledge Distillation + +A majority of the KD methods [25, 37] predominantly concentrate on homogeneous architectures, particularly within feature-based approaches [30, 32, 36], as the intermediate features between such architectures exhibit greater similarity, thereby enhancing the efficiency of the distillation process. For instance, ReviewKD [3] introduces a review mechanism that leverages multi-level information from the teacher model to direct the single-level learning of the student model, achieving commendable performance in the distillation process between CNN-based models. The aforementioned methods exhibit efficacy in distillation processes involving homogeneous architectures. Nonetheless, they fail to consider heterogeneous architectures. As such, they may encounter challenges like view mismatch and teacher unawareness when attempting to transfer knowledge from a heterogeneous teacher model. + +# 2.2. Generic Heterogeneous Knowledge Distillation + +As more model architectures are developed, creating a KD framework that works with any architecture has become crucial. Different architectures have unique biases [27], which require careful design for KD and often limit it to specific teacher-student pairs [1, 20, 29, 39]. OFA-KD [8] solves this by converting student features into a logits space, allowing alignment across architectures by removing architecture-specific details, but it loses important spatial information in features. In this work, we aim to design a feature-based distillation framework that keeps rich spatial information, improving both classification performance and downstream tasks. + +# 2.3. Adaptive Teacher in Knowledge Distillation + +In typical KD approaches [3, 10, 17, 23], the teacher model is first trained in isolation and then used to distill the knowledge to the student model. This results in static knowledge transfer that ignores the student's learning dynamics, often leading to suboptimal outcomes. This phenomenon has also been validated in [7], where they attempted to + +improve student model learning by substituting the conventional teacher trained with cross-entropy loss with one trained using MSE loss. Although this approach yields better performance, training an entirely new teacher model often requires significantly higher computational resources. Another research direction draws inspiration from prompt tuning [13], exploring the possibility of leveraging task-specific prompts that can be adjusted to fine-tune the entire teacher model with minimal parameters [15, 38]. For instance, CAKD [38] integrates adaptable prompts into the teacher model, enabling it to manage distillation-specific knowledge while preserving its discriminative capability. In this paper, we propose using prompt tuning in a generic heterogeneous KD framework to create an adaptive teacher. Unlike previous methods that directly feed the teacher feature, we additionally incorporate student feedback to better align the adaptation with the student's learning process, further improving the performance. + +# 3. Methodology + +In this section, we first review knowledge distillation (KD) and then introduce our PAT framework, which addresses existing issues such as view mismatch and teacher unawareness. We describe the adaptive feedback prompt (AFP) and region-aware attention (RAA) components, and summarize the objective function. An overview of the PAT framework is shown in Fig. 2. + +# 3.1. Preliminaries + +Knowledge Distillation (KD) [10] aims to effectively transfer knowledge from the pre-trained teacher model to a more compact student model. Among the various types of KD, logits and features are the most commonly used forms of knowledge to transfer. + +Logits-based distillation trains the student model to mimic the predictive distribution of the teacher model. This process can be formulated as: + +$$ +L _ {L D} = L _ {K L} \left(p ^ {T}, p ^ {\mathcal {S}}\right), \tag {1} +$$ + +where $p^T$ , $p^S$ represents the teacher and student model's confidence across all classes, respectively, and $L_{KL}$ denotes the KL-divergence function. For simplicity, we omit the temperature term here. + +On the other hand, features-based distillation utilizes intermediate features from the teacher model to train the student model in a more fine-grained manner, which can be expressed as: + +$$ +L _ {F D} = \Sigma_ {i = 1} ^ {4} D \left(F _ {i} ^ {T}, M _ {i} \left(F _ {i} ^ {S}\right)\right), \tag {2} +$$ + +where $F_{i}^{T}$ , $F_{i}^{S}$ denote the features of the teacher and student model in the $i$ -th stage, respectively. All teacher and student models are divided into four stages. $M_{i}$ represents + +the transformation applied to the student feature at the $i$ -th stage, and $D$ denotes the distance function that measures the gap between the teacher and student features, which is typically the Mean Squared Error (MSE) function. + +Overall, while logits-based distillation incurs minimal computational costs, its performance is generally inferior to that of the features-based approach. Despite this limitation, the architecture-agnostic nature of the predictive distribution in logits allows for straightforward application in heterogeneous KD scenarios. Conversely, features-based distillation requires careful designs to address potential bias misalignment but has the potential for superior performance, especially on downstream tasks. In this paper, we develop a generic feature-based distillation framework and mitigate the misalignments by introducing the region-aware attention (RAA) module and adaptive feedback prompt (AFP). + +# 3.2. Region-Aware Attention (RAA) Module + +A key issue in heterogeneous knowledge distillation is the difference in perspective between the teacher and student models, due to their distinct architectural receptive fields. For example, a ViT-based model begins with a broad view, whereas a CNN-based model builds up to a global understanding from local views, reaching full integration in the final layers. When trying to use the traditional stage-wise feature alignment method, this difference in perspective creates a significant challenge for the student model, hindering its ability to learn effectively from the teacher model. + +To address this issue, we introduce a region-aware attention (RAA) module. This module leverages an attention mechanism to help the student model learn to integrate features from different regions across stages, thereby achieving a perspective comparable to the teacher model. Owing to the flexibility of the attention module, RAA can seamlessly integrate into any architecture without requiring a distinct design. The proposed RAA is shown in Fig. 2(a) and is composed of three steps. First, we patchify the student features from each stage $i$ to $\frac{N_q}{4}$ patches to capture regional details within each stage, and then use convolution projectors $C_i$ to map them to a predefined dimension $\mathbb{R}^{\frac{N_q}{4} \times d}$ , where $N_q$ is a hyperparameter that denotes the total number of queries across all four stages. These stage features are then concatenated as $F^S \in \mathbb{R}^{N_q \times d}$ as depicted in Eq. 3. + +$$ +F ^ {S} = \operatorname {C o n c a t} \left(C _ {1} \left(F _ {1} ^ {S}\right),.., C _ {4} \left(F _ {4} ^ {S}\right)\right), \tag {3} +$$ + +Second, We feed $F^S$ into a self-attention module as expressed in Eq. 4, which is defined as: + +$$ +F ^ {S ^ {\prime}} = \operatorname {S o f t m a x} \left(\frac {\left(W _ {q} F ^ {S}\right) \left(W _ {k} F ^ {S}\right) ^ {T}}{\sqrt {d}}\right) W _ {v} F ^ {S}, \tag {4} +$$ + +where $W_{q}, W_{k}, W_{v}$ are the learnable weights, and $d$ is the channel dimension. $F^{S}$ contains features from different + +![](images/911d058a9a040984af67b3313677345cd7768cd94fac09ac00078569e0d89c77.jpg) +Figure 2. A comprehensive depiction of the general structure of our PAT framework and proposed modules. (a) RAA: student features across all stages are concatenated and fed into an attention module to learn how to integrate a new feature with a perspective similar to that of the teacher model. (b) AFP: a prompt-tuning method is introduced to modify the output stage features of the teacher model with respect to the student model's learning process. Note: Only three stages are shown for convenience. In our experiment, all models are split into four stages. + +![](images/63d04261a69ca9e538e8781f336f893746c0a9dfe870d4ced497a429067b65dc.jpg) + +patches and different stages. Through the attention mechanism, the student model learns how to focus on different spatial locations from different stages to blend a new feature with a perspective similar to that of the teacher model. Finally, we divide the blended student features $F^{S'}$ back into four stages after RAA and project each to the same size as the teacher. As the blended student features approximate the teacher's perspective, standard feature matching can subsequently be applied as described in Eq. 2. + +# 3.3. Adaptive Feedback Prompts (AFP) for Teacher + +The existing KD paradigm typically involves training the teacher model in isolation. This independent training means that the teacher model does not account for the subsequent distillation process intended to train the student model. Consequently, the intermediate information generated by the teacher model may not be effective for distillation, leading to suboptimal performance. This problem is particularly pronounced in heterogeneous KD, as models with different architectures have varying inductive biases, making their features less compatible with the student model. + +A naive solution is to optimize the teacher model during the distillation process simultaneously [6]. However, this method requires more computational cost and may lead to catastrophic forgetting [14] in the teacher model. To address + +this problem, we propose an adaptive feedback prompts (AFP) module, which uses prompt tuning [13, 24] to fine-tune the teacher model's knowledge with minimal parameters, aiming not only to eliminate information that is not conducive to distillation but also to make adjustments based on student feedback, while preserving the discriminative capacity of the teacher model. + +In practice, the AFP modules are inserted before the start of each stage in the teacher model, and each consists of two blocks, prompt block $PB$ , and fusion block $FB$ , as shown in Fig. 2(b). To accommodate various architectures, we follow [24] to develop $PB$ that integrates task-specific knowledge through an additional branch without the need to modify any architecture. Unlike the previous method, which directly feeds the teacher's features into the $PB$ [38], we introduce $FB$ before the $PB$ to incorporate the difference of the feature map between the student and teacher model, referred to as student feedback, into the teacher model's features, aiming to make the output prompt able to reflect the student feedback. Specifically, let $M_{i}^{AFP}$ denotes the transformation that transfers the student feature to the same dimension as the teacher's at the $i$ -th stage, we subtract the student features from the teacher features in each stage to create feedback as follows: + +$$ +F e e d b a c k _ {i} = M _ {i} ^ {A F P} \left(F _ {p r e v, i} ^ {S}\right) - F _ {p r e v, i} ^ {T}. \tag {5} +$$ + +This feedback identifies the locations and intensities where the teacher and student features are currently inconsistent. + +During forward, the AFP block inserted before $i$ -th stage takes the $i$ -th stage teacher feature $F_{prev,i}^{T}$ and student feature $F_{prev,i}^{S}$ from the previous iteration, along with the current $i$ -th stage teacher feature $F_{i}^{T}$ as input, and outputs the final feedback enhanced teacher feature $F_{i}^{T^{\prime}}$ with formula as follows: + +$$ +F _ {i} ^ {T ^ {\prime}} = P B _ {i} (F B _ {i} (C o n c a t (F e e d b a c k _ {i}, F _ {i} ^ {T})). \qquad (6) +$$ + +We first concatenate the feedback with the teacher features and input them into a fusion block, resulting in a teacher feature that the feedback has enhanced. This feedback-enhanced feature is then sent to the prompt block to modify the teacher model's output features. In this way, the teacher model can consider the student's learning process via feedback, thus providing more friendly features to the student model during distillation. Note that the feedback is derived by subtracting the teacher and student features from the previous iteration, as utilizing the current teacher and student features to generate feedback may lead to the model easily adapting the teacher features based on this spatial-aligned feedback. Employing features from previous instances enables the model to understand the error patterns, thereby facilitating a beneficial adjustment for the student model. + +Empirically, we find that the teacher features will be altered too much by the AFP modules in some teacher-student model pairs, even making the altered teacher features identical to the student's, rendering feature matching useless. To mitigate this issue, we introduce a regularization loss $L_{Reg}$ to avoid the teacher's features from converging to the student's features, thus preventing the generation of uninformative identity features by the teacher model that offers no value to the student model. The loss is defined as follows: + +$$ +L _ {R e g} = L _ {K L} \left(p ^ {T}, p ^ {T ^ {\prime}}\right), \tag {7} +$$ + +where $p^{T'}$ is the predictive distribution of the teacher model incorporating the AFP modules. By ensuring that the KL-diverge distance between the predictive distributions with and without AFP modules remains minimal, we maintain the discriminative capacity of the teacher model, thereby averting the emergence of non-informative features. + +# 3.4. Overall Objective Function + +By integrating the proposed modules into the general knowledge distillation framework, the overall loss function of PAT is defined as: + +$$ +L _ {P A T} = L _ {C E} + \alpha L _ {K L} + \beta L _ {F D} + \gamma L _ {R e g}, \tag {8} +$$ + +where $L_{CE}$ is the standard cross-entropy loss, $L_{KD}$ denotes the KL-divergence loss between $p^T$ and $p^S$ , and $L_{FD}$ + +denotes the feature matching loss between $F^{T'}$ and $F^{S'}$ . The weights $\alpha, \beta$ , and $\gamma$ balance the contribution of each term. For $L_{FD}$ , we adopt the hierarchical context loss (HCL) from ReviewKD [3] as the distance function $D$ , providing stronger hierarchical supervision. + +# 4. Experiments + +We conduct experiments on various tasks. First, we compare PAT with other KD methods on two image classification datasets. We then apply our method to object detection to show the pros of feature-based distillation. All results of PAT are reported by taking the average over 3 trials. Due to the space constraint, please refer to the supplementary for the implementation details. + +Datasets Two image classification datasets and one detection dataset are adopted for our experiments. (1) CIFAR-100 [16] is a well-known dataset, containing 50K training and 10K test images of size $32 \times 32$ in 100 classes. (2) ImageNet [4] is a large-scale classification dataset, which provides 1.2M images for training and 50K images for validation over 1,000 classes. (3) COCO [18] is an 80-category object detection dataset, which contains 118K images for training and 5K images for validation. + +Models We evaluate our PAT on various networks, including ResNet [9], MobileNetv2 [31], and ConvNeXt [22] as CNN-based models, ViT [5], DeiT [34] and Swin Transformer [21] as ViT-based models, and MLP-Mixer [33] and ResMLP [35] as MLP-based models. + +Baselines We compare with various approaches that are feature-based, such as FitNet [30], CC [26], RKD [25], and CRD [32], as well as the baselines that are based on logits, which include KD [10], DKD [37], DIST [11] and the most recent state-of-the-art (SOTA) OFA-KD [8]. + +# 4.1. Results on Image Classification + +On CIFAR-100, we compare our PAT method with eight other KD methods, encompassing a total of twelve heterogeneous teacher-student pairings. As shown in Table 1, PAT outperforms other methods on most teacher-student pairs, resulting in an average improvement of $8.17\%$ . For instance, we achieve an accuracy of $83.50\%$ on the ConvNeXt-T - ResMLP-S12 pair and $79.59\%$ on the ConvNeXt-T - DeiT-T pair, surpassing not only the other feature-based methods but also obtaining an improvement of $2.28\%$ and $3.83\%$ compared to the prior SOTA logits-based method OFA. Specifically, PAT does not achieve as much improvement on CNN-based students as it does on ViT-based and MLP-based students. Unlike the other two types of students, CNN-based students need additional patch-embedding layers, we speculate that these additional parameters could result in prolonged training epochs, thus only having a small improvement in current settings. + +
TeacherStudentFrom ScratchLogits-basedFeatures-based
T.S.KDDKDDISTOFAFitNetCCRKDCRDPAT
CNN-based students
Swin-TResNet1889.2674.0178.7480.2677.7580.5478.8774.1974.1177.6381.22
ViT-SResNet1892.0474.0177.2678.1076.4980.1577.7174.2673.7276.6080.11
Mixer-B/16ResNet1887.2974.0177.7978.6776.3679.3977.1574.2673.7576.4280.07
Swin-TMobileNetV289.2673.6874.6871.0772.8980.9874.2871.1969.0079.8078.78
ViT-SMobileNetV292.0473.6872.7769.8072.5478.4573.5470.6768.4678.1478.87
Mixer-B/16MobileNetV287.2973.6873.3370.2073.2678.7873.7870.7368.9578.1578.62
ViT-based students
ConvNeXt-TDeiT-T88.4168.0072.9974.6073.5575.7660.7868.0169.7965.9479.59
Mixer-B/16DeiT-T87.2968.0071.3673.4471.6773.9071.0568.1369.8965.3574.66
ConvNeXt-TSwin-P88.4172.6376.4476.8076.4178.3224.0672.6371.7367.0980.74
Mixer-B/16Swin-P87.2972.6375.9376.3975.8578.9375.2073.3270.8267.0378.44
MLP-based students
ConvNeXt-TResMLP-S1288.4166.5672.2573.2271.9381.2245.4767.7065.8263.3583.50
Swin-TResMLP-S1289.2666.5671.8972.8211.0580.6363.1268.3764.6661.7280.94
Average Improvement3.173.16-2.317.47-5.20-0.33-1.40-0.028.17
+ +Table 1. Result on CIFAR-100. Our results are the average over 3 trials. The highest results are indicated in bold, while the second-best results are underlined. + +
TeacherStudentFrom ScratchLogits-basedFeatures-based
T.S.KDDKDDISTOFAFitNetCCRKDCRDPAT
CNN-based students
Swin-TResNet1881.3869.7571.1471.1070.9171.8571.1870.0768.8969.0971.54
Mixer-B/16MobileNetV276.6268.8771.9270.9371.7472.1271.5970.7969.8668.8972.22
ViT-based students
ConvNeXt-TDeiT-T82.0572.1774.0073.9574.0774.4170.4573.1271.4769.1874.44
MLP-based students
Swin-TResMLP-S1281.3876.6576.6776.9977.2577.3176.4876.1575.1073.4077.59
Average Improvement1.571.381.632.060.570.67-0.53-1.722.09
+ +Table 2. Result on ImageNet. Our results are the average over 3 trials. The highest results are indicated in bold, while the second-best results are underlined. + +Due to computational limitations, we select four teacher-student settings to experiment with on ImageNet. The results are presented in Table 2. With an increase in the volume of training data, the majority of methods exhibit a favorable average enhancement. Among them, PAT attains SOTA performance across most teacher-student pairs. For instance, we achieve $72.22\%$ on MobileNetV2 and $77.59\%$ on ResMLP-S12 when distilling from the teacher model Mixer-B/16 and Swin-T, which is $3.35\%$ and $0.94\%$ higher than the baselines, proving our generalizability on a larger dataset. + +Previous feature-based methods achieve inferior perfor + +mance compared to logits-based methods, even getting a negative average improvement. Methods like CC, RKD, and CRD learn from the relationships between the data samples rather than directly imitating features, making them less vulnerable to view mismatch. However, they still underperform as they ignore the teacher unawareness problem. FitNet and our method both imitate the teacher model's features, however, without considering the view mismatch problem, the imitation is less efficient and thus performs badly. Our performance suggests that by tackling the discrepancy in perspectives and lack of awareness in the instructor, a feature-imitated approach can achieve compar- + +
Swin-T & ResNet18Swin-T - MobileNetV2
mAPAP50AP75mAPAP50AP75
Teacher45.1467.0949.2545.1467.0949.25
Student33.2653.6135.2629.4748.8730.90
KD34.0755.2636.4831.4652.4032.74
DKD29.9651.1731.3632.1053.8233.88
OFA33.3754.9835.1331.6952.9132.88
FitNet35.2356.0937.3132.4852.6234.67
PAT35.6256.6738.0432.9754.1835.08
+ +ble or even superior performance in heterogeneous KD scenarios. + +# 4.2. Results on Object Detection + +We extend our method to object detection and follow the setting of DKD [37] to perform distillation between the teacher's and student's backbone features. The results are presented in Table 3. Logits-based methods, as mentioned in DKD, can only achieve inferior performance as they disregard the intermediate features. For example, OFA can not reach good performance owing to the excessive focus on semantic details instead of spatial aspects, which is crucial for detection. Conversely, feature-based methods demonstrate superior performance, with our approach achieving SOTA results. We observe an enhancement of $2.36\%$ for ResNet18 and $3.50\%$ for MobileNetV2 when distilling from the Swin-T teacher model. This underscores that by mitigating view mismatch and teacher unawareness issues, the feature-mimicking technique can effectively leverage the abundant intermediate features for improved performance across classification and downstream tasks. + +Table 3. Results on COCO based on Faster RCNN [28] with FPN [19]. The highest results are indicated in bold, while the second-best results are underlined. + +
RAAAFP w/o FeedbackAFPAcc.
Baseline (FitNet)60.71
✓70.12
✓✓79.13
✓✓79.59
+ +# 5. Ablation Studies + +# 5.1. Effectiveness of each proposed module + +Experiments are conducted to evaluate the effectiveness, where the proposed modules are gradually integrated to measure their influence, and the results are summarized in Table 4. By leveraging the RAA module, the issue of view + +Table 4. The effectiveness of our proposed RAA, AFP on CIFAR-100 with ConvNeXt-T - DeiT-T as the teacher-student pair. + +
Stage 1Stage 2Stage 3Stage 4Mem. (GB)Acc.
Baseline (FitNet)6.1260.71
✓10.7675.43
✓11.5577.34
✓10.3076.26
✓9.0169.65
✓✓✓13.7077.87
✓✓✓12.3178.71
✓✓✓✓14.0279.59
+ +Table 5. Effect of number and position of AFP on CIFAR-100 with ConvNeXt-T - DeiT-T as the teacher-student pair. + +
NqMem. (GB)Acc.
Baseline (FitNet)6.1260.71
3613.7979.03
6414.0279.59
8014.3780.14
14414.5480.89
+ +Table 6. Comparison of the $N_{q}$ in RAA on CIFRA-100. We adopt ConvNeXt-T - DeiT-T as the teacher-student pair. + +mismatch is resolved, leading to a significant improvement in performance compared to the baseline. When we further introduce the AFP module to adapt the teacher model, the student yields larger gains, and the performance becomes the best when student feedback is incorporated into the AFP. + +# 5.2. Effectiveness of number and position of AFP + +Since adopting AFP at every stage is beneficial yet introduces additional parameters, we conduct experiments to investigate the effectiveness of adopting AFP at each stage as in Table 5. Enhancements in performance are observed even with the adoption of AFP in just one of the stages, with optimal outcomes achieved when AFP is implemented across all stages but also with the highest memory usage. In our experiments, we adopt AFP at each stage of the teacher model by default to achieve the best performance. + +# 5.3. Number of queries on RAA + +In RAA, each stage feature of the student is projected into a predefined sequence of shape $\mathbb{R}^{\frac{N_q}{4}\times d}$ for attention computation. Increasing $N_{q}$ allows finer subdivision of features, offering more detailed representations, but also leads to larger attention matrices and higher computational cost. We evaluate the impact of varying $N_{q}$ from 36 to 144 on performance and memory usage. As shown in Table 6, performance improves steadily with larger $N_{q}$ , accompanied by proportional memory growth. Notably, setting $N_{q} = 64$ achieves SOTA on CIFAR-100 with minimal memory usage. By default, we use $N_{q} = 64$ for CIFAR-100 and + +
Teacher +StudentSwin-T +ResNet18ConvNeXt-T +DeiT-TConvNeXt-T +ResMLP-S12
KD78.7472.9972.25
FitNet78.8760.7845.47
PAT w/o KL Loss79.1475.9881.79
PAT w/ KL Loss81.2279.1083.50
+ +Table 7. The effectiveness of loss ${L}_{KL}$ on PAT on CIFAR-100. + +
MethodExtra Para. (M)Epoch (s)Acc.
KD065.7572.99
OFA3.7876.1675.76
FitNet1.1190.4560.78
PAT14.48208.5779.59
+ +Table 8. The complexity of KD methods with ConvNeXt-T - DeiT as the teacher-student pair on CIFAR-100. + +$N_{q} = 144$ for larger datasets such as ImageNet and COCO. + +# 5.4. The performance of PAT without KL loss + +PAT is not purely feature-based, as it also incorporates a logits-based KL-divergence loss, as shown in Eq.8. This raises the question of whether performance gains stem primarily from the logits-matching loss rather than the feature-level alignment. To investigate, we train PAT without the KL loss. As shown in Table7, adding the KL loss improves performance. However, even without it, PAT still achieves performance close to SOTA. For best results, we include the KL loss by default to further enhance overall effectiveness. + +# 5.5. Complexity Analysis + +We also explore the complexity of our method. As shown in Table 8, it is found that logits-based methods, which rely solely on logits for distillation, require significantly fewer parameters compared to feature-based methods, leading to faster training times. In contrast, feature-based methods involve more parameters, which extends the training duration. Although PAT consumes the most parameters, it also achieves the highest performance. Notably, these additional parameters only appear during training and do not add any overhead to the student model during inference. + +For the trade-off between the complexity and performance of PAT, as mentioned in section 5.2 and 5.3, we can achieve faster training by lowering the number of AFP modules, or by decreasing the queries number on RAA. + +# 5.6. Visualization of attention map within RAA + +Direct feature matching in heterogeneous KD is suboptimal due to differing inductive biases across architectures, leading to mismatched feature representations. To address this, PAT leverages attention to guide the student in blending features from different regions and stages, aligning its + +![](images/0e7f2248ab3290f9764384d5c6fc4fbc457822332d8e07e84fdae5b251a49525.jpg) +Figure 3. Visualizations of the attention map within RAA from different model pairs. Queries are sorted based on patch and stage position, as the black arrow shows. + +![](images/7c300c93cec21e99de157e25baea575eafbe87d28ccd71ad441560c0f2207ce7.jpg) + +![](images/3c43aed5509cbf851b1d3c01ce5f99a7f6f0738580776b78e6c248f54249e2be.jpg) + +perspective with the teacher. As shown in Fig. 3, attention patterns vary across teacher-student pairs. For example, the MLP-based student ResMLP-S12 learns from the CNN-based teacher ConvNeXt-T by attending to consistent spatial positions across stages, forming diagonal patterns that reflect local aggregation. In contrast, the CNN-based student ResNet18, learning from the ViT-based teacher SwinT, captures features from neighboring patches, resulting in grid-like patterns indicative of global context aggregation. Similarly, the ViT-based student DeiT-T, when guided by the MLP-based teacher Mixer-B16, exhibits global attention with a strong focus on stage 3, suggesting that key information is concentrated there. + +# 6. Conclusion + +In this paper, we propose a perspective-aware teaching (PAT) framework to facilitate feature-level supervision in the context of heterogeneous KD. First, we introduce region-aware attention to blend the stage features of the student model to align with those of the teacher model, thereby alleviating the issue of view mismatch prevalent between the two models. Moreover, we incorporate the prompt tuning technique to address the teacher unawareness problem and enable to adapt the teacher model's feature utilizing feedback from the student model with minimal parameters. Through the integration of these two components, we can realize feature-level distillation in heterogeneous KD scenarios and achieve promising performance in classification and downstream tasks. + +# 7. Acknowledgments + +This work is partially supported by the National Science and Technology Council, Taiwan, under Grant: NSTC-114-2640-E-A49-011, NSTC-114-2218-E-A49-017, and NSTC-112-2628-E-002-033-MY4, and was financially supported in part by the Center of Data Intelligence: Technologies, Applications, and Systems, National Taiwan University (Grants: 114L900901/114L900902/114L900903), from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education, Taiwan. + +# References + +[1] Samira Abnar, Mostafa Dehghani, and Willem Zuidema. Transferring inductive biases through knowledge distillation. arXiv preprint arXiv:2006.00555, 2020. +[2] Defang Chen, Jian-Ping Mei, Yuan Zhang, Can Wang, Zhe Wang, Yan Feng, and Chun Chen. Cross-layer distillation with semantic calibration. In AAAI, pages 7028-7036, 2021. +[3] Pengguang Chen, Shu Liu, Hengshuang Zhao, and Jiaya Jia. Distilling knowledge via knowledge review. 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Motivation of Perspective invariant 3D object DETection (Pi3DET). We focus the practical yet challenging task of 3D object detection from heterogeneous robot platforms: Vehicle, Drone, and Quadruped. To achieve strong generalization, we contribute: 1) The first dataset for multi-platform 3D detection, comprising more than 51K LiDAR frames with over 250k meticulously annotated 3D bounding boxes; 2) An adaptation framework, effectively transfers capabilities from vehicles to other platforms by integrating geometric and feature-level representations; 3) A comprehensive benchmark study of state-of-the-art 3D detectors on cross-platform scenarios. + +![](images/040088a66d0e9e7d34bca19652d5716912ce5ba08ced9f3d2c4c07c550540120.jpg) + +![](images/a2cf53b9bd4f821df446ee858f51ad82708ea8874073cfb3c5479aa0a8dc7843.jpg) + +# Abstract + +With the rise of robotics, LiDAR-based 3D object detection has garnered significant attention in both academia and industry. However, existing datasets and methods predominantly focus on vehicle-mounted platforms, leaving other autonomous platforms underexplored. To bridge this gap, we introduce Pi3DET, the first benchmark featuring LiDAR data and 3D bounding box annotations collected from multiple platforms: vehicle, quadruped, and drone, thereby facilitating research in 3D object detection for non-vehicle platforms as well as cross-platform 3D detection. Based on Pi3DET, we propose a novel cross-platform adaptation framework that transfers knowledge from the well-studied vehicle platform to other platforms. This framework achieves perspective-invariant 3D detection through robust alignment at both geometric and feature levels. Additionally, we estab + +lish a benchmark to evaluate the resilience and robustness of current 3D detectors in cross-platform scenarios, providing valuable insights for developing adaptive 3D perception systems. Extensive experiments validate the effectiveness of our approach on challenging cross-platform tasks, demonstrating substantial gains over existing adaptation methods. We hope this work paves the way for generalizable and unified 3D perception systems across diverse and complex environments. Our Pi3DET dataset, cross-platform benchmark suite, and annotation toolkit have been made publicly available. + +# 1. Introduction + +LiDAR-based 3D object detection provides detailed spatial and geometric information about objects of interest, attracting significant research attention [1, 39, 48, 115]. Despite this trend, existing datasets [8, 22, 54, 76] and methods [31, 33, 43, 69, 72, 102, 113] predominantly target autonomous vehicles, leaving other platforms underexplored. + +Table 1. Summary of LiDAR-based 3D object detection datasets. We compare key aspects from 'robot platforms', 'scale', 'sensor setups', 'temporal (Temp.), 'multi-conditions, etc. To our knowledge, Pi3DET stands out as the first work to feature multi-platform 3D detection from Vehicle, Drone, and Quadruped, with fine-grained 3D bounding box annotations, conditions, and practical use cases. + +
DatasetVenuePlatform# of FramesLiDAR SetupTemp.Freq. (Hz)ConditionOther Sensors Supported
KITTI [22]CVPR'12✓XX14,9991 × 64No-✓RGB, IMU, Stereo
ApolloScape [28]TPAMI'18✓XX143,9061 × 64Yes2✓RGB, IMU, Radar
Waymo Open [76]CVPR'19✓XX198,0001 × 64, 4 × 16Yes10✓RGB, IMU, Radar
nuScenes [8]CVPR'20✓XX35,1491 × 32Yes2✓RGB, IMU, Radar
ONCE [54]arXiv'21✓XX~ 1M1 × 40No2✓RGB, IMU
Argoverse 2 [85]NeurIPS'21✓XX~ 6M2 × 32Yes10✓RGB, IMU
aiMotive [57]ICLRW'23✓XX26,5831 × 64Yes10✓RGB, IMU
Zenseact Open [2]ICCV'23✓XX~ 100K1 × 128, 4 × 16Yes1✓RGB, IMU
MAN TruckScenes [21]NeurIPS'24✓XX~ 30K6 × 64Yes2✓RGB, IMU, Radar
AeroCollab3D [78]TGRS'24X✓X3,200N/ANo-✓RGB, IMU
Pi3DET (M3ED)Ours✓✓✓51,5451 × 64Yes10✓RGB, IMU, Stereo, Event
+ +With rapid advancements in robotics, autonomous systems such as quadrupeds and drones are becoming increasingly vital for diverse real-world applications [3, 5, 9, 26, 37, 50, 61, 78, 91]. Equipping these emerging platforms with accurate 3D perception capabilities comparable to those of autonomous vehicles is therefore highly significant [6, 23, 34, 38, 48, 89]. Currently, research into non-vehicle platforms remains sparse [14, 41, 53, 64, 78], revealing a critical gap in cross-platform 3D object detection studies. + +A major barrier impeding progress in multi-platform detection is the lack of annotated multi-platform LiDAR datasets. Current benchmarks almost exclusively focus on vehicles [8, 22, 74, 76, 108]. Although some drone datasets exist [9, 78], they often lack comprehensive 3D annotations and sufficient platform diversity. Chaney et al. introduce M3ED [9], a dataset compiled from multiple platforms. However, the lack of annotated 3D bounding boxes currently limits its direct applicability for 3D detection tasks. Training platform-specific models independently is both resource-intensive and impractical for real-world deployment, especially in resource-constrained scenarios. Cross-platform adaptation, transferring knowledge from well-studied vehicle datasets to other platforms like drones and quadrapeds, emerges as a promising alternative. Existing domain adaptation techniques [116], however, primarily tackle cross-dataset shifts and neglect intrinsic geometric discrepancies caused by differences in platform dynamics and sensor viewpoints. + +To address these limitations, we introduce Pi3DET, the first publicly available multi-platform 3D detection dataset. Our dataset consists of 51,545 LiDAR frames with over 250,000 meticulously annotated 3D bounding boxes spanning Vehicle, Drone, and Quadruped. Our dataset is constructed using an automated labeling pipeline, supplemented by extensive manual refinement totaling approximately 500 hours. As detailed in Tab. 1, Pi3DET contains 25 sequences covering diverse environments under varying day and night conditions (examples in Appendix A.3). Analyses of Pi3DET highlight three crucial discrepancies + +across platforms: differences in ego-motion characteristics, variations in point-cloud distributions, and distinct bounding box properties, underscoring the necessity for specialized adaptation methods and techniques. + +Motivated by these insights, we propose Pi3DET-Net, a novel cross-platform adaptation framework. Our approach consists of two stages. In the Pre-Adaptation (PA) stage, we learn global transformations and extract geometric cues from the source platform. In the Knowledge Adaptation (KA) stage, we propagate the acquired knowledge and align features between the source and target platforms to improve cross-platform generalization. In particular, our method effectively bridges the platform gap among heterogeneous robotic systems at both the geometric and feature levels: + +- **Geometry-Level.** We develop Random Platform Jitter (RPJ) to augment source data with simulated ego-motion disturbances, enhancing robustness to platform-specific motion variations. Moreover, Virtual Platform Pose (VPP) projects target platform point clouds into a source-like coordinate frame, mitigating viewpoint discrepancies. + +■ Feature-Level. Our Geometry-Aware Transformation Descriptor (GTD) encodes platform-specific geometric properties (e.g., sensor elevation distributions), guiding effective feature alignment. The proposed KL Probabilistic Feature Alignment (PFA) leverages variational inference to minimize domain-specific distribution gaps, thereby facilitating accurate platform-specific pose adaptation. + +Extensive experiments on KITTI [22], nuScenes [8], and our Pi3DET validate our effectiveness. Specifically, Pi3DET-Net achieves mAP gains of $+11.84\%$ and $+12.03\%$ in Vehicle $\rightarrow$ Drone and Vehicle $\rightarrow$ Quadruped adaptations, respectively. Additionally, cross-dataset experiments show an average improvement of $+25.27\%$ mAP over source-only methods in the nuScenes $\rightarrow$ KITTI scenario. We further establish a comprehensive benchmark on Pi3DET with 18 state-of-the-art detectors, identifying insights to enhance resilience against platform variations. When combined with these detectors, our method consistently boosts performance, + +underscoring its architecture-agnostic nature and wide applicability. In summary, the contributions of this work are: + +- We introduce Pi3DET, a diverse and large-scale multi-platform 3D object detection dataset, serving as a solid foundation for cross-platform 3D detection research. +- We propose a novel cross-platform 3D object detection framework, Pi3DET-Net, to effectively transfer 3D detection capabilities from vehicles to other platforms by integrating geometric and feature-level representations. +- We establish an extensive benchmark, providing crucial insights for future development of generalizable 3D detection systems across heterogeneous robot platforms. To our knowledge, this is the first work in this line of research. + +# 2. Related Work + +Datasets & Benchmarks for 3D Detection. LiDAR-based 3D detection aims to estimate an object's 3D position and geometric dimensions [56, 63, 81]. Typical detectors are classified by their approach to process point cloud data: grid-based (using voxels [15, 42, 46, 55], range grids [18, 79, 112] and BEV grids [49, 75, 84], pillars [43, 67, 83], or cylindrical partitions [11, 65, 120]), point-based (directly learning features from raw points [62, 99, 100, 113]), or hybrid point-grid [47, 70, 72, 73], which often delivers state-of-the-art results but at higher computational cost. Datasets such as KITTI [22], nuScenes [8], Waymo Open [76], and others [6, 28, 54, 85, 88] have driven progress in accuracy [49, 70], robustness [17, 25, 32, 36, 74], and efficiency [95, 101]. Yet, most research targets vehicle-mounted sensors, leaving quadrupeds and drones underexplored despite similar LiDAR payloads. To address this gap, we present Pi3DET, the first publicly available dataset incorporating heterogeneous data from multi-platform setups for 3D object detection. + +Cross-Dataset 3D Detection. Prior work transfers knowledge often in cross-dataset settings. ST3D [96] and $\mathrm{ST3D + + }$ [98] introduced a three-stage approach (pretraining, pseudolabeling, and self-training) to improve generalization on target data. Further work refines pseudo-label accuracy [10, 80, 110, 111, 114] and self-training guidance [104, 119], or leverages unified training sets [16, 105] and knowledge distillation [27, 29, 97]. However, most ignore the more challenging cross-platform scenario. While Wozniak et al. [86] highlight its importance, they lack a suitable dataset for vehicle-to-other-platform experiments. In contrast, we analyze platform-level shifts and propose the first method tailored for cross-platform transfers. Building on Pi3DET, we validate its effectiveness on genuine multi-platform data. Auto-Labeling 3D Object Detection. Accurate point cloud annotations are crucial for 3D detection, yet labeling a single point cloud can take over 100 seconds [117]. To reduce this burden, researchers have explored semi-automated [51, 87] and fully-automated [109] approaches, including active learning [20, 24, 66, 103], weak supervision [45, 58, 59, + +107], and pseudo-label refinement [7, 11, 12, 19, 44, 80, 94]. Recent works integrate vision-language models [52, 90, 92, 107, 117, 118] for greater efficiency. However, these methods primarily target vehicle-mounted platforms. In contrast, we design Pi3DET-Net to address multi-platform auto-labeling, including quadruped and drones, to advance 3D object detection in broader operational scenarios. + +# 3. Pi3DET: Dataset & Benchmark + +# 3.1. Motivation + +While existing LiDAR-based 3D detection datasets predominantly focus on vehicle data, their utility diminishes for other platforms (e.g., drones and quadrupeds) due to diverging operational perspectives. To address this limitation, we introduce Pi3DET (Perspective invariant 3D object DETection), the first multi-platform dataset for LiDAR-based 3D object detection. Built upon M3ED [9], Pi3DET provides annotated LiDAR sequences across Vehicle, Drone, and Quadruped, specifically designed to advance research in multi-platform 3D object detection. + +# 3.2. Dataset Statistics + +Our Pi3DET benchmark spans 25 sequences collected from vehicle, quadruped, and drone platforms, annotated at 10 Hz. Compared to other datasets in Tab. 1, Pi3DET provides 51,545 frames and more than 250,000 box annotations across two object categories (Vehicle and Pedestrian), covering day/night conditions in urban, suburban, and rural areas. We combine an automated labeling pipeline with extensive manual refinement, requiring about 500 hours of human effort. For additional details on the annotation process, dataset statistics, and examples, please refer to Appendix A. + +# 3.3. Perspective Discrepancies Analysis + +To quantify cross-platform gaps, we first formalize the problem setup and analyze geometric discrepancies across three platforms. We define a point cloud as $\mathcal{P}^{\beta} = \{\mathbf{p}_i\}_{i=1}^{N^{\beta}}$ and a single point from the set as $\mathbf{p} = (p^x, p^y, p^z) \in \mathbb{R}^3$ , $\beta$ denotes the platform, including vehicles, drones, and quadrupeds, and $N^{\beta}$ is the number of point clouds for platform $\beta$ . The 3D bounding boxes are denoted by $\mathcal{B}^{\beta} = \{\mathbf{b}_j\}_{j=1}^{M^{\beta}}$ . We denote one bounding box from this set as $\mathbf{b} = (c^x, c^y, c^z, l, w, h, \varphi) \in \mathbb{R}^7$ . Here, $\mathbf{c} = (c^x, c^y, c^z)$ represents the bounding box center, $(l, w, h)$ the dimensions, $\varphi$ the heading angle, and $M^{\beta}$ is the number of bounding box. Additionally, the ego pose is given by a transformation $\mathbf{T} \in \mathrm{SE}(3)$ , decomposed into a rotation matrix $\mathbf{R} \in \mathrm{SO}(3)$ (parameterized by Euler angle $\phi$ , $\theta$ , and $\psi$ for roll, pitch, yaw) and a translation vector $\mathbf{t} = [t^x, t^y, t^z]$ . We further + +![](images/59c5ea54f65cd08dd951b3b8ea1d2af7076ec7263aab23c56671e5ef3208183f.jpg) +Figure 2. Analysis of perspective differences across three robot platforms. We present the statistics of point elevation distribution (upper-left), ego motion distribution (bottom-left), and target bounding box distribution (right), along with means and variances for each platform's data. We use different colors to denote different platforms for simplicity, i.e., Vehicle, Drone, and Quadruped. Best viewed in colors. + +define the distance between the target bounding box and the ego platform in bird's-eye view (BEV) as $\rho$ , and denote the relative pitch from the bounding box to the ego platform in the ego coordinate system as $\theta^r$ . As shown in Fig. 2, we identify three critical cross-platform discrepancies. + +Ego Motion Distributions. Vehicle-mounted LiDAR sensors exhibit stable motion with minimal roll/pitch variance $(\phi, \theta < 5^{\circ})$ . In contrast, drones and quadrupeds suffer significant ego jitter due to dynamic locomotion and aerodynamics, inducing roll/pitch fluctuations up to $20^{\circ}$ , shown in the bottom-left part in Fig. 2. This instability introduces high-frequency perturbations in point cloud geometry. + +Point Elevation Distributions. Beyond the roll and pitch jitter caused by ego motion, the overall distribution of the elevation $p^z$ of the input point cloud varies significantly among the platforms due to their different intrinsic heights. As shown in the upper-left in Fig. 2, for vehicles, most points lie slightly below their own height ( $p^z < t^z$ ). In contrast, on quadrupeds, the points cluster above the height of platform ( $p^z > t^z$ ), while for drones, the points are distributed substantially lower than the drone's altitude ( $p^z << t^z$ ). + +Target Bounding Box Distributions. Variations in platform height influence the relative orientation of the detected object. The right part of Fig. 2 shows the relationship between targets' relative pitch angles $\theta^r$ and BEV distances $\rho$ . Comparatively, drones observe objects with larger downward pitch angles and large variances, indicating that targets are positioned lower relative to the ego platform with a more uneven distribution. In contrast, quadrupeds exhibit larger upward pitch angles, suggesting that objects are relatively higher in their view. Vehicles, benefiting from stable motion, display the smallest variance in pitch angle distribution. + +These discrepancies make single-platform models ineffective for cross-platform deployment. Training separate + +models for each platform is resource-intensive and impractical for real-world scalability. Instead, we aim to propose a unified cross-platform adaptation framework that trains on large-scale readily available source platform data $(S, e.g., \text{vehicle})$ and generalizes to target platform data $(T)$ without target labels, addressing geometric shifts through perspective-invariant learning. + +# 4. Methodology + +As illustrated in Fig. 3, we propose a two-stage Pi3DET-Net consisting of Pre-Adaption (PA) and Knowledge-Adaption (KA) for cross-platform adaptation. For geometric alignment (Sec. 4.1), Random Platform Jitter facilitates robustness against ego-motion variations, while Virtual Platform Pose aligns viewpoints. For feature alignment (Sec. 4.2), KL Probabilistic Feature Alignment aligns target features with the source space, and a Geometry-Aware Transformation Descriptor corrects global transformations across platforms. The training pipeline is illustrated in Sec. 4.3. + +# 4.1. Cross-Platform Geometry Alignment + +As outlined in Sec. 3.3, platform-induced point cloud discrepancies arise from varying ego motions, point elevations, and target bounding box distributions. To mitigate these, we propose two complementary strategies. First, we apply Random Platform Jitter during PA on the source platform, enhancing robustness to pose jitter. Second, we use a Virtual Platform Pose in KA on the target platform to achieve effective scene alignment. Together, these approaches enable smoother geometric adaptation from source to target. + +Random Platform Jitter (RPJ). To emulate the roll and pitch jitters observed on quadruped and drone platforms, we introduce Random Platform Jitter during PA on the + +![](images/fce39dc86a7654f44097e2590a232da68c45619b022657bc4fc19727b8ef4e5e.jpg) +Figure 3. Framework Overview. The proposed Pi3DET-Net consists of two main stages: Pre-Adaptation (PA) and Knowledge-Adaptation (KA), aiming at bridging the gap across heterogeneous robot platforms through alignment at both geometric (Sec. 4.1) and feature levels (Sec. 4.2). On the geometric side, PA employs Random Platform Jitter to enhance robustness against ego-motion variations, while KA uses Virtual Platform Pose to simulate source-like viewpoints to achieve bidirectional geometric alignment across platforms. On the feature side, Pi3DET-Net further incorporates KL Probabilistic Feature Alignment to align target features with the source space, along with a Geometry-Aware Transformation Descriptor to correct global transformations across platforms. + +source platform. Specifically, we sample two angles $\Delta \phi$ and $\Delta \theta$ from a uniform distribution for roll and pitch, and define a composite rotation $\mathbf{R}(\Delta \phi, \Delta \theta)$ . For point $\mathbf{p} \in \mathcal{P}^S$ , bounding-box $\mathbf{b} \in \mathcal{B}^S$ and its center $\mathbf{c}$ , we have: + +$$ +\bar {\mathbf {p}} = \mathbf {R} (\Delta \phi , \Delta \theta) \mathbf {p}, \quad \bar {\mathbf {c}} = \mathbf {R} (\Delta \phi , \Delta \theta) \mathbf {c}. \tag {1} +$$ + +Here, the box dimensions are unchanged, and the heading angle is preserved. The transformed point cloud $\bar{\mathcal{P}}^S$ is then input into the backbone for feature extraction. Exposing the model to these rotated point cloud inputs tends to enhance the robustness to roll-pitch variations on target platforms. + +Virtual Platform Pose (VPP). We establish a virtual pose on the target platform during KA to mimic the source viewpoint and reduce the platform geometry gap. Since input point cloud and bounding box distributions diverge, we define a virtual pose $\bar{\mathbf{T}}$ from the actual ego pose $\mathbf{T}$ . We set roll and pitch to zero $(\bar{\phi} = 0, \bar{\theta} = 0)$ , keep the actual yaw $(\bar{\psi} = \psi)$ and preserve planar coordinates $(\bar{t}^x = t^x, \bar{t}^y = t^y)$ , fixing the height at $\bar{t}^z = t_{\text{vehicle}}^z$ . Given a point cloud $\mathbf{p} \in \mathcal{P}^T$ from target platform, along with the bounding box $\mathbf{b} \in \mathcal{B}^T$ and its center $\mathbf{c}$ , we express them in homogeneous coordinates $\mathbf{P}, \mathbf{C}$ , and then transform them to the following: + +$$ +\bar {\mathbf {P}} = \bar {\mathbf {T}} \mathbf {T} ^ {- 1} \mathbf {P}, \quad \bar {\mathbf {C}} = \bar {\mathbf {T}} \mathbf {T} ^ {- 1} \mathbf {C}. \tag {2} +$$ + +Here, dimensions remain unchanged, while the heading $\varphi$ is offset by $\Delta (\bar{\psi},\psi)$ . The resulting point cloud $\bar{\mathcal{P}}^T$ is used for feature extraction. Transforming both point clouds and + +bounding boxes to this virtual coordinate frame mitigates platform gaps and improves cross-platform adaptations. + +# 4.2. Cross-Platform Feature Alignment + +To address domain shifts across platforms, we leverage both probabilistic modeling and global geometric cues to align cross-platform features. As illustrated in Fig. 3, our feature alignment consists of two key components: 1) a transformation descriptor that learns global geometric invariance; and 2) a probabilistic feature alignment guided by KL divergence. + +Geometry-Aware Transformation Descriptor (GTD). As discussed in Sec. 3.3, differing ego-motion distributions cause global shifts in source and target point clouds. We address these by learning a geometry-aware descriptor on the source platform, then applying it to correct transformations on the target. During PA, we apply global max-pooling to the backbone's feature $\mathbf{F}_b^S$ to obtain a compact vector, which is encoded by a hierarchical convolutional module into a large-scale geometric descriptor $\mathbf{f}_d^S$ . A small regression MLP then predicts the artificially introduced random jitter angles $(\Delta \hat{\theta}, \Delta \hat{\phi})$ from this descriptor, optimizing the following rotation loss: + +$$ +\mathcal {L} _ {\mathrm {r o t}} = \left\| \Delta \hat {\phi} - \Delta \phi \right\| ^ {2} + \left\| \Delta \hat {\theta} - \Delta \theta \right\| ^ {2}. \tag {3} +$$ + +Notably, minimizing $\mathcal{L}_{\mathrm{rot}}$ equips the network with platform-agnostic transformation cues. This descriptor, learned on the source platform, corrects global offsets on the target platform during KA, ensuring robust cross-platform performance. + +Table 2. Comparisons of 3D detection methods for vehicle→drone/quadruped tasks. We report the average precision (AP) in “BEV / 3D” at the IoU thresholds of 0.7 and 0.5, respectively. Symbol $\ddagger$ denotes algorithms w.o. ROS [96]. All scores are given in percentage (%). “-” denotes the code is not available. The Best and Second Best scores under each metric are highlighted in Red and Blue, respectively. + +
#MethodVehicle → QuadrupedVehicle → DroneAverage
PV-RCNN [70]AP@0.7AP@0.5Voxel RCNN [15]AP@0.7AP@0.5PV-RCNN [70]AP@0.7AP@0.5Voxel RCNN [15]AP@0.7AP@0.5AP@0.7AP@0.5
nuScenes [8]Source Platform43.40 / 33.5544.86 / 42.8443.25 / 33.7445.62 / 43.3250.91 / 35.2657.73 / 50.2450.15 / 29.4157.10 / 49.1046.93 / 32.9951.33 / 46.34
ST3D [96]55.40 / 42.0259.59 / 54.7544.54 / 35.9645.81 / 44.3865.05 / 40.0168.93 / 64.0954.62 / 33.7958.45 / 52.8954.90 / 37.9558.20 / 54.03
ST3D‡ [96]55.68 / 44.5059.32 / 55.3245.01 / 37.1346.73 / 45.4565.40 / 43.6369.24 / 64.8855.23 / 36.5159.30 / 54.2355.33 / 40.4458.65 / 54.97
ST3D++ [98]55.76 / 43.5159.93 / 55.2845.56 / 36.9747.28 / 45.8460.91 / 40.0968.96 / 59.9657.02 / 37.5261.30 / 55.4354.81 / 39.5259.37 / 54.13
ST3D++‡ [98]54.96 / 40.8160.47 / 54.6545.69 / 36.7648.30 / 46.0565.50 / 43.4668.99 / 64.6255.92 / 39.4659.93 / 55.1955.52 / 40.1259.42 / 55.13
REDB [13]52.43 / 41.3457.12 / 54.18-/--/-65.31 / 39.1968.74 / 64.13-/--/--/--/-
MS3D++ [80]56.24 / 43.2060.88 / 56.1351.50 / 40.1456.03 / 53.8666.99 / 43.7669.87 / 65.8562.68 / 38.2668.34 / 61.0959.35 / 41.3463.78 / 59.23
Pi3DET-Net56.80 / 46.3661.54 / 57.2054.85 / 42.3857.41 / 55.5465.43 / 45.9469.24 / 65.8765.63 / 44.6272.05 / 63.8360.68 / 44.8365.06 / 60.61
Target Platform54.15 / 40.2458.63 / 54.9654.90 / 39.7456.46 / 55.1967.67 / 46.1170.04 / 66.1468.52 / 46.5370.67 / 61.4261.31 / 43.1663.95 / 59.43
Pi3DET (Vehicle)Source Platform38.61 / 26.8440.64 / 39.2243.95 / 31.2448.22 / 44.1757.29 / 36.6258.92 / 56.1952.85 / 37.9661.10 / 52.4748.17 / 33.1652.22 / 48.01
ST3D [96]49.29 / 38.6951.02 / 49.7147.70 / 37.9148.07 / 47.5960.17 / 33.0162.84 / 54.5153.79 / 40.1865.29 / 53.4052.74 / 37.4556.81 / 51.30
ST3D‡ [96]47.89 / 38.0749.50 / 48.2347.01 / 41.8554.01 / 53.4660.67 / 33.2762.98 / 54.6153.85 / 40.0262.70 / 53.0852.35 / 38.3057.30 / 52.34
ST3D++[98]46.05 / 37.2249.33 / 47.8448.52 / 37.8455.82 / 48.5360.04 / 33.9862.71 / 54.1353.71 / 39.9462.43 / 53.2052.08 / 37.2457.57 / 50.92
ST3D++‡ [98]45.14 / 35.7046.94 / 45.3747.52 / 37.1354.37 / 47.6364.15 / 34.2063.81 / 55.4453.64 / 40.2762.43 / 53.1052.61 / 36.8356.89 / 50.38
REDB [13]46.74 / 38.4750.29 / 49.54-/--/-61.57 / 34.0563.22 / 54.07-/--/--/--/-
MS3D++ [80]53.66 / 40.6655.21 / 53.7853.65 / 41.9354.69 / 54.0066.05 / 41.1767.80 / 63.2653.85 / 40.9162.87 / 53.4456.80 / 41.1760.14 / 56.12
Pi3DET-Net56.19 / 44.2860.35 / 56.2055.54 / 45.1859.48 / 58.9066.26 / 44.4768.25 / 63.3667.87 / 46.8369.95 / 66.2661.47 / 45.1964.51 / 61.18
Target Platform54.15 / 40.2458.63 / 54.9654.90 / 39.7456.46 / 55.1967.67 / 46.1170.04 / 66.1468.52 / 46.5371.67 / 61.4261.31 / 43.1663.95 / 59.43
-Combined All58.21 / 46.2762.18 / 59.6760.96 / 48.1563.04 / 61.0468.44 / 48.1971.11 / 68.2468.90 / 48.8872.55 / 69.1864.13 / 47.8767.22 / 64.53
+ +KL Probabilistic Feature Alignment (PFA). We aim to reduce cross-platform discrepancies by matching the Region-of-Interest (RoI) feature distributions of source and target platforms during KA. + +Specifically, we approximate each platform's RoI features before the detection head with a probabilistic method, ensuring robust distribution alignment. For source-platform RoI feature $\mathbf{F}_r^S$ , a probabilistic encoder $p(\xi^S|\mathbf{F}_r^S) = \mathcal{N}\big(\boldsymbol {\mu}(\mathbf{F}_r^S),\boldsymbol{\sigma}^2 (\mathbf{F}_r^S)\big)$ maps this feature into a Gaussian distribution, which predicts $\boldsymbol {\mu}(\mathbf{F}_r^S)$ and $\sigma^2 (\mathbf{F}_r^S)$ with MLPs. Using the reparameterization trick [30], latent samples $\xi^S = \boldsymbol {\mu}(\mathbf{F}_r^S) + \boldsymbol {\sigma}(\mathbf{F}_r^S)\odot \boldsymbol{\epsilon}$ are generated $(\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I}))$ . Analogous encoding applies to the target-platform RoI feature $\mathbf{F}_r^T$ , producing latent samples $\xi^T$ accordingly. + +Since the true distribution of latent features is unknown, we can only estimate it from latent samples on both platforms. By comparing these samples via the KL term, we have: + +$$ +\mathcal {L} _ {\mathrm {K L}} = D _ {\mathrm {K L}} \left[ p \left(\xi^ {\mathcal {S}} \mid \mathbf {F} _ {r} ^ {\mathcal {S}}\right) \| p \left(\xi^ {\mathcal {T}} \mid \mathbf {F} _ {r} ^ {\mathcal {T}}\right) \right]. \tag {4} +$$ + +The model pushes the target platform's features toward the source manifold. Crucially, this nonadversarial approach provides a stable alignment in the absence of direct target supervision. As investigated by [60], the KL objective not only prevents out-of-distribution samples but also offers a mode-seeking alignment, ultimately improving target performance. For the source platform, we also train a classification head $q(\mathbf{g}|\xi)$ to discriminate foreground from background: + +$$ +\mathcal {L} _ {\mathrm {R o I}} = \mathbb {E} _ {\xi^ {S} \sim p \left(\xi^ {S} \mid F _ {r} ^ {S}\right)} \left[ - \log q \left(\mathbf {g} ^ {S} \mid \xi^ {S}\right) \right], \tag {5} +$$ + +where $\mathbf{g}^S$ is the classification task ground truth. This loss ensures the latent representation $\xi^S$ captures semantic features in the source platform for effective alignment through $\mathcal{L}_{\mathrm{KL}}$ . + +# 4.3. Objective & Optimization + +The overall framework aims to learn global transformations and semantic cues during Pre-Adaptation, then propagate and align target data during Knowledge-Adaptation. + +Pre-Adaptation (PA). In the source platform, our goal is to extract and internalize the necessary knowledge while enhancing geometric robustness through Random Platform Jitter, addressing platform-specific discrepancies through the rotation loss $\mathcal{L}_{\mathrm{rot}}$ , and learning RoI-based semantic features via $\mathcal{L}_{\mathrm{RoI}}$ . We also apply a standard detection loss composed of a classification loss and a bounding-box regression loss: + +$$ +\mathcal {L} _ {\det } = \mathcal {L} _ {\operatorname {c l s}} \left(\hat {\mathcal {B}} ^ {\mathcal {S}}, \mathcal {B} ^ {\mathcal {S}}\right) + \mathcal {L} _ {\operatorname {r e g}} \left(\hat {\mathcal {B}} ^ {\mathcal {S}}, \mathcal {B} ^ {\mathcal {S}}\right), \tag {6} +$$ + +where $\hat{B}^S$ denotes the predicted bounding box. The overall pre-adaptation objective is: $\mathcal{L}_{\mathrm{PA}} = \mathcal{L}_{\mathrm{det}} + \lambda_{\mathrm{rot}}\mathcal{L}_{\mathrm{rot}} + \lambda_{\mathrm{RoI}}\mathcal{L}_{\mathrm{RoI}}$ , where $\lambda_{\mathrm{rot}}$ and $\lambda_{\mathrm{RoI}}$ are weights used to balance the losses. This step trains a robust 3D detector while imparting global geometric awareness for adaptation. + +Knowledge-Adaptation (KA). After PA, we first use the source-platform knowledge to generate pseudo-annotations $\tilde{\mathcal{B}}^{\mathcal{T}}$ on target data, then train jointly on both platforms: + +- Source Platform: To preserve source performance, we disable $\mathcal{L}_{\mathrm{rot}}$ and optimize only detection and RoI classification, i.e., $\mathcal{L}_{\mathrm{KA}}^S = \mathcal{L}_{\mathrm{det}}^S + \lambda_{\mathrm{RoI}}\mathcal{L}_{\mathrm{RoI}}^S$ . +- Target Platform: We encode the learned global descriptor $\mathbf{f}_d^T$ with channel attention (i.e., CA in Fig. 3) and add it to the backbone features as a residual offset, enforce a detection loss, and align RoI features via KL. This process can be formulated as: $\mathcal{L}_{\mathrm{KA}}^T = \mathcal{L}_{\mathrm{det}}^T + \lambda_{\mathrm{KL}}\mathcal{L}_{\mathrm{KL}}$ , where $\lambda_{\mathrm{KL}}$ is used to balance the KL loss. + +The combined objective is $\mathcal{L}_{\mathrm{KA}} = \mathcal{L}_{\mathrm{KA}}^{\mathcal{T}} + \mathcal{L}_{\mathrm{KA}}^{\mathcal{S}}$ . By decoupling geometry learning (during PA) from feature correction + +Table 3. Study on cross-platform 3D detection between drone and quadruped platforms. We report the average precision (AP) in "BEV / 3D" at the IoU thresholds of 0.7 and 0.5, respectively. + +
#MethodPV-RCNN [70]Voxel RCNN [15]
AP@0.7AP@0.5AP@0.7AP@0.5
QuadroneSource Platform27.43 / 11.0836.97 / 27.9233.22 / 20.2041.17 / 33.29
ST3D‡[96]33.85 / 18.4544.35 / 35.8335.21 / 22.8736.05 / 35.52
ST3D++†[98]32.92 / 17.7640.91 / 32.9743.30 / 28.8644.69 / 43.24
REDB [27]37.24 / 20.8944.43 / 37.2944.27 / 30.5546.69 / 44.29
MS3D++ [80]39.74 / 22.3147.59 / 41.6145.84 / 32.2148.27 / 45.87
Pi3DET-Net43.11 / 25.1652.87 / 47.5549.27 / 36.2454.58 / 49.63
Target Platform67.67 / 46.1170.04 / 66.1468.52 / 46.5370.67 / 61.42
Drone QuadrSource Platform27.23 / 20.3630.27 / 28.9232.18 / 23.3533.94 / 32.70
ST3D‡[96]46.06 / 35.1451.17 / 49.5349.04 / 36.9455.73 / 49.73
ST3D++†[98]49.09 / 37.5755.30 / 50.9048.74 / 38.2255.19 / 48.94
REDB [27]47.29 / 35.6753.21 / 49.7649.36 / 38.1155.96 / 50.21
MS3D++ [80]48.24 / 34.1252.43 / 48.6649.76 / 37.5556.17 / 49.97
Pi3DET-Net51.24 / 38.9457.31 / 52.9052.64 / 38.8857.57 / 51.83
Target Platform54.15 / 40.2458.63 / 54.9654.90 / 39.7456.46 / 55.19
+ +(during KA), the geometry-aware transformation descriptor remains focused on platform-induced differences. Meanwhile, RoI feature alignment pulls target features toward the source distribution, narrowing the cross-platform gap and enabling accurate 3D detection on target platforms. + +# 5. Experiments + +# 5.1. Experimental Settings + +Datasets. We evaluate cross-platform and cross-dataset 3D detection using three benchmarks: nuScenes [8], KITTI [22], and our Pi3DET. nuScenes [8] provides 35,149 frames from day and night urban scenes, KITTI [22] provides 14,999 daytime frames, and Pi3DET comprises 51,545 frames spanning urban, suburban, and rural environments. For additional dataset details, please refer to Appendix A. + +Benchmark Setup. We design six cross-platform adaptation benchmarks and two cross-dataset adaptation benchmarks to cover a wide range of scenarios and to demonstrate the generalizability of our method. Due to space limits, please refer to Appendix B.6 for the complete benchmark settings. + +Baselines. We use PV-RCNN [69] and Voxel-RCNN [15] as our detection backbones. Our comparisons include several related cross-domain detection methods ST3D [96], ST3D++ [96], and MS3D++ [80], as well as three baseline training strategies: training on "source data only", training on "target data only", and training on "both source and target data". For more details, please refer to Appendix B.6. + +Implementation Details. Our experiments follow the setting of ST3D++ [98], and are implemented using Open-PCDet [77], with experiments run on two NVIDIA Titan RTX GPUs. We follow the KITTI evaluation protocol by reporting average precision (AP) in both bird's-eye view (BEV) and 3D over 40 recall positions. The hyperparameters are set as $\lambda_{\mathrm{rot}} = 0.1$ , $\lambda_{\mathrm{RoI}} = 0.2$ , and $\lambda_{\mathrm{KL}} = 10^{-4}$ . For more details, please refer to Appendix B.3. + +Table 4. Cross-dataset 3D detection benchmark. Experiments are conducted on the nuScenes [8] $\rightarrow$ KITTI [22] task. We report the average precision (AP) in "BEV / 3D" at the IoU thresholds of 0.7, 0.5, and 0.5 for Car, Pedestrian, and Cyclist classes, respectively. The reported AP is for moderate cases. All scores are given in percentage (\%). Symbol $\dagger$ denotes method w.o. RPJ, since no pitch or roll jitter occurs when both the source and target platforms are vehicles. w.temp indicates the use of temporal information, and w.SN denotes the incorporation of statistic normalization [82]. + +
MethodCar AP@0.7Pedestrian AP@0.5Cyclist AP@0.5Average
Source Dataset51.80 / 17.9039.95 / 34.5717.70 / 11.0836.48 / 21.18
SN [82]40.30 / 21.2338.91 / 34.3611.11 / 5.6730.17 / 20.42
ST3D [96]75.90 / 54.1044.00 / 42.6029.58 / 21.2149.83 / 39.30
ST3D [96] w.SN79.02 / 62.5543.12 / 40.5416.60 / 11.3346.25 / 38.14
ST3D [96] w.temp81.06 / 66.9834.65 / 31.7627.32 / 20.5247.68 / 39.75
ST3D++ [98]80.50 / 62.4047.20 / 43.9630.87 / 23.9352.86 / 43.43
ST3D++ [98] w.SN78.87 / 65.5647.94 / 45.5713.57 / 12.6446.79 / 41.26
ST3D++ [98] w.temp80.91 / 68.2330.48 / 27.8629.88 / 25.5747.09 / 40.55
REDB [13]74.23 / 51.3125.95 / 18.3813.82 / 8.6438.00 / 26.11
DTS [27]81.40 / 66.60- / -- / -- / -
CMDA [10]82.13 / 68.95- / -- / -- / -
PLR [114]73.65 / 66.8442.69 / 35.4717.38 / 15.9544.57 / 39.42
Pi3DET-Net†82.86 / 70.2046.23 / 43.4431.14 / 25.7257.51 / 46.45
Target Dataset83.29 / 73.4546.64 / 41.3362.92 / 60.3262.92 / 60.32
+ +# 5.2. Comparative Study + +We analyze the performance of Pi3DET-Net across various cross-platform and cross-dataset adaptation tasks. + +Adaptation with Vehicle as Source. Tab. 2 presents the cross-platform adaptation results for vehicle $\rightarrow$ quadruped/drone tasks. In these experiments, source data are taken from nuScenes [8] and Pi3DET, while all target data come from Pi3DET. Overall, Pi3DET-Net consistently outperforms the baselines. For instance, on the vehicle $\rightarrow$ quadruped task using nuScenes as source, our method with PV-RCNN achieves a $12.81\%$ gain in $\mathrm{AP}_{3\mathrm{D}}@0.7$ compared to the source-only baseline, validating the effectiveness of our approach. Notably, our method even outperforms target-only training, likely due to the smaller target dataset size. + +Adaptation with Drone and Quadruped as Source. Tab. 3 presents cross-platform detection results between the quadruped and drone platforms. Under our approach, both PV-RCNN and Voxel-RCNN achieve the best performance across all evaluated metrics. For instance, in the drone $\rightarrow$ quadruped task, our method with PV-RCNN improves $\mathrm{AP}_{\mathrm{3D}}@0.7$ by $18.58\%$ relative to the source-only baseline, nearly matching the target-only performance. + +Cross-Dataset Adaptation. To demonstrate the broad applicability of Pi3DET-Net, we evaluate on the cross-dataset task from nuScenes to KITTI. Following [98], we adopt SECOND-IoU [93] as the backbone. Tab. 4 presents the results, which show that Pi3DET-Net achieves state-of-the-art performance on both Car and Cyclist. For Car targets, our $\mathrm{AP}_{\mathrm{3D}}@0.7$ is only $3.25\%$ lower than that of the target-only baseline. Additionally, we design a separate cross-dataset adaptation task from nuScenes to Pi3DET on the vehicle platform, detailed analysis is provided in Appendix C.3. + +Table 5. Ablation study of components in Pi3DET-Net. Experiments are conducted on the vehicle $\rightarrow$ drone/quadruped tasks. We report the average precision (AP) in "BEV / 3D" at the IoU thresholds of 0.7 and 0.5, respectively. All scores are given in %. + +
RPJVPPPFAGTDVehicle → DroneVehicle → Quadruped
AP@0.7AP@0.5AP@0.7AP@0.5
XXXX52.85 / 37.9661.10 / 52.4743.95 / 31.2448.22 / 44.17
✓XXX60.20 / 39.9364.76 / 59.5245.36 / 33.0149.26 / 47.03
X✓XX59.83 / 39.2663.55 / 59.4744.43 / 32.2351.59 / 49.47
✓✓XX64.52 / 41.5066.84 / 60.6848.45 / 36.1053.83 / 51.52
✓✓✓X67.87 / 46.8369.95 / 66.2655.72 / 44.7759.48 / 58.90
✓✓✓✓68.48 / 47.7569.87 / 67.8255.54 / 45.1862.02 / 60.29
+ +Table 6. Cross-platform 3D detection benchmark. We report the average precision (AP) in "BEV / 3D" at the IoU thresholds of 0.7. All scores are given in percentage (\%). "-C" and "-A" denote detectors with the Anchor-based or Center-based detection head. + +
#MethodVehicle +AP@0.7Quadruped +AP@0.7Drone +AP@0.7Average
GridPointPillar [40]51.85 / 44.3436.24 / 14.5149.53 / 27.0245.87 / 28.62
CenterPoint [102]51.90 / 42.1237.74 / 14.6853.14 / 29.2947.59 / 28.70
Part A* [71]54.88 / 48.2345.47 / 20.1056.72 / 34.4452.36 / 34.26
Transfusion-L [4]49.27 / 38.2136.29 / 14.4351.27 / 24.6345.61 / 25.76
HEDNet [106]46.73 / 37.6034.30 / 14.5149.31 / 20.8943.45 / 24.33
SAFNet [35]42.60 / 34.8833.47 / 13.6549.93 / 24.7042.00 / 24.41
Part A*+ Ours53.81 / 47.5644.31 / 23.7359.53 / 38.3152.55 / 36.53
PointPointRCNN [68]49.38 / 43.0341.35 / 23.6952.59 / 38.6747.77 / 35.13
3DSSD [100]46.58 / 39.8842.47 / 23.8951.54 / 37.7846.86 / 33.85
IA-SSD [113]44.00 / 34.9148.11 / 24.8959.69 / 35.7950.60 / 31.86
DBQ-SSD [99]41.28 / 33.1944.27 / 21.8554.65 / 32.0846.73 / 29.04
PointRCNN + Ours51.19 / 48.0942.18 / 26.0757.54 / 41.7050.30 / 38.62
Grid-PointPV-RCNN [69]63.32 / 56.5845.22 / 22.9460.11 / 39.6856.22 / 39.73
PV-RCNN++ [72]64.05 / 57.0147.54 / 22.3560.54 / 40.1057.38 / 39.82
PV-RCNN+-C [72]57.94 / 50.5640.75 / 20.7853.46 / 40.0050.72 / 37.11
VoxelRCNN-A [15]63.00 / 56.9846.78 / 23.3064.46 / 42.7658.08 / 41.01
VoxelRCNN [15]58.39 / 51.1148.30 / 21.6160.29 / 39.1555.66 / 37.29
PV-RCNN++ Ours63.47 / 56.6057.08 / 31.0968.52 / 47.9263.02 / 45.20
+ +# 5.3. Ablation Study + +In this section, we use Voxel-RCNN [15] as the backbone detector to validate the effectiveness of individual components in Pi3DET-Net for cross-platform tasks. + +Random Platform Jitter. As shown in Tab. 5, adding RPJ leads to performance improvements across all metrics. For instance, in the vehicle $\rightarrow$ drone task, the addition of RPJ boosts $\mathrm{AP}_{\mathrm{BEV}}@0.7$ by $7.35\%$ relative to the source-only baseline. These results confirm that simulating ego-motion noise through RPJ effectively augments the source data, thereby enhancing the model's robustness to the jitters observed on non-vehicle platforms. + +Virtual Platform Pose. We also evaluate the impact of Virtual Platform Pose (VPP) in Tab. 5. The results clearly show that VPP enhances Pi3DET-Net's performance, achieving a $7\%$ improvement in $\mathrm{AP}_{3\mathrm{D}}@0.5$ relative to the source-only baseline in the Vehicle $\rightarrow$ Drone task. Notably, when RPJ and VP are combined, they yield greater improvements, see an enhancement of $9.67\%$ in $\mathrm{AP}_{\mathrm{BEV}}@0.7$ . These findings underscore the importance of both geometric alignment strategies in improving cross-platform detection performance. + +KL Probabilistic Feature Alignment. PFA is designed to narrow the cross-platform gap during the Knowledge-Adaption stage. As shown in Tab. 5, incorporating PFA leads + +to significant performance gains on cross-platform tasks. By approximating the RoI features with probabilistic encoders and aligning their distributions using a KL divergence loss, PFA ensures that the target features are gradually pulled toward the source feature manifold. This alignment is crucial for reducing domain discrepancies and improving the overall detection accuracy on the target platform. + +Geometry-Aware Transformation Descriptor. GTD is designed to capture global transformation cues on the source platform during the PA stage and correct global offsets on the target platform during the KA stage. As demonstrated in Tab. 5, incorporating GTD leads to significant performance gains. By learning geometric intrinsic that reflect sensor-specific characteristics such as sensor height and pitch distribution, GTD helps the network to predict and correct spatial misalignments between platforms. + +In Appendix C.3, we provide a detailed analysis of the impact of varying the jitter angles introduced by RPJ across different platforms, where we investigate how different levels of simulated ego-motion affect detection performance. + +# 5.4. Multi-Platform 3D Detection Benchmark + +We establish a benchmark on Pi3DET to evaluate the cross-platform performance of 18 commonly-used 3D detectors by training all models on the vehicle set and testing them on vehicle, quadruped, and drone data (see Tab. 6 and Appendix C.2). Detectors are categorized into grid-based, point-based, and grid-point-based. Although grid-point-based methods excel on vehicles, their performance declines on quadruped and drone platforms, where point-based detectors achieve more balanced results, demonstrating enhanced viewpoint robustness. Furthermore, we apply our RPJ to the top-performing detectors on the vehicle platform. While this augmentation slightly degrades performance on vehicles due to the introduction of unseen noises, it significantly boosts results on the other two platforms. Overall, our findings underscore that effective geometry alignment and robust point-based architectures are crucial for developing unified 3D detectors across diverse platforms. + +# 6. Conclusion + +In this work, we introduced Pi3DET, a large-scale dataset for cross-platform 3D detection that includes diverse samples from vehicle, drone, and quadruped platforms. We proposed a novel adaptation approach that transfers the knowledge of vehicle detectors to other platforms by aligning geometric and feature representations. Extensive experiments show that our method is superior in both cross-platform and cross-dataset 3D object detection. We also establish a cross-platform benchmark on current 3D detectors and provide insights to improve resilience to platform variations, which benefits the research on unified 3D detection systems operating reliably across diverse autonomous platforms. + +# Acknowledgments + +This work is under the programme DesCartes and is supported by the National Research Foundation, Prime Minister's Office, Singapore, under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. This work is also supported by the Apple Scholars in AI/ML Ph.D. Fellowship program. + +The author, Ao Liang, gratefully acknowledges the financial support from the China Scholarship Council. + +Additionally, the authors would like to sincerely thank the Program Chairs, Area Chairs, and Reviewers for the time and effort devoted during the review process. + +# References + +[1] Rashid Abbasi, Ali Kashif Bashir, Hasan J Alyamani, Farhan Amin, Jaehyeok Doh, and Jianwen Chen. Lidar point cloud compression, processing and learning for autonomous driving. IEEE Transactions on Intelligent Transportation Systems, 24(1):962-979, 2022. +[2] Mina Alibeigi, William Ljungbergh, Adam Tondersski, Georg Hess, Adam Lilja, Carl Lindstrom, Daria Motorniuk, Junsheng Fu, Jenny Widahl, and Christoffer Petersson. Zenseact open dataset: A large-scale and diverse multimodal dataset for autonomous driving. 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However, ensuring multi-view consistency, an essential requirement for high-quality inpainting, remains a key challenge. In this work, we present PAInpainter, a novel approach designed to advance 3D Gaussian inpainting by leveraging perspective-aware content propagation and consistency verification across multi-view inpainted images. Our method iteratively refines inpainting and optimizes the 3D Gaussian representation with multiple views adaptively sampled from a perspective graph. By propagating inpainted images as prior information and verifying consistency across neighboring views, PAInpainter substantially enhances global consistency and texture fidelity in restored 3D scenes. Extensive experiments demonstrate the superiority of PAInpainter over existing methods. Our approach achieves superior 3D inpainting quality, with PSNR scores of $26.03\mathrm{dB}$ and $29.51\mathrm{dB}$ on the SPIn-NeRF and NeRFiller datasets, respectively, highlighting its effectiveness and generalization capability. The code will be publicly available at https://pa-inpainter.github.io. + +# 1. Introduction + +As a prominent application in the realm of 3D editing, 3D inpainting plays a pivotal role in various applications and industries, including the metaverse and holographic multimedia production [5, 52]. However, traditional hand-crafted 3D completion approaches, which rely on professional designers and specialized tools, remain labor-intensive and cumbersome. With recent advancements in 3D neural representations [17] and generative models [34], 3D inpainting can be achieved by applying a two-stage paradigm: 1) using a pretrained 2D diffusion model to inpaint masked multiview renderings of the 3D Gaussian scene with missing re + +![](images/c7370df9b8f4969c9d46933dbcdf87a9c86fa1639f120a29250448e391fd4de4.jpg) +Figure 1. Current challenges in 3D Gaussian inpainting: a) the fine-tune based inpainter trained for specific tasks [7] experiences significant performance decline when applied to general inpainting scenarios; b) the joint-view inpainting method [44] struggles with inconsistency across multi-view images, resulting in noisy inpainting results; c) the DU strategy [12] leads to texture degradation in both inpainted multi-view images and the final 3D scene. + +gions; and 2) optimizing the initial 3D Gaussian scene with the inpainted multi-view images [7, 32]. While this efficient framework shows significant potential, multi-view inconsistency remains an inherent challenge in diffusion models due to their independent view processing nature, which hinders high-quality 3D inpainting [22, 44]. + +Existing works have explored various approaches to improve multi-view consistency in 3D Gaussian inpainting, yet new limitations continue to emerge. Fine-tune based inpainting methods adapt diffusion models with additional control conditions (e.g., reference images [7]), but are confined to specific scenarios, as illustrated in Fig. 1(a). Without modifying pretrained diffusion models, the joint-view based inpainting approach [44] processes multi-view images in $2 \times 2$ grid tiles and achieves improved consistency, + +![](images/0a8573f3e324a6622c92fc7bdfa2baae99d2e1e324b97c3c4806f6db5787be0f.jpg) +Figure 2. The overall pipeline of our proposed PAInpainter. Based on the constructed perspective graph, our approach iteratively performs multi-view image inpainting and 3D Gaussian training. The adaptive graph sampling algorithm enables efficient inpaint content propagation across adjacent viewpoints, while consistency verification ensures coherent multi-view inpainting results, thereby improving the 3D inpainting quality. + +yet still exhibits artifacts in challenging regions, as shown in Fig. 1(b). Similarly, DatasetUpdate (DU) [12] alternates between 3D scene optimization and multi-view inpainting while progressively updating the dataset to improve consistency. However, it suffers from texture fading in the final results, as demonstrated in Fig. 1(c). These limitations highlight the persistent challenge of achieving high-fidelity and globally consistent inpainting across multiple views. + +In this paper, we introduce the Perspective-Aware 3D Gaussian Inpainter (PAInpainter) to enhance multi-view consistency. As illustrated in Fig. 2, we propose a novel perspective-aware framework with three key components: perspective graph sampling, inpaint content propagation, and consistency verification. Specifically, we construct a perspective graph that models the spatial relationships among viewpoints. Leveraging adaptive graph sampling and the inherent perspective overlap between neighboring views, we propagate inpainted content across adjacent cameras, which serves as supplementary visual priors for the diffusion model during inpainting, improving fine-grained texture preservation and consistency across multi-view inpainted images. To ensure high-quality and reliable results, we introduce a dual-feature verification mechanism that evaluates both texture and geometric coherence in latent space, effectively identifying and selecting consistent inpainting results. Combined with our framework, the versatile generation capability of the pretrained diffusion model further empowers our approach to handle various challenging 3D inpainting scenarios. + +Our approach demonstrates exceptional performance in high-fidelity 3D Gaussian inpainting across diverse scenarios. Through extensive experiments on three mainstream 3D inpainting datasets, we demonstrate that PAInpainter significantly outperforms existing methods both quantitatively and qualitatively. Additionally, our PAInpainter exhibits robust generalization capability across various sce + +narios. Our main contributions are summarized as follows: + +- We propose a novel perspective-aware framework for 3D Gaussian inpainting that systematically integrates inpainting view sampling, cross-view content propagation, and consistency verification. +- We introduce three effective components: a perspective graph to guide viewpoint sampling for inpainting, a perspective-aware projection strategy to propagate inpainting content, and a dual-feature verification mechanism to ensure multi-view consistency. +- Extensive experiments on diverse 3D scenes demonstrate that PAInpainter outperforms state-of-the-art methods in achieving superior consistency and visual fidelity. + +# 2. Related Work + +# 2.1. 2D Image Inpainting + +2D inpainting methods aim to restore missing or obscured regions in images with coherent textures and structures [3, 30]. Early approaches relied on texture synthesis and pixel interpolation techniques by leverages information from known regions [2, 9, 10]. Learning-based approaches, especially deep learning methods [18, 19, 31, 48, 49] and recent diffusion models [34], have since emerged as powerful alternatives, demonstrating superior capabilities in high-fidelity content completion. The Latent Diffusion Models (LDMs)[34] and its variants[24, 50] achieve remarkable generation results across diverse scenarios. However, these methods process each image independently without considering 3D spatial relationships and geometric attributes among multiple viewpoints, leading to subsequent inconsistency when applied to the 3D domain. + +# 2.2. 3D Scene Inpainting + +3D inpainting extends the content completion task into 3D space. Early approaches focused on geometric completion using traditional representations like point clouds and meshes [8, 46]. Recent advances in neural representations, particularly Neural Radiance Fields (NeRF)[25] and 3D Gaussian Splatting (3DGS)[17], have revolutionized 3D scene modeling. While direct 3D diffusion models [28, 36, 42] face challenges with limited training data and computational complexity, an alternative approach combines pretrained 2D diffusion models with 3D neural representations [15, 20, 21, 23, 26, 32, 39, 44, 45]. This paradigm shows promising results by combining the powerful generation capabilities of 2D diffusion models with real-time 3D reconstruction [7, 22]. Despite the advancement in 3D inpainting efficiency, ensuring geometric and appearance consistency across different viewpoints remains challenging. In this paper, we build our method on 3DGS, which enables fast training and real-time rendering, and achieve improved multi-view consistency by propagating extra prior informa + +![](images/fce27f9e74f09b66b594d284c76983f331f8491963f8a7bc617da7a7d4fbe124.jpg) +Perspective Graph + +![](images/0aad4df12ab52ec0fcd44fe1cb58f293259e535ceb7c9ec6bc0fdbe063ec791e.jpg) +Consistency verification + +![](images/97063ee4302ab4464ea51a71e5905a59cfaf8c728876fe458ba33e77a2908744.jpg) +Projection + +![](images/a010153ab77ac8daca85d1eb1cf321b2dd70f2a42f5144d2324913d0d1a57863.jpg) +Depth estimator + +![](images/57fe9f47d811280b50bbe30017c6fa77889e74250549b6c896b6b64098cf486e.jpg) +Pretrained SD2 inpainter + +![](images/d38bef1165f725a86a6f37888bfe944083788f336390650fda95c65b3dcbe46d.jpg) +Inpaint content propagation +Figure 3. Overview of PAInpainter for multi-view consistent 3D Gaussian inpainting. Our method is built upon the pretrained SD2 [34] and incorporates three key components: 1) perspective graph models spatial relationships among cameras to guide adjacent view sampling; 2) inpaint content propagation transmits inpainting content across adjacent views sampled from perspective graph, providing extra visual priors for diffusion inpainting; 3) consistency verification evaluates inpainted results based on texture and geometric features coherence. The perspective-aware graph sampling contributes to effective content propagation and consistency verification across multiple views. + +tion to guide the diffusion inpainting process. + +# 2.3. Multi-view Consistency + +Multi-view consistency ensures that the generated content in multi-view images of a 3D scene maintains geometric and texture coherence [12, 43]. Recent works have explored two main techniques to address inconsistency arising from 2D diffusion models. The first approach resorts to the diffusion model fine-tuning with additional conditions [16, 29, 43, 47], namely incorporating depth features, task-specific modules, and geometric constraints [6, 7, 22]. However, these methods typically specialize in specific tasks like object removal and struggle to generalize to broader 3D inpainting scenarios. The second technique explores solution without modifying pretrained models [12, 15, 44], but leverages depth priors or additional supervision [27, 32] to enhance cross-view consistency in generation and reconstruction process. While these approaches show potential, they often lack proactive consistency inspection of inpainted images, leading to compromised performance under challenging conditions. To address this limitation, we introduce a dual-feature verification mechanism designed to reject inconsistencies, thereby ensuring coherent inpainting across diverse scenarios for 3D scene restoration. + +# 3. Methodology + +Overview. The key components of PAInpainter are illustrated in Fig. 3. This section first introduces the overall + +framework (Sec. 3.1), followed by the technical details of perspective graph construction, inpaint content propagation, and consistency verification (Sec. 3.2). The adaptive graph sampling strategy and 3D Gaussian training procedure are elaborated in Sec. 3.3. + +# 3.1. Framework + +As shown in Fig. 2, PAInpainter completes unknown regions within a 3D scene by iteratively inpainting multi-view renderings and optimizing the 3D Gaussians with inpainted images. Building upon the high-fidelity image inpainting capabilities of pretrained StableDiffusion2 (SD2) [34], our framework enhances the multi-view inpainting consistency through three key techniques: perspective graph sampling, inpaint content propagation and consistency verification. + +Based on the fact that the cross-attention mechanism of SD2 allows for reference-guided content generation in missing regions [7], we observe that the inpainting consistency significantly degrades with increasing perspective differences between views, as shown in Fig. 1(a). This observation motivates us to sample images with similar perspectives, thereby promoting the generation of consistent content. These adjacent views serve dual purposes: they facilitate effective content propagation by providing reliable texture and geometric priors for masked images, while enabling feature-space consistency verification among inpainting images to mitigate SD2's inherent randomness and select optimal results from multiple candidates. + +Based on these findings, we develop PAInpainter based + +![](images/0bf5d892ae70bc046d2a3412058ad48afe3f844e2b0b948a53f2cb1574b8a794.jpg) +Figure 4. Perspective distance evaluation via feature matching. The color bar indicates the match's confidence. For a given target image, nearby views achieve significantly higher matching score (0.84) compared to distant views (0.74), validating the effectiveness of our perspective-aware graph construction method. This distance metric naturally captures the spatial relationships between different viewpoints. + +on the following iterative framework: + +1. Given a 3D Gaussian scene $\mathcal{G}_u$ with unknown regions, multi-view images $\mathbf{I} = \{I_i\}_{i=1}^n$ with corresponding camera poses $\mathbf{T} = \{T_i \in \mathrm{SE}(3)\}_{i=1}^n$ and masks $\mathbf{M} = \{M_i\}_{i=1}^n$ , we construct a perspective graph $\mathbf{G}$ for $\mathbf{I}$ , where edges encode the perspective distances among views. +2. For each inpainting round, we adaptively sample an anchor image $I_{anchor}$ from the constructed graph and employ SD2 to inpaint it, obtaining $I_{anchor}'$ . We then query its adjacent images from $\mathbf{G}$ to form a subset $\mathbf{I}_{adj}$ . The inpainted content from $I_{anchor}'$ is projected to each image in $\mathbf{I}_{adj}$ , and $I_{anchor}'$ serves as a reference image for following diffusion inpainting of these adjacent views. +3. For images in $\mathbf{I}_{adj}$ , multiple inpainted candidates are generated by SD2. We then compute consistency scores between each candidate and $I_{anchor}'$ with regard to the inpainting regions, selecting the candidate with the highest score as the final inpainting result. +4. We optimize the 3D Gaussian scene $\mathcal{G}_u$ by training on the inpainted images. + +The process iteratively alternates between multi-view inpainting (steps 2-3) and 3D Gaussian optimization (step 4), progressively inpainting and refining the 3D scene. + +# 3.2. PAInpainter + +We now detail the three key modules of PAInpainter for achieving consistent 3D Gaussian inpainting. + +Perspective graph construction. The graph $\mathbf{G}$ underpins our entire inpainting pipeline by modeling the proximity relationships among diverse viewpoints. Although the cameras' poses are available, the view difference, i.e., the captured content in the images, cannot be solely described by the 6-DoF distance due to variations in perspective, orienta + +![](images/9ea14827d7d65fee388149148ece9c3e5bb0c08133870b6a3d7db9ec8a72c6ad.jpg) +Figure 5. Inpaint content propagation mechanism. (a) Using depth information and camera poses, inpainted content from an anchor image is projected onto its adjacent masked views. (b) The projection results on neighboring views sampled from our perspective graph. Thanks to our graph-based sampling strategy, most masked regions in the selected images receive ample projected content (high coverage of effective pixels), offering rich prior information for subsequent SD2 inpainting. + +tion, and scene geometry [1, 40]. To solve this problem, we propose evaluating view similarities through feature matching metrics, as shown in Fig. 4. Specifically, we employ LoFTR [37] for its transformer-based architecture that enables robust feature matching under challenging viewpoint changes. For image pair $(I_i, I_j)$ in the dataset, we extract matches with confidence scores above threshold $\tau$ ( $\tau = 0.4$ fixed in our implementation). The perspective distance is evaluated based on the average confidence score for these matches, where a higher average matching score indicates a smaller distance. In the final graph $\mathbf{G}$ , nodes store images with their camera poses and masks, while edges encode the computed perspective distances. This perspective-aware graph enables effective sampling of adjacent views for consistent inpainting. As demonstrated by our experiments, this strategy provides enhanced robustness to viewpoint variations while preserving geometric interpretability. Inpaint content propagation. To enhance multi-view consistency and high-fidelity inpainting, we feed supplementary priors of masked region along with the image to SD2 via inpaint content propagation. Guided by camera poses sampled from graph $\mathbf{G}$ , we render the anchor image $I_{anchor}$ and its top- $k$ adjacent images $\mathbf{I}_{adj} = \{I_i^{adj}\}_{i=1}^k$ from 3D Gaussian scene $\mathcal{G}_u$ . We first independently inpaint the anchor image $I_{anchor}$ using SD2, obtaining $I_{anchor}'$ , followed by propagating the $I_{anchor}'$ to its adjacent images $\mathbf{I}_{adj}$ with masked regions through perspective projection to offer extra prior for SD2 inpainting, as shown in Fig. 5 (a). + +Specifically, we use ZoeDepth [4] to estimate the depth map $d_{anchor}$ for $I_{anchor}'$ . With $d_{anchor}$ and camera parame + +ters (intrinsic $K$ and extrinsic $T_{anchor}$ ), we inversely project the 2D image $I_{anchor}^{\prime}$ into perspective coordinates by + +$$ +\left[ x _ {c}, y _ {c}, z _ {c} \right] ^ {\top} = K ^ {- 1} \cdot \left(\left[ u, v, 1 \right] ^ {\top} \cdot d\right), \tag {1} +$$ + +where $[u,v,1]^{\top}$ and $d$ represent 2D image coordinate and depth value, respectively, and $[x_c,y_c,z_c]^{\top}$ represents the 3D coordinate. For each adjacent image $I_{i}^{adj}$ with camera pose $T_{i}$ , we transform the 3D point cloud from anchor perspective to the perspective coordinates of $I_{i}^{adj}$ by + +$$ +\left[ x _ {c} ^ {\prime}, y _ {c} ^ {\prime}, z _ {c} ^ {\prime}, 1 \right] ^ {\top} = T _ {i} \cdot T _ {a n c h o r} ^ {- 1} \cdot \left[ x _ {c}, y _ {c}, z _ {c}, 1 \right] ^ {\top}, (2) +$$ + +obtaining $[x_c', y_c', z_c']^\top$ after homogeneous normalization. We project these coordinates onto $I_i^{adj}$ , updating only pixels within the masked region. For regions where projection fails due to view differences or depth estimation errors, we retain the rendering RGB values from 3D Gaussian scene. + +Leveraging our perspective graph sampling strategy, the projection effectively propagates the inpainted content from anchor image to adjacent frames while preserving geometric and texture consistency, as shown in Fig. 5 (b). The propagated adjacent images $\mathbf{I}_{adj}$ are then paired with $I_{anchor}^{\prime}$ as reference guidance for SD2 diffusion inpainting. + +Consistency verification. Obstacles arising from perspective differences make it impossible for consistency verification to rely solely on pixel comparison. Therefore, we elevate the consistency verification process into feature space. We independently generate multiple inpainting candidates for each masked adjacent image. To handle varying 3D inpainting scenarios, we propose verifying consistency by assessing coherence in texture and geometry feature spaces. As shown in Fig. 3, for the inpainted candidates of $I_{i}^{adj}$ , we use ZoeDepth to estimate the corresponding depth maps. We apply a feature extraction model as consistency evaluator (ResNet-18 [13]) to separately extract both RGB and depth features for each candidate, as well as for the inpainted anchor image and its depth map. Finally, we compute the cosine similarity between candidates and the inpainted anchor image based on fused dual features. The overall consistency score is computed as a weighted combination of RGB and depth similarities: $S = \eta S_{rgb} + (1 - \eta)S_{depth}$ , where $\eta$ controls the relative importance of texture and geometry consistency. The candidate with the highest consistency score is then selected as the final inpainting result. The weighting factor $\eta$ is empirically set to 0.7 to balance fine texture details and structural coherence and four candidates generated for each image. + +Given the small perspective differences between adjacent images and our dual-feature coherence approach, our consistency verification mechanism effectively identifies and excludes inconsistent inpainting results. Specifically, by leveraging hierarchical feature extraction capability of ResNet-18 at multiple scales and the complementary nature + +of RGB-depth feature pairs, this method significantly enhances the multi-view consistency of images fed into the 3D Gaussian optimization process, thereby improving the overall quality of 3D Gaussian inpainting. + +# 3.3. Adaptive Sampling & 3D Gaussian Training + +Adaptive sampling. During the iterative process, we strategically sample an anchor image and its $k$ nearest neighbors on our proposed perspective graph $\mathbf{G}$ for inpainting and 3D Gaussian training. In the first iteration, the anchor image is selected from the entire dataset to initialize the process. For each subsequent iteration, we adopt a distance-aware sampling strategy: the anchor image is sampled from the pool of previously inpainted images, excluding both previously selected anchor images and their $k/2$ nearest neighbors from future anchor image selection. Here, $k$ is scene-dependent, determining both the number of adjacent views for inpainting and the spatial separation between anchor images. This spatial constraint ensures well-distributed scene coverage and mitigates the risk of local region trapping. We further maintain a priority queue based on consistency scores from previous iterations, prioritizing images with worse coherence for refinement (the algorithm flowchart in Appendix B.3). This adaptive mechanism progressively improves both global consistency and local detail quality. + +3D Gaussian Training. Given the dataset consisting of inpainted and masked multi-view images, we optimize 3D Gaussians following the vanilla 3DGS framework [17]. The optimization objective combines L1 and D-SSIM losses: + +$$ +\mathcal {L} = (1 - \lambda) \mathcal {L} _ {1} (I _ {i} ^ {\prime} - I _ {i}) + \lambda \mathcal {L} _ {S S I M} (I _ {i} ^ {\prime} - I _ {i}), \lambda = 0. 2, (3) +$$ + +where $I_{i}^{\prime}$ and $I_{i}$ denote the rendering and inpainted images respectively. For masked images, we exclude the missing regions from loss computation during optimization. + +Our method achieves high-quality multi-view consistent inpainting without fine-tuning pretrained diffusion models. As demonstrated in Fig. 7, PAInpainter effectively handles diverse 3D inpainting scenarios. + +# 4. Experiments + +In our experimental evaluation, we conduct comprehensive comparisons between PAInpainter and state-of-the-art approaches across 28 scenes, spanning 4 distinct inpainting tasks. Our framework employs the pretrained StableDiffusion2 (SD2) [34] as the backbone for image inpainting and ZoeDepth [4] for monocular depth estimation. Detailed implementation specifics and explanations of hyperparameters are provided in Appendix B.1 and Appendix B.2. + +Datasets. To rigorously evaluate the effectiveness and generalization capability of PAInpainter, we utilize three mainstream datasets. The first dataset consists of 8 object-centric scenes derived from the NeRF Blender dataset [25], with + +
NeRF Blender [25]SPIn-NeRF [27]NeRFiller [44]
PSNR (dB) ↑SSIM ↑LPIPS ↓FID ↓PSNR (dB) ↑SSIM ↑LPIPS ↓FID ↓PSNR (dB) ↑SSIM ↑LPIPS ↓FID ↓
Masked 3DGS11.570.830.19-13.460.410.40-12.950.760.28-
SD2 [34]20.420.900.09102.223.480.730.23140.320.360.840.17105.2
MVInpainter [7]19.420.810.17148.624.800.740.21152.221.130.800.18117.7
GridPrior + DU * [44]22.770.920.08104.225.190.790.20151.226.970.920.13121.9
NeRFiller * [44]23.270.920.09153.725.200.790.17146.122.350.880.15110.4
PAInpainter (ours)24.190.920.08101.826.030.810.15121.729.510.940.0896.1
+ +Table 1. Quantitative comparison on the multiple datasets. We compare our method against advanced approaches on three datasets. Higher PSNR and SSIM, as well as lower LPIPS and FID indicate better performance. Cells are highlighted as follows: best, second best, third best. Our method surpasses all baselines across these metrics, demonstrating its efficacy and robust generalization. * represents replacing the original NeRF backbone with 3DGS for fair comparison. Detailed performance of each scene are provided in the Appendix C. + +multi-view images at a resolution of $512 \times 512$ . Missing regions are generated by masking the central $192 \times 192$ pixels in each image (as exemplified by the "chair" scene in Fig. 7). Additionally, we use the SPIn-NeRF dataset [27] as the second dataset for 3D unbounded scene inpainting. Since the SPIn-NeRF dataset only covers a single 3D inpainting task (foreground object removal), we also incorporate the dataset introduced by NeRFiller [44], which includes 10 real-world complex 3D inpainting scenes. Collectively, our experimental corpus of 28 scenes (details in Appendix C) encompasses multiple 3D inpainting scenarios: 1) large indoor missing region, 2) object-centric large missing region, 3) object-centric removal, and 4) multiple disjoint missing regions (illustrated in Fig. 7). + +Baselines. We establish comprehensive comparisons with four representative state-of-the-art approaches, each embodying distinct technical paradigms: + +- SD2 [34]. A fundamental baseline that performs independent simultaneous inpainting across all multi-view images; +- GridPrior+DU [44]. An extension of the Dataset Update (DU) framework that processes random image batches in $2 \times 2$ grid patterns during iterative updates; +- NeRFiller [44]. A progressive joint-view inpainting strategy built upon SD2, emphasizing view-consistent content generation; +- MVInpainter [7]. A reference-guided approach that finetunes SD2 and incorporates single-view inpainting results as reference information. + +We configure GridPrior+DU and NeRFiller to process twelve images per batch to meet computational constraints and provide MVInpainter with one inpainted reference image per scene. All above methods are built upon 3DGS and are evaluated on 3D Gaussian scenes with identical masked regions and camera poses to ensure fair comparison. + +Metric. We assess the performance through quantitative analysis of rendered image quality from inpainted 3D Gaussian scenes. Our evaluation protocol employs four well + +established metrics: PSNR [11] for pixel-wise accuracy, SSIM [41] for structural similarity, LPIPS [51] for perceptual quality, and FID [14] for distribution alignment between the generated and ground truth images. For progressive methods that iteratively refine the inpainting results, we evaluate by comparing the rendered images from inpainted 3D scene against the inpainted image of each view after the last iteration. For single-round methods, we adopt the train-test split strategy on inpainted images: $80\%$ of images in the training set are used for optimizing the masked 3D Gaussian scene, while the remaining images as test set serve for evaluating the 3D inpainting results. + +# 4.1. Experimental Results and Analysis + +Quantitative. The experiment results of PAInpainter and state-of-the-art methods are presented in Tab. 1. The Masked 3DGS reports the rendering quality on the initial reconstructed 3D Gaussian scene with missing regions. Our proposed PAInpainter outperforms all other methods across the evaluated metrics. Specifically, on the NeR-Filler dataset, PAInpainter achieves significant improvements with PSNR of $29.51\mathrm{dB}$ , surpassing the strongest baseline (GridPrior+DU) by $2.54\mathrm{dB}$ . This demonstrates its superiority in generating high-quality 3D Gaussian inpainting results and highlights its strong generalization capability across diverse inpainting scenarios. + +In contrast, SD2 inpaints images independently without considering multi-view consistency, resulting in lower-quality renderings of the inpainted 3D scene. However, due to its pretraining on large-scale image datasets, SD2 achieves competitive FID scores, suggesting its ability to generate plausible visual content without fine-tuning. MV-Inpainter, originally designed for object-level and forward-facing task, struggles with general 3D inpainting scenarios, leading to unsatisfactory performance. NeRFiller and GridPrior+DU perform better on structural metrics due to their joint-view mechanism that incorporate cross-view priors. Nevertheless, these two approaches show limitations in perceptual quality, as reflected by higher FID scores. + +![](images/ace43ea3f0039a4cec1ff9aa60a829085f8858a37477b397ac439c91215718d2.jpg) +Figure 6. Qualitative comparison of 3D Gaussian inpainting results. Three scenes are shown (rows): Boot, Norway, and Office. For each scene, we present the initial masked 3D Gaussian scene (blue regions indicate missing content) and inpainting results from different methods. Four viewpoints are rendered to demonstrate multi-view consistency. + +
Graph samplingInpaint content propagationConsistency verificationPSNR (dB) ↑SSIM ↑LPIPS ↓FID ↓
---27.620.9280.100113.7
✓--27.940.9290.091109.4
✓✓-28.520.9320.083101.7
✓-✓28.470.9330.085106.0
✓✓✓29.510.9350.08196.1
+ +Table 2. Ablation study on NeRFiller dataset. Each row represents an ablated setting of our key components. The baseline uses basic iterative framework based on 3DGS without our proposed modules. Check marks (✓) indicate the presence of corresponding module. Results demonstrate PAInpainter (all modules present) achieves optimal performance. + +Compared to previous methods, PAInpainter achieves improvement in both multi-view consistency and perceptual quality. This is particularly evident in its superior FID scores while maintaining leading performance in structural metrics, which indicates that the inpainted content generated by PAInpainter is not only coherent across views but also aligned with the original scene distribution, demonstrating its effectiveness and reliability in 3D inpainting. + +Qualitative. Visualization comparisons are shown in Fig. 6, where PAInpainter exhibits remarkable performance in both detail preservation and multi-view consistency. In the "boot" scene (first row), our method accurately reconstructs the intricate leather textures while maintaining geometric continuity across different viewpoints. This advantage is further evidenced in the "Norway" scene (second row), where PAInpainter faithfully recovers the fine details of the mural paintings (beside the chair) with consistent artistic style and structural integrity. Similarly, in the "office" scene + +(third row), our method precisely reconstructs the architectural elements of the door frame while preserving the surrounding context. Additionally, as shown in the indoor scene in Fig. 7, PAInpainter showcases creativity ability by generating diverse content while maintaining scene consistency. In contrast, existing methods such as GridPrior+DU and MVInpainter, while achieving basic view consistency, often produce over-smoothed or distorted results, particularly in regions requiring high-fidelity detail. This comparison highlights PAInpainter's superior capability in enhancing both global structure coherence and local detail fidelity. + +# 4.2. Ablation Study + +We conduct ablation experiments to validate the effectiveness of each key component in PAInpainter, as shown in Tab. 2. The baseline method adopts a basic iterative framework for multi-view image inpainting without our proposed modules. When incorporating only the graph sampling strategy, the PSNR is improved to $27.94\mathrm{dB}$ , demonstrating that reference-guided inpainting effectively promotes view consistency. Adding either inpaint content propagation or consistency verification further improves performance (PSNR: $28.52\mathrm{dB}$ and $28.47\mathrm{dB}$ , respectively), indicating both modules contribute to high-quality inpainting. + +The PAInpainter equipped with all components achieves the best performance (PSNR: 29.51 dB), showing a significant improvement of 1.89 dB over the baseline. This validates our design: graph sampling provides adjacent views, content propagation enhances inpainting consistency across views, and consistency verification nominates coherent re + +![](images/2cebb88ed0e9d24907cba9528da0456e0a88f431971adc4b9e0d28c7d5a332b2.jpg) +Masked 3D scene + +![](images/216a0ccf76e0eeaae58803790b630e3d576fc569e234ec7b55350b8462f2942d.jpg) +(a) large indoor missing region +Multi-view inpainting + +![](images/b6504c743815f30a2c9da890c6913d3bd9dd501e5103a8e6b7894c0740233a47.jpg) +Inpainted 3D Gaussian scene + +![](images/6284364162fd36d40f1b57ffafb5bc7c179c04800a4b441d324cdee64900cd71.jpg) +Masked 3D scene + +![](images/78d2d9fc2dd5d8cf93e8c10743e1a8ceb973a6b9e17cae2195fbed082f4cf74d.jpg) +(c) Object-centric removal +Multi-view inpainting + +![](images/1a81ad690fb4bd078d8459cd3b80e212087b971b9d51b32a7d3646b8c523de2a.jpg) +Inpainted 3D Gaussian scene + +![](images/b374465bd7a130285fca3edbd51f45696e5feac75f2baf147f7dc5a946cde126.jpg) +Masked 3D scene + +![](images/aa79cc9dd75f718f6949290f67dfe1873c10c0f45ea79c79c5017be00f7d8f1a.jpg) +(b) Object-centric large missing region +Multi-view inpainting + +![](images/e689d8da6af462dd63c1d6b749ab74ea07eebb3c4eb0ee5ebf1944924775d486.jpg) +Inpainted 3D Gaussian scene + +![](images/68ce3a626c5131f4fd988583e70f0460b6ec5acf26268f57a915d4380d813213.jpg) +(d) Multiple disjoint missing regions +Masked 3D scene + +![](images/55a0a596e549801d6710d2c0640ec87a31faf3f29d5d95fa1e7b0cafc3b8dad6.jpg) +Multi-view inpainting + +![](images/2688473834be0bd87f9fafd4511ca1c4e2a90075a34a89f303323cada46e5cf0.jpg) +Inpainted 3D Gaussian scene + +![](images/60b7db94a7a5bfec000583f624f0cf1b94c4c8db807968c352c82724dd0adb77.jpg) +Figure 7. Visualization of PAInpainter on four representative inpainting scenarios. Each scenario shows the input, multi-view inpainting results, and the reconstructed 3D Gaussian scene, demonstrating consistent completion across varying viewpoints. +Figure 8. RGB and depth renderings of inpainted 3D Gaussian scenes from multiple viewpoints. The depth maps reveal consistent geometric reconstruction along with texture restoration. + +sults. Notably, removing either propagation or verification module leads to similar performance degradation, suggesting these components are complementary in maintaining multi-view consistency while preserving texture details. + +These ablation results corroborate our framework and previous experiments, confirming that the combination of all three proposed components is crucial for high-quality 3D Gaussian inpainting. + +# 4.3. Versatility & Geometric Consistency + +We showcase diverse 3D Gaussian inpainting scenarios of PAInpainter in Fig. 7, demonstrating its effectiveness across four distinct inpainting tasks. From object removal to large-area completion, our method consistently generates visually coherent results while preserving scene-specific geometric and textural details. The reconstructed 3D Gaussian scenes exhibit high fidelity across multiple viewpoints, validating the robustness of our approach in handling varying inpaint- + +ing requirements. + +The geometric consistency of our method is further validated through depth visualization, as shown in Fig. 8. Despite the absence of explicit depth supervision during 3D Gaussian optimization, the inpainted regions demonstrate naturalistic depth transitions and structural coherence with surrounding areas. The continuous depth maps demonstrate that strong multi-view consistency of PAInpainter inherently leads to accurate 3D geometry reconstruction, validating the capability in preserving both appearance and structural fidelity across different viewpoints. + +# 5. Conclusion + +In this paper, we present PAInpainter, an effective 3D Gaussian inpainter that substantially enhances multi-view consistency in 3D scene completion. Our technical contributions center on the novel perspective-aware inpainting framework, which integrates a perspective graph for adaptive view sampling, guided content propagation, and consistency verification mechanisms. Through this systematic design, PAInpainter preserves fine-grained scene details while ensuring multi-view consistency. Extensive experiments demonstrate that our method achieves superior performance across diverse inpainting scenarios. + +The current PAInpainter implementation offers promising results while suggesting directions for future enhancements. The key modules in the proposed framework could be integrated into LDM in an end-to-end manner for further improved performance and deployment efficiency. Meanwhile, further exploration of sparse-view scenarios and unbounded outdoor scenes remains valuable for future work. Despite these considerations, PAInpainter demonstrates robust performance and practical utility for applications from stereo vision production to AR/VR development. + +# Acknowledgements + +This research was supported by the Theme-based Research Scheme (TRS) project T45-701/22-R of the Research Grants Council (RGC), Hong Kong SAR. 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(a) Our goal is to generate SAR images at unseen angles using a few samples. (b) The unique electromagnetic imaging mechanism of SAR creates a significant discrepancy between "image rotation" and "target rotation". (c) and (d) show SAR images generated by DIGGAN [9], while (e) and (f) display images generated by our proposed $\Phi$ -GAN. It is evident that our method produces well-detailed results both near seen angles (red) and at unseen angles (blue). All SAR images are single-channel and visualized using the "hot" colormap for enhanced visual interpretation. + +![](images/f83e831401e40dcefdfa541080363f69c06602948df849d8648c0882efd2e730.jpg) +FID: 373.07(DIGGAN) / 87.27(Ours) + +![](images/83d7e181e0cb3294dd5f27150dd7ce051fc05463b0b5457429f37408a6c30bb4.jpg) +SAR vehicles (2S1 Carnation) +SAR airplanes (Kodiak100) + +![](images/e0b1dca3662ec405033d86c35a6c09d3dd251424cfa608b5c7a527ffb6f92e58.jpg) +SAR ships (Cargo) + +# Abstract + +Approaches for improving generative adversarial networks (GANs) training under a few samples have been explored for natural images. However, these methods have limited effectiveness for synthetic aperture radar (SAR) images, as they do not account for the unique electromagnetic scattering properties of SAR. To remedy this, we propose a physics-inspired regularization method dubbed $\Phi$ -GAN, which incorporates the ideal point scattering center (PSC) model of SAR with two physical consistency losses. The PSC model approximates SAR targets using physical parameters, ensuring that $\Phi$ -GAN generates SAR images consistent with real physical properties while preventing discriminator overfitting by focusing on PSC-based decision + +cues. To embed the PSC model into GANs for end-to-end training, we introduce a physics-inspired neural module capable of estimating physical parameters of SAR targets efficiently. This module retains the interpretability of the physical model and can be trained with limited data. We propose two physical loss functions: one for the generator, guiding it to produce SAR images with physical parameters consistent with real ones, and one for the discriminator, enhancing its robustness by basing decisions on PSC attributes. We evaluate $\Phi$ -GAN across several conditional GAN (cGAN) models, demonstrating state-of-the-art performance in data-scarce scenarios on three SAR image datasets. + +# 1. Introduction + +Synthetic Aperture Radar (SAR), an active sensor that transmits and receives high-frequency microwaves, is vital + +in remote sensing due to its all-day, all-weather imaging capabilities [6]. The unique electromagnetic scattering properties and labor-intensive annotation of less interpretable SAR images limit the availability of large-scale datasets, spurring interest in SAR image generation with deep learning models such as generative adversarial networks (GANs) [12]. While GANs have made significant strides in generating realistic images, their inherent instability, exacerbated by limited data, often leads to mode collapse and discriminator overfitting. Techniques such as data augmentation [24, 27, 64], regularization [9, 53, 62, 65], and latent code optimization [17, 58, 66] have been developed to improve GAN stability and have shown success on small-scale datasets like subsets of CIFAR-10/-100 [30] and ImageNet [7]. However, these methods face distinct challenges when applied to the SAR domain, due to the extremely severe data scarcity problem and its special electromagnetic scattering characteristics. + +In practical applications, only a few dozen SAR images per category with limited look angles are available [14], as demonstrated in Figure 1a. Additionally, SAR targets exhibit unique electromagnetic scattering characteristics that vary significantly with the sensor's look angle, known as the "azimuth angle" [49]. Figure 1b illustrates the large discrepancy between "target rotation" and "image rotation" in a SAR image. This variability makes standard augmentation techniques, such as rotations commonly used for natural images, ineffective for SAR targets. Consequently, many traditional data augmentation methods [27, 64, 65] fail in this context. Existing regularization techniques [9, 53, 62, 65], while sometimes effective, do not account for SAR's physical scattering properties, resulting in suboptimal generation performance and limited physical consistency. + +To address these challenges, we propose leveraging the ideal point scattering center (PSC) model to enhance GAN training for SAR image generation. The PSC model simplifies complex radar-object interactions by representing each SAR target as a collection of discrete point scatterers [21]. By estimating the physical parameters of SAR targets using the PSC model, we ensure that generated SAR images maintain physical consistency with real ones and guide the discriminator to make decisions based on electromagnetic features. However, parameter estimation for the PSC model is often computationally expensive [31, 52, 57], making efficient integration with GANs challenging. We found that this issue can be addressed by formulating the parameter estimation as a sparse reconstruction problem, which can be solved through an iterative optimization method [32, 61]. This insight enables the development of a neural module for efficient implementation. + +Building on these findings, we propose $\Phi$ -GAN, a novel SAR image generation method tailored for data-scarce sce + +narios. $\Phi$ -GAN enhances existing cGAN training by integrating the PSC model to penalize physical inconsistencies in generated SAR images and refine the discriminator's decision-making process to prevent overfitting. Specifically, we introduce a neural module that unrolls the Half-Quadratic Splitting (HQS) method to estimate SAR target physical parameters based on the PSC model. This module, with only a few learnable parameters, can be effectively optimized with limited data. By incorporating the frozen physics-aware neural module and the PSC model into the GAN framework, we propose two physical loss functions: one to guide the generator in producing physically consistent results, and another to constrain the discriminator to distinguish between real and synthetic images using key electromagnetic features derived from the PSC model, thus reducing overfitting. + +To the best of our knowledge, $\Phi$ -GAN is the first end-to-end physics-aware regularization method for SAR image generation that integrates the electromagnetic scattering model into GANs to enforce physical consistency and enhance generalization. Extensive experiments and comparisons with state-of-the-art GAN training techniques demonstrate that $\Phi$ -GAN achieves faster convergence in generating crucial electromagnetic scattering features and ensures more stable refinement of generated details. + +Contributions. The main contributions of this paper are as follows: (1) We demonstrate that integrating the PSC model of SAR into existing GAN frameworks significantly enhances their stability and generalization in data-scarce scenarios for SAR image generation. (2) We propose a novel $\Phi$ -GAN, which incorporates a physics-inspired neural module for PSC parameter inversion and two specialized physical losses to effectively regularize GAN training. (3) We show that $\Phi$ -GAN is adaptable to various conditional GAN architectures, enabling robust performance across diverse SAR image generation tasks. + +# 2. Related Work + +# 2.1. Training GANs with Limited Data + +GAN training is inherently unstable, and limited data exacerbates these challenges, making the process more unpredictable. Solutions include data augmentation [5, 19, 24, 27, 51, 64], regularization [9, 53, 62, 65], and latent space optimization [17, 58, 66]. + +Data Augmentation. Apart from some widely-applied general data augmentation methods, strategies like adaptive discriminator augmentation (ADA) [27], Differentiable Augmentation (DiffAugment) [64], and Adaptive Pseudo Augmentation [24] are developed for GAN training. + +Regularization. Various studies have focused on enhancing the discriminator through regularization terms such as weight and gradient penalties [9, 29, 53]. Consistency reg + +ularization with data augmentation has been introduced to GANs to improve training stability. It penalizes the discriminator's sensitivity to semantic-preserving perturbations introduced through data augmentation [53, 62, 65]. + +Latent space optimization. Some researches have focused on optimizing the latent space to better represent unseen classes [66]. Other studies aim to disentangle class-relevant and class-independent representations within the latent space, enabling diverse image generation by modifying class-independent codes even with limited samples [17, 58, 66]. + +While effective for natural images, these methods often underperform in generating SAR images with limited data and may even degrade performance. Although recent studies have incorporated geometry, physics and functionality of targets in real-world to guide generative model training [36, 40, 43], few have considered the unique characteristics of electromagnetic imaging. This motivates us to introduce a specialized GAN framework that leverages physical properties of SAR. + +# 2.2. SAR Image Generation + +Controllable generation based on cGAN. Generating SAR images with a full-range of azimuth angles from limited observations has attracted most attention in recent studies, as demonstrated in Figure 1a. Conditional GANs are the most preferred choice. The input conditions include target class [3, 4, 8, 14, 42, 44, 47, 50, 67, 68], azimuth angle [14, 42, 47, 49, 50], instance semantic map [15], target location [25], etc. Controllable SAR image generation methods based on cGANs typically encode condition factors as input and use multiple auxiliary classifiers to assess whether the generated images align with the input conditions. There are multiple strategies to input the conditions, such as concatenating them with noise vector in the input layer [3, 4, 14, 42, 44, 50, 67, 68], applying a projection module and multiplying with latent features [8, 47], and concatenating with multi-scale features [48, 49]. + +Solutions designed for SAR. Conventional data augmentation and regularization methods for natural images have been applied to SAR [25, 34, 68], but their performance diminishes when training with only a few dozen samples per category. Several enhanced GAN architectures have been developed to reduce model complexity [47, 49] or to improve the feature representation of the discriminator [68]. Some methods have focused on optimizing latent code representation to boost the diversity and quality of generated images [14, 18]. Specifically, studies have identified intrinsic data issues in SAR, such as speckle noise contamination [13, 54] and varying scattering characteristics with target pose [49], which can lead to mode collapse and overfitting in GAN models. Consequently, specific solutions tailored to SAR characteristics have been proposed. To + +mitigate the negative influence of speckled clutter on discriminator's decision-making, prior statistical distributions have been used to guide GANs toward learning SAR images with reduced speckle noise [13, 54] or achieving a desired gray-level distribution [35]. Another significant challenge is the limited scientific validity of SAR images generated by AI models. Data-driven generative models often lack awareness of the physical principles underlying SAR imaging, leading to inconsistency with electromagnetic properties and limited generalization capacity [6, 22]. Electromagnetic scattering models, with their strong theoretical foundation, are highly beneficial for guiding generative model training [10]. However, integrating them with generative AI models for end-to-end training is often expensive and difficult. In our work, a new solution is proposed to develop a physics-inspired module inserted into existing GANs, that inherits the physical interpretability of the electromagnetic model while maintaining efficiency. + +# 3. Method + +# 3.1. Conditional GANs for SAR + +Conditional GANs (cGANs) are employed to generate SAR images with conditions of target label $c$ and azimuth angle $\theta$ . The class information $c$ is encoded in one-hot form. The azimuth angle $\theta$ is represented in a continuous and periodical manner with Cyclic High-frequency information-based Embedding (CHE) method [14], denoted as: + +$$ +r (\theta) = \left[ \sin (\theta), \cos (\theta), \sin (2 \theta), \dots , \sin (5 \theta), \cos (5 \theta) \right] \tag {1} +$$ + +The encoded conditions are then concatenated with the latent code $z$ as the input of the generator, denoted as $\{z, c, r(\theta)\}$ . The training objective of the cGANs can be written below: + +$$ +\mathcal {L} _ {\mathrm {o r i}} ^ {D} = - \mathbb {E} _ {u, c, \theta} [ f (D (u | c, \theta)) ] + \mathbb {E} _ {z, c, \theta} [ f (D (G (z, c, \theta))) ] +$$ + +$$ +\mathcal {L} _ {\mathrm {o r i}} ^ {G} = - \mathbb {E} _ {z, c, \theta} [ f (D (G (z, c, \theta))) ] \tag {2} +$$ + +where $f(\cdot)$ is the binary cross-entropy loss function. + +# 3.2. $\Phi$ -GAN Overview + +The overview of $\Phi$ -GAN is illustrated in Figure 2a. Unlike existing cGANs, $\Phi$ -GAN integrates a physical model component, represented as $\mathcal{F}_{\mathrm{est}} \circ \mathcal{F}_{\mathrm{phy}}$ , and incorporates a discriminator $\mathcal{D}_{\mathrm{img}}$ and a physics-informed regularizer $\mathcal{R}_{\mathrm{phy}}$ , which are responsible for assessing the generated image and the output of the physical model, respectively. Specifically, $\mathcal{F}_{\mathrm{est}}$ estimates the physical parameters of an input SAR image, while $\mathcal{F}_{\mathrm{phy}}$ reconstructs its electromagnetic (EM) scattering features. The EM reconstruction outputs for real and generated SAR images are denoted as $s$ and $\tilde{s}$ , respectively. $\mathcal{D}_{\mathrm{img}}$ and $\mathcal{R}_{\mathrm{phy}}$ independently discriminate between real and generated images, as well as their + +![](images/c1b678a035ebc33094c554684eabbb41cf79c70e5ad107246d2f05d36f701406.jpg) + +![](images/917860ff44a408171102107241f8650c293b776cb8dc74b90ad11199ca2bf32c.jpg) +Figure 2. (a) The proposed $\Phi$ -GAN framework overview. (b) Demonstration of the physics-inspired neural module $\mathcal{F}_{\mathrm{est}}$ for physical parameter inversion and image reconstruction based on PSC model $\mathcal{F}_{\mathrm{phy}}$ . $\mathcal{F}_{\mathrm{est}}$ contains a couple of learnable parameters and $\mathcal{F}_{\mathrm{phy}}$ is an off-the-shelf reconstruction process. (c) Illustration of PSC model $\mathcal{F}_{\mathrm{phy}}$ . (d) Implementation of the $k$ -th stage within $\mathcal{F}_{\mathrm{est}}$ . + +![](images/928d27bc1b7baaae03a35f2ec72410cf843ef0d21f44843844cf56a25c01bed3.jpg) + +![](images/4f4ec18aa6372e733488896a66ef7de00605281de56949ba27975ae85ca4d9dc.jpg) + +reconstructed EM features based on the estimated physical parameters. The final discriminator decision combines the outputs of $\mathcal{D}_{\mathrm{img}}$ and $\mathcal{R}_{\mathrm{phy}}$ . The process is defined as follows: + +$$ +\tilde {u} = \mathcal {G} (z, c, r (\theta)), +$$ + +$$ +s, \tilde {s} = \mathcal {F} _ {\text {e s t}} \circ \mathcal {F} _ {\text {p h y}} (u, \tilde {u}), \tag {3} +$$ + +$$ +d _ {o u t} (u, s) = \alpha \mathcal {D} _ {\mathrm {i m g}} (u) + (1 - \alpha) \mathcal {R} _ {\mathrm {p h y}} (s) +$$ + +To efficiently integrate the physical model into GAN training in an end-to-end manner, we propose a physics-inspired neural module to implement $\mathcal{F}_{\mathrm{est}}$ with a few learnable parameters, as detailed in Section 3.3. Additionally, we introduce two physical loss functions, $\mathcal{L}_{\mathrm{phy}}^{G}$ and $\mathcal{L}_{\mathrm{phy}}^{D}$ . The purpose of $\mathcal{L}_{\mathrm{phy}}^{G}$ is to penalize unrealistic generated SAR images with inconsistent physical parameters, while $\mathcal{L}_{\mathrm{phy}}^{D}$ regularizes the discriminator to make more robust decisions based on the discriminative EM features of targets. These losses complement the original optimization objectives, as outlined in Section 3.4: + +$$ +\mathcal {L} ^ {G} = \mathcal {L} _ {\mathrm {o r i}} ^ {G} + \mathcal {L} _ {\mathrm {p h y}} ^ {G}, +$$ + +$$ +\mathcal {L} ^ {D} = \mathcal {L} _ {\mathrm {o r i}} ^ {D} + \mathcal {L} _ {\mathrm {p h y}} ^ {D}. +$$ + +# 3.3. Physics-Inspired Neural Module + +Based on geometric diffraction theory, the electromagnetic scattering of a target can be approximately represented as the sum of responses from multiple independent ideal PSCs at high frequencies. The response of each PSC is a function of the radar echo frequency $f$ and aspect angle $\phi$ , as illustrated in Figure 2c. The SAR target with $N$ PSCs can be modeled as: + +$$ +E (f, \phi) = \sum_ {i = 1} ^ {N} A _ {i} \cdot \exp (- j \frac {4 \pi f}{c} (x _ {i} \cos \phi + y _ {i} \sin \phi)), \tag {5} +$$ + +where $E$ denotes the measurement in the frequency domain. $A_{i}$ and $\exp (\cdot)$ are the response intensity and the phase information of radar echos of the ith PSC, respectively. $x_{i}$ and $y_{i}$ + +decide the position of each PSC, as demonstrated in Figure 2c. In this work, the physical parameters $A_{i}, x_{i}, y_{i}$ modeled with PSC are first estimated in $\mathcal{F}_{\mathrm{est}}$ and then reconstructed into images in $\mathcal{F}_{\mathrm{phy}}$ . An overview of this process is provided in Figure 2b. + +Previous study [60] has shown that radar echo signals exhibit sparsity in image domain, enabling the use of sparse signal representation for analysis. Thus, the PSC parameters can be estimated by optimizing the following problem: + +$$ +\hat {\mathbf {o}} = \underset {\mathbf {o}} {\arg \min } | | \boldsymbol {\Psi} \mathbf {o} - \mathbf {r} | | _ {2} + \lambda | | \mathbf {o} | | _ {1}. \tag {6} +$$ + +The symbol $\Psi$ represents a dictionary that contains the positional information of PSCs, corresponding to the exponential term in Equation (5). $\mathbf{r}$ denotes the input image after vectorization. $\mathbf{o}$ denotes a sparse vector that stores the response values at each position in the image, corresponding to $\{A_i\}_{i=1}^N$ in Equation (5). $\hat{\mathbf{o}}$ is the estimation of $\mathbf{o}$ and $\lambda$ is a hyperparameter that balances the tradeoff between data fidelity and sparsity. However, existing methods, such as HQS [11], often rely on iterative optimization strategies and manual hyperparameter tuning, which result in low processing speed and suboptimal accuracy. To overcome this challenge, we introduce a neural module $\mathcal{F}_{\mathrm{est}}$ that unrolls the HQS algorithm for efficient, real-time estimation of PSC parameters. This approach provides immediate feedback from the physical model, enabling end-to-end training of $\Phi$ -GAN. + +HQS decomposes the problem into two alternating optimization sub-problems by introducing auxiliary variables. It then gradually converges to the optimal solution of the original problem by alternately optimizing the primary and auxiliary variables. First, for the optimization problem in Equation (6), an auxiliary variable $\mathbf{p}$ is introduced, and the problem is reformulated as: + +$$ +\min _ {\mathbf {o}, \mathbf {p}} \| \mathbf {r} - \boldsymbol {\Psi} \mathbf {o} \| _ {2} ^ {2} + \lambda \| \mathbf {p} \| _ {1}, \quad \text {s u b j e c t t o} \quad \mathbf {o} = \mathbf {p}. \tag {7} +$$ + +Next, $\mathbf{o}$ and $\mathbf{p}$ are alternately optimized using the following optimization strategy: + +$$ +\mathbf {o} ^ {(k)} = \arg \min _ {\mathbf {o}} \left[ \frac {1}{2} \| \mathbf {r} - \boldsymbol {\Psi} \mathbf {o} \| _ {2} ^ {2} + \frac {\mu}{2} \| \mathbf {o} - \mathbf {p} ^ {(k - 1)} \| _ {2} ^ {2} \right], \tag {8} +$$ + +$$ +\mathbf {p} ^ {(k)} = \arg \min _ {\mathbf {p}} \left[ \lambda \| \mathbf {p} \| _ {1} + \frac {\mu}{2} \| \mathbf {o} ^ {(k)} - \mathbf {p} \| _ {2} ^ {2} \right], +$$ + +where $\mathbf{o}^{(k)}$ and $\mathbf{p}^{(k)}$ denote the values of $\mathbf{o}$ and $\mathbf{p}$ at the $k$ -th iteration, respectively, and $k$ represents the iteration count. Once $\mathbf{o}^{(k)}$ is obtained, the proximal gradient algorithm can be directly applied to solve $\mathbf{p}^{(k)}$ . Thus, the closed-form solutions for $\mathbf{o}^{(k)}$ and $\mathbf{p}^{(k)}$ are given as follows: + +$$ +\mathbf {o} ^ {(k)} = \mathbf {p} ^ {(k - 1)} + \mu \boldsymbol {\Psi} ^ {H} (\boldsymbol {\Psi} \boldsymbol {\Psi} ^ {H}) ^ {- 1} (\mathbf {r} - \boldsymbol {\Psi} \mathbf {p} ^ {(k - 1)}), \tag {9} +$$ + +$$ +\mathbf {p} ^ {(k)} = S _ {\rho} \left(\mathbf {p} ^ {(k - 1)} + t \boldsymbol {\Psi} ^ {H} \left(\boldsymbol {\Psi} \mathbf {p} ^ {(k - 1)} - \mathbf {o} ^ {(k)}\right)\right). \tag {9} +$$ + +$S_{\rho}$ is the soft-thresholding function, which is expressed as $S_{\rho}(x) = \text{sign}(x)\max(|x| - \rho, 0)$ . In traditional HQS, the parameters $t$ , $\rho$ , and $\mu$ are typically chosen based on prior information and then held fixed. In this work, we unfold HQS as a neural network and set the parameters at each stage to be learnable. The internal structure of the network stage $k$ is shown in Figure 2d and can be described as follows: + +$$ +\mathbf {o} ^ {(k)} = \mathbf {p} ^ {(k - 1)} + \mu^ {(k)} \boldsymbol {\Psi} ^ {H} (\boldsymbol {\Psi} \boldsymbol {\Psi} ^ {H}) ^ {- 1} (\mathbf {r} - \boldsymbol {\Psi} \mathbf {p} ^ {(k - 1)}), +$$ + +$$ +\mathbf {p} ^ {(k)} = S _ {\rho^ {(k)}} \left(\mathbf {p} ^ {(k - 1)} + t ^ {(k)} \boldsymbol {\Psi} ^ {H} \left(\boldsymbol {\Psi} \mathbf {p} ^ {(k - 1)} - \mathbf {o} ^ {(k)}\right)\right). \tag {10} +$$ + +Building on Equation (10), we designed a two-stage process to construct $\mathcal{F}_{\mathrm{est}}$ , resulting in a total of 6 trainable parameters. The initial values of $t^{(k)}$ , $\rho^{(k)}$ , and $\mu^{(k)}$ for each stage are set to 0.001, 0.005 and 0.001, respectively. + +For each sample, the loss is defined as follows: + +$$ +\mathcal {L} _ {\mathrm {P S C}} = \left\| \mathbf {r} - \boldsymbol {\Psi} \mathbf {o} ^ {(K)} \right\| _ {2} ^ {2} + \lambda_ {1} \left\| \mathbf {o} ^ {(K)} - \mathbf {p} ^ {(K)} \right\| _ {2} ^ {2} + \lambda_ {2} \left\| \mathbf {p} ^ {(K)} \right\| _ {1}. \tag {11} +$$ + +$\| \mathbf{r} - \boldsymbol{\Psi}\mathbf{o}^{(K)}\|_{2}^{2}$ indicates the residual loss between the input image and the reconstructed image, where a lower value indicates a greater consistency. $\Psi \mathbf{o}^{(K)}$ denotes the reconstruction procedure, i.e. $\mathcal{F}_{\mathrm{phy}}$ . $\lambda_1\| \mathbf{o}^{(K)} - \mathbf{p}^{(K)}\|_{2}^{2}$ ensures consistency between the original and auxiliary variables, while $\lambda_{2}\| \mathbf{p}^{(K)}\|_{1}$ enforces sparsity of the variable, demonstrating that the SAR target can be modeled with a minimal number of PSCs. The hyperparameters $\lambda_{1}$ and $\lambda_{2}$ are empirically set to 100 and 200, respectively. More details about the physical model including how complex-valued data is handled can be found in S.M. (Section 1). + +# 3.4. Optimization of Generator and Discriminator + +SAR images differ from natural images due to speckled clutter and discrete target features. Their unique electromagnetic scattering properties pose challenges for training + +GANs, particularly with limited data. While current regularization methods focus on weights, gradients, and general strategies to stabilize training, we propose two physics-based loss functions for the generator and discriminator to effectively integrate SAR domain knowledge. + +The proposed $\Phi$ -GAN framework is illustrated in Figure 2a, and the final output of the discriminators is previously defined as $d_{out}$ in Equation (3). With this structure, the original optimization objectives in Equation (2) for the generator and discriminator are redefined as follows: + +$$ +\mathcal {L} _ {\mathrm {o r i}} ^ {G} = - \mathbb {E} _ {z, c, \theta} [ f (d _ {o u t} (\tilde {u}, s)) ], +$$ + +$$ +\mathcal {L} _ {\mathrm {o r i}} ^ {D} = - \mathbb {E} _ {z, c, \theta} [ f (d _ {o u t} (u, s)) ] + \mathbb {E} _ {z, c, \theta} [ f (d _ {o u t} (\tilde {u}, \tilde {s})) ]. \tag {12} +$$ + +In data-scarce scenarios, the generator faces challenges in capturing the crucial electromagnetic scattering features of SAR targets, limiting its ability to produce realistic SAR images that adhere to physical principles. To address this, we propose a physical loss, $\mathcal{L}_{\mathrm{phy}}^G$ , to ensure the physical consistency of the generated data. This loss imposes constraints on both the physical parameters and the latent embedding space. Specifically, $\mathcal{L}_{\mathrm{phy / s}}^G$ enforces that generated samples have physical parameters similar to those of real samples with the same target label and azimuth angle. Additionally, $\mathcal{L}_{\mathrm{phy / f}}^G$ constrains the latent feature representations of the generated image, denoted as $\{F_{\mathrm{img}}^i (\tilde{u})\}_{i = 1}^M$ , aligned with the real electromagnetic scattering features in the latent space, denoted as $\{F_{\mathrm{phy}}^i (s)\}_{i = 1}^M$ . The overall physical loss for the generator is defined as: + +$$ +\mathcal {L} _ {\mathrm {p h y}} ^ {G} = \beta \mathcal {L} _ {\mathrm {p h y / s}} ^ {G} + \gamma \mathcal {L} _ {\mathrm {p h y / f}} ^ {G}, \tag {13} +$$ + +where $\mathcal{L}_{\mathrm{phy / s}}^{G}$ and $\mathcal{L}_{\mathrm{phy / f}}^{G}$ are image-level and feature-level constraints, respectively, and $\beta$ and $\gamma$ are the hyperparameters to control the balances of them: + +$$ +\mathcal {L} _ {\mathrm {p h y / s}} ^ {G} = \operatorname {M S E} (s, \tilde {s}), +$$ + +$$ +\mathcal {L} _ {\mathrm {p h y / f}} ^ {G} = \sum_ {i = 1} ^ {M} \frac {1}{C ^ {i} H ^ {i} W ^ {i}} | | F _ {\mathrm {p h y}} ^ {i} (s) - F _ {\mathrm {i m g}} ^ {i} (\tilde {u}) | | _ {2}. \tag {14} +$$ + +where $F_{\mathrm{img}}^i$ and $F_{\mathrm{phy}}^i$ denote the $i$ -th layer features of $\mathcal{D}_{\mathrm{img}}$ and $\mathcal{R}_{\mathrm{phy}}$ , respectively. $C^i, H^i, W^i$ represent the number of channel, height and width of the feature map at the $i$ -th stage/layer. + +The discriminator often suffers from severe overfitting, leading to biased decisions based on patterns in speckle noise. To mitigate this, the proposed $\Phi$ -GAN framework introduces an auxiliary physics-informed regularizer, $\mathcal{R}_{\mathrm{phy}}$ which regularizes the main image discriminator, $\mathcal{D}_{\mathrm{img}}$ . We design a physical loss to distill the latent features of $\mathcal{D}_{\mathrm{img}}$ using those of $\mathcal{R}_{\mathrm{phy}}$ . Hierarchical feature alignment between $\mathcal{F}_{\mathrm{phy}}$ and $\mathcal{F}_{\mathrm{img}}$ restricts the primary $\mathcal{D}_{\mathrm{img}}$ to prioritize target EM features over environmental noise to make + +
Method10% MSTAR5% MSTAR
SSIM(↑)VIF(↑)FSIM(↑)GMSD(↓)FID(↓)KID(↓)SSIM(↑)VIF(↑)FSIM(↑)GMSD(↓)FID(↓)KID(↓)
ACGAN0.32240.03860.74320.1510290.04840.45480.30070.03150.72910.1583340.24400.4713
+ADA[27]0.26060.02430.71710.1643320.59370.42400.27860.02350.70950.1667364.56100.5304
+DA[64]0.21680.01880.65700.20181089.47341.80560.20250.01880.66200.1980976.11121.6584
+RLC[53]0.31370.03490.73620.1527286.71480.43150.29050.02930.73030.1573375.50490.5698
+DIG[9]0.32790.03110.72830.1570373.07220.62430.32790.02670.71660.1598438.78450.7002
+Ours0.35830.07810.76220.138587.27190.04140.31410.05470.74410.1485130.23110.0861
+ +Table 1. Comparing SAR image generation results with varying data percentages on MSTAR dataset. ACGAN is applied as the baseline. + +
Method10% MSTAR5% MSTAR
FID(↓)KID(↓)FID(↓)KID(↓)
StyleGAN290.64060.3641339.27880.4286
+Ours174.83290.1752305.05400.3894
StyleGAN2148.35510.1694168.39520.1666
+NosiyTwins[45]152.06120.1749168.07040.1595
+AdaptiveMix[33]146.29010.3641168.70170.1531
+Ours115.96860.0972164.96970.1523
+ +robust decisions, thus alleviate overfitting. The physical loss for the discriminator is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {p h y}} ^ {D} = \gamma \sum_ {i = 1} ^ {M} \frac {1}{C ^ {i} H ^ {i} W ^ {i}} \left(\left| \left| F _ {\mathrm {i m g}} ^ {i} (\tilde {u}) - F _ {\mathrm {p h y}} ^ {i} (\tilde {s}) \right| \right| _ {2} \right. \tag {15} \\ + | | F _ {\mathrm {i m g}} ^ {i} (u) - F _ {\mathrm {p h y}} ^ {i} (s) | | _ {2}) \\ \end{array} +$$ + +By combining Equations (12-15), the generator and discriminator are optimized in an alternating fashion. + +# 4. Experiments + +# 4.1. Datasets and Settings + +Datasets. We apply three SAR image datasets: the Moving and Stationary Target Acquisition and Recognition (MSTAR) (10-class) [1], SAR-Airplane (2-class) [55] and OpenSARShip (2-class) [20]. To create a data-scarce training scenario, we uniformly sample subsets from the original datasets based on the azimuth angles of the targets. Eventually, we obtain $10\%$ and $5\%$ MSTAR dataset with 237 and 121 samples for 10-class, $1\%$ OpenSARShip dataset with 46 samples for 2-class, and $14\%$ SAR-Airplane dataset with 20 samples for 2-class. More details of data processing can be found in S.M. (Section 2). + +Baseline. We use ACGAN [41] and StyleGAN [26] as baseline models in our experiments. To tailor them to our specific task, we implement the following modifications compared to their original configurations. + +- ACGAN [41]: We extend the original auxiliary classifier in ACGAN by adding an angle estimator, enabling simultaneous evaluation of the input conditions for class and azimuth angle. Spectral normalization[39] was utilized to stabilize GAN training. +- StyleGAN [26]/StyleGAN2 [28]: For the generator, the embedded azimuth angle and class information are con + +Table 2. Comparisons based on StyleGAN. + +
Method1% OpenSARShip14% SAR-Airplane10% MSTAR
FID(↓)KID(↓)FID(↓)KID(↓)FID(↓)KID(↓)
CAE[14]41.23700.026934.44760.0180134.86190.1526
CVAE-GAN[18]23.94800.011234.74480.0137495.96820.5147
CVAE-GAN+Ours15.05300.003917.04940.0021104.89760.0662
ACGAN+Ours14.79870.004619.14920.004687.27190.0414
+ +Table 3. Comparisons with SAR image generation methods. + +catenated with the latent noise as input to the mapping network. Meanwhile, the conditional input of the projection discriminator [38] is set to the concatenation of class and azimuth angle embedding. + +Implementation details. All experiments are conducted on NVIDIA GeForce RTX 3090 Ti. Codes were implemented in Python using PyTorch framework. The hyperparameters $\alpha, \beta, \gamma$ in $\Phi$ -GAN are set to 0.6, 1, 10, respectively. The learning rate is set to 0.0002 and Adam is used for optimization. When training $\mathcal{F}_{\mathrm{est}}$ , we adopt the AdamW optimizer with a weight delay of 0.005 and a learning rate of 0.002. + +Evaluation metrics. Fréchet Inception Distance (FID) [16] and Kernel Inception Distance (KID) [2] are applied. Additionally, for the MSTAR dataset, we incorporated four full-reference Image Quality Assessment (IQA) metrics—SSIM [56], VIF [46], FSIM [63], and GMSD [59]—to assess the quality of the generated samples. + +# 4.2. Comparison with State-of-the-art Methods + +Comparisons based on ACGAN. Tables 1 and 4 present a comparison of different stabilizing approaches applied to the ACGAN model on the $5\%$ and $10\%$ MSTAR datasets, as well as the $1\%$ OpenSARShip dataset and $14\%$ SAR airplane dataset. It is noteworthy that the differentiable augmentation (DA) method significantly degrades performance in SAR image generation, and other approaches also show limited effectiveness for this task. This finding confirms that natural image-oriented techniques are not well-suited for SAR data. In contrast, our method achieves superior performance, setting new state-of-the-art results across these SAR datasets. + +Comparisons based on StyleGAN. Table 2 compares our method with StyleGAN-based models. The results indicate that the StyleGAN baseline performs poorly in SAR image generation due to severe data scarcity. However, our + +
Method1% OpenSARShip14% SAR-Airplane
FID(↓)KID(↓)FID(↓)KID(↓)
ACGAN18.28550.008125.22190.0090
+ADA[27]25.09310.013636.78290.0198
+DA[64]37.07230.020347.84090.0253
+RLC[53]20.57350.010631.48130.0157
+DIG[9]23.59850.013521.85730.0066
+Ours14.79870.004619.14920.0046
+ +Table 4. Results on OpenSARShip and SAR-Airplane. + +
MethodSSIM(↑)FSIM(↑)GMSD(↓)FID(↓)KID(↓)
ACGAN0.32240.74320.1510290.04840.4548
w/ Lphy/s0.35140.76110.139297.44720.0671
w/ Lphy/f0.34770.75250.141499.92560.0568
w/ Lphy0.34670.75260.142292.75620.0471
w/ Lphy/f·Lphy0.34890.75150.141895.92900.0493
w/ Lphy/s·Lphy/f0.33570.75860.1419177.18560.2238
Ours0.35830.76220.138587.27190.0414
+ +approach significantly improves the model's generative capabilities. + +Comparisons with SAR image generation methods. We also compare our method with other SAR image generation approaches, including CAE [14] and CVAE-GAN [18], with the results shown in Table 3. It is important to note that CVAE-GAN [18] was not designed for data-scarce scenarios, making it challenging to train on the $10\%$ MSTAR dataset. However, integrating our proposed $\Phi$ -GAN significantly improves its performance, demonstrating the effectiveness of our approach. + +# 4.3. Ablation Studies + +Ablation of each regularization loss. Table 5 discusses the effectiveness of each regularization loss design. The results show that penalizing the inconsistency of physical parameters using $\mathcal{L}_{\mathrm{phy / s}}^{G}$ yields the most significant performance improvement. Notably, applying $\mathcal{L}_{\mathrm{phy}}^{G}$ without constraining $\mathcal{L}_{\mathrm{phy}}^{D}$ results in a performance drop, indicating that discriminator overfitting adversely affects the alignment of generated SAR images with real electromagnetic reconstructions. Combining both feature-level constraints for the generator and discriminator, i.e., using $\mathcal{L}_{\mathrm{phy / f}}^{G}$ and $\mathcal{L}_{\mathrm{phy}}^{D}$ together, results in substantial performance gains. Overall, regularizing both the generator and discriminator at the image and feature levels using the physical model results in the greatest performance improvement. + +Ablation of physics-inspired neural module. To highlight the effectiveness of our proposed physics-inspired neural module, we compare the results by replacing it with an off-the-shelf Harris-Laplacian corner detection method [37], which is widely applied in SAR image analysis to extract the scattering point. The quantitative results are demon- + +![](images/ce880cd6e1b3d6b65026fa0dbfa7a2fd1f6541244518df5019761d8d52a2946b.jpg) +(a) + +![](images/7bee61ac09784922cebf0fa7a96a833164f57c606770f71081c8896655620706.jpg) +(b) +Figure 3. The discriminator output of ACGAN with and without our proposed physics-inspired regularization. + +Table 5. Ablation of each regularization loss. + +
Method10% MSTAR5% MSTAR
FID(↓)KID(↓)FID(↓)KID(↓)
ACGAN290.04840.4548340.24400.4713
Ours(HLC)263.27890.4146428.33640.6817
Ours(PSC)87.27190.0414130.23110.0861
+ +Table 6. Compare the proposed physics-inspired neural module with Harris-Laplacian corner (HLC) detector. + +strated in Table 6. Detailed analyses of Harris-Laplacian corner detection and our proposed method are provided in S.M. (Section 3). + +Hyperparameter ablation. See S.M. (Section 4) + +# 4.4. Discussions + +Stabilizing GAN training. Figure 3a shows that ACGAN training with only $5\%$ data of MSTAR fails to converge, where the discriminator is likely overfitting to the training set and dominating the training process. As a comparison, our method significantly alleviates it and leads to gradual equilibrium, shown in Figure 3b. + +We demonstrate that with our proposed physical consistency regularization, the generator learns to produce outputs that align more closely with real data from a physical perspective more efficiently. As shown in Figure 4a, the generator of baseline model fails to learn high-quality and stable scattering features given the same conditions. The PSC estimation results given in Figure 4b show that the electromagnetic scattering features are changing during training, demonstrating a large difference with the real physical parameters shown in Figure 4f. In comparison, our method leverages the constraint of physical parameters to guide the generator to learn the crucial scattering centers efficiently and correctly. The regularization between the latent features helps to refine the scattering details of SAR target while maintaining the physical consistency, as demonstrated in Figure 4c and d. + +Utility evaluation. In addition to visual quality assessment using IQA metrics, we evaluate the utility of generated SAR images in real-world applications with the "X-Fake" framework [23]. This framework includes a probabilistic evaluator (Prob-Eva) and a counterfactual explainer (CE) to assess target recognition utility. Prob-Eva, a Bayesian neural net + +![](images/995b732e0d861bb9b6d5d5e8eb126d65a761d254967a9a064234729ed105407b.jpg) +Figure 4. The generated SAR images and their associated PSC model reconstruction results during model training (from $200^{th}$ epoch to $2000^{th}$ epoch). (a) and (c) are the generated SAR images of ACGAN and $\Phi$ -ACGAN, respectively. (b) and (d) are the PSC reconstruction results of (a) and (c), respectively. (e) and (f) are the training image and its PSC reconstruction result. + +![](images/084fa37d098f18c094930e7b826280a9a7381abc83ec8130e40b51c97fada7b3.jpg) +Figure 5. We evaluate the generated SAR images by "X-Fake" [23]. (a) Quantitative metrics reported by the Probabilistic Evaluator (Prob-Eva) of "X-Fake". (b) and (e) are generated images by ACGAN and $\Phi$ -GAN, respectively. (c) and (f) are the counterfactual explanation results of (b) and (e), respectively. "c3/0.476" illustrates the predicted label and uncertainty by Prob-Eva. (d) and (g) are differences between generated SAR images and their counterfactual explanations, where the red contents illustrate the missing details of the generated images. (h) and (i) are real SAR images with the given class and azimuth angle conditions, and their PSC reconstruction results, respectively. + +![](images/78e5110076340830c9eb7c5b02541c2bb7147754616441e7456a94f3c194ecde.jpg) + +![](images/40b1028560819351aa84deca520b95965726cb4f6fd9326bb351d92f9cf8e8a6.jpg) + +![](images/a2f3b9da2ee8c5c8764a3412a053b7588b6aa96ebea9a6206edc22b5fe8a037c.jpg) + +work trained on real SAR images, reports higher accuracy and lower uncertainty for more realistic generated images. Figure 5 shows quantitative results, where our method outperforms the baseline by increasing Prob-Eva accuracy by over $20\%$ and significantly reducing uncertainty. Additional comparisons and the utility analyses on SAR target recognition task are provided in S.M. (Section 5 and 6). + +Physical consistency analysis. Since SAR images are difficult for visual interpretation, we leverage the counterfactual explainer (CE) of "X-Fake" to help us investigate the electromagnetic scattering details of the generated data. CE can generate the counterfactual image with inauthentic details of the input SAR image. As demonstrated in Figure 5, the differences between generated SAR image and CE results are computed as $\Delta$ , where the absent scattering details are highlighted in red. We can compare $\Delta$ with real SAR images and their PSC reconstruction results, showing that the generated images of the baseline model lack more details highlighted by the physical parameters of the real SAR images. The results further prove the advantage of maintaining the physical consistency of our method. + +More analyses. The results of limited data training, encoding more angle conditions, and azimuth angle extrapolation, + +are provided in S.M. Section 7, 8, and 9, respectively. + +# 5. Conclusions + +We propose a physics-inspired regularization method, termed $\Phi$ -GAN, to enhance GAN training for SAR image generation. By integrating the electromagnetic physical model directly into the GAN framework in an end-to-end manner, $\Phi$ -GAN ensures that the generated SAR targets align with established physical principles and prevents the discriminator from overfitting. $\Phi$ -GAN outperforms existing data augmentation and regularization techniques in stabilizing GAN training and improving generalization with limited training samples. It achieves superior results compared to state-of-the-art methods across various GAN models and SAR image datasets. + +Limitation and future work. While advanced methods such as diffusion models and NeRF have shown impressive results with natural images, their application to SAR images is still limited. This work represents an initial effort to incorporate physical models into GANs for SAR image generation. Future research will focus on extending these physical models to more advanced generative techniques. + +Acknowledgments. This work was supported by Natural Science Basic Research Program of Shaanxi (Program No.2025JC-QYXQ-032), Guangdong Basic and Applied Basic Research Foundation 2025A1515011368, National Key Laboratory of Microwave Imaging and the Practice and Innovation Funds for Graduate Students of Northwestern Polytechnical University PF2025069. + +# References + +[1] The Air Force Moving and Stationary Target Recognition Database, 2016. 6 +[2] Mikołaj Binkowski, Danica J Sutherland, Michael Arbel, and Arthur Gretton. Demystifying mmd gans. In International Conference on Learning Representations, 2018. 6 +[3] Changjie Cao, Zongjie Cao, and Zongyong Cui. LDGAN: A Synthetic Aperture Radar Image Generation Method for Automatic Target Recognition. 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We refer to this as Subject-to-Video, which extracts subject elements from reference images and generates subject-consistent videos following textual instructions. We believe that the essence of subject-to-video lies in balancing the dual-modal prompts of text and image, thereby deeply and simultaneously aligning both text and visual content. To this end, we propose Phantom, a unified video generation framework for both single- and multi-subject references. Building on existing text-to-video and image-to-video architectures, we redesign the joint text-image injection model and drive it to learn cross-modal alignment via text-image-video triplet data. The proposed method achieves high-fidelity subject-consistent video generation while addressing issues of image content leakage and multi-subject confusion. Evaluation results indicate that our method outperforms other state-of-the-art closed-source commercial solutions. In particular, we emphasize subject consistency in human generation, covering existing ID-preserving video generation while offering enhanced advantages. + +# 1. Introduction + +The rise of diffusion models [18, 39] is rapidly reshaping the field of generative modeling at an astonishing pace. Among them, the advancements in video generation brought by diffusion models are particularly remarkable. In the visual domain, video generation requires to pay more attention to the continuity and consistency of multiple frames compared to image generation, which poses additional challenges. Inspired by the scaling laws of large language models [37, 52, 59], the focus of video generation has shifted towards investigating foundational large models, similar to + +![](images/5f4d828a97e99ce100183cbbef2c4507791ba92711119784c330e4fbc7b2ea14.jpg) +Figure 1. Relationship in cross-modal video generation tasks. + +Sora [28, 36, 41, 60, 64], which have demonstrated promising visual effects and are paving the way for a new era in Artificial Intelligence Generated Content. + +Currently, foundational video generation models focus mainly on two major tasks: text-to-video[36] and image-to-video [2]. Text-to-video (T2V) leverages language models to understand input text instructions and generate visual content describing the expected characters, movements, and backgrounds. While it allows for creative and imaginative content combinations, it often struggles with generating consistently predictable results due to inherent randomness. On the other hand, image-to-video (I2V) typically provides the first frame of an image along with optional text descriptions to transform a static image into a dynamic video. Although it is more controllable, the content richness is often limited by the strict "copy-paste" [4, 41] nature of the first frame. We term the process of subject-consistent video generation as subject-to-video (S2V) [4, 23, 26, 35], which involves capturing the subject from an image and flexibly generating a video based on text prompts, while combining the diversity and controllability of joint image and text inputs. As shown in Figure 1, its essence lies in balancing + +![](images/aa85a7a76820597614594d65916f05c4ba16721075cc609ee2585846eb37f830.jpg) + +![](images/56df83044e9e05ac95694334825c64e74dd016fde049b43aae208caa657c3101.jpg) + +![](images/9ff47fe6995f7141105ac69254b6caec8c631cb660efb0dbd6144004f216a7bb.jpg) + +![](images/e6b9075a98f78205660d348a105bd743e4224ac13c92a78dad0ced48f481c858.jpg) + +![](images/555e27336715320850d7da09e66b84eb32b9f230d8c09669d2946710651d4998.jpg) + +![](images/60403d28879f0b33bbd7990f0800698567bb69304c47e1b2f3976cd00944c459.jpg) + +![](images/48075b2c9969f3745b88df0279a8dc14aefd885ac66aff31bd158ceb4da35d3d.jpg) + +![](images/321b84bc6594ab476232f1ad1d9ce114bc511207c88234e6463e8da711660de2.jpg) + +![](images/d791ecf5ba105052e8aa9b006582fdb638913fa53427d246a8f0e62346379565.jpg) +Figure 2. Subject-consistent video generation examples using our method, with reference images and corresponding generated video frames (text prompts omitted). The last three rows show multiple reference subjects. + +![](images/d8e1f5d007a2a7bbd5fbf38314ef69dea631bdfe83692766f641c167f36b6185.jpg) + +![](images/a751427ff5071efb2567f0e1c98310b1db70fd92d0cb5db7045c2f9e454549c1.jpg) + +![](images/1b0158e4f32fe270de2150d3aded16a10ef85f73b5a51ad56a6afa48f5a51784.jpg) + +![](images/59bd5ba3fd75e3bad6f0d24f3b3c786a9d491502cf7c8d464dd449339f4b2a26.jpg) + +![](images/424d683898e9bce5f1b9f686ac3d5c07cf7f7d750c16f4d01dca3751b1991925.jpg) + +![](images/8ad80d2acf9fe4568b4d476324b015cbdd86fd8236190c020e6db465584d8b51.jpg) + +![](images/73b4a1c5914a121b58cc1afd80a57cb71a414819546a8c32d513a5780a1f18f1.jpg) + +![](images/440830add1f2bd2bacd550b59c58e0ea7c76707692e59706dd5651131f07dc61.jpg) + +text-image dual-modal prompts, requiring the model to simultaneously align text instructions and image contents. + +However, the research on subject consistency in video generation tasks still lags behind image generation scenarios. As text-to-image (T2I) foundation models [11, 29] have matured, subject-to-image (S2I) has evolved from parameter optimization methods [20, 45] to adapter-based training approaches [21, 61], to unified image editing approaches [5, 15, 58], achieving impressive results (refer to Sec 2.2). The most straightforward way to implement S2V is to combine S2I with I2V, but there are two main limitations. First, S2I has greater difficulty in learning subject consistency compared to S2V, as the S2V training data naturally include multi-view dynamic variations, allowing for better understanding of the subject. Second, transitioning from S2I to I2V can lead to information loss. For instance, when generating a back-to-front view motion, the subject's ID information may be lost because the first frame lacks it, which hinders I2V from maintaining ID consistency (see supple + +mentary material). Therefore, subject-consistent generation requires a specialized video model for unified processing. + +Specifically, the subject-consistent video generation task aims to deeply and simultaneously align the content described in the text and images. To achieve this, we propose a data pipeline for the S2V task, producing training data in the form of text-image-video triplets. Two key issues must be addressed. First, prevent the leakage of image content into the generated video. Some methods [4, 16, 23, 30, 62] sample key frames from a video as image conditions to reconstruct the video, but this allows the model to copy-paste image content, reducing text responsiveness. While some approaches enhance data through transformations [4], they fail to address the rigid properties and overall lighting of the image. We focus on constructing cross-video multi-subject pairs to ensure that subjects exhibit non-rigid deformations and color variations while maintaining content matching. Second, address the issue of confusion arising from multi-subject generation. Specifically, when similar + +![](images/1a9a4726b0ccfaf23bbfecb0d1345915c622e006a8c415e4444822204326652b.jpg) +Figure 3. Data processing pipeline for cross-modal video generation. The process involves filtering, adding captions, detection, and matching stages to extract subjects from video clips and align them with the text prompts, ensuring consistent video generation. + +subjects trigger identical textual descriptions, it can lead to content ambiguity. To resolve this, we emphasized distinct descriptions of the subjects' appearances in the video. The appearances of multiple subjects should be distinguishable and precisely match the contents of the sampled reference images. Furthermore, we build a rephraser to rephrase user prompts to include detailed image descriptions. + +Our model design is based on two primary considerations: (1) How to simply and effectively extend a video foundation model to support S2V capabilities; (2) How to achieve a unified framework for single- and multi-subject consistency generation. Thus, we redesigned the imagetext joint injection model based on pre-trained T2V and I2V models [31] to ensure effective cross-modal learning. Specifically, our method is built on the MMDiT [11] architecture. Referring to [55], full self-attention is replaced with window attention to reduce computational costs. VAE [10] and CLIP [63] are used to encode the reference images, and the encoded results are fed into the video and text branches of MMDiT, respectively. The VAE latent provides low-level detail information, while CLIP offers high-level semantic information. Additionally, we introduced a dynamic information injection strategy during attention calculation, allowing the insertion of one or more reference images without affecting the window size and position encoding [49], achieving a unified model architecture for single- and multi-subject consistent video generation. + +In addition, for the S2V task, we constructed evaluation datasets for portrait IDs, single subjects, and multiple subjects, and developed corresponding evaluation metrics. Since the performance of some open-source reproducible projects [4, 16, 23, 30, 62] has not yet matched that of closed-source commercial solutions [27, 35, 40, 41, 54], our focus is on comparing with commercial methods. Overall, our proposed Phantom has the following contributions: + +Concepts. (1) We are the first to clearly define the subject-to-video (S2V) task and clarify its relationship with + +text-to-video (T2V) and image-to-video (I2V); (2) Phantom offers a feasible path for S2V, focusing on high-quality alignment of both textual and visual content. + +Technology. (1) A new data pipeline constructs cross-modal aligned triplet data, effectively addressing the issues of information leakage and content confusion; (2) Phantom offers a unified framework for generating videos from both single and multiple subject references, utilizing dynamic injection scheme of various conditions at its core. + +Significance. (1) Phantom demonstrates superior generation quality, bridging the gap between academic research and proprietary commercialization; (2) the unified consistency generation paradigm covers subtasks such as ID generation and demonstrates significant advantages, indicating that Phantom-like solutions have broad prospects in scenarios such as the film industry or advertising production. + +# 2. Related Work + +# 2.1. Video foundation model + +Early latent diffusion models (LDM) [43] typically utilized U-Net [44] architectures, such as the open-source Stable Diffusion 1.5 [43]. Temporal modules were later added to these models, evolving them into video generation models like Make-A-Video [48], SVD [2], and Animatediff [13]. The DiT [39] architecture, guided by scaling laws, has led to the development of more vision foundation models. Among these, Stable Diffusion 3 introduced MMDiT [11], a dual-stream DiT architecture, which has been adopted in open-source video generation projects such as CogvideoX [60], HunyuanVideo [28] and SeedVR [55]. + +# 2.2. Subject-consistency image generation + +In recent years, significant progress has been made in subject-consistent generation for image tasks. Optimization-based methods [12, 19, 20, 45, 46] training bind image content with special identifiers for text-to- + +![](images/3c5c6fa69c93a8b047cff4fef0479aa5d8dffb022a26e5aa143ef00d41867106.jpg) +Figure 4. Overview of the Phantom architecture. Triplet data is encoded into latent space at the input head, and after combination, it is processed through modified MMDiT blocks to learn the alignment of different modalities. + +image generation. A notable work in the training and inference paradigm is IP-Adapter [61], which freezes the base model weights while only training additional adapters to achieve subject-consistent generation. This approach is also widely used in tasks requiring facial ID consistency [6, 14, 56]. However, these solutions often rely on CLIP [7] or DINO [38] for extracting image semantics, leading to a trade-off between low-level detail reconstruction and flexible text response. Recent advancements have unified image generation and editing tasks [5, 15, 34, 58], enabling various types of editing tasks within a single model, including subject-consistent generation. Compared to adapter-based approaches, this method deeply learns image-text alignment, fully leveraging foundation models and resolving degradation issues from multiple adapters. + +# 2.3. Subject-consistency video generation + +From recent research developments, the advancement of video generation capabilities and algorithmic innovations tends to lag behind image tasks. Similar to image consistency techniques, Kling [27] has released an optimization-based video generation method for facial ID consistency, which requires uploading multiple videos of the same person for optimization, resulting in significant computational costs. Adapter-based approaches have also been attempted for video ID consistency tasks, such as ID-Animator [16] and ConsisID [62]. However, these works have been validated on small datasets (around 10k), which limits their ability to fully align facial information with text descriptions. Recent works like ConceptMaster [23], MovieWeaver [30], and VideoAlchemist [4] have demonstrated capabilities in generating consistent multi-subject videos in general scenarios. However, there are currently no open-source methods for the S2V task, and commercial software's S2V capabilities [27, 35, 40, 41, 54] re + +main state-of-the-art. Therefore, comparing the performance with commercial closed-source solutions is crucial for evaluating the superiority of the proposed method. + +# 3. Phantom + +This section introduces the specific implementation of Phantom. The first subsection describes how to construct cross-modal alignment training data, emphasizing the creation of cross-pair text-image-video triplets to address the "copy-paste" issue. The second subsection presents the design and considerations of the Phantom architecture, focusing on how single and multiple subject features are dynamically injected into the framework. The third subsection introduces key training settings and inference techniques to ensure the efficient implementation of S2V capabilities. + +# 3.1. Data Pipeline + +To achieve subject-to-video (S2V) generation, we constructed a triplet data structure of text-image-video for cross-modal learning (Figure 3), ensuring that videos are paired with both images and text. First, we sampled long videos from Panda70M [3] and in-house sources. These videos were cut into single-scene segments using AutoShot [65] and PySceneDetect [51], and any clips with low quality, aesthetics, or motion levels were filtered out. Next, we used Gemini [50] to generate captions for the filtered video clips, focusing on describing the subjects' appearance, behavior, and the scene. Further, the LLM [37] is utilized to analyze the caption and extract the subject words with appearance descriptions, which are used as prompts for the VLM [1] to obtain the subject detection boxes of the reference frames. At this point, the descriptions of the subjects in the captions can be exactly aligned with the subject elements detected in the reference images. + +![](images/a893d24aead84027ca4cbb93aa3c34fd7e4776a139b6d3ef3284e303b3651b0e.jpg) +Figure 5. Dynamic injection strategy and attention calculation for single or multiple reference subjects in each MMDiT block. + +Although the reference images and text are aligned, the reference images are taken from specific frames within the videos. These image-video pairs are termed "in-pair" data. Some existing methods [4, 23] use in-pair data to train S2V models, ensuring subject consistency between images and videos. However, high visual similarity might cause the model to disregard text prompts, resulting in generated videos that simply copy-paste the input images. To address this issue, we undertake an additional effort to further establish pairings between cross-video clips. We employ the image embedder [47] of the improved CLIP architecture to score and pair subjects detected across different videos. Pairs with scores that are excessively high (indicating a likelihood of copy-pasting) or too low (indicating different subjects) are eliminated. + +After constructing the cross-paired data pipeline, further segmentation is required based on application scenarios. These primary elements include people, animals, objects, backgrounds, and more. Additionally, interactions between multiple elements can further categorize scenarios, such as multi-person interactions, human-pet interactions, and human-object interactions. By segmenting the data sources according to these application scenarios, we can quantitatively supplement missing data types. For example, virtual try-on applications require specific collections of model images and garment layouts. Ultimately, we obtained cross-pair data on the order of one million, among which the data containing human subjects accounted for the largest proportion. In addition, we also added a portion of paired image data to increase diversity. The data sources are Subject200k [5] and OmniGen [58]. + +# 3.2. Framework + +The Phantom architecture, shown in Figure 4, consists of an untrained input head and a trained MMDiT module. The input head includes a 3D VAE [60] encoder and an LLM [59] inherited from the video foundation model [31, 55], which encode the input video and text, respectively. The vision encoder, critically, comprises both a Variational Autoencoder (VAE) [10] and CLIP [42, 63]. The image features $F_{\mathrm{ref.v}}$ concatenated with the video latents $F_{\mathrm{vid}}$ reuse the 3D VAE to maintain consistency in the visual branch input. Meanwhile, the image CLIP features $F_{\mathrm{ref.c}}$ concatenated with the text features $F_{\mathrm{text}}$ provide high-level semantic information, compensating for the low-level features from the VAE. Feature merging involves dimensional alignment, as detailed below, + +$$ +F _ {T} ^ {l _ {1} + l _ {2}, c} = F _ {\text {t e x t}} ^ {l _ {1}, c} \oplus F _ {\text {r e f . c}} ^ {l _ {2}, c}, \tag {1} +$$ + +$$ +F _ {V} ^ {t + n, h, w, c} = F _ {\mathrm {v i d}} ^ {t, h, w, c} \oplus F _ {\text {r e f . v}} ^ {n, h, w, c}, \tag {2} +$$ + +where $\oplus$ denotes concatenation. The concatenated features $F_{T}$ and $F_{V}$ are fed into the visual and text branches of MMDiT, and the model only separates the injected features during the calculation of attention. + +Specifically, the MMDiT block is based on [31, 55] and improved for reference image input, primarily modifying the Attention [53] block, as shown in Figure 5. First, the $Q_{\mathrm{vid}}$ , $K_{\mathrm{vid}}$ , $V_{\mathrm{vid}}$ features calculated from $F_{\mathrm{vid}}$ are divided into windows of size 9. Then, the $Q_{\mathrm{ref\_v}}$ , $K_{\mathrm{ref\_v}}$ , $V_{\mathrm{ref\_v}}$ features calculated from $F_{\mathrm{ref\_v}}$ are dynamically concatenated to the end of each window, while the in-situ features are sequentially shifted to the start of the next window. This approach maintains the window structure while ensuring interaction between video and subject features within each window, as well as adaptive input for single- or multi-subject. Meanwhile, the $Q_{\mathrm{text}}$ , $K_{\mathrm{text}}$ , $V_{\mathrm{text}}$ features calculated from $F_{\mathrm{text}}$ and the $Q_{\mathrm{ref\_c}}$ , $K_{\mathrm{ref\_c}}$ , $V_{\mathrm{ref\_c}}$ features calculated from $F_{\mathrm{ref\_c}}$ are dynamically concatenated. After collecting all reference information, self-attention is calculated within each + +![](images/b8ebfa187aa20b3e8dfe67744b586c14e8da0a7b32003f62a6fe45f61fa0f4ae.jpg) +Figure 6. Video quality evaluation (left) and user study results for multi-subject consistency (right). + +![](images/5eafe02c2a197e01317628ed5e93b01f738112d16670e820fa3d7fbc4fe94b98.jpg) + +window. Then, the dynamically injected reference image features (including ref_v and ref_c) and the text features within each window are extracted from the output features and averaged. This process ensures that the dimensions of the input and output features within the current block remain consistent, thereby facilitating subsequent block computations. + +# 3.3. Training and inference + +Training setup. We employ rectified flow (RF) [32, 33] to construct the training objective and adjust the noise distribution sampling [11]. RF aims to learn an appropriate flow field, enabling the model to efficiently and high-quality generate meaningful data samples from noise. In the forward process of training, noise is added to clean data $x_0$ to generate $x_{t} = (1 - t)\cdot x_{0} + t\cdot \epsilon$ , where $\epsilon$ is Gaussian noise with the distribution $\mathcal{N}(0,\mathrm{I})$ and $t$ is a randomly sampled step scaled to a value between 0 and 1 based on the total steps $(\mathrm{T} = 1000)$ . The model predicts velocity $v_{t}$ to regress velocity $u_{t} = dx_{t} / dt$ , and $v_{t}$ is represented by, + +$$ +v _ {t} = \mathcal {G} _ {\theta} \left(x _ {t}, t, F _ {T}, F _ {V}\right). \tag {3} +$$ + +Thus, the RF training loss is given by, + +$$ +\mathcal {L} _ {\mathrm {m s e}} = \left\| v _ {t} - u _ {t} \right\| ^ {2}. \tag {4} +$$ + +Notably, $v_{t}$ includes additional (n)-dimensional features at the tail (refer to Eq.2), which does not participate in the loss calculation. The model training is conducted in two phases: the first phase trains for 50k iterations at 256p/480p resolution, and the second phase incorporates mixed 720p data, training for an additional 20k iterations to enhance higher resolution generation capabilities. Additionally, since one of the training objectives of VAE is pixel-level reconstruction, the CLIP features can be overshadowed when trained + +together with VAE features. Therefore, we set a relatively high dropout rate (0.7) for VAE during training to achieve balance. The total computational resources consumed approximately 30,000 GPU-hours on A100. + +Inference settings. Phantom inference can accept 1 to 4 reference images and generate corresponding videos by describing the reference subjects using a given text prompt. Note that generating with more reference subjects may lead to unstable results. To align with the training data, the text prompt used in inference must first be adjusted by a rephraser to ensure it accurately describes the appearance and behavior of each reference subject, avoiding confusion between similar subjects (see supplementary materials). The Euler method is used for sampling over 50 steps, and the classifier-free guidance [17] separates the image and text conditions. The denoised output at each step is given by, + +$$ +\begin{array}{l} x _ {t - 1} = x _ {t - 1} ^ {\ominus} + \omega_ {1} \left(x _ {t - 1} ^ {I} - x _ {t - 1} ^ {\ominus}\right) \tag {5} \\ + \omega_ {2} (x _ {t - 1} ^ {T I} - x _ {t - 1} ^ {I}), \\ \end{array} +$$ + +where $x_{t-1}^{\emptyset}$ is the unconditional denoising output, $x_{t-1}^{I}$ is the image-conditioned denoising output, and $x_{t-1}^{TI}$ is the joint text-image conditioned denoising output. The weights $\omega_{1}$ and $\omega_{2}$ are set to 3 and 7.5, respectively. + +# 4. Experiments + +# 4.1. Evaluation materials + +Phantom can be fine-tuned from any video generation base model [31, 55]. The T2V and I2V pre-training stages are excluded from this evaluation. We focus on assessing the subject consistency generation capability, with additional independent evaluations for face ID-based video generation. Due to the lack of an established benchmark for subject-to + +![](images/7c4b28c9b86f0eff88112adfb906b0709a897ab9734984095ba1158f8475268b.jpg) + +![](images/76488e4b8543e155fc7e5333f92c4be6cc87a2c047c4ad622ef9a1c5655775c0.jpg) +The little white dog is bouncing and running from a distance, with the living room in the background, blinking its eyes and smiling at the camera. + +![](images/2e1253fe0f7086c3b55463a16e45fc2eced5cdd3dfd9a5edb356bb4f8c3a324d.jpg) + +![](images/f0dccc5300d5e91e36e39e3a6c00fbebeac18aa385152a3282e8b395a178d5bd.jpg) +This laptop is hovering in the air and spinning. + +![](images/e5102d067889c53257fb36d33f0be5c63695b74a403b40d8ff69c1d7aa648377.jpg) + +![](images/70028ca6ff3d4aa30f1f02d9456520e0bca810ce3447b6716cf6be1ab71c7a21.jpg) + +![](images/a2049ec6caace1f9e7b6c8922c42f5206f8130cbcbe1ffd9c5932c2a3342aefe.jpg) +A man and a dog are playing frisbee in the park. + +![](images/b3c4788f902ec6ebad3bdcc34cccba873350c859d306d0eeeff95127cee9c413.jpg) + +![](images/4349c5ef08761e000d2ec73549d5d27579b7fb90e6a28f6f967ca71f20a646a3.jpg) +A woman strolls in the park wearing a dress, with a large area of beautiful flowers in the background. + +![](images/6cc5bb0f1578c625d37c93ac3a7d0068587eb5da9cd1843bb19fda7cb73c7547.jpg) + +![](images/98fec108e556f0dde3a8e576ed72846fd0ad6d41dd10e65981e9edee0483afb6.jpg) +A man in a black suit, paired with a white shirt and a dark tie, is walking along a busy city street. He is carrying a steaming cup of coffee in one hand. The street is lined with tall buildings and bustling with people. + +![](images/715a70b0649b4b1557bab4ffe6e0049b5d87ff51ef5fb9d57e068e914e43d6ce.jpg) + +![](images/2b7afb98d5753b90d9d2294df8480c8d1dc5111d0b1e3e9a2f85cd26ff0c14d4.jpg) +A little girl in a green and yellow dinosaur costume is bouncing up and down on the sofa. The living room was bright and the sunlight entered through nearby windows. A warm light emanates from the scene. The walls are painted light blue. +Figure 7. Comparison results showing, from top to bottom, single subject, multi-subject, and facial ID-consistent video generation, with four uniformly sampled frames displayed in each case. + +video, we constructed a specific test set and defined evaluation metrics accordingly. + +We collected 50 reference images from different scenarios, covering humans, animals, products, environments, and clothing. Each reference image is paired with 3 different text prompts. To ensure confidence in each case, each text-image pair is generated with three random seeds, resulting in a total of 450 videos. For scenarios with multiple reference images, we mixed the aforementioned reference images and rewrote the text prompts to obtain a test set of 50 groups. Additionally, considering the unique value of portrait scenarios, we collected an additional 50 portrait reference images, including both celebrities and ordinary individuals, for independent evaluation of ID consistency. + +For the S2V task, the existing available state-of-the-art (SOTA) methods are closed-source commercial tools. Therefore, we evaluated and compared the latest capabilities of the SOTA method with those of the SOTA method. + +ities of Vidu [54], Pika [40], and Kling [27]. For the ID-preserving video generation task, the commercial tool Hailuo [35] demonstrated impressive results. We also evaluated an excellent open-source algorithm ConsisID [62]. + +# 4.2. Quantitative results + +We classify the S2V evaluation metrics into three major categories: video quality, text-video consistency, and subject-video consistency. First, the visualization of video quality is shown in the radar chart on the left side of Figure 6. We selected six metrics provided by VBench [24] for testing and supplemented them with four inner model scores such as structure breakdown score. For text-video consistency, we used ViCLIP [57] to directly calculate the cosine similarity score between the text and the video. For single subject consistency, we uniformly sampled 10 frames from each video and calculated the CLIP [7] and DINO [38] fea + +
MethodsIdentity ConsistencyPrompt Following
FaceSim-Arc ↑FaceSim-Cur ↑FaceSim-glink ↑ViCLIP-T ↑
ConsisID0.5380.4170.47021.76
Hailuo-ID0.5420.5040.55723.31
Phantom-ID0.5810.5290.59024.12
+ +Table 1. Comparison of different methods based on identity consistency and prompt following + +
MethodsSubject ConsistencyPrompt Following
CLIP-I ↑DINO-I ↑CLIP-I-Seg ↑DINO-I-Seg ↑ViCLIP-T ↑
Vidu2.00.7060.5110.7240.54422.78
Pika2.10.6970.4980.7120.53423.05
Kling1.60.7320.5540.7150.56921.62
Phantom-IP0.7140.5230.7310.53823.41
+ +ture Direction Scores with the reference image. Additionally, we used grounded-sam to segment the subject part of the video and calculate the CLIP and DINO scores (excluding scene graphs). For ID consistency, we used three facial recognition models to measure similarity [8, 22]. + +The video quality evaluation results, shown on the left side of Figure 6, indicate that Phantom performs slightly worse [24], while excelling in other metrics. As shown in Table 1 and 2, Phantom leads in overall metrics for subject consistency (Identity Consistency) and prompt following. For multi-subject video generation, due to high error rates in automated subject detection and matching, we conducted a user study. We surveyed 20 users, who rated the methods on a scale of 1 to 3 (1: unusable, 2: usable, 3: satisfactory). The evaluation results, displayed in the bar chart on the right side of Figure 6, show that Phantom's multi-subject performance is comparable to commercial solutions, with some advantages in subject consistency. + +# 4.3. Qualitative results + +We present the comparison results of several typical cases in Figure 7. Each generated video is displayed with four evenly sampled frames, including the first and last frames. The first two rows of Figure 7 respectively show the results of generating single- and multiple subject consistency. It can be seen that Vidu [54] and Phantom exhibit balanced performance in subject consistency, visual effect, and text response. Pika [40] performs poorly in subject consistency. Kling [27] has a notable issue: some cases exhibit characteristics analogous to I2V approaches. For instance, the first frame of character videos almost matches the input reference image, leading to low success rates in virtual try-on scenarios. Additionally, the laptop case shows that the compared methods tend to cause deformations in rigid body movements. The last row of Figure 7 shows the results + +Table 2. Comparison of different methods based on single subject consistency and prompt following. Boldface indicates the highest scores in each column, and underline indicates the second-highest scores. + +
MethodsSubject ConsistencyPrompt FollowingVideo Quality
CLIP-I ↑DINO-I ↑ViCLIP-T ↑Aes score ↑Clarity score ↑
w/o CLIP0.6930.51923.6362.0371.40
w/o VAE0.5120.30222.7948.8270.76
w/ All0.7140.52323.4064.3271.72
+ +Table 3. The ablation experiment results of VAE and CLIP. + +![](images/f4c83e539c10c25ce9c0670f60eb790426084c78b9f5b7c091bc98c838d31339.jpg) +Figure 8. Qualitatively display the ablation of VAE and CLIP. + +of video generation for facial ID preservation. The open-source method ConsisID [62] tends to exhibit motion blur, and has weak text response. Hailuo [35] excels in visual aesthetics, but there is some loss in facial similarity. Our results are balanced across all dimensions, with particular advantage in ID consistency. More qualitative analyses are presented in supplementary materials. + +# 4.4. Ablation study + +Selection of visual encoder. Due to differences in training methods, CLIP aligns image-text pairs and tends to extract semantic information, while VAE aims for lossless reconstruction and focuses on detailed information. As shown in Figure 8, faces generated using only CLIP features are smoother and more refined but show decreased similarity. In contrast, faces generated using VAE features are sharper but may amplify undesirable details, making them contain more artifacts. In general object scenarios, CLIP is inadequate at reproducing details like text and patterns, thus primarily serving to supplement VAE's high-level information. Quantitative results in Table 3 show that combining VAE and CLIP features is more advantageous. Additional ablation studies are given in supplementary materials. + +# 5. Conclusion + +We propose Phantom, a method for subject-consistent video generation that achieves cross-modal alignment through text-image-video triplet learning. 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IKDDiT effectively addresses the challenges of open-vocabulary overlay map generation by integrating pre-trained image-text encoders, diffusion models, and masked transformers. Utilizing advanced text-to-image diffusion and image-text discriminative models, it generates high-fidelity overlay maps across multiple photolithography layers, significantly mitigating overlay misregistration errors and minimizing productivity losses caused by wafer rework. Key innovations include an implicit knowledge distillation framework that refines inter-image alignment by decoupling discriminative and generative tasks via an implicit discriminator, as well as a gated cross-attention mechanism to enhance generative performance. + +Experimental results demonstrate that IKDDiT achieves an optimal trade-off between efficiency and accuracy, providing a scalable, robust solution poised to advance overlay map generation in semiconductor processes. + +# 1. Introduction + +The process of fabricating circuit patterns on silicon wafers in semiconductor manufacturing fundamentally relies on multilayer lithography. This technique involves applying a photoresist coating to the wafer, followed by light projection through a photomask containing the requisite circuit patterns. Chip fabrication often involves over 60 photolithography steps, making precise alignment between circuit layers crucial. Any misalignment can result in defects across the entire wafer [1], and the cumulative effect of overlay misregistration errors (OMEs) makes accurate alignment increasingly critical as more layers are added. + +In recent years, deep learning frameworks, particularly + +convolutional neural networks (CNNs), have been employed for overlay map generation in multilayer photolithography [2], which have demonstrated improved accuracy over traditional probabilistic models and classical machine learning methods [3, 4, 5]. While equipment logs are vital for advanced process control (APC) in semiconductor fabrication [6, 7, 8], their use as primary insights for overlay map generation remains underexplored. This gap exists partly because CNN-based frameworks struggle to capture contextual information in textual data, leading to suboptimal representations. + +Since the advent of the transformer model [9], transformers have become foundational in natural language processing (NLP) [10, 11], computer vision [12], and other domains. However, their application to computer vision tasks in semiconductor manufacturing remains underexplored. While recent studies on overlay map generation [2] have incorporated attention mechanisms with CNNs, we demonstrate that reliance on CNN components is unnecessary. A pure transformer architecture, applied directly to sequences of image patches and equipment log data, achieves robust performance in overlay map generation without convolutional operations. + +This research develops a diffusion transformer (DiT) model [13] for photolithography overlay map generation to reduce OMEs and minimize productivity losses from wafer rework. Using equipment IDs, scanner exposure chuck IDs, reticle IDs, equipment logs, and lithography overlay maps from previous layers (as illustrated in Figure 1), we aim to generate the overlay map for the current lithography layer, mitigating scanner capacity losses due to lot splitting and rework during photolithography pilot runs. + +To accelerate convergence in conventional DiT models, we introduce an implicit knowledge distillation method to improve inter-token alignment within the embedding space. Our DiT employs a teacher-student framework, forming pairs based on diffusion noises governed by the same probability flow ordinary differential equation, as shown in Figure 2. By decoupling the encoder and decoder, we handle discriminative and generative tasks independently. The implicit discriminator $D_{\emptyset}$ evaluates the alignment between embedding tokens from the student and teacher encoders, enabling the student model to leverage both the diffusion process and the learnable implicit prior. This combination achieves an optimal balance between training efficiency and generative performance in overlay map generation. The main contributions of this paper are: + +(1) Implicit Knowledge Distillation. We introduce a teacher-student framework with implicit knowledge distillation to improve inter-image alignment. An implicit discriminator aligns embedding tokens from the student and teacher encoders, optimizing both training efficiency and inference performance. + +(2) Unified Contrastive Embedding. We employ + +unified contrastive learning to handle text and label inputs in IKDDiT, enabling more effective representation of equipment logs and IDs in overlay map generation. + +(3) Gated Cross-Attention. We introduce a novel gated cross-attention mechanism in the DiT encoder, enhancing the model's ability to capture complex relationships and improving generation performance in semiconductor manufacturing processes. + +# 2. Related Work + +Photolithography OMEs are managed using dedicated targets in the scribing line and corrected by photolithography scanners via APC systems, which adjust exposure parameters based on prior layer data [14]. However, high spatial frequency often limits traditional correction methods like intrafield high-order controls from meeting overlay specifications. Chue et al. [15] highlighted the importance of spatial coverage and symmetry for reducing correctable OMEs, while Chien et al. [3] and Koay et al. [4] proposed OMEs prediction methods suitable for limited samples. + +Generative AI was first introduced to overlay map prediction by Hsiao and Wang [2], who proposed GAGAN, a self-attention-based generative adversarial network designed to predict OMEs using data from previous layers. While effective, it lacks integration of equipment logs due to CNNs' inherent difficulty in processing textual information and capturing contextual dependencies. In contrast, our proposed IKDDiT leverages a pure transformer architecture to process sequences of image patches from overlay maps and text tokens from equipment logs, showing strong performance without convolutional components. + +With transformers leading in both NLP [9] and computer vision [12], masked training has become common in representation learning [16, 17] and generative modeling [18, 19]. Masked Autoencoder (MAE) [16], for example, predicts continuous tokens directly, improving training efficiency and reducing memory use. Building on this, our work applies masking within DiT to enhance diffusion model training. Recent studies have merged masked training with diffusion models. Wei et al. [20] proposed DiffMAE, using masked autoencoders to denoise patches with varying Gaussian noise levels. Gao et al. [21] introduced MDT, which adds a masked training objective to DiT loss for improved generative performance. Zheng et al. [22] presented MaskDiT, combining generative diffusion with a mask reconstruction task for joint encoder-decoder optimization. + +Unlike prior mask strategies focusing on intra-image learning, IKDDiT introduces self-supervised implicit discrimination through inter-token alignment, integrating generative diffusion with mask reconstruction for joint optimization of the DiT encoder and decoder. + +![](images/ced5a902d0c9bd7e9eacac194fc7f585f3dfee3e43c477205b0eeb3e36e17470.jpg) +Figure 2: Architecture of the IKDDiT, which utilizes pre-trained text encoder $\mathcal{E}_{\varphi_t}$ and image encoder $\mathcal{E}_{\varphi_i}$ , developed through unified contrastive learning, to generate conditional tokens. These tokens are then processed through the teacher and student DiT encoders to perform a self-supervised discriminative process using $D_{\emptyset}$ within the joint embedding space. + +# 3. Method + +# 3.1. Proposed Architecture + +The motivation behind IKDDiT is to leverage self-supervision to enhance DiT training efficiency. As shown in Figure 2, IKDDiT employs a teacher-student framework utilizing masked modeling for implicit knowledge distillation. We apply DiT in the latent embedding space, using a mask $M$ to partition the noisy student input into visible and invisible patches. A pre-trained image-text discriminative model extracts representations of equipment IDs, scanner exposure chuck IDs, reticle IDs, equipment logs, and overlay maps from previous lithography layers. These serve as conditional inputs for both the teacher and student DiT encoders and the student DiT decoder. + +The student DiT encoder compresses visible patches into latent representations $z_{s}$ , which undergo self-supervised learning via an implicit discriminator $D_{\emptyset}$ . This aligns zs with the unmasked latent representations $z_{t}$ from the teacher DiT encoder, enabling the student to learn from the teacher and align their latent spaces. Finally, the student DiT decoder denoises the visible patches and reconstructs the invisible ones. The model is trained to predict scores for unmasked patches and reconstruct masked patches. During inference, all patches are processed for sampling. The following subsections will elaborate on each aspect. + +# 3.2. Latent Masking Strategy + +Building upon the Latent Diffusion Model [23], IKDDiT operates in latent space to reduce computational overhead. Gaussian noise is added to the latent embedding $z$ of an image, which is then partitioned into $p \times p$ tokens, forming a matrix $m \in \mathbb{R}^{c \times N}$ , where $c$ is the number of channels and $N$ is the total number of tokens [13]. A random ratio $r$ of tokens is masked to create $\widehat{m} \in \mathbb{R}^{c \times \widehat{N}}$ , with $\widehat{N} = rN$ . A binary mask $M \in \mathbb{R}^N$ indicates masked (ones) and unmasked (zeros) tokens. The remaining tokens $\widehat{m}$ are fed into the diffusion model. By focusing on visible tokens, IKDDiT prioritizes semantic learning over token reconstruction, outperforming methods that replace masked tokens with learnable tokens and significantly reducing training costs. + +# 3.3. Text and Image Embedding + +In IKDDiT, we train an image-text discriminative model using unified contrastive learning [24], which integrates visual, textual, and categorical data into a unified embedding space. Unlike traditional contrastive learning that focuses on pairwise relationships, this approach aligns semantic information across images, text descriptions (e.g., equipment logs), and categorical labels (e.g., equipment, scanner exposure chuck, reticle IDs) simultaneously. This comprehensive multimodal representation is essential for + +downstream tasks like overlay map generation. + +The architecture of our image-text discriminative model is shown in Figure 3, where equipment IDs, Mask IDs, and equipment logs are fed into a text encoder $\mathcal{E}_{\varphi_t}$ , generating embeddings $\mathcal{T} \in \mathbb{R}^{d_t \times n}$ , while the overlay map is processed by an image encoder $\mathcal{E}_{\varphi_i}$ , generating embeddings $\mathcal{I} \in \mathbb{R}^{d_i \times n}$ . These embeddings are further combined into a joint embedding $\mathcal{I}^{\top} \mathcal{T} \in \mathbb{R}^{n \times n}$ , achieving semantic integration of multimodal data. In this unified embedding space, we employ two contrastive loss functions to promote multimodal alignment. First, the image-to-text contrastive loss $\mathcal{L}_{i2t}$ aims to maximize the similarity between matched image and text pairs while minimizing the similarity of non-matching pairs: + +$$ +\mathcal {L} _ {i 2 t} = - \sum_ {i \in \mathcal {B}} \frac {1}{| \mathcal {P} (i) |} \sum_ {k \in \mathcal {P} (i)} \log \left(\frac {\exp (\tau u _ {i} ^ {T} v _ {k})}{\sum_ {j \in \mathcal {B}} \exp (\tau u _ {i} ^ {T} v _ {j})}\right) \tag {1} +$$ + +where $\mathcal{B}$ represents the current batch; $\mathcal{P}(i)$ is the set of indices of texts matched with image $i$ , $u_{i}$ , and $v_{k}$ are the embedding vectors of images and texts, respectively; $\tau$ is the temperature coefficient. + +Second, the text-to-image contrastive loss $\mathcal{L}_{t2i}$ aligns texts with corresponding images: + +$$ +\mathcal {L} _ {t 2 i} = - \sum_ {j \in \mathcal {B}} \frac {1}{| \mathcal {P} (j) |} \sum_ {k \in \mathcal {P} (j)} \log \left(\frac {\exp (\tau u _ {k} ^ {T} v _ {j})}{\sum_ {i \in \mathcal {B}} \exp (\tau u _ {i} ^ {T} v _ {j})}\right) \qquad (2) +$$ + +where $\mathcal{P}(j)$ is the set of indices of images matched with text $j$ . These two losses enhance multimodal alignment within the embedding space, improving the accuracy of downstream tasks like overlay map generation. By integrating the pre-trained image and text encoders into IKDDiT, we extract features from previous overlay maps, equipment logs, and IDs. This integration enables more accurate and efficient feature representation, further boosting the generative performance of IKDDiT. + +# 3.4. Teacher and Student DiT Encoder + +The teacher and student DiT encoders, $\varepsilon_{\theta_t}$ and $\varepsilon_{\theta_s}$ , comprise multiple Gated Cross-Attention DiT Blocks that integrate self-attention and cross-attention layers for semantic alignment and multimodal fusion, as illustrated in Figure 4. Each block includes Multi-Head Cross Attention, tanh Gating, Feedforward Layers, Multi-Head Self-Attention, and Pointwise Feedforward layers. In this architecture, visual embeddings of visible patches serve as queries $(Q)$ , while conditional embeddings from the text encoder act as keys $(K)$ and values $(V)$ . The Multi-Head Cross Attention module establishes cross-modal alignment, and the tanh gating mechanism [25] refines cross-modal signals by multiplying the output with $\tanh(\alpha)$ , where $\alpha$ is a learnable scalar initialized to zero [26]. This ensures consistent results between vision and condition tokens at initialization, enhancing semantic transfer and training + +![](images/13eb870c36af6a5387127d7c2cebf35640a49a423afe0768474b6d36daf8f1c0.jpg) +Figure 3: The embedding process in unified contrastive learning. These embeddings are subsequently integrated into a unified joint embedding space $\mathcal{I}^{\mathrm{T}}\mathcal{T}$ , enabling effective multimodal alignment. + +stability. After the feedforward layer, the output passes through the Multi-Head Self-Attention module for further feature extraction, followed by the Pointwise Feedforward layer to strengthen the final representation. By alternating between Gated Cross-Attention and Self-Attention modules, this design achieves deep multimodal integration, effectively improving IKDDiT's generative performance. + +# 3.5. Student DiT Decoder + +We enhance MaskDiT [22] by integrating it with the MAE [16] architecture to form the student DiT Decoder $\mathcal{G}_{\theta_s}$ (see Figure 2). To improve flexibility and multimodal fusion, we incorporate Adaptive Layer Normalization blocks [13] that conditionally process embeddings from text, labels, and images. Unlike the student DiT encoder, which processes only visible patches to generate tokens $z_{s}$ , the student decoder handles the complete set of tokens $z_{h}$ . + +After encoding, the student decoder transforms the sequence of image tokens into outputs for noise and diagonal covariance prediction, both matching the shape of the original input. We use a standard linear decoder that, after final layer normalization, linearly maps each token to a $p \times p \times 2C$ tensor, where $C$ is the number of channels in the original input. These decoded tokens are rearranged to reconstruct the initial spatial layout, yielding the predicted noise and covariance outputs. + +# 3.6. Implicit Knowledge Distillation + +In IKDDiT, implicit knowledge distillation promotes semantic alignment in the embedding space through a self-supervised teacher-student framework. Student and teacher embeddings are input into an implicit discriminator $D_{\emptyset}$ , which evaluates whether the student embeddings align closely enough with the teacher embeddings to allow the student encoder to effectively replicate the teacher's representations. This alignment is driven by a combined loss function incorporating InfoNCE loss [27] and discriminator loss, defined as: + +$$ +\mathcal {L} _ {\mathcal {D}} = \mathcal {L} _ {\text {I n f o N C E}} + \lambda_ {\text {d i s t}} \mathcal {L} _ {\text {d i s t}} \tag {3} +$$ + +![](images/78316dab2c1435134c2e84d7cf444e2be847034fab90ffe4b24c7934c459000c.jpg) +Figure 4: Architecture of the teacher and student DiT encoders, incorporating Gated Cross-Attention DiT blocks (highlighted in light blue). + +where $\lambda_{dist}$ modulates the influence of $\mathcal{L}_{dist}$ within $\mathcal{L}_{\mathcal{D}}$ . InfoNCE loss maximizes the similarity between each student embedding $z_{s}$ and its paired teacher embedding $z_{t}$ , while minimizing similarity with other teacher embeddings: + +$$ +\mathcal {L} _ {\text {I n f o N C E}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log \left(\frac {\exp \left(\frac {Z _ {s} ^ {i} , Z _ {t} ^ {i}}{\tau}\right)}{\sum_ {j = 1} ^ {N} \exp \left(\frac {Z _ {s} ^ {i} , Z _ {t} ^ {j}}{\tau}\right)}\right) \tag {4} +$$ + +where $\tau$ is the temperature parameter adjusting similarity sharpness. The discriminator loss is defined as: + +$$ +\mathcal {L} _ {d i s c} = - \mathbb {E} _ {z _ {t}} [ \log D _ {\emptyset} (z _ {t}) ] - \mathbb {E} _ {z _ {s}} [ \log (1 - D _ {\emptyset} (z _ {s})) ] \tag {5} +$$ + +where $D_{\emptyset}(z_t)$ represents the discriminator's prediction of the teacher embedding as real, ideally close to 1, and $D_{\emptyset}(z_s)$ reflects its prediction of the student embedding as generated, ideally close to 0. + +This combined loss $\mathcal{L}_{\mathcal{D}}$ ensures that student embeddings are semantically aligned with the teacher embeddings. + +# 3.7. Training Object + +In training IKDDiT, we decompose the learning process into three parts: (1) score estimation on unmasked tokens, (2) auxiliary reconstruction on masked tokens, and (3) alignment between student and teacher embeddings using the discriminator loss. First, we perform score estimation on unmasked tokens, similar to typical diffusion models, to ensure the model learns meaningful representations of visible patches. The denoising score matching loss on these unmasked tokens is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {D S M} = \mathbb {E} _ {x _ {0} \sim P _ {d a t a}} \mathbb {E} _ {m} | | (M _ {\theta} ((x _ {0} + n) \odot (1 - m), t) \\ - x _ {0}) \odot (1 - m) | | ^ {2} \tag {6} \\ \end{array} +$$ + +where $m$ is a binary mask (1 for unmasked tokens and 0 for masked tokens); $x_0 + n$ represents the diffused image with added noise $n$ ; $M_{\theta}$ processes unmasked tokens using element-wise multiplication $\odot$ , ensuring only unmasked tokens are considered. + +The second part of the training objective involves the reconstruction of masked tokens, which is treated as a mean squared error loss. This auxiliary MAE reconstruction loss promotes a global understanding of the full diffused image, thereby preventing overfitting to visible patches. The reconstruction loss is formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {M A E} = \mathbb {E} _ {x _ {0} \sim P _ {d a t a}} \mathbb {E} _ {m} | | (M _ {\theta} ((x _ {0} + n) \odot (1 - m), t) \\ - \left(x _ {0} + n\right)) \odot m \| ^ {2} \tag {7} \\ \end{array} +$$ + +where the goal is to reconstruct the pixel values for masked patches, encouraging the model to develop a comprehensive understanding of the entire diffused image. + +The third part, the discriminator loss $\mathcal{L}_{\mathcal{D}}$ , aligns student and teacher embeddings, enhancing semantic consistency between them. The final training objective combines these three components, balanced through specific hyperparameters: + +$$ +\mathcal {L} _ {I K D D i T} = \mathcal {L} _ {D S M} + \lambda_ {1} \mathcal {L} _ {M A E} + \lambda_ {2} \mathcal {L} _ {\mathcal {D}} \tag {8} +$$ + +where $\lambda_{1}$ controls the influence of the MAE reconstruction loss, and $\lambda_{2}$ adjusts the weight of the discriminator loss during training. This composite objective ensures the model learns to generate accurate token representations, reconstruct masked tokens, and align student embeddings with teacher embeddings, enhancing semantic consistency and improving performance in overlay map generation. + +# 4. Results + +# 4.1. Implementation + +Model Settings. Our approach builds on the DiT [13] framework, utilizing a latent diffusion model that first trains an autoencoder to map images into a latent space, followed by a diffusion model on these latent variables. Specifically, we pre-train a Variational Autoencoder [28] with an $8 \times$ downsampling factor, reducing a $512 \times 512 \times 3$ image to a $64 \times 64 \times 4$ latent representation. Both the student DiT encoder $\mathcal{E}_{\theta_s}$ and teacher encoder $\mathcal{E}_{\theta_t}$ use IKDDiT-S/B/LX model variants with a patch size of 2, while the student decoder $\mathcal{G}_{\theta_s}$ comprises 8 DiT blocks, inspired by MAE. Table 1 summarizes the parameters and training costs for different IKDDiT scales. We implement $N$ Gated Cross-Attention DiT blocks with a hidden dimension $d$ , scaling $N$ , $d$ , and the number of attention heads $H$ jointly to optimize performance and efficiency. These configurations, ranging from 3.7 to 73.9 GFLOPs, enable thorough assessment of scaling performance. + +Table 1: IKDDiT model configurations. + +
SizeLayers NHidden Size dHeads HParam. (M)FLOSSs (G)
IKDDiT-S12384619.43.7
IKDDiT-B127681281.614.3
IKDDiT-XL28115216417.973.9
+ +Datasets. To evaluate our model, we use the Multimodality Photolithography Overlay Map (MPOM) dataset, a comprehensive, real-world multimodal dataset from the semiconductor industry. MPOM includes photolithography overlay maps (images), equipment logs (text) with 5,781 unique tokens and a total size of 152 GB, and categorical data such as equipment IDs, scanner exposure chuck IDs, and reticle IDs. This dataset serves as a robust basis for validating method's effectiveness. + +Training Details. IKDDiT models are trained with the AdamW optimizer [29] using a batch size of 64 on the MPOM dataset at $512 \times 512$ resolution. Training follows DiT's setup, capped at 1000 iterations, with a linear variance schedule from $10^{-4}$ to $2 \times 10^{-2}$ . The mask ratio for the student view is 0.5, while the teacher view remains unmasked. We use random resized cropping for data augmentation. + +Evaluation Metrics. Aligned with DiT [13], we use Fréchet Inception Distance (FID) [30] as the primary metric to guide design choices, given its widespread use for evaluating diversity and quality in generative models. For consistency, FID is calculated using the ADM TensorFlow suite [31] with identical reference statistics. We also report Inception Score (IS) [32], sFID [33], and Precision/Recall [34] for comprehensive comparison, noting that lower FID and sFID scores are better, while higher IS and Precision/Recall values are preferred. + +# 4.2. Training efficiency + +To assess the convergence of our IKDDiT model, we compare FID scores at different training stages with top baseline models. All models, in XL size, are trained with a batch size of 64 up to 578.1k iterations. As depicted in Figure 5, IKDDiT demonstrates consistently faster convergence. As shown in Table 2, it attains an FID of 6.8 at 500k iterations, surpassing other models. At 250k iterations, IKDDiT achieves an FID of 11.6, outperforming DiT [13], MDT [21], and MaskDiT [22], which reach FID scores of 14.1, 12.2, and 11.9, respectively, at 500k iterations. This demonstrates that IKDDiT converges nearly twice as fast, highlighting the efficiency of self-supervised discrimination in DiT training. + +![](images/53e29ff4fe2064701ac813c5e46d9623578145eb4e26f9c087e43db58ab0448a.jpg) +Figure 5: Comparison of training convergence with SOTA. + +Table 2: Training performance at each iteration. + +
Iterations (k)DiTMDTMaskDiTSD-DiTIKDDiT
25033.125.824.421.911.6
30024.319.419.016.29.3
35018.916.716.013.78.3
40016.614.413.911.57.8
45015.313.212.810.17.1
50014.112.211.99.56.8
+ +# 4.3. Scalability + +To evaluate the scalability of our proposed IKDDiT model, we trained nine model configurations, varying both model size (S, B, XL) and patch size (8, 4, 2). Figure 6 presents the GFLOPs and corresponding FID scores for each configuration after 500k training iterations. Our results demonstrate a clear trend: as model size increases and patch size decreases, diffusion model performance improves significantly. + +# 4.4. Comparison with State-of-the-Art + +We compare against state-of-the-art DiT models in Table 3, where "-G" denotes the classifier-free guidance (CFG). For a fair comparison, all models are evaluated in their XL size, and test results are obtained after 578.1k + +![](images/230e14c7345b39ce0999f85d0baa22194c22f9a5aaaee91dcfbee0a8d19a6811.jpg) +Figure 6: Overlay map generation performance of IKDDiT models at 500K iterations. The bubble size represents GFLOPs, with lower FID-500K indicating better generative performance. + +training iterations with a batch size of 64. The results indicate that IKDDiT outperforms these baselines across a majority of metrics. Specifically, IKDDiT achieves the lowest FID and sFID scores, both with and without CFG, signifying superior fidelity and closer alignment with true data distributions. Additionally, IKDDiT records the highest IS at 197.39 in the standard setting and 189.00 with CFG, demonstrating the model's strong capacity for producing high-quality, diverse overlay map outputs. + +IKDDiT also surpasses other models in Precision, underscoring its ability to generate highly accurate outputs. Although it ranks second in Recall under the CFG setting, slightly behind MDT-G, this minor variance in recall is compensated by IKDDiT's consistency across other metrics, showcasing its robust performance. These findings collectively illustrate IKDDiT's scalability and effectiveness in multimodal integration, confirming its capability to handle the nuanced requirements of overlay map generation with both quality and efficiency. + +# 4.5. Comparison with existing methods + +Table 4 compares the performance of IKDDiT with existing methods. The Pilot Run approach processes a small batch of wafers through lithography equipment, followed by overlay measurements. Then, the APC system averages this limited data to estimate the overlay map for an entire lot of 25 wafers, yielding an overlay misregistration error (OME) rate of $6.8\%$ . In contrast, GAGAN [2], which bases its predictions on previous layer overlay maps, has a higher OME error rate of $9.2\%$ due to the lack of equipment logs, which restrict access to crucial operational parameters and machine-specific information for each lithography layer. IKDDiT, leveraging comprehensive machine insights, achieves the lowest + +OME rate of $3.2\%$ , the largest lot size (24.1), and the least lithography scanner loss $(2.3\%)$ . These results highlight IKDDiT's ability to minimize overlay misregistration errors and productivity losses. + +# 4.6. Visualization + +Figure 7 presents a comparative visualization of overlay maps generated by IKDDiT and state-of-the-art masked DiT models. The left side of the figure specifies the sample conditions, including equipment IDs, scanner exposure chuck IDs, reticle IDs, and equipment logs. Due to space constraints, only log IDs are presented here, with complete details available in Appendix I. The right side displays generated samples from MDT, MaskDiT, SD-DiT, and our proposed IKDDiT, alongside the ground truth collected from real pilot run data. IKDDiT consistently produces samples that closely match the ground truth, highlighting its precision in capturing the critical details required for accurate photolithography overlay map generation. + +Figure 8 illustrates representative samples of overlay map generation with the condition of equipment logs achieved by our proposed IKDDiT model. The equipment logs capture key operational parameters and adjustments across various stages, enriching the model's contextual understanding and enabling it to synthesize overlay maps that reflect specific equipment configurations and conditions. + +Table 3: Quantitative comparison on MPOM. We highlight the top 3 results in each column as Top 1, Top 2 and Top 3. + +
ModelFIDsFIDISPrecisionRecall
DiT [13]13.379.57135.960.690.58
MDT [21]10.419.75133.460.710.64
MaskDiT [22]11.129.13124.600.740.61
SD-DiT [35]8.956.10177.480.730.54
IKDDiT6.645.24197.390.810.62
DiT-G [13]5.4011.27121.070.700.65
MDT-G [21]4.6111.66126.950.710.63
MaskDiT-G [22]4.4910.93117.100.740.64
SD-DiT-G [35]3.618.80159.350.720.60
IKDDiT-G2.686.12189.000.760.67
+ +Table 4: Comparison of performance with existing methods. Lot Size and Scanner Loss are estimated through simulation. + +
Predict MethodOverlay Misregistration Error Rate# Rework (per lot)Lot Size (per lot)Scanner Lost
Pilot Run6.8%3.716.39.1%
GAGAN [2]9.2%2.321.93.8%
IKDDiT-G3.2%0.824.12.3%
+ +![](images/09e9a7221e6081352a8df15c207e230f1059b4d1fd606f2f9193ace00c7e4608.jpg) +Figure 7. Comparison of overlay maps generated by IKDDiT and baseline masked diffusion transformer models. + +# 4.7. Ablation Study + +We conducted a comprehensive ablation study to evaluate the impact of key model configurations and parameters on our proposed method. Experiments were performed using the XL model configuration with default training settings, employing FID as the primary evaluation metric. To expedite assessments, we reduced training iterations to 150k. For additional experimental results, please refer to Appendix G. + +Image-Text Encoder and Attention Mechanisms. Table 5 demonstrates that the integration of our Gated Cross-Attention mechanism with Unified Contrastive Embedding (UCE) yields the best FID score of 24.66, outperforming alternative setups and validating the efficacy of our approach in enhancing generation quality. + +Discriminative Objective. Table 6 highlights the effectiveness of the Implicit Discriminator, which markedly surpasses the self-supervised discrimination approach [35], demonstrating a clear advantage in enhancing the quality of the generated outputs. + +Mask Ratio. Table 7 shows the impact of varying mask ratios on model performance. The FID-15k score improves as the mask ratio increases from $0\%$ to $50\%$ , with the best result achieved at a $50\%$ mask ratio. However, further increasing the mask ratio to $70\%$ leads to a substantial degradation in performance, indicating an optimal balance is achieved at the $50\%$ mask ratio. + +Reconstruction and Discriminator. Table 8 reveals that the optimal FID of 24.66 is achieved with $\lambda_{1} = 0.1$ and $\lambda_{2} = 0.01$ , highlighting the importance of a balanced emphasis on both reconstruction and discriminator losses. Higher values for $\lambda_{1}$ or $\lambda_{2}$ increase FID, suggesting that overemphasis on either objective can hinder performance. + +![](images/3b999231f85dc38ba1a49e72e19bd0fdbd49290992a530453d4ee7381ab2ee0b.jpg) +Figure 8: Overlay maps generated by IKDDiT, conditioned on equipment IDs, chuck IDs, reticle IDs, and equipment logs. + +Table 5: Ablation study on the Image-Text encoder and attention. + +
Multi-head Cross-AttentionAdaptive Normal. LayersGated Cross-Attention
CLIP [36]60.7045.7730.34
UCE [24]49.8337.4224.66
+ +Table 6: Ablation study on the discriminative objective. + +
Discriminative ObjectiveFID-15k
Self-supervised Discrimination [35]30.39
Implicit Discriminator24.66
+ +Table 7: Ablation study on the mask ratio. + +
Mask Ratio0%25%50%70%
FID-15k27.4626.0624.66123.85
+ +Table 8: Ablation study on the reconstruction and discriminator. + +
Hyper.λ1=0λ1=0.01λ1=0.1λ1=1
λ2=042.3747.1729.7233.44
λ2=0.0135.0738.5824.6627.33
λ2=0.140.6745.2129.3532.30
λ2=145.9450.5432.3035.80
+ +# 5. Conclusion + +This paper introduces a novel framework that integrates implicit knowledge distillation with diffusion modeling to advance overlay map generation in semiconductor manufacturing. Experimental results validate the effectiveness of our approach, delivering high-quality outputs with scalable performance. This method represents a significant advancement in generative modeling for open-vocabulary overlay generation, offering promising applications across the semiconductor industry. + +# Acknowledgment + +This work was supported by the National Science and Technology Council (NSTC), Taiwan, under Grant No. 114-2218-E-A49-026. 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Battaglia, "Generating images with sparse representations", arXiv preprint arXiv:2103.03841, 2021.6. +[34] Tuomas Kynk“a”anniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila, "Improved precision and recall metric for assessing generative models", Advances in Neural Information Processing Systems (NeurIPS), 2019. 6. +[35] Rui Zhu, Yingwei Pan, Yehao Li, Ting Yao, Zhenglong Sun, Tao Mei, and Chang Wen Chen, "SD-DiT: Unleashing the power of self-supervised discrimination in diffusion transformer", IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 7, 8. +[36] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever, "Learning transferable visual models from natural language supervision", arXiv preprint arXiv:2103.00020, 2021.8. \ No newline at end of file diff --git a/ICCV/2025/Photolithography Overlay Map Generation with 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0000000000000000000000000000000000000000..928f6103676ef8f9c6530ba2ddb2421e728be0cd --- /dev/null +++ b/ICCV/2025/PhysRig_ Differentiable Physics-Based Skinning and Rigging Framework for Realistic Articulated Object Modeling/full.md @@ -0,0 +1,349 @@ +# PhysRig: Differentiable Physics-Based Skinning and Rigging Framework for Realistic Articulated Object Modeling + +Hao Zhang $^{1*}$ Haolan Xu $^{1*}$ Chun Feng $^{1}$ Varun Jampani $^{2}$ Narendra Ahuja $^{1}$ $^{1}$ University of Illinois Urbana Champaign Stability AI + +haoz19@illinois.edu jamesdemon923@gmail.com chunf2@illinois.edu + +varunjampani@gmail.com n-ahuja@illinois.edu + +![](images/0dbffbe2b4ce8b71fb96a1db9e85d8651a2f2ee76186ca371d211753f6ca77f4.jpg) +Figure 1. PhysRig is a differentiable physics-based skinning approach that models objects as soft-body volumes driven by embedded driving points, enabling realistic deformations and capturing complex dynamics across diverse topologies and motions—from humanoids to dinosaurs and flying creatures. + +# Abstract + +Skinning and rigging are fundamental components in animation, articulated object reconstruction, motion transfer, and 4D generation. Existing approaches predominantly rely on Linear Blend Skinning (LBS), due to its simplicity and differentiability. However, LBS introduces artifacts such as volume loss and unnatural deformations, and it fails to model elastic materials like soft tissues, fur, and flexible appendages (e.g., elephant trunks, ears, and fatty tissues). In this work, we propose PhysRig: a differentiable physics-based skinning and rigging framework that overcomes these limitations by embedding the rigid skeleton into a volumetric representation (e.g., a tetrahedral mesh), which is simulated as a deformable soft-body structure driven by the animated skeleton. Our method leverages continuum mechanics and discretizes the object as particles embedded in an Eulerian background grid to ensure differentiability with respect to both material properties and skeletal motion. Additionally, we introduce material prototypes, significantly reducing the learning space while maintaining high expressiveness. To evaluate our framework, we construct a compre + +hensive synthetic dataset using meshes from Objverse [5], The Amazing Animals Zoo [35], and MixaMo [1], covering diverse object categories and motion patterns. Our method consistently outperforms traditional LBS-based approaches, generating more realistic and physically plausible results. Furthermore, we demonstrate the applicability of our framework in the pose transfer task highlighting its versatility for articulated object modeling. This project is available at https://physrig.github.io/. + +# 1. Introduction + +Skinning and rigging are essential for animating articulated objects and play a critical role in numerous applications, including character animation, motion retargeting, 4D reconstruction, and generative modeling. Among existing approaches, Linear Blend Skinning (LBS) remains the dominant method due to its efficiency and differentiability. However, LBS suffers from severe limitations, including unnatural distortions (e.g., collapsing joints, candy-wrapper artifacts, and volume shrinkage) and an inability to capture the behavior of elastic materials. These artifacts become especially problematic when modeling characters with highly deformable + +regions, such as an elephant's trunk, a human's soft tissue, or flexible appendages. + +To address these shortcomings, we introduce a differentiable physics-based skinning and rigging framework that models articulated object deformation as a volumetric simulation problem. Instead of directly mapping vertices to rigid skeleton transformations, we embed the skeleton into a deformable soft-body volume (e.g., bounded by a set of Gaussians and tetrahedral meshes), which is driven by skeletal motion while respecting fundamental physical principles. In particular, we leverage continuum mechanics and the material point method to establish a fully differentiable deformation process, ensuring that both the material properties and skeletal motion are incorporated in a physically consistent manner. Unlike LBS, which applies simple linear blending, our approach captures intricate material behaviors by modeling stress-strain relationships and dynamic responses to skeletal forces, allowing us to achieve more realistic and physics-driven deformations. + +A major challenge encountered with these physics-based methods is a large number of material parameters and complex particle interactions, which makes optimization challenging. To overcome this, we introduce material prototypes, a vocabulary of primitives that can be combined to represent all material properties, and span common deformation behaviors of articulated objects. This novel approach significantly reduces the learning space while maintaining expressiveness. It provides a structured way to interpolate material properties across different object types, enabling more efficient learning while preserving the diversity of real-world material responses. + +Evaluating physics-based skinning models is challenging due to the lack of suitable benchmark datasets. Existing datasets are primarily built via LBS-based deformations and lack sufficient variation in material properties and deformation types. To address this gap, we construct a comprehensive synthetic dataset incorporating meshes from Objaverse [5], The Amazing Animals Zoo [35], and MixaMo [1], covering a diverse range of objects, motion patterns, and material properties. Using this dataset, we demonstrate that our method outperforms LBS-based approaches, producing more realistic deformations across a variety of articulated objects. Additionally, we showcase the effectiveness of our framework in downstream tasks such as pose transfer and 4D object generation, illustrating its broad applicability. Our key contributions can be summarized as follows: + +- A differentiable physics-based skinning/rigging framework, leveraging continuum mechanics to enable realistic and physically plausible deformations while remaining differentiable. +- A novel material prototype formulation, which reduces the learning complexity by introducing a structured interpolation approach while maintaining high material expres + +siveness. + +- A novel synthetic dataset for evaluating physics-based skinning models, demonstrating our framework's superiority over LBS-based approaches. + +Our approach bridges the gap between physics-based simulation and differentiable learning, providing a powerful tool for articulated object modeling in computer vision and graphics. By introducing a differentiable physics-driven deformation process, our framework enables new opportunities for more accurate, physically consistent skinning and rigging, with broad implications for animation, motion generation, and 4D modeling. + +# 2. Related Work + +Skinning in 4D Modeling and Animation. Skinning is fundamental to 3D character animation, modeling surface deformations induced by skeletal motion [24, 26, 28, 33, 54]. Among various techniques, Linear Blend Skinning (LBS) remains the most widely used due to its simplicity and computational efficiency [20]. + +LBS is integral to many vision tasks, including video-to-3D reconstruction and avatar modeling. Parametric models like SCAPE [2] and SMPL [25] rely on predefined skeletons and skinning weights, limiting their adaptability. Neural implicit approaches [4, 8, 19, 29, 42–44, 50–52] improve generalization but still require precise skeletal information. In avatar modeling, explicit methods [13, 38, 39, 45–48] optimize SMPL parameters, whereas implicit ones [10, 18, 30, 31, 34, 36, 40, 53] leverage neural representations but face challenges in optimization and topological consistency. + +LBS has also been applied to pose transfer [21, 32], with MagicPose4D [49] enabling cross-species motion. However, these methods often require recalculating skeletons and skinning weights for novel motions. Since LBS linearly blends external skeletal motion, it fails to capture true internal deformations, prompting research into physically-based skinning [7, 16, 17, 27]. While such methods better model volumetric changes, their non-differentiability limits integration with deep learning. Our approach introduces a differentiable physics-based skinning model, enabling efficient joint optimization via gradient descent. + +Physical 4D Generation. In multiphysics simulation, the Material Point Method (MPM) [11, 14, 15] excels in handling topology changes and frictional interactions across various materials. Recent works [6, 22, 37, 56] integrate MPM for physically plausible motion but rely on manual parameter tuning. Differentiable approaches [12, 23, 55] learn material properties but are restricted to simple motions. To bridge this gap, we propose PhysRig, a differentiable physics framework that learns material parameters for articulated objects, ensuring physical consistency across complex motions. + +![](images/b15403f6a93a8c62cd8cb80235e58047455088c2baf042c4c4ff5dd6ebd77c65.jpg) +Figure 2. Overview of PhysRig. Given a 3D object, we first compute coarse skinning weights, which initialize embedded driving points for local deformation control. These points, assigned velocities, are linked to an elastic 3D volume with material parameters governing deformation. The differentiable physics-based skinning module generates natural deformations, optimizing velocities and material properties via backward propagation. Finally, multi-view animations illustrate physically plausible shape deformations over time. + +# 3. Method + +In this paper, we introduce PhysRig, a differentiable physics-based skinning framework for 3D object deformation, applicable to meshes, point clouds, and Gaussian representations. If the input is a mesh or a Gaussian representation, we first perform a filling operation to obtain a solid volume in the form of a point cloud, and the total number of points is $N$ . As shown in Fig. 2, unlike traditional Linear Blend Skinning (LBS), which applies a weighted sum of bone transformations, PhysRig employs a differentiable physics simulator (Sec.3.1) to model the 3D object as a volumetric structure. Instead of directly manipulating vertex positions, it embeds driving points within the volume to induce deformation. PhysRig optimizes two key components to achieve fine-grained control and produce the desired deformation: + +- Material properties, including Young's modulus $E \in \mathbb{R}^P$ and Poisson's ratio $\nu \in \mathbb{R}^P$ for $P$ material prototypes. The material properties of all $N$ points are then computed using a function based on the Mahalanobis distance between each point and the material prototypes (Sec. 3.2). These properties govern elasticity and deformation behavior, determining how internal forces propagate through the structure. +- Driving point velocities, $v \in \mathbb{R}^{\{l * M, 3\}}$ , representing the motion of the internal skeletal structure parameterized by transformations $\{\mathbf{t}_0, \dots, \mathbf{t}_M\}$ , $\mathbf{t}_i \in SE(3)$ , where $M$ is the number of virtual joints. These velocities $v$ drive the deformation, with $l = 8$ set by default and the driving points' positions are initialized by coarse skinning weights or uniform sampling (detailed in Sec. 3.3). + +The driving points encode the skeletal motion, propagating movement to the surrounding 3D volume, while the material properties define how internal motion influences the object's + +outer surface. PhysRig can be formulated as: + +$$ +\mathbf {X} ^ {\prime} = \mathcal {F} (\mathbf {X}, E, \nu , v, \Delta t), \tag {1} +$$ + +where $\mathbf{X} \in \mathbb{R}^{N \times 3}$ denotes the initial point positions, and $\Delta t \in \mathbb{R}$ is the time step governing temporal evolution. The function $\mathcal{F}$ computes the deformed positions $\mathbf{X}'$ via a differentiable physics simulation. + +# 3.1. Physics-Based Simulation + +To model object deformations under external interactions, we simulate motion using the principles of continuum mechanics. Our approach represents objects as continuous volumetric materials governed by conservation laws, enabling differentiable physics-based deformation modeling. + +# 3.1.1. Continuum Mechanics Formulation + +We describe the motion of a deformable object using a time-dependent mapping function $\phi$ , which transforms material coordinates $\mathbf{X}$ in the undeformed space $\Omega_0$ to world coordinates $\mathbf{x}$ in the deformed space $\Omega_t$ : $\mathbf{x} = \phi(\mathbf{X}, t)$ . The evolution of $\phi$ is constrained by fundamental physical laws: + +Conservation of Mass. The total mass within a material region remains constant over time: + +$$ +\int_ {B _ {\epsilon} ^ {t}} \rho (\boldsymbol {x}, t) d \boldsymbol {x} = \int_ {B _ {\epsilon} ^ {0}} \rho \left(\phi^ {- 1} (\boldsymbol {x}, t), 0\right) d \boldsymbol {x}, \tag {2} +$$ + +where $\rho (\pmb {x},t)$ is the density field. + +Conservation of Momentum. The motion of the object is dictated by the balance of internal and external forces: + +$$ +\int_ {B _ {\epsilon} ^ {t}} \rho (\boldsymbol {x}, t) \boldsymbol {a} (\boldsymbol {x}, t) d \boldsymbol {x} = \int_ {\partial B _ {\epsilon} ^ {t}} \sigma \cdot \boldsymbol {n} d \boldsymbol {x} + \int_ {B _ {\epsilon} ^ {t}} \boldsymbol {f} ^ {\text {e x t}} d \boldsymbol {x}, \tag {3} +$$ + +where $\pmb{a}(\pmb{x},t) = \frac{\partial^2\phi}{\partial t^2}$ represents acceleration, $\pmb{f}^{\mathrm{ext}}$ denotes external forces, and $\sigma$ is the Cauchy stress tensor, which encodes local deformation behavior. + +# 3.1.2. Material Model and Deformation Representation + +To model elastic responses, we use a constitutive model relating the stress tensor $\sigma$ to the deformation gradient $F = \frac{\partial\phi}{\partial X}$ . We adopt a Fixed Corotated hyperelastic material model, which effectively captures nonlinear deformations while maintaining stability. + +The Cauchy stress tensor is derived from the strain energy density function $\psi (F)$ : + +$$ +\sigma = \frac {1}{\det (F)} \frac {\partial \psi}{\partial F} F ^ {T}. \tag {4} +$$ + +Following the Fixed Corotated model, the strain energy function is given by: + +$$ +\psi (F) = \mu \sum_ {i = 1} ^ {d} \left(\sigma_ {i} - 1\right) ^ {2} + \frac {\lambda}{2} (\det (F) - 1) ^ {2}, \tag {5} +$$ + +where $\sigma_{i}$ are the singular values of $F$ , and the material parameters $\mu$ and $\lambda$ are related to Young's modulus $E$ and Poisson's ratio $\nu$ : + +$$ +\mu = \frac {E}{2 (1 + \nu)}, \quad \lambda = \frac {E \nu}{(1 + \nu) (1 - 2 \nu)}. \tag {6} +$$ + +# 3.1.3. Simulation via the Material Point Method + +We employ the Material Point Method (MPM) [11] to solve the governing equations efficiently. MPM discretizes the object as particles embedded in an Eulerian background grid, enabling robust handling of large deformations while ensuring differentiability. + +Particle-to-Grid (P2G) Transfer. At each simulation step, per-particle mass and momentum are transferred to the grid using B-spline interpolation: + +$$ +\begin{array}{l} m _ {i} v _ {i} = \sum_ {p} N \left(x _ {i} - x _ {p}\right) \left[ m _ {p} v _ {p} + \left(m _ {p} C _ {p} \right. \right. \tag {7} \\ \left. \left. - \frac {4}{\Delta x ^ {2} \Delta t} V _ {p} \frac {\partial \psi}{\partial F} F _ {p} ^ {T}\right) (x _ {i} - x _ {p}) \right] + f _ {i}. \\ \end{array} +$$ + +where: $m_{i}, v_{i}$ are the mass and velocity at grid node $i$ , $N(x_{i} - x_{p})$ is the interpolation kernel, $C_p$ is the velocity gradient at the particle, $f_{i}$ is the external force, $V_{p}$ is the volume of the particle, which scales the contribution of the stress force term. The stress-based force term, $V_{p}\frac{\partial\psi}{\partial F} F_{p}^{T}$ , represents the internal elastic forces exerted by the particle. The factor $V_{p}$ ensures that the contribution is properly scaled according to the physical size of the particle, preventing instabilities when transferring forces to the grid. + +Grid-to-Particle (G2P) Update. After computing velocity updates on the grid, the velocities are interpolated back to particles, and positions are updated: + +$$ +v _ {p} ^ {t + 1} = \sum_ {i} N \left(x _ {i} - x _ {p}\right) v _ {i}, \quad x _ {p} ^ {t + 1} = x _ {p} + \Delta t v _ {p} ^ {t + 1}. \tag {8} +$$ + +Deformation Gradient Update. The velocity gradient and deformation gradient are updated as: + +$$ +\nabla v _ {p} ^ {t + 1} = \frac {4}{\Delta x ^ {2}} \sum_ {i} N \left(x _ {i} - x _ {p}\right) v _ {i} \left(x _ {i} - x _ {p}\right) ^ {T}, \tag {9} +$$ + +$$ +F _ {p} ^ {t + 1} = (I + \Delta t \sum_ {i} v _ {i} \nabla N (x _ {i} - x _ {p}) ^ {T}) F _ {p}. +$$ + +where: $\nabla v_{p}^{t + 1}$ is the velocity gradient at particle $p$ , describing how velocity varies locally. $F_{p}^{t + 1}$ is the updated deformation gradient, tracking material deformation over time. $\nabla N(x_{i} - x_{p})$ is the spatial gradient of the interpolation function, describing how interpolation weights change with position. $I$ is the identity matrix, ensuring that the deformation gradient starts from an undeformed state. $\Delta t$ is the time step, controlling how much deformation accumulates per iteration. By iterating these updates, MPM efficiently captures complex material deformations while maintaining differentiability. + +Driving Points Gradient Update. Driving points influence the motion of specific object regions by modifying the velocities of nearby grid nodes within their control region. The velocity update for a driving point $v_{\mathrm{d},j}$ is determined by the contributions from the affected grid nodes and is given by: + +$$ +v _ {\mathrm {d}, j} \leftarrow v _ {\mathrm {d}, j} + \frac {1}{\left| R _ {c} \right|} \sum_ {i \in R _ {c}} \nabla v _ {i}, \tag {10} +$$ + +where $\nabla v_{i}$ represents the velocity gradient at grid node $i$ within the control region $R_{c}$ . + +# 3.1.4. Optimization Strategy for Inverse Skinning + +Inverse Skinning is the process of recovering underlying motion parameters, such as material properties and driving point velocities, from observed deformations of a 3D object. Unlike traditional skinning methods (LBS), where deformations are computed from transformations and skinning weights, our inverse skinning aims to estimate the driving point velocities $v$ and material properties (Young's modulus $E$ , Poisson's ratio $\nu$ ) that best explain a given motion sequence. This requires optimizing physical parameters to minimize discrepancies between simulated and observed motion. + +Iteritively Optimization. To ensure stability, we adopt an iterative training strategy. First, we initialize the positions of the driving points and estimate their approximate velocities for each frame. We then alternate between the following + +
MethodHumanoid CharacterQuadruped Animal
MichelleOrtizMutantJellymanKayaLeopardMammothStegoKrin
UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓
LBS-12.821.4262.182.9932.022.5123.056.5322.422.0813.032.4132.541.7823.070.6823.030.561
LBS-23.060.8912.932.0113.371.4383.254.1302.971.2143.131.3282.80.8913.640.2023.380.271
LBS-33.320.3723.011.4723.470.8013.663.8113.430.4083.210.4933.250.3463.830.1033.470.048
Ours-init3.192.1052.9112.7552.985.9773.4314.1613.392.0273.431.8223.134.9913.511.6643.630.844
Ours4.70.1394.431.3754.610.5274.341.2144.80.2284.450.2124.590.1274.50.0854.40.032
MethodQuadruped AnimalT-rexPterosaurWhaleAngelfishCobraSharkAve.
CowRaccoonUR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓UR↑CD↓
UR↑CD↓UR↑CD↓
LBS-12.511.3512.291.2432.885.8612.546.7222.770.2923.110.8412.642.7123.270.0782.722.43
LBS-23.01.0192.580.7913.213.7632.784.5122.950.2533.570.6142.792.1333.590.0463.121.56
LBS-32.990.7813.480.3423.250.6873.051.0823.170.1343.610.2093.010.6073.810.0313.350.73
Ours-init3.12.2443.374.7373.176.5742.979.5223.114.5613.810.2963.774.0493.930.1783.344.67
Ours4.240.1874.630.1984.660.5884.490.6534.560.1324.320.0214.760.3724.340.0164.520.37
+ +Table 1. Comparison of different rigging methods for inverse skinning. UR ↑: User Study Rate, CD ↓: Chamfer Distance. LBS-1, LBS-2, and LBS-3 correspond to using RigNet [41], Pinocchio [3], and ground truth skinning weights, respectively, as initialization for jointly optimizing skinning weights and bone transformation. PhysRig utilizes Pinocchio to obtain coarse skinning weights for initializing driving points, and then iteratively learns material parameters and driving point velocities. Our dataset consists of 17 diverse objects among humans, quadrupeds, and other entities, totaling 120 motion sequences. We report the average performance across all motions for objects with multiple motions. The User Study setup is provided in the appendix Sec. A.4 + +two optimization steps: (1) Material Parameter Optimization: Fix the driving point velocities and update the material parameters using all frames as a single batch. (2) Driving Point Velocity Optimization: Fix the material parameters and sequentially update the velocities of the driving points for each frame. The optimization progresses frame by frame, moving to the next frame once the loss falls below a predefined threshold. These two steps are repeated iteratively until either the overall loss falls below a set threshold or the total number of iterations reaches the stopping criterion. + +This strategy is designed to account for the differing requirements of material parameters and velocity optimization. Optimizing material parameters requires information accumulated across multiple frames, as the material properties influence the object's global behavior over time. In contrast, optimizing driving point velocities must be performed sequentially on a per-frame basis. Simultaneously optimizing velocities across multiple frames is ineffective, as accurate simulation of later frames is only meaningful if the preceding frames have already been well-optimized. + +# 3.2. Material Prototype + +To efficiently represent material properties across an object's volume, we introduce material prototypes, each characterized by two learnable parameters: Young's modulus and Poisson's ratio. The material properties at any point within the volume are computed as a weighted sum of these prototypes. The weights are determined using a function based on the Mahalanobis distance between the query position and the prototypes. Specifically, we define each material prototype as a Gaussian ellipsoid, parameterized by its center $\mathbf{C} \in \mathbb{R}^{P \times 3}$ , orientation $\mathbf{V} \in \mathbb{R}^{P \times 3 \times 3}$ , and diagonal scale + +$\Lambda \in \mathbb{R}^{P\times 3\times 3}$ , where $P$ denotes the number of prototypes. The weight assignment follows: + +$$ +W _ {n, p} = \operatorname {s o f t m a x} _ {p \in P} \left(d \left(\mathbf {x} _ {n}, \mathbf {C} _ {p}, \mathbf {Q} _ {p}\right)\right) \tag {11} +$$ + +where $d(\mathbf{x}_n,\mathbf{C}_p,\mathbf{Q}_p)$ is the Mahalanobis distance, defined as: $d(\mathbf{x}_n,\mathbf{C}_p,\mathbf{Q}_p) = (\mathbf{x}_n - \mathbf{C}_p)^T\mathbf{Q}_p(\mathbf{x}_n - \mathbf{C}_p),\quad \mathbf{Q}_p = \mathbf{V}_p^T\boldsymbol{\Lambda}_p\mathbf{V}_p$ . Here, $\mathbf{x}_n$ represents the coordinates of a query point $n$ , and the Mahalanobis distance function ensures that weights are assigned based on the spatial relationship between the query position and the material prototypes. This formulation enables an efficient and differentiable material representation that generalizes across diverse volumetric structures. + +Compared to directly learning per-point material properties or employing a triplane-based function that maps spatial coordinates to material parameters, our material prototype representation offers a significantly more compact and efficient parameterization. By leveraging a small set of prototypes rather than densely modeling every point, we substantially reduce the optimization space while maintaining high expressiveness. Moreover, the prototype-based formulation naturally enforces smooth material transitions, preventing noisy or abrupt variations that are common in per-point learning approaches. This property aligns more closely with the behavior of real-world materials, where material properties exhibit gradual spatial variations rather than sharp discontinuities. + +# 3.3. Driving Point Initialization + +Driving points are a crucial component of PhysRig, as efficiently initializing their positions and velocities significantly + +improves optimization efficiency. To achieve this, we propose a coarse-to-fine initialization strategy based on skinning weights. We first obtain coarse skinning weights using existing rigging models such as Pinocchio [3] or RigNet [41], which provide an approximate mapping between the object's surface and skeletal structure. We then place driving points at joint locations, which naturally reside at the boundaries between adjacent parts. + +# 3.3.1. Affinity-Based Seg via Spectral Clustering + +Given per-vertex skinning weights $\mathbf{W} \in \mathbb{R}^{N \times B}$ , where $N$ is the number of vertices and $B$ is the number of bones, we construct an affinity matrix $\mathbf{A}$ to measure similarity between vertices: + +$$ +A _ {i, j} = \exp \left(- \frac {\| \mathbf {W} _ {i} - \mathbf {W} _ {j} \| ^ {2}}{\sigma^ {2}}\right), \tag {12} +$$ + +where $\sigma$ controls the sensitivity of similarity measurement. A larger $\sigma$ results in smoother clustering, while a smaller $\sigma$ captures finer-scale differences. Using $\mathbf{A}$ , we compute the graph Laplacian: $\mathbf{L} = \mathbf{D} - \mathbf{A}$ , where $D_{i,i} = \sum_{j} A_{i,j}$ . We obtain a low-dimensional embedding by computing the $k$ smallest eigenvectors of $\mathbf{L}$ and apply $k$ -means clustering to segment the object into rigid regions, each assigned a cluster label $c_i$ . Note that $k$ could be different with $B$ . Since the coarse skinning weights may not always meet our expectations, our approach allows for flexible control over the number of parts by adjusting $k$ . + +# 3.3.2. Locating Joint via Skinning Weight Variance + +To extract joint locations, we analyze the segmentation output to identify transition regions where adjacent rigid components meet. A vertex $i$ is classified as a boundary vertex if: $c_{i} \neq c_{j}$ , for some $j \in \mathcal{N}(i)$ , where $\mathcal{N}(i)$ denotes the set of neighboring vertices in the mesh. These boundary vertices form the primary candidates for joint locations. To further refine the detected joints, we analyze variance in skinning weights at boundary vertices. Specifically, we define the joint set $\mathcal{J}$ as: $\mathcal{J} = \left\{i \mid \sum_{b} \left(W_{i,b} - \bar{W}_{\mathcal{N}(i),b}\right)^2 > \tau \right\}$ , where $\bar{W}_{\mathcal{N}(i),b}$ is the mean skinning weight of neighboring vertices of $i$ , and $\tau$ is a threshold for detecting significant weight variations. This step ensures that only regions with meaningful changes in skinning influences are selected as joints. + +# 3.3.3. Driving Points Initialization + +At each identified joint, we uniformly place $l$ driving points to ensure fine-grained control over the deformation of nearby volumetric regions. Each driving point's initial velocity is computed as the average velocity of its surrounding volume, ensuring a smooth and physically consistent initialization: $v_{p} = \frac{\sum_{i\in\mathcal{N}_{p}}v_{i}}{|\mathcal{N}_{p}|}$ , where $\mathcal{N}_p$ represents the set of nearby points influencing the driving point. + +
MichelleLeopardAngelfishConverge Iteration↓
UR↑CD↓UR↑CD↓UR↑CD↓
Mat Field3.311.933.471.583.930.23-
Per-point3.152.313.611.773.730.25-
w/o Locating4.310.1864.230.3583.970.0318000
w/o Vel Init4.080.1834.030.3014.170.0295000
Prototypes: 25-0.147-0.229-0.0232000
Prototypes: 1004.70.1394.450.2124.320.0212500
Prototypes: 200-0.133-0.207-0.0192500
+ +Table 2. Ablation study on material prototypes vs. material field vs. per-point for material representation, the impact of the number of material prototypes, and the effect of driving point initialization, including (i) joint localization and (ii) velocity initialization. + +Although the coarse skinning weights obtained from pre-existing models may not be highly accurate, they provide a decent starting point. Our method refines these initial estimates (velocity) during optimization, ultimately yielding more accurate motion parameters that adapt to the specific material properties of the object. + +![](images/f9d1861b473092c8afdbb8bee9db94a007af107e29fa766bb3f316eb58504f49.jpg) +Figure 3. PhysRig enables pose transfer for generated objects. + +# 4. Experiments + +In this section, we compare PhysRig with the traditional neural Linear Blend Skinning (LBS) method on the inverse skinning task, which serves as a fundamental component for various applications such as 3D video reconstruction and part decomposition. This comparison highlights PhysRig's strong capability in dynamic modeling and optimization for articulated objects. To facilitate the evaluation, we introduce a new dataset, which is constructed from existing datasets (Objaverse, The Amazing Animals Zoo and Mixamo) and includes entities with diverse structural variations. Additionally, we generate a large amount of synthetic data using PhysRig, enabling a more comprehensive analysis of its optimization performance, particularly in learning material properties and driving point velocities. For more details on the dataset (Sec. A.1) and implementation (Sec. A.2), more experimental (Sec. A.3) results, and video results please refer to the supplementary materials. + +![](images/b2b32759dcaa848f9ffc38b6eb678b51c4dba592aeb5032f64a61b3615a635b7.jpg) +Figure 4. Animation results from the PhysRig approach. These results are obtained from the inverse skinning problem by optimizing material properties and driving point velocities to minimize the deviation from the ground truth mesh sequence. + +# 4.1. Inverse Skinning Evaluation + +We evaluate the effectiveness of our inverse skinning method across a diverse set of humanoid characters, quadruped animals, and other articulated entities. We compare against traditional Linear Blend Skinning (LBS) baselines, including RigNet [41], Pinocchio [3], and ground truth skinning weight initialization, as well as the results after driving points initialization before optimization (Ours-init). The evaluation metrics include User Study Rate (UR), which quantifies perceptual quality based on user preferences, with scores ranging from 0 to 5 (higher is better), and Chamfer Distance + +(CD), which evaluates geometric fidelity. + +Table 1 presents the results. Our method consistently outperforms all baselines, achieving the highest UR scores and the lowest CD across all evaluated categories. Notably, on humanoid characters, our method achieves a UR of 4.7 on Michelle and a UR of 4.8 on Kaya, surpassing all LBS-based approaches. Similarly, for quadrupeds, our approach demonstrates superior performance, particularly on the Leopard (UR: 4.45, CD: 0.212) and Stego (UR: 4.5, CD: 0.085), highlighting its robustness across diverse morphologies. Our approach also generalizes well to other articulated entities, such as the Angelfish (UR: 4.32, CD: 0.021) and Pterosaur + +![](images/f3a15725600d2f405c1ec204d63e9e6f5a3232e1be97324c4e8ab975286e1004.jpg) +Ground-Truth Material + +![](images/1b765cd343b40ad849906a63a2e02a379c0aed77ea3ab9f4c05d046498787b82.jpg) + +![](images/d175a293dbeb7e980c5711a4850a9e37020eadf44a0586671a99faac2b1e1675.jpg) + +![](images/c7e65ee70e68fd581fc7a3a7f34e17471b5519e0dd2b05e76dbdc099de4d136a.jpg) + +![](images/f9022dde7256cfc86e0a0b2794c41770a31f23a60c6a5fe9b4639f9b2ae428f3.jpg) + +![](images/691ad0829eff6137e06a855d0fb9c9354b549a1ec7f701312b197ccce8638993.jpg) + +![](images/59968b52ca8406b4662886b92327cee435a10e445f46932cef78b9672f949338.jpg) +Optimized Material + +![](images/fd5ab278403ad16082d8eb8e08928e2c432f89b5f12582afc63db065b8a56d0e.jpg) +Figure 5. Comparison of the learned material properties with ground truth using our method. + +![](images/82eae7aa18f820ff0cd670e5ddda758bc612b754e8df1316503e7fffb60fd3c6.jpg) + +![](images/aefa059e4b49ebcc53af90b4fd9f1f83138087ee34f3aca26709d85d482e88fe.jpg) + +![](images/4c83b934cc8e0b234bd823d0f5555d81a4737707c3b5ea5613e7ac5cbb34ff8d.jpg) + +![](images/9fe586e63d9c297c63bb093bb7c2f22fe92f0c84b8f5a53670c8d28b79613824.jpg) + +![](images/0469ed94acee6925a8b7f740cc07e8ed00e55ff639c2911c8624feeaf540ac42.jpg) + +(UR: 4.49, CD: 0.653), showcasing its effectiveness beyond conventional character rigging. These results indicate that our inverse skinning formulation not only improves perceptual quality but also significantly reduces geometric error compared to existing baselines. For qualitative comparisons and analysis, please refer to the appendix (Sec. A.3). + +# 4.2. Ablation Study + +We conduct an ablation study to analyze the impact of different components in our method, particularly focusing on material representation and driving point initialization. The results are summarized in Table 2. + +Material Representation: We compare our prototype-based material representation against material fields and perpoint assignments. The per-point approach leads to higher geometric error (CD: 2.31 on Michelle, 1.77 on Leopard), indicating that it struggles to find the optimal solution. The material field (triplane) method also underperforms, demonstrating increased Chamfer Distance across all test cases. In contrast, our prototype-based representation significantly reduces CD and achieves high UR scores. + +Effect of Driving Point Initialization: Removing joint localization (w/o Locating) results in increased CD values (e.g., 0.186 on Michelle), requiring 8000 iterations for convergence. Similarly, excluding velocity initialization (w/o Vel Init) leads to a higher CD (0.183 on Michelle) and slower convergence (5000 iterations). These findings suggest that both joint localization and velocity initialization are crucial for improving optimization efficiency and accuracy. + +Effect of Material Prototype Count: We also investigate the impact of the number of material prototypes. Reducing the prototype count to 25 does not degrade performance and instead accelerates convergence, achieving the fastest convergence at 2000 iterations while maintaining competitive accuracy (CD: 0.147 on Michelle). Increasing the prototype count to 100 strikes a good balance between performance and convergence time (UR: 4.7, CD: 0.139 on Michelle, convergence: 2500 iterations). Further increasing the prototypes to 200 yields a marginal improvement in CD (0.133 on + +Michelle) but does not significantly affect UR, suggesting diminishing returns. + +Overall, these results demonstrate that our material prototype representation, combined with joint localization and velocity initialization, leads to improved inverse skinning accuracy and faster optimization convergence. + +# 4.3. Apply PhysRig for Pose Transfering + +As shown in Figure 3, PhysRig enables pose transfer by taking a mesh sequence as input. Inspired by MagicPose4D [49], we first extract the skeleton from the input mesh and align it with the generated mesh. By transferring the bone angles at each frame, we obtain the skeleton sequence for the generated object. This allows us to compute joint velocities between consecutive frames, which serve as the driving point velocities for deforming the generated mesh (volume). Unlike traditional methods that rely on skinning weight, PhysRig achieves more realistic deformations while significantly improving generalization, as it eliminates the need for explicit skinning weight prediction. + +# 5. Conclusion + +We introduced PhysRig, a differentiable physics-based skinning framework that addresses the limitations of Linear Blend Skinning (LBS) by modeling deformations through volumetric simulation. By embedding skeletons into a soft-body representation and leveraging continuum mechanics, our approach achieves realistic, physically plausible deformations while remaining fully differentiable. To enhance efficiency, we introduced material prototypes, reducing learning complexity while maintaining expressiveness. Our evaluation of a diverse synthetic dataset demonstrated superior performance over traditional LBS-based methods. Additionally, PhysRig enables applications such as pose transfer, motion retargeting, and 4D generation, bridging the gap between physics-based simulation and differentiable learning. Future work includes integrating real-world priors and optimizing for real-time applications, expanding PhysRig's potential in animation and simulation. + +# 6. Acknowledgments + +This work was supported by the Office of Naval Research (grant N00014-20-1-2444) and the USDA National Institute of Food and Agriculture (grant 2020-67021-32799/1024178). Support for computational resources was provided by the National Science Foundation (awardOAC 2005572) and the State of Illinois, through Delta [9], a joint effort of the University of Illinois Urbana-Champaign and its National Center for Supercomputing Applications. + +# References + +[1] Adobe. Mixamo. 1, 2 +[2] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 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We develop an efficient method for simulating the dynamic movements of 3D objects with customizable behaviors, and synthesizing interactive 3D dynamics under arbitrary forces (red arrows). Compared to recent methods [13, 21, 47], our approach produces more realistic 3D dynamics with much faster inference times. + +# Abstract + +Recent advancements in 3D generation models have opened new possibilities for simulating dynamic 3D object movements and customizing behaviors, yet creating this content remains challenging. Current methods often require manual assignment of precise physical properties for simulations or rely on video generation models to predict them, which is computationally intensive. In this paper, we rethink the usage of multi-modal large language model (MLLM) in physics-based simulation, and present PhysSplat, a physics-based approach that efficiently endows static 3D objects with interactive dynamics. We begin with detailed scene reconstruction and object-level 3D open-vocabulary segmentation, progressing to multi-view image inpainting. Inspired by human visual reasoning, we propose MLLM-based Physical Property Perception (MLLM-P3) to predict the mean physical properties of objects in a zero-shot manner. The Material Property Distribution Prediction model (MPDP) then estimates physical property distributions via geometry-conditioned probabilistic sampling of MLLM-P3 outputs, reformulating the problem as probability distribu + +tion estimation to reduce computational costs. Finally, we simulate objects in 3D scenes with particles sampled via the Physical-Geometric Adaptive Sampling (PGAS) strategy, efficiently capturing complex deformations and significantly reducing computational costs. Extensive experiments and user studies demonstrate that our PhysSplat achieves more realistic motion than state-of-the-art methods within 2 minutes on a single GPU. Here is our project page. + +# 1. Introduction + +With the development in 3D representation, Neural Radiance Fields (NeRF) [24] and 3D Gaussian Splatting (3DGS) [16] offer new perspectives for 3D reconstruction and 3D representation [35, 39, 51]. However, these approaches are unable to simulate interactions with 3D assets in simulation environments [32, 41], which is a critical for generating realistic object responses to novel interactions, such as external forces or agent manipulations in many applications, e.g., virtual reality [15], embodied intelligence [23]. + +Some recent approaches aim to bridge the gap between rendering and simulation integrating physics-based + +auto param computation fast inference time physics-based deformation static 3D object input scene-wide simulation + +
X✓✓✓XPhysGaussian [42]
XXX✓XDreamGaussian4D [30]
XXX✓XAnimate124 [53]
X✓✓XXPAC-NeRF [20]
X✓✓XXPIE-NeRF [7]
X✓✓XXSpring-Gaus [54]
✓X✓✓XDreamPhysics [13]
✓X✓✓XPhysDreamer [47]
✓X✓✓XPhysics3D [21]
XX✓✓✓Feature Splatting [27]
✓✓✓✓✓PhysSplat
+ +Table 1. Comparison to Concurrent Works. Our method is the only one that can simulate the entire scene at a much faster speed. + +priors into 3D object representations using physical simulators [4, 7, 27]. For instance, PAC-NeRF [20] estimates the geometry and physical parameters of objects from multi-view videos and then integrates physical models with NeRF-based representations. Similarly, PhysGaussian [42] first injects physical parameters into 3DGS objects and then predicts motion using a physics-based simulator. However, both methods are limited in handling real objects, as they require predefined material models or multi-view videos to predict physical properties. + +To automatically set parameters, some approaches [13, 21, 47] leverage video generation models [2] that are trained on real-world video data to estimate the parameters of physical materials. erials. For example, PhysDreamer [47] employs a stable video diffusion model to learn Young's modulus of objects. However, learning material physical properties from video diffusion priors is computationally expensive and time-consuming in practice. Moreover, video diffusion models have limited controllability and often fail to obey physical laws [30, 53]. Additionally, these models are also generally restricted to non-rigid objects, making them unsuitable for deriving the physical properties of large rigid objects (such as cup, bowl, and chairs). However, humans are exceptionally adept at predicting the physical properties of objects based on visual information [8, 9]. We therefore ask this question: how can we develop models for perceiving physics from just visual data? + +To this end, we rethink physics-based simulation and the usage of multi-modal large language model (MLLM), such as GPT-4V [43]. In this paper, we propose PhysSplat, a physics-based method that efficiently transforms static 3D objects into interactive ones capable of responding to new interactions, as shown in Fig. 1. We first segment objects with priors from foundation models [18, 22, 48]. + +Inspired by how humans predict physical properties of objects through visual data, PhysSplat leverages MLLM-based Physical Property Perception (MLLM-P3) to predict the mean values of physical properties. Unlike previous methods [13, 21, 47] iteratively refining physical properties through video analysis, we reformulate this problem to a probability distribution estimation task by predicting the full range of these properties based on the mean value and the object's geometry, reducing computational demands. Finally, PhysSplat simulates object interactions in a 3D scene with driving particles sampled by the Physical-Geometric Adaptive Sampling (PGAS) strategy. Extensive experiments and user studies demonstrate that PhysSplat achieves more accurate physical property prediction and synthesizes more realistic motion with much faster inference time. We provide an overview of the comparison to previous works in Tab. 1. In summary, PhysSplat makes the following contributions: + +- PhysSplat is the first to use MLLM for zero-shot physical property estimation of objects in 3D scenes. +- We reformulate physical property estimation as a probability distribution task, enabling adaptable physical simulations with PGAS in open-world scenes. +- Experiments show PhysSplat effectively predict physical properties and creates realistic 3D dynamics. + +# 2. Related Work + +# 2.1. Dynamic 3D Animation + +The demand for dynamic 3D animation creation has grown significantly across various applications, including video games, virtual reality, and robotic simulation [49, 50, 52]. With the success of video generative models [38], some methods [53] have attempted to leverage video diffusion models to guide the prediction of 3D deformations. For instance, DreamGaussian4D [30] uses pre-generated videos to supervise the deformation of static scenes. However, the deformations produced by these methods may not always be accurate or physically plausible. + +Recent works [25, 54] introduce physics simulation to the 3D deformation and enable synthesizing motions under any physical interactions. Virtual Elastic Objects [4] jointly reconstructs the geometry, appearances, and physical parameters of elastic objects with multi-view data. Spring-Gaus [54] integrate a 3D Spring-Mass model into 3D Gaussian kernels, and then simulate elastic objects from videos of the object from multiple viewpoints. PAC-NeRF [20] and PhysGaussian [42] integrate physics-based simulations with NeRF [24] and 3DGS [16], respectively, to model the deformation of elastic objects. However, these methods either require manual setup of physical properties for 3D objects before simulation or depend on multi-view videos to predict physical properties. + +To avoid manually setting parameters, some works estimate physical material parameters with video generation model [2] to estimate physical material parameters [13]. PhysDreamer [47] and DreamPhysics [13] leverage video generation models to estimate physical material parameter (e.g., Young's modulus), while Physics3D [21] further optimizes a wider range of physical parameters for 3D objects. However, these methods are computationally expensive, as learning material properties through video diffusion priors is time-consuming. Moreover, the controllability of generated videos is limited, often deviating from physical laws [30, 53], which we further demonstrate in the experimental Section 5.3. Additionally, these models are typically restricted to non-rigid objects, making them unsuitable for determining the physical properties of large rigid objects, such as tables, chairs, and sofas. Inspired by how humans perceive physical properties of the objects [8, 9], we propose leveraging multi-modal large language models (MLLMs) to efficiently predict the mean values of physical properties for objects in a 3D scene, enabling faster inference times. We then use the proposed MPDP to predict the full distribution of these properties. + +# 2.2. Visual Physics Perception + +Physics perception is a long-standing challenging problem [40]. Previous studies demonstrate that deep learning models can potentially exhibit physical perception abilities similar to humans [1, 11, 37]. Most prior research focuses on dynamically addressing object properties, either by observing the target's behavior [20] or by interacting with it in a 3D physical engine [26, 44]. Other works also explore the estimation of material properties directly from static images [1, 33]. However, these works mostly focus on specific material properties, such as mass or tenderness, often relying on task-specific data. In contrast, we propose leveraging MLLM, such as GPT-4V [43], to generate a wide range of physical properties such as mass, Young's modulus, and Poisson's ratio in a zero-shot manner. + +# 3. Preliminaries + +# 3.1. Material Point Method + +The Material Point Method (MPM)[12] is a popular simulation framework for multi-physics phenomena due to its capability to handle topology changes and frictional interactions. Unlike mesh-based methods, MPM represents the continuum using particles in a grid-based space, making it well-suited for point-based 3D Gaussian representation. Following PhysGaussian[42], we define each Gaussian kernel's time-dependent state as: + +$$ +x _ {i} (t) = \Delta \left(x _ {i}, t\right), \Sigma_ {i} (t) = F _ {i} (t) \Sigma_ {i} F _ {i} (t) ^ {T}, \tag {1} +$$ + +where $\Delta (\cdot ,t)$ and $F_{i}(t)$ denote coordinate deformation and deformation gradient at timestep $t$ . The viewpoint must also + +adjust with the continuum rotation $\Omega_{i}(t)$ to match the view direction of the spherical harmonic coefficient $C_i$ . + +# 3.2. 3D Gaussian Splatting (3DGS) + +3D Gaussian Splating (3DGS) represents scenes as point clouds, with each point modeled as a 3D Gaussian defined by a center point $\mathcal{X}$ (mean) and a covariance matrix $\Sigma$ . Each Gaussian at $\mathcal{X}$ is given by $G(\mathcal{X}) = e^{-\frac{1}{2}\mathcal{X}^T\Sigma^{-1}\mathcal{X}}$ . $\Sigma$ is decomposed into a scaling matrix $\mathcal{S}$ and rotation matrix $\mathcal{R}$ , such that $\Sigma = \mathcal{R}\mathcal{S}\mathcal{S}^T\mathcal{R}^T$ , with $\mathcal{S}$ and $\mathcal{R}$ stored as vectors $s\in \mathbb{R}^{N\times 3}$ and $r\in \mathbb{R}^{N\times 4}$ , respectively. Differential splating [46] applies a viewing transform $W$ and Jacobian $J$ to compute the transformed covariance $\Sigma' = JW\Sigma W^T J^T$ , enabling novel view rendering. Each pixel color $\mathcal{C}$ is obtained by blending $N$ overlapping points: + +$$ +\mathcal {C} = \sum_ {i \in N} c _ {i} \alpha_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}), \tag {2} +$$ + +where $c_{i}$ and $\alpha_{i}$ denote color and opacity, derived from the Gaussian with covariance $\Sigma$ and optimized parameters. + +# 4. Our Methodology + +Predicting various physical properties of 3D objects from static scene is an extremely challenging task due to limited supervisions. Instead of capturing physical data from generation models or multi-view videos [7, 13, 20, 21, 47, 54], we reformulate this task from a new perspective, decomposing it into a set of sub-tasks. Specifically, as shown in Fig. 2, we first segment the images with a set of foundation models [18, 22, 48] and lift these 2D segmented masks to segment 3D object in the scene via radiance fields rendering (Section 4.1). We propose MLLM-based Physical Property Perception (MLLM-P3) to predict the mean values of these properties (Section 4.2). We then use the Material Property Distribution Prediction (MPDP) model to estimate the full distribution, simulating object dynamics with driving particles sampled using the Physical-Geometric Adaptive Sampling (PGAS) strategy (Section 4.3). + +# 4.1.3D Open-vocabulary Segmentation + +For each scene, we first train a 3DGS model on given images and camera poses. Inspired by prior work [31], we integrate 2D open-vocabulary models like Grounding DINO [22] for detection, SAM [18] for segmentation, and RAM [48] for tagging. These models automatically segment objects in images without textual input. Specifically, we use RAM to tag the image, Grounding DINO to create bounding boxes based on tags, and SAM to refine these boxes into precise masks. This approach enables full automatic image labeling using expert models. + +After 2D open-vocabulary segmentation, each segmented image contains semantic features for each object. + +![](images/00fa9df0a0dd8f75b4757d90a5f7db1dcacffc27f1ce7494871f4648af908c08.jpg) +Figure 2. Overview of PhysSplat .Given a pre-trained 3D scene and its corresponding 2D images, we first perform object-level segmentation of the 3D scene with the prior from a set of foundation meods [18, 22, 48]. We obtain the mean physical properties of the object from the proposed MLLM-P3, and based on this and the object's geometry, we then derive the full distribution using the MPDP model. Finally, we animate the 3D objects using a physics-based simulator with driving particles sampled via the Physical-Geometric Adaptive Sampling (PGAS) strategy. + +We project these 2D masks into 3D space using radiance field rendering. Inspired by recent work [45, 50], each Gaussian retains its original attributes, with a learnable semantic attribute added for encoding object semantics. Using a zero-shot tracker [5], we assign unique IDs to masks across views, helping distinguish categories within the 3D scene through differentiable rendering (see Fig.2). Extracting objects from 3DGS introduces holes, which we inpaint using LaMa[34] to guide 3D Gaussian inpainting, keeping Gaussians outside holes fixed. + +# 4.2. MLLM-based Physical Property Perception + +The variety of materials is vast and often indistinguishable by appearance alone, yet humans can infer material composition through high-level reasoning and visual cues. Recent research [6] shows that multi-modal large language models (MLLM) excel in reasoning and decision-making for complex tasks. Inspired by human reasoning, we propose MLLM-based Physical Property Perception (MLLM-P3), which uses MLLM for open-vocabulary semantic reasoning about materials and their physical properties. + +The segmented 3D scene in Section 4.1 is tightly related to the physical properties of the 3D objects in it. We first select a canonical view and render an object in 3D scene + +based on the 3D Gaussian's semantic attribute introduce Section 4.1. Then we use a VQA model, such as BLIP [19] to produce a text description of the image. This description, along with the image, are then passed to a Multi-modal Large Language Model (MLLM) such as GPT-4V [43], prompting it to return a dictionary containing K candidate materials and information on whether the object is rigid (related to the sampling method in Section 4.3). To address potential hallucination, we compute the CLIP [29] similarity score between the image and the materials in the dictionary to select the most matching material name. Finally, the selected material name, image, and text description provide a structured input to the MLLM, grounding its outputs in a reliable context. This enables the model to return a list of physical properties for the object, $M = \rho, E, \nu$ , where $\rho$ represents the density, $E$ is Young's modulus, and $\nu$ is Poisson's ratio. These material properties are essential for understanding an object's motion under forces. + +# 4.3. Physics-Based Dynamics + +Material Property Distribution Prediction. Even for object composed of a single material, local physical properties exhibit inherent variations across different regions of the object [3]. Additionally, the physical properties esti + +![](images/2e73cf79d8220a2c1aaef5d03e03a5492921c7c0e374739501ef45f9eb34a9c1.jpg) +Random Sampling +Figure 3. Sampling. We design a novel Physical-Geometric Adaptive Sampling (PGAS) strategy that captures the boundary of the object well. We employ PGAS to sample some "driving particles" (in green) and simulate only these particles. For rendering, each particle's position and rotation are derived by fitting a local rigid body transformation based on neighboring driving particles. + +![](images/266d91b8d87c048a6ee7a0be4eaf2b7771c79c8ebafacad86fe432bfbdd4e1f8.jpg) +K-Means Sampling + +![](images/7a6d678a35d73efa1a170ee4aeb69ec60c3ef69298681321d39d9d075cde019f.jpg) +PGAS + +mated by multi-modal large language model (MLLM) may not capture the 3D structure of the object. To address these challenges, we propose material property distribution prediction (MPDP), and reformulate the problem from a regression task to a probability distribution estimation task. + +We train a network $\mathcal{D}_{\theta}$ using part of the synthesized dataset, with the object's point cloud and predicted mean values (Section 4.2) as input. The network is supervised by the physical properties of particles predicted by Physics3D [21]. Instead of using the raw Physics3D [21] results, we normalize them by their mean value, allowing our MPDP to learn the geometry-based distribution of physical properties. With the more reliable mean values from MLLM-P3, our final estimates of physical properties are more accurate. Moreover, our approach is only about $2\%$ as time-efficient as Physics3D [21]. + +The network predicts the geometry-aware probability distribution $\mathcal{P}$ of physical properties across particles, $\mathcal{P} = \mathcal{D}_{\theta}(\mathcal{X})$ . where $\mathcal{X}$ is the position of 3D Gaussians of the object. We then scale the distribution $\mathcal{P}$ by a global mean value predicted by the MLLM in Section 4.2 through element-wise multiplication, yielding the final physical property values for each point in the material field. This approach efficiently estimates per-point physical attributes, such as Young's modulus and Poisson's ratio, across the entire point cloud while avoiding the computational overhead of per-particle calculations. + +Simulation with Physical-Geometric Adaptive Sampling. Rendering high-fidelity 3D scene often needs millions of 3D Gaussians, which is significant computational demands for simulation. To reduce this burden, we implement a sub-sampling approach. Specifically, we design a Physical-Geometric Adaptive Sampling (PGAS) strategy. The original Poisson disk sampling requires that the distance between any two particles be larger than a threshold $r$ . Starting from an initial point, PDS then tries to fill a banded ring between $r$ and $2r$ with new samples. + +Our observation is that softer objects and those with + +complex shapes require more driving particles to accurately simulate their dynamics. To this end, we adaptively adjust the sample radius $r$ based on the object's Young's modulus $E$ predicted in Section 4.2 and curvature $K$ . The curvature $K$ is defined as: + +$$ +C = \frac {1}{n} \sum_ {j = 1} ^ {n} \left(\mathcal {X} _ {j} - \bar {\mathcal {X}}\right) \left(\mathcal {X} _ {j} - \bar {\mathcal {X}}\right) ^ {T}, \tag {3} +$$ + +$$ +K = \frac {\lambda_ {3}}{\lambda_ {1} + \lambda_ {2} + \lambda_ {3}}, \tag {4} +$$ + +where $\mathcal{X}_j$ is the position of the $j$ -th 3D Gaussian of the object, $\tilde{\mathcal{X}}$ is the mean position of all 3D Gaussians, and $\lambda_1, \lambda_2, \lambda_3$ are the eigenvalues of the covariance matrix $C$ . Then, the sample radius $r$ is adjusted as: + +$$ +\hat {K} = \min (V _ {\max }, \max (V _ {\min }, K)), \tag {5} +$$ + +$$ +\hat {r} = \min (r, k \sqrt {\frac {E}{\hat {K}}} r), \tag {6} +$$ + +where we set $V_{max} = 10$ , $V_{min} = 1$ , and $k = \sqrt{10}$ in our paper. Our sampling ensures that the distance between a particle and its nearest neighbor is at least $\hat{r}$ . By using smaller radii for softer materials and high-curvature areas, PGAS captures fine details more accurately, enhancing model resolution in deformation simulations and complex surface reconstruction, as shown in Fig. 3. + +MPM-Driven Physics-Based Dynamics. To model physical properties, we employ MLS-MPM [12] as our simulator. In MPM, a continuum is represented by particles distributed in a grid-based space, offering a distinct advantage over mesh-based methods. MPM can be seamlessly applied to 3D Gaussian Splating (3DGS) in point-based representations. Building on PhysGaussian [42], we define a time-dependent state for each Gaussian kernel as follows: + +$$ +x _ {i} (t) = \Delta \left(x _ {i}, t\right), \quad \Sigma_ {i} (t) = F _ {i} (t) \Sigma_ {i} F _ {i} (t) ^ {T}, \tag {7} +$$ + +where $\Delta (\cdot ,t)$ and $F_{i}(t)$ represent the coordinate deformation and deformation gradient at time $t$ . Additionally, to account for continuum rotation $\Omega_i(t)$ , the rendering viewpoint is adjusted to align with the view direction of the spherical harmonic coefficient $C_i$ . + +# 5. Experiments + +# 5.1. Implementation Details + +We initiate the process by reconstructing 3D Gaussians from multi-view images and execute internal particle filling operations to refine the representation further. Each Gaussian kernel is then associated with a set of physical properties targeted for optimization following [42, 47]. We then discretize the foreground region into a grid structure, typically sized at $64^3$ . For the MPM simulation, we use 768 + +![](images/2e7cee48b8afb537bf881a4cac3fd555d0179bdbe2e76b4240f03030481fa875.jpg) +Figure 4. Qualitative Comparison on PhysDreamer [47]. We compare our results with real captured videos, and some recent SOTA methods [21, 30, 42, 47]. Our PhysSplat produces more realistic damping, closely matching real-world capture. + +sub-steps per interval between video frames, resulting in a sub-step duration of $4.34 \times 10^{-5}$ seconds to ensure precision and accuracy in simulation dynamics. All experiments are conducted on a single NVIDIA 3090 GPU. + +# 5.2. Datasets + +PhysDreamer [47]. We also conduct experiments on the physical simulation of single objects on four real-world static scenes from PhysDreamer [47] for fair comparison. Each scene includes an object and a background. + +Synthesized dataset [21]. Following [21], we utilize BlenderNeRF [28] to synthesize several scenes. Five cases are used to train the proposed MPDP model (as introduced in Section 4.3), while the remaining four cases are reserved for subsequent comparisons. + +# 5.3. Comparison with SOTA Methods + +We chose the performance from real-world static scenes from PhysGaussian [42] for fair comparison. Tab. 2 presents the user study results (RS) and aesthetic score (AS) predicted by LAION aesthetic predictor following [14]. + +Since PhysDreamer [47] has not released its training code, we only compare the four evaluation scene and are unable to report its inference time. PhysDreamer [47] scores lower than DreamGaussian4D [30] in RS and PhysGaussian [42] in AS, which indicates that pre-generated videos may not be a proper ground truth for supervision. Feature Splatting [27] categorizes objects into types like "elastic", "snow", "sand", and "water", directly assigning predefined physical properties, which limits its ability to handle the diverse range of objects. Our PhysSplat achieves better performance in both metrics, which demonstrates that PhysSplat generates videos that are both realistic and physically plausible, with a high degree of naturalness. + +Following [47], we also compare the results with real captured videos in Fig. 4. We utilize space-time slices to present our comparisons, which depict time along the vertical axis and spatial slices of the object along the horizontal axis, as indicated by the red lines in the "object" column. Through these visualizations, we aim to elucidate the magnitude and frequencies of the oscillating motions under scrutiny. PhysSplat generates smooth and realistic motion + +![](images/b4fc4491b0cd7bf82aa8cd7c121ccf8935327cf26f657a9b16329fa96a6a503a.jpg) + +![](images/f5defe0317f5bc3b35037e3bb7e94a2b6857a1967397b22ad74e4091bf6989b4.jpg) + +![](images/b208c3a254469b386fd5163f93d8fe32ac82f36aa4ffb328ed8cbae2088c942e.jpg) +Figure 5. Visual results on synthesized dataset [21] with an external force (red arrows). PhysSplat is able to generate realistic scene movement while maintaining good motion consistency. + +![](images/345a77403607f471aa21d9f94aff4d025f2306d9c2af496aa97636d59f5b041b.jpg) + +![](images/904cdb2d803546b0758bea31eb84fc19eeebcc932f706ccd996e3ab47c2056cf.jpg) + +![](images/55b97e3c5d3947365f668223cecf0176efc73bc1cb88b91a45abba69eea6061d.jpg) + +![](images/aaa7a546521c98b2c724db635396dd8bcb3b19d04eb17da0404735bb76157ca8.jpg) +Figure 6. Visual results on Open-world dataset and 3D assets generated by LGM [36]. + +patterns, accurately capturing the natural flow and details of real-world movements. Please see our project website videos for more video visualization. + +We also evaluate our PhysSplat using the synthesized dataset [21]. We report the quantitative results against recent methods [13, 21, 30, 42] in Tab. 2. Our method still generates the most consistent and natural motions. The visual results are shown in Fig. 5. + +# 5.4. Ablation study + +In this section, we conduct ablation experiments using PhysDreamer [47] dataset to evaluate the effectiveness of our proposed modules. + +Model for physical property perception. In Fig. 7 we compare two methods with our proposed MLLM-P3: 1) GPT: Predicting physical properties using only the image; 2) GPT+BLIP: Predicting properties with both the image and a text description from BLIP; 3) GPT+BLIP+CLIP (MLLM-P3): Generating a dictionary of K candidate materials with GPT, selecting the best match via CLIP, and then predicting properties using the image, description, and chosen material. As shown in Tab. 3, MLLM-P3 performs best because there is inherent uncertainty in predicting materials based on just visual appearance or text description, as shown in Tab. 3. + +Material property distribution prediction. Material + +
MethodRSASTime
PhysDreamer
PhysGaussian [42]4.507.56-
PhysDreamer [47]4.547.71-
Physics3D [21]4.627.831.5h
Feature Splating [27]4.537.49-
DreamGaussian4D [30]4.577.280.1h
PhysSplat4.667.892min
synthesized dataset
PhysGaussian [42]4.947.35-
DreamPhysics [13]5.057.921.5h
Physics3D [21]5.108.011.5h
Feature Splating [27]4.997.27-
DreamGaussian4D [30]4.986.810.1h
PhysSplat5.108.202min
Open-world dataset
Feature Splating [27]4.797.10-
PhysSplat4.967.992min
+ +Table 2. Quantitative comparisons on PhysDreamer [47], synthesized dataset [21], and Open-world dataset [10, 17]. RS (Realism Score) represents user study ratings, while AS (Aesthetic Score) is estimated using the LAION aesthetic predictor. Time measures the inference speed for physics-based 4D generation on an single RTX 4090 GPU. + +
GPTBLIPCLIPw/o MPDPPGASAS
✓✓✓4.47
✓✓✓✓4.59
✓✓✓✓4.64
✓✓✓✓4.62
✓✓✓✓✓4.66
+ +Table 3. Ablation Study on PhysDreamer [47] dataset. AS denotes the average aesthetic quality score predicted using the LAION aesthetic predictor. + +property distribution prediction is designed for complex physical properties distribution. As shown in Fig. 7 and Tab. 3, it is required to achieve optimal performance. + +Sampling strategy selection. Compared to PhysDreamer's K-Means sampling [47], our PGAS strategy generates more temporally coherent results, as shown in Fig. 7 with significantly improved visual metrics in Table 3. This demonstrates PGAS's enhanced capability in reconstructing photorealistic 4D dynamics. + +# 6. Extension to Open-world Scene + +To evaluate the physical simulation accuracy in open-world 3D scenes, we select some multi-object scenes from [10, 17]. Our method simulates multiple objects simultaneously in open-world scenarios, unlike current methods (e.g., PhysDreamer [47] and Physics3D [21]) that handle only sin + +![](images/0789192a3d97c7175b15a6e62a85f719aeed1d94dc9288eb509c4e237be45b00.jpg) +Real Capture + +![](images/c2d18651f644010592bf119fda0d1e43af9e04e31700979e27690708c99931ca.jpg) +Ours + +![](images/0f0485498f050a37b922c5b306f5fefd125cd1e62a9d1535822d5ac34019e01c.jpg) +GPT + +![](images/ded973972459c5b3dac0703b5c2b3ab580d02ad2c759f62206af3649cb28ed8d.jpg) +GPT+BLIP +Figure 7. Ablation study. Visualization of space-time slices for ablation study on PhysDreamer [47]. Our method can generate closer content compared with the real capture. + +![](images/102baeb6d07d5d0d711306dcf2f6d5af1135ed4f80be00a8005a3ceed048c992.jpg) +w/o MPDP + +![](images/270b0dae470c8896b75b09eeabf5e09d2f1f10717298862c0a76ce8322341ef3.jpg) +K-Means Sampling + +gle objects. Therefore, we omit direct comparisons with these methods in open-world settings. Qualitative results are shown in Fig. 6 and on our project page, with quantitative results in Tab. 2. Additionally, we integrate LGM [36] to generate 3D assets from single images and perform physical simulations as demonstrated in Fig. 6. + +# 7. Conclusion + +We introduce PhysSplat, a framework for generating physics-based dynamics and photorealistic renderings. We begin with precise scene reconstruction and object-level 3D open-vocabulary segmentation, followed by multi-view image inpainting. Then, we propose MLLM-based Physical Property Perception (MLLM-P3) to predict mean physical properties of objects. Using these mean values and object geometry, the Material Property Distribution Prediction model (MPDP) then estimates the complete distribution, reframing the task as probability distribution estimation to reduce computational costs. Finally, we simulate objects with particles sampled via the Physical-Geometric Adaptive Sampling (PGAS) strategy. Extensive experiments and user studies show that PhysSplat produces more realistic motion than state-of-the-art methods within much faster inference time. We believe that PhysSplat represents a meaningful advance toward more engaging and immersive virtual environments, unlocking diverse applications from realistic simulations to interactive virtual experiences. + +Limitation and future work. PhysSplat struggles to segment entire objects with occluded objects, leading to unnatural simulations. 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PhysTwin takes sparse videos (three camera views) of deformable objects under interaction as input and reconstructs a simulatable digital twin with complete geometry, high-fidelity appearance, and accurate physical parameters. This enables multiple applications, such as real-time interactive simulation using keyboards and robotic teleoperation devices, as well as model-based robot planning. + +# Abstract + +Creating a physical digital twin of a real-world object has immense potential in robotics, content creation, and XR. In this paper, we present PhysTwin, a novel framework that uses sparse videos of dynamic objects under interaction to produce a photo- and physically realistic, real-time interactive virtual replica. Our approach centers on two key components: (1) a physics-informed representation that combines spring-mass models for realistic physical simulation, generative shape models for geometry, and Gaussian splats for rendering; and (2) a novel multi-stage, optimization-based inverse modeling framework that reconstructs complete geometry, infers dense physical properties, and replicates realistic appearance from videos. Our method integrates an inverse physics framework with visual perception cues, enabling high-fidelity reconstruction even from partial, occluded, and limited viewpoints. PhysTwin supports modeling various deformable objects, including ropes, stuffed animals, cloth, and delivery packages. Experiments show that PhysTwin outperforms competing methods in reconstruction, rendering, future prediction, and simulation under novel interactions. We further demonstrate its applications in interactive real-time simulation and model-based robotic motion planning. Project Page: https://jianghanxiao.github.io/physwin-web/ + +# 1. Introduction + +The construction of interactive digital twins is essential for modeling the world and simulating future states, with applications in virtual reality, augmented reality, and robotic manipulation. A physically realistic digital twin (PhysTwin) should accurately capture the geometry, appearance, and physical properties of an object, allowing simulations that closely match observations in the real world. However, constructing such a representation from sparse observations remains a significant challenge. + +The creation of digital twins for deformable objects has long been a challenging topic in the vision community. While dynamic 3D methods (e.g., dynamic NeRFs [2, 5, 8, 13, 14, 17, 27, 29-31, 39-41, 43, 55, 56, 58, 61], dynamic 3D Gaussians [10, 20, 24, 33, 34, 59, 65, 66, 68]) capture observed motion, appearance, and geometry from videos, they omit the underlying physics and are thus unsuitable for simulating outcomes in unseen interactions. While recent neural-based models [4, 11, 28, 32, 36, 42, 49, 51, 52, 60, 64, 69] learn intuitive physics models from videos, they require large amounts of data and remain limited to specific objects or motions, whereas physics-driven approaches [9, 12, 27, 44, 63, 71, 72] often rely on pre-scanned shapes or dense observations to mitigate ill-posedness. Additionally, it requires dense viewpoint coverage and supports only limited motion + +types, making it unsuitable for general dynamics modeling. + +In this work, we aim to build an interactive PhysTwin from sparse-viewpoint RGB-D video sequences, capturing object geometry, non-rigid dynamic physics, and appearance for realistic physical simulation and rendering. We model deformable object dynamics with a spring-mass-based representation, enabling efficient physical simulation and handling a wide range of common objects, such as ropes, stuffed animals, cloth, and delivery packages. To address the challenges posed by sparse observations, we leverage shape priors and motion estimation from advanced 3D generative models [62] and vision foundation models [23, 46, 48] to estimate the topology, geometry, and physical parameters of our physical representation. Since some physical parameters (such as topology-related properties) are nondifferentiable and optimizing them efficiently is non-trivial, we design a hierarchical sparse-to-dense optimization strategy. This strategy integrates zero-order optimization [18] for non-differentiable topology and sparse physical parameters (e.g., collision parameters and homogeneous spring stiffness), while employing first-order gradient-based optimization to refine dense spring stiffness and further optimize collision parameters. For appearance modeling, we adopt a Gaussian blending strategy, initializing static Gaussians from sparse observations in the first frame using shape priors and deforming them with a linear blending algorithm to generate realistic dynamic appearances. + +Our inverse modeling framework effectively constructs interactive PhysTwin from videos of objects under interaction. We create a real-world deformable object interaction dataset and evaluate our method on three key tasks: reconstruction and resimulation, future prediction, and generalization to unseen interactions. Both quantitative and qualitative results demonstrate that our reconstructed PhysTwin aligns accurately with real-world observations, achieves precise future predictions, and generates realistic simulations under diverse unseen interactions. Furthermore, the high computational efficiency of our physics simulator enables real-time dynamics and rendering of our constructed PhysTwin, facilitating multiple applications, including real-time interactive simulation and model-based robotic motion planning. + +# 2. Related Works + +Dynamic Scene Reconstruction. Dynamic scene reconstruction aims to recover the underlying representation of dynamic scenes from inputs like depth scans [6, 26], RGBD videos [38], or monocular or multi-view videos [1, 5, 24, 31, 34, 39, 40, 43, 56, 58, 61, 67, 68]. Recent advancements in dynamic scene modeling have involved the adaptation of novel scene representations, including Neural Radiance Fields (NeRF) [2, 5, 8, 13, 14, 16, 17, 27, 29, 30, 30, 31, 39-41, 43, 55, 56, 58, 61] and 3D Gaussian splats [10, 20, 24, 33, 34, 59, 65, 66, 68]. D-NeRF [43] extends a canonical NeRF + +on dynamic scenes by optimizing a deformable field. Similarly, Deformable 3D-GS [66] optimizes a deformation field of each Gaussian kernel. Dynamic 3D-GS [34] optimizes the motion of Gaussian kernels for each frame to capture scene dynamics. 4D-GS [59] modulates 3D Gaussians with 4D neural voxels for dynamic multi-view synthesis. Although these methods achieve high-fidelity results in dynamic multiview synthesis, they primarily focus on reconstructing scene appearance and geometry without capturing real-world dynamics, limiting their ability to support action-conditioned future predictions and interactive simulations. + +# Physics-Based Simulation of Deformable Objects. + +Another line of work incorporates physical simulators to perform system identification of physical parameters during reconstruction. Earlier methods relied on prescanned static objects and required clean point cloud observations [9, 15, 19, 21, 35, 44, 47, 57]. Most recent approaches build upon SDF [45], NeRF [3, 12, 27] or Gaussian Splating [22, 63, 71, 72] to support more flexible physical digital twin reconstruction. Several works [12, 22, 63?] manually specify physics parameters, resulting in a mismatch between the simulation and real-world video observations. Other works [3, 27, 45, 71, 72] attempt to estimate physical parameters from videos. However, they are often constrained to synthetic data, limited motion, or the need for dense viewpoints to accurately reconstruct static geometry, limiting their practical applicability. The closest related work to ours is Spring-Gaus [72], which also utilizes a 3D Spring-Mass model for learning from videos. However, their physical model is overly regularized and violates real-world physics, lacking momentum conservation and realistic gravity. Moreover, Spring-Gaus requires dense viewpoint coverage to reconstruct the full geometry at the initial state, which is impractical in many real-world settings. The motions are also limited to tabletop collisions and lack action inputs, making Spring-Gaus unsuitable as a general dynamics model for downstream applications. + +Learning-Based Simulation of Deformable Objects. Analytically modeling the dynamics of deformable objects is challenging due to the high complexity of the state space and the variability of physical properties. Recent works [4, 11, 36, 60, 64] have chosen to use neural network-based simulators to model object dynamics. Specifically, graph-based networks effectively learn the dynamics of various types of objects such as plasticine [51, 52], cloth [32, 42], fluid [28, 49], and stuffed animals [69]. GS-Dynamics [69] attempted to learn object dynamics directly from real-world videos using tracking and appearance priors from Dynamic Gaussians [34], and generalized well to unseen actions. However, these learned models need extensive training samples and are often limited to specific environments with limited motion ranges. In contrast, our method requires only one interaction trial while achieving a broader range of motions. + +![](images/cf02b54ebec8b8e16d7d85c57cc8e0f5849aacc78984600af987513635411b70.jpg) +Figure 2. Overview of Our PhysTwin Framework. We present an overview of our PhysTwin framework, where the core representation includes geometry, topology, physical parameters (associated with springs and contacts), and Gaussian kernels. To optimize PhysTwin, we minimize the rendering loss and the discrepancy between simulated and observed geometry/motion. The rendering loss optimizes the Gaussian kernels, while the geometry and motion losses refine the overall geometry, topology, and physical parameters in PhysTwin. + +![](images/fa946fca8765ed51f4d69ea8d245b8c1b7ae32e788f55a5bf1a4ea3589a28031.jpg) + +# 3. Preliminary: Spring-Mass Model + +Spring-mass models are widely used for simulating deformable objects due to their simplicity and computational efficiency. A deformable object is represented as a set of spring-connected mass nodes, forming a graph structure $\mathcal{G} = (\mathcal{V},\mathcal{E})$ , where $\mathcal{V}$ is the set of mass points and $\mathcal{E}$ is the set of springs. Each mass node $i$ has a position $\mathbf{x}_i\in \mathbb{R}^3$ and velocity $\mathbf{v}_i\in \mathbb{R}^3$ , which evolve over time according to Newtonian dynamics. Springs are constructed between neighboring nodes based on a predefined topology, defining the elastic structure of the object. + +The force on node $i$ is the result of the combined effects of adjacent nodes connected by springs: + +$$ +\mathbf {F} _ {i} = \sum_ {(i, j) \in \mathcal {E}} \mathbf {F} _ {i, j} ^ {\text {s p r i n g}} + \mathbf {F} _ {i, j} ^ {\text {d a s h p o t}} + \mathbf {F} _ {i} ^ {\text {e x t}}, \tag {1} +$$ + +where the spring force and dashpot damping force between nodes $i$ and $j$ are given by $\mathbf{F}_{i,j}^{\mathrm{spring}} = k_{ij}(\| \mathbf{x}_j - \mathbf{x}_i\| - l_{ij})\frac{\mathbf{x}_j - \mathbf{x}_i}{\|\mathbf{x}_j - \mathbf{x}_i\|}$ and $\mathbf{F}_{i,j}^{\mathrm{dashpot}} = -\gamma (\mathbf{v}_i - \mathbf{v}_j)$ , respectively. Here, $k_{ij}$ is the spring stiffness, $l_{ij}$ is the rest length, and $\gamma$ is the dashpot damping coefficient. The external force $\mathbf{F}_i^{\mathrm{ext}}$ accounts for factors such as gravity, collisions, and user interactions. The spring force restores the system to its rest shape, while the dashpot damping dissipates energy, preventing oscillations. For collisions, we use impulse-based collision handling when two mass points are very close, including collisions between the object and the collider, as well as between two object points. + +The spring-mass model updates the system state with a dynamic model $\mathbf{X}_{t + 1} = f_{\alpha ,\mathcal{G}_0}(\mathbf{X}_t,a_t)$ by applying explicit Euler integration to both velocity and position. More formally, + +for all $i$ , $\mathbf{v}_i^{t + 1} = \delta \left(\mathbf{v}_i^t +\Delta t\frac{\mathbf{F}_i}{m_i}\right)$ , $\mathbf{x}_i^{t + 1} = \mathbf{x}_i^t +\Delta t\mathbf{v}_i^{t + 1}$ where $\mathbf{X}_t$ represents the system state at time $t$ , and $\delta$ represents the drag damping. In this formulation, $\alpha$ denotes all physical parameters of the spring-mass model, including spring stiffness, collision parameters, and damping. It also encompasses the parameters related to the control interaction. $\mathcal{G}_0$ represents the "canonical" geometry and topology for the spring-mass system1, and $a_{t}$ represents the action at time $t$ . + +# 4. Method + +In this section, we formulate the construction of PhysTwin as an optimization problem. We then present our two-stage strategy, where the first stage addresses the physics-related optimization, followed by the appearance-based optimization in the second stage. Finally, we demonstrate the capability of our framework to perform real-time simulation using the constructed PhysTwin. + +# 4.1. Problem Formulation + +Given three RGBD videos of a deformable object under interaction, our objective is to construct a PhysTwin model that captures the geometry, appearance, and physical parameters of the object over time. At each time frame $t$ , we denote the RGBD observations from the $i$ -th camera as $\mathbf{O}_{t,i}$ , where $\mathbf{O} = (\mathbf{I},\mathbf{D})$ represents the RGB image $\mathbf{I}$ and depth map $\mathbf{D}$ . + +The goal of our optimization problem is to minimize the discrepancy between the predicted observation $\hat{\mathbf{O}}_{t,i}$ and the actual observation $\mathbf{O}_{t,i}$ . The predicted observation is derived by projecting and rendering the predicted state $\hat{\mathbf{X}}_t$ onto images through a function $g_{\theta}$ , where $\theta$ encodes the appearance + +of the objects represented by Gaussian splats. The 3D state $\hat{\mathbf{X}}_t$ evolves over time according to the Spring-Mass model, which captures the deformable object's dynamics and updates the state using the explicit Euler integration method. The optimization problem is formulated as: + +$$ +\min _ {\alpha , \mathcal {G} _ {0}, \theta} \sum_ {t, i} C \left(\hat {\mathbf {O}} _ {t, i}, \mathbf {O} _ {t, i}\right) \tag {2} +$$ + +s.t. $\hat{\mathbf{O}}_{t,i} = g_{\theta}(\hat{\mathbf{X}}_t,i),\qquad \hat{\mathbf{X}}_{t + 1} = f_{\alpha ,\mathcal{G}}(\hat{\mathbf{X}}_t,a_t),$ + +where $\alpha, \mathcal{G}_0, \theta$ captures the physics, geometry, topology and appearance parameters (Sec. 3); the cost function quantifies the difference between the predicted observation $\hat{\mathbf{O}}_{t,i}$ and the actual observation $\mathbf{O}_{t,i}$ . This cost function is decomposed into three components: $C = C_{\mathrm{geometry}} + C_{\mathrm{motion}} + C_{\mathrm{render}}$ , each capturing the discrepancy between the inferred system states and the corresponding observations from 3D geometry, 3D motion tracking, and 2D color, respectively (we defer the details of each cost component to Sec. 4.2.1 and Sec. 4.2.2). The function $g_{\theta}$ is the observation model, describing the projection from the predicted state to the image plane and rendering image-space sensory observation from the $i$ -th camera. The $f_{\alpha,\mathcal{G}}$ models the dynamic evolution of the object's state under the Spring-Mass model (Sec. 3). + +# 4.2. PhysTwin Framework + +Given the complexity of the overall optimization defined in Eq. 2, our PhysTwin framework decomposes it into two stages. The first stage focuses on optimizing the geometry and physical parameters, while the second stage is dedicated to optimizing the appearance-related parameters. + +# 4.2.1. Physics and Geometry Optimization + +As outlined in our optimization formulation in Sec. 4.1, the objective is to minimize the discrepancy between the predicted observation $\hat{\mathbf{O}}_{t,i}$ and the actual observation $\mathbf{O}_{t,i}$ . First, we convert the depth observations $\mathbf{D}_t$ at each time frame $t$ into the observed partial 3D point cloud $\mathbf{X}_t$ . In the first stage, we consider the following formulation for the optimization: + +$$ +\min _ {\alpha , \mathcal {G} _ {0}} \sum_ {t} \left(C _ {\text {g e o m e t r y}} \left(\hat {\mathbf {X}} _ {t}, \mathbf {X} _ {t}\right) + C _ {\text {m o t i o n}} \left(\hat {\mathbf {X}} _ {t}, \mathbf {X} _ {t}\right)\right) \tag {3} +$$ + +s.t. $\hat{\mathbf{X}}_{t + 1} = f_{\alpha ,\mathcal{G}_0}(\hat{\mathbf{X}}_t,a_t)$ + +where the $C_{\mathrm{geometry}}$ function quantifies the single-direction Chamfer distance between the partially observed point cloud $\mathbf{X}_t$ and the inferred state $\hat{\mathbf{X}}_t$ , and $C_{\mathrm{motion}}$ quantifies the tracking error between the predicted point $\hat{\mathbf{x}}_i^t$ and its corresponding observed tracking $\mathbf{x}_i^t$ . The observed tracking is obtained using the vision foundation model CoTracker3 [23], followed by lifting the result to 3D via depth map unprojection. + +There are three main challenges in the first-stage optimization: (1) partial observations from sparse viewpoints; + +(2) joint optimization of both the discrete topology and physical parameters; and (3) discontinuities in the dynamic model, along with the long time horizon and dense parameter space, which make continuous optimization difficult. To address these challenges, we handle the geometry and other parameters separately. Specifically, we first leverage generative shape initialization to obtain the full geometry, then employ our two-stage sparse-to-dense optimization to refine the remaining parameters. + +Generative Shape Prior. Due to partial observations, recovering the full geometry is challenging. We leverage a shape prior from the image-to-3D generative model TRELLIS [62] to generate a complete mesh conditioned on a single RGB observation of the masked object. To improve mesh quality, the input to TRELLIS is first enhanced using a super-resolution model [48] that upscales the segmented foreground (obtained via Grounded-SAM2 [46]). While the resulting mesh corresponds reasonably well with the camera observation, we can still observe inconsistencies in scale, pose, and deformation. + +To address this, we design a registration module that uses 2D matching for scale estimation, rigid registration, and non-rigid deformation. A coarse-to-fine strategy first estimates initial rotation via 2D correspondences matched using SuperGlue [50], followed by refinement with the Perspective-n-Point (PnP) [25] algorithm. We resolve scale and translation ambiguities by optimizing the distances between matched points in the camera coordinate system. After applying these transformations, the objects are aligned in pose, with some deformations handled by as-rigid-as-possible registration [53]. Finally, ray-casting alignment ensures that observed points match the deformed mesh without occlusions. + +These steps yield a shape prior aligned with the first-frame observations, which serves as a crucial initialization for the inverse physics and appearance optimization stages. + +Sparse-to-Dense Optimization. The Spring-Mass model consists of both the topological structure (i.e., the connectivity of the springs) and the physical parameters defined on the springs. As mentioned in Sec. 3, we also include control parameters to connect springs between control points and object points, defined by a radius and a maximum number of neighbors. Similarly, for topology optimization, we employ a heuristic approach that connects nearest-neighbor points, also parameterized by a connection radius and a maximum number of neighbors, thereby controlling the density of the springs. To extract control points from video data, we utilize Grounded-SAM2 [46] to segment the hand mask and CoTracker3 [23] to track hand movements. After lifting the points to 3D, we apply farthest-point sampling to obtain the final set of control points. + +All the aforementioned components constitute the parameter space we aim to optimize. The two main challenges are: (1) some parameters are non-differentiable (e.g., the radius + +and maximum number of neighbors); and (2) to represent a wide range of objects, we model dense spring stiffness, leading to a parameter space with tens of thousands of springs. + +To address these challenges, we introduce a hierarchical sparse-to-dense optimization strategy. Initially, we employ zero-order, sampling-based optimization to estimate the parameters, which naturally circumvents the issue of differentiability. However, zero-order optimization becomes inefficient when the parameter space is too large. Therefore, in the first stage, we assume homogeneous stiffness, allowing the topology and other physical parameters to achieve a good initialization. In the second stage, we further refine the parameters using first-order gradient descent, leveraging our custom-built differentiable spring-mass simulator. This stage simultaneously optimizes the dense spring stiffness and collision parameters. + +Beyond the optimization strategy, we incorporate additional supervision by utilizing tracking priors from vision foundation models. We lift the 2D tracking prediction into 3D to obtain pseudo-ground-truth tracking data for the 3D points, which forms a crucial component of our cost function as mentioned in Eq. (3). + +By integrating our optimization strategy with a cost function that leverages additional tracking priors, our PhysTwin framework can effectively and efficiently model the dynamics of diverse interactable objects from videos. + +# 4.2.2. Appearance Optimization + +For the second-stage appearance optimization, to model object appearance, we construct a set of static 3D Gaussian kernels parameterized by $\theta$ , with each Gaussian defined by a 3D center position $\mu$ , a rotation matrix represented by a quaternion $q \in \mathbf{SO}(3)$ , a scaling matrix represented by a 3D vector $s$ , an opacity value $\alpha$ , and color coefficients $c$ . We optimize $\theta$ here via + +$$ +\min _ {\theta} \sum_ {t, i} C _ {\text {r e n d e r}} \left(\hat {\mathbf {I}} _ {i, t}, \mathbf {I} _ {i, t}\right) \text {s . t .} \hat {\mathbf {I}} _ {i, t} = g _ {\theta} \left(\hat {\mathbf {X}} _ {t}, i\right), \tag {4} +$$ + +where $\hat{\mathbf{X}}_t$ is the optimized system states at time $t$ , $i$ is the camera index, and $\mathbf{I}_{i,t}, \hat{\mathbf{I}}_{i,t}$ are the ground truth image and rendered image from camera view $i$ at time $t$ , respectively. $C_{\mathrm{render}}$ computes the $\mathcal{L}_1$ loss with a D-SSIM term between the rendering and ground truth image. For simplicity, we set $t = 0$ to optimize appearance only at the first frame. We restrict the Gaussian shape to be isotropic to prevent spiky artifacts during deformation. + +To ensure realistic rendering under deformation, we need to dynamically adjust each Gaussian at each timestep $t$ based on the transition between states $\hat{\mathbf{X}}_t$ and $\hat{\mathbf{X}}_{t + 1}$ . To achieve this, we adopt a Gaussian updating algorithm using Linear Blend Skinning (LBS) [20, 54, 69], which interpolates the motions of 3D Gaussians using the motions of neighboring mass nodes. Please refer to the supplementary for details. + +# 4.3. Capabilities of PhysTwin + +Our constructed PhysTwin supports real-time simulation of deformable objects under various motions while maintaining realistic appearance. This real-time, photorealistic simulation enables interactive exploration of object dynamics. + +By introducing control points and dynamically connecting them to object points via springs, our system can simulate diverse motion patterns and interactions. These capabilities make PhysTwin a powerful representation for real-time interactive simulation and model-based robotic motion planning, which are further described in Sec. 5.3. + +# 5. Experiments + +In this section, we evaluate the performance of our PhysTwin framework across three distinct tasks involving different types of objects. Our primary objective is to address the following three questions: (1) How accurately does our framework reconstruct and resimulate deformable objects and predict their future states? (2) How well does the constructed PhysTwin generalize to unseen interactions? (3) What is the utility of PhysTwin in downstream tasks? + +# 5.1. Experiment Settings + +Dataset. We collect a dataset of RGBD videos capturing human interactions with various deformable objects with different physical properties, such as ropes, stuffed animals, cloth, and delivery packages. Three RealSense-D455 RGBD cameras are used to record the interactions. Each video is 1 to 10 seconds long and captures different interactions, including quick lifting, stretching, pushing, and squeezing with one or both hands. We collect 22 scenarios encompassing various object types, interaction types, and hand configurations. For each scenario, the RGBD videos are split into a training set and a test set following a 7:3 ratio, where only the training set is used to construct PhysTwin. We manually annotate 9 ground-truth tracking points for each video to evaluate tracking performance with the semi-auto tool introduced in [7]. + +Tasks. To assess the effectiveness of our PhysTwin framework and the quality of our constructed PhysTwin, we formulate three tasks: (1) Reconstruction & Resimulation; (2) Future Prediction; and (3) Generalization to Unseen Actions. + +For the Reconstruction & Resimulation task, the objective is to construct PhysTwin such that it can accurately reconstruct and resimulate the motion of deformable objects given the actions represented by the control point positions. + +For the Future Prediction task, we aim to assess whether PhysTwin can perform well on unseen future frames during its construction. For the Generalization to Unseen Interactions task, the goal is to assess whether PhysTwin can adapt to different interactions. To evaluate this, we construct a generalization dataset consisting of interaction pairs performed + +![](images/ebfe4cb5d0510c3bb1e092bf8b737047301d3a6e464897eda3349f3f20b0d626.jpg) +Figure 3. Qualitative Results on Reconstruction & Resimulation and Future Prediction. We visualize the rendering results of different methods on two tasks. For the reconstruction & resimulation task, our method achieves a better match with the observations. For the future prediction task, our method accurately predicts the future state of the objects. In contrast, the baselines fail in most cases: GS-Dynamics [69] tends to remain static, while Spring-Gauss [72] frequently causes the physical model to crash. + +![](images/f2e0758fafcc09e1e426e3e5379595a1ef1b59e0c40d4e8b0f638970bb992b66.jpg) +Figure 4. Qualitative Results on Generalization to Unseen Interactions. We visualize the simulation of a deformable object under unseen interactions using our method and GS-Dynamics [69]. The leftmost image shows the interaction used to train the dynamics models, while the images on the right demonstrate their generalization to unseen interactions. Our PhysTwin significantly outperforms prior work. + +Table 1. Quantitative Results on Reconstruction & Resimulation and Future Prediction. We compare the performance of our method with two prior work, GS-Dynamics [69] and Spring-Gaus [72], on two tasks: reconstruction & resimulation and future prediction. Our PhysTwin framework consistently outperforms the baselines across all metrics. + +
TaskReconstruction & ResimulationFuture Prediction
MethodCD ↓Track Error ↓IoU % ↑PSNR ↑SSIM ↑LPIPS ↓CD ↓Track Error ↓IoU % ↑PSNR ↑SSIM ↑LPIPS ↓
Spring-Gaus [72]0.0410.05057.623.4450.9280.1020.0620.09446.422.4880.9240.113
GS-Dynamics [69]0.0140.02272.126.2600.9400.0520.0410.07049.822.5400.9240.097
PhysTwin (Ours)0.0050.00984.428.2140.9450.0340.0120.02272.525.6170.9410.055
+ +Table 2. Quantitative Results on Generalization to Unseen Interactions. We compare our method with GS-Dynamics [69] on generalization to unseen interactions. Both methods are trained on the same video with a specific interaction and tested on unseen interactions. Our method achieves significantly better results. + +
MethodCD ↓Track Error ↓IoU % ↑PSNR ↑SSIM ↑LPIPS ↓
GS-Dynamics [69]0.0290.03863.425.0530.9340.067
PhysTwin (Ours)0.0130.01872.1826.1990.9380.047
+ +on the same object but with varying motions, including differences in hand configuration and interaction type. + +Baselines. To the best of our knowledge, there is currently no existing work that demonstrates good performance across all three tasks. Therefore, we select two main research directions as baselines and further augment them to match the tasks in our setting (full details in the supplementary). + +The first baseline we consider is a physics-based simulation method for identifying the material properties of deformable objects, Spring-Gaus [72]. Their work has demonstrated strong capabilities in reconstruction, resimulation, and future prediction in its original setting. However, their framework does not support external control inputs, so we augment it with additional control capabilities. + +The second baseline is a learning-based simulation approach, GS-Dynamics [69], which employs a GNN-based neural dynamics model to learn system dynamics directly from partial observations. In their original setting, video preprocessing with Dyn3DGS [34] is required to obtain tracking information. For a fairer comparison, we strengthened it by using our 3D-lifting tracker based on CoTracker3 [23], which provides more efficient and accurate supervision for training the neural dynamics model used by GS-Dynamics. + +Evaluation. To better understand whether our prediction matches the observations, we evaluate predictions in both 3D and 2D. For the 3D evaluation, we use the single-direction Chamfer Distance (partial ground truth with our full-state prediction) and the tracking error (based on our manually annotated ground-truth tracking points). For the 2D evaluation, we assess image quality using PSNR, SSIM, and LPIPS [70], and silhouette alignment using IoU. We perform 2D evaluation only at the center viewpoint due to optimal visibility of objects, with metrics averaged across all frames and scenarios. Specially, for the Spring-Gaus [72] baseline, its optimization process is unstable due to inaccurate physics modeling. Therefore, we report the above metrics only for its successful cases. + +![](images/0d7e2cf972cfa74ecebf4b5fbc10a947df60dc074ae583f4f59f6ea9c30593cb.jpg) +(a) Real-Time Interactive Simulation using Keyboard + +![](images/4e2a616fff47147a6a9a907ffd14fc4fd571fea94c5774a574a8993be31de447.jpg) +Figure 5. Applications of our PhysTwin. Our constructed PhysTwin supports a variety of tasks, including real-time interactive simulation, which can accept input from either a keyboard or a robot teleoperation setup. Meanwhile, PhysTwin also enables model-based robot planning to accomplish tasks such as lifting a rope into some specific configuration. + +![](images/07b920945a093abad30572e367661a5e2e5042e32ad53e0b4b742d86d1f4b733.jpg) +(b) Real-Time Interactive Simulation using Teleoperation + +![](images/1401e8bfb4e1ddc07d4ce08b929c664b578a84223d6c64f9ce4d050c01914a38.jpg) +(c) Model-Based Robot Planning + +# 5.2. Results + +To assess the performance of our framework and the quality of our constructed PhysTwin, we compare with two augmented baselines across three task settings. Our quantitative analysis reveals that the PhysTwin framework consistently outperforms the baselines across various tasks. + +Reconstruction & Resimulation. The quantitative results in Tab. 1 Reconstruction & Resimulation column demonstrate the superior performance of our PhysTwin method over baselines. Our approach significantly improves all evaluated metrics, including Chamfer Distance, tracking error, and 2D IoU, confirming that our reconstruction and resimulation align more closely with the original observations. This highlights the effectiveness of our model in learning a more accurate dynamics model under sparse observations. Additionally, rendering metrics show that our method produces more realistic 2D images, benefiting from the Gaussian blending strategy and enhanced dynamic modeling. Fig. 3 further provides qualitative visualizations across different objects, illustrating precise alignment with original observations. Notably, our physics-based representation inherently improves point tracking. After physics-constrained optimization, our tracking surpasses the original CoTracker3 [23] predictions used for training, achieving better alignment after global optimization (See supplement for more details). + +Future Prediction. Table 1, in the Future Prediction column, demonstrates that our method achieves superior performance in predicting unseen frames, excelling in both dynamics alignment and rendering quality. Fig. 3 further provides qualitative results, illustrating the accuracy of our predictions on unseen frames. + +Generalization to Unseen Interactions. We also evaluate the generalization performance to unseen interactions. Our dataset includes transfers from one interaction (e.g., single lift) to significantly different interactions (e.g., double stretch). We directly use our constructed PhysTwin and leverage our registration pipeline to align it with the first frame of the target case. Fig. 4 shows that our method closely matches the ground truth observations in terms of dynamics. Quantitative results further demonstrate the robustness of + +our method across different actions. In contrast, the neural dynamics model struggles to adapt to environmental changes and diverse interactions as effectively as our approach. Moreover, in unseen interaction scenarios, our method achieves performance comparable to that on the future prediction task, highlighting the robustness and generalization capability of our constructed PhysTwin. + +# 5.3. Application + +The efficient forward simulation capabilities of our SpringMass simulator, implemented using Warp [37], enable a variety of downstream applications. Fig. 5 showcases key applications enabled by our PhysTwin: (1) Interactive Simulation: Users can interact with objects in real time using keyboard controls, either with one or both hands. The system also supports real-time simulation of an object's future state during human teleoperation with robotic arms. This feature serves as a valuable tool for predicting object dynamics during manipulation. (2) Model-Based Robotic Planning: Owing to the high fidelity of our constructed PhysTwin, it can be used as a dynamic model in planning pipelines. By integrating it with model-based planning techniques, we can generate effective motion plans for robots to complete a variety of tasks. + +# 6. Conclusion + +We introduced PhysTwin, a novel framework for constructing physical digital twins from sparse videos, enabling effective reconstruction and resimulation of deformable objects. Our approach excels in predicting future states and simulating object interactions that generalize to unseen actions. We showed the superior performance of our method across various object types, control configurations, and task settings, significantly outperforming prior work. PhysTwin enables various downstream tasks that demand high-speed simulation and accurate future prediction. Moreover, our approach provides valuable insights for robotic manipulation. By bridging perception and physics-based simulation, PhysTwin serves as a crucial tool for guiding robot interactions, making real-world deployment more efficient and reliable. + +# Acknowledgement + +This work is partially supported by the Toyota Research Institute (TRI), the Sony Group Corporation, Google, Dalus AI, the DARPA TIAMAT program (HR0011-24-9-0430), the Intel AI SRS gift, Amazon-Illinois AICE grant, Meta Research Grant, IBM IIDAI Grant, and NSF Awards #2331878, #2340254, #2312102, #2414227, and #2404385. We greatly appreciate the NCSA for providing computing resources. This article solely reflects the opinions and conclusions of its authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the sponsors. 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However, IHI is susceptible to complex errors arising from imaging steps, and its quality is limited by existing signal processing-based reconstruction algorithms. Two key challenges hinder performance enhancement: 1) the lack of training datasets. 2) the difficulty in eliminating IHI-specific degradation components through learning-based methods. To address these challenges, we propose a novel IHI reconstruction pipeline. First, based on imaging physics and radiometric calibration data, we establish a simplified yet accurate IHI degradation model and a parameter estimation method. This model enables the synthesis of realistic IHI training datasets from hyperspectral images (HSIs), bridging the gap between IHI reconstruction and deep learning. Second, we design the Interferometric Hyperspectral Reconstruction Unfolding Transformer (IHRUT), which achieves effective spectral correction and detail restoration through a stripe-pattern enhancement mechanism and a spatial-spectral transformer architecture. Experimental results demonstrate the superior performance and generalization capability of our method. The code and are available at https://github.com/bit1120203554/IHRUT. + +# 1. Introduction + +In the field of remote sensing, hyperspectral images (HSIs) serve as crucial repositories of spectral information related to materials and structures. Among various imaging techniques, Interferometric Hyperspectral Imaging (IHI) captures interferograms using instruments and reconstructs HSIs through algorithms based on the spectral Fourier Transform (FT) relationship between interferograms and HSIs [4, 31]. Benefiting from its strengths in flux and spectral resolution [14, 21], IHI is extensively utilized in large- + +![](images/b2ff3a83b1d1eec28134c9f7ae8d4a5c1cefdbcb1d189235e4fa0d03cf015796.jpg) +Figure 1. Examples of degradation and reconstruction of IHI. (a) Spectral RGB visualization of IHI calibration data across three states: ideal, corrected yet noisy, and degraded, illustrating degradation components such as color shifts and stripe patterns in IHI. (b) Comparison of the same data processed by traditional methods, Restormer, and IHRUT trained on synthetic dataset. IHRUT outperforms the traditional method and the direct learning approach of Restormer. (c) Comparison of PSNR and complexity of learning-based methods highlights IHRUT's superior performance in IHI reconstruction. + +scale tasks aboard spacecraft [32]. + +Despite its advantages, IHI faces significant degradation issues arising from frequent overexposure and low-light conditions in satellite-borne scenarios, as well as complex imaging steps including scanning, interference, and sensing, as depicted in Fig. 2(b). Imaging degradation leads to complex error distributions [22] and significant signal loss (in Fig. 1(a)), posing crucial challenges for reconstruction. However, existing IHI reconstruction methods are constrained in performance (as seen in Fig. 1(b)) and efficiency by traditional frameworks and time-consuming correction steps. Although deep learning methods, including end-to-end networks and model-assisted networks such as Plug and Play [56] and deep unfolding [9, 13, 25], show effectiveness in HSI reconstruction, these methods remain underutilized in IHI tasks. To break the limitations of conventional reconstruction frameworks and enhance the imaging quality of IHI, two primary challenges need to be addressed sequentially. + +The first challenge lies in the lack of datasets for IHI, + +which hinders the application of learning-based methods in IHI. The high cost of data acquisition and significant hardware dependency limit the scale and generalizability of real IHI datasets for training. In the absence of real data, generating synthetic datasets from specific degradation models [16, 41, 52] is a common approach. Nevertheless, existing degradation models in IHI radiometric calibration [39, 43] are primarily based on complex optical processes and are not suitable for data synthesis. Effective simulation methods for IHI are still lacking. + +The second challenge lies in addressing special components of IHI degradation during the adaptation of learning-based methods. Although deep reconstruction networks possess powerful representation capabilities, they face difficulties in addressing specific characteristics of IHI degradation through direct learning without priors. For instance, in Fig. 1(c), stripe patterns caused by the scanning mechanism of IHI are difficult to eliminate through global spectral processing and denoising in Restormer [48], shown as the vertical stripe noises in the result. To better address degradation, priors and optimizations targeting these characteristics are necessary for reconstruction networks. + +In this paper, we propose a novel method for IHI reconstruction. To address the lack of datasets for learning, we propose a novel IHI data synthesis pipeline. Specifically, we establish a practical and accurate degradation model adaptable to data synthesis by simplifying the imaging physics through matrix operations. Based on the calibration and solution of the proposed model, we provide a method for generating realistic IHI datasets from HSIs. Furthermore, based on the generated dataset, we propose an Interferometric Hyperspectral Reconstruction Unfolding Transformer (IHRUT) optimized for addressing the IHI degradation components. Instead of direct learning without priors, we introduce a deep unfolding architecture and integrate the degradation model to guide the reconstruction process. Focusing on the specific characteristics of degradation, we introduce a stripe-pattern enhancement mechanism for an adaptive spatial-spectral transformer network. IHRUT exhibits low complexity and outstanding enhancement performance in IHI reconstruction, as illustrated in Fig. 1(c). Our contributions are summarized as follows: + +- We establish an accurate and simplified IHI degradation model based on imaging physics and experiments with radiometric calibration data. +- We propose a calibration-based model parameter estimation and data simulation pipeline to extract key features of degradation and generate realistic IHI datasets. +- We propose the IHRUT, an unfolding transformer network for IHI reconstruction tasks, which is verified to be effective and lightweight in reconstruction experiments. + +# 2. Related Works + +In this section, we review the researches most relevant to our work, including IHI, along with methods for dataset synthesis and HSI reconstruction. + +# 2.1. Interferometric Hyperspectral Imaging + +IHI stems from the FTS theories [4, 14, 31] and is composed of two parts as imaging and reconstruction. For imaging, existing IHI instruments are categorized into temporal, spatial, and spatio-temporal modulated types, each with distinct imaging processes, such as TS-SHIS [29] and LASIS [44]. For reconstruction, existing algorithms primarily consist of the following steps: correction for bad pixel [12, 28], trend terms [49], and phase [17, 35], followed by apodization [15, 36], FTS transformation and post-processing. Despite these model-driven methods, Chen et al. [10] recently attempted learning-based FCUN for reconstruction. However, FCUN is limited in reconstruction of pixel without considering spatial domain characteristics of HSIs. The lack of data restricts the development of learning-based IHI reconstruction with superior performance. + +# 2.2. Degradation Modeling and Dataset Synthesis + +Learning-based restoration [30, 40, 55] approaches typically draw their potential from data. However, the acquisition of large-scale real datasets is often challenging, and one solution is using degradation models as priors to generate synthetic datasets [24]. Common models include Gaussian white noise and homoscedastic Gaussian noise [1, 16, 37], among others. Wei [41, 42] introduced a camera calibration-based, precise noise model that allows simulated data to yield low-light noise recovery akin to real-data training outcomes. Zhang [52-54] extended this to HSI denoising, presenting a realistic dataset and an HSI noise model. These methods provide inspirations for addressing the challenges in existing IHI calibration and generating training data. + +# 2.3. Hyperspectral Image Reconstruction + +Existing HSI reconstruction focus on tasks such as RGB or infrared-to-HSI conversion [18, 46], and compressed sensing imaging (SCI) [2, 23]. Deep learning approaches outperforms traditional model-driven methods [5, 47] in terms of performance and generalization. These methods are categorized into two types: end-to-end (E2E) and model-aided networks. E2E methods directly learn the reconstruction mapping, with examples including CNN-based TSA-Net [33] and HDNet [20], RNN-based BIRNAT [11], and transformer-based MST, MST++, and CST [6-8]. Model-aided networks, exemplified by Deep Plug-and-Play (PnP) [56] and Deep Unfolding (DU), integrate iterative optimization with deep learning. Among these, DU adopts the same training strategy as E2E methods, thereby enhancing + +the network's adaptability to iterations compared to PnP, and achieving superior restoration performance. Examples include GAP-Net [34], transformer-based DAUHST [9], Proximal Gradient Descent (PGD)-based RDLUF [13], and Memory-Augmented MAUN [19]. However, for IHI tasks, these algorithms have yet to be applied and optimized. + +# 3. Method + +IHI is essentially a hardware-encoded, software-decoded process. Given a scene $\mathbf{C}$ , the observed image $\mathbf{I}_d$ and reconstructed HSI $\mathbf{C}'$ are obtained by: + +$$ +\mathbf {I} _ {d} = G _ {\Omega} (\mathbf {C}), \mathbf {C} ^ {\prime} = G ^ {\prime} (\mathbf {I} _ {d}), \tag {1} +$$ + +where $G_{\Omega}$ is the imaging process and $G'$ is the IHI reconstruction algorithm. Our research focuses on optimizing $G'$ , with the overall architecture shown in Fig. 2(a). We model $G$ into a simplified degradation model with calibration methods, and generate simulated data from the model. To overcome the limitations of $G'$ , we design and train IHRUT tailored to the degradation characteristics, achieving performance optimization. + +# 3.1. Degradation Modeling + +Our degradation model is based on LASIS [44], a scanning-based interferometric imaging spectrometer. The size of the sensor array in LASIS is $W \times L$ , where each unit is responsible for scanning a column ( $H \times 1 \times 1$ ) of the interferogram with a specific optical path difference (OPD). The errors are highly correlated within each signal column, but vary significantly between different columns depending on the response capabilities of sensors. We refer to this characteristic as the stripe pattern, which serves as a basic assumption of our degradation model. The degradation model is divided into two stages: optical and electronic. + +Optical Degradation. Optical degradation corresponds to various error terms during the propagation of light through the optical path of interferometer into the sensors. + +The input light signal can be considered as a hyperspectral signal in a certain wavelength range $[\lambda_{\mathrm{min}},\lambda_{\mathrm{max}}]$ . Assuming expression of the signal in the form of wavenumber $\nu$ ( $\nu = 1 / \lambda \in [1 / \lambda_{\mathrm{max}},1 / \lambda_{\mathrm{min}}]$ ) is $\mathbf{B}_0(\nu)\in \mathbb{R}^{H\times W\times N}$ . According to theories of IHI [4], $\mathbf{B}_0$ is Fourier transform-related to the interferogram. However, due to the imaging system's varying sensitivity to light in different frequencies, the actual captured spectral signal is the result of the original signal multiplied by a coefficient vector $\mathbf{A}$ in the spectral domain. Additionally, pose deviations in the interferometer lead to asymmetry in the interferogram, introducing a complex component as phase error into $\mathbf{A}$ . We define $\mathbf{A}\in \mathbb{C}^{W\times N}$ as the absolute response coefficient, and the interferogram signal can be represented as: + +$$ +\mathbf {I} _ {1} (l) = \mathcal {F} \left\{\mathbf {A} (\nu) \odot \mathbf {B} _ {0} \right\}, \tag {2} +$$ + +where $\odot$ is element-wise multiplication, and $l$ denotes OPD. + +In the process of Eq. 2, $\mathbf{I}_1$ is still approximately zero-centered. Nevertheless, the actual interferogram is superimposed with background light on each pixel, rendering all pixel values non-negative. The background light can be regarded as a partial component of the incident light, and its value is proportional to the average spectral brightness of the pixels in $\mathbf{B}_0$ . Finally, when the interferogram signal containing background light propagates to the sensor, the actual interferogram signal on the image plane is non-uniform due to instrument errors, differences in sensor units, and the frame transfer effect of the CCD. This non-uniformity disrupts the smoothness of the interferograms in the $W$ and $L$ -directions, as shown in Fig. 2(b). Let $\beta (\nu)\in \mathbb{R}^{W\times L}$ denote the background coefficient, and $\mathbf{M}\in \mathbb{R}^{W\times L}$ denote the non-uniformity as relative response coefficient, the overall model for optical degradation is: + +$$ +\begin{array}{l} \mathbf {I} _ {O} = \mathbf {M} \odot \left(\mathbf {I} _ {1} + \boldsymbol {\beta} \odot \mu_ {N} (\mathbf {B} _ {0})\right) \\ = \mathbf {M} \odot \left(\mathcal {F} \left\{\mathbf {A} \odot \mathbf {B} _ {0} \right\} + \boldsymbol {\beta} \odot \mu_ {N} (\mathbf {B} _ {0})\right), \tag {3} \\ \end{array} +$$ + +where $\mu (\cdot)$ denotes the mean value and $\sigma (\cdot)$ denotes the standard deviation. + +Electronic Degradation. Electronic Degradation refers to a series of random noises introduced during the signal conversion process after the light enters the sensors. + +After entering the sensor, the light signal undergoes the photoelectric effect. Due to the quantum property of light, the number of photoelectrons collected by the sensor within the exposure time is inevitably uncertain and follows a Poisson distribution, introducing shot noise, as: + +$$ +\begin{array}{l} \mathbf {I} _ {2} = \mathbf {K} \odot \left(\mathbf {I} _ {O} + \mathbf {N} _ {\text {s h o t}}\right), \\ \left(\mathbf {I} _ {O} + \mathbf {N} _ {\text {s h o t}}\right) \sim \mathcal {P} \left(\mathbf {I} _ {O}\right), \tag {4} \\ \end{array} +$$ + +where $\mathcal{P}(\cdot)$ denotes the Poisson distribution, $\mathbf{K}\in \mathbb{R}^{1\times W\times L}$ is the system gain related to the sensitivity (ISO) of the sensor array. The amplitude of shot noise is dependent on the signal $\mathbf{I}_O$ . + +Subsequently, the photoelectrons are converted into voltage signals via the readout circuit of the CCD sensor and then digitized through analog-to-digital conversion. In this process, a series of signal-independent degradations are introduced in the form of non-zero mean noise. In the noise, dark current $\mathbf{D} \in \mathbb{R}^{W \times L}$ is the main non-zero mean component, while zero-mean readout noise $\mathbf{N}_{\mathrm{read}}$ constitutes the remaining part. The amplitude of $\mathbf{N}_{\mathrm{read}}$ formed by different sensor units varies significantly due to the stripe pattern characteristic, but their normalized results are approximately uniform Gaussian noise. Let $\sigma_{\mathrm{read}} \in \mathbb{R}^{W \times L}$ denote the amplitude of readout noise on the sensor array, then the full model of electronic degradation can be expressed as: + +$$ +\begin{array}{l} \mathbf {I} _ {d} = \mathbf {K} \odot \left(\mathbf {I} _ {O} + \mathbf {N} _ {\text {s h o t}}\right) + \mathbf {D} + \mathbf {N} _ {\text {r e a d}}, \tag {5} \\ \mathrm {N} _ {\text {r e a d}} \sim \mathcal {N} (0, \sigma_ {\text {r e a d}}), \\ \end{array} +$$ + +![](images/2f2122f5e36cf34c5435e0747e3fc7593acd907744a69aea18198a733fd72baa.jpg) + +![](images/f1492e93011d01f19db4fe469e45a003948154ffaa5397a19fbb101d056ef14f.jpg) +Figure 2. (a) Our overall research framework. We estimate the parameters of the degradation model and incorporate HSI to generate synthetic dataset. Then, we train IHRUT on the synthetic dataset to endow it with the capability of real IHI reconstruction. (b) The degradation model is divided into 2 stages: electronic and optical degradation. + +where $\mathbf{I}_d$ is the degraded interferogram according to Eq. 1, and $\mathcal{N}(\mu, \sigma)$ denotes the Gaussian distribution. + +# 3.2. Calibration and Simulation + +Parameter estimation involves separation and extraction of degradation components from the radiometric calibration data captured by the LASIS instrument. The calibration data consists of two parts: the absolute calibration data $\mathbf{I}_A$ , which includes uniform light interferograms $\mathbf{I}_{Ai}$ ( $i = 1, \dots, n$ ) with varying brightness levels, along with their corresponding spectra $\mathbf{B}_{Ai}$ ( $i = 1, \dots, n$ ) (expressed in wavenumbers). The relative calibration data $\mathbf{I}_R$ is captured with an interferometer-removed instrument, including a dark measurement $\mathbf{I}_{R0}$ and a series of uniform light measurements $\mathbf{I}_{Ri}$ ( $i = 1, \dots, n$ ) without interference patterns. + +The parameters for electronic degradation can be derived from $\mathbf{I}_R$ . The dark current $\mathbf{D}$ is obtained by calculating the mean value of $\mathbf{I}_{R0}$ along the $H$ -direction, while the standard deviation of the remaining noise yields $\sigma_{\mathrm{read}}$ . Subsequently, compute the mean and variance for each $\mathbf{I}_{Ri}$ along the $H$ -direction as $\mu_H(\mathbf{I}_{Ri})$ and $\sigma_H^2 (\mathbf{I}_{Ri})$ . By eliminating the signal-independent component $(\mathbf{D}$ and $\sigma_{\mathrm{read}}^2)$ , the mean and variance of the signal-dependent component are estimated as $\mu_{\mathrm{shot}}$ and $\sigma_{\mathrm{shot}}$ . Since the Poisson distribution exhibits the property that the variance equals the mean $(\sigma^{2}(\mathbf{N}_{\mathrm{shot}}) = \mathbf{I}_{O})$ , $\mathbf{K}$ can be derived from the ratio of + +$$ +\boldsymbol {\sigma} _ {\text {s h o t}} \approx \mathbf {K} ^ {2} \odot \sigma^ {2} (\mathbf {N} _ {\text {s h o t}}) \text {t o} \boldsymbol {\mu} _ {\text {s h o t}} \approx \mathbf {K} \odot \mathbf {I} _ {O}, \text {a s}: +$$ + +$$ +\mathbf {D} = \mu_ {H} (\mathbf {I} _ {R 0}), \sigma_ {\text {r e a d}} = \sigma_ {H} (\mathbf {I} _ {R 0}), +$$ + +$$ +\mathbf {K} _ {i} = \frac {\boldsymbol {\sigma} _ {\text {s h o t}}}{\boldsymbol {\mu} _ {\text {s h o t}}} = \frac {\sigma_ {H} ^ {2} \left(\mathbf {I} _ {R i}\right) - \boldsymbol {\sigma} _ {\text {r e a d}} ^ {2}}{\mu_ {H} \left(\mathbf {I} _ {R i}\right) - \mathbf {D}}. \tag {6} +$$ + +The parameters for optical degradation are estimated after eliminating electronic degradation components from $\mathbf{I}_R$ and $\mathbf{I}_A$ . For modulation factor $\mathbf{M}$ , we divide it into two components as $\mathbf{M} = \mathbf{M}_R \odot \mathbf{M}_A$ . $\mathbf{M}_R$ is caused by sensor non-uniformity and is extracted from $\mu_H(\mathbf{I}_R)$ , while $\mathbf{M}_A$ arises from distortions in the scanning process and can be obtained through frequency domain analysis of $\mu_H(\mathbf{I}_A)$ . Subsequently, we obtain $\mathbf{I}_{Ai}'$ by removing $\mathbf{M}$ and $\mathbf{D}$ from $\mu_H(\mathbf{I}_{Ai})$ . The parameter $\mathbf{A}$ can be derived by comparing the wavenumber representations of $\mathbf{B}_{Ai}$ and $\mathbf{I}_{Ai}'$ , while $\beta$ can be extracted from the portions of $\mathbf{I}_{Ai}'$ outside the main signal bands in $\mathbf{B}_{Ai}$ , as: + +$$ +\mathbf {I} _ {A i} ^ {\prime} = \left(\mu_ {H} \left(\mathbf {I} _ {A i}\right) - \mathbf {D}\right) / \mathbf {M}, \quad \mathbf {A} _ {i} = \mathbf {B} _ {A i} / \mathcal {F} \left\{\mathbf {I} _ {A i} ^ {\prime} \right\}, \tag {7} +$$ + +$$ +\beta_ {i} = (\mathbf {I} _ {A i} ^ {\prime} - \mathcal {F} \{\mathbf {B} _ {A i} \}) / \mu_ {N} (\mathbf {B} _ {A i}). +$$ + +During the actual process of parameter selection, relatively accurate values of $\mathbf{K}$ , $\mathbf{M}$ , $\mathbf{A}$ , and $\beta$ can be obtained by averaging the estimations from multiple $i$ . Additionally, we observed that the parameters for electronic degradation exhibit randomness depending on the state of the sensors, while their logarithms demonstrate a linear correlation [42]. + +![](images/abb6d0e5a1f9bdffdaac2a34e898bbe46d581293ba3fd0a91a7d1da5226c208e.jpg) +(a) IHRUT Architecture + +![](images/9b9984c1925632215d832bd8f5cc803a7fb47e51b421a0e315de47cfed92eb57.jpg) +(b) Data Module + +![](images/f474ace0a000c0fc53e6cc37a63164b5149328416ea4484fe1f86172beebabb7.jpg) +(c) Prior Module + +![](images/8c971553539e6c1ef416c49ef96b291bd69008023eaa20457efb26b392780671.jpg) +(d) Stripe Pattern Enhancement (SPE) +Figure 3. The Architecture of IHRUT network. (a) The overall unfolding framework (b) The stripe-adaptive momentum Data module (c) The lightweight Prior module with stage interaction (d) The Stripe Pattern Enhancement (SPE) module, which is the core of IHRUT. + +To enhance the robustness of the model, we introduce an auxiliary parameter as electronic gain $e$ , and select the degradation parameters with the following operation: + +$$ +\log \left(e ^ {\prime}\right) \sim \mathcal {N} (0, e), \mathbf {K} ^ {\prime} = e ^ {\prime} \cdot \mathbf {K}, +$$ + +$$ +\mathbf {D} ^ {\prime} = e ^ {\prime} \cdot \mathbf {D}, \sigma_ {\text {r e a d}} ^ {\prime} = e ^ {\prime} \cdot \sigma_ {\text {r e a d}}, \tag {8} +$$ + +where $\mathbf{K}^{\prime}$ , $\mathbf{D}^{\prime}$ , and $\sigma_{\mathrm{read}}^{\prime}$ are the selected parameter values. By substituting HSI into the calibrated degradation model, realistic IHI data can be readily generated. Further details of the degradation model are in the Supplemental Document. + +# 3.3.IHRUT Network + +Degradation-guided Unfolding Architecture. Deep unfolding for HSI reconstruction integrates deep denoising networks with model-driven iterations. They model the imaging process with operations as $\mathbf{y} = \mathbf{F}\mathbf{x} + \mathbf{n}$ (with $\mathbf{F}$ as the imaging matrix and $\mathbf{n}$ as noise) and formulate the following optimization problem: + +$$ +\hat {\mathbf {x}} = \min \frac {1}{2} \| \mathbf {y} - \mathbf {F x} \| ^ {2} + \tau J (\mathbf {x}). \tag {9} +$$ + +Typical unfolding methods, such as Generalized Alternating Projection (GAP) and Proximal Gradient Descent (PGD) [13, 34], decompose the above optimization problem into data and prior subproblems, resulting in iterative updates as: + +$$ +\mathbf {z} _ {k + 1} = \mathbf {x} _ {k} + \rho \mathbf {F} ^ {T} (\mathbf {y} - \mathbf {F} \mathbf {x} _ {k}), \tag {10} +$$ + +$$ +\mathbf {x} _ {k + 1} = P (\mathbf {z} _ {k + 1}), +$$ + +where $\rho$ is a scale-invariant linear transformation that depends on the specific iterative method, and $P$ denotes a denoising network. + +For IHI, since the discrete FT can be represented as a matrix, the degradation model can also be transformed and introduced into Eq. 10. Specifically, by eliminating the signal-independent terms in the degradation model, let $\mathbf{F}\mathbf{x} = \mathbf{K}\odot \mathbf{M}\odot \mathcal{F}\{\mathbf{A}\odot \mathbf{x}\}$ . Given that $\mathbf{F}$ is invertible, let $\mathbf{F}'$ be the inverse of $\mathbf{F}$ , and define $\alpha = \rho \mathbf{F}^T\mathbf{F}$ . The iterative updates can then be rewritten as: + +$$ +\mathbf {z} _ {k + 1} = \mathbf {x} _ {k} + \boldsymbol {\alpha} \mathbf {F} ^ {\prime} (\mathbf {y} - \mathbf {F} \mathbf {x} _ {k}), +$$ + +$$ +\mathbf {x} _ {k + 1} = P \left(\mathbf {z} _ {k + 1}\right). \tag {11} +$$ + +The above formulation transforms the IHI problem and allows the unfolding methods for HSI reconstruction to be extended to IHI reconstruction. Our network is structured as shown in Fig. 3(a). The network mainly consists of two submodules: Data and Prior, with Stripe-Pattern Enhancement (SPE) attention being the core mechanism. + +Stripe Pattern Enhancement (SPE) Attention. In view of the stripe pattern characteristic, the degradation of IHI results exhibit strong correlations within and significant differences across $(H\times 1\times 1)$ -sized stripes. Conventional spectral mappings like convolution or channel attention cannot independently model and eliminate the spectral characteristics across stripes. SPE is designed to address this issue by independently modeling stripe-wise spectral characteristics in the attention mechanism. As shown in Fig. 3(d), SPE maps input $\mathbf{x}$ via a depth-separable convolution embedding subnet $C_1$ . Subsequently, $H$ -direction average pooling and subnet $C_2$ are applied to leverage the low-rank characteristics of HSI and obtain a stripe-pattern attention map of size $W\times d_{\mathrm{in}}$ . The feature from $C_1$ is further rescaled by the attention map and mapped to dimension $d_{\mathrm{out}}$ via a convolu + +tion, as: + +$$ +\begin{array}{l} \operatorname {A t t n} = C _ {2} \left(\operatorname {A v g P o o l} _ {H} \left(C _ {1} (\mathbf {x})\right)\right), \\ \operatorname {S P E} (x) = C _ {1} \left(C _ {1} (x) - C _ {1} (x)\right) \end{array} \tag {12} +$$ + +$$ +\operatorname {S P E} (\mathbf {x}) = \operatorname {C o n v} _ {1 \times 1} \left(C _ {1} (\mathbf {x}) \odot (\text {A t t n})\right). +$$ + +The design of SPE provides adaptability in handling stripe patterns and is applied across various parts of IHRUT. Adaptive Momentum Data Module. In the data module of IHRUT, we introduce two branches: projection and momentum. The projection branch uses the residual $(\mathbf{y} - \mathbf{F}\mathbf{x}_k)$ for fidelity optimization, while the momentum branch, inspired by momentum gradient descent methods [3, 45], fuses iterative history across stages via $(\mathbf{x}_k - \mathbf{x}_{k-1})$ to enhance robustness. Subsequently, during the fusion of $\mathbf{x}_k$ with both branches, we introduce a stripe-adaptive learning approach that involves two steps with SPE integration. As shown in Fig. 3(b), input $\mathbf{y}$ is mapped by a global $\mathrm{SPE}_0$ ( $d_{\mathrm{in}} = L$ , $d_{\mathrm{out}} = K$ ) for weighting to the projection at each stage. The fusion of branches $\mathbf{r}_k$ is further weighted by internal $\mathrm{SPE}_k$ and combined with $\mathbf{x}_k$ to produce $\mathbf{z}_k$ : + +$$ +\mathbf {r} _ {k} = \operatorname {S P E} _ {0} (\mathbf {y}) \cdot \mathbf {F} ^ {\prime} (\mathbf {y} - \mathbf {F} \mathbf {x} _ {k}) + \left(\mathbf {x} _ {k} - \mathbf {x} _ {k - 1}\right), \tag {13} +$$ + +$$ +\mathbf {z} _ {k} = \mathbf {x} _ {k} + \operatorname {S P E} _ {k} (\mathbf {r} _ {k}). +$$ + +This process assigns adaptive stripe-wise weights to both the projection and momentum branches, endowing the module with sufficient flexibility. + +Lightweight Cross-stage Prior Module. Originating from a U-shaped structure, our lightweight prior module replaces layer-wise dimension doubling with uniform dimensionality across layers, as shown in Fig. 3(c). Additionally, to mitigate information loss during iterations, we introduced a cross-stage feature fusion mechanism. This mechanism integrates the features $\mathbf{f}_k$ with the downsampled features of the current stage, replacing the encoder in the U-shaped network. The decoders (IHRTrans) employ spatial-spectral transformer blocks with window-based multi-head self-attention (W-MSA) and SPE for adaptive stripe pattern correction and denoising. The output is then used as $\mathbf{f}_{k + 1}$ and fed into the subsequent stage. The design of the prior module provides adequate performance while significantly reducing complexity (requiring only $50\%$ of the computational cost and parameters compared to recent U-shaped transformer-based methods [13, 25], as shown in Tab. 2). + +# 4. Experiments + +# 4.1. Datasets and Settings + +In this section, we briefly introduce the experimental setup. All datasets (interferometric and spectral) are preprocessed to conform to the standard LASIS data format shown in Tab. 1. The detailed implementation and data preparation process are described in the Supplemental Document. + +Synthetic Datasets. We prepare two HSI source datasets for simulation, namely HSOD-BIT [38] and Houston. + +HSOD-BIT is a multi-spectral HSI dataset consists of 319 fine-quality HSIs originating from objective detection. The dataset possesses suitable wavelength range (400-1000 nm) and a high resolution of $1240 \times 1680 \times 200$ . We randomly selected and preprocessed 50 images, generating 276 patches of $256 \times 256 \times 70$ for trainning and 6 scenes for testing. Houston is a commonly-used HSI in remote sensing of size $349 \times 1905 \times 144$ in $380 - 1050 \mathrm{~nm}$ , which is used as one scene for cross-domain test of methods. The size of 7 testing scenes is $256 \times 2048 \times 70$ . + +Real LASIS Dataset. We use absolute calibration data captured by the LASIS instrument (mentioned in Sec. 3.2) as our testing dataset. The dataset includes real interferograms captured in uniform light and corresponding ideal HSIs as the ground truth. The formats of all real data are shown in Tab. 1, with a size of $H = 120$ . + +
HSIwavenumberinterferogram
widthW=2048
channelsΛ =70N=221L=256
center--l =35
range[450,900] nm[0,0.0034] nm-1[-5140.8,32313.7] nm
resolution6.52nm-146.88nm
+ +Table 1. The standard data format of the LASIS instrument in our research. All data used in the IHI reconstruction experiments require preprocessing to align with this format. + +Implementation. Our degradation model and the proposed IHRUT network, along with other comparative methods, are implemented based on Numpy and PyTorch. The learning-based methods are trained on a single RTX 3090 with the Adam optimizer, where $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ . The total number of training epochs for all methods is 300, using a cosine annealing scheduler and linear warm-up. The batch size is 1, and the initial learning rate is 1e-4. The optimization objective of learning is the L1 loss. + +Evaluation Metrics. The reconstruction quality is evaluated by peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), while the complexity of the model is assessed by GFLOPs (evaluated on training patches) and the number of parameters (in millions). + +# 4.2. Degradation Model Validation + +To verify the effectiveness of our degradation model, we train the 5-stage IHRUT network with data simulated from our model along with 6 comparative models, and analyze the reconstruction performance on real testing dataset. Among these models, model $m_{1}$ is used for guiding traditional reconstruction. The models $m_{2}$ and $m_{3}$ serves as ablations of our optical parts (such as $\mathbf{M}$ ). $m_{4}$ and $m_{5}$ are equipped with Gaussian white noise and standard noise model $(\mathbf{N}_{\text{shot}}, \mathbf{N}_{\text{read}})$ for comparison. With our design of pixel-wise noise modeling for the stripe-pattern noise dis + +
AlgorithmsparametersGFLOPsHSOD-BITHoustonCalibration (Real)
s1s2s3s4s5s6avgs1s1s2s3avg
traditional--21.3821.6620.6018.9623.2721.6721.2620.5531.9526.4122.7927.05
0.9060.8990.9080.8880.9220.9220.9080.9270.9300.9240.9010.918
F'--25.7326.2926.4524.8627.6126.5326.2525.5231.3330.1028.9230.12
0.8480.8320.8580.8180.8640.8890.8510.9150.8470.8070.7650.806
DRUNet32.73M148.6333.0035.5735.1337.1735.3234.5835.1330.9937.3032.0528.5632.64
0.9770.9680.9760.9770.9770.9830.9760.9850.9840.9730.9580.972
Restormer26.18M146.6827.5129.4029.0028.1529.6127.2328.4825.5433.7328.7124.9529.13
0.9150.8990.9190.8880.9250.9330.9130.9440.9080.8570.8040.856
SCUNet9.74M49.1632.9435.8135.0337.2135.0535.0535.1831.5737.1331.5028.4232.35
0.9740.9660.9740.9750.9750.9810.9740.9850.9810.9650.9480.965
SST4.16M274.6026.8130.1129.8828.1730.7927.1028.8125.0933.1727.7725.4128.78
0.9370.9280.9440.9230.9480.9500.9380.9560.9350.8960.8620.897
BERT1.45M92.6433.5336.2535.4035.5535.9534.2135.1531.7637.9434.3730.5434.28
0.9460.9390.9540.9390.9560.9620.9490.9700.9490.9190.8850.918
GAP-net4.39M77.2319.7419.5819.1721.2320.2619.6519.9418.5821.1919.3017.0819.19
0.5950.5630.6350.5630.6120.6470.6030.6560.6100.4670.3440.474
PADUT-513.86M201.5940.7537.6736.3338.4937.6535.7638.3431.6634.3529.2525.7529.78
0.9880.9760.9820.9860.9840.9890.9840.9910.9880.9850.9800.984
RDLUF-39.29M155.7243.5241.4741.0044.1342.7443.3442.7038.4640.9537.5434.3437.61
0.9830.9750.9820.9800.9840.9870.9820.9910.9850.9770.9650.976
MAUN-74.78M165.9244.2641.6341.4645.3443.3843.9343.3339.7240.9639.1834.3038.15
0.9900.9820.9870.9890.9880.9910.9880.9950.9950.9940.9880.992
IHRUT-53.20M106.3645.1242.8242.4546.4243.8244.8544.2539.7342.4040.5135.4739.46
0.9910.9820.9870.9880.9870.9910.9880.9940.9950.9930.9880.992
IHRUT-74.42M145.8045.2542.6442.4646.5643.9844.9144.3039.8642.1340.6636.0439.61
0.9910.9820.9870.9890.9880.9920.9880.9950.9950.9940.9880.992
+ +Table 2. Comparison of reconstruction methods on (a) 6 synthetic scenes of HSOD-BIT. (b) 1 synthetic scene of Houton. (c) 3 real scenes of Calibration datasets with average values of 1000, 2000, and 3000. PSNR/SSIM (upper and lower entry in each cell, respectively) and complexity of different methods are shown. IHRUT demonstrates low complexity and superior performance. + +
ModelParametersMetrics
OpticalElectronicPSNR / SSIM
m1Trad.-27.05 / 0.918
m2A,β-26.20 / 0.863
m3A,β,M-33.96 / 0.839
m4A,β,MGaussian Noise37.95 / 0.965
m5A,β,MStandard Noise38.82 / 0.987
m6A,β,MOur Noise (pixel-wise)39.28 / 0.988
oursA,β,MOur Noise + e39.46 / 0.992
+ +Table 3. Validation of degradation model on real dataset. Among the models, $m_4$ is equipped with Gaussian white noise [37] for, and $m_5$ with standard noise model $(\mathbf{N}_{\text{shot}}, \mathbf{N}_{\text{read}})$ for comparison. Our model achieve the optimal performance. + +tribution, $m_{6}$ outperforms standard noise model by 0.64dB. Furthermore, the introduction of $e$ effectively enhances robustness (+0.18 dB). The comparative results validates the rationality and accuracy of our degradation model structure. + +# 4.3. Reconstruction Experiments + +Comparative Methods. In the experiments, the proposed IHRUT is compared with three categories of methods: (1) traditional methods such as the LASIS restoration method from the Xi'an Institute of Optics and Mechanics, and $\mathbf{F}^{\prime}$ mentioned in Sec. 3.3. (2) End-to-End (E2E) networks without priors in learning, which integrate FT as a preprocessing step with general restoration networks like + +DRUNet, Restormer, and SCUNet [48, 50, 51], as well as HSI denoising networks like SST and SERT [26, 27]. (3) Deep Unfolding HSI reconstruction methods adapted for IHI such as GAP-Net, PADUT, RDLUF, and MAUN [13, 19, 25, 34]. For each unfolding method, the results shown in Tab. 2 are for the optimal number of stages, while the analysis of different stage numbers can be found in the Supplemental Document. + +Simulated IHI Reconstruction. Tab. 2 presents the quantitative results of all methods on 6 scenes of HSOD-BIT and 1 scene of Houston. Our IHRUT achieves the best performance across all metrics, showing an average advantage of $0.85\mathrm{dB}$ over MAUN. The Houston remote sensing scene poses a challenge to the cross-domain generalization ability of reconstruction algorithms. Some methods, such as PADUT, show degraded performance, while IHRUT maintains superior performance with $0.14\mathrm{dB}$ than MAUN. As shown in Fig. 4(a) and Fig. 4(b), the visualization of the reconstruction errors further validates the quantitative results. E2E methods tend to leave noticeable color differences and stripe noises, whereas IHRUT achieves the smallest reconstruction errors, confirming its effectiveness in detail enhancement. + +Real IHI Reconstruction. Tab. 2 displays the quantitative results on 3 scenes of the real calibration dataset. For E2E methods that do not incorporate degradation priors, even + +![](images/e522bff1d624bf8e8f59ab8416976685a467d058369ee9f5eea2cf3241b62a9e.jpg) +(a) + +![](images/19239f51934585424db865387b58c1583349d6276347b11dc19a585fc912d57f.jpg) + +![](images/361d92c9cc11ad6ea2fbdcbe9b53728d3e003aa1a9bfa47b7b4204163ba5b30a.jpg) + +![](images/ecd8e1da41c86627db9b026dd593eb9b5ee4a93cd67cbd2993982767fe734397.jpg) + +![](images/d2821ac443636505dcfb449002ee9cb02315e7802805117cfc1329ffc118930c.jpg) + +![](images/949f71f361e3cd32a4c3238701c8965a6e96f5d75cfeaa37cf4eb64362ce4ec0.jpg) + +![](images/8b13f440f75dd9a285c47b40246e3ec3f2408423f7323aec5a7aca7c039f7271.jpg) + +![](images/560d99073a10df1045cceda73caa5a92325e3ac4ed54c3fe29612bd72f3168af.jpg) + +![](images/2ebbd962c5816e9df92f9eb8ae05dfc9b2182be562077153e2a47cdb03cbd068.jpg) + +![](images/b637c62a699d35861bb7b9eda625897eab3cec8402144679cb830809f38ebcfa.jpg) + +![](images/a743abad84821e48a5138685e9d6b8422bbecb2c28925bcf114eb1fbe80c44cd.jpg) + +![](images/e0896899cee6962ddcbd3769f84c603c903bd1e1e8bbba4f749c9b5bfa00c572.jpg) + +![](images/3b0a935311af64518584d088d3cfbf9b6618ffc3b47ef55ad1a25be38ded6250.jpg) + +![](images/6ebdcf96dd4f1b5971c6eb1e8dcd437c777563d09145689a10c2c665e5edb81f.jpg) + +![](images/30dd6c9e5fb4829e8421935c72aa74857a52cdf6f42048f523e60e82049290a6.jpg) + +![](images/4c58b784f49ca07cf9360106091fe098520e4f17e0d72179ffbdc476003242ad.jpg) + +![](images/c15ddf68372fd6726f47c5aecf5bb4a9d1f220b3e6a4a25ad8f8a42953fafce3.jpg) + +![](images/427e2a244971ba1abbb0c750a504fb9e03c34b258e3540cb17af86908cf6ce44.jpg) + +![](images/4b27898517f735d832aaaa0143db28fc4b78b08d20ff062db6c7a47f16d02052.jpg) + +![](images/89a591d83a02ae33f593923b26a5ee3839a6755793706f78cbe0e06c56bdfae9.jpg) + +![](images/e14a7f7be524a5dfa67faaad5e49db082407334a602bc08b11a21068faa12026.jpg) + +![](images/daecdd8f69dbbbfe72b76b487a4240a53587c35feb47fda37c91e6c4dae80279.jpg) + +![](images/7a331ed12717787ffe824e12f652640ecf98b8ecfb5933730a36cb079e4f2070.jpg) +GT + +![](images/a8206cad84888965372558cc9d317a26ddc9f139bab5ecf393ab6a5b1ce306ce.jpg) +traditional + +![](images/88a9194ea2e38488a313f19c372e076e41b6b9d24606edd7e86f942bfc522658.jpg) +F + +![](images/99fa921ba989b9d8205b3ee952b5441bf0264b07606fe3cdd6064c2830ed2e97.jpg) +Restomer + +![](images/d85de21797a9f7b5c8d60056f9294f8b3d66c3e6b4e8abe5207537ab9b2f4db3.jpg) +SCUNet + +![](images/0d19375c2ad880d37ddab615336ce70c5f12ecfe4c75b39380df1300e57dcb85.jpg) +SERT + +![](images/55c6b1077d200c237c4826502ce84725ea7d13940739e05d56983a43eee1df28.jpg) +GAPNet + +![](images/a43a6942a5682ab8c93745fa48013aeece38f61c6cc5123adae8ec89abdf1f28.jpg) +RDLUF-3 + +![](images/04e850297ceb91e9693e2ff6eb61da6d4393500c2d9f7c3377029de2c4cd3143.jpg) +MAUN-7 + +![](images/95ec906ed7f1f48d93ae534b98047f1ea34ffe27ade04151effbd9196345f9a5.jpg) +IHRUT-7 + +![](images/a9fc4e5668b33787ddf446003b6057a3f83f56d9bc011a9e69d07095613d0a2e.jpg) + +the better-performing SCUNet and SERT exhibit a gap of approximately 4 dB compared to recent unfolding methods, demonstrating the challenges in addressing the degradation process. Among the unfolding methods, our IHRUT shows a significant advantage, with an average PSNR improvement of approximately 1.4 dB compared to MAUN. In the visualization results shown in Fig. 4(c), most reconstruction methods retain varying degrees and types of noise, while IHRUT outperforms other methods in terms of noise removal. + +Complexity. As shown in Tab. 2, IHRUT benefits from its lightweight design and exhibits lower complexity compared to other unfolding methods. Particularly, the 5-stage version of IHRUT achieves a low complexity while maintaining high performance. + +
baselineDataPriorMetrics
SPE0SPEkMom.C-Stg.SPEPSNR/SSIM
✓34.37 / 0.934
✓✓38.73 / 0.982
✓✓✓39.10 / 0.983
✓✓✓✓39.12 / 0.984
✓✓✓✓✓39.35 / 0.985
✓✓✓✓✓✓39.46 / 0.992
+ +# 4.4. Ablation Study + +Under the validated overall efficacy of the proposed framework, ablation experiments are conducted in two stages. First, a comprehensive breakdown ablation is performed on every major component integrated in IHRUT. As reported in Table 4, the SPE mechanism emerges as the most critical contributor, delivering a performance gain exceeding $5\mathrm{dB}$ , whereas the momentum mechanism and cross-stage fusion play auxiliary roles in boosting quality of reconstruction. + +![](images/9ae2b1c3477deebe17a6373fff76c4575dc9b458c142c8e08602fb76bd174e96.jpg) +Figure 4. Comparison of reconstructed HSI with error maps $(10\times$ amplified). We select Synthetic (a) Scene 2 from HSOD-BIT and (b) Scene 1 from Houston cropped by $256\times 256$ , along with Real (c) Scene 3 from Calibration dataset cropped by $64\times 64$ . The error map exhibits the spectral absolute error of IHI reconstruction results by 8 algorithms and IHRUT with 7 stages. The region within the box is chosen for analysis of the reconstructed spectra and zoom in for a more detailed examination. + +![](images/a0c88807f8714eb34bcd64abb07ee6f281637e4966896d2284dfd7abd2fac481.jpg) +Figure 5. Error map $(20\times)$ visualization of Tab. 5. + +![](images/3e15ae41e07bc143cfe6fcc538bfc498aca168cc18639bf0705c1f346ac34949.jpg) + +![](images/b2effeb2a8fa7f66f1a442c2962613043535b8f594d685d8305049331b929309.jpg) + +![](images/238260606ba17db7e7c5b607cccad691610cfc72eb1ad9e75ff9aa2b41698d76.jpg) + +![](images/2c99ef0f7def48ee05a6f45f458c671f4925d25ea0e1b2aea1cd4d453c108e1c.jpg) + +![](images/bda09c06bca34ebd9e1429d20ea0b666d8a1c352b8955f6bbcb3f5ebd8f582ac.jpg) + +Subsequently, we undertake a detailed comparative analysis of our SPE and Momentum Branch against channel-attention (Tab. 5 a,b,c) and existing momentum branches (Tab. 5 d,e). As illustrated in Tab. 5 and Fig. 5, the stripewise attention introduced by SPE yields superior flexibility, and the two successive weighting operations within our momentum pathway further elevate the overall performance. + +Table 4. Break down ablation of IHRUT (5-stages) on Calibration dataset. CA denotes replacing SPE with channel attention. + +
Data Moduleabc
zk-xkCA(CA·δ+m)CA(SPE0·δ+m)SPEk(CA·δ+m)
PSNR/SSIM38.55/0.98438.66/0.98438.60/0.985
Data Moduled (like [3, 45])eours
zk-xkCA·δ+CA(m)SPEk·δ+SPE0(m)SPEk(SPE0·δ+m)
PSNR/SSIM38.31/0.98338.40/0.98539.46/0.992
+ +Table 5. Analysis of the Data Modules with different components and momentum branches (e.g., $z_{k} - x_{k}$ in the table) in 5-stg IHRUT. Here, $\delta = \mathbf{y} - \mathbf{F}\mathbf{x}_{k}$ and $m = \mathbf{x}_k - \mathbf{x}_{k - 1}$ . + +# 5. Conclusion + +In this paper, we focus on enhancing the performance of IHI reconstruction through learning approach. We establish a simplified yet accurate degradation model and calibration method to extract degradation priors from IHI imaging. Leveraging the model, we conduct synthesis for realistic data to tackle the lack of dataset. Based on degradation model, we design the IHRUT network. Within a low-complexity spatial-spectral unfolding architecture, it is optimized for the stripe characteristics of IHI degradation. In experiments involving training with simulated data and joint testing with simulated and real data, IHRUT demonstrates outstanding performance. We hope our work could provide inspiration for further researches on optical spectroscopy instruments. + +# Acknowledgements + +This work was supported by the National Key R&D Program of China (2022YFC3300705), the National Natural Science Foundation of China (62331006, 62171038, and 62088101), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pages 1692-1700, 2018. 2 +[2] Gonzalo R Arce, David J Brady, Lawrence Carin, Henry Arguello, and David S Kittle. Compressive coded aperture spectral imaging: An introduction. IEEE Signal Processing Magazine, 31(1):105-115, 2013. 2 +[3] Amir Beck and Marc Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202, 2009. 6, 8 +[4] Robert Bell. 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Krishnan +University of Toronto + +rahulgk@cs.toronto.edu + +# Abstract + +Physical reasoning remains a significant challenge for Vision-Language Models (VLMs). This limitation arises from an inability to translate learned knowledge into predictions about physical behavior. Although continual fine-tuning can mitigate this issue, it is expensive for large models and impractical to perform repeatedly for every task. This necessitates the creation of modular and scalable ways to teach VLMs about physical reasoning. To that end, we introduce Physics Context Builders (PCBs), a modular framework where specialized smaller VLMs are fine-tuned to generate detailed physical scene descriptions. These can be used as physical contexts to enhance the reasoning capabilities of larger VLMs. PCBs enable the separation of visual perception from reasoning, allowing us to analyze their relative contributions to physical understanding. We perform experiments on CLEVRER and on Falling Tower, a stability detection dataset with both simulated and real-world scenes, to demonstrate that PCBs provide substantial performance improvements, increasing average accuracy by up to $13.8\%$ on complex physical reasoning tasks. Notably, PCBs also show strong Sim2Real transfer, successfully generalizing from simulated training data to real-world scenes. + +# 1. Introduction + +Physical reasoning is a fundamental component of human intelligence, enabling interpretation of complex interactions, prediction of future events, and understanding of causal relationships in real-world environments [22]. For humans, the ability to understand the physical world is developed early and operates intuitively [3, 30, 38]. However, phys + +ical reasoning remains a significant challenge for artificial intelligence (AI) systems [10, 23, 35, 45], despite advances in computer vision and Vision-Language Models (VLMs) [2, 25, 26, 32, 36, 39, 46]. + +VLMs are remarkably successful on many predictive problems, spanning a broad range of tasks. This makes their use central to real-world applications requiring expertise in a variety of tasks, such as robotics and embodied AI [17, 28]. However, current VLMs consistently fail at physical reasoning tasks, struggling with basic spatial relationships (e.g., object positioning, counting) [33], object attributes [40], and physical interactions (e.g., stability assessment, dynamics prediction) [10, 14]. While humans leverage causal or physically guided knowledge for physical understanding of the world [5], the mechanisms by which VLMs make predictions are not well understood. This leads to two important questions: what factors contribute to the lack of physical understanding in VLMs, and how can we improve it? + +One potential explanation for such limitations lies in VLMs' training data. VLMs are created by fusing the representations of image and text encoders using datasets like MSCOCO [27] and Conceptual Captions [34], which focus on general scene descriptions but lack annotations of physical relationships. Our experiments with standard benchmarks like CLEVRER [45] confirm this hypothesis, demonstrating that fine-tuning on physics-focused data can enable a relatively small VLM to approach state-of-the-art results achieved by specialized architectures [11, 45]. However, as the ecosystem of open and closed source models grows, repeatedly fine-tuning each VLM for every regime of physical concepts it cannot reason about becomes impractical; there is a need for practical, performant and modular tools to augment VLM capabilities. + +To this end, we introduce Physics Context Builders (PCBs): specialized VLMs that are fine-tuned on simul + +tion data to generate fine-grained physical descriptions that can be used by larger VLMs. Simulation can provide precise annotations of controllable physical interactions of interest, which can serve as scalable training data to teach models about physical phenomena. We show how to embed the knowledge of physical concepts into PCBs and how they can transfer this knowledge to larger VLMs; this enables us to effectively separate visual perception from reasoning, using PCBs as perception modules, while leaving reasoning to larger models. See Fig. 1 for a demonstration of PCBs. + +PCBs offer a practical and modular approach to enhance the physical reasoning of existing large-scale VLMs without requiring expensive or infeasible modification of the larger foundation models. Our experiments on standard benchmarks demonstrate effective integration of PCBs with standard commercial VLMs. Moreover, they show that PCBs trained with simulation data successfully generalize to real-world scenarios, effectively performing simulation-to-reality (Sim2Real) transfer. In summary, our contributions are: + +1. We introduce a modular framework where specialized VLMs are fine-tuned to generate detailed physical scene descriptions, enhancing the physical reasoning capabilities of foundation models without their modification. +2. We demonstrate the effectiveness of separating visual perception from reasoning through our PCB approach, providing insights into how each component contributes to physical understanding. +3. We show how simulation can be leveraged to train specialized modules that transfer successfully to real-world scenarios, avoiding expensive simulations at inference. + +# 2. Related Work + +# 2.1. Physical Reasoning in Vision Models + +Physical reasoning presents significant challenges for vision models, including both specialized architectures and large-scale VLMs. Recent benchmarks demonstrate that current VLMs struggle with basic physical understanding, often failing at tasks such as counting, depth reasoning, and physical interaction prediction [14, 26, 39]. These limitations are not unique to VLMs; physical reasoning has also proven difficult for single-purpose models, necessitating specialized architectures such as physics-inspired predictive models [4, 13, 16], neural-symbolic executors [9, 20, 48], differentiable physics engines [12, 42], simulation-in-the-loop approaches [29, 49], and task-specific architectures [11]. However, large VLMs are not easily amenable to architectural modifications and require alternative approaches to enhance their capabilities, which we consider in this work. + +# 2.2. Evaluating Physical Reasoning in VLMs + +Several recent works have evaluated physical reasoning capabilities in vision-language models. Nagar et al. [31] bench + +mark zero-shot visual reasoning in both large language models (LLMs) and VLMs. They find that underlying LLMs, when provided with textual scene descriptions, consistently outperform VLMs that use visual embeddings. Their analysis shows that this performance gap is due to VLMs' difficulty in translating visual information into accurate representations for reasoning. Our work builds on this insight by developing a modular approach to bridge this gap without requiring extensive retraining of VLMs. + +Concurrently, Chow et al. [10] introduce PhysBench, a comprehensive benchmark for evaluating physical understanding in VLMs. Their work reveals that VLMs' physical reasoning does not scale proportionally with model size, training data, or input frame count. They identify perceptual and knowledge gaps as the primary sources of errors and propose using vision foundation models like Depth Anything [44] and SAM [21] to enhance visual perception. While our approach shares the goal of improving physical reasoning, we take a different direction by leveraging simulation data to train specialized context builders rather than relying on generic vision foundation models. + +# 2.3. Simulation for Physical Understanding + +Simulation has long been recognized as a valuable tool for teaching machines about physical dynamics [5]. Previous approaches have incorporated simulation directly into the inference pipeline [29, 42, 43], requiring computationally expensive simulators at inference time. In contrast, our method leverages simulation only during the training phase to generate rich physical descriptions, eliminating the need for simulation during inference while still benefiting from the detailed annotations that simulations provide. + +# 2.4. Enhancing General Capabilities of VLMs + +Recent work has explored modular approaches to enhance VLM capabilities without full model retraining. Chain-of-thought prompting techniques [41] leverage large language models' reasoning abilities by encouraging step-by-step thinking, while multimodal chain-of-thought approaches [47] extend this to vision-language tasks. Our Physics Context Builders build on these ideas by creating modular components that specialize in translating visual inputs into detailed physical descriptions. + +# 3. Understanding the Effect of Training Data on Physical Reasoning + +We begin by investigating why current VLMs struggle with physical reasoning. After outlining our experimental setup, covering datasets, models, and training procedures, we present results showing how fine-tuning with physics-focused data significantly improves performance. We then analyze the trade-off between data quantity and quality. + +![](images/a7fb1cbf7ecee302adf2f7f9b3194c5eaca2079205e7cd9a860458bb0af376de.jpg) +Figure 1. Physics Context Builders (PCBs) pipeline. The training phase (top) shows how physics simulators generate images/videos with corresponding annotations, which are converted into two types of physical descriptions: Human-like Narration (providing natural language scene descriptions with object properties and spatial relationships) and Structured Physics (offering frame-by-frame structured descriptions with physical properties). These descriptions serve as training data for fine-tuning a relatively small VLM into specialized PCBs. During the inference phase (bottom), a trained PCB processes a new image/video and generates detailed physical context about the scene, which is then provided to a foundation model (e.g., GPT-40) alongside a user query to produce physically grounded responses. + +![](images/8132855b0e9af9d18d8eb998db28446a055dd50a5646a3f52cf727e7339147c4.jpg) +Figure 2. Datasets used for experiments: Falling Tower representing static physics in simulated and real environments; CLEVRR representing dynamic physics in a simulated environment. + +# 3.1. Experimental Setup + +Datasets. We utilize two benchmarks: CLEVRR [45] for dynamic physical reasoning and Falling Tower for static stability detection (Fig. 2). + +- CLEVRER [45] is an established benchmark containing 10,000 training videos, 5,000 validation videos, and 5,000 test videos, each paired with multiple questions across four categories: descriptive, explanatory, predictive, and counterfactual. The training set consists of 109,952 descriptive, 16,799 explanatory, 7,179 predictive, and 18,642 counterfactual questions. All descriptive questions are open-ended. Other question types are multiple-choice with up to four options and may have multiple correct answers. We report the accuracy of the models stratified + +by the question types. For multi-choice questions, we report both per-option accuracy, which measures the model's overall correctness on single options across all questions, and per-question accuracy that measures the model's performance on full questions, requiring all the choices to be selected correctly. Since the test set answers are not publicly available, we evaluate on the validation set. + +- Falling Tower is a dataset we create to complement CLEVRER by focusing on static physics. Similar to ShapeStacks [15] and block towers in [24], it features stacked objects but extends previous work by including question-answer pairs and simulation-generated annotations. The dataset contains 4,864 images of stacked objects (with 15 object types across 3 shapes and 5 colors) and 72,775 QA pairs, with $75\%$ used for training and $25\%$ for evaluation. Questions and corresponding answers are generated by applying transformation functions to the simulation annotations, converting it into natural language questions and calculating the answers. For instance, to assess the stability of a stacked tower of objects, we compare the initial and final positions of the objects to determine if significant movement occurred. If an object remains within a predefined threshold, it is considered stable. Questions are then categorized into descriptive (e.g., "How many objects are in the scene?") and stability (e.g., "Will this collection of objects remain stationary?"). This + +dataset also enables the evaluation of Sim2Real transfer; we include 20 real-world images captured with 3D-printed objects with 100 human-generated QAs. For more details on Falling Tower, see Appendix C. + +Models and evaluation. We evaluate several zero-shot baselines, including GPT-4o, GPT-4o-mini [1, 19], Gemini-1.5-Pro [37], and PaliGemma-3B-mix (a variant fine-tuned on academic datasets) [6] with chain-of-thought prompting to encourage explicit reasoning. To study training data effects, we fine-tune PaliGemma-3B on CLEVRR and Falling Tower independently using Low-Rank Adaptation (LoRA) [18], minimizing the auto-regressive negative log-likelihood of the answers, conditioned on the questions and input video/image. For videos, we sample 8 frames and append them to the input context, except for the Gemini model, where we use the entire video as the input since they support native video processing. For all models, we take the final answer after the reasoning chain for evaluation. Appendix A.1 provides more details on the training procedure. + +Framing the questions. For all questions, including the open-ended and multi-choice ones, we provide the potential options in the question statement. For CLEVRR, we reframe multi-choice questions as a set of binary questions, asking whether each option is a valid answer. This yields significant improvement in the accuracy of all the evaluated models, as reported in Appendix B.1. + +# 3.2. Is Physics-Focused Training Data Enough? + +Tabs. 1 and 2 present our results for the Falling Tower and CLEVRER benchmarks. Several key insights emerge: + +Zero-shot VLMs struggle with physical reasoning despite strong descriptive capabilities. On Falling Tower, large models like GPT-4o and Gemini-1.5-Pro demonstrate near-perfect accuracy (95-100%) on descriptive questions, both in simulated and real environments. However, their performance drops substantially on stability questions, with accuracy ranging from only 55-60% (barely above random guessing). Similarly, on CLEVRR, while GPT-4o achieves 62.7% accuracy on descriptive questions, its performance falls to 30.7%, 30.3%, and 18.7% on explanatory, predictive, and counterfactual questions, respectively. This substantial performance gap highlights that while VLMs have developed strong capabilities for high-level scene understanding and description, they lack the abilities needed to predict outcomes or explain causal relationships accurately. + +Fine-tuning with physics-focused data substantially improves physical reasoning. Unsurprisingly, the fine-tuned PaliGemma-3B model shows dramatic improvements across + +![](images/b67ae204e20224fc4a6ca6300d46d861e5907f740c8c26aef6d2929e910f62f7.jpg) +Figure 3. The amount of training data vs. performance on different QA types in Falling Tower. + +all tasks. On Falling Tower, it achieves perfect descriptive accuracy (100%) and substantial gains in stability prediction (up to 28% compared to GPT-4o). On CLEVRER, the improvements are even more significant, reaching close to the state-of-the-art results by Aloe, a specialized architecture trained on CLEVRER (Descriptive: 94.0%, Explanatory: 96.0%, Predictive: 87.5%, Counterfactual: 75.6%) [11]. These results demonstrate that targeted fine-tuning with physics-focused data can significantly enhance physical reasoning capabilities, enabling a 3B parameter model to outperform much larger state-of-the-art models. See Appendix D.1 for a comparison to other specialized baselines. + +Sim2Real transfer is successful. The fine-tuned model maintains strong performance when transferring from simulated to real-world images in Falling Tower. It achieves $100\%$ accuracy on descriptive tasks and $70.0\% / 65.0\%$ accuracy on object / tower stability questions, respectively. + +# 3.3. Ablation Studies: Not All Data is Equal + +To gain deeper insights into how training data composition affects physical reasoning capabilities, we conduct several ablation studies. We provide more ablations in Appendix B. + +Specificity of QA types in fine-tuning. Tab. 3 shows the impact of using different subsets of QA pairs for fine-tuning on Falling Tower. Fine-tuning with only descriptive questions achieves perfect descriptive accuracy but fails to improve stability prediction (remaining at the baseline level). Interestingly, fine-tuning with only stability questions not only improves stability prediction substantially but also yields moderate improvements in descriptive tasks, particularly for object identification (41.2% vs. 8.5% baseline). However, the best performance comes from fine-tuning on the full QA dataset. This highlights the need to carefully select data to cover all QA types, which can be seen as a limitation of targeted fine-tuning in VLMs. + +Data efficiency varies by task type. Fig. 3 illustrates how accuracy varies with the amount of training data for different + +Table 1. Performance of zero-shot VLMs and the fine-tuned model on the Falling Tower benchmark. The second number after the first slash is the Sim2Real accuracy. + +
CategoryModelDescriptive [sim acc. / real acc.]Stability [sim acc. / real acc. / real F1]
num. obj.num. obj. ↑↓obj. ↑↓obj. stabletower stable
RandomRandom33.325.014.350.050.0
Zero-shot CoTGPT-4o99.3 / 100.091.4 / 100.099.4 / 95.056.9 / 60.0 / 63.359.6 / 55.0 / 54.2
GPT-4o-mini94.9 / 89.561.3 / 84.287.9 / 73.749.0 / 52.6 / 55.053.1 / 36.8 / 19.8
Gemini 1.5 Pro97.2 / 95.089.9 / 100.097.8 / 95.054.6 / 80.0 / 80.060.5 / 60.0 / 60.1
PaliGemma-3B-mix91.4 / 90.044.5 / 70.073.0 / 65.051.0 / 75.0 / 68.639.1 / 65.0 / 51.2
Fine-tuned QAPaliGemma-3B-Fine-Tuned100.0 / 100.0100.0 / 100.0100.0 / 95.084.6 / 70.0 / 73.087.6 / 65.0 / 64.4
+ +Table 2. Performance of zero-shot VLMs and the fine-tuned model on the CLEVRER benchmark. + +
CategoryModelDescriptiveExplanatoryPredictiveCounterfactual
per ques.per opt.per ques.per opt.per ques.per opt.
RandomRandom28.811.850.025.050.07.450.0
Zero-shot CoTGPT-4o62.730.765.530.347.618.760.2
GPT-4o-mini49.59.351.844.945.115.651.0
Gemini 1.5 Pro58.615.761.232.049.617.655.6
PaliGemma-3B-mix38.96.633.444.748.77.749.8
Fine-tuned QAPaliGemma-3B-Fine-Tuned92.994.798.283.683.668.488.7
+ +Table 3. Effect of fine-tuning PaliGemma-3B on different QA types in Falling Tower. + +
Fine-tuning DataDescriptive [acc.]Stability [acc.]
num. obj.num. obj.↑↓ obj.obj. stabletower stable
No Fine-tuning50.921.28.551.039.1
Stability QAs52.426.041.284.486.5
Descriptive QAs100.0100.0100.051.039.1
All QAs100.0100.0100.084.687.6
+ +QA types in Falling Tower. Descriptive questions reach near-saturation with only $\sim 10\%$ of the data, showing the model can quickly learn basic scene understanding. In contrast, stability questions benefit more from extra data, though with diminishing returns. Even with $100\%$ of the available data, the model does not reach perfect performance on stability questions (87.6% for tower stability). This shows that increasing dataset size alone is insufficient; improvements in physical reasoning also require diverse, targeted supervision. + +# 4. Physics Context Builders: A Modular Approach to Physical Reasoning + +While fine-tuning with physics-focused data can significantly enhance physical reasoning in VLMs, it presents notable practical limitations. Fine-tuning state-of-the-art foundation models like GPT-4o or Gemini is often expensive or even impossible due to their closed-source nature and computational requirements. Furthermore, the task-specific nature of fine-tuning, as seen in Sec. 3, means separate models + +may be needed for different physical reasoning tasks, which limits the generalizability of the approach. To address these challenges, we introduce Physics Context Builders (PCBs) – a modular and efficient approach that enhances physical reasoning capabilities of existing VLMs without modifying them directly. PCBs leverage the strong in-context learning abilities of large language models [8, 41], which have shown impressive performance with textual scene descriptions [31]. + +# 4.1. Methodology + +PCBs are specialized VLMs fine-tuned on simulation data to generate detailed physical descriptions of visual scenes. Rather than directly answering questions, PCBs act as perception modules that translate visual inputs into rich textual descriptions capturing the physical properties and dynamics of a scene. These descriptions then serve as enhanced context for larger VLMs, enabling more accurate physical reasoning through in-context learning. Fig. 1 provides an overview of our approach. PCBs offer several advantages: + +- Modularity: PCBs can be fine-tuned and deployed independently of the foundation model. +- Efficiency: Only smaller, specialized models need to be fine-tuned, rather than larger VLMs. +- Flexibility: Different PCBs can be developed for different physical phenomena, creating a toolbox of physical reasoning enhancers. +- Compatibility: PCBs work with any (vision) language model capable of in-context learning, including closed-source commercial models. + +# 4.1.1. Physical Context Generation + +Using annotations from the simulator, PCBs generate question-agnostic descriptions that capture the physical essence of a scene. We consider two context types: + +(1) Human-like Narration (HN): Produces intuitive natural language descriptions of the scene's physical properties and events that can be more aligned with foundation models: + +# Human-like Narration (HN) + +Scene History: + +Here are the relevant observations prior to the 1st collision: + +- Object 0 (the blue rubber sphere) enters the scene and moves toward the 1st collision site. +- Object 1 (the gray rubber sphere) is moving toward the 1st collision site. +- Object 2 (the purple rubber sphere) remains stationary in the scene and does not participate in the collision. + +Finally, Object 0 collides with Object 1... + +(2) Structured Physics (SP): Provides frame-by-frame structured observations in a format similar to a physics simulation output, with standardized tags for physical properties. This structured approach helps models capture precise temporal relationships and physical properties: + +# Structured Physics (SP) + +
[FRAME][OBJECTS][OBJ]SPHEREBLUERUBBER[LOC]
(1.0, 2.3)[VEL]0.5[ENERGY]1.2[/OBJ][OBJ] SPHERE
GRAYRUBBER[LOC](3.2, 1.5)[VEL]0.8[ENERGY] 1.7
[/OBJ]...[/OBJECTS][COLLISION\_PAST][COLLISION]
[OBJ]SPHEREBLUERUBBER[/OBJ][OBJ]SPHERE GRAY
RUBBER[/OBJ][LOC](2.1, 1.9)[/LOC][/COLLISION]
[/COLLISION\_PAST][/FRAME]
+ +# 4.1.2. Training PCBs + +We train PCBs by fine-tuning a pre-trained VLM to generate physical descriptions from visual inputs. Specifically: + +1. We use PaliGemma-3B as the base pre-trained VLM due to its strong vision-language capabilities and reasonable computational requirements. +2. We apply LoRA-based fine-tuning [18], minimizing the auto-regressive negative log-likelihood of the context descriptions conditioned on the input video/image. See Appendix A.2 for more details. +3. For videos (e.g., in CLEVRER), we sample 8 frames and append them to the input context. +4. Fine-tuning jointly optimizes both vision and language components to ensure alignment between visual features and linguistic representations. + +The training data is generated from the same simulations used to create the QA pairs, but focuses on comprehensive scene descriptions rather than specific questions and answers. + +This approach enables PCBs to provide rich context independent of the specific reasoning task. + +# 4.2. Experimental Results + +We evaluate the effectiveness of PCBs by integrating them with three foundation models: GPT-4o, GPT-4o-mini, and Gemini-1.5-Pro. In each experiment, we first pass the visual input to the appropriate PCB, which generates a physical description. This description is then provided as additional context to the foundation model along with the user's question and the video/image. + +# 4.2.1. PCB Performance on Falling Tower + +Tab. 4 shows the performance of foundation models augmented with PCBs on Falling Tower. For additional experiments, see Appendix D.2. Several key findings: + +- Substantial improvement in stability tasks: PCBs provide remarkable gains in stability prediction, with GPT-4o-PCB showing up to $25.5\%$ improvement in tower stability assessment. These gains are even more pronounced for smaller models like GPT-4o-mini, which sees a $31.6\%$ improvement in tower stability prediction. +- Modest gains in descriptive tasks: Since foundation models already perform well in descriptive tasks, PCBs offer limited additional benefits in this area, with improvements mainly in the more challenging descriptive tasks like identifying objects above/below others (e.g., $13.0\%$ improvement for GPT-4o-mini). +- Effective Sim2Real transfer: PCB-augmented models show improved generalization to real-world scenarios, with GPT-4o-PCB achieving a $15.0\%$ gain in real-world tower stability prediction compared to zero-shot. +- Model size effects: Interestingly, the smaller GPT-4o-mini model shows greater relative improvements when augmented with PCBs compared to larger ones, possibly due to its more limited perception. + +# 4.2.2. PCB Performance on CLEVRR + +Tab. 5 presents results for CLEVRER, a more challenging benchmark that requires dynamic physical reasoning: + +- Human Narration vs. Structured Physics: Human-like narration (HN) consistently outperforms structured physics (SP) descriptions across all models and question types. This can be due to foundation models' better understanding of natural language descriptions compared to more structured, technical formats. +- Strong improvements in descriptive and explanatory tasks: PCBs provide substantial gains in descriptive accuracy (up to $16.2\%$ for GPT-4o-mini) and explanatory reasoning (up to $19.9\%$ for Gemini 1.5 Pro). +- Limited gains in counterfactual reasoning: While PCBs improve counterfactual reasoning (1.7–9.5% gains), the improvements are more modest, reflecting the intrinsic complexity of this task, even with enriched context. + +Table 4. Performance of foundation models augmented with Physics Context Builders (PCBs) on the Falling Tower benchmark. HN refers to Human Narration style PCB. The numbers in parentheses indicate improvements over the respective zero-shot baselines. The second number after the slash is the Sim2Real accuracy and the third number after the second slash is the F1 score on Sim2Real. + +
CategoryModelDescriptive [sim acc. / real acc.]Stability [sim acc. / real acc. / real F1]
num. obj.num. obj. ↑↓obj. ↑↓obj. stabletower stable
Zero-shot CoTGPT-4o99.3 / 100.091.4 / 100.099.4 / 95.056.9 / 60.0 / 63.359.6 / 55.0 / 54.2
GPT-4o-mini94.9 / 89.561.3 / 84.287.9 / 73.749.0 / 52.6 / 55.053.1 / 36.8 / 19.8
Gemini 1.5 Pro97.2 / 95.089.9 / 100.097.8 / 95.054.6 / 80.0 / 80.060.5 / 60.0 / 60.1
VLM + PCB (HN)GPT-4o-PCB99.5 / 100.097.6 / 100.099.5 / 95.076.7 / 75.0 / 73.885.1 / 70.0 / 65.6
(+0.2) / (0.0)(+6.2) / (0.0)(+0.1) / (0.0)(+19.8) / (+15.0) / (+10.5)(+25.5) / (+15.0) / (+11.4)
GPT-4o-mini-PCB99.9 / 95.074.3 / 90.097.5 / 95.075.0 / 70.0 / 73.084.7 / 40.0 / 33.8
(+5.0) / (+5.5)(+13.0) / (+5.8)(+9.6) / (+21.3)(+26.0) / (+17.4) / (+18.0)(+31.6) / (+3.2) / (+14.0)
Gemini 1.5 Pro-PCB97.9 / 100.097.5 / 100.097.4 / 94.775.9 / 73.7 / 76.784.9 / 57.9 / 59.1
(+0.7) / (+5.0)(+7.6) / (0.0)(-0.4) / (-0.3)(+21.3) / (-6.3) / (-3.3)(+24.4) / (-2.1) / (-1.0)
+ +Table 5. Performance of foundation models augmented with Physics Context Builders (PCBs) on the CLEVRR benchmark. HN is Human Narration and SP is Structured Physics. The numbers in parentheses indicate improvements over the respective zero-shot baselines. + +
CategoryModelDescriptiveExplanatoryCounterfactual
per ques.per opt.per ques.per opt.
Zero-shot CoTGPT-4o62.730.765.518.760.2
GPT-4o-mini49.59.351.815.651.0
Gemini 1.5 Pro58.615.761.217.655.6
VLM + PCB (HN)GPT-4o-PCB75.6 (+12.9)41.6 (+10.9)67.0 (+1.5)28.2 (+9.5)68.4 (+8.2)
GPT-4o-mini-PCB65.7 (+16.2)26.8 (+17.5)62.2 (+10.4)17.3 (+1.7)52.8 (+1.8)
Gemini 1.5 Pro-PCB72.8 (+14.2)35.6 (+19.9)70.8 (+9.6)26.2 (+8.6)64.9 (+9.3)
VLM + PCB (SP)GPT-4o-PCB70.0 (+7.3)34.9 (+4.2)61.1 (-4.4)19.2 (+0.5)63.3 (+3.1)
GPT-4o-mini-PCB58.6 (+9.1)19.2 (+9.9)58.9 (+7.1)16.2 (+0.6)51.8 (+0.8)
Gemini 1.5 Pro-PCB67.4 (+8.8)30.5 (+14.8)68.7 (+7.5)21.1 (+3.5)60.5 (+4.9)
+ +Remark. For CLEVRER, we omit PCB evaluation on predictive questions since our current PCBs are designed to describe observed scenes rather than predict future events. Future work could address this by developing predictive PCBs that generate plausible future scene descriptions based on simulation rollouts. + +# 4.3. Multi-Agent Framework for PCB Integration + +Given the ability of foundational models to interpret the overall context of scenes effectively, we explore whether they can reliably select the appropriate PCB when provided with a question-image pair. We utilize a multi-agent triage model inspired by OpenAI's Swarm architecture [7]. As illustrated in Fig. 4, our multi-agent framework consists of: + +1. A Triage Agent that analyzes the user query and visual input to identify the required type of physical reasoning. +2. Multiple PCBs, each specialized for different physical phenomena (e.g., stability analysis, collision detection, motion tracking). +3. A Foundation Model that receives the PCB-generated context and the original query to produce the response. + +In our evaluation, each input consists of a natural language question from a QA dataset paired with a corresponding scene image. This input is initially processed by GPT-4o or GPT-4o-mini that routes the query to one of two specialized PCBs: the PCB for the Falling Tower dataset, or PCB + +![](images/0b5d87816d234820f280173c324f5404a712d53ca7f42488fb01b21174e2f9fb.jpg) +Figure 4. Multi-agent framework for PCB integration. A triage agent selects the appropriate PCB based on the user query, and the PCB generates a detailed scene description that enriches the foundation model's context. + +designed for analyzing motion and object interactions as in the CLEVRER dataset. As shown in Tab. 6, both GPT-4o and GPT-4o-mini achieve excellent F1-Scores, effectively routing queries to the appropriate PCB. These results suggest that PCBs in a multi-agent framework offer a promising approach, with foundation models capable of reliably selecting + +Table 6. Accuracy and F1-scores for selecting the correct Physics Context Builder using the triage agent in a two-agent setup. + +
TaskMetricGPT-4o / GPT-4o-mini
Stacked ObjectsAccuracy (%)87.67 / 97.00
F1-Score0.9326 / 0.9782
Dynamic SceneAccuracy (%)94.67 / 98.67
F1-Score0.9403 / 0.9785
+ +the correct PCB based on the question-image pair. + +# 5. Discussion + +Our results demonstrate that Physics Context Builders (PCBs) offer a promising approach to enhancing physical reasoning in Vision-Language Models (VLMs). PCBs increase the average performance of GPT-4o (GPT-4o-mini) by $11.1\%$ ( $11.8\%$ ) on CLEVRER and $8.2\%$ ( $13.8\%$ ) on Falling Tower. These improvements are particularly notable given that no modification to the foundation models was required. Despite these gains, large VLMs still exhibit sub-optimal performance in tasks requiring deeper reasoning, such as counterfactual questions (with improvements limited to 1.7-9.5%) and explanatory questions. While enhancing visual perception through PCBs is important, especially for descriptive tasks, the subpar performance on more involved reasoning tasks calls for additional interventions to achieve a comprehensive physical understanding. + +Besides the performance gain, our findings confirm the value of simulation data in addressing the limitations of VLMs. Unlike simulation-in-the-loop approaches [12, 29, 42, 43], which require computationally expensive simulators during inference, our method uses simulation only to generate synthetic data (context descriptions) for fine-tuning smaller VLMs. This approach is more efficient at inference while still leveraging the rich annotations that simulations can provide. The effectiveness of PCBs in generalizing from simulated to real-world data further supports this approach, as demonstrated by the successful Sim2Real transfer in the Falling Tower benchmark. + +PCBs provide a modular and efficient framework for enhancing the physical reasoning capabilities of foundation models without requiring direct fine-tuning. Generating rich physical context from visual inputs enhances the perceptual ability of foundation models, resulting in more accurate reasoning across diverse physical tasks, from static stability to dynamic collision detection. The multi-agent framework further enhances this approach by enabling adaptive selection of specialized PCBs based on the specific reasoning task. + +# 6. Limitations and Future Work + +While our work demonstrates the effectiveness of PCBs across benchmarks, several limitations remain. First, our + +current benchmarks focus on a relatively constrained set of physical phenomena—primarily rigid body dynamics and stability. This limits our ability to evaluate how well these approaches generalize to the full spectrum of physical reasoning that humans perform intuitively, such as fluid dynamics or object manipulation. + +Second, our framework requires annotated data, which naturally comes from simulation. For unannotated videos, such as those available on YouTube, the lack of structured annotations presents a challenge. An important open problem is how PCBs could extract detailed physical descriptions from real-world videos without explicit annotations, potentially through self-supervised learning or by leveraging other foundation models to generate pseudo-annotations. + +Third, the performance improvements, while substantial, still leave room for further enhancement, particularly for complex reasoning tasks like counterfactual/predictive questions. Since PCBs inherently perform direct translation from visual signals to text, they lead to strong descriptive capabilities in the foundation models. However, this translation process does not capture all the visual cues needed for more complex reasoning. Hence, we hypothesize that more comprehensive textual descriptions, possibly containing counterfactual/predictive information, could significantly improve the performance of PCBs on these challenging tasks. + +A promising future direction is to tackle more complex physical reasoning tasks that require larger-scale simulations. This might involve integrating advanced physics engines that simulate phenomena like fluid dynamics, deformable materials, and articulated mechanisms. Notably, while these simulations could become computationally expensive for simulation-in-the-loop approaches during inference, our PCB framework uses simulation data only for fin-tuning and therefore does not add significant computational burden at inference time. + +Another avenue for future work is to explore how multiple PCBs could be composed or chained together to handle scenarios requiring reasoning about multiple physical phenomena simultaneously. For instance, reasoning about a scene involving both rigid body dynamics and fluid interactions might benefit from specialized PCBs for each phenomenon, with their outputs combined to provide comprehensive context to the foundation model. + +# Acknowledgements + +We thank Brian Jeong for 3D printing the parts used in the Falling Tower dataset. 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Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents Pi-GPS, a novel framework that unleashes the power of diagrammatic information to resolve textual ambiguities, an aspect largely overlooked in prior research. Specifically, we design a micro module comprising a rectifier and verifier: the rectifier employs MLLMs to disambiguate text based on the diagrammatic context, while the verifier ensures the rectified output adherence to geometric rules, mitigating model hallucinations. Additionally, we explore the impact of LLMs in theorem predictor based on the disambiguated formal language. Empirical results demonstrate that Pi-GPS surpasses state-of-the-art models, achieving a nearly $10\%$ improvement on Geometry3K over prior neural-symbolic approaches. We hope this work highlights the significance of resolving textual ambiguity in multimodal mathematical reasoning, a crucial factor limiting performance. The code for Pi-GPS is publicly available at: https://github.com/hellozting/Pi-GPS. + +# 1. Introduction + +Geometry Problem Solving (GPS) aims to derive solutions from a textual problem description and its corresponding diagram. As a distinct and pivotal aspect of multimodal mathematical reasoning, GPS requires a nuanced understanding of visual shapes, intricate spatial relationships, symbolic abstraction, and logical inference across both textual and diagrammatic inputs. This makes it a long-standing challenge in mathematical reasoning and artificial intelligence [8, 14, 21, 28, 35]. While recent notable milestones [3, 33] such as the gold-medal-level solution to geometry problems using AlphaGeometry2 [11] have ex + +
Problem TextParsing Text Formal LanguageDiagram
The rectangle is inscribed into the circle. Find the exact circumference of the circle.InscribedIn(Rectangle($) ,Circle($)) Find(CircumferenceOf(Circle($)))8 in: A 6 in: B
The two polygons are similar. Find UT.Similar(Polygon($1),Polygon($2)) Find(LengthOf(Line(U,T))))R +S +U +V +D +E +F +G +H +I +J +K +L +M +N +O +P +Q +R +S +T +U +V +W +X +Y +Z
Find the area of the shaded region. Round to the nearest tenth.Find(AreaOf(Shaded(Shape($))))A +D +E +C +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +C +D +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +D +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +C +c +d +e +f +g +h +i +j +k +l +m +n +o +p +q +r +s +t +u +v +w +x +y +z
+ +Figure 1. Illustrating the ambiguity presented in text. Text alone offers insufficient information to resolve the ambiguity, and disambiguation becomes straightforward when supported by a diagram. + +hibited remarkable achievements, these efforts predominantly focus on language processing, neglecting the diagrammatic component of the problem. However, GPS transcends language-based reasoning, demanding a profound understanding and manipulation of diagrammatic information, an enduring challenge in the field. + +Existing approaches to GPS can be broadly categorized into symbolic [4, 30] and neural-based methods [8, 13, 16-18, 22, 31, 37, 38, 40, 42-45]. Symbolic methods, grounded in formal logic and mathematical rigor, rely on explicit theorem databases and symbolic manipulation to construct logically sound reasoning paths. These methods excel in providing interpretable steps and ensuring formal correctness. However, the predefined rules may struggle to accommodate diverse problem types. In contrast, neural-based approaches leverage data-driven learning to generate solution paths from vast training datasets. These models offer flexibility and scalability, handling problems of varying complexity. However, their reliance on large, high-quality annotated datasets and the lack of rigorous correctness guarantees pose significant limitations. Therefore, many works [21, 25, 36, 46] attempt to combine the procedural power of symbolic models with the general power of neural models. Such hybrid approaches in general involves two key steps: parsing and reasoning. Parsing entails ex + +tracting formal language representations from the diagram and the accompanying text, while reasoning employs these parsed elements to predict and apply relevant theorem rules, ultimately constructing a logical path that leads to the final solution. This paper also builds on this emerging direction, offering novel insights about the pivotal role of diagrammatic information. + +In this paper, we propose Pi-GPS, unleashing the power of diagrammatic information for enhancing geometry problem solving. Our work is inspired by the observation that text often conveys ambiguity in ways that diagrams, by nature, cannot easily accommodate [32]. However current approaches typically parse text and diagrams independently, resulting in ambiguities remain unresolved in text and further undermines the subsequent theorem prediction stage as the predictor's understanding of the problem is constrained. For instance, consider a text reference to "a shape." This could refer to a variety of geometric forms, such as a triangle, rectangle, or circle. Yet the text alone offers insufficient information to resolve the ambiguity. In contrast, we can easily disambiguate the reference when supported by a diagram, as the visual context clarifies the intended meaning. Figure 1 provides several examples that highlight the ambiguities present in the text. + +In light of this, our objective is to enhance geometry problem solving by introducing a micro module that resolves textual ambiguities through the diagrammatic information. We identify three primary sources of these ambiguities: (1) unspecified points (e.g., missing point names), (2) unspecified shapes (e.g., missing shape names), and (3) unspecified areas (e.g., computing shaded areas). To address these, we leverage Multimodal Large Language Models (MLLMs) to develop an error-correcting tool, rectifier, capable of automatically detecting and rectifying these ambiguities given the diagram as input. Additionally, we design a verifier to mitigate MLLM's hallucination by verifying the disambiguated text aligns with diagrammatic heuristics (e.g., closed-loop shapes), which we show is pivotal in the experiments. We also explore the impact of recent advanced LLMs for reasoning, o3-mini [24], in predicting theorem order, and present valuable analysis. + +Experimentally we demonstrate our framework Pi-GPS, by resolving ambiguities in text, significantly outperforms state-of-the-art baselines on both Geometry3K [21] and PGPS9K [42] benchmarks. We hope this work will draw attention to the crucial need for resolving text ambiguity in formal language space, an aspect often overlooked in previous research, and underscores its significance in advancing geometry problem solving. + +In summary, our key contributions are: + +- Perspective. We identify that text ambiguity is a key factor hindering the performance of geometry problem solving, which has been overlooked in prior works. + +- Methodology. We propose a micro module to address text ambiguity, comprising a rectifier and a verifier. The rectifier powered by a MLLM refines text with diagrammatic information, while the verifier ensures alignment with diagrammatic heuristics. These components work in tandem to reduce ambiguity, which is further evaluated on theorem prediction using a strong reasoning LLM. +- Evaluation. The resulting framework, Pi-GPS, achieves the state-of-the-art performance, with a nearly $10\%$ improvement on Geometry3K over prior neural-symbolic approaches. We also provide strong evidence supporting the efficacy of the proposed module, and present an in-depth analysis. + +# 2. Related Works + +Geometry Problem Solving. Recent advancements in automated GPS [4, 28, 30] have attracted considerable attention due to the inherent complexity and unique challenges it presents. One prominent approach to GPS has been the use of language models that treat it as a specialized form of text generation. Notable examples include GeoQA [8] and Uni-Geo [9]. These models leverage large-scale pre-trained language models to generate solutions by interpreting geometry problems as text-based tasks. PGPS-Net [42] improved upon these models by enhancing the performance of neural network-based approaches. These methods struggle to accurately capture the complex relationships between geometric entities in diagrams. LANS [18] circumvents this issue by incorporating diagram annotation, however, such annotations are not always accessible. Additionally, the vector representations used by these models lack interpretability, resulting in unreliable or inconsistent solutions. In contrast, symbolic systems approach GPS from a more structured, interpretable angle, such as GEOS [29] and InterGPS [21]. They convert problem statements and diagrams into structured formats, enabling the application of symbolic solvers based on known geometric theorems. This approach enhances the interpretability of the problem solving process, yielding more precise solutions. A significant advancement in GPS was the introduction of PGDP [41], the first end-to-end diagram parsing method for geometry problems. This was further used in works like GeoDRL [25] and E-GPS [36], which enhanced solution accuracy and robustness through techniques such as theorem library augmentation and theorem sequence prediction. Our study introduces a novel micro module to resolve ambiguities in textual problem statements, which is orthogonal and can be plugged into existing neural-symbolic frameworks. + +MLLMs for Mathematical Reasoning. Early research in multimodal learning focused on leveraging attention mechanisms to align image and text representations. A key breakthrough came with CLIP [27], which learned transferable visual representations through natural language su + +![](images/fcefb908d5267ed869c5c02c8f09f69681dd100e32693c9baf3c8a06a5a6c2c6.jpg) +Pi-GPS framework + +![](images/7339cc63f8632cff105b0d4b3866507389ad1226d152a2a4823406296cf630c8.jpg) +Text disambiguation module +Figure 2. Illustrating the pipeline of our Pi-GPS: the overall framework is shown on the left and the text disambiguation module is depicted on the right, which plays a crucial role in resolving text ambiguity, enhancing performance. REX stands for regex pattern matching. + +pervision, laying the foundation for subsequent large-scale multimodal models. Building on this, the LLaVA series [13, 19, 31] introduced visual instruction-tuning, linking a visual encoder to a language model via a simple multi-layer perceptron. Subsequent works [2, 7, 20, 34] expanded MLLMs by incorporating novel visual perception modules and hybrid vision encoders, enhancing their ability to address increasingly complex tasks. As model scale has grown, so too has their ability to perform sophisticated contextual and mathematical reasoning [5, 12, 26]. More recently, models like MathGLM-Vision [39] and Math-LLaVA [31] have introduced chain-of-thought reasoning and intermediate-step generation, enabling problem solving by breaking down complex tasks into manageable steps. Despite their impressive contextual reasoning abilities, MLLMs still face challenges such as hallucination, which is particularly problematic in mathematical reasoning tasks. In our work, we utilize MLLMs to generate diagrammatic information for text disambiguation, framing this as a more tractable task within the zero-shot capabilities of these models. + +# 3. Method + +In geometry problem solving, the Diagram represents the geometric figure, while the Problem Text provides the textual description, including the problem's objective (e.g., "Find the length of EH"). The goal is to solve for the correct answer corresponding to the given pair. To achieve this, we propose Pi-GPS, as illustrated in Figure 2. The framework comprises a parser and a reasoner. Distinct from previous symbolic approaches, we propose a text disambiguation module that leverages the diagrammatic information to resolve text ambiguity, and we introduce a theorem predictor using an LLM given the disambiguated formal language. + +# 3.1. Parser + +Text Parser. A critical step in solving geometry problems is extracting relevant information from the problem statement, particularly identifying the premises and the goal of the problem. This extraction process can be categorized into rule-based methods and deep neural network-based methods. Traditional rule-based parsing techniques have been shown to provide relatively precise results. Although deep neural networks excel in sequence-to-sequence (Seq2Seq) tasks such as machine translation, previous research [21] suggests that Seq2Seq-based semantic parsers struggle with geometry problems. This is primarily due to the limited size of geometric datasets and the tendency of neural parsers to introduce noise into the output. + +To achieve more accurate parsing, we utilize a rule-based text parser following [21, 25, 36]. This parser analyzes the problem text by applying regular expressions to identify basic elements, numerical values, and their interrelationships. The parser automatically generates a set of propositions $P_T$ and identifies the problem target $t^*$ from the text. + +Diagram Parser. As with previous work [25, 36], we employ PGDPNet [41], an end-to-end neural network-based model that efficiently extracts basic elements such as points, lines, and circles from geometric figures along with their logical relationships, and generates a formal set of propositions. This approach achieves state-of-the-art performance in geometric diagram parsing. + +Text Disambiguation Module. Previous studies [25, 36] have typically concatenated the parsing results from text and diagram parsers in a straightforward manner. While each parser performs well within its respective modality, the disconnect between textual and visual representations often leads to unresolved ambiguities, impeding subsequent solving process and thus degrading the overall accuracy. To + +
Problem TextFormal / Disambiguated FormalDiagram
The rectangle is inscribed into the circle Find the exact circumference of the circleInscribedIn(Rectangle(),Circle()) Find(CircumferenceOf(Circle()))8 in: A 6 in: B C D E F G H I
InscribedIn(Rectangle(A,B,E,D), Circle(C)) Find(CircumferenceOf(Circle(C)))
Q is the centroid and BE = 9. Find BQ.IsCentroidOf(,Point(Q),Shape($)A B C D E F G H I
IsCentroidOf(,Point(Q) Triangle(A,C,B))
Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated.Regular(Polygon($) Find(AreaOf(Shaded(Shape($))))A B C D E F G H I
Regular(Triangle(A,E,G)) Find(Minus(AreaOf(Triangle(A,E,G)), AreaOf(Circle(D))))
+ +Figure 3. Illustrating several examples, showing the proposed text disambiguation module is capable of resolving text ambiguity. + +overcome this issue, we propose a novel module incorporating a rectifier and a verifier, as illustrated in Figure 2. + +(i) Rectifier using MLLM. The primary objective of the rectifier is to resolve ambiguities in the output of the text parser by leveraging the diagram through a MLLM. Upon analyzing the sources of ambiguity, we categorize the root causes into three distinct types, which are as follows: + +- Unspecified points: The text parser can identify specific geometric shape but fail to associate them with explicit points. For example, in the relationship CircumscribedTo (Square(), Circle)), the parser recognizes that a square is circumscribed to a circle but does not specify the defining points (vertices) of the square or circle. +- Unspecified shapes: The text parser, although capable of recognizing certain geometric constructs, fails to correctly map or associate them with predefined shapes or geometric entities in the system. This limitation is evident in expressions like IsAltitudeOf(Line(C,P), Shape($)), where the absence of explicit shape identification impedes effective interpretation. +- Unspecified areas: The text parser indicates that the formal language specifies graphical elements, such as Find(AreaOf(Shaded(Shape($))). This implies the need to determine the area of a shaded region, typically representing areas of interest within a diagram. + +The rectification process begins by employing regular expressions to identify unknown identifiers, represented by the symbol '$', and determine the type of ambiguity. For each identified ambiguity, a specific prompt is crafted based on its nature, and the MLLM is used to resolve the issue by referencing both the Diagram and Problem Text. The incorporation of diagrammatic information is crucial, as it provides supplementary context to improve resolution accuracy. However, the potential for hallucination must be carefully managed, as it could compromise the accuracy of the rectification. Meanwhile, generating output in a formal + +language poses a significant challenge for MLLMs, as absolute precision is essential, any deviation such as an incorrect character and misplaced parenthesis can invalidate the output. This motivates us to design a verifier based on diagram heuristics, ensuring its correctness. + +(ii) Verifier using Diagram Heuristics. We propose a Logical Reasoning Verifier that utilizes diagram heuristics derived from the diagram parser to ensure the consistency of outputs generated by the MLLM with the provided geometric diagram. This verifier incorporates three key heuristics for examining the rectified output: + +- Entity existence verification. MLLMs may generate geometric entities such as points, lines, or circles that do not correspond to actual elements in the diagram. We use the entity instances identified by the diagram parser to cross-check the MLLM's output, ensuring consistency with the original diagram. +- Shape closure and order validation. A common issue occurs when points within a geometric shape fail to form a closed figure or are ordered incorrectly. For instance, a pentagon labeled Pentagon(A,B,D,E,C) may be erroneously output as Pentagon(A,B,C,D,E). To rectify this, we construct a graph representing the diagram, checking for connectivity and cyclic properties, and ensure each node has the correct degree for valid closure. If the points are ordered incorrectly, we reorder the vertices based on the graph structure to ensure proper shape formation. +- Geometry consistency of vertices. The MLLM-generated vertices may not always align with the intended geometry shape. We apply analytical geometry techniques to verify that the vertices match the intended shape based on their coordinates. + +When discrepancies arise, feedback from the verifier is incorporated into the rectifier, creating a loop that allows the MLLM to iteratively adjust and refine its output. Experimental results demonstrate that the verifier plays a crucial role in ensuring adherence, thereby enhancing geometric problem solving accuracy. + +# 3.2. Reasoner + +The reasoner typically comprises a predictor for theorem order prediction and a solver that applies the theorems in the predicted order to derive the final solution. + +Theorem predictor. Accurately predicting the correct sequence of theorems is essential for deriving solutions and ensuring the interpretability. Previous approaches [21, 36] have used transformer-based models, framing theorem sequencing as a sequential prediction task. Additionally, some study [25] has applied reinforcement learning to improve theorem prediction accuracy. However, a major limitation of these methods is their reliance on annotated problem solving sequences for training, which are often scarce or expensive to generate, particularly in specialized domains + +
MethodsAccuracyStepsQuestion TypeGeometric Shape
AngleLengthAreaRatioLineTriangleQuadCircleOther
Human [21]56.9-53.759.357.742.946.753.868.761.758.3
Human Expert [21]90.9-89.992.093.966.795.992.290.589.992.3
Gemini 2 [15]60.7-58.961.857.568.854.162.745.557.758.3
Claude3.5 Sonnet [6]56.4-54.957.353.664.649.458.640.957.953.9
GPT-4o [1]58.6-55.659.355.170.651.460.443.159.056.7
Inter-GPS [21]57.57.159.161.730.250.059.366.052.445.548.1
GeoDRL [25]68.4-75.570.522.683.377.876.062.959.448.1
E-GPS [36]67.91.63–2.2878.367.227.772.276.175.659.455.051.8
Pi-GPS (ours)77.82.31–4.1283.981.459.081.279.683.976.473.069.4
+ +Table 1. Comparison of geometry problem solving on the Geometry3K dataset. Our method consistently outperforms all baseline models. Accuracy, Steps, and additional metrics are reported for different question types and geometric shapes. Best results are highlighted in bold. + +requiring domain-specific expertise. Building on recent advancements, we draw inspiration from AlphaGeo [33], which demonstrates the potential of LLMs in symbolic deduction. In this work, we explore the application of advanced LLMs, specifically the o3-mini [24], by prompting the model with a library of geometry theorem knowledge. The model then generates the most appropriate order of theorems based on disambiguated text and diagram formulas. This approach reduces dependence on labeled data and leverages the generalization capabilities of modern LLMs. + +Solver. Our solver framework builds upon the approach in [21] and incorporates the expanded theorem library from [25]. We have modified the logical framework to accommodate the extended formal language, specifically to address shadow regions and other special cases. The solver, along with the extended theorem library, is also employed in the experimental baselines for a fair comparison. + +# 4. Experiments + +# 4.1. Settings + +Datasets. We conduct experiments using the Geometry3K [21] and PGPS9K [42] datasets. Geometry3K consists of 3,002 geometry problems, partitioned into 2,101 for training, 300 for validation, and 601 for testing. Each problem is accompanied by a geometric diagram, problem text, and formal language parsing annotations. It covers a diverse range of geometric shapes, including lines, triangles, circles, quadrilaterals, and other polygons, making it a comprehensive benchmark. PGPS9K, an expanded version of Geometry3K, contains 9,022 geometry problems paired with 4,000 unique diagrams. Of these, 2,891 problems with 1,738 diagrams are sourced from Geometry3K, while the remaining problems are collected from five widely-used mathematics textbooks for grades 6-12, covering nearly all plane geometry problem types for these educational levels. + +Metrics. Building on the methodologies of prior studies [21, 42], we adopt two evaluation schemes: Completion and Choice, to assess the numerical performance of our + +methods. The Completion metric gauges the model's ability to generate the first executable solution program as its final output. The Choice metric measures the model's ability to correctly select an option from four candidates, with random selection as a fallback when the generated answer does not match any provided options. Performance is evaluated based on accuracy. + +Baselines. We conduct a comprehensive comparison between our proposed method and state-of-the-art models across various categories to analyze their performance in geometry problem solving tasks. For neural solvers, we evaluate several prominent models: NGS [8], which uses a ResNet-101 architecture for encoding geometric diagrams; Geoformer [10], which employs the VL-T5 model for diagram encoding followed by a Transformer-based processing architecture; SCA-GPS [23], which introduces a novel strategy for geometric problem-solving; PGPSNet [42], which combines CNN and GRU encoders to enhance geometric reasoning; LANS [18], a layout-aware neural solver; as well as GOLD [40], which converts geometry diagrams into natural language descriptions. In the realm of neural-symbolic solvers, we compare with the classical Inter-GPS [21] and two advanced models: GeoDRL [25], which improves Inter-GPS's search strategy by integrating logical graph deduction and deep reinforcement learning; and E-GPS [36], which combines top-down and bottom-up reasoning to match the performance of other methods with fewer steps and improved explainability. Additionally, we report results from leading MLLMs, including QwenVL [7], GPT-4o [1], Gemini 2 [15], and Claude 3.5 Sonnet [6], which represent cutting-edge visual reasoning capabilities. It is important to note that our method does not require ground-truth parsing (neither diagram annotation nor text annotation). We adopt the expanded theorem set from GeoDRL, which is also utilized by other methods that require a theorem base for fair comparison. + +# 4.2. Results + +We present a detailed comparison of our method with both MLLMs and neural-symbolic baselines on the Geometry3K + +
CategoryMethodGeometry3KPGPS9K
CompletionChoiceCompletionChoice
MLLMsQwen-VL [7]22.126.720.123.2
GPT-4o [1]34.858.633.351.0
Claude 3.5 Sonnet [6]32.056.427.645.9
Gemini 2 [15]38.960.738.256.8
Neural MethodsNGS [8]35.358.834.146.1
Geoformer [10]36.859.335.647.3
SCA-GPS [23]-76.7--
GOLD* [40]-62.7-60.6
PGPSNet-v2-S* [43]65.276.460.369.2
LANS (Diagram GT)* [18]72.182.366.774.0
Neural-symbolic MethodsInter-GPS [21]43.457.5--
GeoDRL [25]57.968.455.666.7
E-GPS [36]-67.9--
Pi-GPS (ours)70.677.861.469.8
+ +dataset, as summarized in Table 1. Our method consistently outperforms all baseline models, demonstrating superior performance, and even surpassing human experts in certain subcategories, such as the ratio question type. While MLLMs excel in general multimodal tasks, they exhibit limitations when applied to specialized mathematical geometry problems. These challenges stem from MLLMs' difficulty in accurately parsing geometric diagrams, performing complex reasoning, and executing precise numerical computations. In contrast, our method not only achieves significantly better results but also offers greater interpretability. Compared to neural-symbolic baselines, our approach achieves the highest performance, with an impressive improvement of nearly $10\%$ over the two strong baselines, EGPS and GeoDRL. This improvement highlights the substantial impact of text ambiguity, an often overlooked factor in prior work. Our category analysis reveals that text ambiguity affects all categories, with the most significant impact observed in the area question type, where the text frequently refers to "the area" without a specific identifier, exacerbating the ambiguity. + +To further validate the effectiveness of our approach, we present additional comparisons on the PGPS9K dataset for both completion and choice evaluation tasks, as shown in Table 2. Notably, compared to the state-of-the-art neural-symbolic method, GeoDRL, our method achieves improvements of $5.8\%$ and $3.1\%$ on the PGPS9K dataset in terms of completion and choice respectively. These results highlight the efficacy of our approach in interpreting the semantic intent of problem statements, a capability enabled by the integration of our text disambiguation module. Additionally, we provide a comprehensive comparison with + +Table 2. Comparison on Geometry3K and PGPS9K. Our method achieves the best performance (highlighted in bold) compared to the neural-symbolic methods. Note that all baselines except LANS use parsed results, while LANS uses textual clauses and point positions from diagram annotations. * indicates that GOLD, PGPSNet and LANS are trained on the larger dataset, PGPS9K. + +
Text disam.Theorem pred.CompletionChoiceSteps
60.770.62.85-6.03
✓68.976.62.85-6.03
✓63.272.32.31-4.12
✓✓70.677.82.31-4.12
+ +Table 3. Illustrating the effect of text diambiguation module (Text disam.) and theorem predictor (Theorem pred.) on Geometry3K. The text disambiguation module plays a critical role with its especially significant impact in driving performance improvement. + +competitive neural methods. Notably, LANS [18], the top-performing neural model, relies on textual clauses and point positions derived from diagram annotations. This reliance on ground-truth annotations significantly boosts performance. Both LANS and PGPSNET were trained on the large-scale PGPS9K dataset. However, neural-based methods typically suffer from a lack of interpretability. In contrast, our method advances the field of interpretable geometry problem solving by addressing the critical issue of text ambiguity, a challenge often overlooked in previous work. + +# 4.3. Analysis + +We provide an in-depth analysis about the framework of our Pi-GPS by conducting comprehensive ablation studies on Geometry3K dataset. + +Text disambiguation module is pivotal in Pi-GPS. We first conduct an ablation study to analyze the impact of two key components in Pi-GPS: the text disambiguation module and the theorem predictor utilizing an LLM. When the theorem predictor is disabled, a traversal strategy is employed. The comparison results are presented in Table 3. Notably, + +
MethodCompletionChoice
Ours w/o Text disam.63.272.3
+ Rectifier (general prompt)62.471.9
+ Rectifier (specific prompt)64.273.3
+ Verifier70.677.8
+ +the superior baseline performance relative to prior work is largely attributed to our self-trained PGDP model, which may exhibit enhanced diagram parsing capability. However, even with this strong baseline, both proposed components continue to significantly improve performance. Specifically, by integrating the proposed theorem predictor, the number of solving steps is reduced. More importantly, the text disambiguation module plays a critical role in Pi-GPS, with its impact being especially pronounced in driving overall performance improvement, a consistent enhancement of over $5\%$ across all cases. + +The verifier is critical in text disambiguation module. We further examine the roles of the rectifier and verifier components within the text disambiguation module. The experimental results, summarized in Table 4, also report the influence of a tailored prompt designed to address specific text ambiguity scenarios identified via regular expression (regex) pattern matching. A key observation is that, without a tailored prompt, applying the general rectifier degrades performance due to hallucinations and uncertainties inherent in MLLMs. These factors introduce erroneous modifications, reducing disambiguation accuracy. In contrast, incorporating a tailored prompt improves performance beyond the baseline, underscoring the importance of domain-specific guidance in enhancing the rectifier's effectiveness. This suggests that explicit contextual cues help mitigate unintended alterations and improve rectification precision. Additionally, the verifier significantly enhances disambiguation, yielding performance gains of $4\% -6\%$ . This highlights its critical role in enforcing consistency and correctness by systematically validating and refining rectified outputs. These findings collectively demonstrate that effective coordination between rectification and verification, along with domain-specific prompting, is essential for robust and accurate text disambiguation. + +Theorem order prediction is a more manageable task for LLMs. In our framework, we integrate an LLM to facilitate theorem prediction. A natural baseline is to directly employ an LLM to solve problems using the parsed formal representations. Given the growing interest in LLMs for mathematical reasoning, this approach warrants thorough investigation. We conduct experiments and evaluate LLMs and MLLMs on their ability to directly solve the problem. The results are summarized in Table 5. We have several + +Table 4. Illustrating the roles of the rectifier and verifier in the text disambiguation module on Geometry3K. + +
TaskModelsCompletionChoice
Direct solv. (MLLM)GPT-4o34.858.6
Gemini 238.960.7
Direct solv. (LLM)GPT-4o36.559.7
DeepSeek-R163.972.2
o3-mini66.475.5
o3-mini w/o Text disam.61.470.4
Theorem pred. (LLM)o3-mini (ours)70.677.8
+ +Table 5. Illustrating different roles of (M)LLMs in GPS. While advanced LLMs exhibit strong mathematical reasoning in direct solution generation, our approach, leveraging LLMs for theorem prediction, improves both performance and interpretability. + +key observations. (1) MLLMs struggle with geometry reasoning from raw inputs. When treated as LLMs and provided with parsed text and diagram formal representations, MLLM, GPT-4o in this case, outperform their direct processing of original problem text and diagrams. This suggests that current MLLMs face challenges in extracting logical information from visual diagrams. (2) o3-mini exhibits superior reasoning capabilities. Among the evaluated LLMs, o3-mini consistently achieves the best performance when directly applied to problem solving, reaffirming its effectiveness in mathematical reasoning tasks. (3) Ambiguities in parsed input significantly degrade performance. When tested with ambiguous parsed text and diagram representations, o3-mini's accuracy drops substantially. This again validates our observation that disambiguating textual input is important to enhance the model's reasoning capabilities, as even strong LLMs struggle with unresolved ambiguities in mathematical relationships. (4) Theorem prediction enhances both accuracy and interpretability. Rather than directly solving the problem, our method leverages LLMs to predict a sequence of theorems from a predefined theorem base, followed by a dedicated solver. This structured approach not only improves accuracy but also enhances interpretability, which is particularly valuable in educational settings where step-by-step justifications are crucial. + +The effect of different LLMs in theorem predictor. We further conduct an ablation study on different LLMs used in our theorem predictor, with results on the Geometry3K dataset presented in Table 6. Compared to the vanilla traversal-based approach, incorporating LLMs improves solving accuracy while reducing the number of steps required, thereby enhancing overall efficiency. Notably, all evaluated LLMs achieve comparable performance, suggesting that theorem order prediction is a well-developed application for LLMs, demonstrating their robustness and reliability in this task. + +The effect of different MLLMs in rectifier. In our approach, the rectifier within the text disambiguation module utilizes MLLMs to enhance performance. To explore the impact of different MLLMs on the rectification pro + +
PredictorCompletionChoiceSteps
Traversal68.976.62.85 - 6.03
Claude 3.5 Sonnet70.277.52.75 - 4.60
GPT-4o69.477.22.62 - 4.41
Gemini 269.877.22.52 - 4.29
o3-mini70.677.82.31 - 4.12
+ +Table 6. Illustrating the effect of different LLMs used in theorem prediction on Geometry3K. All evaluated LLMs achieve comparable performance. + +![](images/d5212dd5d9c7aa51b99e0b2fe399d40c743f1f1ff12c702650605a411baea15b.jpg) +Figure 4. Illustrating the effect of different MLLMs used in rectifier within text disambiguation module. + +cess, we conduct an ablation study evaluating multiple well-established MLLMs and present the results in Figure 4. The findings indicate that all tested models, regardless of their inherent capabilities and design variations, yield substantial improvements over the baseline. This demonstrates that our method's effectiveness is not dependent on a specific MLLM but rather highlights its robustness and broad applicability across diverse architectures, reinforcing its generalizability. + +# 5. Conclusion + +In this work, we present Pi-GPS, a novel framework that integrates diagrammatic information to enhance geometry problem solving by resolving textual ambiguities. Central to our approach is a rectifier-verifier module, where the rectifier leverages MLLMs to refine textual descriptions using diagrammatic context, while the verifier ensures geometric consistency. This framework significantly improves problem representation, thereby improving the problem solving performance. Empirical evaluations on the Geometry3K and PGPS9K benchmarks demonstrate that Pi-GPS outperforms state-of-the-art neural-symbolic methods, achieving nearly a $10\%$ performance gain on Geometry3K. These results advocate the critical role of ambiguity resolution in multimodal mathematical reasoning, a challenge that has been largely overlooked and warrants greater attention from the research community. + +![](images/f86cbef901ed9f6fb04952baffb41e614b38744f0c89bfe9cab6be7ad394680f.jpg) +Figure 5. Illustrating the limitations in current GPS framework. + +# 6. Limitations + +While this work successfully identifies text ambiguity and introduces a dedicated module to resolve it, significantly enhancing system performance. Several limitations still remain as illustrated in Figure 5. These limitations highlight key areas for future improvement and offer directions for advancing automated geometric probe solving systems. + +- Limited Text Parsing Capability: The current text parser struggles to accurately map certain syntactic variations to their formalized representations. Despite the integration of our text disambiguation module, these challenges persist, often leading to incomplete or erroneous formalizations. +- Inadequate Diagram Parsing for Complex Relations: The diagram parser struggles to accurately identify complex geometric relationships, such as tangency, due to their subtle and often implicit nature. This limitation hampers precise geometric analysis and interpretation, as misrecognition can distort structural understanding and compromise downstream computations. +- Insufficient Theorem Base: The absence of essential theorems necessary for solving specific problem categories significantly constrains the system's ability to generate comprehensive and accurate solutions. 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Pinco generates high-quality images with rich and diverse backgrounds from given foreground subjects and text descriptions. The four images on the left are generated by Hunyuan-Pinco and those on the right by Flux-Pinco, exhibiting its outstanding capabilities in foreground consistency preservation, rational spatial arrangements, and diverse background generation. + +![](images/445a50b2c92708b6d5ad28eca5a08c5f40ef920ba61165240a9d0d00050242cd.jpg) + +![](images/62608882a417c453914fee8bf1d872d2688ef9ddfad2331371561fa4f848929c.jpg) + +![](images/42db9b11c1e4f067d309b121d91bd6caf4a0b2973714af30a2c34386cb446657.jpg) + +![](images/4722d3bb3b925c6b1d2575f382923cb56d276f3642c305e3e541a1e4622a461d.jpg) + +![](images/0fad32165a2b445e11265de73bec98af290e58df37369cb2fc870f768fa1a0ce.jpg) + +![](images/3f831e6161ce45b1f7805ed82dc935975646cb10c55490f1282bc03fa8d04009.jpg) + +# Abstract + +Foreground-conditioned inpainting aims to seamlessly fill the background region of an image by utilizing the provided foreground subject and a text description. While existing T2I-based image inpainting methods can be applied to this task, they suffer from issues of subject shape expansion, distortion, or impaired ability to align with the text description, resulting in inconsistencies between the visual elements and the text description. To address these challenges, we propose Pinco, a plug-and-play foreground-conditioned inpainting adapter that generates high-quality backgrounds with good text alignment while effectively preserving the shape of the foreground subject. Firstly, we design a Self-Consistent Adapter that integrates the fore + +ground subject features into the layout-related self-attention layer, which helps to alleviate conflicts between the text and subject features by ensuring that the model can effectively consider the foreground subject's characteristics while processing the overall image layout. Secondly, we design a Decoupled Image Feature Extraction method that employs distinct architectures to extract semantic and spatial features separately, significantly improving subject feature extraction and ensuring high-quality preservation of the subject's shape. Thirdly, to ensure precise utilization of the extracted features and to focus attention on the subject region, we introduce a Shared Positional Embedding Anchor, greatly improving the model's understanding of subject features and boosting training efficiency. Extensive experiments demonstrate that our method achieves superior performance and efficiency in foreground-conditioned inpainting. + +# 1. Introduction + +Visual generative models [9, 48] have made significant progress recently and have demonstrated exceptional potential in various applications, including image editing [24, 30, 39, 62], image restoration [11, 14, 15, 29, 38, 55], and generative safety [35, 51, 52, 58]. Among these applications, a notably promising yet challenging task is foreground-conditioned inpainting, which focuses on generating high-quality backgrounds based on a provided text description while maintaining the integrity of the given foreground subject. It is closely related to the conventional text-guided image inpainting task [9, 25, 48, 68], which involves inpainting content within a small region based on a brief text description. However, the foreground-conditioned inpainting task presents greater challenges due to the following reasons: 1) It requires inpainting a larger area (the background region) with a more complex text description, and 2) It is crucial to preserve the integrity of the foreground subject's shape while ensuring harmonious coordination between the foreground subject and the background. + +Conventional text-guided image inpainting methods based on T2I diffusion models can be classified into three categories: 1) Sampling modification methods [2, 3, 9, 12, 40, 64], which adjust the diffusion sampling strategy to achieve inpainting, such as through latent space replacement. Although these methods can be seamlessly adapted to various diffusion backbones, they may disrupt the original latent distribution, leading to irrational layout compositions or unreasonable object placements (Fig. 2). 2) Model fine-tuning methods [45, 60, 68], which typically involve modifying the network structure of pre-trained T2I models and utilizing relatively small-scale datasets. These methods can cause the model to forget pre-trained knowledge and make it prone to fitting the distribution of the fine-tuned training dataset, ultimately affecting the quality and diversity of the generated images. 3) Conditional injection methods [1, 13, 21, 25, 63], which incorporate information from the preserved region into the frozen T2I model via a side-branch mechanism. Most of these methods [1, 21, 25] employ the ControlNet [63] structure, replicating half or the entire T2I model for inpainting injection. However, as the scale of the T2I model increases, these side-branch models become increasingly cumbersome and impractical to implement. Additionally, adding extra control information after the completion of text cross-attention may result in a decline in text-image consistency. + +To address these issues, we propose Pinco, a powerful yet efficient plug-and-play adapter that empowers DiT-based models for consistent foreground-conditioned inpainting. We design three innovative modules: 1) Self-Consistent Adapter. To effectively inject the subject features into the base T2I model, we need a suitable condition injection mechanism, where conventional condition injec + +tion methods based on image prompt adapter inject the feature through cross-attention layer and integrate it with the text cross-attention in the base model. However, such integration by directly adding outputs of subject cross-attention and text cross-attention can easily cause conflicts between text and the injected subject information, resulting in a mismatch between the text and generated background. Therefore, we propose a Self-Consistent Adapter, which makes an innovative shift by integrating subject-aware attention into the self-attention layer, effectively alleviating the conflicts between text and subject features. 2) Decoupled Image Feature Extraction. The conventional feature extractors, CLIP and VAE encoder, used in controllable T2I models are both suboptimal for our subject feature extraction: CLIP encoder only captures abstract global semantic information, while VAE encoder provides a limited amount of shape features, which is insufficient to meet the requirements of strict contour preservation in our task. To address these issues, we propose a novel Semantic-Shape Decoupled Extractor, using different architectures for the extraction of semantic and shape features from different sources, ensuring effective extraction of subject features with fine details of subject shape, achieving high-quality preservation of the subject outline and effectively avoiding expansion. 3) Shared Positional Embedding Anchor. To ensure precise utilization of subject features, subject-aware attention should be concentrated in the subject region. In light of this, we propose a Shared Positional Embedding Anchor that combines positional embeddings with subject features before the calculation of subject-aware attention. This approach achieves a decay in attention weights as the distance from the subject region increases, thereby concentrating attention inside the subject region. This operation greatly enhances the model's understanding of subject features and improves training efficiency. Extensive experiments demonstrate that our method achieves superior foreground-conditioned inpainting performance and efficiency. + +We summarize our contributions in four-fold: + +1. We propose Pinco, a powerful yet efficient plug-and-play adapter that can be seamlessly integrated with DiT-based models to achieve high-quality foreground-conditioned inpainting. With a small number of training parameters, it only increases negligible inference latency compared to the base model, while ensuring high-quality generation of rich and diverse backgrounds. +2. We propose Self-Consistent Adapter, a mechanism that injects subject feature through cross-attention, and innovatively integrates this subject-aware attention into the self-attention layer of the base model, effectively alleviating the conflicts between text and subject features. +3. We propose a Decoupled Image Feature Extraction strategy, which decouples the extraction of the semantic and spatial features of the subject, ensuring effective extrac + +tion of subject features with fine details of subject shape, and enhancing the preservation of the subject shape. + +4. We propose a Shared Positional Embedding Anchor, which combines positional embedding with subject features before attention calculation to constrain the activated region in the subject-aware attention, ensuring precise utilization of subject features. + +# 2. Related Work + +# 2.1. Controllable Image Generation + +There are various approaches to control generative diffusion models, some of which may represent promising directions for subject-driven, prompt-guided image synthesis. Certain methods [8, 20, 41, 49] achieve personalization by individually fine-tuning for each given subject. Despite their success, these methods require re-tuning to each new concept and fail to maintain the exact details of the subject. To address these challenges, some methods [10, 16, 42, 61, 63] reuse certain modules of the base model to achieve general feature extraction from reference images, and inject these extracted features into the frozen base model without subject-specific tuning. However, as the scale of the T2I models increases, these methods become increasingly impractical. In contrast, IP-Adapter [61] utilizes a lightweight decoupled attention mechanism to incorporate semantic features of the reference subject into the model. Another methods [6, 22, 36, 37] directly alter the attention map during sampling to facilitate subject generation, which carries the risk of compromising the inherent textual coherence. + +# 2.2. Image Inpainting for Foreground Condition + +With the impressive performance of T2I diffusion models [18, 43, 45, 48] in image generation, a variety of diffusion-based inpainting methods [9, 17, 25, 26, 48, 53, 68] have been proposed. 1) some methods [2, 3, 9, 12, 64] utilize a classic unmask region copying strategy, replacing known areas with the original image during the diffusion model's inference. However, this approach is rigid and often overlooks the semantic information of the foreground subject, causing shape expansion problems. 2) To avoid this problem, some methods [40, 60, 68] ensure the preservation of the subject by modifying and fine-tuning the model. PowerPoint [68] fine-tunes a text-to-image model with two learnable task prompts to achieve the subject semantic understanding. However, this approach can be challenging to train and may compromise the model's inherent text-to-image capabilities, leading to unalignment between the generated background and the input text. 3) Other methods [13, 21, 25, 63] inject the information of known area by side-branch injection. BrushNet [25] adopts a hierarchical approach by gradually incorporating the full UNet feature + +![](images/b51c320044011d57d2957c044c9f8cfdca361b3761215d38b15e9f394884850c.jpg) +Figure 2. Foreground-conditioned inpainting results of three existing T2I Inpainting methods, Pixart- $\alpha$ (sampling strategy modification), SDXL-Inpainting (Model fine-tuning), BrushNet (Conditional injection), and ours. Existing methods suffer from issues such as shape expansion and unreasonable spatial relationships between the foreground subject and background. + +![](images/c760fecd00945251364ce66180a9790b96fd436c9e7d96819c804e355af2827c.jpg) + +![](images/7ede22151e07eb304d862f67673ba7d9b3788bf1a02d71e70aa9e441f085a248.jpg) + +![](images/258cc6072289e2b86c92d707580b56dd3943f972ce4b1d73d1adbf19de63d3d7.jpg) + +![](images/22133978fc86664b2e705a7af51951af4ea5448c9c88b5515c44c1c785be427b.jpg) + +layer-by-layer into the pre-trained UNet. These ControlNet-style methods have extensive training parameters, and the pattern of injecting features after text cross-attention can lead to a deterioration of text alignment, as the visual features may dominate the generation. To address these challenges, we propose Pinco, a plug-and-play and lightweight adapter method, which requires very few parameters while efficiently injecting the characteristics of the subject. + +# 3. Preliminaries + +# 3.1. Diffusion Models + +The diffusion models [47, 67] encompass forward and reverse processes. In the forward process, a noise is added to a clean image $x_0$ in a closed form. In the reverse process, given input noise $x_{T}$ sampled from a random Gaussian distribution, a trainable network $\epsilon_{\theta}$ estimates the noise at each step $t$ conditioned on $c$ . The diffusion model training aims to optimize the denoising network $\epsilon_{\theta}$ so that it can accurately predict the noise given the condition $c$ : + +$$ +\mathcal {L} = \mathbb {E} _ {x _ {0}, c, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t, c) \| _ {2} ^ {2} \right]. \tag {1} +$$ + +In our scenario, the condition $c$ includes detailed text descriptions as well as independent foreground regions. + +# 3.2. Diffusion Transformer (DiT) + +Pinco is built upon the Diffusion Transformer (DiT) [44], which is a transformer-based diffusion method that operates on latent patches with a series of transformer blocks (DiT Blocks). Notably, the DiT Block enhances standard normalization layers with adaptive layer normalization (AdaLN). Additionally, the DiT Block incorporates Rotary Positional Embedding (RoPE) [50], which captures both absolute and relative positional dependencies and introduces a two-dimensional RoPE to extend its functionality to the image domain. In this work, Pinco is integrated with two kinds of DiT models: 1) Hunyuan-DiT [31], which further utilizes cross-attention mechanism for fine-grained text understanding similar to Stable Diffusion [48]; 2) FLUX.1 [27], a MM-DiT model that emphasizes the use of MM Attention [19] to enhance the alignment between text and visual information. + +![](images/497da52c96e4c4ed7709aff66a43f24aa85c3c26e2d4e003f8d284ef8b8afd56.jpg) +Figure 3. The framework of our Pinco, a plug-and-play inpainting adapter that can be seamlessly integrated with a text-to-image DiT model for consistent foreground-conditioned inpainting. Pinco consists of three modules: a Decoupled Feature Extractor used to extract subject feature, a Shared Positional Embedding Anchor used to ensure foreground attention, and a Self-Consistent Adapter injecting subject feature on the self-attention layer. + +# 4. Method + +Overview. Pinco is a plug-and-play inpainting adapter that can be seamlessly integrated with a text-to-image DiT model to enable consistent foreground-conditioned inpainting. The inputs to our inpainting system consist of a subject image $I$ , a mask image $m$ , and a text prompt $T$ (describing the desired background), with the subject depth image $d$ and Sobel image $s$ as conditioning signals. Pinco aims to inpaint the background region so that the generated background is consistent with the text description and visually natural, while the foreground subject remains unchanged. + +Fig. 3 shows the framework of Pinco and base DiT model. Pinco first extracts the semantic and spatial features of the subject image through a Decoupled Image Feature Extractor (Sec. 4.2). Then Pinco injects the extracted subject feature into the base model through a Self-Consistent Adapter (Sec. 4.1), which designs a subject-aware attention to inject subject features, and innovatively integrates it into the self-attention layer of the base model. Before the subject-aware attention calculation, Pinco designs a Shared Positional Embedding Anchor (Sec. 4.3), which combines positional embedding with the subject feature to constrain the activated area in subject-aware attention to the subject region. After the subject information is effectively injected and utilized, we employ the diffusion denoising of the base model to generate high-quality backgrounds. + +# 4.1. Self-Consistent Adapter + +In foreground-conditioned inpainting, the features of the foreground subject need to be injected into the base T2I diffusion model. Classical methods for adding image conditions in T2I models mainly fall into three categories: 1) Concatenating condition images through input channels, which requires significant training overhead for fine-tuning. 2) Creating a side branch injection by copying part of the base model [25, 63], which adds many parameters and can slow down inference. 3) Training a lightweight image prompt adapter [34, 56, 57, 61] through decoupled cross-attention mechanism, which has been proven effective. A + +naive way to use such adpater is designing a cross-attention between the latent and subject features, and integrating it with the text cross-attention output. However, using this approach can lead to a disharmonious result. Since the text is often complex and primarily about the background, such integration can cause conflicts between text features and subject features, resulting in: 1) subject outward expansion or distortion in the generated image; and 2) a mismatch between the text and the generated background. + +To tackle these challenges, we draw inspiration from the analyses of cross-attention and self-attention presented in previous works [34, 56], which show that the self-attention map can be effectively leveraged to preserve the spatial structural characteristics of the original image. This observation indicates that self-attention is more closely aligned with the layout of the final output, thereby presenting a promising pathway for enhancing the results of foreground-conditioned inpainting. Building on this understanding, we propose Self-Consistent Adapter, which makes an innovative shift by integrating subject-aware attention directly into the self-attention layer. For DiT with normal attention [31, 43], subject-aware attention is the cross-attention between the latent and subject features, and our mechanism can be expressed as follows: + +$$ +\begin{array}{l} Z = \alpha \odot \text {S e l f - A t t e n t i o n} (Q, K, V) \tag {2} \\ + \beta \odot \text {C r o s s - A t t e n t i o n} (Q, K _ {\text {s u b}}, V _ {\text {s u b}}), \\ \end{array} +$$ + +where $\alpha$ and $\beta$ are parameters used to tune the injection strength, $Q$ is the query, $K, K_{sub}, V$ and $V_{sub}$ are the key and value calculated from latents and subject feature. We also employ Zero-init Tanh Gating [65] to progressively control the strength of injection into the base model. This approach avoids conflicts between subject features and text, thereby better preserving the subject shape in the generated image and maintaining the alignment between the background and text. + +We find our Self-Consistent Adapter is also applicable to MM-DiT [19, 27] that uses MM-Attention, a variant of self-attention. For MM-DiT, we design subject-aware attention as a MM-Attention that fuses the latent and subject features + +![](images/a0bc91b7d1e10df42d39974fdbdc6c4289881b6a07c9a1731d86d7deacc0e994.jpg) +Figure 4. Quantitative comparison of state-of-the-art inpainting methods and our Pinco. Our method is capable of generating coherent, detailed and rational backgrounds following the provided text, while effectively mitigating the problem of subject expansion. + +(detailed architecture in #Suppl Fig. S1). The modified attention mechanism is as follows: + +$$ +\begin{array}{l} Z = \alpha \odot \operatorname {M M} - \operatorname {A t t e n t i o n} (Q, K, V) \\ + \beta \odot \text {M M - A t t e n t i o n} (Q, [ K, K _ {\text {s u b}} ], [ V, V _ {\text {s u b}} ]), \tag {3} \\ \end{array} +$$ + +where $[\cdot, \cdot]$ denotes concatenation across tokens dimension. + +# 4.2. Decoupled Image Feature Extractor + +For T2I-model-based foreground-conditioned inpainting, the features of the foreground subject need to be extracted and injected into the base model, where the subject feature is commonly extracted from the concatenation of the subject image, the mask image and other images related to the subject (e.g., depth map and Sobel image). Previously, image feature extraction of controllable T2I models [25, 45, 61, 68] mainly relied on CLIP or VAE encoder. However, the CLIP image encoder primarily captures the high-level global semantic information of the overall image, while the VAE encoder can hardly preserve the strict contour of the subject, both of which cannot meet the requirement of foreground high-consistency. Therefore, we propose a Semantic-Shape Decoupled Image Feature Extractor to ensure the sufficient extraction of both semantic and shape information of the given subject. + +Our Semantic-Shape Decoupled feature extractor consists of three parts: semantic feature extraction, shape feature extraction, and feature fusion. 1) Semantic Feature Extraction. The semantic and textural features of the subject are mainly extracted from the 3-channel (RGB) subject image (with background removed). To align the extracted feature with the data distribution of the pre-trained diffusion model, we reuse the original VAE encoder $\varepsilon$ as the semantic feature extractor, which reduces the overhead of addi + +tional training. 2) Shape Feature Extraction. It is crucial to maintain the details of the subject's shape in foreground-conditioned inpainting. Inaccurate shape feature extraction can lead to the expanding of the subject shape in the output image. Therefore, to accurately extract subject shape features, we leverage the subject's mask, depth map, and Sobel images to supplement the shape details of the subject. To ensure effective extraction of the local shape details, we construct a convolutional feature extractor to extract shape features. 3) Feature Fusion. After extracting semantic and shape features, both features are channel-wise concatenated together, and an MLP module is used to fuse them: + +$$ +F = \operatorname {M L P} \left(\left[ \varepsilon (I), \operatorname {C o n v} ([ m, d, s ]) \right]\right). \tag {4} +$$ + +Through this decoupled feature extraction method, we can not only fully utilize the information contained in the provided condition images, but also extract fine details of the subject shape, thereby significantly reducing the outward expansion of the subject shape in the output image. + +# 4.3. Shared Positional Embedding Anchor + +After obtaining a high-quality subject feature from the decoupled image feature extractor (Sec. 4.2), we use a subject-aware attention layer to fuse the subject feature with the latent feature, which is then integrated with self-attention layer by Self-Consistent Adapter (Sec. 4.1). However, we observe that when the subject feature is directly fed into the subject-aware attention without incorporating positional embeddings, the attention tends to disperse into regions that resemble the texture and content of the subject (Fig. 7). This leads to a situation in the generated images where, although the texture and partial semantics of the + +Table 1. Quantitative comparison between Pinco and previous methods. Pinco demonstrates the best subject shape preservation and text alignment effects, while also having very few training parameters. + +
Architecture & BackboneMetrics MethodsTrainable ParametersImage QualityForeground ConsistencyText AlignmentRationality
TPRFID ↓OER(SAM2.1)↓OER(BiRefNet) ↓LPIPS ↓VQAScore↑FV2Score ↓GPT4o↑
UNetSD1.5SD1.5 ControlNet29.59%84.2822.00%52.28%0.0085550.84922.83%4.012
HD-Painter0.00%88.7522.04%37.56%0.0071710.81313.26%4.624
PowerPaint-V20.06%88.5233.80%44.89%0.0105140.80122.74%4.669
BrushNet-SD1.541.86%84.1619.60%36.19%0.0057790.86819.67%4.335
SDXLSDXL inpainting100.00%83.6025.24%30.77%0.0079460.84713.96%4.536
LayerDiffusion24.67%107.9820.31%27.81%0.0079960.86417.34%4.358
BrushNet-SDXL12.69%87.0028.25%18.91%0.0057760.8709.83%4.621
Colors Inpainting100.00%85.5921.47%14.40%0.0042230.8915.27%4.418
DiTHuynuan-DiTHY-ControllNet31.20%85.3111.78%11.95%0.0061980.8775.00%4.576
HY-Pinco (ours)11.37%84.2511.51%10.00%0.0044410.9013.16%4.790
FluxFlux Controlnet15.25%111.9128.11%22.30%0.0045020.91613.17%4.629
Flux-Pinco (ours)12.56%103.417.87%6.84%0.0042390.9182.99%4.735
+ +subject are preserved, the shape and outline of the subject undergo notable changes. + +In fact, when calculating the cross-attention between the latent and subject features, the region outside the subject should be less focused, i.e., the attention in positions outside the subject region should be suppressed. To solve this issue and ensure the precise utilization of the subject feature, we propose a Shared Positional Embedding Anchor, which assembles positional encoding in the calculation of key to effectively leverage the positional information, suppressing the phenomenon of attention dispersion, thereby concentrating attention in the subject area. Recall that the subject-aware attention is calculated by Cross-Attention $(Q,K_{sub},V_{sub})$ , where query $Q$ is calculated from the latent, and key $K_{sub}$ , value $V_{sub}$ from the subject features. We reuse the rotary positional embedding (RoPE) of the base model and add it to the subject features when mapping it to the key of the subject-aware attention. This operation allows the interaction between the subject features and the latent space to focus on the same local area of the subject's contours, mitigating the influence of subject information on the global context. + +# 5. Experiments + +# 5.1. Experimental Settings + +Datasets. To enable our training pipeline, we first collected 88K images of real-world photography. Among these, 19K images are classified as high-quality, characterized by their exceptional aesthetic quality and clear foreground-background relationships. Subsequently, we utilized BiRefNet [66], ZoeDepth [5] and OpenCV's built-in methods to generate accurate subject segmentation masks, depth maps and Sobel edge drafts, respectively. Next, we leveraged Hunyuan-Vision to create rich image descriptions, including spatial relationships and detailed descriptions of lighting, style, and background composition. Finally, we manually removed data with unreasonable descriptions or inaccurate segmentation masks. + +For the evaluation, we randomly collected images of 300 everyday items. Each image is paired with the aforementioned + +tioned features and three scene descriptions generated by GPT4o. Additionally, we used two random seeds for each scene description, resulting in a total of 1,800 generation tasks (300 images $\times$ 3 prompts $\times$ 2 seeds) for each method. Implementation Details. We apply Pinco on two DiT backbones, Hunyuan-DiT [31] and FLUX.1 [27], and denote them as HY-Pinco and Flux-Pinco respectively. For Hunyuan-DiT, we use Eq. 2 for Self-Consistent Adapter; while for FLUX.1, we use Eq. 3. For both HY-Pinco and Flux-Pinco, we use the same shared positional embedding anchor. The learning rate was maintained at 0.0001, using a 1K-iteration warmup. To amplify training data, we dynamically cropped each image into different sizes, including 1:1, 16:9, and 9:16 aspect ratios. During evaluation, we generate images at a resolution of $1024\times 1024$ for assessment. We used the default parameters of each model for comparison. Following BrushNet [25], to ensure the visual consistency of foreground subjects, we introduced the two-stage compositing process after image generation1. Specifically, the original subject image is precisely aligned and overlaid onto the generated image within the unmasked region, preserving critical visual details while maintaining contextual coherence. + +Evaluation Metrics. We evaluate Pinco using 8 metrics, considering foreground consistency, text alignment, composition rationality, and image quality. + +1) Foreground Consistency: First, we individually measure the foreground subject's structural and perceptual consistency. To quantify structural preservation, we employ two off-the-shelf models (BiRefNet and SAM2.1-Large [46]) and adopt Object-Extend-Ratio (OER) [7] to evaluate the consistency between the subject shape in the generated image and the ground truth subject shape. OER is computed as: $\mathrm{OER} = \sum \mathrm{ReLU}(M_s - M_g) / \sum M_g$ , where $M_s$ , $M_g$ are the generated and ground truth mask of the foreground region. Since we use a two-stage compositing pipeline, a low OER metric is particularly crucial for good inpainting quality. Second, to assess perceptual consistency within + +![](images/d682e1e3d43f297056aea1d1e57b78f7fd4b19243181f864f6866e25f96561e3.jpg) +Figure 5. User Study. The images generated by Pinco received more preference from the participants compared to BurshNet [25], KColors-IP [54], Flux-IP [13] and SDXL-IP [45]. + +foreground regions, we compute the LPIPS metric within the foreground subject area. + +2) Text Alignment: We follow Imagen3 [4] to use VQAS-core [33] for alignment, given its high correlation with human assessments. In addition, we utilize the Florence-2 [59] to measure the subject redundancy, as some models fail to establish semantic associations with the foreground region and have multiple repeated subjects. +3) Composition Rationality: In many cases, it is challenging to generate images with reasonable compositions, resulting in object misalignment, imbalanced proportions, and spatial disarray. To address this, we leverage GPT-4o to evaluate each image based on three aspects: placement, size, and spatial relationships. Each image is scored on a scale of 1, 3, or 5, and the average score determines the rationality. The detailed prompt is provided in the #Suppl. +4) Image Quality: We evaluate FID [23] on MSCOCO [32]. We also evaluate Trainable Parameters Ratio (TPR). + +# 5.2. Comparisons + +We conduct both quantitative and qualitative comparisons, along with a user study, to demonstrate the superiority of our Pinco. We quantitatively compare our Hunyuan-Pinco (HY-Pinco) and Flux-Pinco with eight UNet-based models: SD1.5 backbone (ControlNet inpainting [63], HD-Painter [40], PowerPaint [68], and BrushNet-SD1.5 [25]), SDXL backbone (SDXL inpainting [45], layerdiffusion [28], BrushNet-SDXL [25], and Kolors inpainting [54]) as well as two DiT-based models: HY-Controlnet, and Flux ControlNet [13]. Additionally, we add Adobe Firefly [1] in qualitative comparison. + +Quantitative Comparison. As shown in Tab. 1, even with a smaller number of learning parameters, Pinco achieved leading results across various evaluation metrics. Our HYPinco and Flux-Pinco outperform others, notably in OER scores, demonstrating exceptional ability to maintain the subject's shape integrity and preserve contours and details. On the same base model, compared to ControlNet, Pinco shows a higher VQA-Score and a lower FV2Score. This highlights its outstanding capabilities in following the contents of the input prompts. Finally, GPT4o awarded Pinco + +Table 2. Ablation quantitative comparison on Pinco modules. + +
ModelsTPR ↓FID ↓VQAScore ↑OER(SAM2.1) ↓OER(BiRefNet) ↓FV2Score ↓GPT4o ↑
Pinco-wo-RoPE10.46%86.130.892290.44%68.64%7.37%4.820
Pinco-vae-only9.48%86.130.88936.11%14.58%8.15%4.688
Pinco-Cross11.37%85.610.89214.55%10.24%3.51%4.745
Pinco-Self (ours)11.37%84.250.90111.51%10.00%3.16%4.790
+ +![](images/fb104fa4e00ee5fdfdbcbe63f36b1d36aa10e47fd9e1105c5268e16d2c9284e6.jpg) +Figure 6. Qualitative Ablation Comparisons of Pinco, Pinco-Cross, Pinco-VAE and Pinco-w/oRoPE. + +the highest rationality score, showing its effectiveness in accurately managing the spatial relationship between the given foreground subject and the generated content. + +Qualitative Results. The qualitative comparison with previous image inpainting methods is illustrated in Fig. 4. In foreground-conditioned inpainting tasks that involve complex textual descriptions, many methods neglect to draw certain objects in the background (such as the beach chairs referenced in the prompt for the images in the 5th row). Additionally, some approaches face challenges with subject expansion, a problem particularly noticeable with the vacuum cleaner in the 6th row. Most methods also fail to adequately consider the spatial relationships between the subject and the background, leading to subjects appearing disproportionately large or mispositioned within the scene (as seen with the oversized humidifier on the bed in the 4th row). In contrast, our HY-Pinco and Flux-Pinco effectively generate coherent and detailed backgrounds that align with the provided text while successfully mitigating the issue of subject expansion, achieving enhanced image synthesis quality. These results substantiate the strong generalization capability of the Pinco adapter when implemented with different DiT-based architectures. More comparisons can be found in the #Suppl. + +User Study. We compared with four representative competitors for this user study. 31 participants took part in our user study, with each participant evaluating 40 sets of questions. Each set included two randomly arranged side-by-side images generated by Pinco and another method. Participants were asked to select the superior image based on several criteria, including foreground consistency preservation, text alignment, and overall image quality. The user voting results in Fig. 5 demonstrate that Pinco is more favored by participants, as our model consistently received higher preference scores across all comparisons, indicating its effectiveness in producing high-quality results. + +![](images/cf656212d207437427728c3998403afd965b8bbd62f655a4f3f2fc8b21ebe4f9.jpg) +Figure 7. The attention maps of the model with rope and the model without rope. As the inference progresses, the model with RoPE gradually focuses its attention on the main subject, while the model without RoPE tends to focus on an incorrectly shaped subject and its attention map is scattered. + +# 5.3. Ablation Study + +To validate the effectiveness of the proposed key components, we perform extensive ablation studies on HY-Pinco. + +Impact of Self-Consistent Adapter Injection. Fig. 6 shows that injecting subject features into the cross-attention layer can lead to three significant issues: text-driven shape expansion (illustrated in the first row of images), illogical spatial arrangements (notably in the second row, where the washing liquid appears to float), and inadequate text alignment (as seen in the third row, which fails to include the "scattered glasses" mentioned in the prompt). The quantitative analysis presented in Tab. 2 further highlights the advantages of incorporating in the self-attention layer, effectively mitigating shape expansion and ensuring a more coherent output. This reinforces the idea that self-attention is more aligned with the overall image layout. Furthermore, our empirical observations indicate that self-attention injection significantly boosts training efficiency and leads to much faster convergence compared to the cross-attention layer. More results are presented in the #Suppl. + +Impact of Decoupled Image Feature Extractor (DIFE). The comparison of the expansion rate metric is presented in Tab. 2, highlighting the performance difference between the Variational Autoencoder (VAE) and the Decoupled Image Feature Extractor (DIFE) as feature encoder. Notably, the use of DIFE results in a significant reduction in the OER(SAM2.1), decreasing it by $24.6\%$ compared to the VAE approach. Also, the OER(BiRefNet) is reduced by $4.58\%$ when employing DIFE. Furthermore, the visual comparison in Fig. 6 reveals that relying solely on VAE for extracting subject features tends to have noticeable shape expansion. This observation confirms the effectiveness of DIFE in mitigating such issues, highlighting its advantages in maintaining the integrity of the extracted features. + +Impact of Shared Positional Embedding Anchor. Fig. 6 + +![](images/525fc78d99ef1070b211575b7190c9addb43e0e6936be1cb27aa2ca910691bc6.jpg) +Figure 8. The convergence process of Pinco with RoPE and without RoPE. Without the help of a positional embedding anchor, the model fails to converge and can not generate an image of the correct subject. + +illustrates that in the absence of a shared positional embedding anchor, the generated images primarily retain the subject's color distribution and abstract semantic information, while the subject's shape and texture are largely compromised. A closer examination of the attention maps in Fig. 7 reveals a phenomenon of attention dispersion when position embedding is not utilized. This suggests that the model tends to focus on global features, neglecting the local shape details of the subject. In contrast, the attention map of the model that incorporates the shared positional embedding anchor is well-aligned with the subject's outline. Additionally, as shown in Fig. 8, the model with the positional embedding anchor effectively concentrates on the subject area when injecting subject features, leading to a significant improvement in consistency and convergence efficiency. + +# 6. Conclusion + +In this paper, we introduce Pinco, a novel plug-and-play adapter for diffusion transformers in foreground-conditioned inpainting. Pinco effectively addresses the challenges of generating high-quality backgrounds while preserving the consistency of the foreground subject. Our proposed Self-Consistent Adapter facilitates a harmonious interaction between foreground features and the overall image layout, mitigating conflicts that can arise from text and subject discrepancies. The Decoupled Image Feature Extraction method leverages distinct architectures to capture both semantic and shape features, achieving improved feature extraction and fidelity in shape preservation. Additionally, the Shared Positional Embedding Anchor allows for a more precise focus on the subject region, further enhancing the model's performance and training efficiency. Extensive experimental results confirm that Pinco outperforms existing methods, providing a robust solution for high-quality foreground-conditioned inpainting with good text alignment and subject shape preservation. + +# Acknowledgments + +This work was supported by National Natural Science Foundation of China (No. 62302297, 72192821, 62272447, 62472282, 62472285), Young Elite Scientists Sponsorship Program by CAST (2022QNRC001), the Fundamental Research Funds for the Central Universities (YG2023QNB17, YG2024QNA44), Beijing Natural Science Foundation (L222117), Tencent Marketing Solution Rhino-Bird Focused Research Program (Tencent AMS RBFR2024005). + +# References + +[1] Adobe firefly, 2023. Accessed: 2023-10-04. 2, 7 +[2] Omri Avrahami, Dani Lischinski, and Ohad Fried. 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Conde, Zihao Lu, Radu Timofte + +Computer Vision Lab, CAIDAS & IFI, University of Wurzburg, Germany + +https://github.com/mv-lab/AISP + +![](images/ff169de0697becde69265cb550ae121910f0627632907eb2d9eff5a2cf10311d.jpg) +ISP sRGB +Figure 1. Given an image and text prompts for how to edit the image, our multi-task image processing model edits the image considering the human instructions. PixTalk, covers over 40 transformations that can be commonly found in photography software (e.g. Adobe Lightroom), and it generalizes of-the-shelf on real-world photographs from diverse cameras and sensors. + +![](images/37d8f64318f31283d9e4e00262b46deb4872a76654e1fa967732749ff3b0464d.jpg) +This image is too dark, please increase the exposure. + +![](images/c9044ebf50f1d7819a3b7d839dfc1612c4386039ed35997bc6880f5697fd984d.jpg) +The enitre image looks flat, I want an image with higher contrast. + +![](images/7cf923e40de7cb52b774558b977a7a6697e6b338148498ecf15503c65292bc31.jpg) +The image looks too dark and cold, make it a bit warmer and brighter. + +![](images/6a021e8378b4609b1a66a7491bad3e54b298c94ea639f22573cc182f2797e91d.jpg) +Can you make my photo look like in winter? + +# Abstract + +Text-guided image generation and editing is emerging as a fundamental problem in computer vision. However, most approaches lack control, and the generated results are far from professional photography quality standards. In this work, we propose the first approach that introduces language and explicit control into the image processing and editing pipeline. PixTalk is a vision-language multi-task image processing model, guided using text instructions. Our method is able to perform over 40 transformations – the most popular techniques in photography, delivering results as professional photography editing software. Our model can process 12MP images on consumer GPUs in real-time (under 1 second). As part of this effort, we propose a novel dataset and benchmark for new research on multi-modal image processing and editing. + +# 1. Introduction + +Image signal processing and computational photography have witnessed remarkable advancements due to the integration of deep learning techniques [1, 12, 17, 25, 38, + +49, 57]. These improvements are often in post-processing rather than capture [5, 46, 54], which might include color enhancement, white balance correction, denoising and other computational photography techniques [14]. Indeed, smartphones compensate for the physical limitations by using more complex Image Signal Processors (ISPs) that include deep models for image enhancement. Such neural models run in dedicated on-device GPUs and NPU's [24]. + +Despite the advancements in computational methods, the inherent hardware advantages of DSLM (Digital Single Lens Mirrorless) cameras make them superior in capturing realistic images that are closer to the human perception. + +The camera ISP typically "offers" a single output i.e. the models are deterministic, offering a single input-output stop. For this reason, photographers often rely on third-party software for advanced editing and enhance further the images (e.g. Adobe Lightroom). The control over the image processing and editing process is key to obtain optimal results, and a positive user experience. + +Contributions We propose an efficient text-guided model for realistic image editing and photo-finishing. Our method, PixTalk, is a multi-task image processing model, able to + +perform over 40 transformations –the most popular techniques in photography–, delivering results as professional photography editing software. PixTalk is also extremely efficient, being able to process 12MP images on consumer GPUs in real-time (under 1 second). We also propose a large-scale dataset for text-guided image editing including high-resolution images from diverse cameras. We show diverse samples of our method in Figure 1. + +# 2. Related Work + +Multi-Task Image Processing. Single task methods for image enhancement and restoration are well-studied, however, their real-world applications are limited due to their lack of flexibility i.e. allocating different models, and select the adequate model on demand. + +All-in-One image restoration is emerging as a new research field in low-level computer vision [31, 34, 35, 39, 41, 55, 59, 60]. These methods use a single neural network to tackle different degradation types. However, these approaches lack controllability and struggle to scale (i.e. tackle over 10 tasks, process high-resolution images) + +Text-guided Image Manipulation. In the recent years, multiple methods have been proposed for text-to-image generation and text-based image editing [4, 6, 16, 18, 28, 37, 43]. Models such as SDEdit [37], Magic [28], Pixwizard [32] and TurboEdit [50] use text prompts to describe images or actions, and powerful diffusion-based models for generating the corresponding images. Our work is inspired in InstructPix2Pix [6] and InstructIR [10], methods that enable editing images from simple instructions, as opposed to complex captions or descriptions of the input or output images. Therefore, the users can transmit the task in natural written text, without requiring to provide further image descriptions or sample reference images. + +Language Models as Agents and UIs. As the performance of Large Language Models (LLMs) continues to improve, they are able to assist in more daily tasks. Research on using LLMs to control operations has also become increasingly popular [3, 19, 47, 51, 56]. These works prove that UI elements can be operated using LLMs e.g. Ferret-UI [56] understands mobile UI screens. + +Inspired by these works, we believe that interaction through natural language with LLMs can also enable more flexible control in image processing, specially in computational photography applications. InstructPix2Pix [10] demonstrate the power of text guidance for image restoration. This implies an advancement with respect to previous end-to-end one-stop models (i.e. a deterministic uncontrollable output), which improves user experience. + +# 3. PixTalk Dataset + +Following previous works [6, 10], we solve the instruction-based image processing task as a supervised learning problem. First, we identify the most popular transformations based on the post-processing workflows of photographers, then, we create a large dataset of RAW and sRGB processed image pairs using professional image editing software. Next, we label each transformation function with text prompts. Finally, we train and evaluate the model using the prompts and paired images. We explain in detail how the image data is generated in Sec. 3.1, we explain how all prompts are processed in Sec. 3.2, and our model in Sec. 4. + +Why previous datasets are not enough? The popular MIT5K dataset [7] provides 5000 DSLR images, for each RAW there are only five variants edited by photographers – in the literature we often see only the Photographer C variant. Other datasets [29] are not publicly available or the variants correspond to simple color transformations i.e. 3D LUTs [13]. For this task, we require a substantial variety of editing operations and styles for each image. Furthermore, we require the corresponding text descriptions (or prompts) for each transformation. + +# 3.1. Generating 100.000 1MP Training Pairs + +Our objective is to construct a dataset with broad applications in image processing and editing. To achieve this, we use a wide variety of cameras: Samsung S9, iPhone Xs, Vivo X90, Google Pixel 7, Nikon D3200, Nikon D700, Canon EOS 5D, Sony Alpha 7M3 – unlike previous datasets [7] we use smartphones, DSLR, and DSLM cameras with great variety of sensors. + +We use Adobe Lighthroom, a software widely used by professional photographers for post-processing and edition, to process the RAW images using a range of commonly applied functions during the photo-finishing procedure, then we create the corresponding prompts for each operation (task). Note that we filter and process the images manually. + +Our dataset includes a variety of image transformations (over 40), we provide some samples in Figures 2. All the transformations are described into details in the supplementary material, also we provide additional samples. + +For general illuminance transformations, we provide global adjustments, such as exposure and contrast, as well as local modifications, such as highlights and shadows correction. For each transformation we consider increasing and decreasing (e.g. exposure+, exposure-, contrast+, contrast-). + +Our color transformations, we apply global saturation adjustments, color vibrance, and color channel specific modifications (e.g. enhance only red channel). We include six fundamental white balance (WB) options for different common light conditions [2] (e.g. daylight, shade, cloudy). Also, different color temperatures e.g. 2700k, + +![](images/5743ee4f22d5630ae1184b9d9729d6d57c07e1ba73e4e192b87d0995684a2e56.jpg) + +![](images/e4526b71b46a87e091c9bcc5b663513f74e5ce1978d40167b4171b6c32cbdfe3.jpg) + +![](images/dac4b00dc31e6c23be24e451a7775173acb175078515e5166293acf2def119e2.jpg) + +![](images/b4740969dd36d6ef88f0fd45a9004ddbe5a2a623ed161584aba9a3289386a9dc.jpg) + +![](images/043454782b5425204b1c076def768a9eb199282b4d836e1f232371bcd4686a4f.jpg) +Input + +![](images/2cd7665ebb3b55f2bd8630e94ae6899ed856cce7917629fc824948d82da903bb.jpg) +Contrast $[- / + ]$ + +![](images/129bf0f6e682ce299f4c28bda473c487933f3eeb27d937a16f7a179dc7128fe8.jpg) +Exposure $[- / + ]$ + +![](images/a26d776bd6d0798b40bf0004203be045ef5b1f82f47b207ac5de946d99f2ca83.jpg) +Sharpness $[- / + ]$ + +![](images/d6f107d055ea870193f8b0d02f5e24a70b301b77b81d15162d4fa3dd30cfe53c.jpg) +Input + +![](images/c19ace335bf2e0e236a4169dcc9c91caa26e6c426b500976c6e13f5253d62ee0.jpg) +Highlight $[- / + ]$ + +![](images/a2b5ea142e74242b0dc32036475a60c9a9db418a4bcd96c946773789fb10a619.jpg) +Shadow[-/+] + +![](images/26f6a115f2e0f5b18b2a133a74c5d2a4a55e103754b9f8dd2850760f6223af20.jpg) +Vibrance [-/+] + +![](images/edf971164819c8115256e7a1b893ceefaa6a7d0a31e61bffab4009642ca65522.jpg) +Input + +![](images/0266d61efa96e919d8d6740312bc0c1714fbd1b081631cf73823edb2c58c8ba0.jpg) +Color Temperature 2700k + +![](images/2047f7fa7d3999f1d33e989bb9b8f97088c9ff831cb6ec32b224b604fd79dd60.jpg) +Color Temperature 4500k + +![](images/a938f55997649423772c49049f238f75deca3125cdcd65e77e79722bcf0e7290.jpg) +Color Temperature 7500k + +![](images/2e3b4129ce2bdcf52d1df21482286961bd6f3e9def464393ce3e19ff87a969d5.jpg) +Input + +![](images/f17041343ee7c95462d37fd004b4bbd86bf2e67e8b32096a44e13f07466c72fc.jpg) +White Balance Flash + +![](images/349b3d38316c13ddf6f6a451a3badf5a3ba3f2f3daf033368db014624e33e314.jpg) +White Balance Fluorescent + +![](images/7093d71aee5aafe74682faa392cdd98d6971f2318dafdd69e9b17b805f60d1be.jpg) +White Balance Shade + +![](images/98f18d4e726a516cb763fd2977efaf78f38257a2a4ab86553d06bb9efbcd3c1d.jpg) +Input +Input +Figure 2. PixTalk Dataset samples. For each input image, we show the different variants produced by retouching and editing the photograph using professional software. Note that the desired sRGB images have been obtained directly from the corresponding RAW images, and are uncompressed. We include diverse white balance versions [2], and popular color grading presets. + +![](images/6bc24ddbbdd5497df2308a5118dd089dca6336b46a3c048a4ca5631222196d2c.jpg) +Color Grading C1 +"Can you reduce the noise?" + +![](images/354092db3fbcd20b0c923713c92c304e6b14808e6d18d33e3bd588d9d8ec172e.jpg) +Color Grading C2 +Input + +![](images/3d538b6f61fe41eb7b6cfcefc3b26491791d420001b88bcc808422fd7016b83d.jpg) +Color Grading C3 +"Add more details" + +4500k, 5500k, 7500k. Furthermore, we include 6 popular options of color grading for global/separated hue and saturation edition, including 2 global settings and 4 highlight/midtones/shadow separated settings. + +For details and spatial transformations, we use mainly two sets of functions at different strength levels. Denoising with 3-stop intensities (20/30/50 of 100) to remove noise and smooth the image at different levels of intensity. Sharpness with two options for increasing and decreasing. + +Finally, we also consider complex and popular pre-sets, each contains a combination of numerous local and global transformations such as white balance adjustment, clarity enhancement, enhanced contrast and saturation adjustment and vibrance changes (e.g. instance Provia-Std, Classic-Neg, and Anime-style presets). + +Diversity of Devices and Robustness The variety in design years, sensor types, sensor sizes, and camera design makes the dataset highly robust against specific performance biases affecting image quality. These images range in resolution from 6 to 24 megapixels, and include a wide variety of scenes: day, night, landscapes, portraits, etc. All images were captured with low ISOs at the reasonable shutter speeds to ensure image quality. + +Train-Test Split Most methods for image enhancement and restoration train on image patches due to the GPU memory limitations. We extract 1MP $(1000\times 1000)$ nonoverlapping crops from 250 high-resolution sRGB images (inputs and the corresponding enhanced variants), and we train the models using these crops. We use $\approx 106.000$ pairs input-enhanced of 1MP images for training. + +The testset contains 40 images with 12MP resolution from diverse sensors not present in the training set. For each image we generated manually different edited versions. The testset represents $\approx 10,000$ 1MP cropped pairs. + +We provide more details in the supplementary. + +# 3.2. Generating Prompts for Training + +Following previous works [6, 10, 28, 50], we aim to use prompts that allow users to make a wide variety of photo adjustments and editions. For each transformation or task, we write manually at least 10 prompts with different "tone" i.e. novice, casual, expert photographer. To obtain more diverse descriptions, we use GPT-4o and Llama-3 [45] to augment these prompts, and use hundreds per task. Finally, we filter and remove the prompts that are incorrect or ambiguous. During training and inference, for each input image, we sample random prompts depending on the desired task. + +# 4. PixTalk Model + +In this section, we introduce our PixTalk model, a text-guided approach that offers control and interpretability. + +
FeaturesDiffusion [6, 28, 50]InstructIR [10]PixTalk Ours
Generative✓✓××
Artistic✓✓×✓
Realistic Result50×/50✓✓✓
Operations∞750
Fast (< 5s)×✓✓✓
Resolution1 MP2 MP24 MP
GPU Poor / Mobile××✓×✓✓
+ +Table 1. Comparison of text-guided image editing approaches. Diffusion-based methods [6, 28, 50] often present realistic results, yet in many cases the results include obvious hallucinations and artifacts. Such models mainly offer removal, replacement and addition of elements into the image, yet in virtually infinite variants. Our method offers realistic results, covers a wide range of transformations, tackles high-resolution, and it is extremely efficient. + +PixTalk consists on two elements: (i) The image model is based on well-known image processing pipelines [14, 27, 46], it performs the photo-finishing and editing. (ii) The language model that processes the user prompts and controls the editing process. In Table 1, we compare PixTalk with other text-guided image editing approaches. + +Using RAWs or SRGBs? Most smartphones do not allow to store RAW images due to memory limitations. We design our method to be "sensor-agnostic" and process input RGB images independently of the sensor. We acknowledge that using RAW images could be beneficial and closer to professional software pipelines, thus, it is our future work. + +# 4.1. Text Encoder + +Our text encoder maps the user prompt into a tokenized vector representation -a text embedding-. Following [10], we use a sentence transformer [42] (BGE-micro-v2), and we also fine-tune the text encoder using a learnable adapter: + +$$ +\mathbf {e} = \operatorname {n o r m} (\mathbf {W} \cdot \mathrm {E} (p)) \tag {1} +$$ + +where $p$ is the user prompt, $\operatorname{E}(p)$ represents the encoded prompt, $\mathbf{W} \in \mathbb{R}^{d_p \times d_v}$ is a learned adapter [20] that maps dimensions from $d_p$ to a lower-dimension $d_v$ , and norm is the 12-norm. In our experiments, $d_p = 384$ , and $d_v = 256$ . + +We also use a task classification loss where we predict the underlaying task (or operation) from each prompt [10]. Assuming that each task is a class, we use a simple transformer-style FFN head to classify the task given the text embedding $\mathbf{e}$ . Considering the number of tasks, and the variety of prompts, this is necessary to train properly our model, otherwise, training collapses. + +![](images/7609bbe15cebc1d81047685aaa5f565ba82cd18f57f6509582e770042c4b63d0.jpg) +Figure 3. Illustration PixTalk, our model for image retouching and enhancement. PixTalk includes global and local illumination transformations, advanced white balance, multiple color transformations, denoising and sharpening. + +# 4.2. Text-guided Operations + +In this Section we explain briefly each neural block in the Text-guided Operations part of PixTalk. These blocks are illustrated in Figure 3 in blue, from left to right we define them as $f_0 \circ \dots \circ f_4$ ( $n = 5$ blocks). + +# 4.3. Language Model Controller + +Our text encoder produces an embedding $\mathbf{e}$ . Following a mixture of experts (MoE) architecture, our controller $\mathbf{C}$ assigns a weight $\mathbf{w}_i$ to each text-guided block $i.e.$ each subblock (see Fig. 3 blue) is considered a task-specific expert. + +Based on the instruction embedding $\mathbf{e}$ , we weight the blocks using $\mathbf{C}(\mathbf{e}) = \sigma (\mathbf{e}\cdot \mathbf{W}_{\mathbf{c}})$ , where $\mathbf{W}_{\mathbf{c}}$ is the learnable projection of the controller, and $\sigma$ is the Sigmoid activation. + +In comparison with popular MoEs [36], we use a sigmoid activation instead of softmax, which allows the controller to "select" more than one block. + +The output from the block $f_{i}$ is obtained as: + +$$ +f _ {i} \left(f _ {i - 1}, y\right) = \left(w _ {i} f _ {i} \left(f _ {i - 1}\right)\right) + \left(1 - w _ {i}\right) y \tag {2} +$$ + +Each block takes as input the output from the previous block. We define the input RGB image as $y$ . For instance, the output from the first block is: + +$f_{0}(y) = w_{0}f_{0}(y) + (1 - w_{0})y$ where $y = f_{-1}$ + +This formulation ensures that the input $y$ is not processed by unnecessary blocks i.e. blocks $f_{i}$ with $w_{i} = 0$ . During inference this implies "jumping or skipping" the processing (and computation) of such unnecessary blocks depending on the instruction. We can select top- $k$ experts. Considering $k = 1$ (i.e. we select the block $f_{i}$ with the highest weight $w_{i}$ ), we would select only the block with the highest weight (importance) according to the language model. We use as threshold $w_{i} \geq 0.7$ for the selection of a block. The residual $y$ helps to avoid artifacts. + +# 4.4. Illumination and Tone Mapping + +A tone map is usually designed as a 1D lookup table (LUT) that is applied per color channel to adjust the tonal values of the image [13, 14, 62]. We could also apply 3 1D LUTs (one curve per channel) or a 3D LUT. PixTalk uses a NILUT [13] to learn such curves as an implicit neural representation. We use a simple conditional NILUT [13] with 16 channels and 3 layers, which allows to emulate a wide range of conditions. The condition vector is obtained by projecting e into the required dimension. We complement this with two inverted residual blocks [44] for local enhancement. + +# 4.5.Customized White Balance (WB) + +We define a learnable dictionary $D_{wb} \in \mathbb{R}^{N \times 3}$ of $N$ white balance and digital gains i.e. each learnable gain is a triplet of scalars $(g_d, g_r, g_b)$ . We apply each parameter $g$ as described by [2, 11] and obtain $I_{wb} \in \mathbb{R}^{N \times H \times W \times 3}$ , which represents a linear decomposition of the results from applying each $g_i$ to the input image. A learned projection $\mathbf{W}_{\mathbf{wb}}$ produces a set of weights $\mathbf{w}_{wb} \in \mathbb{R}^N$ from the instruction e i.e. based on the user instruction, the model selects the optimal WB. The linear combination of $I_{wb}$ and $\mathbf{w}_{wb}$ produce our white balanced image. To ensure we keep the physical meaning and interpretability of the learned WB gains, we found sufficient to initialize the parameters using a uniform distribution $\mathcal{U}(1,2)$ that encourages non-negative gains and a reasonable range for pixel gains. + +# 4.6. Color Enhancement + +We perform color correction as a pixel-wise dynamic convolution [9], therefore, we learn $k$ kernels that represent color correction matrices (CCMs). Smartphones typically use different CCMs depending on specific light conditions and capture modes (e.g. indoor, landscapes), therefore, we found optimal to learn 16 CCMs. + +We use a linear layer $\mathbf{W}_{\mathbf{cc}}$ to infer the optimal combination of CCMs for a given text instruction $\mathbf{e}$ and im + +age pooled features. This is done by predicting a vector of weights $\alpha$ for each kernel $\mathbf{k}_i$ . Then, these weights are applied as a dynamic convolution [9]. The kernel selection depends on the user prompt and the local image descriptor. + +During inference, we select the top-10 kernels i.e. kernels with the largest weight (importance), this allows to save computation without performance loss. + +$$ +f _ {2} \left(f _ {1}\right) = f _ {1} * \sum_ {i = 1} ^ {k} \alpha_ {i} \cdot \left(\mathbf {k} _ {i}\right) \tag {3} +$$ + +# 4.7. Denoising, Sharpening and Refinement + +Despite recent enhancement in sensors and lens performance, noise and sharpness remain an issues. + +We use a state-of-the-art denoising method tailored for mobile devices [12, 21]. This model consists on a simplified UNet that can process high-resolution images under $100\mathrm{ms}$ on mobile GPUs and NPUs. + +For sharpening and refinement we use a mobile super-resolution network, SCSRN [22], adapted to not perform up-sampling. The shallow model consists on a series of separable convolutions with residual connections [23]. + +# 5. Experimental Results + +Metrics We report standard metrics PSNR and SSIM [48]. Additionally we also use $\Delta E$ (DeltaE), since it is correlated with human color perception. + +Other methods We adapt CycleISP [58], InvISP [53], and STAR [61] to modulate their features following InstructIR [10]. We reduce the number of blocks in these models to meet certain efficiency. We also use a conditional neural implicit LUT (CNILUT) [13] where the condition vectors are predicted by the language model. We consider InstructPix2Pix [6] and Ledits++ [4] as zero-shot foundational models for image editing using text. + +We also do an experiment where we freeze PixTalk, and we use LLaVa-1.5 [33] as the language controller. We feed into the multi-modal LLM a down-sampled version of the image (224px) and the text instructions, then the model predicts the optimal combination of blocks for PixTalk. Given a very low-resolution image, after fine-tuning, the model can predict accurately the "optimal" transformation. + +Technical Details We provide in-depth technical and implementation details in the supplementary material including the loss function, optimizer, hyper-parameters, pretraining, and image augmentations. + +Quantitative Results In Table 2 we provide a benchmark using the proposed testset (see Sec. 3.1). PixTalk is outstanding in terms of efficiency-performance trade-off. Moreover, due to the shallow (regularized) image model, + +![](images/70638c0950051b97cb2d44602fd490f3faded38ef703e70fd92cf3fd98dca452.jpg) +Figure 4. Results per task using PixTalk. We display the average PSNR and $\Delta \mathrm{E}$ in 30 tasks. This proves that our method is able to produce results equivalent to professional software i.e. the difference between the references, and our enhanced images is minimal. + +our method does not produce hallucinations. Considering the comparison between the test inputs and edited images, our method improves the baseline PSNR by 8.3dB, and the DeltaE improvement is 6.23 - on average. As we show in Figure 4, and attending to the average $\Delta E < 2.5$ , the difference between our outputs and professional editors is unnoticeable to the human eye in most cases. + +Qualitative Results Figure 5 showcases the effectiveness of using language to control how the ISP produces different variants of the image according to the users instructions. In Figure 6 we present qualitative results of our method for white balance correction. PixTalk is able to emulate advanced AWB algorithms [2] and render multiple styles. Our PixTalk, a single model, is able to perform multiple tasks, providing high-quality and high-resolution images without artifacts that closely resembles the professional photographer edition. In Figure 7 we show the robustness of PixTalk to different kinds of prompts. In Figure 8 we compare PixTalk with our reference methods InstructPix2Pix [6] (diffusion-based) and InstructIR [10]. We provide more extensive qualitative results in the supplementary material, including high-resolution uncompressed images. + +
InputCycleISP [58]InvISP [52]STAR [61]CNILUT [13]InstructIR [10]InstPix2Pix † [6]Ledits++ † [4]LLaVA-1.5 [33] (Ours)PixTalk (Ours)
Params.1M1M3M0.3M1.8M1B1B7B0.1M
PSNR30.2030.9232.5728.0738.1022.6824.6837.9037.80
SSIM [48]0.9450.9470.9470.9600.9480.6800.74320.9500.950
+ +Table 2. PixTalk Benchmark. We report the average PSNR/SSIM across all the 40 target variants. PixTalk is the only method that can process 12MP images in regular 24Gb GPUs in real-time. The other methods were evaluated on crops. † denotes zero-shot evaluation. + +![](images/c5947989302fe4fc34b325384dc5a405c323656783072973021d2dd2f0f9a8a0.jpg) +"Make the shadow brighter" + +![](images/ee37f0e8fdb6b4a548bf04aab1cf9bbc31cb58c594d82a1b8ab166b256256e8a.jpg) +"Darken the highlight for more sky detail" $\longrightarrow$ "Enhance the color for pink sunset scene" + +![](images/db25e76cd12c0f40310740db0e161b7fdb4b098becc5c21964a1c26158ded554.jpg) + +![](images/b62f0694809eb8179819b6a31f5496a560e3c4ea749d46f2ee17ca6a0a7fe974.jpg) + +![](images/2ff5d22ac41754f56149d8e075b169aebdacf3fe330a73afcbbe6567315729d3.jpg) +"Increase the contrast of my photo" $\longrightarrow$ "downgrade the saturation and light" $\longrightarrow$ "enhance the colors a bit more" +Figure 5. Control via prompts. We can prompt multiple instructions (like a chat, from left to right) to apply different transformations to the images. Note that PixTalk works with a wide variety of text instructions. We highlight in red the input images. + +![](images/37cb48da80449002b65d83218f04656b961c7b0612840ad28e78df2be290846b.jpg) + +![](images/881861bfa9d21be230895dea844dc2cc6a34d6186276ad76a675375bcb2489e1.jpg) + +![](images/3915c8a357ec54b7fe788627702507cad091bb1ea6452d2d7759aba4b928f9eb.jpg) + +How sensitive is the model to the prompts? Any Language Model (LM) is sensitive to the prompts, from ChatGPT to PixTalk. For this reason, prompt tuning is a research area by itself [30, 40, 45]. As with LLMs, the quality of the results produced by PixTalk is proportional to the quality of the user prompt i.e. ambiguous and naive prompts such as "enhance it", do not allow our model to achieve optimal performance. We provide some samples using adversarial or out-of-distribution instructions i.e. instructions not related to the domain of the model, in Figure 7. + +# 5.1. Applications and Efficiency + +To the best of our knowledge, PixTalk is the only method that can process 12MP images on regular GPUs. + +Is it realistic to run this pipeline on mobile devices? Recent advancements [8, 15, 26] in the LLM community show that modern smartphones can host LLMs. Our method can be easily deployed into a smartphone -indeed, most smartphones already use more complex imaging pipelines than PixTalk-, being the language model optimization the most difficult part. How do we improve previous approaches? By integrating human instructions, PixTalk enables users to control the editing process as we show in Figures 5 and 8. + +Unlike classical deterministic image enhancement methods, which produce a single and unchangeable result, PixTalk allows for controllable enhancements. + +# 6. Discussion and Concluding Remarks + +We propose PixTalk, a multi-task model for image editing and post-processing, guided using text instructions. Our method is able to perform over 40 popular transformations in photography, delivering results as professional photography editing software (e.g. Adobe Lightroom). Moreover, our model can process 12MP images on consumer GPUs in real-time. Our dataset and results represent a novel benchmark for text-guided image editing. + +We acknowledge some limitations that could be improved in future works, mostly related to the language model. For instance, the robustness to text ambiguity and language sensitivity. We also plan to release a larger dataset for the community. We do not identify any ethical risk, since the generative capabilities of our model are limited. + +# Acknowledgments + +This work was partly supported by the The Humboldt Foundation (AvH). + +![](images/152ec905b45b71f62745dc3b7c8565b37f0cc5eaf97857698dd20f08260558b0.jpg) + +![](images/7367c6657215c0d136d00fe500a421152352e518a214dc5387fa14fdb0890636.jpg) +Input sRGB + +![](images/d2f8b4735178d14e1051beacf008aa152ad7fd31472719482d00f0e6b6fdfa41.jpg) + +![](images/2832448e6380584ed59ae56392128aaf3b7aa1886cf4127e3f6f80f547a5798e.jpg) +Fluorescent WB Afifi et al. [2] + +![](images/2c1635ac83c106ca3d9af177f86a31e1e7d59627b3e866bcfb43d383f05ca71c.jpg) + +![](images/d083b066c19f968986cca366a32a774ec4faf9827f0a74e4c9a5c883984138a6.jpg) +Shade WB Afifi et al. [2] + +![](images/41c164ac2373f001c72bd81db100e58511ba513c86f23042f6559e4fa665197e.jpg) + +![](images/ec0899c6b13554207e490ac4b725d9f6a93b78a48d6ced90ef7f2564a3eb4a29.jpg) +"Use cold tones" PixTalk (Ours) + +![](images/7249225a7132533e5dd88426b1d2e22c7afa3610f0ed651e8b8b2ea06ae30e7e.jpg) + +![](images/540022d4c3b860f7d62adfd402ca2e4fd83739e67f43f8b4acf59b70d77b6c65.jpg) +"Apply shade light" PixTalk (Ours) + +![](images/726b0cb6b31764db77c1dc5992a1676ce0540326227b933a3f9fa88c3bf18848.jpg) + +![](images/541618b55d5e997e2fe31d18efbdb487d4cf62a043eae780834d9f0a449ef02b.jpg) +Figure 6. Real-world AWB. Samples of Automatic White Balance (AWB) correction on photos captured from unknown cameras [7]. + +![](images/7f118b144331562d66aba766fba8f3b6204586b96c86effdb0fab4e1bd331107.jpg) + +![](images/59de9a449cdfd7e6914a33caf7cec64ceb3134a2e6579c6706be6b16ed99ab4c.jpg) + +![](images/0173d7ccd2b553b08129b029c84cc7a2ca0ce87410130bd82f267f189ece00f9.jpg) +[Expert] $\checkmark$ "Increase contrast, adjust WB, and flat the color" +[Unsupported] $\times$ "Describe the image", "Add a house in the lake" [Vague] $\times$ "Enhance this", "I do not like it, fix it" + +![](images/4c6d2fccc05f543a2d8219764372d03b3650fbf80c30a690c2bd98b08266a421.jpg) + +![](images/bb6681c9f63298531012c54cf3c507d882f71d89986478818741d1690345e1e8.jpg) +[Novice] $\checkmark$ "I want richer and vibrant colors" + +![](images/fc727a816ca2edf48bad1e139e14a4620e15c4ea4f75343387c06d91bb88adef.jpg) + +![](images/00d692bcda7ebab6f01281876333a1e576cd405a1c1be7adbee00fb44a68309b.jpg) +Figure 7. Adversarial and OOD samples of PixTalk Robustness. We show how PixTalk process different types of prompts. The first row gives positive examples of prompts for PixTalk, the second row shows the negative examples and the robustness of the model. PixTalk does not hallucinate or generate unpleasant artifacts. + +![](images/99edffdf9247e70f0999c9a0ac8a5189b3d719b120fefea43afb968163f9301d.jpg) +Input +Figure 8. Comparison between models. We show two examples of different instructions applied to the input image -from left to right-. Images are captured by photographers using a professional DSLM Sony Alpha 7 camera. Note that InstructIR [10] and InstructP2P [6] cannot process the full-resolution images (24 MP) due to their high computational complexity, thus, we feed into those models a downsampled image $(\times 4)$ . In contrast, PixTalk allows precise control of colors and real-time processing at high-resolution. + +![](images/b177e9660018bb455f76d2d628729206d036f3de7ccf2c07d8e2e53fe5eca59b.jpg) + +![](images/4d0b7c9de65edf83837fdf1ff834f78c33339ec7dbb4d897bf61ea08492ef033.jpg) +InstructIR [10] + +![](images/90ed29d9f1f5c6c91a7330eb17088a3ae8e1fc0c98e26855d852905e7f5ff8ee.jpg) + +![](images/46de2819574ce0fe4e0084cc23602c39a2e87129711989ef493b16531d98c5dd.jpg) +InstructP2P [6] + +![](images/548078543b8b4277f1a42aade61a3e34bca93059bc3664603449b16e5928e2cf.jpg) + +![](images/0e6f3fc0bfe883128d069a78fc7976045ae09764a97ee6f3c743cd598d880e00.jpg) +PixTalk + +![](images/8dfcda50735e045f0adfb8ef2f0c9ef769d018ddcbc49d8c58eeda229535a185.jpg) + +![](images/d7f434bdd27241d809dfcd5ab70847d77e409bdb1a6bcdf9b80cf8f5c1481242.jpg) +InstructIR [10] +"Make the colors warmer like sunset" + +![](images/5fffb42a12bdce6a52f369d00e296a23295c8c08fa401a194c2378a611039e85.jpg) + +![](images/0c5ad10c935e819074c53ae8afad5e25a8b05e1e100d934243647e08aa81e524.jpg) +InstructP2P [6] + +![](images/6bac3bd596adb77c4f5f7cb9fc21c9cbf6e59820fc49b8137cc2176243b3958b.jpg) + +![](images/c1cec3b6804dd23dc667c375cb7ddd6c85e0ebe2241d2077f7a1baba3f991324.jpg) +PixTalk + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. 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To produce natural stitched images, we first determine the middle plane through homography decomposition and globally project the original images toward the desired plane. Compared with unidirectional homography transformation, it evenly spreads projective distortion across two views and decreases the proportion of invalid pixels. Then, the bidirectional optical flow fields are established to carry out residual pixel-wise deformation with projection-weighted natural coefficients, encouraging pixel motions to be as unnoticeable as possible in non-overlapping regions while smoothly transitioning into overlapping areas. Crucially, this flexible deformation enables PixelStitch to align large-parallax images and preserve the structural integrity of non-overlapping contents. To obtain high-quality stitched images in the absence of labels, a comprehensive unsupervised objective function is proposed to simultaneously encourage content alignment, structure preservation, and bidirectional consistency. Finally, extensive experiments are conducted to show our superiority to existing state-of-the-art (SoTA) methods in the quantitative metric, qualitative appearance, and generalization ability. The code is available at https://github.com/MakiseChris666/PixelStitch + +# 1. Introduction + +Image stitching is a practical technology that composes multiple overlapped images into a single panorama with a wide field-of-view (FoV). It has been widely applied to var + +![](images/171c5a6fd79599ef72e653f64515f19fd425438f5c17467d5152a15b4e934b02.jpg) +(a) Input images and virtual midplane. + +![](images/42e45663c7401ef19c82434261aa6a5874d7715183e07d7cb3688fcc4c385bb2.jpg) +(b) The result of global bidirectional alignment. + +![](images/a9fa3b981068a924e624882853a098410d953c5f0bd22f24a12a9b04d1de599d.jpg) +(c) The result of pixel-wise bidirectional warp. +Figure 1. Our motivation (a) and two-stage bidirectional warped results (b)(c). We zoomed in on a far and a near area to show parallax alignment and the outlines of the stitched images indicate our natural structures. + +ious fields, such as medical imaging, panoramic photography, virtual reality, etc. In practice, image stitching is often confronted with diverse challenging scenes (e.g., large parallax, unnatural distortion, etc), which makes it hard to produce high-quality stitched results. + +To address these issues, various techniques are introduced to traditional feature-based image stitching. On the one hand, spatially adaptive warps have been proposed to achieve parallax-tolerant stitching [4, 8, 16, 18, 19, + +[24, 25, 38], which requires considerably flexible deformation and easily causes unnatural distortion. On the other hand, shape-preserving warps based on global similarity [4-6, 24, 37] or structure constraints [5, 6, 10, 20, 22, 37] are capable of creating a natural panorama, but typically compromised to a certain extent on alignment accuracy. Few methods can well achieve both alignment and naturalness at the same time. Besides, there is an increasingly complicated trend in hand-craft features required in traditional methods, from SIFT [26] keypoints [2] to line segments [21], large-scale edges [6], depth maps [23], semantic planes [17], and even SAM [3]. However, the more features are leveraged, the higher quality of textures is required, leading to unstable performance in a variety of scenarios. + +Recently, learning-based methods have become a new trend in image stitching techniques, which are free of constructing hand-crafted features and robust to some challenging cases (e.g., low light, low texture, etc). Among these methods, unsupervised learning plays an important role in its capability to be trained on unlabeled datasets and superior generalization ability [27, 31, 40] to supervised learning. The key of unsupervised image stitching is to model differential spatial transformations and formulate unsupervised objective functions, such as reconstruction [29], differentiable TPS [1] transformation [31] and pixel-level deformation [11], etc. These methods perform well on seamless image stitching but care less about providing natural and rarely distorted panoramic views. + +In this paper, we investigate structure-preserving warps from the perspective of unsupervised learning and propose a global-to-pixel bidirectional warp (termed PixelStitch) to simultaneously realize robust, accurate, and natural image stitching. First of all, we address the problem of projective distortion from a single-perspective view by assuming there exists a middle imaging plane between the input views (Fig. 1a). Particularly, we present a homography decomposition algorithm to determine this plane and project the original images to it. Compared with it, existing single-perspective methods [20, 22] struggle to find an appropriate trade-off between alignment accuracy and projective distortion, while multiple-perspective methods [4, 6, 37] suffer from structural distortion when transitioning from homography to similarity. The proposed homography decomposition provides a new perspective to create a visually natural image by carrying out bidirectional global warping and spreading projective distortion evenly across two views, as shown in Fig. 1b. It neither produces distorted transitions as multiple-perspective methods nor inhibits alignment as single-perspective methods. + +Subsequently, we propose to estimate structure-preserving bidirectional optical flow fields and then carry out residual deformation. Current learning-based pixelwise solutions [11, 15, 32] mainly focus on accurate op + +tical flow prediction, and tend to show their superiority of parallax-tolerant alignment. Different from them, we concentrate on providing both accurate and natural results, which inspires us to dig into bidirectional pixel-wise deformation, as shown in Fig. 1c. Compared with the unidirectional warp, the bidirectional one has a higher performance ceiling by distributing the deformation burden to two views. However, unstable alignment and unexpected distortion could easily occur as the bidirectional warp is more challenging to control without a stable reference image. To this end, we leverage learnable content selection masks to guide a partial-to-whole diffusion on the alignment area to facilitate stable convergence. Furthermore, projection-weighted natural coefficients (PN-Coef) are presented to incorporate naturalness into the bidirectional optical flow fields, which preserves non-overlapping regions as intact as possible while smoothly transitioning into overlapping areas. Besides, to optimize the network parameters without labels, an unsupervised comprehensive objective is designed to achieve accurate alignment, pixel-wise structure preservation, and reasonable bidirectional consistency. + +Extensive experiments demonstrate our superiority over other SoTA methods in terms of accuracy, distortion, and naturalness. The main contributions are concluded with: + +- We present PixelStitch, a global-to-pixel bidirectional warp for natural image stitching. It learns the deformation regulations merely by watching the input images and outperforms existing SoTA solutions by a large margin. +- For global alignment, the virtual midplane is raised for the first time (to our knowledge), into which the individual input images are projected. We propose a homography decomposition algorithm to determine the expected plane, distributing the projective distortion over both views. +- For pixel-wise warp, we establish bidirectional optical flow fields to align large-parallax contents in overlapping areas. Besides, projection-weighted natural coefficients and a comprehensive unsupervised objective are formulated to preserve structures of non-overlapping regions. + +# 2. Related Work + +# 2.1. Traditional Feature-Based Methods + +# 2.1.1. Towards Better Alignment + +SIFT [26] has been an irreplaceable feature in traditional image stitching since it was first leveraged to calculate a robust global transformation in AutoStitch [2]. For better alignment, various methods are then proposed to achieve spatially-varying warps, such as DHW [8], SVA [25], APAP [38], ELA [18], TFA [19], WRBIS [16], etc. These methods tend to introduce increasingly flexible warps to improve alignment capability but often cause unnatural distortion. + +![](images/e6b6db96a94a6fcbbe5faaa58dbadea286e0e535780381a5c962be46b013cf4e.jpg) +Figure 2. An overview on PixelStitch. Our framework consists of two stages: global bidirectional alignment and pixel-wise bidirectional warp. In the first stage, a homography transformation is estimated and then decomposed to determine the middle plane for the input images. In the second stage, the warped images are used to predict bidirectional flow fields ( $F_{1}$ and $F_{2}$ ), specifying pixel-wise deformation to eliminate residual misalignments and preserve natural structures. + +# 2.1.2. Towards Less Distortion + +To suppress distortion and obtain more natural panoramas, two categories of methods arose: single-perspective and multiple-perspective. Single-perspective methods parameterize distortions as additional terms in their energy functions, such as QH [20], SPW [22], LPC [10], etc. Multiple-perspective methods adopt global similarity that is less likely to cause distortion and smoothly transition into it in non-overlapping areas, such as SPHP [4], ANAP [24], GSP [5], etc. Moreover, DFW [21] leveraged line segments extracted by LSD [35] as another feature together with keypoints to preserve line structure consistency, which is then adopted in extensive line-guided solutions [10, 22, 37]. Recently, more and more various feature consistencies have been proposed to preserve further structure, like large-scale edges [6], depth maps [23], semantic planes [17], and even SAM segmentation [3]. + +In sum, traditional methods rely on various hand-craft features, which could easily lead to unstable performance under some challenging scenes. Besides, few methods contribute to both alignment accuracy and structure naturalness, which is another limitation. + +# 2.2. Deep Learning-Based Methods + +In contrast to feature-based methods, learning-based methods are capable of learning dense semantic features from abundant data, which adapt to various circumstances robustly. Initially, Nie et al. [28, 30] constructed a synthetic stitching dataset and proposed a CNN-based baseline following the traditional pipeline. To free from unavailable data labels in the real world, the reconstruction-based methods [12, 29] presented to eliminate misalignments by reconstructing stitched images from semantic features. Then, differentiable elastic warps [13, 31, 41] are proposed to realize mesh-level flexible deformation. To further increase the alignment ability, pixel-level warps are formulated in supervised [15] and unsupervised [11] manners. + +Although these learning-based solutions perform well on alignment accuracy, they care less about creating visually + +natural panoramas. In this work, we consider both accuracy and naturalness, contributing to a novel method for generating well-aligned and natural stitched results. + +# 3. PixelStitch + +The pipeline of PixelStitch is shown in Fig. 2, which consists of two stages: global bidirectional alignment and pixelwise bidirectional warp. In the first stage, we present a homography decomposition algorithm to determine the middle plane $(\pi_{mid})$ for the input images $(I_1$ and $I_{2}$ ) and project them from respective image planes $(\pi_{1}$ and $\pi_{2}$ ) to the middle one. It evenly distributes the projective distortion across two views and concludes with two globally warped images $(I_1^{mid}$ and $I_2^{mid})$ . In the second stage, the warped images are used to predict bidirectional flow fields $(F_{1}$ and $F_{2})$ , which specify bidirectional pixel-wise deformation to eliminate residual misalignments and preserve natural structures. + +# 3.1. Global Bidirectional Alignment + +To determine the middle plane, an intuitive idea is to solve the relative pose (rotation and translation) between two cameras, and then we can find the pose of the virtual middle camera. However, even if we solve the pose, it is hard to complete the re-projection process (from image to 3D to image) since the depth and intrinsic are typically unknown. Instead, we assume the image content is on the same plane and adopt homography to represent their relative transformation. Then, we try to decompose it into two special transformations, which map from respective image planes to the virtual middle plane. + +# 3.1.1. Homography Estimation + +Homography transformation is a geometric mapping between two image planes, which can be represented by a $3 \times 3$ matrix $H$ . It should satisfy the following properties [9]: + +1. Invertibility. If we sequentially adopt $H$ and $H^{-1}$ to warp an image, the image will remain original. +2. Multiplicability. If $H = H_{1}H_{2}$ , warping an image using $H_{1}$ and $H_{2}$ sequentially will obtain the same result as + +using $H$ + +In the first stage, we leverage the homography to coarsely align the input images, which provides the global alignment for the subsequent pixel-wise warp. Note that arbitrary homography estimators can be used for our warp pipeline as our focus is on how to decompose an existing homography into two desired intermediate transformations. + +# 3.1.2. Homography Decomposition + +Projective distortion appears when we project one image onto another image plane if the estimated homography overly aligns some local regions and ignores the global content. Compared to its appearance in the original, it typically enlarges the region of an object [20], yielding unnatural visual effects. To address it, we propose to distribute the projective distortion from one view to two views. In particular, we assume that there is a middle plane between two image planes so that we can map the two planes to the intermediate one, which could effectively relieve distortion without losing alignment accuracy. + +Therefore, we propose a homography decomposition algorithm to split a single homography into two to apply bidirectional alignment. As shown in the blue part of Fig. 2, let $H$ , $H_{1}$ and $H_{2}$ be the homography transformations to project from $\pi_{1}$ to $\pi_{2}$ , $\pi_{1}$ to $\pi_{mid}$ and $\pi_{mid}$ to $\pi_{2}$ , respectively. Then the three will satisfy: + +$$ +H = H _ {1} H _ {2}. \tag {1} +$$ + +As $H$ can be solved by an arbitrary homography estimation method, we only need to determine either $H_{1}$ or $H_{2}$ . After that, $H_{1}$ (or $H_{2}^{-1}$ ) can be used to warp $I_{1}$ (or $I_{2}$ ) to get $I_{1}^{mid}$ (or $I_{2}^{mid}$ ). + +As our purpose is to evenly distribute projective distortion to two views, we expect the deformation degrees of $I_1^{mid}$ and $I_2^{mid}$ to be close. From this point, we force $H_1$ and $H_2$ to be the same, denoted as $H^* = H_1 = H_2$ . Then we can get: + +$$ +H = \left(H ^ {*}\right) ^ {2}. \tag {2} +$$ + +To solve $H^{*}$ , we can do eigenvalue decomposition to $H$ and get: + +$$ +H = P d i a g (\Lambda) P ^ {- 1} = \left(P d i a g \left(\Lambda^ {\frac {1}{2}}\right) P ^ {- 1}\right) ^ {2}. \tag {3} +$$ + +So we can conclude with: + +$$ +H ^ {*} = P d i a g \left(\Lambda^ {\frac {1}{2}}\right) P ^ {- 1}. \tag {4} +$$ + +# 3.2. Pixel-Wise Bidirectional Warp + +Given coarsely aligned images $(I_1^{mid}$ and $I_2^{mid})$ , our goal of the second stage is to predict two flow fields $(F_{1}$ and $F_{2})$ to conduct unsupervised pixel-wise deformation. We use $F * I$ or $F * p$ to represent warping image $I$ or point $p$ by + +![](images/8727461771416acd01200b303fb2c809c1ff388945d92e81f9250ba57a97e8cc.jpg) +Figure 3. Left: PN-Coef calculation. Right: inverse PN-Coef calculation + +![](images/7a6ceabcd2e0ecb234e8b74b9feec88f7d733f949b49c1c56eca02d6916ab52e.jpg) + +$F$ . The final results can be represented by $I_1^F = F_1 * I_1^{mid}$ and $I_2^F = F_2 * I_2^{mid}$ . + +In practice, the forward warping process can easily produce invalid holes and meaningless interpolation (e.g., multiple points might be mapped to the same location). To this end, we estimate inverse optical flow fields $(F_{1}^{-1}$ and $F_{2}^{-1})$ that adopt backward sampling interpolation. + +# 3.2.1. Network Architecture + +Our network consists of two branches: bidirectional warping field estimator and content selection mask generator. + +Bidirectional Warping Field Estimation. We adopt RAFT [34] as a baseline of optical flow estimators. In particular, we estimate the bidirectional optical flow maps between $I_1^{mid}$ and $I_2^{mid}$ by transposing their order. The output flows are denoted as $C_1$ and $C_2$ , which will be further refined with projection-weighted natural coefficients to get final optical flows $F_1$ and $F_2$ . + +Content Selection Mask Generation. Simply training the pixel-wise warping field estimator to align the overlapped areas can be unstable and usually results in a convergence failure. To this end, we design a convolutional network to predict probability masks $(S_{1}$ and $S_{2})$ by Sigmoid function from the coarsely aligned images. The masks are used to select matched contents in $I_1^{mid}$ and $I_2^{mid}$ since similar contents are supposed to produce similar masks. We encourage the overall masks to gradually increase to one, making a partial-to-whole diffusion of selected contents. It could select a part of associated contents at the very beginning to give a clear optimization direction and thus guide the model to converge robustly. + +# 3.2.2. Projection-Weighted Natural Coefficients + +In this section, we propose projection-weighted natural coefficients (PN-Coef) to refine the primary optical flows $C_1$ and $C_2$ . Our refinement aims to keep the non-overlapping area as intact as possible while not interfering with the smoothness of final flows. From this point, we expect a pixel-wise smooth mask that has small weight values in non-overlapping areas. As illustrated in Fig. 3 (left), we + +define PN-Coef as: + +$$ +W (p) = \frac {\overrightarrow {c _ {1} p} \cdot \overrightarrow {c _ {1} c _ {2}} - \overrightarrow {c _ {1} p _ {0}} \cdot \overrightarrow {c _ {1} c _ {2}}}{\overrightarrow {c _ {1} p _ {1}} \cdot \overrightarrow {c _ {1} c _ {2}} - \overrightarrow {c _ {1} p _ {0}} \cdot \overrightarrow {c _ {1} c _ {2}}}, \tag {5} +$$ + +where $c_{1}$ and $c_{2}$ denote the centers of $I_{1}$ and $I_{2}$ . $p_{0}$ and $p_{1}$ are defined as: + +$$ +\left\{ \begin{array}{l} p _ {0} = \operatorname {a r g m i n} _ {p _ {i} \in I _ {1} ^ {m i d} \cup I _ {2} ^ {m i d}} \left\{\overrightarrow {c _ {1} p _ {i}} \cdot \overrightarrow {c _ {1} c _ {2}} \right\}, \\ p _ {1} = \operatorname {a r g m a x} _ {p _ {i} \in I _ {1} ^ {m i d} \cup I _ {2} ^ {m i d}} \left\{\overrightarrow {c _ {1} p _ {i}} \cdot \overrightarrow {c _ {1} c _ {2}} \right\}. \end{array} \right. \tag {6} +$$ + +We depict the calculation of PN-Coef in Fig. 3 (left), where $d_0, d_1$ and $d_p$ are the projected points of $p_0, p_1$ and $p$ . Following the figure, the coefficient can be defined in a more concise way: + +$$ +W (p) = \frac {\left| \overrightarrow {d _ {0} d _ {p}} \right|}{\left| \overrightarrow {d _ {0} d _ {1}} \right|}. \tag {7} +$$ + +According to the position of $d_{p}$ , the coefficients could vary smoothly along the connection line of the centers and produce smaller weights for non-overlapping regions of $I_1^{mid}$ , which are subsequently adopted to refine $C_1$ . Symmetrically, $1 - W$ is adopted to refine $C_2$ and the refinement operation can be described as: + +$$ +F * p = W (p) \cdot (C * p - p) + p. \tag {8} +$$ + +However, only inverse optical flows are obtained by our network, so it is required to inverse the coefficients as well. For a point $p_F = F * p$ , we expect its inverse coefficient $W_{inv}(p_F)$ to equal to $W(p)$ , so that $W$ and $W_{inv}$ will be consistent. Therefore, $W_{inv}$ should satisfy: + +$$ +W _ {i n v} \left(p _ {F}\right) = W (p) = W \left(F ^ {- 1} * p _ {F}\right) = \tag {9} +$$ + +$$ +W \left(W _ {i n v} \left(p _ {F}\right) \cdot \left(C ^ {- 1} * p _ {F} - p _ {F}\right) + p _ {F}\right). +$$ + +Then we can solve $W_{inv}(p_F)$ out of this equation. The inverse PN-Coef calculation is depicted in Fig. 3 (right), where $p_F = F * p$ and $p' = C^{-1} * p_F$ . Following the figure, Eq. (9) can be rewritten in a more concise way: + +$$ +\frac {\left| \overrightarrow {p p _ {F}} \right|}{\left| \overrightarrow {p ^ {\prime} p _ {F}} \right|} = \frac {\left| \overrightarrow {d _ {0} d _ {p}} \right|}{\left| \overrightarrow {d _ {0} d _ {1}} \right|}. \tag {10} +$$ + +Note that it is the formula for $C_1$ refinement. For $C_2$ , the following equation is adopted: + +$$ +\frac {\left| \overrightarrow {p p _ {F}} \right|}{\left| \overrightarrow {p ^ {\prime} p _ {F}} \right|} = 1 - \frac {\left| \overrightarrow {d _ {0} d _ {p}} \right|}{\left| \overrightarrow {d _ {0} d _ {1}} \right|}. \tag {11} +$$ + +# 3.3. Unsupervised Pixel-Wise Optimization + +We aim to constrain the network to accurately align the overlapping area between two images, while smoothly extending the warp fields to the non-overlapping area with little distortion. Besides, the bidirectional consistency is presented to facilitate network convergence in our optimization. The total optimization objective is defined as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {a l i g n}} + \lambda_ {\text {b i c}} \mathcal {L} _ {\text {b i c}} + \mathcal {L} _ {\text {s t r}}, \tag {12} +$$ + +where $\mathcal{L}_{\text{align}}$ is to align images in the overlapping area, $\mathcal{L}_{\text{bic}}$ is to maintain bidirectional consistency, and $\mathcal{L}_{\text{str}}$ is to preserve the image structure and suppress distortion. + +# 3.3.1. Alignment Term + +The alignment term consists of two constraints: similarity constraint $\mathcal{L}_{sim}$ and content matching constraint $\mathcal{L}_{match}$ . It is defined as: + +$$ +\mathcal {L} _ {\text {a l i g n}} = \lambda_ {\text {m a t c h}} \mathcal {L} _ {\text {m a t c h}} + \mathcal {L} _ {\text {s i m}}. \tag {13} +$$ + +Content Matching Constraint. Ideally, the predicted probability masks $S_{1}$ and $S_{2}$ should be consistent between matched points, so we first obtain the matched content mask by + +$$ +S _ {m} = \left(F _ {1} * S _ {1}\right) \odot \left(F _ {2} * S _ {2}\right), \tag {14} +$$ + +where $\odot$ denotes element-wise multiplication. Then we encourage $S_{m}$ to gradually increase to one. The loss can be defined as: + +$$ +\mathcal {L} _ {\text {m a t c h}} = \sum_ {p _ {i} \in I _ {1} ^ {F}} | 1 - S _ {m} (p _ {i}) |. \tag {15} +$$ + +Similarity Constraint. The aligned images are supposed to be as similar as possible in the overlapping area, so we leverage structural similarity (SSIM) [36] with the window size of $11 \times 11$ to robustly measure the similarity between the two images. The loss of similarity constraint can be formulated as: + +$$ +\mathcal {L} _ {s i m} = \sum_ {p _ {i} \in I _ {1} ^ {F}} M _ {o l p} (p _ {i}) \cdot S _ {m} (p _ {i}) \cdot \left(1 - S S I M \left(I _ {1} ^ {F} (p _ {i}), I _ {2} ^ {F} (p _ {i})\right), \right. \tag {16} +$$ + +where $M_{olp}$ is a mask representing the overlapping area in the image. It is defined as: + +$$ +M _ {o l p} (p) = \left\{ \begin{array}{l l} 1 & \text {i f} p \text {i n o v e r l a p p e d a r e a}, \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {17} +$$ + +# 3.3.2. Bidirectional Consistency Term + +Bidirectional warping is more likely to fail compared to unidirectional warping because it has more degrees of freedom and there is no stable reference as we simultaneously warp two images. Thus, we propose bidirectional consistency to encourage $F_{1}$ and $F_{2}$ to warp images in opposite directions, preventing the result from shifting which causes distortion and even convergence failure. + +More specifically, we expect each pair of points at the same location of two images to be warped in opposite directions. Let $p_1^F$ be $F_1 * p$ and $\overrightarrow{p_2^F}$ be $\overrightarrow{F_2 * p}$ for some point $p$ . Then we constrain that $\overrightarrow{pp_1^F}$ and $\overrightarrow{pp_2^F}$ are colinear and counter-directional. + +However, as our model outputs inverse optical flow, it is unable to meet the consistency by directly constraining $p$ . + +![](images/8126816ffdcf702a29bfdb6da655bb0e7654cf01c7f2c06335ac4343688e6272.jpg) +Figure 4. Diagram of flow uniformity constraint. It encourages opposite grid edges (e.g. edges marked in blue) to be parallel, promoting a uniform change of pixel motions. + +Instead, we expect another consistency between $F_{1}$ and $F_{2}$ . We notice that if the following constraints are satisfied for a pair of matched points $q_{1} \in I_{1}^{mid}$ and $q_{2} \in I_{2}^{mid}$ : + +$$ +\left\{ \begin{array}{l} C _ {1} * q _ {1} = q _ {2}, \\ C _ {2} * q _ {2} = q _ {1}. \end{array} \right. \tag {18} +$$ + +Then following Eq. (10), we can get the inverse PN-Coef for $q_{1}$ out of the following equation: + +$$ +\frac {| \overrightarrow {q _ {1} q} |}{| \overrightarrow {q _ {1} q _ {2}} |} = \frac {| \overrightarrow {d _ {0} d _ {q}} |}{| \overrightarrow {d _ {0} d _ {1}} |}, \tag {19} +$$ + +where $q = F_1^{-1} * q_1$ and $d_q$ is the projected point of $q$ . So we can get: + +$$ +\frac {| \overrightarrow {q _ {2} q} |}{| \overrightarrow {q _ {1} q _ {2}} |} = 1 - \frac {| \overrightarrow {q _ {1} q} |}{| \overrightarrow {q _ {1} q _ {2}} |} = 1 - \frac {| \overrightarrow {d _ {0} d _ {q}} |}{| \overrightarrow {d _ {0} d _ {1}} |}, \tag {20} +$$ + +which is consistent to Eq. (11). It implies $q$ also equals to $F_{2}^{-1}*q_{2}$ . Meanwhile, $\overrightarrow{qq_1}$ and $\overrightarrow{qq_2}$ are colinear and counter-directional, which exactly satisfies our bidirectional consistency. According to Eq. (18), the loss of bidirectional consistency is defined as: + +$$ +\mathcal {L} _ {b i c} = \sum_ {p _ {i} \in I _ {1} ^ {m i d}} \left| C _ {2} * C _ {1} * p _ {i} - p _ {i} \right|. \tag {21} +$$ + +# 3.3.3. Structure Term + +The structure term consists of two constraints: smoothness preservation constraint $\mathcal{L}_{smo}$ and flow uniformity constraint $\mathcal{L}_{uni}$ . It is defined as: + +$$ +\mathcal {L} _ {s t r} = \lambda_ {s m o} \mathcal {L} _ {s m o} + \lambda_ {u n i} \mathcal {L} _ {u n i}. \tag {22} +$$ + +Smoothness Preservation Constraint. Drastic changes in optical flows can cause distortion and make results unnatural. To make flows smooth, we design a loss of smoothness that is defined as: + +$$ +\mathcal {L} _ {s m o} = \sum_ {p _ {i} \in I _ {1} ^ {m i d}} | f (p _ {i}) - \frac {\sum_ {i , j \in [ - k _ {s} , k _ {s} ]} f \left(p _ {i} + (i , j)\right)}{(2 k + 1) ^ {2}} |, \tag {23} +$$ + +Table 1. Quantitative comparison of warp on UDIS-D dataset [29]. The best is marked in red and the second best is in blue. HD is for homography decomposition and BPW is for bidirectional pixelwise warp. + +
mSSIM↑
EasyModerateHardAverage
APAP[38]0.8680.7700.5870.726
ELA[18]0.9050.8190.6420.774
LPC[10]0.8150.6730.4850.640
GES-GSP[6]0.8760.7240.4520.661
UDIS++[31]0.8800.7920.6320.755
PixelAlign[11]0.9280.8880.7840.858
Ours0.9450.9010.8000.874
w/o HD0.9460.9000.8010.874
w/o BPW0.9390.8890.7790.860
w/o HD & BPW0.9400.8910.7800.861
w/o Lbic0.8720.7890.6630.763
w/o Lmatch0.8990.8340.7280.811
w/o Lbic & Lmatch0.8740.7930.6700.768
+ +where $f(p) = F * p - p$ . This loss constrains the motion of every point to be close to its neighboring points to preserve smoothness. Besides, it also helps flows to transition smoothly from overlapping to non-overlapping regions, which additionally suppresses distortion. + +Flow Uniformity Constraint. Warping at the pixel level is easier to cause distortion compared to warping by a mesh field as the points can move more freely. Hence, it is crucial to apply a structural constraint to maintain the natural contents. Mathematically, a flow field can be regarded as a pixel-level mesh field, which inspires us to design a structure constraint from grid level. The flow uniformity constraint encourages opposite edges in grids formed by the flow to be parallel, promoting the flow to vary uniformly (Fig. 4), benefitting to shape preservation. In our pixel-wise model, this constraint can be formulated as: + +$$ +\mathcal {L} _ {u n i} = \sum_ {p _ {i} \in I _ {1} ^ {m i d}} \sum_ {(i, j) \in \{(0, 1), (1, 0) \}} (1 - \frac {\overrightarrow {p _ {i} p _ {i} ^ {(i , j)}} \cdot \overrightarrow {p _ {i} ^ {(j , i)} p _ {i} ^ {(1 , 1)}}}{\| p _ {i} p _ {i} ^ {(i , j)} \| \| p _ {i} ^ {(j , i)} p _ {i} ^ {(1 , 1)} \|}, \tag {24} +$$ + +where $p^{(i,j)} = p + (i,j)$ . Moreover, we also adopt it on $4\mathbf{x}$ and $16\mathbf{x}$ downsampled optical flows to build multi-scale colinear constraints. + +# 4. Experiments + +# 4.1. Implementation Details + +# 4.1.1. Dataset + +We train our model on UDIS-D dataset [29], which consists of 10,440 image pairs for training and 1,106 pairs for testing. Besides, we also test our model on extensive traditional datasets to show its generalization ability. + +# 4.1.2. Training Details + +We train our model for 100 epochs with Adam optimizer [14]. The initial learning rate is set to $10^{-4}$ with an expo + +Table 2. Quantitative comparison of warp on traditional datasets. The best is marked in red and the second best is in blue. PA is for PixelAlign [11]. + +
DatasetmSSIM ↑
APAPELAGES-GSPLPCUDIS++PAOurs
train[38]0.3840.4660.4080.2980.4350.7570.647
conssite[38]0.4950.6260.7300.4980.4710.6830.773
building[24]0.4870.6120.7220.4250.5080.7240.732
fence[24]0.5340.6490.7420.4460.5750.7180.803
carpark[8]0.7450.8090.7900.6890.8140.8220.920
temple[8]0.6720.7930.7310.7640.6760.7680.911
campus[4]0.4430.5520.5310.3420.382-0.620
garden[4]0.4310.5690.7250.4510.3270.8180.705
parksquare[18]0.6660.8040.8700.6740.6930.8230.896
lawn[18]0.7020.8320.8400.6280.5620.8810.893
racetracks[18]0.4590.6180.2950.4330.5640.5820.617
cabin[18]0.5080.8490.7150.4840.6620.7670.895
theater[18]0.6240.8650.7300.4990.5660.8220.913
footpath[18]0.6470.7610.7200.5220.5510.7670.856
window[21]0.7990.8380.7960.7990.8140.8600.861
door[21]0.8620.9110.9060.8460.8890.9350.943
four[21]0.8290.9020.8360.8060.8450.9360.950
chessgirl[25]0.7330.7590.7940.6970.7350.7830.800
+ +![](images/ccd0c2a38072dcc9766b864d5d59629d461dc8047b6fa35e4d481dc454235e3e.jpg) + +![](images/7f6911ec4e1e80ca799416e2177b88378d0e4ba356ec2364f5053687fb9f1bf5.jpg) + +![](images/7585c964d0b75ce81ffd437dce0a85d91d9f437026a046b5ebc550feef3ae528.jpg) + +![](images/69d6b80c82a0b48d2d6d6d0740ce80333c6db5bfb0516af1235e34ebd9bc0366.jpg) + +![](images/6dc629d43b035dffec180002e3a38b0f578d90748e3fa3f40f3375c0e65f19fb.jpg) +PixelAlign + +![](images/f65f4d2ddacce3d99facb72f95c7104204c37cc1344c5230f6a277fb9260eb22.jpg) +Figure 5. A case from UDIS-D dataset [29]. We zoom in on regions to show the alignment performance (red boxes) and projective distortion handling (yellow circles). Blue arrows indicate the deformative distortion. + +nentially decaying rate of 0.97. The size of the correlation neighborhood $(k)$ is set to 13. All inputs are resized to $440 \times 440$ to apply multi-batch training with the batch size set to 8. Similar to RAFT [34], we apply the loss function to every iteration as: + +$$ +\mathcal {L} = \sum_ {i = 1} ^ {N} (\gamma \cdot \omega^ {t - 1}) ^ {N - i} \cdot \mathcal {L} _ {i}, \tag {25} +$$ + +where $N$ is the iteration number, $L_{i}$ is the loss computed in $i$ -th iteration, and $t$ is the current epoch number. We set $N = 4$ , $\gamma = 0.8$ and $\omega = 0.99$ . For the hyper-parameters, we set $\lambda_{match} = 0.005$ , $\lambda_{bic} = 1.0$ , $\lambda_{smo} = 10.0$ (along with $k_{s} = 7$ ) and $\lambda_{uni} = 3.0$ . All implementations are based on PyTorch using a single NVIDIA RTX 4090. + +# 4.1.3. Homography Estimator + +Arbitrary homography estimator could be adopted in our method. On UDIS-D dataset, the homography estimation part of $\mathrm{UDIS + + }$ [31] is leveraged for the best performance. On traditional datasets, we adopt VGG [33] $^+$ RANSAC [7] following PixelAlign [11] for generalization. + +# 4.2. Results + +We compare our method with various typical methods, including feature-based methods (i.e., APAP [38], ELA [18], LPC [10], GES-GSP [6]), and learning-based methods (i.e., $\mathrm{UDIS}++$ [31], PixelAlign [11]). Average fusion is adopted to blend the warped images, which can better highlight the misalignments and distortion. All results are generated by the official codes. Results may be cropped for better visualization. + +# 4.2.1. Quantitative Results + +We adopt masked SSIM [36] (denoted as mSSIM) as quantitative metrics, which means we only compute SSIM in overlapping regions. Tab. 1 and Tab. 2 demonstrate the objective results on the UDIS-D and other traditional datasets. Some methods may fail under some challenging situations, and we substitute them with original images (i.e., warping with the identity matrix). + +# 4.2.2. Qualitative Results + +Qualitative comparisons of different cases are shown in Fig. 5 and Fig. 6. We highlight misalignments, projective distortion, and deformative distortion with boxes, circles and arrows to show the superiority of our method. + +# 4.2.3. Inference Time + +Our method is capable of aligning images in a practical and stable time. On the "temple" dataset [8] (with input resolution of $730 \times 487$ and output resolution of $1153 \times 558$ in our experiment), the elapsed time is 10.19s on CPU (Intel i7-10875H 2.30GHz) and 0.25s on GPU (NVIDIA RTX 4090), where our homography decomposition, bidirectional warping field estimation and PN-Coef calculation only take $63.2\%$ time on CPU and $14.9\%$ time on GPU. + +# 4.3. Ablation Studies + +# 4.3.1. Model Convergence + +We evaluate constraints that should help the model converge in our method, including bidirectional consistency + +![](images/d4e9ef4116f9887b46ed75d73b7caa7bcf40e843fb5cf09b4c04937bbc6f174e.jpg) + +![](images/44685b4fa0805abd0c62cf687aa6247a9644bd423a5c3db078fd558b0648c57c.jpg) +LPC + +![](images/e225840ac5336e605e209fa845dec106e9398765e0c8b322be22c3b0af79a701.jpg) +PixelAlign + +![](images/aff5b7342c2419947d579b0753709ff5dbbeb43fdba53f782aad49c0901ab1c9.jpg) +GES-GSP +ELA + +![](images/6cb2b9f9bedd2d355893b7f2e11a3b2cd3f06d4c2566a1c5337189fdbdc7d77e.jpg) +UDIS++ + +![](images/2d79900880f3fed87831f10938279f44c31b715737566af786e8503683543f31.jpg) +Ours + +![](images/11e6d8556d0ae9b22ce1cc25a0f75d8f3c0cb0e608bd05e5f024c2c16807dd12.jpg) +Figure 6. A case with large parallax from [39]. Red boxes indicate misalignments and the yellow circle indicates distortion. +Figure 7. Comparison on results of (a) no pixel-wise warp, (b) unidirectional pixel-wise warp, and bidirectional warp with (c) trivial weight (all 0.5), (d) PN-Coef and (e) inverse PN-Coef respectively. + +![](images/ccb0b5a01fb7b4ee87e915eb6b0d92bdc7e2e5129db629d5c529671ba81c5107.jpg) + +![](images/b4a1bc4a9e4a55c91707c87b44501b36276b3e7b18c1eb8f9cb95522010ef1be.jpg) + +![](images/c682b4fbc77442fa01fcd7bfce569ea467681cc98c24aa54e422aa90dd789915.jpg) + +![](images/873f9f77aa256283f22f731d29f17920d2b16925b13a6f4b3053cef4c449e652.jpg) + +![](images/ca2d8634ce8d22ddf92979e958ef62bc740160d464c6286f2c9c0e143ff2b999.jpg) +w/o HD +Resolution: $1064 \times 859$ Invalid Area: $28.79\%$ +Figure 8. Ablations on homography decomposition (HD). The yellow arrow indicates projective distortion. + +![](images/bfcc2361dec5a7f136a847613123a2169111b67b068a794fb4242936746b3503.jpg) +Ours +Resolution: $915 \times 620$ Invalid Area: $11.33\%$ + +and content selection mask, to show their effectiveness. We adopt the same metric as quantitative experiments to show whether the model converges properly. Results are shown in Tab. 1. + +# 4.3.2. Structural Constraints + +We study structural constraints on their capability to preserve image structure, as shown in Fig. 9. The colinear constraint eliminates blurs and the smoothness preserving constraint suppresses unnatural deformation. Additionally, the average mSSIM without $\mathcal{L}_{str}$ is 0.877, showing that $\mathcal{L}_{str}$ has little adverse impact (3.4%) on alignment accuracy. + +# 4.3.3. Bidirectional Warp + +We demonstrate the superiority of bidirectional warps compared to unidirectional ones. For the bidirectional pixelwise warp, we additionally study the effectiveness of PN-Coef on shape preservation by trivially setting it to all 0.5 + +![](images/4b53258976809d9aa7478c68398efd3cb4f4e08fa3acb9208c5a701f7e1860f9.jpg) +w/o Lsmo & Lcol +w/o Lcol +w/o Lsmo +Ours +Figure 9. Ablation study on structural constraints. + +(denoted as "Trivial Weight"), and the effectiveness of inverse PN-Coef is studied as well. Results are shown in Fig. 7 and Fig. 8. Also, ablations in Tab. 1 show that homography decomposition has no adverse impact on alignment accuracy and bidirectional pixel-wise warp can improve it. + +# 5. Conclusions + +In this paper, we introduce a novel solution of global-to-pixel bidirectional image stitching, named PixelStitch. First, we propose homography decomposition to apply bidirectional global alignment, which determines the virtual middle plane and spreads projective distortion evenly to two views, contributing to a more natural pre-alignment. Then, we elaborately design projection-weighted natural coefficients to estimate smooth, shape-preserving bidirectional optical flow fields. In the absence of stitching labels, an unsupervised comprehensive objective is established with an alignment term, a structure term, and a bidirectional consistency term. Extensive experiments are conducted to show that PixelStitch outperforms existing SoTA methods with a strong capability of obtaining structure-preserving stitched results. + +# Acknowledgement + +This work was supported by the National Natural Science Foundation of China (No.U2441242, No.62172032) + +# References + +[1] Fred L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on pattern analysis and machine intelligence, 11(6):567-585, 1989. 2 +[2] Matthew Brown and David G Lowe. Automatic panoramic image stitching using invariant features. International journal of computer vision, 74(1):59-73, 2007. 2 +[3] Wenxiao Cai and Wankou Yang. 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Language-guided 3D Object Placement in Real 3D Scenes: Given a text prompt, the task is to find a valid placement for an asset, requiring semantic and geometric understanding of the scene, the asset's shape, and spatial relationships. Colored dots show referenced objects (for visualization only, not given to the model), and the yellow arrow indicates the predicted frontal direction. + +![](images/55a16c273123ade78968d2520a131b7431d33deca391c375cc2b894bba50fea4.jpg) + +# Abstract + +We introduce the task of Language-Guided Object Placement in Real 3D Scenes. Given a 3D reconstructed point-cloud scene, a 3D asset, and a natural-language instruction, the goal is to place the asset so that the instruction is satisfied. The task demands tackling four intertwined challenges: (a) one-to-many ambiguity in valid placements; (b) precise geometric and physical reasoning; (c) joint understanding across the scene, the asset, and language; and (d) robustness to noisy point clouds with no privileged metadata at test time. The first three challenges mirror the complexities of synthetic scene generation, while the metadata-free, noisy-scan scenario is inherited from language-guided 3D visual grounding. We inaugurate this task by introducing a benchmark and evaluation protocol, releasing a dataset for training multi-modal large language models (MLLMs), and establishing a first nontrivial baseline. We believe this challenging setup and benchmark will provide a foundation for evaluating and advancing MLLMs in 3D understanding. + +# 1. Introduction + +At two to three years old, neurotypical children learn to follow two-step instructions like "Get your shoes and put them on the shelf" [42]. These tasks may appear simple, yet children need time to grasp basic vocabulary and to learn the physical affordances of both 3D objects and scene layout. Perhaps AIs could obtain similar capabilities. + +In this paper, we focus on the novel task of language-guided 3D object placement in a reconstructed real 3D scene. As in the shoe example, the goal is to find a valid placement of the object among multiple configurations that satisfy the instruction. As shown in Figure 1, the placement must also respect the physical constraints of the space and of the 3D asset. Excelling at this task would unlock applications such as instructing a robot, through language, to move a real object to a new location. It is also relevant to augmented reality (AR). For instance, a shopper wearing an AR headset could use natural-language commands to anchor a virtual product on a real-world surface or reposition digital décor anywhere in the room. + +MLLMs have recently shown strong performance on language-guided 3D scene understanding tasks, including visual question answering [11, 22, 23], visual grounding [25, 62], and synthetic scene generation [18, 44, 55]. We study language-guided 3D asset placement in reconstructed scenes, a problem closest to grounding and to synthetic scene generation, yet distinct in that it requires addressing all of the following challenges simultaneously: + +i. Ambiguity of solutions. 3D visual grounding typically admits a single correct match, whereas 3D placement is inherently one-to-many: multiple placements can satisfy the instruction [6, 19]. This complicates both benchmarking and data construction, which must accommodate multiple valid answers. +ii. Intrinsic 3D reasoning. Many constraints are geometric and cannot be resolved from 2D projections alone. For example, "place the asset in between the chair and the table, hidden from the window" requires reasoning about free space and spatial relationships in 3D. +iii. No privileged information at test time. In contrast with synthetic scene generation, we require just the reconstructed 3D scene. We are not given layouts [38, 44], scene graphs [61], object properties, or clean geometry [24, 55] to aid with making a prediction. +iv. Joint reasoning over scene, asset, and language. The asset's size and shape restrict feasible placements; given the same scene and instruction, a large object has fewer valid locations than a small one. Among the valid options, the model must follow the user's stated intent rather than default to common sense priors [36, 56]. + +The highlight of this paper is the introduction of a challenging novel task, which we call PLACEIT3D: language-guided 3D placement on real scenes. To the best of our knowledge, no existing benchmarks, datasets, or methods directly address this problem. To advance research in this area, we make three key contributions, summarized here: + +- We introduce PLACEIT3D-benchmark for language-guided placement with 3,500 evaluation examples, each consisting of a real ScanNet scene [15], a PartObjaverse-Tiny asset [54], and a guiding prompt. Our evaluation protocol accounts for placement ambiguity, enabling fair comparison across methods. +- We present PLACEIT3D-dataset, a large-scale training dataset with 100,505 training and 2,566 validation examples, each annotated with all valid placements that can be used for training MLLMs. Like the benchmark, it uses ScanNet scenes and PartObjaverse-Tiny assets. +- We propose PLACEWIZARD, a proto-method for this task built on recent 3D LLMs [25]. It uses a modified form of spatial aggregation, an asset encoder, and rotation prediction, outperforming existing baselines. + +# 2. Related Work + +3D and Large Language Models. 3D LLMs [35] are a subclass of MLLMs that jointly process point clouds/meshes and text. They typically align 3D features to the language space with lightweight projection layers or cross-attention adapters, mirroring strategies from image-grounded MLLMs (VLMs) [5, 9, 13, 27, 29, 30, 32]. For grounding and QA, 3D-LLM [22] fuses point clouds with 2D image features; Reason3D [25] routes a pre-trained point encoder through a Q-Former [31] and a decoder guided by both the 3D input and the LLM output. ScanReason [62] interleaves grounding and reasoning during inference. However, none of these systems addresses language-guided object placement, which requires reasoning about free space, spatial relations, and asset properties. We introduce a 3D LLM baseline designed to model these factors. + +3D object placement and scene generation. Early 3D layout work posed furniture arrangement as optimization over ergonomic or aesthetic constraints, sampling layouts that satisfy manually encoded rules and user constraints [36, 56]. Data driven methods replaced hand tuning with spatial priors learned from example scenes, yielding placement masks that reflect one-to-many valid locations [6, 8, 19]. Neural methods extend these priors to full indoor synthesis with scene graphs, transformers, or diffusion models [18, 38, 47, 49, 51, 53, 61], and hybrid systems mix learned priors with explicit geometric constraints [18, 55]. [14] pioneered the use of language as a control signal for 3D scene generation. Later systems parse text into spatial constraints or scene graphs to infer feasible regions [6-8, 34]. Recent LLM and VLM based methods broaden this paradigm [20, 44, 47, 55]. When it comes to real-world (i.e. non-synthetic) scenes, most existing methods are image-based, predicting plausible 2D placement regions [33, 39, 40, 60, 63]. RoboPoint [58] extends this by performing language-guided placement in images and then lifting the results to 3D using depth. Concurrent work FirePlace [24] focuses on synthetic, clean environments. In contrast, we tackle language-guided placement in reconstructed real-world scenes, which requires intrinsic 3D reasoning, no privileged test-time annotations, and joint understanding of scene geometry, object shape, and instruction intent. Inspired by optimization methods, our dataset and benchmark ensure geometric feasibility for all candidate placements. + +Datasets for language-guided 3D tasks. Most language and 3D datasets based on ScanNet [15] focus on tasks like text grounding [1, 2, 10, 26], VQA [4], captioning [12], and instruction following [59]. Larger real-scene corpora [3, 50, 64] and synthetic embodied benchmarks [37, 41, 52] expand this scope. Yet none address language-guided object placement with its one-to-many valid solutions and explicit valid placement enumeration; our ScanNet-based benchmark and dataset aim to fill this gap. + +![](images/c4973eca8b8e12ea2cba6e7fac12d4bdf7a605e02973484e60f8b771f186bb3f.jpg) +(a) + +![](images/8e982bd432cf902106b2afafbcd907ba0e9bbc6c535f256e810f0e61153503cd.jpg) +Input +(b) + +![](images/3509080b49b642f648ac4ed7ac3ed382ce9e94e8f7059ee74500eed4408e56d4.jpg) +Rotations +Figure 2. PLACEIT3D-dataset creation. Given a scene and an asset as input (a) the goal is to create a prompt (f) and corresponding mask $\mathcal{M}$ of valid placements (e). We start by finding the set of points which are physically plausible placements, shown in red in (b). We consider eight equally spaced rotation angles, which condition the valid placements. For this example, angle $0^{\circ}$ has more valid placements than $45^{\circ}$ . To generate the language constraints, we use the ground truth scene graph (c). Object anchors are selected from the scene graph and combined with relationship types to create a constraint and corresponding validity mask (d). The different placement constraints are combined in the final output by intersecting the validity masks (e) given a mask of valid dense placements. Based on each selected set of anchors and constraint relationships, a natural language prompt is created using templates (please, see supplemental for more details). + +![](images/761dd663a53195d643b76bb22f8afc3db420bbe1c3e18cfad64a68bfb522bb29.jpg) +Plausible placement generation + +![](images/f602a24696824567af614865a46622d1bbcbd876e8017264e9746ab44c128ef9.jpg) + +![](images/b43fd7f3c0a4a8592bfe5635a2e04e2900292e7e2b8b0dfaf635acf7660257e4.jpg) +(c) + +![](images/9a1b34dc5531d2007fdc81e15b2c86f9f110f571ac448e04319b08026b280127.jpg) +Dense placements + +![](images/e15b49da72612ca38ec96d7c869682bd32581b70b43c5b7434771df358b887be.jpg) +anchors: ["sofa", "bed"] + +![](images/d6af2fb5d4c7c5a585a290c2f80dd0ce30689b52fea9bd6231012feeef7966c8.jpg) +constraints "near", anchors: "backpack" +(f) +"Place the asset near the backpack and between the sofa and the bed." + +![](images/0581b3588a7f5278fe6b4e909d680f0675057d2a43fce3f85f6eecb0896cd9c2.jpg) +Output +(e) +constraints:"[near","between"] +anchors +[["backpack"],["sofa", "bed"]] + +# 3. Language-Guided 3D Object Placement + +We introduce the task of language-guided 3D object placement on 3D reconstructed scenes. Given the point cloud of scene, a 3D asset, and text describing where the asset should be placed in the scene, the goal is to find a valid position and orientation for the asset that is physically plausible and adheres to the language prompt. + +This task is inherently ambiguous because, in general, multiple valid placements exist. The multiple placements in Fig. 2 (c) demonstrate this ambiguity and illustrate the complexity of our task when compared with related tasks like object grounding, which typically has a single solution. + +Simplifying assumptions. Given the ambiguity and complexity of our task, we make some simplifying assumptions to make the problem tractable. First, we assume the vertical orientation of the scene is fixed and given by the Z-axis. We also assume we know the vertical orientation of the asset as well as its frontal direction. The asset is always placed on a horizontal surface, and only the yaw angle is considered, i.e. rotation around the vertical axis. + +# 3.1. Physical plausibility and language constraints + +Valid placement in this task must satisfy a core set of common constraints. The first, physical plausibility, requires that the object does not intersect the scene mesh and rests on a surface. This constraint is language-independent and always enforced. + +Beyond physical plausibility, the language instruction + +specifies how the object should be placed in the scene. Placement is often relative to an "anchor", a named object instance that must be inferred at test time. In practice, "language constraints" capture both semantic and physical aspects of the placement. These language constraints are organized into three distinct groups: + +Spatial constraints: These constraints specify the object's location relative to one or more scene anchors. This group includes: (i) near and adjacent: the object is positioned within a specified distance from an anchor. (ii) on: the object should directly rest on top of an anchor. (iii) between: the object must be placed between two anchors. (iv) above and below: the object is located above or below an anchor. + +Rotational constraint: This constraint focuses on the orientation of the object relative to scene anchors. The object is positioned so that it faces the anchor. + +Visibility constraints: The object is either within the anchor's line of sight (visible) or hidden from it (not visible). + +A candidate placement is considered a valid placement if and only if it simultaneously satisfies every constraint in that prompt. + +Prompt creation: We generate language prompts using a template-based system, where each constraint is expressed through predefined sentence templates. A random subset of constraints and anchor objects from ScanNet annotations is sampled for each prompt. Prompts that cannot be satisfied due to conflicting or overly restrictive constraints, such as "place the asset on the table and below the desk", are discarded during a verification step. Template details are provided in the supplemental material. + +![](images/dc2be94d3ad525fb948f4647316e94b48a93ff77a3ceb50621f7783ff4c569d7.jpg) +Figure 3. PLACEWIZARD overview. A point encoder extracts features from the 3D scene, which are then complemented with positional embeddings. Spatial pooling reduces feature dimensions, and a Q-Former merges the pooled features with trainable queries $Q$ (Section 4.1). The asset is encoded into a single vector by using a pretrained asset encoder followed by max-pooling (Section 4.2). This vector together with a size embedding is passed to a projection layer that aligns the features with the LLM space. The LLM take as input (i) the output of the Q-Former, (ii) the text prompt, and (iii) the projected asset features and predicts three special tokens [ANC], [LOC] and [ROT]. A transformer based decoder takes as input the features associated with the three special tokens and the pooled scene features and performs a few self and cross attention operations (Section 4.3). Three heads produce the final outputs: $\mathcal{M}_{loc}$ the valid placement mask; $\mathcal{M}_{anc}$ an auxiliary mask that localizes the object anchors; and $\mathcal{M}_{rot}$ a mask indicating which rotation angles are valid at each location. + +# 3.2. PLACEIT3D-benchmark + +Each benchmark example consists of a 3D scene mesh, a 3D asset, and a language prompt comprising one or more 3D placement constraints. A placement method takes this triplet as input and predicts a placement, defined by a 3D translation vector $\mathbf{t}$ and a yaw angle $\alpha$ . Our evaluation protocol checks whether each constraint and all constraints collectively are satisfied. + +# 3.2.1. Checking validity of each 3D constraint + +We use a rule-based system to verify if a predicted placement satisfies 3D constraints, using ground truth oriented bounding boxes from ScanNet for anchor objects. Each constraint type is evaluated based on its specific properties, often allowing small deviations via thresholds. + +Physical plausibility: We use trimesh [16] to check for intersections between the object and the scene and whether the object is placed on a surface. + +Spatial constraints: For the near and adjacent constraints, we compute the distance from the posed asset to the anchor object. We check the on, above, and below relationships by comparing the value of the z-coordinate of the placed object with the z-coordinate of the anchor object. For the between relationship, we check if the placed asset is close to a line connecting the centers of the two anchor objects. + +Rotational constraint: We compute a cone around the frontal vector of the posed asset and check that the anchor object intersects with that cone. + +Visibility constraint: To determine visibility from a given anchor, we render the object and scene from a camera at the anchor point facing the object, and check if any pixels in the image correspond to the object. + +More details are available in the supplemental material. + +# 3.2.2. Benchmark metrics + +To evaluate placement performance, we compute metrics that capture constraint validity overall and by subgroup: + +- Global Constraint Accuracy: The percentage of all constraints (across all groups) that are correctly satisfied over the entire dataset. It provides a holistic measure of the overall placement quality. +- Complete Placement Success: The percentage of perfect valid placements, where every constraint—including physical plausibility—is satisfied. This is a strict metric that reflects the robustness of the placement method under full constraint satisfaction. +- Language Adherence Success: The percentage of placements that satisfy all language-based 3D constraints, excluding physical plausibility. It measures whether the model fully adheres to the language instructions. +- Subgroup Metrics: In addition to the overall metrics, we report accuracies across constraint groups. + +# 3.2.3. Benchmark statistics + +The benchmark contains 3,500 evaluation examples, combining a total of 142 different scenes from ScanNet [15] and 20 different assets from the PartObjaverse-Tiny + +dataset [54]. Statistics for the number of constraints and type of constraints are shown in Table 1. + +
Constraints per sample#Type#
One900Spatial4,208
Two1,871Rotational1,503
Three or more729Visibility1,210
+ +Table 1. Benchmark statistics for the number and types of language constraints per sample. Physical plausibility is evaluated in all samples and thus excluded from this table. + +# 3.3. PLACEIT3D-dataset: Training dataset + +Although our benchmark protocol allows offline method evaluation, we need a practical, less computationally costly approach to create a large-scale dataset for training, especially for obtaining the full set of valid placements. + +Here we describe PLACEIT3D-dataset, our training dataset for the task of guided placement. The dataset consists of 100,505 training examples, sourced from 565 distinct ScanNet scenes and 20 unique assets. It includes a total of 83,530 spatial constraints, 34,445 rotational constraints, and 18,746 visibility constraints. Among these examples, 65,586 contain a single constraint, 26,395 have two constraints, and 8,524 include three or four constraints. Used throughout this paper, this training dataset is a subset, for practical purposes, of the PLACEIT3D-dataset-full corpus we are also sharing. PLACEIT3D-dataset-full has $\sim 4\mathrm{M}$ examples: the 565 scenes x 140 objects x 50 prompts. + +Dataset parametrization We denote the point cloud of the scene as $\mathbf{X} \in \mathbb{R}^{N \times 6}$ , where each point $\mathbf{x}_i$ , $i \in \{0, \dots, N-1\}$ contains the 3D position for that point, as well as color information. Given a scene, an asset, and a prompt, we represent the set of valid ground truth placements for the asset as a binary mask $\mathcal{M}$ defined over the point cloud of the scene, associating a label $m_i \in \{0,1\}$ to each 3D point $\mathbf{x}_i$ . For each point $i$ with label $m_i = 1$ , i.e., a valid placement, we also define a binary mask over a discretized set of yaw angles indicating if the angle is valid for that specific location: $\alpha_i = \{\alpha_i^y \in \{0,1\} | y = 0, \dots, 7\}$ , where each $y$ corresponds to a $45^\circ$ interval. Note that there is a fixed transform between the parametrizations used in the benchmark and the training dataset. While for the benchmark we parametrize the position of the center of the asset, for the training set, we consider contact points between the scene geometry and the asset's bottom surface. + +Computing valid placement masks We create the valid placement masks $\mathcal{M}$ by using a combination of the rule-based system defined above and a few approximations to make it more efficient. More details on the approximations are available in the supplemental material. We treat each constraint independently, obtaining a valid + +mask per constraint $\mathcal{M}_c$ with $c\in \mathcal{C}$ , where $\mathcal{C} = \{\text{physical, spatial, rotational, visibility}\}$ . The final mask is given by the intersection of all the constraints that apply to that example, so + +$$ +\mathcal {M} = \bigcap_ {c \in \mathcal {C}} \mathcal {M} _ {c}. \tag {1} +$$ + +For the physical plausibility constraint we use a set of heightmaps to capture the different horizontal surfaces of the scene. We then compute the asset height and footprint and, for each point on a horizontal surface, check if the placement is valid. For the visibility constraint we use the same procedure as the benchmark, but use two approximations for efficiency: the asset is replaced by its bounding box, and a fixed rotation angle is used. + +# 4. PLACEWIZARD: Method Description + +Background. We briefly introduce Reason3D [25] as our method builds upon it. Given a textual prompt and a colored point cloud $\mathbf{X} \in \mathbb{R}^{N \times 6}$ as input, Reason3D performs dense 3D grounding, finding all the points in the point cloud that satisfy the prompt. A point encoder [45] extracts features $F_{X} \in \mathbb{R}^{N \times d}$ from the input point cloud, where $d$ is the feature dimension. These are aggregated into superpoints [28] obtaining superpoint features $F_{S} \in \mathbb{R}^{M \times d}$ , with $M \ll N$ , reducing the overall complexity. + +Next, the superpoint features $F_{s}$ are projected into the embedding space of an LLM via a Q-Former block [31]. This model updates the learnable query vectors $Q$ , resulting in $Q'$ . From $Q'$ and the input text, the LLM generates a response containing two special tokens, namely [LOC] and [SEG]. These tokens guide the model in two stages: coarse localization followed by precise mask prediction. + +In practice, the Reason3D method uses a single token, [LOC], for datasets that contain small scenes, such as ScanNet, since hierarchical subdivision is not required. We will describe their method using this simplified version. + +Finally, the last-layer embeddings associated to [LOC] are first projected via an MLP and then given as input to the Mask Decoder, which performs cross-attention [48] with $F_{s}$ . The decoder produces an object-level binary segmentation mask over superpoints, which is upsampled into $\mathcal{M}_{loc} \in \{0,1\}^{N}$ to provide a segmentation mask on the full point cloud. + +Figure 3 provides an overview of our method. In the following subsections, we detail our approach and emphasize the key modifications to the Reason3D architecture necessary for addressing language-guided placement instead of standard 3D visual grounding. + +# 4.1. Scene encoding + +Similarly to Reason3D, we use the point encoder from [45] to extract features $F_{X} \in \mathbb{R}^{N \times d}$ from the 3D scene. We use an additional positional embedding feature $F_{X}^{pos} \in \mathbb{R}^{N \times d^{*}}$ , for points in the point cloud, encoding their location, which is concatenated with the previous features. + +Spatial pooling. Reason3D uses Superpoints [28] to reduce computational complexity and memory usage by pooling individual point features into a single feature per superpoint. Although effective for their task, this coarse representation limits performance for our placement task. + +For example, Superpoints will generally cluster all points belonging to horizontal or vertical surfaces – such as floors, tabletops and walls – into single Superpoints, which is clearly undesirable for accurate 3D placement of assets. To address this, we instead use uniform spatial pooling to aggregate features. Specifically, we use farthest point sampling [21] to select $M$ center points, then assign each point in the cloud to its nearest center based on Euclidean distance. This approach keeps the method computationally efficient while maintaining sufficient granularity for accurate asset placement. The level of granularity reflects a trade-off between computational cost and the model's ability to reason over fine-grained geometric details. This trade-off is evident in Table 2, where comparing row A with row B shows that finer sampling enables better spatial reasoning. Please see supplementary material for a visualization. + +Our spatially aggregated features $F_{S}$ are passed as input to the Q-Former block [31], which also takes as input a set of trainable queries and learns to project the features into the LLM embedding space. + +# 4.2. Asset encoding + +When compared with other tasks, our language-guided placement task has an additional input, the 3D asset point cloud. We encode the asset using a Point-BERT encoder [57] trained on the Objaverse [17] dataset. This encoder predicts a sequence of feature vectors that are max-pooled to obtain a single feature embedding. + +Encoding the scale of the input asset is essential to facilitate a valid placement. Since the asset encoder assumes a normalized point cloud in a unit sphere, we separately encode the size of the asset by taking the asset's dimensions in the X, Y, and Z axes. The $F_{A}$ feature for the asset is a combination of the asset encoding and scale embeddings and is projected to the LLM space using an MLP. + +# 4.3. Placement decoder + +We instruct our LLM to output three special tokens, namely a [LOC] token, an [ANC] token, and a [ROT] token. The features associated with the three special tokens are passed as input to the decoder, where they undergo a few self-attention layers. These are followed by a few cross-attention + +layers between the updated token features and the asset features $F_{A}$ and the pooled scene features $F_{S}$ . + +Each individual head takes the feature of the associated token after attention, the asset feature $F_{A}$ , and the scene feature $F_{S}$ and predicts the corresponding output. The Placement Mask Head takes the [LOC] token embedding and predicts $\mathcal{M}_{loc} \in [0,1]^N$ , a mask over the scene point cloud encoding the regions where the input asset can be placed satisfying the input prompt. The Rotation Head takes the [ROT] token embedding and predicts $\mathcal{M}_{rot} \in [0,1]^{N \times 8}$ indicating for each point in the point cloud, the validity of a discretized set of rotation angles. Finally, the Anchors Mask Head takes the [ANC] token and predicts $\mathcal{M}_{anc} \in [0,1]^N$ , a mask encompassing the masks of all the anchor objects. This is used only as an auxiliary task, to help the network identifying anchors in the prompt. The head architectures are depicted on the right side of Figure 3. + +# 4.4. Losses + +We use a combination of Binary Cross Entropy (BCE) and Dice [43] losses when comparing a ground truth mask $\bar{\mathcal{M}}$ with a predicted mask $\mathcal{M}$ , so + +$$ +\mathcal {L} _ {s e g} (\bar {\mathcal {M}}, \mathcal {M}) = \operatorname {B C E} (\bar {\mathcal {M}}, \mathcal {M}) + \operatorname {D i c e} (\bar {\mathcal {M}}, \mathcal {M}). \tag {2} +$$ + +The loss for the rotation prediction is given by + +$$ +\mathcal {L} _ {\text {r o t}} = \operatorname {B C E} \left(\bar {\mathcal {M}} _ {\text {r o t}}, \mathcal {M} _ {\text {r o t}}\right), \tag {3} +$$ + +where $\bar{\mathcal{M}}_{rot} \in \mathcal{M}_{rot} \in \{0,1\}^{N \times 8}$ is the ground truth indicator mask for valid rotation angles, per point in the scene point cloud. + +The loss for the LLM is a cross-entropy loss, comparing the ground truth text $\bar{Y}$ with the predicted text $Y$ : $\mathcal{L}_L = \mathrm{CE}(\bar{Y}, Y)$ . Note that the ground truth text $\bar{Y}$ for our task, follows a simple format, e.g. "Sure, it is [LOC][ANC][ROT]", since the LLM is not required to predict articulated responses or explain placement decisions. Instead, the information useful for placement should be encoded in the embeddings for the special tokens. Finally, our total loss is defined as + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s e g}} (\bar {\mathcal {M}} _ {\text {l o c}}, \mathcal {M} _ {\text {l o c}}) + \mathcal {L} _ {\text {r o t}} + \mathcal {L} _ {\text {s e g}} (\bar {\mathcal {M}} _ {\text {a n c}}, \mathcal {M} _ {\text {a n c}}) + \mathcal {L} _ {L}. \tag {4} +$$ + +# 4.5. Inference + +At inference time, our method takes the network predictions for placement, $\mathcal{M}_{loc}$ , and rotation, $\mathcal{M}_{rot}$ , and extracts a single valid placement by finding the point in the point cloud with the maximum value in $\mathcal{M}_{loc}$ : $\hat{\mathbf{x}} = \mathrm{argmax}_{m\in \mathcal{M}_{loc}}m$ . We apply a fixed offset to point $\hat{\mathbf{x}}$ , half the asset height, to get the predicted 3D translation vector $\hat{t}$ . This is due to the differences in parametrization between the training dataset and the benchmark. To predict the rotation angle, we use $\mathcal{M}_{rot}^{\hat{\mathbf{x}}} \in [0,1]^8$ , which encodes the validity of discretized rotations for $\hat{\mathbf{x}}$ . The predicted angle $\hat{\alpha}$ is obtained by taking the argmax over this vector. + +
Method ablationSubgroup metricsGlobal metrics
NameSpatial aggr.Pos. emb.Asset encoderAnchor pred.Rot pred.Decode assetPhysicalSpatialRotationalVisibilityLanguage adherence successGlobal constraint accuracyComplete placement success
Baseline — OpenMask3D [46] + rules61.628.66.553.421.829.211.7
Baseline — OpenMask3D [46] + LLM5.835.310.561.518.426.71.6
A — Reason3D [25]Superpoints-text---53.937.56.657.018.144.813.2
Buniform-text---56.347.48.656.118.448.910.1
Cuniform✓text---58.649.77.959.120.050.410.9
Duniform✓PointBert---57.947.17.558.517.249.39.6
Euniform✓PointBert✓--57.554.310.058.822.242.512.3
Funiform✓PointBert✓✓-55.650.814.757.820.851.011.4
G — PLACEWIZARDuniform✓PointBert✓✓✓58.856.617.361.225.954.915.0
+ +Table 2. Quantitative results: We compare our full method with variations where some components are removed. The results validate our design choices, and they show improvements over OpenMask3D [46] with rule-based and LLM-based asset placement and Reason3D [25]. + +# 5. Experiments + +We validate our method PLACEWIZARD for the task of language-guided object placement on the benchmark described in Section 3.2. Our metrics, described in Section 3.2.2, measure prediction validity. All values are percentages, where higher is better. Implementation details are in the supplemental material. + +# 5.1. Quantitative results + +In the absence of prior work on language-guided 3D object placement in real scenes, we implemented two baselines by integrating OpenMask3D [46], an open vocabulary grounding method, with two different placement strategies: (1) a rule-based optimization approach, similar to the one used during training data generation in Section 3.3, and (2) an LLM-based system that uses GPT-4o, with the estimated scene graph provided as part of the input prompt. We evaluate both baselines against our proposed method. Since OpenMask3D requires explicit object queries, we use ground truth anchor descriptions (rather than full placement instructions) to retrieve relevant regions. Due to its frequent failure to accurately detect floor regions, we substitute in ground truth floor masks, while other anchor objects are selected based on the highest similarity scores. Once anchor masks are obtained, asset placement is performed either by the rule-based strategy or inferred via the LLM. + +Table 2 presents both baseline comparisons and ablation results. Our method, row G, consistently outperforms both baselines across all overall evaluation metrics. The LLM-based system often produces physically implausible placements, primarily because it lacks direct access to the 3D geometry of the scene. In contrast, the rule-based system, which leverages both asset and scene meshes, can produce more plausible placements, albeit at the cost of expensive collision checks during inference. By comparison, our method's end-to-end design eliminates the need for such costly test time operations, making it more scalable. + +able for large and complex scenes. Additionally, we observe that our method more accurately follows the user's language instructions than either baseline. Finally, the relatively low scores across all methods under the strictest evaluation metric, Complete Placement Success, which requires both physical plausibility and full adherence to all language constraints, highlight the inherent difficulty of the task. + +# 5.1.1. Ablations + +Table 2 also shows results for different ablations of our method. We start with an adaptation of the Reason3D [25] model to our task. One by one, we incrementally modify it using our novel components. Each row in the table introduces a single new modification, as compared to the previous row. We evaluate and report the model's performance until we reach PLACEWIZARD, our final method. All models are trained on our training dataset PLACEIT3D-dataset. For the methods that do not predict rotation (rows A, B, C, D, and E) we set the predicted rotation angle to 0. We describe the different variants below. + +A. The asset dimensions are encoded in text and provided as part of the prompt: "The asset dimensions are $X Y Z \, \text{cm}$ , where X, Y, and Z are integer values in cm. +B. This variant uses our proposed uniform spatial pooling approach instead of the original superpoints pooling. +C. Positional embedding features $F_{X}^{pos}$ for points in the point cloud are added to the scene encoding. +D. We incorporate the asset encoder instead of only providing the asset dimensions in the text prompt to the LLM. +E. We introduce the anchor prediction auxiliary loss. In [1], predicting anchor objects leads to better 3D visual grounding. We find that this holds for our task as well. +F. We introduce a rotation prediction head, enabling the model to predict also the rotation mask $\mathcal{M}_{rot}$ . +G. This variant defines our final method, where the asset feature $F_{A}$ is added as an additional input to the placement decoder. This integration helps the decoder reason more effectively about the asset's geometry in relation to the scene. + +![](images/56b80fee41de01632c898af3428d33e33249ce971519f5af4b2f2573463b308e.jpg) + +![](images/f959c40e3bb0c3ba38cc37339974c066f2a29f17528c53b1d13fb69c8546c673.jpg) + +![](images/ff23651b33a5dc203b50f668678494aa03170c90c9dcc2b7f0a770891d986c9c.jpg) + +![](images/bbb0f2e41250e71e7aa40756e08b212c712414c1a0d3f3358128535b40c6ad9b.jpg) + +![](images/46487b63bf529709f028f0eec1fb076dcfa1fbba35e3ad76e7a6e895b0383641.jpg) + +![](images/4f53a9bddc752fb5dc7256951f5a7ddf9215cc5dd38657a57e961fda49b9562e.jpg) + +![](images/bf85143fc455b3b7e5bee65b9d051052e6e0c4f6a8fd055d29e7ac9de17f365c.jpg) + +![](images/20b9d90bb3b5e17a06c005faa7495a7bff7fda7fb17c1cf60be6136f54b71174.jpg) + +![](images/f32150bc5932eb206eca97d7ee8a5400c3c920ef61594c5206ccf87f022a5c7b.jpg) + +![](images/04eb2329b72ed09b950fe9583ad608bacdd27f6556fa8de292ce9320118f865a.jpg) + +![](images/4cc4254647cc706ffdcfda7cd64f4e8f50ba2407a74e6cde4a8c3baf07f9e7b6.jpg) + +![](images/a3ca48f303f3b82a786bec23956110d86a1b215a27680dacbb0c19036e878092.jpg) + +![](images/f8d745f64529217503e81044bfa0ba3afaf667a2a3c979940df3ddc00258df6d.jpg) +Figure 4. Qualitative benchmark results. Colored highlights indicate anchors referenced in the textual prompts (predictions are generated entirely from point clouds, with anchor information provided only as text). The asset position is marked with a yellow circle, and a yellow arrow denotes the frontal orientation. Our method successfully follows language instructions and meets the specified constraints. The top-right example illustrates a placement that satisfies constraints but slightly intersects with the scene mesh. The bottom-right example demonstrates a failure case where one constraint is not met (highlighted in red). + +![](images/fcb66d3556ffa47ae954b1eb085acb221cbe23c1898f49f8c8dcdaa8f4440375.jpg) + +![](images/58377d82f06fa45de1bfd9ae362ee35e0cf39e1f3700cdcaa9df73049b87c2df.jpg) + +![](images/eca95bec7bd06ad9c5c48caa308603af9aa1baf6f817ec06faf16e4dd220f169.jpg) + +The results in Table 2 validate our design choices. Using spatial aggregation instead of superpoints improves over almost all metrics (compare row B with row A). The inclusion of the anchor prediction head as an auxiliary sub-task also improves performance (row E vs row D). Finally, the use of our rotation head combined with passing the asset encoding as input to the decoder gives our final best-performing method (row G, which we use in the qualitative results). + +# 5.2. Qualitative Results + +In Figure 4, we show the results of our method PLACEWIZ-ARD on benchmark examples, demonstrating its ability to follow language instructions and satisfy constraints. While most placements are accurate, some cases exhibit minor intersections with the scene mesh or constraint failures. + +# 6. Limitations and Future Work + +Our novel task formulation currently has several limitations. First, we focus exclusively on placing objects on horizontal surfaces. Extending this to support arbitrary contact points would enable broader applications, such as hanging a clock on a vertical wall. Second, our dataset and method do not address inconsistencies in language guidance, where instructions may not align with the actual scene. Addition- + +ally, both the dataset and the benchmark rely on synthetic rule-based optimization without human verification. This limits annotation quality, especially in edge cases, and consequently affects both prediction accuracy and evaluation reliability. Despite these limitations, we believe our work lays the groundwork for further research in this area. Our method can also be seen as a specialist model, as it is trained and evaluated solely on the guided placement task. Exploring how to integrate this task into a more generalist framework remains an important direction for future work. + +# 7. Conclusion + +We introduced a new task, benchmark, and dataset for language-guided object placement in real 3D reconstructed scenes, connecting natural language understanding with spatial reasoning over both scenes and assets. The benchmark is designed to reflect the inherent ambiguity of placement, where multiple valid solutions are possible. We also proposed a baseline method built on recent advances in 3D LLMs, supported by ablation studies that highlight the impact of key architectural and design choices. Benchmark results show considerable room for improvement, and we hope this work provides a foundation for advancing research in 3D spatial reasoning. + +# 8. Acknowledgments + +We thank Jakub Powierza and Stanimir Vichev for their help with the experimental infrastructure. 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The focus is on a mannequin dressed in a floral-patterned jacket and a blue scarf, ... + +Output (Layout + Image) +Input (Caption) +![](images/f06e529f2606bb3a6d7ccc73825bfcb95cbca48eaf42462839a6ec789c2c9d10.jpg) +This is a photograph showcasing the interior of a church. The interior of the church is lavishly decorated, with a dome featuring exquisite carvings... + +![](images/60c288bb1ddc8781a56c513a788304a98b20cda0df2987deb75c8606af6ef417.jpg) +Output (Layout + Image) + +![](images/57c7d9868e71789cacc87da1b126f87acdde0a3e886e0ea9332016f49bdd4be2.jpg) + +# (b) Layout-to-Image Generation + +![](images/3c28e5a96227065d1dbcf2e97053fdc3f4cd8f5bb0cb66156059418a3990c929.jpg) + +![](images/ca3b4f11fab9af83635045a20829efaf54d3eb3e841d7b15087a97f881393212.jpg) + +![](images/999258e4ddc2c22051f76a8296459737d2f3ebaaf99a4d321d0e2aa259a669ef.jpg) +Figure 1. PlanGen models layout planning and image generation jointly, allowing layout planning before generating corresponding images, and the two processes are completed in a unified model. PlanGen can perform multi-type tasks related to layout, including a) layout-image joint generation, b) layout-to-image generation, c) image layout understanding and d) layout-guided image manipulation. + +![](images/9df79a67e4b003e1efd7477b83132433e0acb164b6fea2a7c9e7be7d0488f8b8.jpg) + +![](images/e5b876116bfe64cb46104c69ea67fa72775d4d83e5d058f777131e50593ec602.jpg) +(c) Image Layout Understanding + +![](images/032963372d6965deef30d30542346bce331cd0fccaedc237d843cb90633e1e33.jpg) + +![](images/bb64e0169b62d5c510e6f89eca62ae7f9a695c5597ea95e9d7d4bdc564c09506.jpg) + +![](images/e82c5e96cb4b0a4094673e938eb4736a3cd0720a821f95b8ac4bc3fc3273209f.jpg) + +![](images/221e89bcf85ca8b908cc06ed399a62637a821439bd903a8571f16b7b6ea530d6.jpg) +(d) Layout-guided Image Manipulation + +![](images/912c89119e6ce62a024189f9991e2fad233dfcc50994a9b8b5a982756a1859f5.jpg) + +![](images/b1a3be3db6e9717be231bb533725dcca62e374ddebbf4cb6cc3924eedbcf7e0b.jpg) + +![](images/ae23047ea7e45581884ec7847c93213776135b98b227d534075d93488560c9bc.jpg) + +# Abstract + +In this paper, we propose a unified layout planning and image generation model, PlanGen, which can pre-plan spatial layout conditions before generating images as shown in Figure 1. Unlike previous diffusion-based models that treat layout planning and layout-to-image as two separate models, PlanGen jointly models the two tasks into one autoregressive transformer using only next-token prediction. + +PlanGen integrates layout conditions into the model as context without requiring specialized encoding of local captions and bounding box coordinates, which provides significant advantages over the previous embed-and-pool operations on layout conditions, particularly when dealing with complex layouts. Unified prompting allows PlanGen to perform multitasking training related to layout, including layout planning, layout-to-image generation, image layout understanding, etc. In addition, PlanGen can be seamlessly expanded to layout-guided image manipulation thanks to the well-designed modeling, with teacher-forcing content + +manipulation policy and negative layout guidance. Extensive experiments verify the effectiveness of our PlanGen in multiple layout-related tasks, showing its great potential. The code is available at: https://github.com/360CVGroup/PlanGen. + +# 1. Introduction + +In recent years, the field of image synthesis has received widespread attention from the community, and technologies such as GAN [24, 39, 81], autoregressive image generation [27, 44, 63, 68], and diffusion models [36, 62] have made great progress. Among them, diffusion models dominate because of their more stable training, sampling diversity, and high quality. Recently, autoregressive image generation has been widely explored because of its scalability and compatibility with large language models (LLMs). + +With the continuous advancement of text-to-image foundation models [6, 28, 29, 53, 58, 60], their applications in various scenarios [9, 18, 32, 70, 71, 84, 85, 91, 92] have become increasingly diverse. While fundamental text-to-image models primarily focus on text-image alignment, users often have more specific requirements regarding the spatial arrangement and interactions between objects. As shown in Figure 2, recent diffusion-based methods [14, 45, 73, 82, 89] introduce layout conditions into the image generation process. Despite the promising results, it faces two shortcomings: 1) Inability to expand to layout-image joint generation, which leads to reliance on another layout planning model. 2) Suboptimal encoding of layout condition, which is mainly caused by embed-and-pool operation on local captions to unify layout conditions for facilitating model training. + +We propose an autoregressive visual-language model, PlanGen, which can complete layout planning and layout-to-image generation in a unified model. Just like thinking about what object each area should be before generating an image, such an explicit planning process allows the model to enjoy more powerful image generation capabilities. PlanGen takes layout conditions as context input, with extremely strong flexibility and scalability, no need to compress the layout conditions as previous methods [45, 73, 82, 89], allowing as detailed and complex local descriptions as possible, leading to a more aligned layout-to-image generation thanks to transformer's long context dependencies. PlanGen allows multi-task training related to layout through unified prompting, including layout planning, layout-to-image generation, and image layout understanding. Additionally, through teacher-forcing content manipulation and negative layout guidance, PlanGen can be extended to layout-guided image manipulation without specialized training. + +Our contributions are summarized as follows: (1) We + +![](images/bda38cd1c85a973bd1c7b86f55fb5207d609213b595fbedfaa2a7ba757fb53a1.jpg) +(a) Text-to-Image + +![](images/94c7991933ec8ad73e3dd9ad55d73324f30a723fef595e8bca521b21080aec09.jpg) +(b) Separated Models for Text-to-Layout & Layout-to-Image + +![](images/6f3f36f88b8c8963a9b18e808059f0087df6da778b691e155b8d90858bd301fc.jpg) +(c) Unified Model for Layout-Image Joint Generation +Figure 2. Different paradigms of image generation. a) The naive text-to-image cannot control the layout of the generated images. b) Previous methods use two independent models to complete layout planning and image generation. c) We adopt a unified model to complete layout planning and image generation. + +present the first layout-image joint generation model based on the autoregressive vision-language model. (2) We propose a unified prompting paradigm to allow layout-image joint modeling, as well as multitasking training related to layout conditions. (3) We further extend PlanGen to layout-guided image manipulation through teacher-forcing content manipulation and negative layout guidance. + +# 2. Related Works + +Vision-Language Models (VLMs) In recent years, large vision-language models [1, 2, 8, 38, 49, 90] have made remarkable breakthroughs. As a critical research direction, unified model with understanding and vision generation abilities [13, 17, 22, 67, 74, 76, 78, 86, 88] is being widely explored. Early approach SEED-X [22] applies another independent diffusion model to complete the visual generation task. Show-o [78] performs autoregressive and discrete diffusion modeling in one transformer. Transfusion [88] and MonoFormer [86] integrate the diffusion process into next-token prediction. Emu3 [74], Janus [76] as well as Janus-Pro [13] only use next-token prediction in training and also achieve promising results. + +Autoregressive Image Generation Autoregressive image generation models [27, 30, 44, 63, 65, 66, 68] have recently received widespread attention from the community due to their scalability and compatibility with LLMs. LLamaGen [63] apply the original "next-token prediction" paradigm of LLMs to the visual generation domain. MaskGIT [11] introduces a bidirectional transformer decoder and predicts randomly masked tokens by attending to tokens in all directions, instead of decoding images sequentially following the raster scan ordering. VAR [68] re + +defines the autoregressive image generation as a coarse-to-fine process, i.e. "next-scale prediction", showing promising results. MAR [44] performs autoregressive image generation in a continuous-valued space, with additional diffusion MLPs to model the per-token probability distribution. + +Layout-to-Image Generation The layout-to-image generation methods can generally be categorized into training-free [12, 77] and training-based [14, 20, 26, 45, 54, 73, 82, 89] approaches. Early methods, such as CAG [12], which do not require training, laid the foundation for the field. Recent research, however, has primarily focused on training-based approaches. For instance, GLIGEN [45] explored specialized attention mechanisms, while HiCo [14] investigated methods for controlling the introduction of conditions, which can be used seamlessly as plugins. Furthermore, the introduction of CreatiLayout [82] in MM-DiT [16, 43] has further advanced controllable image generation based on layout design. + +Image Manipulation The huge advances in image generation have also promoted research on image manipulation, i.e. image editing. The task is also dominated by diffusion-based models. Early training-free methods [10, 34, 50, 69], such as Prompt-to-Prompt [34], complete the image editing process by manipulating attention mechanisms. To edit real images, it is also necessary to inversion the real images, and the editing effect is not ideal. Some methods [3, 15, 51, 52] have been proposed to achieve diversified editing like object dragging. Instruction-based methods [7, 21, 23, 31, 33, 37, 83, 87] represented by InstructPix2Pix [7] use natural language instructions to complete image editing, which relies on training on large-scale instruction editing datasets. + +# 3. Methods + +# 3.1. Overview + +As shown in Figure 3, PlanGen based on the architecture of the autoregressive vision language model, supports layout-image joint generation in one transformer with causal attention. Given a text prompt $T$ by the user, instead of directly generating the image, PlanGen performs spatial layout planning first to obtain the layout condition $C$ , which imagines the desired position of each subject in the text prompt, and then completes the image generation process under the condition of both text prompt $T$ and planned layout $C$ . + +# 3.2. Joint Generation Modeling + +# 3.2.1. Unified Prompting + +As shown in Figure 4a, the layout planning and image synthesis of PlanGen are performed in sequence during the same round of inference. We use newly inserted special tokens and to mark the beginning and the end of the layout condition. After the + +layout condition is planned, we use to trigger the image generation process. + +To help the model understand the layout condition, as shown in Figure 4b, we use and to wrap local descriptions like Qwen [4]. Each local description corresponds to a bounding box coordinate list, which is placed between and . The coordinate list contains four integers standardized to 0-1000, representing the upper left corner and the lower right corner of the bounding box. + +Thanks to the flexible context length in autoregressive models, local descriptions in PlanGen can be as detailed as needed, in contrast to the previous diffusion-based methods [45, 73, 82, 89] which need to perform pooling or truncation operations to reduce and unify the length of the local description embeddings. In addition, due to the parallel training advantages of autoregressive transformers, layout planning and layout-to-image generation can perform training in the same batch. + +# 3.2.2. Image Layout Understanding Learning + +The ability to understand the layout of real images can help the model generate images that are more in line with the layout conditions, intuitively, because this can further strengthen the model's in-depth understanding of the relationship between layout conditions and corresponding images. In addition, including the task of image layout understanding to PlanGen can move further towards a more general layout VLM. + +Given an image $I$ , we expect PlanGen to be able to analyze its layout conditions. Specifically, we first extract high-dimensional image features from $I$ using SigLIP [80] encoder, then flatten and map them into the text feature space, following Janus-Pro [13]. The prompt paradigm of image layout understanding is illustrated in Figure 4c. In order to reduce the difficulty of directly predicting the layout conditions, we predict the caption first before predicting the layout conditions. + +# 3.2.3. Training Objectives + +The training of all tasks in PlanGen is based on next-token prediction. We assume a sequence with $M$ text prompt tokens $\mathbf{t} = \{\mathbf{t}_1, \mathbf{t}_2, \dots, \mathbf{t}_{\mathbf{M}}\}$ , $N$ layout tokens $\mathbf{l} = \{\mathbf{l}_1, \mathbf{l}_2, \dots, \mathbf{l}_{\mathbf{N}}\}$ , $X$ image tokens to be generated $\mathbf{g} = \{\mathbf{g}_1, \mathbf{g}_2, \dots, \mathbf{g}_{\mathbf{X}}\}$ . Without loss of generality, we introduce layout planning and layout-to-image generation that can be trained in parallel separately. + +Layout Planning We maximize the likelihood of layout tokens given text prompt tokens and all previously generated layout tokens by employing the standard language modeling objective: + +$$ +\mathcal {L} _ {L P} = \sum_ {i} \log p _ {\theta} \left(\mathbf {l} _ {\mathbf {i}} \mid \mathbf {t}, \mathbf {l} _ {< \mathbf {i}}\right), \tag {1} +$$ + +![](images/9c48f41400ddc51af529fa6bdd8817dbd62f4bbe5ad7ccee56d0a6c905e826c0.jpg) +Figure 3. Upper: PlanGen models layout planning and image generation jointly in an autoregressive visual-language model through a unified prompting design with the next-token prediction training objective. Lower: Illustration of PlanGen's multitasking related to layout: a) layout-image joint generation, b) layout to image generation, c) image layout understanding and d) layout-guided image manipulation. + +(a) Prompt for Layout-Image Joint Generation + +![](images/95cc46b88f3806b63e2f57512c61d7cf3421c4b3f21c9e29dbd8440c38a76d7a.jpg) + +(b) Prompt Example for Layout Condition + +![](images/5d416dbfaecca390ce38b02e744afe5d464cdf7e3407f16f147345f01cde74d8.jpg) + +(c) Prompt for Image Layout Understanding + +![](images/856037bfcce04de767254b74028add85a35afe0bd2340d876de926edbd0fec51.jpg) +Figure 4. Prompt design of PlanGen. a) Prompt for Layout-Image Joint Generation. b) Prompt Example for Layout Condition. c) Prompt for Image Layout Understanding. + +where $p$ indicates the conditional probability of PlanGen, parameterized by weights $\theta$ . + +Layout-to-Image Generation Similarly, we maximize the likelihood of image tokens given text prompt tokens, layout tokens, and previously generated image tokens, as formulated below: + +$$ +\mathcal {L} _ {L I G} = \sum_ {i} \log p _ {\theta} \left(\mathbf {g} _ {\mathbf {i}} \mid \mathbf {t}, \mathbf {l}, \mathbf {g} _ {< \mathbf {i}}\right) \tag {2} +$$ + +Image Layout Understanding The task requires the introduction of $K$ conditional image tokens $\mathbf{q} = \{\mathbf{q}_1, \mathbf{q}_2, \dots, \mathbf{q}_K\}$ . We maximize the likelihood of layout tokens as follows: + +$$ +\mathcal {L} _ {I L U} = \sum_ {i} \log p _ {\theta} \left(\mathbf {l} _ {\mathbf {i}} \mid \mathbf {q}, \mathbf {t}, \mathbf {l} _ {< \mathbf {i}}\right) \tag {3} +$$ + +The total training loss is summarized as follows: + +$$ +\mathcal {L} = \alpha \mathcal {L} _ {\mathrm {L P}} + \beta \mathcal {L} _ {\mathrm {L I G}} + \gamma \mathcal {L} _ {\mathrm {I L U}}, \tag {4} +$$ + +where $\alpha, \beta, \gamma$ are the hyperparameters to balance different losses, which are all set to 1 empirically in our experiments. + +# 3.3. Layout-guided Image Manipulation + +Benefiting from the modeling paradigm defined by layout conditions, PlanGen could control the generation of the contents of the local area based on the corresponding local captions and bounding boxes, which allows us to easily extend PlanGen to layout-guided image manipulation without further task-specific training. + +# 3.3.1. Teacher-forcing Content Manipulate + +One difficulty in image manipulation is to keep non-edited areas unchanged, and previous diffusion model-based approaches often require targeted training or inverse processes to achieve this goal, as its implicit features are difficult to manipulate directly. In the paradigm of autoregressive image modeling, we can achieve this through teacher-forcing. + +Specifically, we can pre-calculate token position set $\mathcal{P}_{edit}$ based on the bounding boxes to be edited. For tokens within $\mathcal{P}_{edit}$ that require editing, we perform layout-to-image token sampling $\mathcal{F}$ , or else we directly select pre-calculated tokens at corresponding mapped positions. The prediction process of the i-th image token $e_i$ is defined as follows: + +
DatasetLayout PlanningLayout-to-Image Gen.Image Lay-out Und.# Samples
HiCo [14]✓✓✓1,250,466
LayoutSAM [82]✓✓✓2,665,509
OpenImage [42]✓✓✓1,743,042
LayoutGPT [19]✓✗✗40,481
+ +Table 1. Statistics of datasets used for training. + +$$ +\mathbf {e} _ {\mathrm {i}} = \left\{ \begin{array}{l l} \mathcal {F} (\mathbf {t}, \mathbf {l}, \mathbf {e} _ {< \mathrm {i}}, i) & \text {i f} i \in \mathcal {P} _ {\text {e d i t}}, \\ \mathcal {M} (i, \mathbf {o}) & \text {i f} i \notin \mathcal {P} _ {\text {e d i t}}, \end{array} \right. \tag {5} +$$ + +where $\mathbf{o}$ represents the image tokens of the original image, and $\mathcal{M}$ maps the i-token to corresponding image token in $o$ . + +# 3.3.2. Negative Layout Guidance + +To further improve editing quality, we propose negative layout guidance to unlock the huge potential of layout-based image manipulation methods. Existing methods often struggle to solve the artifacts after object deletion, as previous methods [64, 75] have pointed out. + +Thanks to our token-based layout conditions, we can easily incorporate negative layout guidance into the classifier-free guidance to suppress the generation of artifacts without causing additional inference overhead. + +$$ +\tilde {e _ {\theta}} (\mathbf {t}, \mathbf {l}, \mathbf {g} _ {< \mathbf {i}}) = e _ {\theta} (\tilde {\mathbf {t}}, \tilde {\mathbf {l}}, \mathbf {g} _ {< \mathbf {i}}) + s \cdot (e _ {\theta} (\mathbf {t}, \mathbf {l}, \mathbf {g} _ {< \mathbf {i}}) - e _ {\theta} (\tilde {\mathbf {t}}, \tilde {\mathbf {l}}, \mathbf {g} _ {< \mathbf {i}})), \tag {6} +$$ + +where $e_{\theta}$ and $\tilde{e}_{\theta}$ indicates predicted logits and modulated final logits, $\tilde{\mathbf{t}}$ and $\tilde{\mathbf{l}}$ are negative text prompt tokens and negative layout tokens respectively. Specifically, for the object deletion task, $\tilde{\mathbf{t}}$ denotes the global negative text prompt, and an empty text is sufficient. $\tilde{\mathbf{l}}$ represents the negative grounding condition of the deleted area, where the bounding box indicates the region to be removed and a corresponding textual description can be: "an object, artifacts, disharmonious abrupt objects, messy background, noisy environment". The guidance scale $s$ is set to 5. + +# 4. Experiments + +# 4.1. Training Datasets + +As shown in Table 1, we use two existing large-scale layout-to-image datasets in training, including HiCo [14] derived from GRIT-20M [56] and LayoutSAM [82] derived from SAM [40]. In addition, we also introduce OpenImage V6 [42] dataset. We apply MiniCPM [55] to caption the images and use object class names as local captions, which complements the long local captions in HiCo and LayoutSAM. Furthermore, considering that these three datasets focus on complex prompts and layouts, we also introduce pure planning data constructed by LayoutGPT [19]. + +# 4.2. Implementation Details + +Our experiment is based on pre-trained Janus-Pro 1.5B [13]. The training batch sizes of layout-image joint training, image layout understanding, and pure layout planning are 3, 3, and 2 respectively. We train our PlanGen for 200,000 steps on $8 \times 80$ GB NVIDIA A100 GPUs with AdamW [48] optimizer, and the learning rate is set to 5e-5 with a total batch size of 64. Images are uniformly processed to $384 \times 384$ resolution. + +# 4.3. Layout Planning + +Settings. We compare PlanGen's layout planning ability with existing powerful foundational LLMs: (1) Qwen2.5-7b-instruct [25] (2) Llama3.1-8b-instruct [49]. We use in-context learning to make LLMs generate layout conditions according to global captions. We conduct evaluations on PlanGen-1K benchmark, which is derived from LayoutSAM-Eval, used for multitasking evaluation related to layout. Considering that the layout planning has a high degree of freedom, it is not reasonable to compare the results with ground truth layouts. Following [82], we use PlanGen to perform layout-to-image generation for layouts predicted by different methods and indirectly judge the quality of the layout by judging the quality of generated images. We calculate (1) PickScore, which derives from the preference predictor, (2) CLIPScore, which measures the CLIP [57] image-text similarity between the generated images and corresponding text prompts, (3) FID [35] and (4) Inception Score (IS) [61]. + +Results. As shown in Figure 5, PlanGen can generate reasonable layouts from complex global captions. Compared with Qwen2.5-7b-instruct and Llama3.1-8b-instruct, the local descriptions of bounding boxes generated by PlanGen are more detailed and specific, which promotes the consistency of the generation results with the global captions. Furthermore, the planned layouts enjoy more reasonable spatial relations, resulting in better image quality. The quantitative analysis in Table 3 also confirms the advantage of PlanGen in layout planning. Compared with the other two LLMs, the image results generated based on PlanGen's layout predictions have lower FID and are even close to the results generated by using ground-truth layout conditions. + +# 4.4. Layout-to-Image Generation + +Settings. Layout-to-image generation was dominated by diffusion-based models. We evaluate PlanGen's ability of layout-to-image with (1) GLIGEN [45] (2) Ranni [20] (3) MIGC [89] (4) InstanceDiff [73] (5) HiCo [14] (6) Creatilayout [82]. We conduct evaluations on LayoutSAM-Eval benchmark following [82] and report region-wise quality and global-wise quality. The region-wise quality includes spatial, color, texture, and shape scores obtained from MiniCPM [55], while the global-wise quality includes + +![](images/4e349dd72d2e9499f593edc74500f5859448ed5143003dff9fc6cab8d3751041.jpg) +This is a photo showcasing a traditional Asian cultural scene, with a woman in a pink top and a traditional conical hat standing in the foreground, her back to the camera, facing a towering pagoda. The pagoda is a multi-tiered tower with a pointed top, its architectural style and color harmoniously blend with the surrounding environment. The sky is clear, with a few white clouds leisurely floating by, adding a touch of tranquility and harmony to the scene. + +![](images/f5051d8f6003b8d013c1534f7aed85eb2ed462b6c2c55289fb709820f567030f.jpg) + +![](images/202394d05f8b389204199627f42c6ac21f61680040f8692e2020ae39946d60c1.jpg) + +Figure 5. Examples for layout planning. Compared with Qwen-2.5-7b-instruct [25] and Llama-3.1-8b-instruct [49], PlanGen generates more reasonable layout conditions from complex global captions. We use PlanGen to conduct layout-to-image generation for the layout conditions generated by the three methods to further observe the quality of the layout conditions. +![](images/becf46f96837b99d878fdbc2134b8c97b1871d306bbcf34788fa7d1d324e97b6.jpg) +This is a street-style photo showcasing a fashionable young woman. The woman is wearing a bright red long coat, paired with a black crop top and ripped jeans, and black and white patterned high heels. She is carrying a black handbag and has a black choker around her neck. The background is a blurred city street scene, with parked cars and a blurred cityscape visible. + +![](images/c3aa91db7def94f56301f8f0ace9ba60d97fe502e5df1a18ed79d549116d7026.jpg) + +![](images/2ab18322b538c2ab56b5f3927d13243cf215b97fe85a2cceef8e92ced3c14490.jpg) + +![](images/bbaaa86affdb36672c864118ce4c820249ecec096c3203681f8585b30b6c1c2c.jpg) +Figure 6. Qualitative comparisons of PlanGen with other baselines on layout-to-image generation task, including GLIGEN [45], InstanceDiff [73], and CreatiLayout [82]. PlanGen generates realistic images that meet the layout conditions, which has obvious advantages compared to previous diffusion-based methods. + +
TypeMethodRegion-wise QualityGlobal-wise Quality
Spatial ↑Color ↑Texture ↑Shape ↑IR ↑ [79]Pick ↑ [41]CLIP ↑FID ↓IS ↑
Real Images98.9598.4598.9098.80-----
GLIGEN [45]77.5349.4155.2952.72-10.3120.7832.4221.9220.57
Ranni [20]41.3824.1025.5723.35-28.4620.4931.4027.2419.81
DiffusionMIGC [89]85.6666.9771.2469.06-13.7220.7131.3621.1919.65
InstanceDiff [73]87.9969.1672.7871.089.1421.0131.4019.6720.02
HiCo [14]87.0469.1972.3671.1012.3621.7032.1822.6120.15
CreatiLayout [82]92.6774.4577.2175.9369.4722.0234.0119.1022.04
ARPlanGen92.2182.6986.5385.3639.5821.4331.9613.9119.31
+ +Table 2. Layout-to-image quantitative comparison on the LayoutSAM-Eval. Only PlanGen is based on the autoregressive paradigm. + +
MethodPick↑CLIP ↑FID ↓IS↑
GT Layout21.4431.9148.6713.97
Qwen2.5-7b-it [25]20.9231.47472.3813.44
Llama3.1-8b-it [49]21.0131.64464.0713.77
PlanGen21.4231.9350.7315.44
+ +traditional indicators like FID, IS, and so on. More details can be found in [82]. + +Results. As shown in Figure 6, PlanGen could generate corresponding images based on given layout conditions, and the generated results show a high degree of consistency with the layout conditions. In the 1st row, only PlanGen generates a reasonable "ancient stone castle". Although Creati-Layout has a higher image aesthetics and realism, it produces a result of the separation of the upper and lower parts of the image, which is not harmonious. We observe that the results generated by InstanceDiff lack sufficient realism and tend toward animation style. GLIGEN will ignore certain layout information in some cases, such as the 2nd row, missing "clear blue water". PlanGen is generally capable of generating realistic images and meeting layout conditions. However, it shows limitations in generating human figures, as evidenced in the last row. This is consistent with the quantitative results in Table 2, PlanGen performs well in region-wise quality and significantly exceeds previous diffusion-based methods, thanks to its strong understanding of the layout context. In addition, the FID metric of PlanGen also leads other methods, verifying its excellent image generation quality. + +# 4.5. Image Layout Understanding + +Settings. Image layout understanding has similarity to grounding detection to some extent, both to obtain local captions and corresponding bounding box coordinates, but + +Table 3. Layout planning quantitative comparison of PlanGen with Qwen2.5-7b-instruct [25] and Llama3.1-8b-instruct [49] on PlanGen-1K. + +
MethodAP↑AP50↑AP75↑AR↑
Grounding-DINO [47]50.0061.6654.9269.34
Janus-Pro-7B [13]0.280.740.244.81
Qwen-VL-Chat [4]5.169.175.8220.64
Qwen-VL-2.5-8B [5]6.6913.526.8223.37
CogVLM-grounding [72]9.0513.039.9529.27
PlanGen33.4844.7636.7150.98
+ +Table 4. Image layout understanding quantitative comparison of PlanGen with Grounding-DINO [47], Qwen-VL-Chat [4] and CogVLM-grounding [72] on PlanGen-1K. + +image layout understanding does not aim at detecting objects in the figure as its ultimate goal. We compare PlanGen's image layout understanding ability with specialized grounding detection model (1) Grounding-DINO [47] and LLMs with grounding capability (2) Janus-Pro-7B [13] (3) Qwen-VL-Chat [4] (4) Qwen-VL-2.5-8B [5] and (5) CogVLM-grounding [72]. We conduct the evaluation on our PlanGen-1K benchmark, reporting AP, AP50, AP75, and AR. Additional details are provided in the supplemental material. + +Results. As shown in Table 4, compared with Qwen-VLChat and CogVLM-grounding, PlanGen, specially trained in image layout understanding, achieves excellent layout understanding capabilities with higher AP and AR metrics. It should be noted that PlanGen can even be close to the performance of Grounding-DINO, which is often a specialized tool for data annotation, showing PlanGen's promising prospects. + +# 4.6. Image Manipulation + +Settings. In this part, we focus on comparing the object deletion ability of PlanGen. We choose two classic diffusion-based baselines: (1) Instruct-Pix2Pix [7] (2) SD-Inpainting [59], which is specially trained inpainting model, because it is difficult to manipulate the latent directly in + +![](images/f43315d6ed080c84668474e3c160372c956cdfba0c280c328d285f70336f2878.jpg) +Figure 7. Qualitative comparisons of PlanGen with Instruct-Pix2Pix [7] and SD-Inpainting [59] on the object removal task. The red areas of images in the 1st column are the objects to be deleted. + +the diffusion model, while PlanGen could conduct image generation and editing in one unified model. We report the following indicators in 200 object removal cases derived from COCO [46] test set, including (1) Success Rate (SR), we calculate it by asking the visual language model MiniCPM [55] whether there are objects to be deleted in targeted area. (2) LocalCLIP, which measures the deletion ability by evaluating the image-text similarity of the local image areas and the corresponding local descriptions. (3) IS, which measures the quality of the image. + +Results. As shown in Figure 7, PlanGen has more obvious advantages when deleting objects, and can more thoroughly delete objects in local areas, making it less likely to leave artifacts or cause image quality to decline. This is consistent with the results in Table 5, and PlanGen achieves the highest deletion success rate. As illustrated in the first row of Figure 7, when the bed is removed, PlanGen also generates a light reflection on the floor originating from the window. Instruct-Pix2Pix often causes most of the entire image to change, and it is often impossible to completely delete. SD-Inpainting is prone to leaving artifacts in the area to be deleted, affecting the quality of the image. Additional image manipulation examples for more editing types are provided in the supplemental material. + +# 4.7. Ablation Study + +In Table 6, we perform a series of ablation experiments on a subset of the training dataset. We compare the different encoding types of numerical values and find that PlanGen can achieve better results by directly considering the values as texts rather than encoding them into special tokens. In addition, we also ablate the impact of different tasks adopted in the experiment. The introduction of image lay + +
MethodSR ↑LocalCLIP ↓IS ↑
Instruct-Pix2Pix [7]40.0023.659.20
SD-Inpainting [59]66.5022.617.73
PlanGen77.5021.968.45
+Neg. Layout Guidance86.5021.908.43
+ +Table 5. Object removal quantitative comparison of PlanGen with Instruct-Pix2Pix [7] and SD-Inpainting [59]. + +
LIGLPILUEncSpatial ↑Color ↑Texture ↑Shape ↑
✓××N87.1972.2577.1876.35
✓✓×N83.2569.4673.7370.28
✓✓✓N87.5268.1474.5571.26
✓✓✓S81.9459.6167.6566.34
+ +Table 6. Ablation studies about the task types used in PlanGen's training and the encoding type of numerical values (Enc). "LIG" stands for Layout-to-Image Generation, "LP" for Layout Planning, and "ILU" for Image Layout Understanding. "S" refers to encoding numerical values into special tokens, whereas "N" means treating numerical values as normal text. + +out understanding can improve the effect of the model. The model trained with all tasks has a similar effect as the model trained with layout-to-image task alone, which verifies the effectiveness of PlanGen using multi-task training. In addition, in Table 5, we ablate the impact of whether negative layout guidance is used on the object deletion task. By introducing this strategy, we observe that the deletion success rate has been greatly improved. + +# 5. Discussion + +In this work, we demonstrate a unified model that integrates layout planning and layout-to-image generation into an autoregressive vision-language model, which also has the ability to understand the layout of real images. It performs well in layout planning, layout-to-image, and image layout understanding tasks, showing the great potential of a unified model. In addition, it can be expanded into image manipulation without further training with teacher-forcing content manipulation and negative layout guidance. + +While promising, our work still faces several challenges, firstly, our experiments are trained on image resolution of $384 \times 384$ due to limited training resources. Experiments at higher resolutions will help further improve the model's effect. 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The proposed hybrid method processes an input image by detecting scale and orientation features (e.g., by SIFT [18] or SuperPoint [8] + SelfScaleOri [11]) alongside line segments (from LSD [32] or DeepLSD [24]). It then estimates the affine rectification, ensuring that lines parallel in the real world appear parallel in the rectified image. + +# Abstract + +We propose a method for affine rectification of an image plane by leveraging changes in local scales and orientations under projective distortion. Specifically, we derive a novel linear constraint that directly relates pairs of points with orientations to the parameters of a projective transformation. This constraint is combined with an existing linear constraint on local scales, leading to highly robust rectification. The method reduces to solving a system of linear equations, enabling an efficient algebraic least-squares solution. It requires only two local scales and two local orientations, which can be extracted from, e.g., SIFT features. Unlike prior approaches, our method does not impose restrictions on individual features, does not require class segmentation, and makes no assumptions about feature interrelations. It is compatible with any feature detector that provides local scale or orientation. Furthermore, combining scaled and oriented points with line segments yields a highly robust algorithm that outperforms baselines. Extensive experiments show the effectiveness of our approach on real-world images, including repetitive patterns, building facades, and text-based content. The code is publicly available here. + +# 1. Introduction + +Planar affine rectification—the transformation of an imaged plane into one where affine invariants, such as parallelism and area ratios, are preserved [10]—is a fundamental pre- + +processing step in computer vision. It is crucial for tasks such as image registration [13, 14, 21], stitching [15], scene understanding [30], image editing [19], and metric rectification [10]. Affine rectification recovers the orthographic appearance of a plane, differing from the real-world surface only by an affine transformation. + +A common approach estimates the rectifying homography by mapping the vanishing line of the plane to the line at infinity. This requires detecting two vanishing points, which can be inferred from parallel lines in the scene [10]. However, line-based methods face challenges: detecting truly parallel lines is nontrivial, small errors in line detection can significantly impact homography estimation, and many images lack prominent linear structures (e.g., polka-dot patterns, as illustrated in Fig. 2). + +Scale-based methods [5] offer an alternative by leveraging local scale variations induced by projective transformations. These approaches match at least three point-and-scale features, providing a predictable measure of distortion. However, just as line-based methods fail in the absence of linear structures, scale-based methods struggle with linedominated patterns, where scale variations are unreliable. They also require grouping scale features into consistent classes, adding complexity to feature selection. + +Other methods, such as [26], estimate rectification using affine-invariant features, which encode local scale, orientation, and full affine shape. These techniques rely on detectors such as Affine-SIFT (ASIFT) [22] or learned feature extractors such as AffNet [20]. Although robust to view- + +![](images/09ccb2f49598adc5fa2ab8ba83a4d9a998e5859667636d67919b7aa503a96114.jpg) +(a) + +![](images/27eb86748a89b0c06f2e4f27d3b773564e677c65e39e50d4f8d3fe6a50c00e97.jpg) +(b) + +![](images/6bd3a4369d2abb435251e6950a2f1d74b1682a0ea873e320d9a17581e8e2f765.jpg) +(c) +Figure 2. Inadequate patterns for line-based methods. Plots (a)-(b) depict images without prominent linear features, whereas (c)-(d) contain linear structures that are insufficiently distinct for reliable vanishing point estimation. + +![](images/cf7ad70fd4f01f8ddafb6ce28faaaaf2de32baf0c9faa8a032fb8db271d4c6f3.jpg) +(d) + +point changes, these methods are computationally expensive, as ASIFT simulates multiple viewpoints and AffNet requires deep networks, making them less practical. + +We propose a method that jointly exploits cheap-to-extract scale and orientation features for affine rectification. Unlike affine frames, which are costly to compute, scale and orientation features can be detected separately with minimal overhead. Together, they provide complementary constraints, ensuring robustness across diverse image types. The method is flexible, as it can incorporate features from any detector that provides information on either scale or orientation. Our key contributions are as follows: + +- We derive a novel linear constraint that relates variations in orientations to the rectifying homography, expanding the available constraints for affine rectification. +- Building on the proposed constraint, we propose efficient solvers to estimate the homography. +- We propose a hybrid rectification method that can incorporate any type of feature—lines, SIFT keypoints, or other detected structures—as long as they provide scale or orientation information, ensuring broad applicability. + +Our method provides a fast and generalizable method for rectification leveraging scale and orientation constraints. + +# 2. Related Work + +Various methods have been proposed for planar affine rectification, each differing primarily in the assumptions they make about the structure of the imaged scene. These assumptions typically involve the presence and spatial relationships of different features, such as lines, scales, local affine frames, and texture patterns. The general strategy across these methods is to establish correspondences among coplanar features and use them to estimate the projective transformation that best explains their observed distortion. + +Affine rectification is equivalent to finding the projective transformation that maps the vanishing line of a plane to the line at infinity. A widely used approach estimates this transformation by identifying two vanishing points [10], which define the vanishing line and enable rectification. However, detecting vanishing points is challenging. Schaffalitzky et al. [29] proposed a method to locate vanishing points using equidistant parallel lines in the imaged plane. Clark et al. + +[6] extended this idea to document rectification by analyzing 2D projection profiles, identifying the horizontal vanishing point, and using variations in line spacing to infer the vertical vanishing point. Pautrat et al. [25] proposed a method to find orthogonal vanishing points assuming that we have prior knowledge about the up direction in the image. However, line-based methods are sensitive to detection inaccuracies—small errors in line orientations can lead to significant errors in vanishing point estimation. Moreover, they perform poorly in images with dense textures or patterns lacking prominent linear structures (e.g., polka dots). + +Several approaches exploit texture to estimate the vanishing line. Criminisi et al. [7] proposed a method to extract plane vanishing lines from homogeneously textured images. Liu et al. [17] introduced a technique that detects periodic textures by identifying their underlying lattice structure, segmenting the region into equal tiles, analyzing their symmetry group, and extracting representative motifs. Rasmussen [27] focused on road rectification, using dominant texture orientations and a voting mechanism to infer vanishing points in images of poorly structured roads. + +Chum et al. [5] derived a linear constraint that links local-scale variations to the parameters of the rectifying homography. Their method requires three point-and-scale features to estimate the homography, which makes it an efficient alternative to line-based approaches. Scale-based methods are effective when dealing with patterns that contain repeated elements, where scale variations can be reliably estimated. However, they struggle with line-dominated patterns, as linear structures do not provide meaningful scales. In addition, these methods require the grouping of scale features, adding complexity to feature selection. + +Since projective transformations affect the spatial arrangement of repeated elements in an image, several approaches leverage repeated patterns for rectification. Leung et al. [12] grouped such elements into a graph, encoding spatial relationships and using affine transformations between neighboring nodes. Schaffalitzky and Zisserman [28] proposed a method that identifies repeated elements in a plane and estimates a global parametric transformation to recover the vanishing line. Later, they extended this approach to handle nonlinear geometric patterns [29]. Pritts et al. [26] combined scale-based constraints [5] with $\mathrm{MSER} + \mathrm{LAF}$ features to cluster intra-pattern correspondences, leveraging repeated motifs to improve rectification accuracy. A common limitation of these methods is their reliance on complex data structures to track inter-pattern relationships, making them computationally demanding. + +# 3. Rectification with Scales and Orientations + +Geometric Preliminaries. A projectivity, also known as a homography, is an invertible mapping $h(\mathbf{x}) : \mathbb{P}^2 \to \mathbb{P}^2$ that maps lines to lines. It is represented by a non-singular ma + +![](images/baa778fe11c03b8aa1405a04dde041501869dd932e73a43b46ff02bec020ab86.jpg) +Figure 3. Qualitative rectification results using the proposed method with both SIFT features and LSD line segments (SIFT+LSD), using only SIFT orientations and scales, vanishing point estimation from LSD line segments, and local scale estimation from SIFT features [5]. The proposed method with SIFT+LSD consistently outperforms baselines, achieving superior rectification on challenging patterns. + +trix $\mathbf{H} \in \mathbb{R}^{3 \times 3}$ , where $\mathbf{x}$ is a homogeneous vector. The aim of affine rectification is to estimate a homography $\mathbf{H}$ that removes projective distortion, leaving only affine transformations. This can be achieved by finding a homography: + +$$ +\hat {\mathbf {H}} = \left[ \begin{array}{c c c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ h _ {7} & h _ {8} & 1 \end{array} \right], \tag {1} +$$ + +where $h_7$ and $h_8$ are the projective distortion parameters. The goal is to formulate constraints that express local scale and orientation variations as linear equations. + +Rectification via Vanishing Points. Affine rectification can be accomplished by identifying the vanishing line of the imaged plane. This line corresponds to the line at infinity in the rectified image. A standard approach [10] is to find two vanishing points, $\mathbf{v}_1$ and $\mathbf{v}_2$ , each corresponding to the intersection of a different set of parallel lines in the world plane, in order to calculate the vanishing line $\mathbf{l}_{\infty} = \mathbf{v}_1 \times \mathbf{v}_2$ . Given $\mathbf{l}_{\infty} = [a, b, c]^T$ , the homography that maps it to $[0, 0, 1]^T$ (the line at infinity) has $\mathbf{l}_{\infty}$ as its last row. This method depends on reliable parallel lines that may not always be present. + +Rectification via Local Scale Variations. An alternative approach leverages local scale variations. Chum et al. [5] derived a constraint relating the change in the local scale, $\sigma \in \mathbb{R}$ , at a point $(x,y)$ to the parameters of the rectifying homography. The transformed scale, $\sigma^{\prime}$ , is given by $\sigma^{\prime} = \alpha^{3}(h_{7}x + h_{8}y + 1)^{-3}$ , where $\alpha$ is a global affine scale factor. Rearranging this results in a linear constraint: + +$$ +\left[ \begin{array}{c c c} x & y & - \sigma^ {- 1 / 3} \end{array} \right] \left[ \begin{array}{c c c} h _ {7} & h _ {8} & \alpha \end{array} \right] ^ {T} = - 1. \tag {2} +$$ + +At least three such constraints are needed to estimate $h_7$ and $h_8$ . However, this method's success hinges on reliable local-scale estimates and can fail in scenes dominated by linear features where significant scale changes are absent. + +We present a novel method for planar affine rectification that combines local scale and orientation. The objective is to estimate a projectivity $h(\mathbf{x}):\mathbb{P}^2\to \mathbb{P}^2$ , represented by homography $\mathbf{H}\in \mathbb{R}^{3\times 3}$ , that removes projective distortion. Our approach exploits two types of local image features: + +- Scale features: Points $(x,y)$ associated with a relative local scale $\sigma \in \mathbb{R}^{+}$ , indicating the size of the feature. +- Orientation features: Points $(x, y)$ associated with a dominant orientation $\theta \in [0, \pi)$ (line orientations are periodic with period $\pi$ ) of a local image structure. + +For example, SIFT [18] and LAFs [23] provide both. Alternatively, a combination of detectors (e.g., SIFT for scale and a line segment detector for orientation) can be employed. + +# 3.1. Modified Scale Constraint + +We build upon the work of Chum et al. [5], who established a linear relationship between homography $\mathbf{H}$ and the induced local scale change. For a homography, the local-scale transformation at a point $(x,y)$ is: + +$$ +s (\mathbf {H}, x, y) = \det (\mathbf {A}) \left(h _ {7} x + h _ {8} y + 1\right) ^ {- 3}, \tag {3} +$$ + +where $\operatorname{det}(\mathbf{A})$ accounts for the affine scaling. We distinguish between the feature scale $\sigma$ (a property of the detected feature) and the scale change $s$ (a function of the homography), following the notation of [5]. While $\sigma$ is strictly positive, $s$ can be any real number. However, for physically meaningful rectifications, the homography should not + +![](images/497d8e86c41201e86af463a9100517dffdde3db61295d0d94c34673104cc93c7.jpg) +(a) + +![](images/b16f071ea0d6aa7418fb3627feee02b61b0b48f795dee846e42062a656f44a70.jpg) +(b) +Figure 4. Projective transformation of lines with either $h_7$ or $h_8$ set to zero: (a) $h_7 = 0, h_8 = 5 \cdot 10^{-4}$ ; (b) $h_7 = 0, h_8 = 0$ ; (c) $h_7 = 5 \cdot 10^{-4}, h_8 = 0$ . The horizontal or vertical lines remain parallel, with their vanishing point located at infinity. + +![](images/2ea4006b3a4538a1e8f7a6d3955b0310e7c040c3d05ce42590f96ee5b383392d.jpg) +(c) + +map positive scales to zero or negative values. In [5], the scale in the target (rectified) domain is assumed to be unity. Therefore, the observed feature scale $\sigma^{\prime}$ in the input image is related to the scale change by: + +$$ +\sigma^ {\prime} (\mathbf {H}, x, y) = \det (\mathbf {A}) \left(h _ {7} x + h _ {8} y + 1\right) ^ {- 3}. \tag {4} +$$ + +This formulation assumes that $(x,y)$ are coordinates in the affinely rectified plane. However, we only have access to the coordinates in the input image. Let $(x',y')$ be the coordinates in the image, and $(x,y)$ be the corresponding coordinates in the rectified plane. The inverse homography, which maps points from the input image to the rectified plane, is: + +$$ +\hat {\mathbf {H}} ^ {- 1} = \left[ \begin{array}{c c c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - h _ {7} & - h _ {8} & 1 \end{array} \right]. \tag {5} +$$ + +The relationship between the coordinates is: + +$$ +\left[ \begin{array}{l} x \\ y \\ 1 \end{array} \right] \propto \hat {\mathbf {H}} ^ {- 1} \left[ \begin{array}{l} x ^ {\prime} \\ y ^ {\prime} \\ 1 \end{array} \right] = \left[ \begin{array}{c} x ^ {\prime} \\ y ^ {\prime} \\ - h _ {7} x ^ {\prime} + - h _ {8} y ^ {\prime} + 1 \end{array} \right]. \tag {6} +$$ + +Thus, + +$$ +\left[ \begin{array}{l} x \\ y \end{array} \right] = \left(- h _ {7} x ^ {\prime} - h _ {8} y ^ {\prime} + 1\right) ^ {- 1} \left[ \begin{array}{l} x ^ {\prime} \\ y ^ {\prime} \end{array} \right]. \tag {7} +$$ + +Substituting $x$ and $y$ into Eq. (4) and letting $\operatorname{det}(\mathbf{A}) = \alpha^{-3}$ , we obtain $\sigma'(\mathbf{H}, x', y') = \alpha^{-3}(-h_7x' - h_8y' + 1)^3$ . Dropping the primes for simplicity (now using $x$ and $y$ for input image coordinates), and rearranging, we arrive at: + +$$ +\left[ \begin{array}{c c c} x & y & \sigma^ {1 / 3} \end{array} \right] \left[ \begin{array}{c c c} h _ {7} & h _ {8} & \alpha \end{array} \right] ^ {T} = 1. \tag {8} +$$ + +This scale constraint allows us to estimate the rectifying homography from scale variations. To ensure valid solutions, we need $\operatorname{det}(\mathbf{A}) = \alpha^{-3} > 0$ , preventing reflections or degenerate transforms. This is equivalent to requiring $\alpha > 0$ . + +# 3.2. Orientation Constraint + +Derivation of Linear Constraint. We now derive a novel constraint based on local orientation changes induced by the + +homography $\mathbf{H}$ . Consider an orientation feature defined by a point $(x,y)$ and an angle $\theta \in [0,\pi)$ . We represent the corresponding projective line in homogeneous form as: + +$$ +\mathbf {l} (x, y, \theta) = \left[ \begin{array}{l l l} \sin \theta , & - \cos \theta , & y \cos \theta - x \sin \theta \end{array} \right] ^ {T}. \tag {9} +$$ + +Given two orientation features, their associated lines, $\mathbf{l}_1 = \mathbf{l}(x_1,y_1,\theta_1)$ and $\mathbf{l}_2 = \mathbf{l}(x_2,y_2,\theta_2)$ , intersect at a point $\mathbf{v}$ in the input image as: + +$$ +\mathbf {v} = \mathbf {l} _ {1} \times \mathbf {l} _ {2} = \left[ \begin{array}{c} v _ {x} \\ v _ {y} \\ v _ {w} \end{array} \right] = \left[ \begin{array}{c} A _ {2} \cos \theta_ {1} - A _ {1} \cos \theta_ {2} \\ A _ {1} \sin \theta_ {2} - A _ {2} \sin \theta_ {1} \\ \sin \theta_ {2} \cos \theta_ {1} - \sin \theta_ {1} \cos \theta_ {2} \end{array} \right], \tag {10} +$$ + +where $A_{i} = y_{i}\cos \theta_{i} - x_{i}\sin \theta_{i}, i\in \{1,2\}$ . After rectification by $\hat{\mathbf{H}}^{-1}$ , we assume that these lines become parallel. Thus, their intersection $\mathbf{v}$ is a vanishing point, which must lie on the vanishing line, defined by $\mathbf{l} = \left[-h_7 - h_8\quad 1\right]^T$ . The condition that $\mathbf{v}$ lies on $\mathbf{l}$ gives us the constraint $\mathbf{v}^T\mathbf{l} = 0$ . By rearranging, and including $\alpha$ in the equation to maintain consistency with the scale constraint in Eq. (8), we obtain a constraint linear in the homography parameters: + +$$ +\left[ \begin{array}{l l l} v _ {x} & v _ {y} & 0 \end{array} \right] \left[ \begin{array}{l l l} h _ {7} & h _ {8} & \alpha \end{array} \right] ^ {T} = v _ {w}. \tag {11} +$$ + +This orientation constraint provides additional information to constrain the homography. + +Normalization Considerations. It is common to normalize homogeneous coordinates $\mathbf{v} = [v_x, v_y, v_w]^T$ by setting $v_w = 1$ (for finite points). However, normalization can lead to numerical instability in the context of Eq. (11). + +Consider a scenario in which the image is affected by a projective distortion where $h_7$ or $h_8$ is close to zero (e.g., the images in Fig. 4). In such cases, the vanishing point associated with certain orientation features might lie far from the origin, even at infinity. If the feature detector introduces small errors in orientation estimation, the computed $v_w$ can become small but non-zero (i.e., $0 < |v_w| \ll 1$ ). The distance from the vanishing point $\mathbf{v}$ to the vanishing line $\mathbf{l}$ is $d(\mathbf{v}, \mathbf{l}) = |-v_xh_7 - v_yh_8 + v_w|$ . If we normalize $\mathbf{v}$ to $\hat{\mathbf{v}} = \mathbf{v} / v_w$ , the distance becomes: + +$$ +d (\hat {\mathbf {v}}, \mathbf {l}) = \left| - \frac {v _ {x}}{v _ {w}} h _ {7} - \frac {v _ {y}}{v _ {w}} h _ {8} + 1 \right|. \tag {12} +$$ + +Observing that $d(\mathbf{v}, \mathbf{l}) = |v_w| \cdot d(\hat{\mathbf{v}}, \mathbf{l})$ and $|v_w| < 1$ , we can conclude that the normalization amplifies the numerical error, since $d(\mathbf{v}, \mathbf{l}) < d(\hat{\mathbf{v}}, \mathbf{l})$ . However, empirically, normalizing each vanishing point by the maximal of the absolute values of its coordinates stabilizes the overdetermined solution (Eq. (14)). Thus, we always divide by the maximal element of $|v_x|, |v_y|$ , and $|v_w|$ . + +# 3.3. Hybrid Homography Estimation + +A minimal solver requires the fewest constraints necessary to uniquely determine the parameters $h_7$ , $h_8$ and $\alpha$ . We propose a solver that combines scale and orientation: + +- Two scale features: $(x_{1},y_{1},\sigma_{1})$ and $(x_{2},y_{2},\sigma_{2})$ , each contributing a constraint via Eq. (8). +- Two orientation features: Defining a vanishing point $\mathbf{v} = [v_x, v_y, v_w]^T$ , providing a constraint via Eq. (11). + +This leads to the following $3 \times 3$ linear system: + +$$ +\mathbf {A} = \left[ \begin{array}{l l l} x _ {1} & y _ {1} & \sigma_ {1} ^ {1 / 3} \\ x _ {2} & y _ {2} & \sigma_ {2} ^ {1 / 3} \\ v _ {x} & v _ {y} & 0 \end{array} \right], \mathbf {x} = \left[ \begin{array}{l} h _ {7} \\ h _ {8} \\ \alpha \end{array} \right], \mathbf {b} = \left[ \begin{array}{l} 1 \\ 1 \\ v _ {w} \end{array} \right]. \tag {13} +$$ + +This system is solvable, providing a unique estimate for $\{h_7,h_8,\alpha \}$ , except for degenerate cases (which are discussed in the supplementary material). + +There are two alternative solver configurations. One may use three scale features and their corresponding constraints (Eq. (8)) to obtain a $3 \times 3$ system. This is equivalent to the method of [5]. It is also possible to exploit two pairs of orientation features as they define two distinct vanishing points, leading to two constraints of the form in Eq. (11). This eliminates the need to estimate $\alpha$ , reducing the system to two equations in two unknowns ( $h_7$ and $h_8$ ). However, the vanishing points must be distinct; an arbitrary selection of orientation features will not, in general, lead to a valid solution. This is equivalent to the line-based solution. + +Overdetermined Solver. When more than the minimal number of constraints are available, the system becomes overdetermined. Let $n \geq 2$ be the number of scale features and $m \geq 1$ be the number of vanishing points derived from orientation features. We can then formulate an LS solution to estimate $\{h_7, h_8, \alpha\}$ . The overdetermined system consists of $n + m$ linear equations, represented as $\mathbf{A}\mathbf{x} = \mathbf{b}$ , where $\mathbf{A} \in \mathbb{R}^{(n + m)\times 3}$ and $\mathbf{b} \in \mathbb{R}^{(n + m)}$ as follows: + +$$ +\mathbf {A} = \left[ \begin{array}{c c c} x _ {1} & y _ {1} & \sigma_ {1} ^ {1 / 3} \\ \vdots & \vdots & \vdots \\ x _ {n} & y _ {n} & \sigma_ {n} ^ {1 / 3} \\ v _ {x} ^ {(1)} & v _ {y} ^ {(1)} & 0 \\ \vdots & \vdots & \vdots \\ v _ {x} ^ {(m)} & v _ {y} ^ {(m)} & 0 \end{array} \right], \quad \mathbf {b} = \left[ \begin{array}{c} 1 \\ \vdots \\ 1 \\ v _ {w} ^ {(1)} \\ \vdots \\ v _ {w} ^ {(m)} \end{array} \right]. \tag {14} +$$ + +Here, $\{(x_i,y_i,\sigma_i)\}_{i = 1}^n$ represents the set of $n$ scale features, and $\{\mathbf{v}^{(j)} = [v_x^{(j)},v_y^{(j)},v_w^{(j)}]^T\}_{j = 1}^m$ represents the set of $m$ vanishing points derived from the orientation features. If we have $k\geq 2$ orientation features, we can generate up to $\binom{k}{2}$ candidate vanishing points by taking all pairwise intersections of the corresponding lines. + +The least-squares solution is obtained using the Moore-Penrose pseudo-inverse as $\left[h_7\quad h_8\quad \alpha \right]^T = \mathbf{A}^\dagger \mathbf{b}$ , where $\mathbf{A}^{\dagger}$ is the pseudo-inverse of $\mathbf{A}$ . This approach provides a robust estimate of the rectifying homography parameters, even with noisy or redundant constraints. + +# 4. Robust Estimation with Hybrid RANSAC + +Detecting features in images is inherently noisy, and real-world images often contain several planar regions. Thus, robustly estimating the projective transformation is essential. Conventional RANSAC frameworks [1, 3, 9] generally focus on a single feature type, which does not suffice for our approach that employs both scale and orientation features. The hybrid RANSAC framework in [16] uses both point and line features for 3D scene reconstruction. We propose a similar hybrid framework that combines scale and orientation features to reliably estimate the rectifying homography. These hybrid frameworks differ from [4], which uses a single feature type with multiple minimal solvers. + +# 4.1. Geometrically Meaningful Residuals + +We define a model as $\mathcal{M} = (h_7, h_8, \alpha)$ , where $h_7$ and $h_8$ are the parameters of the (warping) homography $\hat{\mathbf{H}}$ , and $\alpha$ is the global scale factor related to the affine part of the decomposition $\mathbf{H} = \mathbf{A}\hat{\mathbf{H}}$ , with $\operatorname*{det}(\mathbf{A}) = \alpha^{-3}$ . For a model $\mathcal{M}$ , we compute residuals for both scale and orientation features to quantify their agreement with the model. + +Residual for Scale Features. Given the rectifying homography $\hat{\mathbf{H}}^{-1}$ , the local scale change at a point $(x,y)$ is: + +$$ +s (x, y; \hat {\mathbf {H}} ^ {- 1}) = (- h _ {7} x - h _ {8} y + 1) ^ {- 3}. \tag {15} +$$ + +For a scale feature $(x,y,\sigma)$ , the rectified scale $\sigma'$ under model $\mathcal{M}$ is as follows: + +$$ +\begin{array}{l} \sigma^ {\prime} (x, y, \sigma ; \hat {\mathbf {H}} ^ {- 1}) = s (x, y; \hat {\mathbf {H}} ^ {- 1}) \cdot \sigma \tag {16} \\ = (- h _ {7} x - h _ {8} y + 1) ^ {- 3} \sigma . \\ \end{array} +$$ + +Inliers are expected to have a rectified scale close to the global scale, $\sigma^{\prime}\approx \alpha^{-3}$ . The residual function is defined as: + +$$ +\begin{array}{l} r _ {\sigma} (x, y, \sigma ; \mathcal {M}) = \left| \log \left(\frac {\sigma^ {\prime} (x , y , \sigma ; \hat {\mathbf {H}} ^ {- 1})}{\alpha^ {- 3}}\right) \right| \tag {17} \\ = \left| \log \left(\alpha^ {3} (- h _ {7} x - h _ {8} y + 1) ^ {- 3} \sigma\right) \right| \\ \end{array} +$$ + +A feature is labeled an outlier if $\sigma' \leq 0$ , as this is physically impossible. The log-scale ensures symmetry: if $\sigma' = c \cdot \alpha^{-3}$ or $\sigma' = \frac{1}{c} \cdot \alpha^{-3}$ for $c \geq 1$ , the residual is the same. + +Residual for Orientation Features. To compute orientation residuals, we analyze how local orientations transform under the homography $\hat{\mathbf{H}}^{-1}$ . Following [5], we consider the Jacobian of the homography. Let $h^{-1}(\mathbf{x})$ be the mapping from the input image coordinates $\mathbf{x} = [x,y]^T$ to the rectified coordinates $\mathbf{x}' = [x',y']^T$ as follows: + +$$ +\left[ \begin{array}{l} x ^ {\prime} \\ y ^ {\prime} \end{array} \right] = h ^ {- 1} (x, y) = \left(- h _ {7} x - h _ {8} y + 1\right) ^ {- 1} \left[ \begin{array}{l} x \\ y \end{array} \right]. \tag {18} +$$ + +The Jacobian of $h^{-1}$ is: + +$$ +\mathbf {J} _ {h ^ {- 1}} (x, y) = \lambda \left[ \begin{array}{c c} - h _ {8} y + 1 & h _ {8} x \\ h _ {7} y & - h _ {7} x + 1 \end{array} \right], \tag {19} +$$ + +where $\lambda = (-h_7x - h_8y + 1)^{-2}$ is a coefficient that we can omit for the purpose of this derivation. Given an orientation $\theta$ at $(x,y)$ , the transformed orientation $\theta'$ in the rectified image is obtained by applying the Jacobian to a unit vector in the direction of $\theta$ as follows: + +$$ +\left[ \cos \theta^ {\prime}, \quad \sin \theta^ {\prime} \right] ^ {T} \propto \mathbf {J} _ {h ^ {- 1}} (x, y) \left[ \cos \theta , \quad \sin \theta \right] ^ {T}, \tag {20} +$$ + +giving + +$$ +\theta^ {\prime} = \arctan \frac {\sin \theta - h _ {7} (x \sin \theta - y \cos \theta)}{\cos \theta + h _ {8} (x \sin \theta - y \cos \theta)}. \tag {21} +$$ + +For an orientation feature $(x,y,\theta)$ , the residual is the difference of the rectified orientation $\theta^{\prime}$ and the expected orientation $\phi$ (derived from the vanishing point). Since orientations are periodic with period $\pi$ , we use $\psi(x) = 2x \pmod{2\pi}$ . The residual used in RANSAC is as follows: + +$$ +r _ {\theta} (x, y, \theta ; \mathcal {M}) = \min \left(s \left(\theta^ {\prime}, \phi\right), 2 \pi - s \left(\theta^ {\prime}, \phi\right)\right), \tag {22} +$$ + +where $s(\theta', \phi) = \frac{1}{2} |\psi(\theta') - \psi(\phi)|$ , and $\theta'$ is computed using Eq. (21). This measures the angular difference as an arc length, making thresholds directly interpretable in radians. + +# 4.2. Scoring Function for Model Comparison + +We use robust scoring [31] to evaluate candidate models within RANSAC. Given a model $\mathcal{M}$ , residuals $r_{\sigma}$ and $r_{\theta}$ , and inlier thresholds $T_{\sigma} > 1$ and $T_{\theta} > 0$ , we define inlier sets $S_{\sigma} = \{(x,y,\sigma) \mid r_{\sigma}(x,y,\sigma; \mathcal{M}) \leq T_{\sigma}\}$ and $S_{\theta} = \{(x,y,\theta) \mid r_{\theta}(x,y,\theta; \mathcal{M}) \leq T_{\theta}\}$ . Each inlier score is a truncated quadratic of its residual: + +$$ +s _ {\sigma} (x, y, \sigma ; \mathcal {M}) := 1 - \left(\frac {r _ {\sigma} (x , y , \sigma ; \mathcal {M})}{T _ {\sigma}}\right) ^ {2} \tag {23} +$$ + +and $s_{\theta}$ is calculated similarly. These scores range from 0 to 1. The overall model score $s(\mathcal{M})$ is the sum of its inliers' scores. It ranges from 0 (worst) to $|S_{\sigma}| + |S_{\theta}|$ (perfect fit). We select the model with the highest score, i.e., given two models, $\mathcal{M}_1$ and $\mathcal{M}_2$ , we prefer the former if $s(\mathcal{M}_1) > s(\mathcal{M}_2)$ . + +# 4.3. Multiple Scale Feature Classes + +Images can display $k \geq 2$ scale feature classes, each with a unique real-world scale $\sigma_{i}$ , where $1 \leq i \leq k$ . An affine transformation $\mathbf{A}$ uniformly rescales all features, such that, in the rectified image, the scale for the $i$ -th class features becomes $\sigma_{i} \cdot \operatorname*{det}(\mathbf{A}) = \sigma_{i} \alpha^{-3}$ . Despite the unknown relative scale differences between $\sigma_{1}, \ldots, \sigma_{k}$ , all scales can be used together to estimate the homography. We define $k$ parameters, $\alpha_{1}, \ldots, \alpha_{k}$ , one for each feature class, where $\alpha_{i} = \sigma_{i}^{-1/3} \alpha$ accounts for the relative scale of class $i$ , including the shared homography parameters $h_{7}$ and $h_{8}$ . + +Each class $i$ provides at least one constraint (Eq. (8)) involving $\alpha_{i}$ . Furthermore, at least one orientation constraint (Eq. (11)) is necessary. This configuration results in $k + 2$ unknowns and at least $k + 1$ constraints, requiring one additional scale constraint from any scale feature class to fully determine the system. Assuming, without loss of generality, that the extra scale constraint comes from the first class $(\alpha_{1})$ , the resulting linear system $\mathbf{A}\mathbf{x} = \mathbf{b}$ is as follows: + +$$ +\mathbf {A} = \left[ \begin{array}{c c c c c c c} x _ {1} & y _ {1} & \sigma_ {1} ^ {1 / 3} & 0 & \dots & 0 & 0 \\ x _ {2} & y _ {2} & 0 & \sigma_ {2} ^ {1 / 3} & \dots & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots & & \vdots & \vdots \\ x _ {k} & y _ {k} & 0 & 0 & \dots & 0 & \sigma_ {k} ^ {1 / 3} \\ x _ {k + 1} & y _ {k + 1} & \sigma_ {k + 1} ^ {1 / 3} & 0 & \dots & 0 & 0 \\ v _ {x} & v _ {y} & 0 & 0 & \dots & 0 & 0 \end{array} \right] \tag {24} +$$ + +where $\mathbf{x} = [h_7, h_8, \alpha_1, \alpha_2, \ldots, \alpha_k]^T$ is the vector of unknowns, $\mathbf{b} = [1, \ldots, 1, v_w]^T$ is the inhomogeneous part, $(x_i, y_i, \sigma_i)$ for $i = 1 \ldots k$ represents a scale feature from the $i$ -th class, and $(x_{k+1}, y_{k+1}, \sigma_{k+1})$ provides the additional scale constraint (assumed to be from class 1). Vanishing point $\mathbf{v} = [v_x, v_y, v_w]^T$ comes from the orientation constraint. Vector $\mathbf{b}$ has $k + 1$ entries of 1, followed by $v_w$ . This formulation requires pre-classification of scale features. However, this is often impractical. We propose an iterative strategy instead: + +1. Initial Estimation: Run hybrid RANSAC (Section 4) using all scale features $S_{\sigma}$ and all orientation features $S_{\theta}$ . This yields initial inlier sets $S_{\sigma}^{(1)}$ and $S_{\theta}^{(1)}$ . +2. Iterative Refinement (for $i = 1$ to $k - 1$ ): Store the current inlier sets $S_{\sigma}^{(i)}$ and $S_{\theta}^{(i)}$ . Rerun the hybrid RANSAC, using only scale features not yet assigned to a class $(S_{\sigma} \setminus \bigcup_{j=1}^{i} S_{\sigma}^{(j)})$ and the orientation features from the previous iteration's inlier set, $S_{\theta}^{(i)}$ . This yields new inlier sets $S_{\sigma}^{(i+1)}$ and $S_{\theta}^{(i+1)}$ . +3. Final System: After $k - 1$ iterations, we have $k$ disjoint scale inlier sets, $S_{\sigma}^{(1)}, \ldots, S_{\sigma}^{(k)}$ , and a nested sequence of orientation inlier sets, $S_{\theta}^{(k)} \subseteq \dots \subseteq S_{\theta}^{(1)}$ . We construct the final system (Eq. (24)) using the $k$ scale inlier sets and the smallest orientation inlier set, $S_{\theta}^{(k)}$ . + +# 4.4. Sample Degeneracy and Inaccuracy Test + +We identify two degenerate sample configurations in the supp. material that lead to singular solutions that can be easily detected. Here, we introduce a quick test for inaccurate, albeit non-degenerate, models. A valid minimal sample of two scale and two orientation features, forming four 2D points $S = \{(x_i,y_i)\}_{i=1}^4$ , should lie on a plane $\mathcal{P}$ . According to [5], in a pinhole camera model, the vanishing line of $\mathcal{P}$ should not intersect the convex hull $\operatorname{Conv}(S)$ . Hence, if the vanishing point $\mathbf{v}$ , derived from the orientation features (Eq. (10)), falls within $\operatorname{Conv}(S)$ , it is best to discard + +![](images/0a51dbc699562ced46e041ab3635c448fc093eb99d9ba172496e38e351224251.jpg) +(a) + +![](images/5bd1e631d4688bbbb5da55fb881bdfba674cb9b13c6fea14de3170fb5338d1ce.jpg) +(b) +Figure 5. Base patterns for data generation: (a) checkerboard, (b) polka-dot, and (c) linear. The images shown are undistorted, without projective transformation. + +![](images/a391ef0915e2ce5948be7ffacdd1e7fbea8a6130025d94bb40ee092c7aeb33dc.jpg) +(c) + +the sample. Filtering out degenerate and unreliable samples accelerates RANSAC and improves homography estimation by avoiding poor feature configurations. + +# 5. Experiments + +Metrics. Given a homography $\mathbf{H}$ and its estimate $\tilde{\mathbf{H}}$ , we define the affine rectification error for a point $(x,y)\in \mathbb{P}^2$ as $e(x,y) = \sqrt{(x - \tilde{x})^2 + (y - \tilde{y})^2}$ , where $(\tilde{x},\tilde{y})$ is the transformation of $(x,y)$ under $\tilde{\mathbf{H}}^{-1}\mathbf{H}$ . A perfect estimate, i.e., $\tilde{\mathbf{H}} = \mathbf{H}$ , yields $e(x,y) = 0$ for all pixels $(x,y)$ . + +To evaluate affine rectification methods, we compute the average error over a set $S$ of sampled pixels in an $800 \times 600$ image $I$ . Given a known homography $\mathbf{H}$ applied to $I$ , and its estimation $\tilde{\mathbf{H}}$ , the error is: $e(I) = \frac{1}{|S|} \sum_{(x,y) \in S} e(x,y)$ . We construct $S$ using pixels at intervals of 50 pixels in both dimensions, i.e., $x \in \{0, 50, 100, \ldots, 800\}$ and $y \in \{0, 50, 100, \ldots, 600\}$ . + +Baselines. We compare our method against the standard vanishing point-based estimator from GC-RANSAC library [1, 2]. Furthermore, we integrate our approach and the solver from [5] into the same framework, ensuring consistency across all pipeline elements. + +Data Pre-processing. We extract scale and orientation features using the SIFT [18] detector as implemented in OpenCV. Line features are obtained using the LSD [32] algorithm, also from OpenCV. + +Data Generation. We evaluate our method on three types of patterns, visualized in Fig. 5. The first is a checkerboard pattern that contains both dominant line features and strong scale features, making it suitable for all methods. The second is a polka-dot pattern, which provides strong scale features but lacks orientation cues. The third consists of orthogonal line segments, simulating cases where no strong scale features are available. + +Each pattern is transformed by a homography as described in Eq. (1). For evaluation, we sample $h_7$ and $h_8$ within the range $[-0.2, 0.2]$ with a step size of $2 \times 10^{-5}$ and run 100 independent tests per setting to account for the randomness in robust estimation. Gaussian blurring in then applied with a $11 \times 11$ kernel ( $\sigma = 1.5$ ) to simulate more realistic conditions. + +![](images/8dcddb79ac8074f96e08cf011c792e7bf0055298317b6d3cab98805ad94c981d.jpg) + +![](images/4ae5001836b48dedcbb4352c415a98d82e1740022bd1b972d2ab4d86407285bd.jpg) + +![](images/c98842a67a6848091c6c2270008516d463a382af7ba5472bfd5ba59958d6b16f.jpg) + +![](images/c8a401b60fa7cd457b6ef938fe3e057d6fa1d81e4d547b53f421f10d8ef9fc65.jpg) + +![](images/137c170fc7b89d98c144479f935e65773e16062fc16c41bab793db3fdbbe0319.jpg) + +![](images/e2bdd92a51be55405e1230165d8bd704e68a3a5441b5ef454c3400e6ccec3abf.jpg) + +![](images/636e9f268471dc416e83cdccffbca971a935efce1b6c7b91bf7dbcc4fdd29a2a.jpg) + +![](images/104b937c890084ddeee8af6faec91451c0a6e4e22948e74575235e6b74530675.jpg) + +![](images/af3bdd7a1c14475a4510619a4330550e0c510e25469161b10c30595ed4ce4544.jpg) + +![](images/9a2f39b6f87067a97720954608c8151c6440cc96f8abb6baec9fea4310514234.jpg) +Figure 6. Results per pattern and estimation method. Columns (left to right): checkerboard, polka-dot, and linear patterns. Rows (top to bottom): proposed method with SIFT + LSD features, with SIFT features, vanishing points estimation, and scale-based estimation. 3D surface plots represent the median error across 100 iterations for each pair $(h_7, h_8)$ . Median error values exceeding 0.1 are truncated for better visualization. + +![](images/ca4f37c675390ce0c7a0c978b045089c7006c054c98b5e13ef7596009575ce71.jpg) + +![](images/0ed20014ac27629437ca89f6b48e2aef70cc7b1efd9688bcef0751b5480fbc1b.jpg) + +Results are shown in Fig. 6, with each column representing a pattern: (1) checkerboard, (2) polka-dot, and (3) line segments. Each row corresponds to a different method, with the top row showing the proposed hybrid approach that integrates SIFT features [18] and LSD line segments [32]. As expected, the scale-based method of [5] performs well on patterns with observable scale features (i.e., checkerboard and polka-dot) but fails on line-based patterns. Conversely, the line-based method excels when strong orientation features are present (i.e., checkerboard and linear pattern), but fails on the polka-dot pattern. Our method without line features behaves similarly to Chum et al. [5], performing well only when scale features are present. This is expected as SIFT alone struggles with purely line-based patterns. When integrating both point and line features, the proposed hybrid method achieves robustness across all patterns, matching the accuracy of the best method for each case. This highlights the strength of our hybrid approach for rectifying diverse patterns in the real world. + +In Fig. 7, we present recall curves as a function of the error threshold, defined as the ratio of the projection error to the diagonal length of the image. The results align with previous observations: each method performs well when applied to its preferred pattern but fails on others. In contrast, the proposed hybrid approach consistently matches + +![](images/2c7902a1ceff7ed7109bb449f29a30b8faa4e105904ce91f6c964f46c3c72c7d.jpg) +(a) + +![](images/611b82949f31bade1ec6501bdbae6749ded93368975acee134bec50475c8b1a6.jpg) +(b) + +![](images/813b4543db993ec7113b30cdf23b2a406a871d4cda068883358832a15e1f5c13.jpg) +(c) + +![](images/e777c6a1fd6fb33e19d90e26a05a1ad3085484ec182bf8f1ce4aedae9a495957.jpg) +Figure 7. Recall plots showing the ratio of median errors on (a) checkerboard, (b) polka-dot, and (c) linear patterns. The error is computed as the ratio of rectification error to the image diagonal. The horizontal axis represents the error threshold, while the vertical one indicates the ratio of errors below the threshold. Curves close to the top-left corner signify high accuracy. + +![](images/3f40c37c52f71608dd5e7709073d45b6a467580835c6ef9ea97e460f69bc1c4d.jpg) +Figure 8. Multiscale Results. Left to right: undistorted pattern with two scale classes, error plot from the proposed method, error plot from the method of Chum et al. [5]. Both plots depict the median error over 100 iterations for each $(h_7, h_8)$ pair + +![](images/3b4f0024805a9c17f6444fc925c7652056f899b68775a92ae83462418d929e50.jpg) +Figure 9. Results using the proposed method, with scale and orientation features from SuperPoint [8] + SelfScaleOri [11], combined with line segment orientations from DeepLSD [24]. All plots depict the median error over 50 iterations for each $(h_7, h_8)$ pair. + +![](images/57472fcdf2ee8dace8cc59558903c8795a38be0daaaf59c2964ed1a11e1ecf1f.jpg) + +![](images/ad737802102da1652928b03ef6c5540cf606e87e64b093ea781521d203f46cc8.jpg) + +![](images/01e8465f6b2cfe1c3c8dbc4b3d8a0737d15d6516e37d485b92c3db10f89ae0a9.jpg) + +the accuracy of the best-performing method for each pattern, demonstrating its robustness. + +Multi-Scale Experiments. Fig. 8 presents results for patterns with two scale classes. We compare against the method of Chum et al. [5], which we adapt within the proposed multi-scale framework (Sec. 4.3) for applicability. Both methods achieve good accuracy in this multi-scale setting, but the proposed hybrid estimation reduces high-error peaks, demonstrating improved robustness. + +Learned Detectors. Fig. 9 presents results using orientation and scale features detected by a combination of SuperPoint [8] and SelfScaleOri [11], with line features extracted using DeepLSD [24]. Although the rectifications appear to be reasonably stable, these learned features prove less effective for rectification than SIFT [18], as indicated by the superior performance observed in other experiments. + +Real-World Experiments. This section presents qualitative rectification results on real-world images. Quantitative evaluation is not provided because of the lack of datasets containing pattern images with corresponding ground-truth distortions. Fig. 3 shows input images alongside their rectified counterparts produced by the tested methods. The proposed approach consistently achieves accurate rectification, as evidenced by previously distorted parallel lines becom + +ing truly parallel. While baseline methods perform well in some cases, they fail in others (e.g., the vanishing point-based approach fails on the Star Wars text, and the scale-based method fails on the building facade). + +# 6. Conclusion + +We presented a novel planar affine rectification method that exploits local scale and orientation changes under projective distortion. By deriving a new linear constraint on orientations and integrating it with an existing scale constraint, we formulated an efficient LS solution requiring only two scale and two orientation features, readily obtainable from standard detectors like SIFT. Our approach imposes no feature segmentation, inter-feature dependencies, or geometric assumptions, making it more flexible than prior methods. We achieve robust rectification across diverse patterns by combining point- and line-based constraints. Experiments confirm its superior accuracy and reliability, further enhanced by a tailored RANSAC framework that filters degenerate samples. The method works with any detector providing scale or orientation. + +Acknowledgment. This work was supported by an ETH Zurich Career Seed Award. + +# References + +[1] D. Barath and J. Matas. Graph-cut RANSAC. In Proc. IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2018. 5, 7 +[2] D. Barath and J. Matas. Progressive-x: Efficient, anytime, multi-model fitting algorithm. In Proc. IEEE/CVF Int. Conf. Comput. Vis. (ICCV), 2019. 7 +[3] D. Barath, J. Noskova, M. Ivashechkin, and J. Matas. MAGSAC++, a Fast, Reliable and Accurate Robust Estimator. In Proc. of the IEEE/CVF Conf. Comput. Vis. Pattern Recog. (CVPR), pages 1304-1312, 2020. 5 +[4] F. Camposeco, A. Cohen, M. Pollefeys, and T. Sattler. Hybrid Camera Pose Estimation. In Proc. IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), pages 136-144, 2018. 5 +[5] O. Chum and J. Matas. Planar Affine Rectification From Change Of Scale. In Computer Vision - ACCV 2010, pages 347-360, Berlin, Heidelberg, 2011. 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Recent methods formulate this problem as 2D pixel-level segmentation through convolutional networks or query-based architectures, which purely rely on 2D pixel features while neglecting the inherent 3D spatial nature of planar surfaces. To address this limitation, we propose an end-to-end Plane Reconstruction, Aggregation, and Splatting (PlaneRAS) framework that explicitly leverages 3D geometric reasoning combined with online planar primitive reconstruction. Our framework introduces two core components: 1) a reconstruction module utilizing customized planar primitives to compactly represent 3D scene, and 2) a recovery module that aggregates local primitives to derive globally consistent plane instances. The proposed 3D-aware representation enables direct integration of pretrained geometric priors, significantly enhancing performance beyond conventional 2D-centric approaches. Extensive experiments on ScanNet and NYUv2 datasets demonstrate state-of-the-art results across various evaluation metrics, resulting from our explicit 3D geometric modeling and effective fusion of cross-dimensional features. + +# 1. Introduction + +3D plane recovery from a single image is a fundamental task in 3D scene understanding [3, 12, 15, 19, 26, 31, 36]. The goal of this task is to detect 3D plane instances existing in an image, which usually comprises predicting the plane parameters and corresponding segmentation masks. The reconstructed planes serve as the simplified proxies of the whole scene and facilitates various applications, such as robotics navigation [33, 39, 45], augmented reality [24], and autonomous driving systems [5]. + +Early methods rely heavily on hand-crafted features [12, 15, 19] to extract explicit geometric elements [2, 9, 12, 26, 31] and infer plane instances based on strong assump- + +![](images/f0cbc4de7439196c9c2309e35883522dc05a04b7829cae17ab873d5bf7fbae9b.jpg) +Conventional Implicit Query-Based Framework +Figure 1. Comparisons of our PlaneRAS framework with existing implicit query-based methods. Most existing methods treat 3D plane recovery as a pixel-level instance segmentation problem, which ignores the 3D structural prior of the scene. Differently, we propose to reconstruct explicit planar primitives and aggregate them in the 3D space. We then splat them onto the image plane to obtain per-pixel plane masks using our designed plane kernel. Our framework facilitates the integration of 3D structural knowledge. + +tions [2, 9, 12, 26]. However, they demonstrated limited adaptability in complex real-world scenarios due to inherent technical constraints. The advent of neural networks has revolutionized this field through end-to-end learning frameworks. PlaneNet [27] pioneered deep learning-based solutions by proposing a Convolutional Neural Network (CNN) architecture that simultaneously segments planar instances and regresses plane parameters from monocular images, while establishing the widely adopted ScanNet-plane benchmark. Building upon this foundation, PlaneRCNN [28] extended the Mask-RCNN [17] framework to overcome the limitation of fixed plane number prediction through dynamic instance segmentation. Recent transformer-based architectures have introduced new paradigms for planar recovery. PlaneTR [40] adapted the DETR [4] framework by integrating a line segment detection branch to enhance geometric consistency in plane segmentation. PlaneRecTR [37] further advances this direction through a unified transformer architecture that jointly optimizes plane detection, segmentation, and parameter regression tasks. The above methods typically conduct plane re + +covery prediction leveraging convolution or attention mechanism based 2D image features. Despite some progress, the 2D cues available in single images remain fundamentally insufficient to accurately characterize real-world 3D spatial configurations, particularly considering that planar surfaces inherently possess holistic 3D structural properties. + +To address this, we propose an end-to-end Plane Reconstruction, Aggregation, and Splatting (PlaneRAS) framework to explicitly reconstruct planar primitives in the 3D space, as shown in Figure 1. Our core insight is to reconstruct the complete 3D scene with a set of local planar primitives and simultaneously perform 3D plane instance segmentation on the primitives. Specifically, we initialize a set of planar primitive queries with extracted depth information and use image cross-attention to update them with visual information. We then assign each local plane to its most similar cluster centroid in the 3D space through similarity metric analysis. To obtain 2D image plane segmentation masks, we design a customized plane kernel to project 3D planes onto 2D images through plane splatting. Extensive experiments on the public ScanNet and NYUv2 datasets demonstrate that our PlaneRAS outperforms existing methods by lifting pixel features into an explicit 3D representation space. Notably, the explicit 3D plane representation inherently facilitates the integration of prior knowledge from readily available 3D pre-trained models, which enables our method to surpass existing baseline performance by significant margins across multiple evaluation metrics. + +# 2. Related Work + +Single-View Plane Recovery. Early works on single-view plane recovery often rely on strong prior assumptions, such as the Manhattan World hypothesis [9, 13], or manually extracted geometric cues to infer the distribution of planes [2, 9, 25, 31, 35, 49]. These methods struggle to adapt to the complex real world, significantly limiting their practical applicability. With the advent and rapid progression of neural networks [16, 17], learning-based method has demonstrated remarkable generalizability, significantly surpassing traditional approaches in an end-to-end manner [27, 28, 48]. PlaneNet [27] pioneered the application of convolutional networks for end-to-end plane prediction and introduced the Scannet-Plane dataset. However, due to the inherent limitations of convolutional architectures, it was constrained to predicting a fixed number of planes. PlaneRCNN [28] addressed this limitation by adopting Mask-RCNN [17] instance segmentation framework to extract plane segmentation masks, thus overcoming the fixed plane prediction constraint. Recently, with the emergence of query-based learning paradigms, researchers have begun applying these techniques to plane recovery tasks [4, 7]. For example, PlaneTR [40] utilizes learnable queries to detect potential planes and estimate their parameters, while incor + +poring line priors from a pretrained line segment model. PlaneRecTR [37] proposed a unified query approach to integrate multiple plane-related subtasks, achieving superior performance through multi-task collaboration. + +Despite significant improvements in existing methods, we find that current methods directly employ the 2D feature maps to infer the plane information without utilizing any spatial priors, which is suboptimal for accurately capturing the 3D structure of scenes. Thus we propose a new framework to reconstruct and perceive the scene at the same time, enabling the integration of explicit spatial constrains to facilitate the performance of both stages. + +Offline Plane Reconstruction. Different from generalizable methods, offline plane reconstruction approaches perform per-scene optimization to recover planar structures [6, 18, 42, 44, 46, 47, 51]. These methods typically follow a reconstruction-clustering paradigm, where a detailed 3D representation of the entire scene is first constructed, followed by plane instance extraction via geometric clustering [18, 42, 44]. With the advancement of Neural Radiance Fields (NeRF) [32] in recent years, several works such as PlanarNeRF [6] and NeuralPlane [47] have extended NeRF to support planar representations. These approaches typically introduce a semantic branch into the NeRF architecture to render plane instance masks. By leveraging differentiable volume rendering, they enable 2D annotations to be backpropagated into the 3D space, thus supporting plane mask rendering from novel viewpoints. + +However, NeRF-based methods suffer from two fundamental limitations: computationally intensive rendering and the lack of explicit 3D geometric representations [6, 14, 47]. These inherent constraints have motivated recent research to explore alternative strategies for 3D scene parameterization [18, 41, 53]. MonoPlane [53] leverages monocular geometric cues extracted from pre-trained models [10] and sequentially fits each plane instance using a proximity-guided RANSAC framework [1, 11]. PlanarSpatting [41] and Planar Gaussian Spatting [50] incorporate recent advances in 3D Gaussian Spatting (3D-GS) [23] to enable faster scene reconstruction and real-time inference. Nevertheless, such geometry-driven clustering approaches depend heavily on iterative optimization and precise geometric reconstruction, while inherently lacking semantic awareness. In contrast, our framework enables feed-forward plane recovery by combining semantics-aware image features with online 3D-aware clustering. + +# 3. Proposed Approach + +In this section, we elaborate on our PlaneRAS framework. Section 3.1 presents the comprehensive architecture of the framework. Section 3.2 details our planar primitive reconstruction pipeline. Section 3.3 introduces the deep aggregation strategy to optimize the final plane predictions. + +![](images/929ae71677a575186dd43ce788d1ee5d6f729a3ec930e87f27a1ddf873a4c85c.jpg) +Figure 2. Our PlaneRAS mainly consists of four stages: (1) Image feature extraction to extract multi-scale features; (2) Planar primitive reconstruction to explicitly represent the scene with planar primitives; (3) Planar primitive aggregation to segment the planar primitives directly within 3D space; (4) Planar primitive splatting to render the depth and plane mask for supervision of geometry and segmentation. + +# 3.1. Overview + +The query-based reasoning framework has demonstrated notable success in plane recovery tasks [37, 40], where these approaches employ learnable queries to aggregate visual features and subsequently decode them into plane instances. Formally, given a single image $I \in \mathbb{R}^{H \times W \times 3}$ , the objective is to predict a dense binary mask $m_i \in [0,1]^{H \times W}$ and a 3D parameter $\tilde{n} \doteq n / \tilde{d} \in \mathbb{R}^3$ for each plane instance, where $n \in \mathbb{R}^3$ is the surface normal and $\tilde{d}$ indicates the distance from the plane to the camera center. + +Our core insight lies in enhancing the query-driven learning paradigm through explicit integration of 3D structural priors, ultimately leading to more precise plane instance predictions in complex 3D scenarios. Specifically, we present a hierarchical query learning framework to achieve our online reconstruction and clustering methodology. As illustrated in Figure 2, a backbone model takes an image $I$ as input and outputs the multi-scale image feature maps: + +$$ +\mathbb {F} = \left\{F _ {i} \in \mathbb {R} ^ {H _ {i} \times W _ {i} \times C _ {i}} \right\} _ {i = 1} ^ {4}, \tag {1} +$$ + +where $H_{i} = H / 2^{i},W_{i} = W / 2^{i}$ . We then feed the features $\mathbb{F}$ into the planar primitive reconstruction module, in which $M$ learnable local queries $\hat{\mathcal{Q}} = \{\hat{Q}_i\in \mathbb{R}^C\mid i = 1,\dots ,M\}$ are used to interact with these features and further decoded into corresponding planar primitive parameters: + +$$ +\mathcal {P} = \left\{P _ {i} = \left(c _ {i}, q _ {i}, s _ {i}, o _ {i}\right) \in \mathbb {R} ^ {1 1} \mid i = 1, \dots , M \right\}, \quad (2) +$$ + +where the plane center $c_{i}\in \mathbb{R}^{3}$ , the normal quaternion $q_{i}\in$ + +$\mathbb{R}^4$ , the plane scale $s_i \in \mathbb{R}^3$ and the opacity $o_i \in \mathbb{R}$ compose each planar primitive. + +All refined local queries $\hat{\mathcal{Q}}$ are sent to the primitive aggregation module to generate $N$ global queries $\mathcal{Q} = \{Q_i\in$ $\mathbb{R}^C\mid i = 1,\dots ,N\}$ . Intuitively, we regard the N global queries $\mathcal{Q}$ as cluster centers and utilize the dot product similarity between local and global queries as a distance metric to calculate the probabilities $\hat{S} = \{\hat{S}_i\in \mathbb{R}^N\mid i =$ $1,\ldots ,M\}$ of assigning each local primitive to the corresponding cluster centers. This approach enables us to obtain segmentation results $\hat{S}$ directly within 3D space. Finally, we employ the splatting algorithm to convert the 3D segmentation probabilities into the pixel-level plane segmentation prediction $S\in \mathbb{R}^{N\times H\times W}$ + +# 3.2. Planar Primitive Reconstruction + +Inspired by GaussianFormer [22], we initialize a set of 2D anchors to aggregate information from the input image $I$ . Each anchor consists of a plane property $\hat{\mathcal{P}}_i$ and learnable plane query $\hat{\mathcal{Q}}_i$ , where property $\hat{\mathcal{P}}_i$ has almost the same elements as the final planar primitive parameter $\mathcal{P}_i$ except for the 3D center $c_i$ . Instead, We define the center of $\hat{\mathcal{P}}_i$ in the coordinate of the camera space: $\hat{c}_i = (u_i, v_i, z_i)$ . + +As shown in Figure 2, the reconstruction module takes 2D anchors and multi-scale features $\mathbb{F}$ as input. The 2D anchors are iteratively refined through self-encoding and cross-attention with $\mathbb{F}$ : + +$$ +\mathcal {Q} _ {i} = \mathrm {D A} \left(\mathcal {Q} _ {i}, \pi (\hat {\mathcal {P}} _ {i}), \mathbb {F}\right), \tag {3} +$$ + +where DA, $\pi (\cdot)$ denote the deformable attention func + +tion and the multi-layer perceptron (MLP) layers for Self-encoding. In the refinement stage, we decode the intermediate properties $\tilde{\mathcal{P}}$ from the plane query $\hat{\mathcal{Q}}$ with an MLP operation and accumulate the offsets of centers while directly replace other properties: + +$$ +\hat {\mathcal {P}} = \operatorname {M L P} (\hat {\mathcal {Q}}), \hat {\mathcal {P}} = (\hat {c} + \tilde {c}, \tilde {q}, \tilde {s}, \tilde {o}). \tag {4} +$$ + +After refinements, we backproject the center $\hat{c}$ to camera space to generate the final planar primitives $\mathcal{P}$ . + +# 3.3. Planar Primitive Aggregation + +Once the scene is represented by a set of planar primitives, we need to further extract the final plane instances through an online aggregation process. Inspired by previous query-based works [37, 40], we propose using a set of global plane queries $\mathcal{Q}$ as 3D aggregation centers, which is motivated by the observation that planar primitives belonging to the same plane instance exhibit similar geometric parameters. + +We initialize a set of global queries $\mathcal{Q}$ to represent physically existing plane instances. Each global query $\mathcal{Q}_i$ is iteratively refined by performing masked attention interactions with the local ones $\hat{\mathcal{Q}}$ directly in 3D space. The updated global queries $\mathcal{Q}_i$ are then decoded into 3D parameters $\tilde{n}_i$ and the probabilities $p_i$ , where $p_i$ is the probability to judge whether the $i^{th}$ query corresponds to a plane. + +Following Mask2Former [7], we formulate the aggregation probabilities $\hat{S}_i$ for each local query $\hat{\mathcal{Q}}_i$ in the form of dot product with all global queries $\mathcal{Q}$ : + +$$ +\hat {\mathcal {S}} _ {i} = \sigma \left(\hat {\mathcal {Q}} _ {i} ^ {\top} \cdot \mathcal {Q}\right) \in \mathbb {R} ^ {1 \times N}, \tag {5} +$$ + +where $\sigma(\cdot)$ denotes the Sigmoid function. The probability set $\hat{S}$ encodes instance-level affinity relationships, where higher values indicate stronger associations between local primitives and global plane instances. Finally, we employ the previously reconstructed planar primitives to render the 3D probabilities $\hat{S}$ onto the 2D image domain: + +$$ +\mathcal {S} = \text {P l a n e S p l a t t i n g} (\mathcal {P}, \hat {\mathcal {S}}). \tag {6} +$$ + +where $S \in \mathbb{R}^{N \times H \times W}$ . Each channel $S_{i}$ of $S$ is considered as the binary mask of $i^{th}$ prediction. The splatting process ensures geometric coherence between 3D plane representations and their 2D semantic segmentation results. Our key distinction lies in that we conduct segmentation directly in the compact 3D space, while existing methods operate solely based on 2D feature maps. + +# 3.4. Planar Primitive Representation + +Considering the predominance of planar structures in indoor scenarios, we propose a custom plane kernel based on 2D Gaussian Splatting [21] in order to mitigate the radial opacity decay inherent in conventional 2D Gaussian distributions as visually demonstrated in Figure 3. The standard 2D Gaussian distribution achieves maximum opacity + +![](images/73bc933785e07c8ab100af41bf079eafd0e2dc0ad6069910ac77bae64ed757ee.jpg) +(a) 2D Gaussian kernel. + +![](images/a527c00c5306de380f8e3a7437a4916a2e0235a7d3d79769c1d9a15ad4509fc2.jpg) +(b) Our plane kernel. +Figure 3. Comparison with 2D Gaussian kernel. (a) 2D Gaussian kernel exhibits rapid attenuation along radial directions. (b) Our plane kernel preserves extended planar regions with substantially improved spatial consistency. + +at the primitive center while exhibiting rapid attenuation along radial directions. While this translucent configuration facilitates effective modeling of intricate color variations in offline reconstruction paradigms, it compromises the structural fidelity to planar elements, such as walls and floors, which require constant opacity across their surfaces to maintain geometric integrity. Consequently, we introduce a plane-constrained kernel formulation that fundamentally redefines the opacity dynamics through: + +$$ +\mathcal {G} (u, v) = \sigma (\lambda (1 - | u |) \sigma (\lambda (1 - | v |)), \tag {7} +$$ + +where $\sigma(\cdot)$ is the Sigmoid function and $\lambda$ is set to 5.0 to control the flatness of the kernel. We employ the product of two Sigmoid functions to ensure that the majority of the rectangular region remains close to a constant value, while maintaining the end-to-end differentiability. Assisted by our plane kernel, we are able to construct the entire scene using a set of planar primitives $\mathcal{P}$ and subsequently obtain the rendered depth $d \in \mathbb{R}^{H \times W}$ and segmentation masks $S$ through the splatting algorithm. + +# 3.5. End-to-End PlaneRAS Framework + +The overall framework primarily consists of two stages: reconstruction and aggregation. The reconstruction stage employs planar primitives $\mathcal{P}$ as geometric proxies to represent the entire scene. In the subsequent aggregation stage, probability distributions $\hat{S}$ are estimated to characterize the affiliation of each primitive $\hat{\mathcal{Q}}_i$ with specific aggregation centroids $\mathcal{Q}$ . These reconstructed geometric primitives $\mathcal{P}$ , together with the inferred segmentation probabilities $\hat{S}$ , are then used to generate the depth map $d$ and planar segmentation masks $\mathcal{S}$ for final supervision. + +Pretrained Model. Inspired by previous offline approaches [18, 53], pretrained monocular networks are leveraged to estimate an initial geometric structure. To refine this estimate, offset predictions are introduced to recover more accurate metric geometry. Specifically, the final depth $z$ and normal $q$ of the planar primitives in Eq. (2) are expressed as the sum of a pretrained component and a learned residual: + +$$ +z = z _ {p r e d} + z _ {p r i o r}, q = q _ {p r e d} + q _ {p r i o r}, \tag {8} +$$ + +where $z_{pred}$ and $q_{pred}$ are iteratively refined by the reconstruction module via Eq. (4), while $z_{prior}$ and $q_{prior}$ are obtained through bilinear interpolation from the monocular predictions at the $(u, v)$ coordinates of each primitive. + +Reconstruction Loss. We employ an L1 loss to supervise the rendered depth maps for reconstruction. Additionally, the plane mask and parameter labels are used to directly supervise the normals of the primitives: + +$$ +\mathcal {L} _ {d} = \frac {1}{| \mathcal {D} |} \sum_ {(x, y) \in \mathcal {D}} \| d (x, y) - \hat {d} (x, y) \| _ {1}, \tag {9} +$$ + +$$ +\mathcal {L} _ {n} = \frac {1}{| \mathcal {P} |} \sum_ {p \in \mathcal {P}} \left(1 - \frac {n _ {p} ^ {\top} \hat {n} _ {p}}{\| n _ {p} \| \| \hat {n} _ {p} \|}\right), \tag {10} +$$ + +where $\mathcal{D}$ is the set of valid pixels in plane mask region; $\mathcal{P}$ is the planar primitive set; $d$ and $\hat{d}$ is the rendered and ground-truth plane depth separately; $\hat{n}$ is the ground-truth plane normal vector. + +Aggregation Loss. We simply borrow the corresponding procedure in PlaneRecTR [37] to supervise our rendered mask $S$ and clustering center $(p_i, \tilde{n}_i)$ . Bipartite matching is firstly used to find the optimal correspondence $\hat{\sigma}$ between $M$ predicted planes and $T$ ground truth planes. Then the aggregation loss is defined as: + +$$ +\mathcal {L} _ {a g g} = \sum_ {i = 1} ^ {T} \left(2 \mathcal {L} _ {\mathrm {c l s}} ^ {(i)} + \mathcal {L} _ {\text {p a r a m}} ^ {(i)} + \mathcal {L} _ {\text {m a s k}} ^ {(i)} + 2 \mathcal {L} _ {\text {d e p t h}} ^ {(i)}\right), +$$ + +where $\mathcal{L}_{cls}$ is a plane classification loss for the existence probability $p_i$ ; $\mathcal{L}_{param}$ is a plane parameter loss for plane parameter regression; $\mathcal{L}_{mask}$ is a segmentation loss to supervise mask prediction $S$ ; $\mathcal{L}_{depth}$ is an auxiliary for per plane depth supervision. Notably, we do not directly predict dense per-plane depth for each global query $\mathcal{Q}_i$ . Instead, the rendered depth $d$ is multiplied with the rendered aggregation probabilities $S_i$ to generate per-plane depth. + +Loss Functions. The total loss is computed as the sum of the reconstruction and aggregation losses described above: + +$$ +\mathcal {L} = \mathcal {L} _ {d} + \mathcal {L} _ {n} + \mathcal {L} _ {a g g}. \tag {11} +$$ + +In contrast to conventional single-view reconstruction methods that often emphasize photorealistic rendering quality, PlaneRAS explicitly prioritizes geometric fidelity, with an emphasis on reconstructing fine-grained local geometry to support higher-level 3D understanding. + +# 4. Experiments + +# 4.1. Experimental Settings + +Our experimental setup follows PlaneRecTR [37] to ensure a fair comparison. The network is trained on the ScanNet [8] training set, and evaluated on both the NYUv2 [38] dataset and the ScanNet validation set. ScanNet is a large-scale RGB-D video dataset containing 1,513 indoor scenes. + +We use plane annotations processed by PlaneNet [27] for both training and evaluation. The processed dataset includes 50,000 training images and 760 testing images, all at a resolution of $256 \times 192$ . NYUv2 is a standard indoor RGB-D dataset. For evaluation, we use plane annotations generated by PlaneAE [48]. The processed version used in our experiments consists of 654 testing images, also at a resolution of $256 \times 192$ . + +# 4.2. Evaluation Metrics + +We adopt per-plane and per-pixel recalls to evaluate plane recovery task following previous methods. The recall metrics are defined as the percentage of correctly predicted ground truth plane instances (pixels). A plane is considered being predicted correctly if its Intersection over Union (IOU) is larger than 0.5 and the plane parameter error is less than a threshold. Plane segmentation performance is evaluated by three popular metrics: rand index (RI), variation of information (VI) and segmentation covering (SC). + +On the NYUv2 dataset, we evaluate the performance of depth estimation in the planar region using popular depth metrics: mean relative error of absolution (Rel), mean $\log_{10}$ error $(\log_{10})$ , root mean square error (RMSE) and threshold accuracy $(\delta_i < 1.25^i, i = 1,2,3)$ . + +# 4.3. Implementation Details + +Our network is implemented using Detector2 [43]. Training is conducted on the ScanNet training set for a total of 34 epochs using a single NVIDIA RTX 3090 GPU. We employ the AdamW optimizer [30] with an initial learning rate of $1 \times 10^{-4}$ and a weight decay of $1 \times 10^{-5}$ . The batch size is set to 16. For pretrained monocular networks, depth maps are predicted using Metric3D [20], while normal maps are obtained from Omnidata [10] following AlphaTablets [18]. During reconstruction, 2D anchors $\hat{\mathcal{P}}$ with a resolution of $48 \times 64$ are randomly distributed across the image plane and then refined into planar primitives $\mathcal{P}$ . Subsequently, 20 aggregation centroids $\mathcal{Q}$ are generated to represent the final plane instances, following the design of PlaneRecTR [37]. + +# 4.4.Quantitative Results + +In this section, we present extensive quantitative evaluations towards previous state-of-the-art (SOTA) plane recovery methods: PlaneNet [27], PlaneRCNN [28], PlaneAE [48], PlaneTR [40], PlaneRecTR [37], MonoPlane [53], PlaneAC [52], PlanePDM [34]. + +Plane Segmentation. Table 1 shows the segmentation accuracy on the unseen ScanNet and NYUv2 datasets. We achieve a new SOTA plane segmentation performance on both datasets by a large margin across all three metrics. Following PlaneRecTR, we also replace the ResNet-50 backbone [16] with SwinTransformer-B [29] to train an enhanced version with much better performance. They + +![](images/899f961948c5a2136cbc8e558e0710edd35f79ee24391977cabbb86a46b473e6.jpg) + +![](images/30571302c604af989bf8bff94f5dfb361a8ef73780dfd0f42bc39d7690a82fb5.jpg) +Figure 4. Per-pixel and per-plane recalls on the ScanNet dataset. + +![](images/92324ccac46bb109c3832efd3dc10e272e9466024056a477ea5ab0f89a4483bb.jpg) + +![](images/6b003a56cb5edf9bfd7203449ee7a6a5e4e069d7983b1ed304aeb1073bfa74df.jpg) + +
MethodScanNetNYUv2
VI↓RI↑SC↑VI↓RI↑SC↑
PlaneNet [27]1.2590.8580.7161.8130.7530.558
PlaneRCNN [28]1.3370.8450.6901.5960.8390.612
PlaneAE [48]1.0250.9070.7911.3930.8870.681
PlaneTR [40]0.7670.9250.8381.1630.8910.712
PlaneRecTR [37](ResNet50)0.6980.9360.8541.1300.9050.722
PlaneRecTR(Swin-B)0.6510.9430.8661.0450.9150.745
PlaneAC [52]0.6580.9340.8521.0150.9070.743
PlanePDM [34]0.8390.9240.8331.2120.8980.725
Ours(ResNet50)0.6100.9490.8801.0540.9190.753
Ours(Swin-B)0.5930.9500.8830.9870.9260.771
+ +demonstrate our efficiency and highlight the significance of 3D geometric priors in achieving robust plane recovery. + +Plane Recovery. Figure 4 shows per-pixel and per-plane recalls of depth and plane normal on the ScanNet dataset. Depth thresholds vary from 0.05 to 0.6 meters and normal thresholds vary from 2.5 to 30 degrees. Our method significantly outperforms all baseline methods with all thresholds. This progress can be attributed to the synergistic interaction between our precise mask prediction and the plane parameter regression framework that demonstrates significantly lower estimation errors compared to existing state-of-the-art approaches. As reported in Tabel 3, our normal and offset errors reach $(7.77^{\circ},106.61\mathrm{mm})$ while PlaneRecTR has $(10.23^{\circ},165.13\mathrm{mm})$ . The parameter estimation errors reduced by $24.05\%$ in normal and $35.44\%$ in offset. + +Depth Accuracy. Table 2 reports pixel-wise depth accuracy within planar regions. While our method lags behind PlaneRecTR in Rel and $\delta_{1}$ , it achieves state-of-the-art performance in RMSE and accuracy under relaxed thresholds, highlighting its strength in capturing global geometric structure. This reflects the effect of pretrained depth priors, which, though lacking metric scale, enforce strong structural constraints. However, their tendency to over-smooth leads to reduced performance on stricter metrics such as $\delta_{1}$ . + +# 4.5. Qualitative Results + +We present qualitative results on the unseen ScanNet validation set. As can be shown in Figure 5, our PlaneRAS manages to achieve superior performance in both precise plane segmentation and absolute-scale depth estimation. Even in regions with substantial ground truth (GT) noise con + +Table 1. Comparison of plane segmentation results on the ScanNet dataset and NYUv2 dataset. + +
MethodRel ↓ log10 ↓ RMSE ↓ δ1 ↑ δ2 ↑ δ3 ↑
PlaneNet [27]0.2360.1240.91353.078.390.4
PlaneRCNN [28]0.1830.0760.61971.893.198.3
PlaneAE [48]0.2050.0970.82061.387.295.8
PlaneTR [40]0.1950.0950.80363.388.296.1
PlaneRecTR [37](ResNet50)0.2020.1000.72959.587.496.0
PlaneRecTR(Swin-B)0.1570.0730.54774.294.299.0
PlanePDM [34]0.1910.0890.789---
Ours(ResNet-50)0.1800.0880.54764.497.399.1
Ours(Swin-B)0.1650.0800.48871.697.899.3
+ +Table 2. Depth accuracy comparison on the NYUv2 dataset. + +tamination, the proposed framework maintains robust plane recovery capabilities. Nevertheless, we observe localized boundary perturbations in segmentation outputs, which we attribute to the intentionally limited number of planar primitives employed for scene reconstruction. Specifically, our primitive count remains orders of magnitude below conventional requirements for offline reconstruction systems (e.g., millions of primitives in 2D Gaussian Splitting [21] or Planar Splitting [41]). The limited parameter space restricts the model capacity to precisely estimate 3D scaling factors per primitive and will propagate errors to the 2D domain. + +Figure 6 visualizes detailed comparisons to PlaneRecTR, where our method present more reasonable mask in align with spatial variations. As discussed in 4.4, our method inherit the global geometric coherence from pretrained model. Thus, our predictions are more faithful to depth information, leading to a better prediction in those flatten regions. + +# 4.6. Experimental Analysis + +Effect of the Reconstruction Kernel. Our planar primitive is derived from 2D Gaussian splatting [21] for indoor scene reconstruction. Although uniform opacity distributions over the primitive parameter space appear intuitively aligned with the plane structure, we still need to conduct quantitative comparison with the bell-shaped Gaussian distribution to demonstrate the strength of our design. As evidenced in Table 3, the 2D Gaussian kernel demonstrates inferior segmentation performance compared to our plane kernel, suggesting that the exponential decay characteristic of conventional Gaussian distributions compromises structural coherence in indoor geometric reconstruction tasks. + +Effect of the Planar Primitive Number. We also investigate the impact of the total number of planar primitives, + +![](images/a44925a8b794e399ed96df384033e62b7b6bf56db5923437a22686bc91f3d087.jpg) +Figure 5. 3D plane recovery results of PlaneRAS on the ScanNet dataset. + +
Kernel ResolutionPriorPer-Pixel/Per-Plane Recalls ↑Plane SegmentationPlane Parameters Estimation Errors ↓
DepthNormalDepthNormal
@0.10m@0.60m@5°@30°VI↓RI↑SC↑Normal(°)Offset(mm)
Plane48 × 64✓80.23/67.6887.51/76.6980.35/61.0887.15/75.220.6100.9490.8807.77106.61
Plane48 × 64✓✓81.31/67.8887.70/76.6080.28/61.4987.33/75.090.6080.9480.8797.88111.64
Plane48 × 6453.03/45.6683.72/72.1665.34/50.5683.83/70.790.7010.9360.85610.04161.56
2D GS48 × 6451.66/42.9781.50/57.4062.40/47.1081.68/66.460.7620.9300.84010.15162.40
Plane36 × 48✓79.03/67.6687.62/78.7479.08/60.1687.26/77.060.6300.9470.8757.40105.53
Plane24 × 32✓78.06/66.1586.79/77.1777.87/58.2386.45/75.550.6530.9440.8697.85111.13
+ +Table 3. Ablation studies under different experimental settings on the ScanNet dataset. + +with the results presented in Table 3. The $48 \times 64$ configuration aligns with the resolution of the full feature map, implying that a planar primitive is predicted for each pixel feature. In comparison, the $36 \times 48$ and $24 \times 32$ configurations correspond to further downsampled versions of the feature map, leading to coarser spatial granularity in primitive prediction. Across all primitive resolutions, our method consistently achieves segmentation results that surpass those of existing state-of-the-art benchmarks. These findings underscore the potential of employing more effective geometric + +representations for scene reconstruction and segmentation. + +Effect of Pretrained Models. As shown in Eq. (8), pretrained monocular geometric priors are employed to enhance the reconstruction accuracy of planar primitives. Table 3 demonstrates that depth and normal priors exhibit complementary effects in improving geometric aggregation, with depth contributing a substantially greater impact. Our non-prior model achieves comparable performance to PlaneRecTR, while significant performance gains emerge when integrating pretrained depth priors. + +![](images/72ed5d8421de0069537052c1fe2eced8963b1002951f261c0468371e313dc60a.jpg) + +![](images/116bbb3d146338408133ba2eaeac1d71ab760e22d2223075add90bde704731e2.jpg) + +![](images/2bbf4b5a179c5904259efa7ed13d199b6ee6f829459440fc720fae546348f939.jpg) + +![](images/a4a67601f5754d8a1b8c8158e1b9cb82edc521db19fe5f3dae5427d36f00e88e.jpg) + +![](images/102e3fcd2e2f63243389896ada2947e97bba0245b171dfd6c29767b5f85c28cc.jpg) + +![](images/1c8f0f8d6c06fc58366e5472487d16c26857d5d74023e15fb3a53a19ac6186ce.jpg) + +![](images/2d4d22937670ced5675309fb5f820aed4457f99755c2097f0bb8773ffd607d5a.jpg) + +![](images/7bf564b0f6c08b07dec5f6c385483bd01f744be7b8d779ce6adc5aa3ee9aabfe.jpg) + +![](images/e6a8117e1244450fb0fc518f1fa6adef4d3dbebf2bcf7ea8f534b359b3c6099c.jpg) +(a) Input + +![](images/f67290c054f94bed18a66c212da1b840acaece585e933ab065fdc67eca023a48.jpg) + +![](images/9ce0308852d4c75195e6705aaa01f3d0f2fc607a0f6ec5f509e45110756c9d30.jpg) + +![](images/1391de98cf755eebce871c6c869b8c9046d0f74bc70ef579df9781bf9a90226f.jpg) + +![](images/45ab9eacf5d71717ce2da6ae3d06058d17d294aa1438eba9e7c6854adb8fe9c2.jpg) + +![](images/5de8a8fd9b43eeb83861592270f4d9904529e2ab08589d78b81600cfd5a76210.jpg) + +![](images/d493a035760d1febf4553495dc688e65413cdae3c6d815f38ca48679511935c3.jpg) + +![](images/44ad3aee5b0f7be6f69fd3d97f22eb98b5e242ed8587df44818a4773039ddaed.jpg) + +![](images/5a553d2925de119e801443d1557b2aef577b01475310ef8237f0805787364e99.jpg) + +![](images/ad97f49bd58b6ad6fd8e95a7067ebff107d6459e306c829e59bf563865523b83.jpg) +(b) PlaneRecTR Mask + +![](images/9a611c8236d31fb1bbca88ec75554115b19871aec1edaa8e527bbd81608d7535.jpg) + +![](images/84b76d8f03c075b1d367599bb07c60e803fda879a90da049837a6d0623ab4870.jpg) + +![](images/d39832ea0768a9817ce19c3c65244238dacc7a331c54803d2bca282ea59c3dcc.jpg) + +![](images/d9b3367a21e8a691117193049c973f2139ad0479d4ab2ba6305a5e2c2608a693.jpg) + +![](images/874a3aa90e04d1c180e0fb95d62b82aaeb5b223c989df28780009e2f6fead08f.jpg) + +![](images/d3a1e080c0cfe5cf9ec6b57980811d2822766f4c377c003b93323a09bdfbf9f7.jpg) + +![](images/b6593c93a2fa39bda3aae6c903cd51d9b5306407289c9f11f306ed922c29925d.jpg) + +![](images/b5e8b4dd0b141eac593a41826c36f7e12c4f3bd8dc8ffd3d63bb204d508f1a89.jpg) + +![](images/cb9bb3ffc3b9362e7c59ac557d80dc8500bf0100eef14f0d93c279780a091d25.jpg) +(c) Ours Mask + +![](images/2fa3e2e2ff3e9fda9d2775b3f1672c2229aa8b8ef772fa8e2cee456415eb26c3.jpg) + +![](images/5c99d32da5bb21892af6889982f822f6e0b14e3c686bc950643bfdf3be033393.jpg) + +![](images/a4c8569b26abd9424c9550ecc17d4536986c631a0e46121869c0d72bc7815a8e.jpg) + +![](images/3465e6841d0703ee8297f5c06eb2711e609d118ea1e8bef78b6c0ecffd0b519e.jpg) + +![](images/dda310dd6e40b360495dc4ef1c33f03ba826f4fba653dcba381d217ba2e1cec0.jpg) + +![](images/651ab9601e8aa78251b0a48c0797f2a23d3ebf5930ef18906028a68a7b932d98.jpg) + +![](images/cd99ced033359e7f178fc1f5609a53917eb6e1f3824d2010063964fc9984d98f.jpg) + +![](images/295ef739db4f3a88d4207f739fd4d4487728be57b39ca5617e01422e1713d5df.jpg) + +![](images/bce13761caddacfd6f29ce5861c1864dbf7bcace3e7f7470d18947febf2f8f5d.jpg) +(d) GT Mask + +![](images/85b9b8156d4af3a0f9a438cd2e5984569e00a30d4f06fbbc9767394752c0477b.jpg) + +![](images/d292537019492283e603217552a65451962620ec33a0fc8eb8a10c80b183436e.jpg) + +![](images/4c3c72a897d2e49b3cd335f3c94c23a041ca56cfeb88278ee613b4f44d186384.jpg) + +![](images/85e3ce89024c0e8f231c972a8c1fb335d70cb0823408132cf7822ad4dabe4103.jpg) + +![](images/3d69a719b6c587afa9827894681356e3a2036a9b08d2f159044122e23626e503.jpg) + +![](images/82971d9114547c5c0cf981c270db1746d41ff1ffa9d1f91929698e5c313a910a.jpg) + +![](images/91f110f2c6dd137cdfc480107f3966db0a5d89fa86cd08bda1f11d5c713478aa.jpg) + +![](images/ba4b7e89ea5b7e78956cde814c90990e0f847ac9e7964b6b6ddfe09d41e5114d.jpg) + +![](images/9b353e0117363553b81dab0423e468e3d1dad4feb199c91d1f0837d46e029e02.jpg) +(e) PlaneRecTR Depth +Figure 6. Comparison of plane reconstruction results on the ScanNet (top 5 rows) and NYUv2-Plane (bottom 4 rows) datasets. + +![](images/dcca661e64ea51c043a74454ac0e932513c77e48a4fa7b09ba5ccf41b661ff61.jpg) + +![](images/a0b952b6e2ed61902953fa8675f959bcaa5949139f640390b6db8ee328c179d4.jpg) + +![](images/25b8ab83ed7b9ae381a3840a5bf843e036c7f4af445fe28c259049f29c9bdc2f.jpg) + +![](images/4825e848e48d5a833eda07a2406c164ac73473599ac60050dfda20763c421bef.jpg) + +![](images/2af5d08337b4ca644c9d7ca932bb0851b9dcfa59257aa3b0e6a492f1097e1047.jpg) + +![](images/d983efbcd763616689c38513743602101c5f892e50e973cc7ed2fa54751a4b11.jpg) + +![](images/c5b9de217cb557cc6510f313d802c5a5f53f1d8c1912fcdf7ec23a129cc12ee4.jpg) + +![](images/5d1262f208a5b206fae1d07a797912e810586b5b47ce37e6a7a73e9749c4e405.jpg) + +![](images/3ea169ed41f1696afdbdb55f21ef3e73bc92ed310be4f99c72500c8e5c84470b.jpg) +(f) Ours Depth + +![](images/d5ede905006c0bea94d3a615ab8f0d29e2fa3c99a95b04a6ab9f5d5f1910f182.jpg) + +![](images/764083d66e6e54ae06e662ecd1f44c330e9d295dc95a7c4bcf06c6d21e29e1c3.jpg) + +![](images/c03e436abb112dbd6a4b0667085952eeb16d5247a4021f00566bccbda942149d.jpg) + +![](images/fd1773b41db050b6c20accb67c91c50a9622f7c234ed167175b8dec93df10a3c.jpg) + +![](images/455da0042333644186c0627357aa93606ff8fb97b7b79b9439235e1e755dbdd5.jpg) + +![](images/e71d650f90d91b7caa601baaf4427d303aa81125501776aab3c18f23acc28b1e.jpg) + +![](images/f6026e7d05228c69cc9dcb502e2b8624ae8f5021996fd57ff67d98b75e99d9c6.jpg) + +![](images/15ecca4dd8538f791b04d37a52197c1ea391609e91f2a8f8cc41cf678bc1ada3.jpg) + +![](images/2365979e1376ee30a1827d767f810ff9be8b9879600aa7f9de6a5d7724d2e311.jpg) +(f) GT Depth + +# 5. Conclusion + +This paper presents PlaneRAS, a novel framework for simultaneously reconstruction and plane recovery from a single image. Unlike existing 2D-centric methods, PlaneRAS directly performs plane recovery within the reconstructed 3D space. To fully exploit geometric priors inherent in the scene and enhance plane recovery performance, we propose a planar primitive representation that seamlessly integrates explicit monocular geometric priors from pretrained models. Extensive experiments on ScanNet and NYUv2 + +datasets demonstrate SOTA performance in various metrics. Ablation studies further validate the effectiveness of our design choices, particularly the integration of planar primitives and monocular priors. + +Limitations. PlaneRAS relies on single-view inputs, which are inherently limited by depth ambiguity. Moreover, We observe that the full 3D planar representations are susceptible to domain shift, which negatively impacts generalization. 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Although some methods integrate extra information to generate identity-aware descriptions, the player identities are sometimes incorrect because the extra information is independent of the video content. This paper proposes a player-centric multimodal prompt generation network for identity-aware sports video captioning (LLM-IAVC), which focuses on recognizing player identities from a visual perspective. Specifically, an identity-related information extraction module (IRIEM) is designed to extract player-related multimodal embeddings. IRIEM includes a player identification network (PIN) for extracting visual features and player names, and a bidirectional semantic interaction module (BSIM) to link player features with video content for mutual enhancement. Additionally, a visual context learning module (VCLM) is designed to capture the key video context information. Finally, by integrating the outputs of the above modules as the multimodal prompt for the large language model (LLM), it facilitates the generation of descriptions with player identities. To support this work, we construct a new benchmark called NBA-Identity, a large identity-aware basketball video captioning dataset with 9,726 videos covering 9 major event types. The experimental results on NBA-Identity and VC-NBA-2022 demonstrate that our proposed model achieves advanced performance. Code and dataset are publicly available at https://github.com/Zeyu1226-mt/LLM-IAVC. + +# 1. Introduction + +Video captioning is a critical research topic in video understanding with the aims of generating precise descriptions to comprehend the visual contents of the given videos. It has attracted increasing attention due to a variety of its applica + +![](images/b80a11ca27f3fdb34c83f5dbd5bda694b76c1e39189e9f769d39587afa17341a.jpg) +Figure 1. Caption comparison of current sports video captioning methods and our method. The different player names are marked red and blue. The actions are marked pink and cyan. The green checkmarks indicate correct name/action predictions, while the red crosses indicate incorrect ones. + +tions including sports video understanding [24, 29, 33, 45, 47], video storytelling [19] and online video search [16, 25]. + +The traditional video captioning methods [21, 38, 39, 44, 50] achieve impressive results in open domains, which provide only a broad summary of the visual content, as shown in Fig. 1 (a). However, in some specific scenarios, such as sports live text broadcast, the players' identities and the actions are crucial, as audiences are particularly interested in these details. Such requirements cannot be satisfied by the general descriptions. Anonymous methods replace entities in descriptions with special tokens (e.g., [PLAYER] and [TEAM]) [24, 28, 33, 34] or numeric IDs (e.g., "PLAYER0961226") [45]. They can provide detailed actions and distinguish different entity types. However, their descriptions are still missing entity identities, specifically player names, as shown in Fig. 1 (b). + +Recently, some methods [29, 47, 48] have introduced extra information, such as game news, player statistics, and the candidate player list, to generate descriptions with player identities. Due to the fact that the extra information is independent of the video clips, player identities in the descriptions are derived from the static extra information + +rather than from the video clips themselves. These methods do not truly recognize player identities from the video clips, but rather make inferences based on extra information. The player identities may be incorrect, as shown in Fig. 1 (c). + +The above methods fail to correctly describe players' identities, which has become a major backlog for sports video captioning. In fact, player identities are implied within the video clips, but most datasets [4, 6, 9, 30, 33, 34, 49, 54] do not include the entity names, which makes it impossible to generate the identity-aware descriptions. Although some existing sports video captioning datasets include player names [29, 47, 48], they lack the necessary annotations to facilitate the development of models with visual mining capabilities. For instance, player bounding boxes could help build models to directly recognize player identities in visual content. If we could re-organize video clips around individual players to obtain the player-centric video clip set, it is possible to develop a player identification network for identity-aware video captioning. + +In this paper, we collect 40 NBA full games during 2022-2023, and organize a player-centric video clip set to link each player with all of his video clips. Based on this set, a player identification network (PIN) is developed to extract players' visual features and names from the given videos. A bidirectional semantic interaction module (BSIM) is designed to augment the player visual features by interacting with the video features. The above two modules form an identity-related information extraction module (IRIEM), which outputs the identity-related multimodal embeddings. A learnable approach is adapted by utilizing a designed visual context learning module (VCLM) to learn video context information, which is then concatenated with the identity-related multimodal embeddings as the prompt for the LLM to generate descriptions with player names. To support this, we propose an identity-aware basketball video captioning dataset NBA-Identity, which involves 9,726 videos, 321 players with bounding boxes, and 9 major kinds of events. + +The main contributions of this paper are: + +- We propose a player-centric multimodal prompt generation network for LLM-based identity-aware basketball video captioning (LLM-IAVC), which jointly utilizes player identity features and contextual video information to guide LLM in generating identity-aware descriptions. +- A large identity-aware basketball video captioning dataset NBA-Identity is constructed. This dataset contains the largest number of videos among identity-aware sports video captioning datasets. Its captions cover 9 major events in the basketball domain. +- Extensive experiments on our NBA-Identity and VC-NBA-2022 [47] datasets demonstrate that the proposed model achieves state-of-the-art performance without the need for additional knowledge assistance. + +# 2. Related Works + +Video Captioning. Video captioning aims to comprehend the video content and produce descriptions in natural language automatically. Recent researches [21, 38, 39, 44, 50] primarily emphasize generation methods based on sequence learning, where a visual encoder extracts relevant visual features from videos, and a decoder then generates descriptions in a sequential manner. Researchers have attempted to employ various visual encoders, including ResNet [13], Vision Transformer (ViT) [10], and C3D [12], to extract different 2D/3D video features. In this work, our LLM-IAVC employs the encoder-decoder framework and integrates the pre-trained model Timesformer [3] as the visual encoder to encode the spatiotemporal information in videos. Unlike most models that use LSTM [7] or Transformer [42] as the text decoder, we employ the LLM for the naturalness and accuracy of generated text. + +Sports Video Captioning. It aims to recognize player identities and key event types, generating accurate descriptions in fluent and natural language to ensure alignment with the video content. Anonymous methods utilize special tokens (e.g., [PLAYER] and [TEAM]) [24, 28, 33, 34] or entity types (e.g., "Batter" in baseball) [15, 17] in descriptions to represent entities. These methods still cannot generate descriptions with specific entity names. Extra information based methods [29, 47, 48] generate descriptions that include player names by incorporating extra game-related information. This type of method guesses player identities from a pool of candidate information but does not genuinely recognize players' identities from a visual perspective. Different from the above methods, this paper focuses on extracting identity-related information directly from the video clips, which is helpful for preserving the consistency of the descriptions and the video clips. + +Large Language Models. LLMs (e.g., LLaMa2 [41] and GPT4 [1]) exhibit proficiency in a variety of language tasks given their powerful reasoning ability. Recent works [26, 36, 53] attempt to empower LLMs with visual understanding ability on downstream tasks like visual question-answering, video grounding, and video anomaly detection. With its impressive text generation capabilities, we employ various lightweight LLMs as the decoders, including GPT-2 [31], Qwen2.5 [40], and Llama3.2 [23], to generate high-quality descriptions for the sports video captioning task. Instead of manually designing a sentence as a prompt, we automatically generate a multimodal prompt that includes identity-related information and visual context, helping the LLM better understand the video content. + +# 3. Methods + +As shown in Fig. 2, LLM-IAVC mainly consists of three main components: 1) identity-related information extrac + +![](images/54bdb5fe3866643e4f1368fac88b52b732b712d8ca1546c34be8c2996afb1b50.jpg) +Figure 2. Illustration of the proposed identity-aware basketball video captioning model. During training, the player sequences corresponding to the input video are located from the player-centric video clip set based on the video ID, and their visual features are extracted via a pre-trained player identification network. During inference, a multi-object tracker extracts player sequences, and the player identification network extracts their visual features and identities. The top- $k$ players with the highest confidence are selected for further processing. + +tion module (IRIEM), 2) visual context learning module (VCLM), and 3) LLM-based decoder. The IRIEM includes the player identification network (PIN) and the bidirectional semantic interaction module (BSIM). The red line represents the training flow and the blue line represents the inference flow. The black flow represents the shared process for training and inference. In the following subsections, we will describe each component in detail. + +# 3.1. Player Identification Network + +Since player identities are inherently embedded in video clips, a straightforward approach is to develop a player identification module that directly recognizes player identities from visual content. Based on the player names in captions, each video clip is associated with specific players. Therefore, all training video clips from 40 full games are automatically re-organized as the player-centric video clip set. The player sequences could be obtained by their bounding boxes. The player identification network is developed to extract the identity-related visual features from the player sequences. Fig. 3 shows the training process of the player identification network, which consists of TimeSformer as the visual backbone and a fully connected layer as the classification head. + +Let $P_B = \{p_1, p_2, \ldots, p_n\}$ represent the player sequence, where $p_n$ denotes the $n$ -th the cropped bounding box. The player sequence feature $\mathbf{F}_P \in \mathbb{R}^{1 \times D_{time}}$ is extracted by TimeSformer [3]. Then $\mathbf{F}_P$ is fed into a classifi + +![](images/089a94846d892d8f8fc5158153dadc5ed84c164fc82b9973b9d582ac532ac9c5.jpg) +Figure 3. Training for the player identification network, including TimeSformer as the visual backbone and a classification head. + +cation network to obtain classification probabilities. + +$$ +o _ {P} = \mathbf {W} _ {f} \left(\mathbf {F} _ {P}\right) = \mathbf {W} _ {f} \left(\operatorname {M} _ {\text {t i m e}} \left(P _ {B}\right)\right), \tag {1} +$$ + +where $\mathbf{W}_f\in \mathbb{R}^{D_{time}\times D_c}$ is a fully connected layer. $D_{time}$ is the hidden size of TimeSformer $\mathrm{M}_{\mathrm{time}}$ . $D_{c}$ is the number of player classes. The player identification network is trained with a cross-entropy loss: + +$$ +\mathcal {L} _ {\text {p l a y e r}} = - \frac {1}{N _ {b}} \sum_ {n = 1} ^ {N _ {b}} \sum_ {i = 1} ^ {D _ {C}} y _ {n, i} \cdot \log (p _ {n, i}), \tag {2} +$$ + +where $N_{b}$ is the batch size. $y_{n,i}$ and $p_{n,i}$ are the true label and predicted probability for sample $n$ and class $i$ . + +# 3.2. Bidirectional Semantic Interaction Module + +The BSIM is designed to strengthen the association between player identity-related visual features and overall video content through information exchange, ensuring that player identities are more effectively integrated into the visual context. BSIM involves a multi-head self-attention module, a multi-head cross-attention module, and an MLP layer. The BSIM aims to associate video and player features and we define this operation for the multi-head self-attention mechanism with the input vector $\mathbf{I}$ : + +$$ +\operatorname {M S A} (\mathbf {I}) = \delta \left(\frac {\mathbf {I W} _ {Q} \cdot \left(\mathbf {I W} _ {K}\right) ^ {\top}}{\sqrt {D}}\right) \cdot \mathbf {I W} _ {V}, \tag {3} +$$ + +where $\mathbf{W}_Q$ , $\mathbf{W}_K$ and $\mathbf{W}_V$ are learnable query, key, and value parameter matrices, respectively. $D$ is the dimension of the input vector $\mathbf{I}$ . $\delta(\cdot)$ is the softmax function. The multi-head cross-attention mechanism is the variant of the multi-head self-attention mechanism, where the query comes from one input vector $\mathbf{I}_1$ while the key and value come from another input vector $\mathbf{I}_2$ : + +$$ +\operatorname {M C A} \left(\mathbf {I} _ {1}, \mathbf {I} _ {2}\right) = \delta \left(\frac {\mathbf {I} _ {1} \mathbf {W} _ {Q} \cdot \left(\mathbf {I} _ {2} \mathbf {W} _ {K}\right) ^ {\top}}{\sqrt {D}}\right) \cdot \mathbf {I} _ {2} \mathbf {W} _ {V}. \tag {4} +$$ + +The BSIM is shown in Fig. 4. The visual features of the $k$ player sequences are concatenated into a player feature $\mathbf{F}_k\in \mathbb{R}^{k\times D_{time}}$ , which is then interacted with the video feature $\mathbf{V}_v$ through the bidirectional semantic interaction module. Specifically, the video feature $\mathbf{V}_v$ and player feature $\mathbf{F}_k$ each pass through a multi-head self-attention layer for self-enhancement: + +$$ +\left\{ \begin{array}{l} \mathbf {V} _ {v} ^ {\prime} = \operatorname {M S A} _ {1} \left(\ell_ {1} \left(\mathbf {V} _ {v}\right)\right) \\ \mathbf {F} _ {k} ^ {\prime} = \operatorname {M S A} _ {2} \left(\ell_ {2} \left(\mathbf {F} _ {k}\right)\right) \end{array} , \right. \tag {5} +$$ + +where $\ell (\cdot)$ denotes the Layer Normalization layer. + +Then $\mathbf{V}_v^{\prime}$ and $\mathbf{F}_k^{\prime}$ are associated through an information exchange sub-module: + +$$ +\left\{ \begin{array}{l} \mathbf {V} _ {v} ^ {\prime \prime} = \mathbf {W} _ {u 1} \mathrm {M C A} _ {e v} \left(\ell_ {3} \left(\mathbf {W} _ {d 1} \mathbf {V} _ {v} ^ {\prime}\right), \ell_ {4} \left(\mathbf {W} _ {d 2} \mathbf {F} _ {k} ^ {\prime}\right)\right) \\ \mathbf {F} _ {k} ^ {\prime \prime} = \mathbf {W} _ {u 2} \mathrm {M C A} _ {v e} \left(\ell_ {4} \left(\mathbf {W} _ {d 2} \mathbf {F} _ {k} ^ {\prime}\right), \ell_ {3} \left(\mathbf {W} _ {d 1} \mathbf {V} _ {v} ^ {\prime}\right)\right) \end{array} , \right. \tag {6} +$$ + +where $\mathbf{W}_d\in \mathbb{R}^{D_{time}\times D_{down}}$ and $\mathbf{W}_u\in \mathbb{R}^{D_{down}\times D_{time}}$ denote the linear down- and up-projection matrices. $\mathrm{MCA}_{ev}(\cdot)$ and $\mathrm{MCA}_{ve}(\cdot)$ denote entity-to-video multihead cross-attention and video-to-entity multi-head cross-attention, respectively. + +Finally, the outputs of BSIM are as follows: + +$$ +\left\{ \begin{array}{l} \mathbf {V} _ {b s i} = \ell_ {5} \left(\varrho_ {1} \left(\mathrm {M L P} _ {1} \left(\phi_ {1} \left(\mathbf {V} _ {v} ^ {\prime \prime}\right)\right)\right) + \mathbf {V} _ {v} ^ {\prime \prime}\right) \\ \mathbf {F} _ {b s i} = \ell_ {6} \left(\varrho_ {2} \left(\mathrm {M L P} _ {2} \left(\phi_ {2} \left(\mathbf {F} _ {k} ^ {\prime \prime}\right)\right)\right) + \mathbf {F} _ {k} ^ {\prime \prime}\right) \end{array} , \right. \tag {7} +$$ + +![](images/a205a7ca534ece556c82eaa51ff2f91996ceb5b59787bedb5e3cb47bf5741942.jpg) +Figure 4. The bidirectional semantic interaction module. + +where $\varrho (\cdot)$ denotes the Dropout layer. $\phi (\cdot)$ denotes the GELU activation function [14]. And MLP $(\cdot)$ denotes the multilayer perceptron layer. + +# 3.3. Visual Context Learning Module + +The visual context learning module (VCLM) aims to learn the video context information $\mathbf{V}_c\in \mathbb{R}^{N_q\times D_{time}}$ . As shown in Fig. 2, we randomly initialize $N_{q}$ learnable query vectors $\Theta \in \mathbb{R}^{N_q\times D_{time}}$ . VCLM extracts a kind of "global" and "overview" semantic information from the original video features through learnable query vectors to help the model capture the overall dynamic background of the video content. Learnable vectors not only provide contextual information, but also act as a bridge between the visual and textual spaces. These vectors can be automatically adjusted during training to better fit the semantic mapping between vision and text. We use self- and cross-attention to aggregate video context information: + +$$ +\mathbf {V} _ {s e l f} = \delta \left(\frac {\boldsymbol {\Theta} \mathbf {W} ^ {Q _ {1}} \cdot \left(\boldsymbol {\Theta} \mathbf {W} ^ {K _ {1}}\right) ^ {\top}}{\sqrt {D _ {t i m e}}}\right) \cdot \boldsymbol {\Theta} \mathbf {W} ^ {V _ {1}}, \tag {8} +$$ + +$$ +\mathbf {V} _ {p v} = \tau_ {p} + \mathbf {V} _ {v}, \tag {9} +$$ + +$$ +\mathbf {V} _ {c r o s s} = \delta \left(\frac {\mathbf {V} _ {s e l f} \mathbf {W} ^ {Q _ {2}} \cdot \left(\mathbf {V} _ {p v} \mathbf {W} ^ {K _ {2}}\right) ^ {\top}}{\sqrt {D _ {t i m e}}}\right) \cdot \mathbf {V} _ {p v} \mathbf {W} ^ {V _ {2}}, \tag {10} +$$ + +$$ +\mathbf {V} _ {c} = \operatorname {F F N} (\operatorname {M L P} \left(\mathbf {V} _ {\text {c r o s s}}\right)), \tag {11} +$$ + +where $\mathbf{V}_v\in \mathbb{R}^{N_v\times D_{time}}$ is the video feature extracted by TimeSformer [3]. $N_{v}$ is the number of frames. $\tau$ is the position embedding and helps the model distinguish the sequence of frames and capture temporal dependencies. $\mathbf{W}^{Q_1}\in \mathbb{R}^{D_{time}\times D_{time}}$ $\mathbf{W}^{K_1}\in \mathbb{R}^{D_{time}\times D_{time}}$ $\mathbf{W}^{V_1}\in \mathbb{R}^{D_{time}\times D_{time}}$ $\mathbf{W}^{Q_2}\in \mathbb{R}^{D_{time}\times D_{time}}$ $\mathbf{W}^{K_2}\in$ $\mathbb{R}^{D_{time}\times D_{time}}$ and $\mathbf{W}^{V_2}\in \mathbb{R}^{D_{time}\times D_{time}}$ are learnable matrices. FFN $(\cdot)$ denotes the feed-forward network. + +# 3.4. Large Language Model Based Decoder + +We use a pre-trained LLM as the decoder. First, the pretrained LLM is employed to extract the corresponding textual feature $\mathbf{E}_n\in \mathbb{R}^{1\times D_{llm}}$ for each player's name in the player sequence. Then, we concatenate $k$ name features into $\mathbf{E}_k\in \mathbb{R}^{k\times D_{llm}}$ . To enhance generalization and adaptability, a multimodal prompt is provided to the LLM, which includes video context information $\mathbf{V}_c$ , video feature $\mathbf{V}_{bsi}$ , player feature $\mathbf{F}_{bsi}$ , and player name feature $\mathbf{E}_k$ . This prompt enables the model to generate captions $\hat{\mathbf{C}}$ that accurately incorporate player identities. + +$$ +\hat {\mathbf {C}} = \Psi_ {l l m} \left(\left[ \mathbf {W} _ {c} \mathbf {V} _ {c}, \mathbf {W} _ {v} \mathbf {V} _ {b s i}, \mathbf {W} _ {f} \mathbf {F} _ {b s i}, \mathbf {W} _ {n} \mathbf {E} _ {k} \right]\right), \tag {12} +$$ + +where $\mathbf{W}_c\in \mathbb{R}^{D_{time}\times D_{llm}}$ $\mathbf{W}_v\in \mathbb{R}^{D_{time}\times D_{llm}}$ $\mathbf{W}_f\in$ $\mathbb{R}^{D_{time}\times D_{llm}}$ and $\mathbf{W}_n\in \mathbb{R}^{D_{llm}\times D_{llm}}$ are linear projection layers that map each feature into the embedding space of the LLM. $D_{llm}$ is the hidden size of the LLM. $\Psi_{llm}(\cdot)$ denotes the LLM-based decoder, and $[\cdot ]$ denotes the concatenate function in Python. + +# 3.5. Training and Inference + +During the training stage, the video_id and game_id are utilized to query the player-centric video clip set, retrieving the corresponding key player sequences and player names. The player identification network extracts player visual features from player sequences, while player names are encoded into textual features using an LLM. Following the conventional training pattern for caption generation, we utilize cross-entropy loss to optimize our LLM-IAVC: + +$$ +\mathcal {L} _ {\Phi} = - \sum_ {t = 1} ^ {N _ {g}} \log \left(\mathrm {P} \left(\beta_ {t} ^ {*} \mid \beta_ {0: t - 1} ^ {*}, \mathbf {F} _ {\text {p r o m p t}}; \Phi\right)\right), \tag {13} +$$ + +$$ +\mathbf {F} _ {\text {p r o m p t}} = \left[ \mathbf {W} _ {c} \mathbf {V} _ {c}, \mathbf {W} _ {v} \mathbf {V} _ {b s i}, \mathbf {W} _ {f} \mathbf {F} _ {b s i}, \mathbf {W} _ {n} \mathbf {E} _ {k} \right], \tag {14} +$$ + +where $\left\{\beta_0^*,\beta_1^*,\dots,\beta_{N_g}^*\right\}$ is the set of ground-truth tokenized tokens. $N_{g}$ denotes the number of tokens. And $\Phi$ denotes the optimized parameters. + +At the inference stage, there are some differences compared to the training stage. We utilize the pre-trained multi-object tracking model SportsMOT [8] to extract multiple player sequences. These sequences are then processed by the player identification network to recognize player identities. The identified sequences are ranked based on confidence scores, and the top- $k$ sequences are selected. The visual features of these top- $k$ players are concatenated to form the player feature representation $\mathbf{F}_k$ . Additionally, the names of the top- $k$ players are encoded into textual features using a pre-trained LLM, resulting in a concatenated feature representation $\mathbf{E}_k$ . Finally, as in Eq. (12), this concatenated feature serves as input prompt to the LLM, generating the corresponding description. + +
DatasetDomainBboxVideoSentenceOneMulti.Total Dur(h)
Anonymous
MSVD [6]OpenNo1.9k70k✓5.3
ActivityNet-Caption [4]OpenNo20k100k✓840
MSR-VTT [49]OpenNo10k200k✓41.2
TACoS [35]CookingNo12711.8✓-
YouCook [9]CookingNo882.7k✓2.3
YouCook2 [55]CookingNo2k15.4✓176
SVCDV [30]VolleyballNo4.8k44k✓-
Soccer captioning [11]SoccerNo22k22k✓-
SoccerNet-Caption [24]SoccerNo0.9k36k✓715.9
MatchTime [33]SoccerNo0.9k36k✓715.9
SoccerReplay-1988 [34]SoccerNo150k150k✓3,323.0
FSN [51]BasketballNo2k6.5k✓-
BH-Commentary [54]BasketballNo4.3k4.3k✓10.1
NSVA [45]BasketballYes32k44.6k✓84.8
Identity-aware
MPII-MD [37]MovieNo68.3k68.3k✓73
Movie101 [52]MovieNo30k30k✓92
Goal [29]SoccerNo8.9k22k✓25.5
VC-NBA-2022 [47]BasketballNo3.9k3.9k✓-
NBA-IdentityBasketballYes9.7k9.7k✓8.9
+ +Table 1. Comparison of existing video captioning datasets. "Bbox" denotes whether the dataset includes entity bounding boxes. "One" means each video is paired with only one caption, while "Multi." means multiple different captions. + +# 4. Experiments + +LLM-IAVC is compared with existing video captioning models on NBA-Identity and VC-NBA-2022 [47] datasets. We further conduct ablation studies to assess the contribution of each component in LLM-IAVC. + +# 4.1. Datasets and Metrics + +We collect 40 games data from the NBA 2022-2023 season to construct an identity-aware basketball video caption dataset NBA-Identity. It includes 9,726 videos, 321 players with bounding boxes, and 9 major kinds of events (e.g., "block", "foul", "defensive rebound", "offensive rebound", "turnover", "two-point (2-pt) shot", "three-point (3-pt) shot", "layup" and "assist"). Notably, "foul" includes "personal foul", "personal take foul", "shooting foul", "offensive foul", and "loose ball foul". Similarly, "turnover" includes "lost ball; steal by [player]", "bad pass; steal by [player]", "lost ball", "bad pass", "offensive foul", "traveling", "step out of bounds", "discontinued dribble", and "out of bounds lost ball". Our NBA-Identity covers 26 fine-grained event types. And it is divided into training and testing sets based on game instances. 8,667 clips from 35 games for training, 1,059 clips from 5 games for testing. As shown in Tab. 1, open-domain datasets (including cooking) typically provide multiple captions per video clip, whereas sports and movie datasets usually have only one. This may be due to: 1) the higher difficulty and cost of obtaining domain-specific annotations, and 2) the uniqueness of terminology in specialized fields like sports. To facilitate identification, we also provide key player bounding boxes. + +VC-NBA-2022 is an identity-aware basketball video captioning dataset, which includes 9 types of fine-grained shooting events, 286 players, and over 3.9k videos. The training set contains 3,162 videos and the testing set contains 786 videos. We employ the typical captioning met + +
ModelLearning-rateHidden sizeBatch size
GPT-2 [31]5e-576864
Qwen2.5-0.5B [40]7e-589632
Qwen2.5-1.5B [40]5e-51,53632
Qwen2.5-3B [40]1e-52,0488
Llama3.2-1B [23]5e-52,04832
Llama3.2-3B [23]7e-63,0728
+ +Table 2. Training parameters for different variants of LLM-IAVC. + +rics, including BLEU [27], Rouge-L [20], METEOR [2] and CIDEr [43] to evaluate the performance of LLM-IAVC. + +Compared to VC-NBA-2022, Our NBA-Identity extends VC-NBA-2022 with the following key differences: 1) More video clips; 2) More event types; 3) More realistic video clips: Video clips of NBA-Identity are in MP4 format with variable lengths based on event duration, while clips in VC-NBA-2022 are uniformly sampled to 72 frames. 4) All captions in NBA-Identity are directly obtained from live broadcast platforms without any modifications, making them authentic, while the textual annotations in VC-NBA-2022 have been manually revised into structured subject-verb-object formats. 5) Captions include shot distance, making generation more challenging and realistic. More details about the proposed dataset and metrics can be found in Supplementary materials. + +# 4.2. Implementation Details + +The hidden size $D_{time}$ of TimeSformer is 768. Each video clip in NBA-Identity has up to 60 frames, with frame and player image sizes of $224 \times 224$ . Since descriptions of the dataset mention at most two players, the top-2 player sequences are selected for visual feature extraction. We stack 1 visual context learning module block and 1 bidirectional semantic interaction module layer for LLM-IAVC. The number of learnable query vectors is set to 32 for visual context learning module. And the $D_{down}$ is set to 512 for bidirectional semantic interaction module. For player identification network training, the Adam [18] optimizer is used with a learning rate of 5e-5 for 50 epochs, covering 321 player identities. The number of images in player sequence is set to 20. LLM-IAVC is trained for 100 epochs on both datasets. Variants of LLM-IAVC utilize different LLMs as decoders, including GPT-2, Qwen2.5, and Llama3.2, with training parameters detailed in Tab. 2. The Adam optimizer is used across all variants, with a beam search size of 5 for decoding. All experiments run on an NVIDIA 4090 GPU. For example, with LLama3.2-3B (batch = 8), training and testing per epoch take 221.2s and 115.3s, respectively, with 0.3s per caption generation. + +# 4.3. Results on NBA-Identity and VC-NBA-2022 + +Compared models. The proposed LLM-IAVC is compared with 5 advanced video captioning models, including Clip4Caption [39], SwinBERT [21], CoCap [38], Om + +niViD [44], KEANet [47] and EIKA [48]. Clip4Caption employs CLIP [32] to acquire the aligned visual-text representation for better generating the text descriptions. SwinBERT introduces Video Swin Transformer [22] to encode spatiotemporal representations from video frames. CoCap utilizes the motion vector feature, residual feature, and video feature through the action encoder. Then, the fused features are sent to the decoder to generate video captions. OmniViD is a unified generative framework that can address various video tasks, including action recognition, video captioning, video question answering, dense video captioning, and visual object tracking. KEANet and EIKA utilize the candidate player list to generate the descriptions with player identities. + +Quantitative results analysis. In Tab. 3, LLM-IAVC significantly outperforms the other 6 methods on CIDEr. This is due to CIDEr's sensitivity to unique or infrequent words like names, with accurate name prediction boosting scores. Traditional methods perform worse as they cannot directly recognize player identities from video. While KEANet and EIAK use a predefined candidate player list, they lack visual recognition, leading to less accurate player names. + +LLM-IAVC includes multiple variants with different LLM decoders, such as GPT-2 [31], Qwen 2.5 [40] and Llama 3.2 [23]. Each variant takes either visual context alone or a multimodal prompt combining visual and identity features as input. Results show poor performance with visual context alone, while multimodal prompts significantly enhance generation quality. For example, adding prompts boosts the CIDEr score of LLM-IAVC (Llama 3.2-3B) by $40.9\%$ and BLEU-4 by $4.3\%$ , as the prompts provide richer visual context and player identity information for better video understanding. Among decoders, LLaMA outperforms Qwen and GPT-2 due to its superior architecture and pre-training process, leading to better contextual understanding and generation. + +Due to resource limitations, we are unable to develop larger models. However, our approach is lightweight, allowing for easy deployment and training. These results underscore the capability of our model to generate accurate names and fine-grained actions in live text broadcast task. + +Qualitative results analysis. Fig. 5 presents qualitative results on NBA-Identity and VC-NBA-2022. LLM-IAVC takes two input types: video-only and multimodal prompts. The video-only model struggles to understand player identities and actions, leading to inaccurate names, though they may resemble real names (e.g., "Justin Jackson" vs. "Jayson Tatum"). By integrating video context and player identities, the generation quality is significantly improved, enabling more accurate descriptions of player names and actions. Moreover, shot distance is crucial in practical applications. It can be observed that traditional and extra information enhanced methods fail to accurately determine + +
MethodNBA-IdentityVC-NBA-2022
CIDErMETEORRouge-LBLEU-4CIDErMETEORRouge-LBLEU-4
Traditional methods
Clip4Caption [39]21.721.037.66.570.426.751.228.8
SwinBERT [21]23.520.737.17.569.126.549.028.4
CoCap [38]22.720.037.77.570.527.450.728.9
OmniViD [44]39.621.637.78.371.227.550.729.2
Extra inforamaion enhanced methods
KEANet [47]50.122.738.18.5138.528.054.932.4
EIKA [48]55.722.738.69.0140.729.556.836.7
LLM-IAVC without prompt
LLM-IAVC (G)46.817.534.09.287.427.753.830.5
LLM-IAVC (Q-0.5B)54.317.933.811.588.127.654.230.8
LLM-IAVC (Q-1.5B)58.818.838.512.390.027.555.231.0
LLM-IAVC (Q-3B)61.818.239.014.7101.228.055.532.2
LLM-IAVC (L-1B)60.318.033.214.090.027.355.331.4
LLM-IAVC (L-3B)66.518.234.514.2103.128.555.732.8
LLM-IAVC with prompt
LLM-IAVC (G)94.122.035.417.0139.029.057.837.2
LLM-IAVC (Q-0.5B)87.621.536.416.0139.429.255.736.8
LLM-IAVC (Q-1.5B)97.122.140.016.7141.530.157.437.8
LLM-IAVC (Q-3B)103.522.941.217.7147.830.756.838.3
LLM-IAVC (L-1B)88.321.640.115.3139.330.057.337.7
LLM-IAVC (L-3B)105.323.042.518.8150.730.957.938.6
+ +shooting distance. While our method doesn't explicitly predict it in NBA-Identity, providing richer and more detailed features as prompts allows the model to approximate the real shot distance more closely (e.g., "6 ft" vs. "4 ft"). Though distance estimation remains a challenge, our model is a flexible and extensible baseline that can incorporate a distance evaluation module for improved accuracy. + +# 4.4. Ablation Study + +Backbone of player identification network. We compare different backbones for the player identification network in Tab. 4, treating player identification as a classification task where each class represents a player identity. We employ Multi-class Classification Accuracy (MCA) and Mean Per Class Accuracy (MPCA) metrics from the group activity recognition domain [46] to assess the performance of the player identification network. A higher MCA indicates stronger overall recognition ability across all player categories. A higher MPCA reflects a better measure of the model's generalization ability, especially in scenarios with imbalanced player categories. The TimeSformer-based [3] player identification network achieves the highest MCA $(91.40\%)$ and MPCA $(89.13\%)$ , demonstrating superior ac + +Table 3. Quantitative comparison results on NBA-Identity and VC-NBA-2022 datasets. Within each unit, we denote the best performance in RED and the second-best performance in BLUE. G, Q, and L represent GPT-2, Qwen2.5, and Llama3.2, respectively. + +
BackboneInput sizeMCAMPCA
ResNet-18 [13]320×18086.46%79.74%
ResNet-50 [13]320×18090.12%85.30%
C3D [12]320×18050.86%43.32%
I3D [5]320×18060.24%57.20%
Vison Transformer [10]224×22487.12%80.06%
TimeSformer [3]224×22491.40%89.13%
+ +Table 4. Impact of different backbones on player classification. + +
ModelVCLMPINBSIMCIDErBLEU-4
①66.514.2
②✓66.815.0
③✓95.116.4
④✓✓99.717.7
⑤✓✓103.418.1
⑥✓✓✓105.318.8
+ +Table 5. Ablation on NBA-Identity. + +curacy and balanced player recognition. + +Contribution of each component. As shown in Tab. 5, ablation experiments assess the contributions of the visual context learning module (VCLM), player identification network (PIN), and bidirectional semantic interaction module (BSIM). Without any components, model ① performs + +![](images/7eaea95fd73fe00ff022f96d21694616b37130a485722bcbfbdd157e0564c9c7.jpg) +Figure 5. Qualitative results on NBA-Identity and VC-NBA-2022 datasets. "Model w/o" refers to the model using only video as input, without a prompt. "Model w/%" refers to the model with a multimodal prompt as input. G, Q, and L denote GPT-2, Qwen2.5-3B, and Llama3.2-3B, respectively. Different entity names are marked red and blue. And the specific visual scenes are marked green. + +![](images/02eacde6917f7d62d7ebcf2aead915db0b2832bb45be1874fd94614e6fcb5a88.jpg) + +
ModelVideoPlayerCIDErBLEU-4
①✓101.718.0
②✓102.318.3
③✓✓105.318.8
+ +Table 6. Ablation on the output of BSIM. + +poorly due to the challenge of identifying players in complex sports scenes. Adding VCLM (model ②) slightly improves performance by helping the model focus on key video regions instead of scanning all frames. While contextual information enhances feature connections, the limited improvement reflects the difficulty of recognizing player identities from visual content. + +Model ③ extends Model ① by incorporating the PIN, significantly boosting performance (CIDEr: $66.5 \rightarrow 95.1$ ). Based on this, model ④ further improves performance by leveraging key video content. Video content provides details on player actions and positions. Integrating this with player identities helps the model accurately associate players with their actions, leading to more precise descriptions. As a result, Model ⑤ significantly outperforms Model ③. Model ⑥ integrates all components, achieving the best performance. These results confirm the effectiveness of each module, highlighting the crucial role of visual-based player identification in identity-aware sports video captioning. We further explore the impact of the BSIM module outputting only a single enhanced feature (either video or player) on model performance. In Tab. 6, BSIM performs worse when outputting only one enhanced feature compared to using + +both. The enhanced player features contribute the most to overall performance. + +# 5. Conclusion, Limitation and Future Work + +We propose a player-centric multimodal prompt generation network for identity-aware basketball video captioning. An identity-related information extraction module is designed to help the LLM recognize player identities and generate descriptions with player names. To support this work, we construct a large identity-aware basketball video captioning dataset containing 9,726 videos, 321 players with bounding boxes, and 9 major event types. Extensive experiments validate the effectiveness of our method. + +As an initial exploration of player recognition for identity-aware sports video captioning, our work still has some limitations. Firstly, the model heavily relies on the performance of the player identification network. Future work should fully utilize the player-related knowledge, such as player numbers and jersey colors, to improve identity recognition accuracy. Secondly, the model struggles to infer shot distances, and the distance evaluation module should be added to address this issue. Thirdly, the dataset needs to include more event types to make it more comprehensive. Despite these limitations, we believe that recognizing player identities from a visual perspective is a key breakthrough for identity-aware sports video captioning and offers valuable insights. 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Prior methods enhance spatial coherence by modifying intermediate attention. But, this coherence isn't consistently propagated to the final output due to subsequent operations such as projections. Additionally, intermediate attention lacks direct interaction with text representations, such semantic discrepancy limits the full potential of CLIP. + +In this work, we propose a training-free, feedback-driven self-adaptive framework that adapts output-based patch-level correspondences back to the intermediate attention. The output predictions, being the culmination of the model's processing, encapsulate the most comprehensive visual and textual semantics about each patch. Our approach enhances semantic consistency between internal representations and final predictions by leveraging the model's outputs as a stronger spatial coherence prior. We design key modules, including attention isolation, confidence-based pruning for sparse adaptation, and adaptation ensemble, to effectively feedback the output coherence cues. Our method functions as a plug-in module, seamlessly integrating into four state-of-the-art approaches with three backbones (ViT-B, ViT-L, ViT-H). We further validate our framework across multiple attention types (Q-K, self-self, and Proxy augmented with MAE, SAM, and DINO). Our approach consistently improves their performance across eight benchmarks. + +# 1. Introduction + +Open-vocabulary semantic segmentation seeks to localize segments and align visual features with novel class descriptions [6, 49, 53]. CLIP models [9, 39], trained on web-scale datasets [40, 52], have demonstrated remarkable zero-shot performance in open-vocabulary tasks due to strong visual-text alignment [28, 39, 58]. However, adapting CLIP for + +![](images/8aa3f79b5241fb4d75f16c172080449162775187342ad343e870aeba4fe1dda7.jpg) + +![](images/dcd8a2fc18524c0e2879f5a7e017b59e0d2c45cda9fc2996b72885edadb0e28f.jpg) +Figure 1. Comparison with the existing training-free methods. Top: Prior works refine intermediate attention but face limitations: (1) improvements may not propagate to final segmentation; (2) attention lacks direct class information. Bottom: We introduce a feedback-driven self-adaptive mechanism that reintegrates semantic outputs with visual and textual cues into CLIP. Our approach is orthogonal to existing methods and serves as a plug-in. + +semantic segmentation remains challenging [64] since its pretraining primarily contrasts global image-text representations, limiting fine-grained localization and causing spatial misalignment in patch-level features [27, 44]. + +Previous efforts to enhance visual localization have primarily focused on fine-tuning CLIP for segmentation tasks [7, 37, 45, 51, 59]. However, fine-tuning compromises CLIP's robust generalization [12, 13, 47, 64]. Consequently, recent studies have shifted toward a training-free paradigm, addressing the factors contributing to localization degradation in CLIP. ClearCLIP [26] identifies residual connections as a major source of noisy segmentation, while + +![](images/b7a9f478afbe8f81ef6179b9382e294d4103a6bd5703428c3ffae0b4a92a3bd4.jpg) +(a) +Atn of [27] +Figure 2. Effectiveness of our feedback self-adaptive mechanism on an image segmented into grass and cat. The attention maps correspond to a reference patch (red dot) on the cat face. In (a), the reference patch misaligns with grass in the attention map, causing incorrect segmentation in (b). Our proposed FSA adjusts (a) using output predictions to generate semantically aligned attention, focusing on cat in (c), and corrects segmentation in (d). + +![](images/290554c73182a3a8e54b32ef1a058b189ba1bdf03e8a6adcd0af59e2dc43d027.jpg) +(b) +Seg of [27] + +![](images/a930180233e12ecee636e8de60c84decc157fe5b25997e6b399ed656f8ae199e.jpg) +(c) +Atn of [27] $^+$ FSA Seg. of [27] $^+$ FSA + +SCLIP [44] highlights the role of self-attention in disrupting spatial information arrangement. Since attention maps capture relationships among patches, patches with similar semantics should be strongly attended to reinforce spatial coherence. Building on this idea, recent works have modulated attention mechanisms, such as replacing Q-K attention with self-self [2, 26, 29, 44] or Proxy attentions [27], both demonstrating improved intermediate spatial consistency. + +However, the final segmentation relies on the output predictions rather than the intermediate attention. Enhanced intermediate coherence may deteriorate due to subsequent operations and hence, might not translate into improved segmentation results. More importantly, intermediate attention does not interface directly with class information. Therefore, neglecting the crucial interplay between intermediate attention and output predictions incorporating text representation is inherently sub-optimal. The output predictions intuitively represent the model's most refined patch-level semantic understanding, encapsulating high-level visual and textual features. We posit that patches with similar predictions likely belong to the same or related class. Leveraging the semantic coherence extracted from the output prediction can provide valuable feedback for further spatial information rearrangement refinement. + +Building upon this idea, we propose a training-free Feedback-driven Self-adaptive Attention (FSA) framework that adapts output semantic cues back into CLIP through a feedback loop. Specifically, we compute pairwise patch similarities between their class predictions, which provides a stronger prior for guiding intermediate attention than using intermediate representations alone. Modulating the original attention maps with these output-based similarities improves consistency between internal representations and final predictions, enhancing information aggregation among semantically similar patches and improving segmentation accuracy. Fig. 1 shows a high-level comparison with the existing methods. The visual example in Fig. 2 demonstrates that our FSA successfully incorporates the semantic cues at the output to correct the wrongly seg + +
TTAKDOur feedback mechanism
Minimizes entropy using output logits.Treats output logits as soft labels.Computes patch semantic similarity from output logits.
+ +Table 1. Similarity of our FSA with other learning paradigms. + +mented patches. Our FSA is an unsupervised adaptation method [5, 31] that leverages the model's self-outputs, sharing similarities with learning paradigms such as test-time adaptation (TTA [34, 41, 42]) and knowledge distillation (KD [22, 54, 56, 61, 62]), as shown in Table 1. + +To focus on the modulation only on the initial intermediate attention maps, we introduce attention isolation to ensure that the initial output predictions reflect the influence of the original attention rather than interference from subsequent operations. Additionally, we propose confidence-based pruning to filter out irrelevant patches while enhancing the impact of semantically relevant regions. Furthermore, we design three adaptation strategies and integrate them into an ensemble to achieve consistent improvements across diverse attention configurations and backbones. + +To demonstrate the versatility of our FSA framework, we integrate it into four SoTA methods: MaskCLIP [64], SCLIP [44], ClearCLIP [26], and ProxyCLIP [27]. Additionally, we validate FSA across various attention types, including Q-K, self-self, and Proxy attention, augmented by MAE [21], SAM [25], and DINO [5, 38]. Evaluated on eight open-vocabulary segmentation benchmarks, our FSA consistently enhances performance across these configurations. Our contributions are summarized as: + +- We introduce a feedback-driven self-adaptive mechanism that refines the attention process by integrating output-derived semantic coherence cues back into the model. +- We develop key modules, including attention isolation, sparse attention via confidence-based pruning, and adaptation ensemble, to effectively propagate semantic coherence cues from the output. +- Our FSA is training-free, and its adaptation process preserves the original model parameters. +- Our FSA functions as a plug-in module that enhances existing methods and attention configurations, demonstrating effectiveness across eight benchmarks. + +# 2. Related work + +Open-vocabulary segmentation. CLIP's large-scale pretraining has enabled strong zero-shot transfer for open-vocabulary semantic segmentation [23, 24, 28, 58], but its global-level pretraining leads to patch-level localization issues [64]. Fine-tuning on segmentation datasets helps address this by enabling local-to-global alignment, often using self-distillation [7, 30, 48] or integrating spatial coherence from stronger VFMs into CLIP [45, 51, 59]. However, fine-tuning can reduce CLIP's robustness [47], prompting a shift + +to training-free approaches that modulate problematic components of CLIP for improved performance. For example, ClearCLIP [26] improves segmentation by altering connections in the last attention block, while MaskCLIP [64] enhances localization with the value embedding. Methods like GEM [2], CLIPSurgery [29], and SCLIP [44] replace the original Q-K attention with self-self attentions. ProxyCLIP [27] combines CLIP and VFMs, leveraging spatial feature correspondence for state-of-the-art performance. However, most approaches focus on modulating the forward pass, neglecting spatial consistency and class information encoded in the output predictions. + +Output-based knowledge transfer. Output predictions have been effectively used across various machine learning areas, including self-distillation, model compression, domain adaptation, self-supervised learning, uncertainty estimation, and iterative refinement. Self-distillation leverages predictions for intra-model knowledge transfer [33], enhancing generalization and compression [20, 22, 60]. In domain and test-time adaptation, output entropy is minimized to adapt models dynamically without additional labeling [43, 46]. Self-supervised learning employs predictions to create pseudo-labels or enforce consistency across augmented views, refining representations without labeled data [8, 11, 18]. For uncertainty estimation and model calibration, analyzing prediction logits helps assess prediction confidence, with techniques like temperature scaling enhancing reliability [19, 55, 57]. Iterative refinement in vision tasks uses predictions to progressively improve predictions, boosting spatial consistency and segmentation accuracy [4, 10, 32]. These approaches highlight the versatility of output logits for adaptation, optimization, and feedback across diverse tasks. In this work, we introduce a new training-free self-adaptation method that utilizes patch similarity in the output to reorganize the spatial correspondence of intermediate attentions. + +# 3. Preliminaries + +Segmentation using CLIP ViT. ViT is composed of attention blocks [16]. Let $\boldsymbol{x} \in \mathbb{R}^{L \times v} = [x_1, \ldots, x_L]^T$ denote the patch tokens, where $L$ is the number of patches and $v$ is the visual feature dimension. Note, we drop CLS token and layer norm [1] for simplicity and follow ProxyCLIP [27] and ClearCLIP [26] to modulate the last layer. The resulting visual dense patch features are then obtained by: + +$$ +\boldsymbol {Q} = \boldsymbol {x} \cdot W _ {Q}, \quad \boldsymbol {K} = \boldsymbol {x} \cdot W _ {K}, \quad \boldsymbol {V} = \boldsymbol {x} \cdot W _ {V}, \tag {1} +$$ + +$$ +\boldsymbol {z} = \boldsymbol {y} ^ {\prime} + \operatorname {F F N} \left(\boldsymbol {y} ^ {\prime}\right), \quad \boldsymbol {y} ^ {\prime} = \boldsymbol {x} + \operatorname {P r o j} \left(\operatorname {A t t n} ^ {\text {i n i t}} \cdot \boldsymbol {V}\right) \tag {2} +$$ + +$$ +\boldsymbol {Z} ^ {\text {d e n s e}} \in \mathbb {R} ^ {L \times d} = \mathcal {P} (\boldsymbol {z}), \tag {3} +$$ + +where $W_{Q}, W_{K}, W_{V}$ , Proj are the projection matrices, FFN is the feed-forward network. $\mathcal{P}$ projects the visual features with dimension $v$ to the visual-text shared space with + +![](images/721d63dc3655cf7ea627499c878d6e0b3df8143d80721b7489869880397198ce.jpg) +Figure 3. Semantic coherence retention between attention and final predictions (higher is better) and mIoU improvements averaged on 8 benchmarks. Our self-adaptive attention feeds the patch-wise semantics at output back to modulate the intermediate attention to both improve semantic retention and final mIoU. + +dimension $d$ , $(\cdot)$ is the matrix multiplication, $\mathrm{Attn}^{init} \in \mathbb{R}^{L \times L}$ represents the initial attention maps, which can be the default attention (SoftMax $\left(\frac{Q K^T}{\tau}\right)$ , where $\tau$ is the scaling factor) or other attention configurations, such as self-self $(Q - Q, K - K, V - V)$ [35, 44] and Proxy [27] attention. Note that, in certain methods, e.g., ProxyCLIP and ClearCLIP, the residual and FFN in Eq. 2 are omitted in the final layer. + +To obtain the text representation $T \in \mathbb{R}^{c \times d}$ , we input a text prompt, "A photo of a [CLASS]", combined with $c$ class names into the text encoder. Finally, the patch predictions are computed by taking the cosine similarity: + +$$ +\boldsymbol {Y} ^ {\text {d e n s e}} \in \mathbb {R} ^ {L \times c} = \cos \left(\boldsymbol {Z} ^ {\text {d e n s e}}, \boldsymbol {T}\right). \tag {4} +$$ + +The segmentation map $\mathcal{M} \in \mathbb{R}^{L \times 1}$ is obtained by arg max along the $c$ dimension of $\pmb{Y}^{\mathrm{dense}}$ . + +Motivation. CLIP demonstrates limited localization for segmentation [64]. Since attention governs the arrangement of spatial information [44], recent studies have empirically shown that self-self [35, 44] and Proxy attention [27] exhibit stronger local feature correspondence. However, segmentation ultimately depends on output predictions rather than intermediate attention. The spatial coherence established in Attn $^{init}$ may be disrupted by subsequent operations, preventing it from being fully conveyed to the final output. + +We first examine such spatial coherence retention by comparing the intermediate attention Attn $^{init}$ (final layer as in ProxyCLIP) and the final segmentation map $\mathcal{M}$ . Intuitively, if two patches have high mutual attention scores, they should be ideally predicted to the same class. For the $i^{th}$ patch, we identify the $k$ patches with Top- $k$ score in the $i^{th}$ row of Attn $^{init}$ and check whether any of the $k$ patches is predicted as the same class of $i^{th}$ patch in $\mathcal{M}$ : + +$$ +\text {R e t e n t i o n} = \frac {1}{L} \sum_ {i = 1} ^ {L} \max _ {j \in \operatorname {T o p} - k \left(\operatorname {A t t n} _ {i} ^ {i n i t}\right)} \mathbb {I} \left(\mathcal {M} _ {i} = \mathcal {M} _ {j}\right), \tag {5} +$$ + +where $\mathbb{I}$ is an indicator that equals 1 if the condition is + +![](images/eabc36aeddaef02ac2e6b830cb0f04ba905ec007e7421469bc0e1c16b7254faf.jpg) +Figure 4. Overview of our feedback-driven self-adaptive attention framework. We isolate the contribution of initial attention using a dual branch with uniform attention. Pairwise patch similarity is then calculated by applying KL divergence to the output logits. A confidence-based pruning step follows to eliminate irrelevant patches and amplify the correlation between related patches. The resulting sparse feedback attention is adapted back to the initial attention maps using three operations, which are subsequently ensembled. + +met. To avoid self-comparisons, we set the diagonal elements $\left(\mathrm{Attn}_{ii}^{init}\right)$ to zero. Fig. 3 shows the average Top-10 retention across 8 benchmarks for various attention configurations. Obviously, such spatial coherence is not fully retained in the final predictions. Furthermore, the attention map does not interface with class information directly. In contrast, output predictions capture comprehensive visual semantics and integrate class information from textual features. This motivates our feedback self-adaptive approach, which leverages these outputs as semantic cues to rearrange and modulate spatial information in the intermediate attention $\mathrm{Attn}^{init}$ . Our method enhances semantic consistency and segmentation performance, as demonstrated in Fig. 3. In Appendix C, we demonstrate another metric and show the retention degradation after each operation. + +# 4. Method + +In this section, we present the feedback self-adaptive attention (FSA) framework (Fig. 4). We first construct effective self-adaptive attention through attention isolation (Sec.4.1) and confidence-based pruning (Sec.4.2). Then, we adapt the self-adaptive attention to modulate the spatial information in the initial attention Attn $^{init}$ (Sec.4.3). + +# 4.1. Stand-alone intermediate attention isolation + +The initial attention map, $\mathrm{Attn}^{init}$ , serves as the foundation for spatial coherence, determining both the selection of correlated patches and the intensity of their attention. Thus, our objective is to modulate $\mathrm{Attn}^{init}$ solely for spatial knowledge rearrangement. However, as shown in Eq. 2-4, the logits are derived through a sequential process: $\mathrm{Attn}^{init} \cdot V \rightarrow$ sub-modules (projections, FFN, etc.) $\rightarrow$ text $\rightarrow$ logits. Consequently, the dense logits, $Y^{dense}$ , do not exclusively re + +flect the independent contribution of $\mathrm{Attn}^{init}$ , as it functions merely as an intermediate measure within this pipeline. + +To address the interference, we devise an isolation procedure that preserves the stand-alone contribution of $\mathrm{Attn}^{init}$ in $\mathbf{Y}^{dense}$ , making it crucial that output relationships reflect only the initial attention maps. Specifically, we attach a parallel branch with a manually crafted uniform attention map $\mathrm{Attn}^{uni} = \frac{1}{L}\mathbf{1}_{L\times L}$ , ensuring every patch is equally attended. The resulting logits $\mathbf{Y}^{dense}$ are obtained following the same steps in Eqs. 2-4. Both $\mathrm{Attn}^{uni}$ and $\mathrm{Attn}^{init}$ traverse identical sub-modules and text-alignment stages, allowing us to isolate the learned attention's net effect by subtracting the uniform-based logits from the original. Therefore, we can pinpoint how much of the final logits is genuinely driven by the learned selective attention patterns rather than a globally "spread out" context. The resulting subtraction is then transformed into a probability distribution via softmax: + +$$ +\boldsymbol {Y} _ {i s o} ^ {d e n s e} = \operatorname {S o f t m a x} \left(\boldsymbol {Y} ^ {d e n s e} - \boldsymbol {Y} _ {u n i} ^ {d e n s e}\right). \tag {6} +$$ + +We then quantify the relationships between patches by calculating pair-wise KL divergence: + +$$ +\mathcal {D} (i, j) = \mathrm {K L} (\boldsymbol {Y} _ {i s o, i} ^ {d e n s e} \| \boldsymbol {Y} _ {i s o, j} ^ {d e n s e}), \tag {7} +$$ + +where $\mathcal{D} \in \mathbb{R}^{L \times L}$ records the divergence for each pair of patches. To emphasize patch correspondence rather than difference, we convert the divergence to similarity as: + +$$ +\mathcal {S} \in \mathbb {R} ^ {L \times L} = \frac {1}{\mathcal {D} + 1}. \tag {8} +$$ + +The KL divergence, bounded in $[0, -\infty]$ , is mapped to $[0, 1]$ , with a score of 1 indicating maximum similarity. + +When attention isolation is applied, the output logits align better with the intermediate attention, leading to further segmentation gains. + +# 4.2. Confidence-based sparse attention + +The similarity map $S$ not only encodes visual semantic coherence among patches but more importantly, it integrates class cues from text representations. Capturing each patch's response to each class offers a robust foundation for adapting attention with contextually relevant cues. However, in segmentation tasks, patches may belong to various classes, each with unique semantic information. Since $S$ contains similarities for every patch pair, low-correlated patches can dilute the relationships between strongly correlated patches. Thus, it is effective to suppress irrelevant patches while amplifying semantically coherent ones. + +To this end, we propose a confidence-based sparse attention. Specifically, we first normalize each row of $S$ using softmax to obtain $\hat{S}$ , resulting in a confidence distribution across patches. Let $\hat{S}_i$ denote the $i^{\text{th}}$ row which represents the confidence of similarity between the $i^{\text{th}}$ patch and all other patches. We sort $\hat{S}_i$ in descending order $(\hat{S}_i^{\text{sorted}})$ and record the sorting indices $(idx)$ . For each position, we compute the cumulative confidence probability: + +$$ +\mathcal {C} _ {i, j} ^ {\text {s o r t e d}} = \sum_ {k = 1} ^ {j} \hat {\mathcal {S}} _ {i, k} ^ {\text {s o r t e d}}. \tag {9} +$$ + +We then revert to their original order using $idx$ : $\mathcal{C}_i = \mathcal{C}_i^{\mathrm{sorted}}[idx]$ . Repeating for each row yields the final cumulative confidence map $\mathcal{C}$ . We then set a confidence level $p$ to selectively amplify higher similarity values with adaptive exponential scaling and fully suppress the others: + +$$ +\mathcal {S} _ {i, j} ^ {\text {s p a r s e}} = \left\{ \begin{array}{l l} \mathcal {S} _ {i, j} \cdot e ^ {\lambda \cdot \mathcal {S} _ {i, j}}, & \text {i f} \mathcal {C} _ {i, j} \leq p \text {o r} j = 1 \\ - \infty , & \text {o t h e r w i s e}, \end{array} \right. \tag {10} +$$ + +where $\lambda$ and $p$ are the only hyperparameters in our method, controlling the scaling sharpness and the cutoff confidence, set empirically to 2 and 0.45, respectively. Finally, we convert the sparse similarity map into our feedback attention: $\mathcal{A}^f = \mathrm{softmax}(S^{sparse})$ . + +In summary, our confidence-based sparse attention (Eq. 9 & 10) can be interpreted as: selecting patches starting with the highest confidence until cumulative confidence of selected patches reaches $p$ . It emphasizes semantically coherent patches while ignoring low-confidence ones. A pseudo-code can be found in the supplementary. + +# 4.3. Feedback self-adaptive attention + +The resulting attention $\mathcal{A}^f$ captures the ultimate semantic relationships between pairs of patches, derived from the initial attention. We reintegrate this feedback into the original pipeline (Eq. 2-4) to enhance the spatial arrangement + +of information. Specifically, we propose three training-free adaptations to modify the interaction with $V$ in Eq. 2: + +$$ +\operatorname {A t t n} ^ {i n i t} \cdot \boldsymbol {V} \xrightarrow {\text {a d a p t a t i o n}} \left\{ \begin{array}{l l} \mathcal {A} ^ {f} \cdot (\operatorname {A t t n} ^ {i n i t} \cdot \boldsymbol {V}), & (1 1) \\ \operatorname {A t t n} ^ {i n i t} \cdot (\mathcal {A} ^ {f} \cdot \boldsymbol {V}), & (1 2) \\ \mathcal {A} ^ {f} \cdot \boldsymbol {V}. & (1 3) \end{array} \right. +$$ + +Eq. 11 captures the Attninit-driven relationships first, then selectively amplifies or suppresses them based on feedback, effectively introducing a two-step refinement. Eq. 12 immediately influences $\mathbf{V}$ before initial attention is applied, giving higher priority to semantic coherence and confidence information from the output logits. Eq. 13 emphasizes only the feedback-driven information solely relying on the output semantic coherence and confidence. We observe that each of the three adaptations offers distinct benefits depending on the backbone, attention configuration, and benchmark. To leverage their combined strengths, we propose an ensemble approach by isolating $\mathbf{V}$ in Eq. 11-13: + +$$ +\left(\frac {\mathcal {A} ^ {f} \cdot \operatorname {A t t n} ^ {i n i t} + \operatorname {A t t n} ^ {i n i t} \cdot \mathcal {A} ^ {f} + \mathcal {A} ^ {f}}{3}\right) \cdot V. \tag {14} +$$ + +We denote the adapted logits from Eq. 11-14 as $\mathbf{Y}_1^{dense}$ , $\mathbf{Y}_2^{dense}$ , $\mathbf{Y}_3^{dense}$ , and $\mathbf{Y}_{\text{ens}}^{dense}$ which are processed using the arg max to generate the adapted segmentation map. + +# 5. Experiments + +In this section, we first validate our FSA framework by integrating it with various SoTA methods and attention configurations. We then conduct comprehensive ablation studies to assess the effectiveness of each proposed component. + +# 5.1. Implementation details and datasets + +Architectures. To show the versatility of FSA, we test on 3 backbones: ViT-B/16 and ViT-L/14 from CLIP [39], and ViT-H/14 from OpenCLIP [9]. We adopt DINO ViT-B/8 [5] for ProxyCLIP as default unless specified otherwise. + +**Implementations.** Our FSA functions as a plug-in module that can be integrated into SoTA methods, modifying only the model component. Note that, we preserve their original data processing pipeline. For example patch size and stride size are kept the same. All experiments report mean Intersection over Union (mIoU) on validation sets, without training or post-processing. Implementation is based on the MMSegmentation codebase [14]. + +Datasets. We follow TCL [6], ProxyCLIP [27], SCLIP [44] and CLIP-DINOiser [50] to evaluate on eight standard benchmarks: (i) with background class: PASCAL VOC [17] (VOC), PASCAL Context [36] (Context), and COCO Object [3] (Object); and (ii) without background class: PASCAL VOC20 [17] (VOC20), PASCAL Context59 [36] (Context59), COCO Stuff [3] (Stuff), Cityscapes [15] (City), and ADE20K [63] (ADE). + +
ModelsMethodsVOCContextObjectVOC20Context59StuffCityADEAvg.
CLIP ViT-B/16MaskCLIP\(_{ECCV^*22}\) [64]38.823.620.674.926.416.412.69.827.9
+ FSA47.731.029.278.334.221.428.416.035.8 (+7.9)
SCLIP\(_{ECCV^*24}\) [44]59.130.430.580.434.222.432.216.138.2
+ FSA61.533.333.982.836.824.434.717.540.6 (+2.4)
ClearCLIP\(_{ECCV^*24}\) [26]51.832.633.080.935.923.930.016.738.1
+ FSA53.036.633.281.333.824.330.817.438.8 (+0.7)
ProxyCLIP\(_{ECCV^*24}\) [27]61.335.337.580.339.126.538.120.242.3
+ FSA (Ours)63.736.138.082.339.927.038.820.543.3 (+1.0)
CLIP ViT-L/14MaskCLIP\(_{ECCV^*22}\) [64]23.311.77.229.412.48.811.57.213.9
+ FSA44.826.827.873.929.419.023.116.232.6 (+18.7)
SCLIP\(_{ECCV^*24}\) [44]43.522.325.069.125.217.618.610.929.0
+ FSA48.127.830.879.930.320.427.115.935.0 (+6.0)
ClearCLIP\(_{ECCV^*24}\) [26]46.129.626.780.030.119.927.915.034.4
+ FSA47.530.827.980.430.220.427.216.835.2 (+0.8)
ProxyCLIP\(_{ECCV^*24}\) [27]60.634.539.283.237.725.640.122.642.9
+ FSA (Ours)61.834.940.284.138.125.941.222.943.6 (+0.7)
CLIP ViT-H/14MaskCLIP\(_{ECCV^*22}\) [64]31.413.316.241.715.88.417.710.419.3
+ FSA44.827.727.671.330.520.726.119.033.4 (+14.1)
SCLIP\(_{ECCV^*24}\) [44]43.823.524.667.525.616.819.511.329.1
+ FSA48.128.429.176.431.320.629.118.135.1 (+6.0)
ClearCLIP\(_{ECCV^*24}\) [26]46.027.127.978.129.819.328.316.034.1
+ FSA47.231.128.378.628.520.629.318.735.3 (+1.2)
ProxyCLIP\(_{ECCV^*24}\) [27]65.035.438.683.339.626.842.024.244.4
+FSA (Ours)67.936.340.285.740.527.343.624.545.8 (+1.4)
+ +Table 2. Integration of FSA into the state-of-the-art methods for open-vocabulary semantic segmentation on eight standard benchmarks. Our feedback self-adaptive framework consistently improves previous approaches across all datasets and three different backbones. + +
CLIPVFMsMethodsV21C60ObjV20C59StfCityADEAvg.
ViT-B/16SAMProxy59.333.635.480.437.025.037.019.140.8
ViT-B/16+ FSA60.734.035.881.837.425.237.919.341.5 (+0.7)
MAEProxy52.230.430.876.333.523.130.117.136.7
ViT-B/16+ FSA54.330.931.378.133.923.433.617.537.9 (+1.2)
DINOv2Proxy58.633.837.083.037.225.433.919.741.1
ViT-B/14+ FSA59.233.937.484.037.525.534.419.741.4 (+0.3)
ViT-L/14SAMProxy57.232.636.582.335.624.239.120.741.0
ViT-B/16+ FSA58.533.038.083.136.124.540.521.041.8 (+0.8)
MAEProxy49.027.831.678.330.220.831.817.235.8
ViT-B/16+ FSA52.829.934.980.232.522.634.719.038.3 (+2.5)
DINOv2Proxy56.633.036.785.236.224.635.221.641.1
ViT-B/14+ FSA57.433.338.085.836.524.736.121.941.7 (+0.6)
ViT-M/14SAMProxy63.534.136.784.037.925.041.122.043.1
ViT-B/16+ FSA64.934.437.685.538.025.142.621.943.7 (+0.6)
MAEProxy54.729.832.280.632.921.834.919.438.3
ViT-B/16+ FSA58.732.035.282.235.324.037.921.340.8 (+2.5)
DINOv2Proxy61.534.037.386.137.826.237.823.443.0
ViT-B/14+ FSA63.034.438.587.438.426.439.723.743.9 (+0.9)
+ +# 5.2. Main results + +Integration into the SoTA methods. Table 2 reports the integration of our FSA with training-free SoTA methods including: MaskCLIP [64], SCLIP [44], ClearCLIP [26] and ProxyCLIP [27]. Our method consistently improves all of them across all eight benchmarks. Notably, we surpass MaskCLIP by a significant margin of $+7.9$ mIoU, $+18.7$ mIoU and $+14.1$ mIoU using ViT-B/16, L/14, and H/14, respectively. Obvious improvement is also observed on SCLIP. ProxyCLIP leverages external knowledge from VFMs, providing strong spatial coherence. However, our FSA system further enhances performance across diverse + +Table 3. Integration of our FSA into ProxyCLIP with various VFMs. Consistent improvements across VFMs, benchmarks, and backbones highlight the versatility and effectiveness of our FSA. + +
CLIPAttentionV21C60ObjV20C59StfCityADEAvg.
VIT-B/16Q-K34.819.021.476.121.514.215.910.726.7
+ FSA40.722.223.576.925.216.420.112.329.7 (+3.0)
Q-Q55.631.732.981.435.523.930.317.938.7
+ FSA56.932.234.281.935.924.231.218.239.3 (+0.6)
K-K54.531.530.077.535.423.433.018.137.9
+ FSA57.532.633.380.436.224.133.518.439.5 (+1.6)
V-V51.429.730.174.132.821.530.916.235.8
+ FSA54.431.431.978.434.622.632.217.237.8 (+2.0)
VTL/14Q-K34.719.224.775.721.314.620.611.027.7
+ FSA40.822.027.777.324.116.524.312.230.6 (+2.9)
Q-Q49.226.731.180.129.519.830.616.635.5
+ FSA50.426.931.480.429.819.930.716.835.8 (+0.3)
K-K49.326.628.776.630.720.531.817.035.2
+ FSA51.127.330.378.530.820.431.717.235.9 (+0.7)
V-V47.427.031.078.729.820.231.118.035.4
+ FSA49.427.731.479.730.620.631.818.336.2 (+0.8)
VIT-H/14Q-K36.620.923.781.523.015.525.313.430.0
+ FSA46.324.730.883.526.918.130.815.534.6 (+4.6)
Q-Q51.126.829.779.129.919.632.717.735.8
+ FSA52.827.730.579.230.820.434.018.636.7 (+0.9)
K-K51.627.230.173.530.320.034.018.835.7
+ FSA53.428.130.875.031.220.834.219.536.6 (+0.9)
V-V51.228.130.080.231.021.333.719.736.9
+ FSA52.728.630.780.531.721.634.419.937.5 (+0.6)
+ +Table 4. Integration of our FSA into Q-K and self-self attention. Our method consistently shows improvements across all attention configurations. Specifically, we improve the original Q-K by a large margin, which is less effective in localization. + +CLIP architectures, pushing their boundaries. + +Integration with various attention configurations. The proposed feedback self-adaptive mechanism operates independently of the specific intermediate attention, demonstrating its versatility when integrated with various attention configurations. Table 3 shows results of applying our method to ProxyCLIP with different VFMs (MAE [21], + +![](images/2fe429683d7e58c962c93e9d99d89d5c568227278a3ac0806f3a7540c38091cb.jpg) +Input image + +![](images/ae5aa8721642e3911825a15d9455ea6361ff29bfb5aaf52a9091d54c7ba750f1.jpg) +Attention map of ProxyCLIP + +![](images/b61aef5eee6cc6fbef23f27e5534075ecf3f06a5e5ae683fe83911b081fdf713.jpg) +Segmentation map of ProxyCLIP + +![](images/cdb991a0a0cfcfcb3057cb92b977ad1a7fd6563530368c9a30f7778ab40bdb6f.jpg) +Our self-adapted attention map + +![](images/79c4041975f09a04f9c4c2062e14ba17769533969001efee2c87024dc757683b.jpg) +ProxyCLIP + our FSA + +![](images/749536f06f630b8b0afc8bacf110b5892c79cc6cd2ac2b4460ad11e477f1526e.jpg) +Ground truth segmentation map + +![](images/76e9ff65707783c356ef2afdadf14dbeaec0424f5d055773c74ebd835a9475cf.jpg) +Figure 5. Visualization of segmentation results of ProxyCLIP integrated with our FSA. The attention maps $(2^{nd}$ and $4^{th}$ columns) correspond to the reference patch shown in the $1^{st}$ column. ProxyCLIP produces with holes within the same object due to weak attention across regions of the object. In contrast, our FSA effectively aggregates similar patches, enabling the correction of missegmented regions. + +![](images/6b3c10c258429a9bc7f9868c6351d6aa51732858c3b2989403d9973b9ab708e9.jpg) +Input + +![](images/4fc19e280ff8e6b353511b4b38fd3597efbe34b6110c5c91be4ba8481cb39fda.jpg) + +![](images/d3516e3f70139272abb1a99316236914a8bd9b875fe915906262ea56931ed70a.jpg) +MaskCLIP + +![](images/2b4766640e0c76c25b479cb21b39f8e96a7630e1ba3b106bea590bd79def99b7.jpg) + +![](images/adc76cf2254f22d4ed1506193eec5fde09ba8ddda441a5071888e3ca98393a19.jpg) ++ FSA + +![](images/32ece473f470d6be76a44458847e2259f2bf62a5ed95f9b0582d0c0d35b117e6.jpg) + +![](images/80fdfa82a590919f13d9bf00aae0b85d162be4dbb035d8382b5ce18ecd8b4346.jpg) +GT + +![](images/1914633ac2b7f9c96ce4c22aeb82d9024249f6dd7c7e69602ee9f99efa06e91b.jpg) + +![](images/12328b7ba25b724b129a76fc637e0c2fee66a3f7e73c445d0d058cb7453b5212.jpg) +Input + +![](images/cd724d2347efef34e498da88880f747fb9099b407b6472446221318b9868f16f.jpg) + +![](images/6dd818a19316ef11a0447c73d3391d94a07425b4d47514484133e8135d6126b6.jpg) +SCLIP + +![](images/04d6500dd15c13942f3d665409e408b35536a1246769bf6b6f3de4775adb7cea.jpg) + +![](images/7933bedd4e18cb160347343bbca48484c8e1b74908792c54fea142befa32ddbb.jpg) ++ FSA + +![](images/7b8a60d4051ac0e7dbbd042d398b537be57b01d9db635be5a1fea06aeaf00257.jpg) + +![](images/42ad55e739e2c101f087620424e2347bdf3c282ad791d8c03b7bbaef73f48399.jpg) +GT + +![](images/889ac2918f70011601c2e67496c27f4c5a44850a454b76c541dcd21d3a83839c.jpg) + +![](images/aac5693a58a40d4fc653b29dd4dc829c908d1d6852f422da22a29ce9ee9ad921.jpg) +Input + +![](images/183050a0323151b4c4165354d81ffd216477ffb7e014becbff3161f2a364a235.jpg) + +![](images/dc2eb48f48c454c4cad0af29fd8c11f0287f5c8e2cd78d6cfcec4022c50dfabe.jpg) +ProxyCLIP +Figure 6. Qualitative results. By integrating our feedback self-adaptive mechanism, we correct missegmented patches, ensuring consistent segmentation within each object. + +![](images/b3bb8e33e1063bdd3c10b4312f76808d249544c1cf653a28b23a4e04667d0fe1.jpg) + +![](images/de5c2905d3774a934a9eed9bf35b92828bac588668318ffef17c7d781714e26b.jpg) ++ FSA + +![](images/3048778be49be916ec441c1bea38958d8e776caebd9070544865a9e64e95ba53.jpg) + +![](images/310a456c0932db4f19874bab9b6f9a2e703194a15607741ad8e91442a90379d4.jpg) +GT + +SAM [25], and DINOV2 [38]), each displaying varying levels of spatial correspondence. Despite these differences, our method proves flexible, achieving consistent improvements across all VFMs, benchmarks, and backbones. Notably, while MAE shows weaker baseline performance, our feedback correction enhances it by $+1.2\mathrm{mIoU}$ , $+2.5\mathrm{mIoU}$ and $+2.5\mathrm{mIoU}$ across the three backbones. + +We also integrate our method with inherent Q-K and self-self attention mechanisms using the codebase from ProxyCLIP. As summarized in Table 4, improvements are observed across all attention types on the three backbones. + +
ScalingPruningViT-B/16ViT-L/14ViT-H/14
XX22.623.525.5
XFixed ratio36.637.841.0
XFixed threshold37.238.640.1
XConfidence-based38.239.442.5
✓Confidence-based43.343.645.8
+ +Table 5. Ablation on confidence-based pruning with ProxyCLIP over 8 benchmarks. Our adaptive confidence-based pruning selects relevant patches while suppressing irrelevant ones. Additionally, adaptive exponential scaling emphasizes the importance of these selected patches, further enhancing their contribution. + +The most significant gains are seen with Q-K attention (+3.0 mIoU, +2.9 mIoU, and +4.6 mIoU), as it is less effective for patch-level alignment. Overall, our self-adaptive framework is compatible with various attention configurations, yielding performance gains ranging from +0.3 mIoU to +4.6 mIoU as shown in Tables 3 and 4. + +Qualitative comparison with SoTA. Fig. 5 illustrates that ProxyCLIP often focuses on object edges, resulting in unstable segmentation. By integrating our adaptive FSA, we refine the intermediate attention to focus solely on the main regions of the same object, thereby improving the segmentation. Fig. 6 presents additional qualitative results with our FSA incorporated into MaskCLIP, SCLIP, and ProxyCLIP. Leveraging the feedback mechanism, we corrects misclassified regions, leading to more consistent segmentation. Additional results are provided in Appendix B. + +# 6. Ablation studies + +Confidence-based pruning. We generate sparse feedback attention through confidence-based pruning, highlighting semantically related patches likely belonging to the same class. As shown in Table 5, both fixed-ratio and threshold-based pruning improve segmentation by filtering irrelevant patches, while confidence-based pruning achieves greater + +![](images/378bb87e9d7bee58e496ab5bb7345c1e9cd8d5bc38c2a1518dbb55e402064b97.jpg) +Figure 7. Sensitivity on $p$ (left) and $\lambda$ (right) with ViT-L/14. As $p$ increases, mIoU rises then falls with added irrelevant patches. $\lambda$ adjusts amplification and remains stable between 1 and 2.5. + +
Attention isolationMaskCLIPSCLIPProxyCLIP
w/o FSA (baseline)13.929.042.9
X29.8 (+15.9)33.2 (+4.2)43.4 (+0.5)
✓32.6 (+18.7)35.0 (+6.0)43.6 (+0.7)
+ +gains by adaptively selecting correlated patches. Additionally, adaptive exponential scaling amplifies relative differences in patch similarity, further enhancing segmentation. + +Fig. 7 illustrates the sensitivity of parameters $p$ and $\lambda$ using ViT-L/14 on the VOC dataset. As $p$ increases, more relevant patches are included; however, beyond a certain point, irrelevant patches are also incorporated, which affects attention on spatially correlated patches. Increasing $\lambda$ improves relative distances between patch similarities, allowing relevant patches to dominate. Performance remains stable between 1.0 and 2.5 but decreases when too few patches dominate, potentially excluding important patches. Fig. 9 shows the distributions of row-wise pruning ratios, underscoring the necessity of an adaptive pruning mechanism. + +![](images/3a878c47d0b437475f57993bbe5e927ed671d7ef3900e1fd52ad3aef9e5c8e7c.jpg) +Figure 8. Qualitative results on attention isolation (iso.). + +![](images/aef0146b14248ec5e2a9890c5a83e8d0e2123c97d4a84cfa64649ba62dec6d64.jpg) + +![](images/8a703d17eb6b7c31afa48dbd99aa574f3007de9cc8db6938db074e6540cc782f.jpg) + +![](images/2cae517f7975c3ccfd412a50ab540908debb1d82878b12f189df2170b14735b6.jpg) + +![](images/f6e100b8a18322940142c587d808a3713c26b1fe102a583fa58dbe546379f794.jpg) + +Attention isolation. Our feedback attention modulates the intermediate attention, making it crucial that output relationships reflect only the initial attention maps. As shown in Table 6, we observe improvements over 3 methods even without isolation. When attention isolation is applied, the output logits align better with the intermediate attention, leading to further segmentation gains. The qualitative examples in Fig. 8 also demonstrate that attention isolation is + +![](images/95275ba3057a80fcc7e821c70c358db7dc10e3a78cd9bf90c3e018107d57f1a4.jpg) +Figure 9. Distribution of pruning ratio. The variety of distribution demonstrates the necessity of our adaptive mechanism. + +Table 6. Validation on attention isolation with ViT-L/14. Such isolation ensures that the output logits directly reflect the intermediate attention, enabling more consistent feedback adaptation. + +
Y1denseY2denseY3denseMaskCLIPSCLIPProxyCLIP
w/o FSA (baseline)13.929.042.9
✓32.1 (+18.2)34.2 (+5.2)43.5 (+0.6)
✓31.8 (+17.9)33.9 (+4.9)43.4 (+0.5)
✓30.9 (+17.0)34.5 (+5.5)43.5 (+0.6)
Ensemble32.6 (+18.7)35.0 (+6.0)43.6 (+0.7)
+ +Table 7. Validation on ensembling with ViT-L/14. Our ensembling strategy combines the strengths of each adaptation, resulting in consistent and enhanced segmentation across methods. + +
MethodsViT-B/16ViT-L/14ViT-H/14
Proxy12.9ms20.1ms28.1ms
+FSA13.6ms21.1ms29.2ms
+ +Table 8. Speed on V100 GPU with patch resolution of ${224}\mathrm{x}{224}$ . + +effective in removing noise in segmentation maps. + +Ensembling on adapted attentions. Table 7 presents the individual segmentation results for each adaptation strategy in Eqs. 11-13. While each method shows improvement, the best performance varies across SoTA methods. Our ensembling strategy combines their strengths, resulting in consistent and enhanced segmentation performance. + +Cost analysis. Table 8 reports speed averaged over 3 trails of 100 forward passes. As we only modify the last attention as in ProxyCLIP, FSA only adds $3 - 5\%$ overhead. + +Iterative adaptation. Intuitively, our FSA supports iterative adaptation, but, further improvement is not observed. + +# 7. Conclusion + +In this work, we introduce FSA, a novel training-free self-adaptive framework that enhances spatial coherence in attention maps by leveraging the model's own patch predictions as feedback. 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Existing IP protection methods primarily focus on embedding watermarks into generated images by altering the structure of the diffusion process. However, these approaches inevitably compromise the quality of the generated images and are particularly vulnerable to fine-tuning attacks, especially for open-source models such as Stable Diffusion (SD). In this paper, we propose PlugMark, a novel plug-in zero-watermarking framework for diffusion models. The core idea of PlugMark is based on two observations: a classifier can be uniquely characterized by its decision boundaries, and a diffusion model can be uniquely represented by the knowledge acquired from training data. Building on this foundation, we introduce a diffusion knowledge extractor that can be plugged into a diffusion model to extract its knowledge and output a classification result. PlugMark subsequently generates boundary representations based on this classification result, serving as a zero-distortion watermark that uniquely represents the decision boundaries and, by extension, the knowledge of the diffusion model. Since only the extractor requires training, the performance of the original diffusion model remains unaffected. Extensive experimental results demonstrate that PlugMark can robustly extract high-confidence zero-watermarks from both the original model and its post-processed versions while effectively distinguishing them from non-post-processed diffusion models. + +# 1. Introduction + +In recent years, generative AI has witnessed tremendous success, with numerous generative models emerging, particularly diffusion models. Models like DALL-E2 [43], GLIDE[39] and Stable Diffusion (SD) [44] have shown remarkable capabilities to generate high-quality images. Con + +sequentially, various downstream services incorporate well-trained large diffusion models like SD or their fine-tuned versions into essential frameworks. As designing and training an efficient diffusion model requires substantial computational resources and these models carry valuable assets for developers, their intellectual property (IP) could raise serious issues of IP infringement and economical disputes. Furthermore, dissemination of trained models can trigger ethnical concerns, and model misuse can be contentious. Therefore, safeguarding their IP and the traceability of stolen models has become an increasingly critical concern. + +Actually, there is a demand for the verification of stolen models coupled with full access to the parameters, known as the 'white-box' scenario. This scenario arises in several contexts: First, it typically occurs when models are deployed on devices that grant complete access to the owners [36, 37]. Second, the administrators of model marketplaces, such as Model Zoo[47], ONNX, and Hugging Face $^1$ , have full access to models. They aim to foster original development while penalizing plagiarism to maintain a healthy ecosystem for developers. Furthermore, as [7, 37, 40] illustrates, models leaks are a significant issue. A common practical scenario involves a two-step verification process: an owner initially uses black-box techniques (i.e., analyzing only the inputs and outputs) to assess potential piracy. If sufficient suspicious evidence is gathered, the second step is to verify the ownership using 'white-box' methods with access to the suspect parameters, which is usually implemented by law enforcement. This underscores the critical need for effective white-box IP protection techniques, especially for open-source models like SD. + +Watermarking [26, 31] has emerged as a promising approach for tracking the IP of models. Particularly, zero-watermarking [15, 56] is extremely appealing as it leverages inherent characteristics of models as watermarks, avoiding any alteration to model. Early watermarking methods for models primarily focus on embedding watermarks into parameters or activations [4, 50, 52], which proves unsuitable + +![](images/0e546866c72c82328f668662b75a5cbcfea2c6dd33baa0badee32ea750b85c5f.jpg) +Figure 1. Illustration of zero-watermarking. The knowledge of diffusion models is represented by unique decision boundaries that are further characterized by the boundary representants, i.e., the boundary samples. Therefore, the representations of decision boundaries serve as a zero-watermark to uniquely identify the diffusion model. + +for generative models[33]. Meanwhile, two key challenges persist in IP protection of diffusion models. Firstly, existing IP protection mechanisms primarily focus on 'black-box' scenarios rather than 'white-box' scenarios. Current methods, known as diffusion-native watermarking[5, 13, 14, 18, 27, 62, 65], merge watermarks into the generation process by modifying the diffusion pipeline. However, such alterations introduce noise into generated images, thereby compromising image quality. In sensitive applications such as autonomous driving[16, 54] and image restoration[11, 61], even a $1\%$ loss in quality can be intolerable. Secondly, since diffusion models are often open-sourced or could be leaked, embedded watermarks are susceptible to removal through fine-tuning or pruning, resulting in ineffective IP tracking. It is imperative to develop an IP tracking method that remains strong robustness while introducing no harm to the fidelity of generated images in white-box scenarios. + +To address these challenges, we propose PlugMark, a novel zero-watermarking framework for IP protection and traceability of diffusion models. The foundation of our approach is based on two key observations: (1) A deep learning (DL) classifier can be uniquely characterized by its decision boundaries [2, 51]. (2) The middle layers of a deep neural network (DNN) contain its unique knowledge [32, 46, 49], and for a diffusion model, this unique knowledge is encapsulated within its UNet, which contains semantic information [1]. Building on these two observations, PlugMark employs a plug-in mechanism that connects a knowledge extraction module to the denoising features from the UNet module and outputs a classification result. In this way, the implicit knowledge extracted from the diffusion model can be uniquely identified by its decision boundaries. Since the denoising features vary across different timesteps, we introduce a method to quantify the timestep selection process using variance values to enhance robustness against fine-tuning and pruning. This ensures that the extracted knowledge remains stable under such modifications. + +Subsequently, we propose a novel representation that uniquely represents these boundaries. As shown in Fig.1, this representation serves as a unique zero-watermark for the diffusion model, consisting of data points near the decision boundary. To identify these points, we employ adversarial example methods. Unlike traditional methods + +[2, 3, 17] that struggle with generating resilient boundary points, we develop a new gradient-based approach that more accurately generates data points defining the decision boundaries. This method leverages multimodal points by integrating image and text embedding data, thereby aligning more closely with the generative process of diffusion models like SD. + +A key advantage of PlugMark is that only the knowledge extraction module requires training, leaving the diffusion model itself unchanged, thereby ensuring that model performance is not compromised. When verifying a suspect model, it is sufficient to access its UNet features and plug the pre-trained knowledge extraction module into them. By comparing the matching accuracy of boundary representations with the target model, model owners can accurately determine whether the suspect model is derived from the target diffusion model. Our contributions are as follows: + +- We propose PlugMark, the first plug-in zero-watermarking framework for diffusion models, which enables IP traceability for any diffusion module without compromising model performance. +- We introduce the idea of "boundary representation as a unique zero-watermark to represent the extracted knowledge of diffusion models" by generating accurate representations tailored for diffusion models. +- To enhance robustness against fine-tuning and pruning, we develop a mechanism to quantify the timestep selection process in diffusion models, identifying stable features as knowledge that resist such modifications. + +# 2. Related Work + +# 2.1. DNN Watermarking + +Currently, model watermarking can be categorized into two main types: white-box and black-box schemes, depending on whether having access to the model's internal content. White-box watermarking typically embeds watermarks into the model's parameters [4, 50, 52] or activations [8] and is generally applied to standard DNN models. On the other hand, black-box watermarking only requires access to the model's inputs and outputs. They embed watermarks or specific patterns in the output through adversarial training [69] or backdoor [23, 25, 48] mechanisms and directly ex + +tract the watermarks from the outputs. Recently, blackbox methods have been widely applied to GAN models [12, 42, 60, 66, 70]. However, these techniques usually require modifications to the model's structure, which compromises its performance. + +# 2.2. Diffusion Model Watermarking + +Numerous watermarking methods have also been widely employed to protect the IP of diffusion models. Most of these methods adopt a black-box approach, embedding watermarks into generated images by fine-tuning the generation process of the diffusion model. Some methods focus on fine-tuning the latent decoder or the backbone [13, 14, 27, 30, 38, 57, 62], while others introduce backdoors [41, 68, 71] to facilitate watermark detection. In these approaches, the watermark can be extracted by inputting the generated image into a watermark decoder or a trigger set into the model. However, these methods primarily focus on the model's output rather than targeting the intellectual property of the model itself. Additionally, the requirement for fine-tuning inevitably degrades the model's generative performance. Moreover, watermarks embedded by these methods are vulnerable to removal through post-processing techniques such as fine-tuning and pruning, as they rely heavily on the integrity of the generation pipeline. In contrast, PlugMark adopts a zero-watermarking mechanism, which verifies the intellectual property of models without modifying them. Instead of altering the model, PlugMark leverages the model's intrinsic features for traceability to resist fine-tuning and pruning. Furthermore, our approach is adaptable to all types of diffusion models. + +# 3. Preliminary + +# 3.1. Diffusion Models + +The Diffusion Model is a generative framework that learns the data distribution $p(z_0)$ by gradually adding and removing Gaussian noise to the images [10, 64]. It consists of two processes. The forward process gradually adds noise to the previous variable, as follows: + +$$ +z _ {t} = \sqrt {1 - \beta_ {t}} z _ {t - 1} + \beta_ {t} \epsilon , \epsilon \sim \mathcal {N} (0, I), \tag {1} +$$ + +where $\beta_{t}$ controls the noise schedule. Let $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \prod_{s=1}^{t} \alpha_{s}$ , the process is simplified as: + +$$ +z _ {t} = \sqrt {\bar {\alpha} _ {t}} z _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon . \tag {2} +$$ + +Given the noisy tensor $z_{t}$ , the reverse diffusion process optimizes a denoising model $\epsilon_{\theta}(z_t,t)$ to learn the initial noise $\epsilon$ , that is then used to obtain an estimate of $z_{0}$ [22]. + +# 3.2. Adversarial Boundary Samples + +The concept of boundary samples refers to samples that lie near the decision boundary of a classifier, initially pro + +posed [20] for knowledge extraction purposes. These samples can serve as representations of the classifier's decision-making process. In IPGuard[2], adversarial examples are used to generate boundary samples of images to represent the knowledge of a classifier. In [51], boundary samples are united as a matrix to represent the knowledge of a classifier. There were also several other classic methods for generating adversarial examples, including the Fast Gradient Sign Method (FGSM)[17], Iterative Gradient Sign Method (IGSM)[29], and Carlini and Wagner's methods[3] (CW). However, the adversarial outputs using IPGuard, FGSM and IGSW are not close enough to the actual decision boundary, and CW and MinAD cost sustainable resources thus not suitable for diffusion models with many parameters due to their inefficiency. In this work, we leverage a gradient descent-based approach and propose a more efficient and accurate strategy for extracting boundary samples, which better captures the boundary knowledge representation for classifiers. + +![](images/c30d2d9cdaa1df00190bc5d1849f706858e352d37f47f638ffc5bd63689bc1ef.jpg) +Figure 2. The threat model considered in PlugMark. + +# 4. Problem Definition + +The threat model considered in our work is illustrated in Fig. 2. It involves two entities: the Diffusion Model Owner and the Attacker. The Owner trains a diffusion model for specific tasks, while the Attacker illegally acquires it through malware infection[24, 55] or insider threats[6]. The Attacker then fine-tunes or prunes it on new tasks and datasets, subsequently claiming ownership of the customized model. To verify whether the suspect model is a post-processed version, the Owner leverages boundary representations generated from the target diffusion model and its associated diffusion knowledge extractor. These representations are applied to the suspect diffusion model equipped with the same extractor for validation. + +In practice, the watermarking scheme must satisfy the + +![](images/41c21a490c776f76e7ef18701c17f5081844de21565826420d12663c5dcc6254.jpg) +Figure 3. The architecture of proposed PlugMark.(a)In the Diffusion Knowledge extractor(DKe), (1) we uniformly select $h$ timesteps and perform $s$ forward processes for each timestep to obtain the upblock features, followed by selecting the Min- $k$ timesteps based on the variance value of the features. (2)During the training of DKe, the whole diffusion pipeline is frozen. Noise at the Min- $k$ timesteps is added, and the resulting upblock features, weighted by the variance, are concatenated. They are further passed through a ResNet-like block to acquire classification logits. (b) Based on these logits, we devise a multimodal adversarial example method to create sample pairs (Image, Text) near the decision boundary as the Boundary Representation of Knowledge (BRoK). + +following objectives: (1) Fidelity: The model's generateive performance should remain unaffected. (2) Robustness: The post-processed versions of the model can be verified after fin-tuning and pruning. (3) Uniqueness: The verification process should distinguish post-processed models from unrelated or reinitialized models. + +# 5. Methodology + +# 5.1. Overview + +Fig. 3 shows the detailed architecture of PlugMark. In the design of PlugMark, we observe that a classifier model can be uniquely characterized by its decision boundaries on a training dataset. For diffusion models, the UNet architecture encapsulates intrinsic knowledge uniquely learned from the dataset. To leverage this insight, we propose a plug-in Diffusion Knowledge Extractor (DKe) to extract the knowledge within the diffusion model and map it to a classification result. In this way, this knowledge behaves similarly to a classifier, allowing the decision boundaries derived from the classification result to serve as a unique representation of the extracted knowledge. (i.e., the diffusion model itself.) + +However, the classification result may be influenced by various factors, such as noised images and texts. To address this, we introduce the Boundary Representation of Knowledge (BRoK), which generates a multimodal representation of the decision boundary. This representation + +functions as a zero-watermark, enabling effective tracking and authenticating of the diffusion model. For different suspect models, we can simply connect them to a pretrained DKe. By evaluating the matching accuracy of the generated boundary representations on them, we can determine whether a suspect model is derived from the target model. Meanwhile, throughout the knowledge extraction process, the parameters of the diffusion pipeline remain frozen, ensuring that the generative capabilities are unaffected. + +# 5.2. Plug-in Diffusion Knowledge Extraction + +For DKe, the primary goal is to fully extract the knowledge within the diffusion model and map it to a classification result. To enhance the accuracy of the classification, it is crucial to extract as much knowledge as possible from the diffusion model. + +Therefore, during the training of DKe, prompts that describe the target label and images are set as inputs. As the main generative capability of a diffusion model resides in its UNet, inspired by [1], we add the $t_{th}$ timestep noise to the input image and connect the upblock features at the $t_{th}$ timestep of the UNet to DKe. Compared to downblock, upblock is seen as a more suitable choice as it retains information from both downblock layers and previous stages. + +However, the core generativeness of the UNet architecture lies in its multi-timestep denoising process. Simply selecting a single timestep is insufficient to comprehensively + +capture the model's knowledge, while incorporating too many timesteps would significantly increase computational costs during training. To address this issue, we propose a deterministic timestep selection mechanism that balances efficiency and functionality. + +Timestep selection mechanism. Before training DKe, we sample $h$ timesteps uniformly from the range of 0 to 1000: + +$$ +T = \left\{t _ {0}, t _ {1}, \dots , t _ {h} \right\}. \tag {3} +$$ + +By performing $s$ times of forward processes through UNet, the features for each timestep $t$ are obtained as: + +$$ +F = \left\{f _ {t, i} \right\} _ {i = 1} ^ {s}. \tag {4} +$$ + +Then we calculate the variance of feature propagation across different forward processes: + +$$ +\sigma_ {t} ^ {2} = \frac {1}{s} \sum_ {i = 1} ^ {s} \left(f _ {t, i} - \mu_ {t}\right) ^ {2}, \tag {5} +$$ + +where $\mu_t$ is the average value over $t$ : + +$$ +\mu_ {t} = \frac {1}{s} \sum_ {i = 1} ^ {s} f _ {t, i}. \tag {6} +$$ + +We hypothesize that variance serves as an uncertainty measure for each timestep $t$ [53, 58, 63], and features from timesteps with lower uncertainty contribute more robustly to fine-tuning. Therefore, we select $k$ most stable timesteps with the lowest uncertainty: + +$$ +\operatorname {M i n} k = \arg \min _ {t \in T} \sigma_ {t} ^ {2}. \tag {7} +$$ + +During training DKe, we perform weighted fusion of features over these selected timesteps: + +$$ +f _ {\text {f i n a l}} = \frac {\sum_ {i = 1} ^ {k} \mathcal {W} \left(t _ {\min _ {i}}\right) f _ {t _ {\min _ {i}}}}{\sum_ {i = 1} ^ {k} \mathcal {W} \left(t _ {\min _ {i}}\right)}, \tag {8} +$$ + +where $\mathcal{W}$ are the weights determined by the variance: + +$$ +\mathcal {W} \left(t _ {\text {m i n} _ {i}}\right) = \frac {1}{\sigma_ {t _ {\text {m i n} _ {i}}} ^ {2}}, \quad i \in [ 1, \dots , k ]. \tag {9} +$$ + +These uncertainty-weighted features are then fed into a residual network (similar to ResNet-18)[19], to extract important features, and the output is pooled and mapped to a classification result. This enables DKe to accurately predict the class based on the extracted knowledge. + +# 5.3. Boundary Representation Generation + +Since the output of DKe is a classification result, it can be uniquely characterized by its decision boundaries. To represent these boundaries, we leverage data samples that lie + +![](images/6228023831022747ec7affc6254c877b152274592e491b51b2eaf6f1a8ca03c2.jpg) +Figure 4. Illustration of Boundary Representation of Knowledge (BRoK). By leveraging adversarial example methods, the sample pairs (Image, Text) are generated to identify the boundary between Class1 and Class2. + +near the decision boundary. However, directly identifying such samples is challenging. To address this issue, we propose a method for generating adversarial samples situated near the decision boundaries. + +Given that the knowledge encapsulated in the diffusion model is influenced by both the textual prompt and the corresponding image, we introduce a multimodal strategy that employs sample pairs (Image, Text) to represent the boundary, as illustrated in Fig. 4. To accurately depict a classification decision boundary, multiple such sample pairs (Image, Text) are combined to form a Boundary Representation of Knowledge(BRoK): + +$$ +\left\{\left(\operatorname {I m a g e} _ {i}, \operatorname {T e x t} _ {i}\right), \left(\operatorname {C l a s s} _ {1}, \operatorname {C l a s s} _ {2}\right) \right\} _ {i} ^ {\beta}, \tag {10} +$$ + +where $(\mathrm{Class}_1, \mathrm{Class}_2)$ denotes the class pair that is separated by the boundary and $\beta$ refers to the number of sample pairs within one BRoK. + +Sample Generation. For a classifier model, the logits before final prediction can be represented as $\{l_1,\dots ,l_c\}$ where $c$ is the number of classes, and the predicted label is: + +$$ +y = \arg \max _ {i} l _ {i} (x). \tag {11} +$$ + +For a sample pair that lies on the decision boundary between classes $i$ and $j$ , we assume this pair has the highest logit values for both classes: + +$$ +C B = \{x \mid \exists i, j, i \neq j \text {a n d} l _ {i} (x) = l _ {j} (x) \geq \max _ {t \neq i, j} l _ {t} (x) \}, \tag {12} +$$ + +where $l_{i}(x)$ is the logit of class $i$ , and the condition $l_{i}(x) = l_{j}(x)$ implies that the point $x$ is on the boundary between classes $i$ and $j$ . As we aim to find the sample pairs near the boundary, we relax the conditions. The optimization loss functions for generating boundary samples are as follows. + +Similarity Loss. Intuitively, for a sample pair near the boundary between class $i$ and class $j$ , the logits on these two classes should be as close as possible. To formalize this, we introduce a threshold $T_{s}$ . The logit distance between these + +two classes should not exceed this threshold threshold $T_{s}$ . Accordingly, the similarity loss is defined as: + +$$ +L _ {s i m} = \max \left(0, \left(l _ {i} - l _ {j}\right) ^ {2} - T _ {s}\right). \tag {13} +$$ + +In this way, the distance between the sample and the boundary is limited to be less than $\sqrt{T_s}$ . + +Max Margin Loss. The predicted logits for classes $i$ and $j$ should exceed the maximum predicted logit of other classes $l_{\mathrm{other}}$ by a margin $m$ that regulates the difference between the predicted logits of the two selected classes and the rest classes. Accordingly, the Margin loss is defined as: + +$$ +L _ {m a r} = \operatorname {R e L U} \left(l _ {\text {o t h e r}} - l _ {i} + m\right) + \operatorname {R e L U} \left(l _ {\text {o t h e r}} - l _ {j} + m\right). \tag {14} +$$ + +Finally, the total loss is computed as: + +$$ +L = \lambda_ {s} L _ {\text {s i m}} + \lambda_ {m} L _ {\text {m a r}}, \tag {15} +$$ + +where $\lambda_{s}$ and $\lambda_{m}$ are the weighting factors assigned to respective losses. The objective is $L = 0$ , which indicates a sample pair is near the boundary. + +# 5.4. Watermark Verification + +For a target diffusion model, we plug it to the Plug-in DKe. After training the DKe, we generate multiple BRoKs from it, which serve as the zero-watermark. For a suspect diffusion model, we directly plug it to the pre-trained DKe and input the sample pairs from the BRoKs to verify whether the top-2 logits of the output match the class pair of BRoK. The matching accuracy is calculated as: + +$$ +r = \frac {1}{\text {n u m}} \sum_ {i = 1} ^ {\text {n u m}} \frac {\alpha_ {i}}{\beta_ {i}}, \tag {16} +$$ + +where $\alpha_{i}$ is the number of matched pairs between suspect model and target model, $\beta_{i}$ denotes the total number of sample pairs in the BRoK corresponding to the $i$ -th boundary, and num is the number of BRoKs, i.e., boundaries. + +# 6. Experiments + +Dataset. We utilize CIFAR-10[28], CIFAR-100 and MNIST[9] datasets to extract the knowledge of diffusion models. The CIFAR-10 and MNIST contain 10 classes each, while the CIFAR-100 dataset consists of 20 superclasses and 100 subclasses. Since our goal is to extract knowledge, we focus exclusively on the 20 superclasses in CIFAR-100. For CIFAR-10, MNIST and CIFAR-100, we generate 10, 10 and 20 BRoKs respectively, each consisting of 10 sample pairs. + +Baseline Methods. We adopt the state-of-the-art methods Stable Signature [14], WatermarkDM [71] and AquaLoRA [13] as the baselines for comparison. + +Experiment Settings. We adopt the AdamW optimizer with a learning rate of $1 \times 10^{-3}$ for training the DKe + +and 0.01 for generating the BRoK, with a weight decay of $1 \times 10^{-4}$ . We set $h = 100$ and the time of forward processes $s = 3$ and choose the Min-5 timesteps. The hyperparameters are set as follows: $\lambda_{s} = 0.3$ , $\lambda_{m} = 0.5$ , $m = 20$ , $T_{s} = 0.5$ . We use Stable-Diffusion-v2 as the base model, and set 2 types of suspect models as the post-processing versions: (1) Fine-tuning. Models are fine-tuned for 100, 1000, and 20k steps using Dreambooth[45] on personalization tasks, and the 200k-steps version is from Hugging face; (2) Weight pruning. Model parameters with the smallest values are pruned at a ratio $\rho$ . And models reinitialized are seen as negative models. + +Evaluation Metrics. We use FID (Frechet Inception Distance)[21] to evaluate the fidelity of the diffusion models. Additionally, besides matching accuracy, we use true positive rate (TPR) with false positive rate (FPR) at $10^{-6}$ as a metric. For our method, we compare it between 300 stolen models and 300 negative models. And for the compared black-box methods, we generate 1000 watermarked and unwatermarked images from the COCO2014[34] dataset, respectively. + +# 6.1. Robustness against Fine-tuning and Pruning + +We train the DKe plugged into the target diffusion model across different datasets and generate BRoKs as zero-watermarks. Then we plug the trained DKe into the post-processed and negative models to evaluate matching accuracy. As shown in Table 1, PlugMark achieves an accuracy approximately exceeding $70\%$ after fine-tuning for 100, 1000, 20k, and even 200k steps as well as under weight pruning with ratios $\rho \in [0.1, 0.2, 0.3]$ . In contrast, the accuracy for negative models is only around $10\%$ , demonstrating that PlugMark shows strong robustness and uniqueness, as it can successfully distinguish between post-processed versions and unrelated models. More details about fine-tuning settings are in Appendix Sec.D.1. + +It is worth noting that the matching accuracy on CIFAR-100 is slightly lower compared to CIFAR-10 and MNIST. This discrepancy arises because CIFAR-100 contains more classes, which increases the difficulty for DKe to achieve high classification precision. It leads to a decrease in the precision of the extracted knowledge, and thus the decision boundary is less explicit. Consequently, the generated BRoKs are less robust against post-processing. + +# 6.2. Comparison with Baseline Methods + +As shown in Table 7, we compare the effectiveness of PlugMark with the baseline methods. Since PlugMark does not modify the diffusion model, its FID remains identical to that of the non-watermarked model, ensuring high fidelity. In contrast, other methods require fine-tuning the diffusion pipeline, leading to a degradation of the image quality. Due to DreamBooth's optimization of all backbone + +
DatasetFine-tuningPruning(ρ)Negative
Origin100 steps1000 steps20k steps200k steps0.10.20.3
CIFAR-10100.0099.1898.8372.5569.8298.0086.6781.5510.00
CIFAR-10098.3697.0094.4369.1868.3693.3381.6378.3615.13
MNIST100.0098.6798.5073.5069.3397.6785.9580.609.33
+ +Table 1. Matching accuracy (%) on fine-tuned, pruned, and negative models for DKe trained on different datasets, respectively. + +
MethodZero-watermarkingFID↓Accuracy↑/TPR(FPR=10-6)
OriginFinetune(100 steps)Finetune(1000 steps)Prune(0.1)
None-24.25----
Stable Signature [14]X24.7798.30/0.99768.43/0.02051.02/0.00148.33/0.002
AquaLoRA[13]X24.8895.79/0.97070.13/0.03550.13/0.00350.00/0.001
WatermarkDM[68]X25.92-/0.828-/0.735-/0.229-/0.000
PlugMark✓24.25100.00/1.00099.18/1.00098.83/0.99598.00/1.000
+ +Table 2. Comparison of results between baseline models and PlugMark. The compared methods embed a 48-bit message, and the reported accuracy (%) represents the rate of correctly detected bits. For WatermarkDM, since the watermark is an image, the accuracy cannot be calculated. TPR denotes true positive rate with false positive rate (FPR) at $10^{-6}$ . Additional explanations of it are in Appendix Sec.I. + +weights, the other methods barely retain watermarks after 1000 steps fine-tuning, and watermarks are nearly destroyed under weight-pruning at $\rho = 0.1$ . However, our method maintains a TPR of around 1.00 for these post-processed models. We attribute it to the fact that the boundary representations are derived from the knowledge encapsulated in the multiple timesteps of a diffusion model, reflecting the model's generative capabilities. Even after fine-tuning or pruning, this knowledge remains robust and hard to eliminate. Additional results on robustness against fine-tuning are provided in Appendix Sec. B, Sec. C, and Sec. D.2. + +# 6.3. Impact of Timesteps Selection + +We evaluate the impact of the number of selected timesteps and the selection mechanism on the matching accuracy of the diffusion model fine-tuned for 1000 steps. As shown in Fig. 5(a), increasing the number of timesteps significantly enhances the matching accuracy. This improvement is attributed to the fact that more timesteps provide DKe with more comprehensive knowledge, leading to more accurate classification results. Consequently, the generated BRoKs exhibit higher precision, thus stronger robustness against fine-tuning. Additionally, we compare random timestep selection with the certainty-measured mechanism. The results demonstrate that selecting timesteps based on higher certainty substantially enhances robustness against fine-tuning. However, when the number of selected timesteps exceeds 5, the improvement in the matching accuracy turns less pronounced. Considering a higher number of timesteps results in increased time and resource costs, selecting a moderate number of timesteps is the optimal choice. + +# 6.4. Effects of Number of Sample Pairs and BROks + +We evaluate the impact of the number $(\beta)$ of sample pairs per BRoK and the total number of BRoKs on the robustness against models fine-tuned for 1000 steps. As shown in Fig. 5(b), increasing $\beta$ initially enhances the matching accuracy significantly. However, excessive sample pairs lead to a decline in accuracy. Similarly, more BRoKs generally improve the accuracy by providing a more comprehensive boundary representation of the knowledge, but an excessive number of BRoKs might reduce it. We observe that the inclusion of a few inaccurate samples that are not sufficiently close to the boundary might lead to the decrease. Therefore, considering both robustness and efficiency, it is optimal to select a moderate number of BRoKs and sample pairs per BRoK. In our experiments, we generate 10 and 20 random BRoKs for CIFAR-10 and CIFAR-100, respectively, with each BRoK consisting of 10 sample pairs. + +# 6.5. Effectiveness of the Generation of BRoK + +To validate the effectiveness of BRoK generation in PlugMark, we evaluate the robustness of BRoK generated by different adversarial sample methods against fine-tuning. As shown in Table 3, while all methods maintain a relatively high TPR on the original model, their performance declines sharply after just 100 steps of fine-tuning. After 2000 steps, all methods except PlugMark nearly lose their robustness. This is because the boundary samples generated by these methods fail to characterize the decision boundary, resulting in a lack of unique link to the model. Consequently, they are unable to resist fine-tuning. + +
Modelorigin100 steps2000 steps
FGSW[17]0.8330.5130.001
CW[3]0.7670.4390.003
IPguard[2]0.9200.6620.005
PlugMark1.0001.0000.991
+ +![](images/cc5ba53256868c824b63d03c494314062f17031a6d1bde8c90275b6e10e8d6f6.jpg) +Figure 5. The impacts of the number $(k)$ of timesteps and $\beta$ of BRoK on the matching accuracy + +![](images/b2fdbdc7b51f642a5496c6a68dd084b0489180f62a1d590019dc479125690164.jpg) + +![](images/c01ea6761874f800a67ef09bdd53f5a0a2b37d0861dc157c7899ad1fba2e7407.jpg) +Figure 6. The impacts of $m$ and $T_{s}$ on matching accuracy and time cost + +![](images/1f0e2a7d9ff451add4d84388eca98287f0cf109d9f7f5613197db4b30296f389.jpg) + +# 6.6. Impacts of $T_{s}$ and $m$ in Loss Function + +In the loss functions, $T_{s}$ controls the logit difference between the two classes near the boundary, while $m$ regulates the difference between the logits of these two classes and the other classes. We evaluate the time cost and matching accuracy of BRoK on a model fine-tuned for 1000 steps with different values of $m$ and $T_{s}$ . + +As shown in Fig. 6, PlugMark's robustness to fine-tuning improves as $m$ increases, but the gain becomes marginal beyond a certain point. The time cost remains manageable for $m \leq 25$ , but rises sharply afterward. Since smaller values of $m$ already provide reasonable robustness, we set $m = 20$ to balance efficiency and robustness. Regarding $T_{s}$ , larger values push boundary samples farther from the decision boundary, reducing matching accuracy as the samples fail to accurately represent the boundary. Meanwhile, very small values of $T_{s}$ (particularly $T_{s} < 1$ ), significantly increase time consumption. To ensure both efficiency and robustness, we set $T_{s} = 0.5$ . + +# 6.7. Ablation Study + +We conduct an ablation study to assess the significance of different components of PlugMark, including the DKe and + +Table 3. TPR for different adversarial example methods + +
ComponentsOriginPrune (0.1)Finetune (1000 steps)
DKe(image),BRoK(image)91.1842.7540.67
DKe(image+text)+BRoK(image)92.0961.9066.09
DKe(image+text)+BRoK(image+text)94.6390.0085.18
DKe(image+text+time)+BRoK(image+text)99.0994.9094.82
DKe(image+text+time+uncertainty)+BRoK(image+text)100.0098.0098.83
+ +Table 4. Matching accuracy (%) with different components + +BRoK generation. As shown in Table 4, first, during the training of DKe, the UNet's semantic knowledge is deemed to be guided by both image and textual inputs. When only image inputs are used, the classification precision drops significantly, leading to more ambiguous decision boundaries. This ambiguity hinders the generation of the unique boundary representations for the diffusion model's knowledge, resulting in a substantial decrease in matching accuracy under pruning and fine-tuning. Meanwhile, in BRoK, we introduce multimodal sample pairs (image, text) as the representation of the boundary to better represent the boundary characteristics. Compared to only generating images as the representation, these multimodal pairs provide a more accurate depiction of the boundary, significantly enhancing the reliability of its uniqueness and robustness against fine-tuning and pruning. + +Additionally, in DKe, we integrate features from multistimesteps to comprehensively represent the knowledge of diffusion models. Compared to single-timestep features, this approach substantially improves matching accuracy, demonstrating its effectiveness in delivering the knowledge of the diffusion model, thereby mitigating the impact of fine-tuning and pruning. Moreover, the uncertainty-based mechanism for selecting the most stable timesteps outperforms random selection, further boosting its robustness against model modifications. + +# 7. Conclusion + +Existing watermarking schemes for Stable Diffusion models often introduce model distortions and struggle to maintain robustness for post-processed versions. To address these issues, we propose PlugMark, a plug-in zero-watermarking framework for diffusion models that enables IP traceability without compromising model fidelity. Considering the rationale that the diffusion model knowledge learned from a training dataset can be uniquely represented by a boundary through a classification task, we leverage the boundary representation as a unique zero-watermark to verify unauthorized use or redistribution of models. Extensive experiments demonstrate its effectiveness and adaptiveness without altering the model's fidelity. We look forward to extending this "knowledge as watermark" mechanism into more models. + +# Acknowledgements + +# References + +[1] Dmitry Baranchuk, Ivan Rubachev, Andrey Voynov, Valentin Khrulkov, and Artem Babenko. Label-efficient semantic segmentation with diffusion models. In The Tenth International Conference on Learning Representations, 2022. 2, 4 +[2] Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. 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However, these approaches have two limitations: (1) they inefficiently require both 2D and 3D modalities as inputs, even though the inherent multi-view properties of 3D point clouds already contain 2D modality. (2) input 2D modality causes the reconstruction learning to unnecessarily rely on visible 2D information, hindering 3D geometric representation learning. To address these challenges, we propose a 3D to Multi-View Learner (Multi-View ML) that only utilizes 3D modalities as inputs and effectively capture rich spatial information in 3D point clouds. Specifically, we first project 3D point clouds to multi-view 2D images at the feature level based on 3D-based pose. Then, we introduce two components: (1) a 3D to multi-view autoencoder that reconstructs point clouds and multi-view images from 3D and projected 2D features; (2) a multi-scale multi-head (MSMH) attention mechanism that facilitates local-global information interactions in each decoder transformer block through attention heads at various scales. Additionally, a novel two-stage self-training strategy is proposed to align 2D and 3D representations. Our method outperforms state-of-the-art counterparts across various downstream tasks, including 3D classification, part segmentation, and object detection. + +# 1. Introduction + +3D vision is a critical research area with applications in autonomous driving [7, 14, 23, 31, 34, 57, 75] and robotics [26, 47, 54, 62, 76, 77], thanks to its ability to model and interpret the real world. However, manually collecting and annotating 3D point cloud data is both expensive and time-consuming, posing significant challenges for developing effective 3D models. Consequently, self-supervised learning (SSL) of 3D representations has emerged as a key research direction. + +Current self-supervised learning (SSL) approaches for + +3D data primarily focus on two types of feature learning: (1) Semantic and Textual Representations and (2) 3D Geometric Features. Methods such as I2P-MAE [71] and ReCon [42] fall into the first category, where their primary contribution lies in leveraging foundation models for knowledge distillation and semantic feature extraction. However, a fundamental limitation remains: there is no established 3D foundation model specifically designed for geometric feature distillation. Unlike 2D vision, where large-scale pre-trained models provide strong transferable representations, 3D data lacks an equivalent foundation model capable of effectively capturing and distilling geometric information. This limitation makes it impractical to rely solely on existing foundation models for 3D geometric learning. Therefore, developing self-supervised strategies that directly enhance geometric feature learning is critical for advancing 3D representation learning. Moreover, geometric features are inherently complementary to semantic features derived from foundation models, and thus a stronger understanding of 3D geometry can further improve overall model performance. + +Recent works have leveraged 2D images to enhance 3D self-supervised learning [4, 9, 10, 18, 27, 37, 42, 58]. Specifically, methods such as Joint-MAE [18] and Pi-MAE [4] utilize masked images and point clouds as inputs to reconstruct complete images and point clouds. However, we argue that using both 2D and 3D modalities as inputs in these MAE-based methods presents two significant drawbacks. First, incorporating both 2D and 3D modalities as input for training is redundant and inefficient. Point clouds inherently encapsulate multi-modal data, as they can be directly translated into multi-view depth images or rendered as 2D images. This eliminates the necessity for input images for 2D reconstruction. Secondly, using 2D images as input may cause the network to rely heavily on visible 2D information when predicting masked regions. Specifically, when 2D view information is directly provided, it inadvertently "leaks" viewpoint semantic information to the network. Consequently, the underlying multi-view geometric information is neglected, preventing the network from developing a comprehensive understand + +ing of how the 2D view should appear from different angles. As a result, the model is unable to develop multi-view geometric representations, which is essential for effective 3D representation learning, as highlighted in previous studies [8, 19, 20, 50, 53, 68, 69]. + +To address these limitations, we propose leveraging the intrinsic multi-modal nature of point clouds without the redundant use of input images, thereby enhancing the efficiency and effectiveness of 3D self-supervised learning. More formally, we introduce an innovative method called Multiview Masked Learner (Multiview-ML), designed to extract the multi-view 2D information inherently embedded within 3D point clouds, thus advancing 3D representation learning. Specifically, we input point clouds into an initial encoder to obtain intermediate 3D encoded tokens. Using the provided pose information, we then project these intermediate 3D tokens onto 2D image tokens through our proposed view-based feature projection (see Figure 2a). The projected multi-view 2D tokens and the original 3D tokens, augmented with modality, positional, and pose embeddings, are then fed into a fusion encoder to obtain the corresponding encoded 3D and multi-view 2D features. Subsequently, we pass these features into two separate decoders to independently reconstruct the complete multi-view 2D images and 3D point clouds. + +Furthermore, to enhance the integration of local attention mechanisms for reconstruction, we introduce a MultiScale Multi-Head (MSMH) attention mechanism—a simple yet effective module that provides broader local and global attention. Unlike previous standard attention mechanisms, MSMH organizes tokens into distinct, non-overlapping local groups. Self-attention is then applied within each subgroup rather than across all individual tokens. Additionally, we implement a multi-scale design with varying group sizes, allowing smaller groups to capture fine-grained local details while larger groups capture broader global context. Finally, we concatenate the multi-scale attention features to ensure the model effectively acquires both local and global information. + +Moreover, unlike previous methods [18, 38], which primarily focus on reconstructing raw masked inputs, our approach involves reconstructing masked 2D and 3D representations within a latent space, drawing inspiration from the SimSiam [6]. We propose a two-stage training procedure to enhance multi-modal masked representation learning: Stage One: 3D to multi-view autoencoder (teacher model) takes the complete point cloud as input and outputs both the reconstructed point cloud and multi-view images. The autoencoder extracts latent features that contain rich geometric information, effectively restoring the point cloud and multi-view images. Stage Two: We introduce a student network based on a masked autoencoder, which leverages masked point clouds to predict features generated + +by the teacher encoder in the first stage. Notably, our objective function is designed to predict latent space features instead of 3D point clouds. This ensures that the student model learns well-aligned and contextualized representations across modalities. + +We conducted extensive experiments to validate our Multiview-ML approach. Our method significantly outperforms previous approaches across downstream tasks such as 3D shape classification, part segmentation, and object detection, underscoring its effectiveness in learning robust 3D geometric representations. A key insight from our study is the limited effectiveness of using 2D images as input for 3D geometric learning through MAE. We believe this finding presents an intriguing opportunity in the design space for developing learning strategies for 3D representation learning. Our key contributions are summarized as follows: + +- We propose a 3D to multi-view autoencoder that reconstructs point clouds and multi-view images solely from 3D point clouds, eliminating the need for additional input images and enhancing the 3D geometric feature learning. +- We propose a Multi-Scale Multi-Head (MSMH) attention mechanism that integrates local and global contextual information by organizing distinct, non-overlapping local groups at multiple scales within reconstructed features. +- We develop a two-stage training strategy for multimodality masked feature prediction, enhancing the alignment between 2D and 3D representations by having the student network predict the teacher's latent features from masked point clouds. +- Our method outperforms existing approaches across various downstream tasks, underscoring the importance of leveraging the inherent multi-view 2D information in point clouds for effective 3D representation learning. + +# 2. Relative Work + +Masked Autoencoder for Point Cloud. MAE [21] masks random patches of an input image and reconstructs the missing pixels, effectively learning modality-specific representations. This approach has achieved significant success across various domains [12, 43, 44, 48, 49]. Recently, Point-BERT [65] and Point-MAE [38] adapted MAE to reconstruct masked 3D point clouds. Furthermore, Zhang et al.[70] proposed PointM2AE, which uses pyramid architectures to capture both fine-grained and high-level semantic features of 3D shapes. However, these methods primarily focus on a single 3D modality. In contrast, multimodality MAE[2, 15] has drawn attention to learning multiple modalities complementary representations. Yet, research on multi-modality masked autoencoders for point cloud learning remains limited. Few Recent frameworks, such as Joint-MAE [18] and PiMAE [4], propose 2D-3D MAE approaches by reconstructing 2D and 3D inputs. However, we argue that utilizing 2D input is redundant, + +![](images/531a315924b898be1029af0ee524f35c5f7a3dc87c08b10c30d494a993baf80f.jpg) +Figure 1. Overview of the stage one training process of the teacher model. The input point clouds are first encoded into intermediate 3D tokens using a 3D encoder. Leveraging the provided pose information, these tokens are projected onto multi-view (MV) 2D image tokens through our proposed view-based feature projection method. Modality and pose embeddings are then added to both the projected 2D tokens and the intermediate 3D tokens. These tokens are concatenated and refined by a multi-modal fusion module. Finally, the refined features are fed into two separate decoders that independently reconstruct the complete multi-view 2D images and the 3D point clouds. + +as 3D data already includes multi-view 2D information. Unlike previous works that require both 3D point clouds and corresponding images for 3D representation learning, Multiview-ML uses only 3D point clouds as input, fully leveraging multi-view information to enhance learning efficiency. + +Multimodal Feature Learning. Recent studies [1, 16, 17, 22, 25, 28-30, 36, 45, 52, 61, 66, 67, 72, 74] have demonstrated that pre-trained multimodal models offer highly transferable representations, significantly boosting performance across various downstream tasks. For example, CrossPoint [1] employs contrastive learning to align point clouds with their corresponding 2D images in a shared latent space. MVTN [19] enhances 3D object understanding by exploiting multi-view image correspondences. Sautier et al.[51] introduce an object-level contrastive loss between 2D and 3D representations, while TAP[58] presents a 3D-to-2D generative pre-training strategy. Unlike prior one-stage approaches that focus solely on reconstructing point clouds, our two-stage strategy emphasizes better alignment between 2D and 3D representations. In this work, we propose a novel two-stage pre-training framework that enhances the alignment of 2D and 3D representations, ensuring that our model learns well-aligned and contextualized multimodal features. + +# 3. Method + +This section introduces our proposed Multiview-ML. In Sec.3.1, we describe how 3D point clouds are projected into multi-view 2D depth maps and encoded with positional, + +modality, and pose embeddings. Sec.3.2 details our proposed 3D to multi-view encoder architecture, which integrates these multi-view 2D tokens with the original 3D tokens through a fusion encoder. Additionally, Sec.3.3 and Sec.3.4 present the Multi-Scale Multi-Head (MSMH) decoder and our two-stage training strategy, respectively. + +# 3.1. 3D to Multi-view Projection and Encoding + +Depth Map Projection. To establish 2D-3D correspondence, we project the 3D point clouds into multi-view 2D depth images. These depth images then guide the reconstruction from 3D to 2D. We utilize PyTorch3D [46] to project the 3D coordinates onto 2D coordinates using the provided pose information. The 2D coordinates are subsequently converted into token indices $\hat{I} \hat{dx}$ using the following formulation: + +$$ +I \hat {d} x = \hat {X} / (H _ {i} / / H _ {t}) * H _ {t} + \hat {Y} / (W _ {i} / W _ {t}), \qquad (1) +$$ + +where $H_{i}$ , $W_{i}$ represents the height and width of the depth map. $H_{t}$ , $W_{t}$ represents the height and width of the 2D token map size. We project 3D coordinates $(X,Y,Z)\in \mathbb{R}^{3}$ to 2D coordinates $(\hat{X},\hat{Y})\in \mathbb{Z}^{2}$ in a specific view. In our experiments, we use a projected image size of $224\times 224$ and an image token size of 16, resulting in 196 tokens per image view. + +Positional Encodings. Following Point-MAE [38], our method applies positional encodings to all 3D-related attention layers. For point tokens, we utilize a two-layer MLP to encode their corresponding 3D coordinates into $C$ -channel vectors $\mathbf{O}^{3D}$ , those are then added element-wise to the token features before being fed into the attention layer. Addi + +![](images/72dc35e16472b69c456091d4401b84e4fbfe675585c93e82a373ac8167de1808.jpg) +(a) 3D to multi-view tokens-level projection. + +![](images/1330e5f8ea4cc3a4ff09731cc68bf8519d99a886ab385b7303af89d5babe0f34.jpg) +(b) Model architecture of 3D to multi-view encoder. +Figure 2. (a) Feature-level projection of 3D point tokens to multi-view 2D tokens. Those point tokens are grouped based on their corresponding image token indices, forming aggregated image token features. (b) The 3D to multi-view encoder for Multiview-ML. Encoded point tokens obtained from 3D encoder are processed by projection heads, projected into multi-view image token positions, and padded to full image token sizes. Those image tokens are concatenated with point tokens and sent to the fusion encoder to further extract both 2D and 3D information. + +tionally, we add modality-specific 2D sinusoidal positional embeddings $\mathbf{O}^{2D}$ to the image tokens $\mathbf{I}$ . + +Modality Encodings. To enhance the model's ability to distinguish between different modalities within the shared encoder, we add modality-type embeddings $\mathbf{M}^{2D}$ and $\mathbf{M}^{3D}$ to the point tokens $\mathbf{P}$ and image tokens $\mathbf{I}$ , respectively, before sending them to the fusion decoder. We employ two-layer MLP to encode the modality classes of tokens. + +Pose Encodings. In the 3D to multi-view autoencoder, our method uses masked 3D tokens to reconstruct fully original depth images from various poses. To incorporate view information into the decoder, we utilize a two-layer MLP to encode the view information of each depth map as $\mathbf{V}^k$ for a specific pose $k$ and add it to image tokens before the decoding stage. + +3D to 2D multi-view features projection. After obtaining the point tokens $\mathbf{P} \in \mathbb{R}^{N_1 \times D}$ from the initial encoder, we project them into the 2D token space of a specific view, as illustrated in Figure 2a. Tokens are then divided into groups $\{\mathbf{T}_i^g\}_{i=1}^G$ according to the index $I\hat{dx}$ obtained from the formula described in Eq. 1. The number of groups $G$ is dynamic, depending on the specific projection. We apply max-pooling and average-pooling to aggregate point tokens that are projected onto the same image tokens. The fused point features are then converted into the image space using an MLP layer: + +$$ +\mathbf {I} ^ {g} = \operatorname {M L P} \left(\left\{\operatorname {M a x} \left(\mathbf {T} _ {i} ^ {g}\right) + \operatorname {A v e} \left(\mathbf {T} _ {i} ^ {g}\right) \right\} _ {i = 1} ^ {G}\right) \tag {2} +$$ + +As illustrated in Fig. 2a, $\mathbf{I}^g$ cannot be directly mapped to every corresponding 2D view token, leaving certain regions + +of the projected 2D images blank. Hence, when the number of $\mathbf{I}^g$ is smaller than the 2D image token size (196 in our case), we apply padding for alignment. Subsequently, another MLP layer projects $\mathbf{I}^g$ into the specific view $k$ , incorporating modality and pose embeddings: + +$$ +\mathbf {I} _ {k} ^ {f} = \mathrm {M L P} (\operatorname {P a d} (\mathbf {I} ^ {g}) + \mathbf {M} ^ {2 D} + \mathbf {V} ^ {k} + \mathbf {O} ^ {2 D}). \qquad (3) +$$ + +# 3.2. 3D to Multi-view Encoder + +To ensure a fair comparison with previous methods [18, 38], make our 3D-to-multi-view encoder identical to the plain transformer by adopting the same architecture and equally partitioning its layers into two parts. The first part functions as the 3D encoder $\mathcal{E}$ , responsible for extracting 3D token embeddings, while the remaining layers serve as the multimodal fusion encoder $\mathcal{E}_r$ . Initially, token features $\mathbf{P}$ are extracted from input point clouds using $\mathcal{E}$ . These point cloud token features are then mapped to a multi-view image feature space through MLP layers, incorporating 2D modality embeddings and corresponding pose embeddings. This process generates multi-view image tokens $\{\mathbf{I}_k^f\}_{k=1}^K$ for each specific view $k$ as detailed in the Eq. 3. As illustrated in Fig. 2b, we concatenate the multi-view image features $\{\mathbf{I}_k^f\}_{k=1}^K$ with point features $\mathbf{P}^f$ to form a unified embedding. This unified embedding is subsequently processed by the fusion encoder $\mathcal{E}_f$ as follows to obtain refined output $\mathbf{P}^e$ and $\{\mathbf{I}_k^e\}_{k=1}^K$ : + +$$ +\mathbf {P} ^ {e}, \{\mathbf {I} _ {i} ^ {e} \} _ {k = 1} ^ {K} = \mathcal {E} _ {f} \left(\operatorname {C o n c a t} (\mathbf {P} ^ {f}, \{\mathbf {I} _ {k} ^ {f} \} _ {k = 1} ^ {K})\right), \tag {4} +$$ + +![](images/d45dd4158f7939c72441b4297d4177c73eb7da1fc00efc011c5ee2f7fa77c62a.jpg) +Figure 3. Illustration of the second-stage training process. In this stage, the pre-trained 3D to multi-view encoder from the first stage act as teacher models, guiding the learning of the student model, which consists of a 3D to multi-view encoder and two MSMH decoders. The training involves two key objectives: (1) Inter/intra model distillation: Global features, obtained by max-pooling from both the teacher and student models, are distilled to transfer global information from the teacher model and ensure feature alignment. (2) Token-level reconstruction: Outputs of the teacher encoder are aligned with the student decoder's predictions for masked tokens feature prediction, facilitating the learning of well-aligned, contextualized representations across both 2D and 3D modalities. + +here, $K$ represents the number of views for depth map projection and reconstruction. It is worth noting that even if we refer to the shared encoder and the fusion encoder as different components, they are still the same as the original baseline encoder. + +# 3.3. Decoder with Multi-Scale Multi-Head Attention + +To effectively capture both local intricacies and global contexts, we introduce an advanced Multi-Scale Multi-Head (MSMH) attention mechanism. This module enables each attention head to independently perform self-attention across various local scopes within point clouds and image segments. Specifically, MSMH attention organizes tokens into distinct, non-overlapping local groups and applies self-attention within each subgroup rather than across all individual tokens. Additionally, our multi-scale design incorporates varying group sizes, allowing smaller groups to capture fine-grained local details while larger groups capture broader global context. We then concatenate the multi-scale attention features to ensure the model integrates both local and global information effectively. By enhancing the baseline model's decoder, we replace the conventional Multi-Head Attention mechanism with our proposed MSMH attention, facilitating the nuanced capture of both local and global attention dynamics in every decoder block. + +More formally, the MSMH module is structured with $h$ + +parallel multi-scale heads, mathematically represented as: + +$$ +\operatorname {M S M H} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {C o n c a t} \left(\mathrm {S H} _ {1}, \dots , \mathrm {S H} _ {h}\right) W ^ {O} \tag {5} +$$ + +Where SH represent ScaleHead. Unlike conventional Multi-Head Attention (MHA) approaches, each head $i$ in our model performs self-attention within distinct, nonoverlapping local scales of size scale $i$ . This is achieved by partitioning the input matrices $\mathbf{Q}\mathbf{W}_i^Q,\mathbf{K}\mathbf{W}_i^K,\mathbf{V}\mathbf{W}_i^V\in \mathbb{R}^{n\times C}$ into smaller segments $\mathbf{Q}_{\mathrm{scale}_i},\mathbf{K}_{\mathrm{scale}_i},\mathbf{V}_{\mathrm{scale}_i}\in \mathbb{R}^{m\times \mathrm{scale}_i\times C_k}$ , where $n = m\times \mathrm{scale}_i$ . + +$$ +\mathrm {S c a l e H e a d} _ {i} = \mathrm {S A} (\mathbf {Q W} _ {i} ^ {Q}, \mathbf {K W} _ {i} ^ {K}, \mathbf {V W} _ {i} ^ {V}, \mathrm {s c a l e} _ {i}). (6) +$$ + +where SA represents ScaleAttention. The pseudocode of the ScaleAttention is provided in the Appendix. This is followed by a standard self-attention process: $\mathbf{H}_{scale_i} = \mathrm{Attention}(\mathbf{Q}_{scale_i},\mathbf{K}_{scale_i},\mathbf{V}_{scale_i})$ on these partitioned inputs. Finally, $\mathbf{H}_{scale_i}\in \mathbb{R}^{m\times scale_i\times C_k}$ is reshaped to $\mathbf{H}\in \mathbb{R}^{n\times C_k}$ to get the output. + +In the proposed MSMH module, individual attention heads capture information at multiple local contexts, and the final projection matrix determines the weighting of each head, facilitating interactions across scales. By allowing each head to focus on varying spatial dimensions, the MSMH mechanism facilitates a more dynamic and flexible interpretation of data, effectively capturing both intricate details and broad patterns. This innovative approach significantly enhances the modeling of local and global relationships. + +
MethodFoundation modelScanObjectNN [56]ModelNet40 [59]
NeededOBJ-BGOBJ-ONLYPB-T50-RSw/o Votew Vote
Point-MAE [38]×90.0288.2985.1893.293.8
Joint-MAE [18]×90.9488.8686.07-94.0
TAP [58]×90.3689.5085.67--
Point-GPT [5]×91.690.086.994.094.2
Point-M2AE [70]×91.2288.8186.4393.494.0
Ours (Point-MAE)×93.32 (3.3 ↑)92.69 (4.4 ↑)88.93 (3.8 ↑)93.8 (0.6 ↑)94.1 (0.3 ↑)
Ours (Point-M2AE)×95.10 (↑ 3.9)93.56 (4.8 ↑)90.37 (3.9 ↑)94.0 (0.6 ↑)94.4 (0.4 ↑)
ACT [13]✓93.2991.9188.2193.7-
I2P-MAE [71]✓94.1591.5790.1193.794.1
ReCon [42]✓95.1893.6390.6394.194.5
Ours (I2P-MAE)✓95.72 (↑ 1.57)94.28 (2.71 ↑)91.36 (1.25 ↑)94.0 (0.3 ↑)94.3 (0.2 ↑)
Ours (ReCon)✓96.03 (↑ 0.85)95.32 (1.69 ↑)92.06 (1.43 ↑)94.3 (0.2 ↑)94.7 (0.2 ↑)
+ +Table 1. Shape classification performance on ScanObjectNN and ModelNet40, measured by accuracy (%). [Key: Best results]. + +# 3.4. Multi-modality Masked Feature Prediction + +Our model, as depicted in Fig. 3, adopts a dual-branch strategy. In this setup, each branch processes different types of inputs: the teacher branch processes unmasked, complete point cloud data, while the student branch deals with the corresponding masked data. During training, the flow of gradients through the teacher branch is intentionally stopped, encouraging the student branch to closely mimic the representations provided by the teacher. + +Specifically, the teacher branch's encoders take in un-masked point cloud data to produce aligned and context-rich target representations. The student model is then tasked with reconstructing these target 2D and 3D representations using only the visible (unmasked) 3D inputs. The reconstruction loss is quantified as follows: + +$$ +\mathcal {L} _ {\text {i n t r a}} = \operatorname {M S E} \left(\operatorname {M L P} \left(\mathbf {P} _ {\text {i n s}} ^ {\text {p r e}}\right), \mathbf {P} _ {\text {i n s}} ^ {\text {t e a}}\right) + \operatorname {M S E} \left(\operatorname {M L P} \left(\mathbf {I} _ {\text {i n s}} ^ {\text {p r e}}\right), \mathbf {I} _ {\text {i n s}} ^ {\text {t e a}}\right) \tag {8} +$$ + +$$ +\mathcal {L} _ {\text {i n t e r}} = \operatorname {M S E} \left(\operatorname {M L P} \left(\mathbf {P} _ {\text {i n s}} ^ {\text {p r e}}\right), \mathbf {I} _ {\text {i n s}} ^ {\text {t e a}}\right) + \operatorname {M S E} \left(\operatorname {M L P} \left(\mathbf {I} _ {\text {i n s}} ^ {\text {p r e}}\right), \mathbf {P} _ {\text {i n s}} ^ {\text {t e a}}\right) \tag {9} +$$ + +Finally, we sum up all three losses as the final loss for our method: + +$$ +\mathcal {L} _ {\text {f i n a l}} = 0. 5 \mathcal {L} _ {\text {i n t r a}} + 0. 5 \mathcal {L} _ {\text {i n t e r}} + \mathcal {L} _ {\text {t o k e n}} \tag {10} +$$ + +In the first stage of training, the teacher model is trained on a raw input reconstruction task using full point cloud data without masking. The objective is to reconstruct both the complete point clouds and the corresponding multi-view depth images. Loss functions for this phase include Chamfer Distance for 3D coordinates and Mean Squared Error (MSE) for the 2D depth images across multiple views: + +$$ +\mathcal {L} _ {\text {t o k e n}} = \frac {1}{n} \sum_ {i = 1} ^ {n} \operatorname {M S E} \left(\mathbf {P} _ {i} ^ {\text {p r e}}, \mathbf {P} _ {i} ^ {\text {t e a}}\right) + \frac {1}{k m} \sum_ {i = 1} ^ {m} \sum_ {k = 1} ^ {K} \operatorname {M S E} \left(\mathbf {I} _ {i k} ^ {\text {p r e}}, \mathbf {I} _ {i k} ^ {\text {t e a}}\right) \tag {7} +$$ + +Furthermore, we introduce instance-level intra- and inter-modality losses. Our approach shares similarities with SimSiam [6] in encouraging representations from one view to predict those from another. However, our method extends SimSiam to a multi-modal framework tailored for masked autoencoder networks. Specifically, we pool the representations from visible input tokens and use MLP layers to predict both 2D and 3D instance-level representations derived from the complete inputs. This design enhances the learning of meaningful representations across modalities. The intra- and inter-modality distill losses are formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t e a c h e r}} = \frac {1}{n} \sum_ {i = 1} ^ {N} \operatorname {C h a m f e r} \left(\mathbf {P} _ {i} ^ {\text {p r e}}, \mathbf {P} _ {i} ^ {\text {g t}}\right) \\ + \frac {1}{k m} \sum_ {i = 1} ^ {k} \sum_ {j = 1} ^ {M} \operatorname {M S E} \left(\mathbf {I} _ {i j} ^ {\text {p r e}}, \mathbf {I} _ {i j} ^ {\text {g t}}\right). \tag {11} \\ \end{array} +$$ + +After pre-training the teacher model, we leverage the pre-trained teacher from the first stage and keep it frozen during the main training phase. This two-stage design ensures that the student models learn well-aligned and contextualized representations across modalities. + +
Method[P]mIoUcmIoU1
PointNet [39]80.3983.70
Transformer [64]83.4285.10
Point-BERT [64]✓84.1185.60
Point-MAE [38]✓-86.10
Joint-MAE [38]✓85.4186.28
Point-M2AE [70]✓84.8686.51
ACT [13]✓84.6686.14
I2P-MAE [71]✓85.1586.76
ReCon [42]✓84.8086.40
Ours(Point-MAE)✓85.5886.79
Ours(Point-M2AE)✓85.6686.91
+ +# 4. Experiments + +# 4.1. Self-Supervised Pre-training + +Datasets. In our experiments, we use several datasets, including ShapeNet [3], ModelNet40 [59], ScanObjectNN [56], ShapeNetPart dataset [63], and ScanNetV2 dataset [11]. The ShapeNet [3] comprises about 51,300 clean 3D models. The widely adopted ModelNet40 [59] consists of synthetic 3D shapes of 40 categories, of which 9,843 samples are for training and the other 2,468 are for validation. The ScanObjectNN [55] contains 11,416 training and 2,882 validation point clouds of 15 categories. ShapeNet [3] dataset. ScanObjectNN is divided into three splits for evaluation, OBJ-BG, OBJ-ONLY, and PB-T50-RS. ShapeNetPart [63] is a widely used dataset for 3D semantic segmentation, which consists of 16,881 models across 16 categories. The ScanNet [11] is an indoor scene dataset consisting of 1,513 reconstructed meshes, among which 1,201 are training samples and 312 are validation samples. + +# 4.2. Downstream Tasks + +Shape Classification. We evaluate our method on the ModelNet40 [59] and ScanObjectNN [56] datasets, representing synthetic and real-world 3D objects, respectively. Data augmentation techniques, including random scaling and translation, are applied during training. For fair comparison on ModelNet40, we adopt the standard voting method [33] used in Point-BERT. As shown in Table 1, our method achieves $94.4\%$ accuracy, outperforming training from scratch by $3.0\%$ and surpassing the baseline PointM2AE by $0.4\%$ , a notable gain given the dataset's limited size. For ScanObjectNN, we evaluate across OBJ-BG, + +Table 2. Part segmentation on ShapeNetPart [63]. $\mathrm{mIoU}_C$ (\%) and $\mathrm{mIoU}_I$ (\%) denote the mean IoU across all part categories and all instances in the dataset, respectively. [P] represents fine-tuning after self-supervised pre-training. + +
Methods[P]AP25AP50
VoteNet [41]58.633.5
PointContrast [60]✓59.238.0
DepthContrast [73]✓64.042.9
DPCo [24]✓64.241.5
3DETR [35]62.137.9
+Point-BERT[65]✓61.038.3
+Point-MAE [38]✓62.840.1
+MaskPoint [32]✓63.440.6
+ACT [13]✓63.541.0
+PiMAE [4]✓63.140.8
+TAP [58]✓63.041.4
+ Ours✓63.943.3
+ +Table 3. 3D object detection results on ScanNet dataset. We adopt the average precision with 3D IoU thresholds of 0.25 $(AP_{25})$ and 0.5 $(AP_{50})$ for the evaluation metrics. [P] represents fine-tuning after self-supervised pre-training. + +OBJ-ONLY, and PB-T50-RS splits, where our method significantly surpasses Point-MAE and Point-M2AE. Notably, we also outperform Joint-MAE [18], which adopts a multimodality MAE framework but neglects the intrinsic multiview nature of point clouds. This highlights the importance of leveraging multi-view geometric information in 3D pre-training for enhanced representation learning. Furthermore, our method outperforms foundation model-based approaches such as ACT[13] and I2P-MAE[71] and achieves results comparable to the SOTA ReCon [42]. While I2P-MAE and ReCon primarily focus on semantic feature distillation, our method advances 3D geometric learning. To validate its generality, we integrate our 3D-to-multi-view projection and MSMH module into both I2P-MAE and ReCon, enabling multi-view image reconstruction from 3D input. Experimental results confirm that our approach enhances existing methods, demonstrating that the 3D geometric features learned through our method are complementary to the semantic features distilled from foundation models. By leveraging the inherent multimodal nature of point clouds, our method complements foundation models and strengthens 3D representation learning. + +Part Segmentation. We evaluate our method's representation learning capability on the ShapeNetPart dataset [63], which contains 14,007 and 2,874 samples with 16 object categories and 50 part categories for training and validation. Following previous method [38], we sample 2,048 points from each input instance and adopt the same segmentation head [39, 40] for the fair comparison, which concatenates the output features from different transformer blocks of the encoder. The head only conducts simple upsampling for point tokens at different stages and concatenates them alone with the feature dimension as the output. We report + +
Token RecInstance RecMSMHPB-T50-RS
---85.18
✓--87.07
-✓-86.26
--✓86.03
✓✓-88.11
✓-✓87.92
-✓✓87.19
✓✓✓88.93
+ +mean IoU (mIoU) for all instances, with IoU for each category. Table 2 indicates that our method improves the baseline method Point-MAE and surpasses the state-of-the-art method Point-M2AE in all settings. + +3D Object Detection. To demonstrate the generality of the proposed method, we also pre-train the Multiview-ML on the indoor ScanNetV2 dataset [11] and subsequently fine-tune our method on the object detection task. Our baseline is 3DETR [35]. We utilize the same backbone as 3DETR. The Table 3 indicates that Our method achieves $63.9\mathrm{AP}_{25}$ $(+1.8)$ and $43.3\mathrm{AP}_{50}$ $(+5.4)$ compared to the baseline on the ScanNetV2 [11] dataset. Furthermore, we benchmark our method against PiMAE [4]. PiMAE is designed to leverage both masked single RGB images and point clouds for reconstructing the original image and point clouds. Despite PiMAE's ability to enable point clouds to learn texture information from images, it overlooks the multi-view attributes of point clouds. Our method's considerable superiority over PiMAE underscores the critical importance of leveraging multi-view information for effective 3D representation learning. + +# 4.3. Ablation Study + +The Effectiveness of Each Proposed Component. The ablation study presented in Table 4 underscores the substantial impact of our proposed 3D to multi-view Multi-Modal Learner in advancing 3D representation learning, particularly in comparison to the baseline Point-MAE [38], which relies solely on the 3D modality. Our method, which directly reconstructs multi-modality masked representations from visible point clouds, already demonstrates a significant performance boost over Point-MAE. This observation underscores the efficacy of token-level representation prediction for 3D representation learning. Moreover, our approach leverages instance-level intra and inter-modality representation prediction, further enhancing performance. By utilizing global features of masked tokens to predict global representations derived from complete inputs, the network gains a deeper understanding of global information and becomes more robust, thus improving representation learning. + +Table 4. Ablation study for the effectiveness of each proposed component on the 3D classification task in ScanObjectNN dataset. + +
Input ModalityOutput ModalityPB-T50-RS
3D3D86.76
3D2D84.25
3D & 2D3D & 2D87.02
3D3D & 2D88.93
+ +Table 5. Ablation study for the effectiveness of input and output modalities on the 3D object classification task in ScanObjectNN dataset. + +The Effectiveness of Input and Output Modality. We introduce a novel method to reconstruct both 3D and 2D multi-view representations using only 3D data. Our ablation study (Table 5) demonstrates the effectiveness of the 3D to multi-view feature projection technique. By maintaining consistent settings for masked token reconstruction, intra/inter-level representation predictions, and Multi-Scale Multi-Head Attention, our approach with solely 3D input and output significantly outperforms the baseline Point-MAE, highlighting its strength in 3D representation learning. Incorporating both 3D and 2D inputs for reconstructing 3D and 2D outputs yields only marginal gains, similar to findings in Joint-MAE [18]. Notably, our method, which exclusively uses 3D inputs, demonstrated the best overall performance. We argue that adding 2D depth leads the network to heavily rely on the visible 2D information to predict the masked 2D content without the need to fully understand the multi-view geometry setting and thus degrade the representation learning. This finding illustrates the added value of integrating multi-view and pose-related information into the 3D representation learning paradigm + +# 5. Conclusion + +This paper introduces Multiview-ML, an novel method for 3D representation learning that capitalizes on the multiview nature of 3D point clouds. Unlike previous approaches, our method uniquely employs masked point clouds to reconstruct their original forms and generate multiple depth images from different views. This approach harnesses the multi-view features and spatial information within point clouds, distinguishing our method from existing multi-modal MAE techniques. Additionally, we introduce a multi-scale multi-head attention mechanism that enhances the interplay between local and global perspectives within each decoder transformer block, utilizing attention heads across various scales. Finally, a novel self-training strategy is proposed, aiming to generate aligned and context-rich masked 2D and 3D representations based on the initial learning objectives. Our experimental results showcase the superior performance of Multiview-ML over current leading SSL 3D learning methods across various downstream applications, highlighting its effectiveness in fully leveraging the multi-view attributes of 3D data. + +# References + +[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding. 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However, they tend to overconstrain the model to learn the details of the masked region, resulting in failure to capture generalized features. To address this limitation, we propose PointGAC, a novel clustering-based MPM method that aims to align the feature distribution of masked regions. Specially, it features an online codebook-guided teacher-student framework. Firstly, it presents a geometry-aware partitioning strategy to extract initial patches. Then, the teacher model updates a codebook via online $k$ -means based on features extracted from the complete patches. This procedure facilitates codebook vectors to become cluster centers. Afterward, we assign the unmasked features to their corresponding cluster centers, and the student model aligns the assignment for the reconstructed masked features. This strategy focuses on identifying the cluster centers to which the masked features belong, enabling the model to learn more generalized feature representations. Benefiting from a proposed codebook maintenance mechanism, codebook vectors are actively updated, which further increases the efficiency of semantic feature learning. Experiments validate the effectiveness of the proposed method on various downstream tasks. Code is available at https://github.com/LAB123-tech/PointGAC. + +# 1. Introduction + +Self-supervised point cloud representation learning aims to extract robust and generalizable feature representations from large-scale unlabeled data [32, 33]. These learned representations can significantly improve various downstream applications, including object classification [30], semantic segmentation [21, 23, 24], point cloud completion [50], and other 3D understanding tasks [35, 38, 39]. Due to its ability to learn without relying on annotated data, self-supervised point cloud representation learning has attracted increas + +![](images/53266e98193e794d153db2dd8c52f15a163dd63c1006963d9216fa8a018e9fc9.jpg) +Figure 1. Fundamental concept of PointGAC. Both the unmasked teacher features and the reconstructed masked features at corresponding positions are assigned to the same cluster center over the codebook. This clustering paradigm avoids forcing the student model to overfit the exact feature details of the teacher model. + +ing research interest. This is achieved by designing pretext tasks that encourage the model to capture meaningful geometric features. Among these, masked point cloud modeling is a prominent approach in vision transformers. + +Inspired by the success of MAE [16], masked point cloud modeling [7, 28, 34, 44, 56, 58] aims to train models capable of reconstructing the coordinates of masked regions using the visible portions of the point cloud. However, these coordinate-based reconstruction approaches focus on capturing surface details, limiting their effectiveness in learning semantic information and resulting in inferior performance in downstream tasks. To mitigate this limitation, recent works [10, 17, 25, 42, 43, 48, 53] adopt a teacher-student framework, where instead of reconstructing coordinates, the student model is trained to align with the masked features extracted by the teacher model. However, a notable drawback of these approaches is that they tend to over-constrain the student model, forcing it to regress the point-wise feature details of the teacher, which prevents it from learning more generalized features. Moreover, these methods often overlook geometric consistency when constructing local point cloud patches, making it challenging for the model to learn meaningful representations. + +To address these issues, we propose PointGAC, a novel clustering-based approach that aims to learning the similarity of features in their distribution, as illustrated in Fig. 1. PointGAC begins by partitioning the input point cloud into + +non-overlapping, geometrically homogeneous patches. After embedding the patches, the teacher model updates an online codebook by leveraging the features extracted from the complete patch embeddings. As a result, codebook vectors gradually evolve into cluster centers. The student model is tasked with reconstructing the masked features from the visible patch embedding. Finally, the reconstructed masked features and the unmasked teacher features at the corresponding locations are assigned to the same cluster center to achieve feature alignment. This clustering paradigm enables the student model to learn the cluster centers to which the masked point cloud patches belong. It avoids the need of point-wise feature alignment, facilitating the learning of more generalized feature representations in the student network. Moreover, we find that many vectors in the codebook remain unpudated and become dead vectors. Therefore, we design a codebook maintenance mechanism to revitalize these dead vectors. It helps to improve the efficiency of masked feature alignment over the codebook. Our method presents a general solution for point cloud-based semantic analysis. Experimental results demonstrate its efficacy across a variety of downstream tasks. The contribution can be summarized as follows: + +- We propose a novel online codebook-guided teacher-student framework that follows a clustering-based paradigm to accomplish MPM tasks. This framework predicts the cluster center to which the masked region belongs, effectively avoiding the problem of over-constraining the model. +- We propose a geometry-aware partitioning strategy to divide the point cloud into geometrically homogeneous patches. This strategy ensures geometric consistency within each local point cloud patch, enhancing the quality and efficiency of feature learning. +- We design a codebook maintenance mechanism to increase the update frequency of the codebook vectors. It improves the efficiency of masked feature alignment. + +# 2. Related Work + +Masked point modeling. Inspired by the success of Mask Image Modeling (MIM), MPM has also gained increasing attention in point cloud research. The pioneering algorithm [52] introduces a trained tokenizer, allowing pretraining to be performed through masked token prediction. However, the tokenizer is trained offline, making it immutable during pretraining. Other works[18, 44, 54] explore multitask learning to embed both local and global contexts for point cloud pretraining. Several studies [28, 48, 55] are dedicated to designing complex models, leading to significant advancements in the reconstruction of point cloud geometric structures. However, the model spends significant resources to accurately recover the position of each point, which may not be important for downstream tasks re + +lated to semantic understanding. Hence, certain algorithms [10, 17, 43, 48, 53] shift their focus toward reconstructing the features of masked regions. + +Although existing methods have achieved impressive results, they are regression-based approaches for reconstructing the information of the masked regions. Such regression-based algorithms tend to over-constrain the model, leading it to focus excessively on reconstructing details while failing to learn more generalizable features. In this paper, we adopt a clustering-based method to identify which cluster center in the codebook the masked features belong to. This allows the model to avoid this problem. + +Codebook for representation learning. The codebook is widely used as a feature representation method in computer vision. In generative models, [40, 46] leverages the codebook to map continuous features to discrete tokens, facilitating the diverse visual outputs from the textual descriptions. Inspired by this, subsequent studies [3, 11] represent the object as a series of discrete tokens to capture structural patterns. Several methods [1, 2, 5, 12] utilize a codebook to align representations of different augmented views in the clustering space. SwAV [5] adopts an optimal transport strategy [8] that assumes a uniform assignment of each batch data to all prototypes, while MSN [2] and PAWS [1] employ entropy-based regularization [19] to encourage balanced prototype usage. However, such an assumption may not hold in our setting due to the imbalanced and potentially diverse semantic distribution within each mini-batch. Instead, we adopt an online k-means algorithm to progressively update the codebook and introduce a maintenance mechanism to improve its utilization efficiency. + +# 3. Method + +Overview. Fig. 2 shows the architecture of the proposed PointGAC, adopting an online codebook-guided teacher-student framework. Given an input point cloud $P$ with $N$ points, we first partition it into $L$ non-overlapping refined patches using a geometry-aware partitioning strategy. The central points are then processed through an MLP layer to obtain the positional embedding for each patch. Each patch undergoes the operation of normalization before being passed into a mini-PointNet for patch embedding. All patch and positional embeddings are summed to form input features for subsequent teacher-student framework. + +In the teacher branch, input features are fed into an encoder to update codebook vectors via online k-means clustering. Encoded teacher features are matched with the codebook to generate teacher assignments, which serve as the target for the student model to learn. In the student branch, the task is to recover the masked features from partially visible features, obtaining the reconstructed features. Then, the reconstructed features are accomplished by matching with the codebook to generate student assignments. Then, + +![](images/48fcbc5ce98bc395276e74f49cf505b1fb1abebd1f283cc694cda14803ef243f.jpg) +Figure 2. The framework of PointGAC. This framework utilizes an online codebook to achieve feature alignment. It aligns the reconstructed features on the student side with the encoded features on the teacher side at corresponding positions. + +the teacher and student assignments are aligned using a KL divergence loss. During training, gradients are propagated only through the student branch, while the teacher encoder is updated using an Exponential Moving Average (EMA) of the student encoder's parameters. In the following, we will detail the key components of the proposed algorithm. + +# 3.1. Geometry-aware Partitioning Strategy + +In MIM tasks, due to the regular and structured nature of images, algorithms [4, 15, 57] typically divide images into non-overlapping grids. However, since point clouds are unordered and unstructured data, the vast majority of current algorithms rely on a combination of FPS (Farthest Point Sampling) and KNN (K-Nearest Neighbors) to construct overlapping point cloud patches. A major drawback of these methods is the leakage of information from visible patches to masked patches due to the information redundancy between patches, which reduces the practicality. To address this issue, Wang et al. [48] introduced an optimal transport-based approach to partition the point cloud into non-overlapping patches. However, it overlooks the geometric properties of the point cloud. + +To overcome such limitations, we propose a geometry-aware partitioning strategy that divides a point cloud into non-overlapping and geometrically consistent patches, as shown in Fig. 2 (blue area). To group points with similar geometric features, we apply Potts Energy Segmentation (PES) [13, 22] for coarse partitioning, formulated as: + +$$ +\arg \min _ {g \in \mathbb {R} ^ {d g}} \sum_ {i \in P} \| g _ {i} - f _ {i} \| ^ {2} + \mu \sum_ {(i, j) \in E _ {\mathrm {n n}}} w _ {i j} [ g _ {i} - g _ {j} \neq 0 ], \tag {1} +$$ + +where $f_{i}$ is the original geometric feature of point $i$ , as defined in [22], $g_{i}$ is the target geometric label, $P$ represents the point cloud, $E_{nn}$ is the set of edges that connect neighboring points, defining the local neighborhood structure, $w_{ij}$ is the weight determining the influence of the pairwise interaction between points $i$ and $j$ . The Iverson bracket [·] + +equals 1 if the condition holds and 0 otherwise. The factor $\mu > 0$ regulates the coarseness of the resulting partition. This enables the generation of meaningful, non-overlapping geometric segments. + +In MPM, a fixed number of patches is required, whereas PES produces a varying number of segments across different point clouds. To reconcile these differences, we use FPS to sample $L$ central points (along with their geometric labels) from the geometric segments. Then, we assign each point to related central point, thereby forming $L$ refined patches. This assignment satisfies two conditions: 1) All points within a patch belong to the same geometric segment; 2) Different patches belong to the same segment contain a similar number of points. We denote the assignment by a matrix $Q$ , whose elements $Q_{ij} \in [0,1]$ . + +To enforce the first condition, we define a mask matrix $M$ with elements $M_{ij} \in \{0,1\}$ , where $M_{ij} = 1$ if the central point and its assigned points share the same geometric label, and 0 otherwise. We then apply $M$ to $Q$ via the Hadamard (element-wise) product $Q \circ M$ to guide the assignments. The second condition can be approximated as $\sum_{i}(Q \circ M)_{ij} / L = N / L$ . Since FPS sampling tends to select more central points from segments containing a larger number of points, it naturally balances the partitioning. Consequently, there is no need to enforce explicit constraints at the level of each individual segment. To satisfy both constraints, we formulate the assignment process as a masked optimal transport, expressed as: + +$$ +\min _ {Q} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {L} M _ {i j} Q _ {i j} T _ {i j}, \text {s . t .}, \sum_ {i = 1} ^ {N} \frac {(Q \circ M) _ {i j}}{L} = \frac {N}{L}, \tag {2} +$$ + +where $T$ is the cost. Following [31], the solution to this problem is achieved based on Sinkhorn algorithm [8]. This process yields refined patches $\{P_1,\dots ,P_L\}$ that are geometrically aware, ensuring each patch consists exclusively of points from the same geometric segment. + +Patch embedding layer. To extract features from the achieved patches, patch embedding layers are designed. Each refined patch is normalized by subtracting its center. The resulting patches are then processed by a mini-PointNet [36] to generate patch embeddings $E \in \mathbb{R}^{L \times D}$ ( $D$ is the dimension), which can be expressed as: + +$$ +E = \operatorname {P o i n t N e t} \left(\left\{P _ {1}, \dots , P _ {L} \right\}\right), \tag {3} +$$ + +Notably, patch sizes are not uniform. To enable parallel feature extraction across different patches, we construct a mask matrix $H \in \mathbb{R}^{N \times N}$ over the entire point cloud, where $H_{i,j} = 1$ indicates that points $i$ and $j$ belong to the same patch. Max pooling is then applied to regions where the mask matrix has a value of 1 in each row. Meanwhile, position embeddings $PE \in \mathbb{R}^{L \times D}$ are extracted from the patch center using an MLP layer. Finally, the patch embeddings $E$ and the positional embeddings $PE$ are summed to obtain $F$ , which serves as input features for subsequent modules. + +# 3.2. Teacher-Student Framework + +To achieve feature alignment in a self-supervised manner, we employ a teacher-student framework, where the student branch reconstructs masked features based on the knowledge provided by the teacher branch. + +Teacher branch. Given the input feature $F$ , the encoder applies a self-attention mechanism to encode $F$ . It is composed of $n$ standard transformer blocks. Specially, the encoded teacher feature within the $i$ -th transformer block of the encoder can be formulated as: + +$$ +T _ {i} = \operatorname {A t t n} (Q, K, V) = \operatorname {S o f t M a x} \left(\frac {Q K}{\sqrt {D}}\right) V, \tag {4} +$$ + +where $Q = T_{i - 1}W_{Q}$ $K = T_{i - 1}W_{K}$ , and $V = T_{i - 1}W_{V}$ with $W_{Q},W_{K}$ , and $W_{V}$ being learnable parameters. Furthermore, $T_0 = F$ + +Subsequently, we utilize the encoded teacher features to update the codebook $C = [c_{1}, c_{2}, \ldots, c_{K}]$ where each vector $c_{k} \in \mathbb{R}^{1 \times D}$ represents a D-dimensional vector. The codebook is updated using an online k-means algorithm [46]. For each teacher feature, we identify the most similar codebook vector. We use $n_{k}^{(t)}$ to denote the number of features assigned to $c_{k}$ at the $t$ -th iteration in the pretraining. We also use $m_{k}^{(t)}$ to represent the element-wise sum of these features. To maintain a stable update processing, we utilize an exponential moving average: + +$$ +N _ {k} ^ {(t)} = \gamma N _ {k} ^ {(t - 1)} + (1 - \gamma) n _ {k} ^ {(t)}, +$$ + +$$ +M _ {k} ^ {(t)} = \gamma M _ {k} ^ {(t - 1)} + (1 - \gamma) m _ {k} ^ {(t)}, +$$ + +where $N_{k}^{(t)}$ is the accumulated count of the features assigned to $c_{k}$ at the $t$ -th iteration, with $N_{k}^{(1)} = 1$ as the initial value. $M_{k}^{(t)}$ is the accumulated element-wise sum of these + +features and $M_{k}^{(1)}$ is initialized as the $k$ -th codebook vector. Then, $c_{k}$ is given by $c_{k} = M_{k} / N_{k}$ . We set $\gamma = 0.99$ to ensure that the update processing remains stable, allowing the codebook vector to become the cluster center gradually. Teacher assignment generation. To assign the encoded teacher features to cluster centers within the codebook, we compute the soft assignment of encoded teacher features across the codebook. Given the encoded teacher features $T = \{t_i\}_{i=1}^L$ , $t_i \in \mathbb{R}^{1 \times D}$ , the soft assignment $Q_{t} \in \mathbb{R}^{L \times K}$ is computed as the following formula: + +$$ +Q _ {t} = \operatorname {S o f t M a x} \left(\frac {T C}{\tau_ {t}}\right), \tag {6} +$$ + +where $\tau_{t}$ is the temperature coefficient used to adjust the smoothness of $Q_{t}$ . In our experiments, we adopt a cosine annealing strategy to adjust the value of $\tau_{t}$ . At the early stage, $\tau_{t}$ is relatively large, resulting in smoother distribution. As training progresses, we gradually reduce $\tau_{t}$ , which results in highly peaky distribution. Essentially, $Q_{t}$ encodes the cluster center over the codebook to which the teacher feature belongs. We use these generated assignment vectors $Q_{t}$ as the supervision signals for the student branch. + +Student branch. The task of the student branch is to reconstruct the masked feature from the visible features. With a predefined masking ratio $r$ , we apply random masking to the input feature $F$ . The masked features are denoted as $S_{m} \in \mathbb{R}^{\lfloor Lr\rfloor \times D}$ , and the visible features are denoted as $S_{v} \in \mathbb{R}^{\lceil L(1 - r)\rceil \times D}$ , where $\lfloor \cdot \rfloor$ and $\lceil \cdot \rceil$ denote the floor and ceiling functions, respectively. On the student side, apart from possessing an encoder with the same structure as the teacher model, it also includes a decoder that comprises $m$ transformer modules. The student encoder extracts features from $S_{v}$ , yielding the encoded student features $S_{E}$ . Then, $S_{E}$ is concatenated with the learnable mask embeddings $S_{a} \in \mathbb{R}^{\lfloor Lr\rfloor \times D}$ and added to the full set of positional information $PE$ , serving as the input to the decoder. After being processed by the decoder, the reconstructed feature $S_{R} \in \mathbb{R}^{Lm\times D}$ is used to align the encoded teacher features. + +Student assignment generation. The reconstructed features $S_{R}$ and the teacher features $T$ at the masked locations should be assigned to the same cluster center to achieve feature alignment. We compute the soft assignment $Q_{s} \in \mathbb{R}^{L \times K}$ of the features $S_{R}$ over the codebook $C$ using the following formula: + +$$ +Q _ {s} = \operatorname {S o f t M a x} \left(\frac {S _ {D} C}{\tau_ {s}}\right), \tag {7} +$$ + +where $\tau_{t}$ is the temperature parameter that controls the sharpness of the soft assignment. In the experiments, we set $\tau_{s}$ to a constant value that is larger than $\tau_{t}$ . It ensures the student assignment $Q_{s}$ is smoother in distribution compared to the teacher assignment $Q_{T}$ , helping the reconstructed feature to better align to the teacher feature. + +# 3.3. Codebook Maintenance Mechanism + +The codebook vectors are designed to serve as cluster centers for the patch features. However, many vectors remain unused and gradually become 'dead vectors' since online k-means are based on the nearest-neighbor lookup. To analyze this issue, we record the update frequency of all codebook vectors after training. The frequency matrix (1, K) was reshaped to (H, W) for visualization. As shown in Fig. 3(a), without any perturbation, many codebook vectors exhibit low update frequencies. For this issue, we experimentally introduced random perturbations to codebook vectors during training and observed it improved codebook utilization to some extent, as shown in Fig. 3(b). + +Building on this insight, we propose a codebook maintenance mechanism, which applies varying degrees of meaningful perturbations to each codebook vector based on its update frequency. For each codebook vector $c_{k}$ , we assign the most similar teacher feature $t_{k}$ from the current batch of data to update it. The principle is that frequently updated codebook vectors receive minimal perturbations, whereas infrequently updated or dead vectors undergo larger perturbations. Specially, we count the number of times the codebook vector is updated, denoted as $x$ . Then, we compute a weight that determines the magnitude of the perturbation to be added. The weights $\alpha_{k}$ are computed as: + +$$ +\alpha_ {k} = \frac {1}{1 + e ^ {\epsilon (x - \bar {x})}}, \tag {8} +$$ + +$$ +c _ {k} \leftarrow c _ {k} \cdot \left(1 - \alpha_ {k}\right) + t _ {k} \cdot \alpha_ {k}, +$$ + +where $\bar{x}$ is the average of the maximum and minimum update counts among all the codebook vectors. $\epsilon$ is a small value used to smoothly adjust the weights assigned to different codebook vectors. As illustrated in Fig. 3(c), the majority of the codebook vectors exhibit a high update frequency, indicating that they are being sufficiently updated at this stage. Experiments discuss the improvement. + +# 4. Experiments + +Pre-training dataset. We pre-trained the proposed model on ShapeNet55 [6], which consists of 52,472 unique 3D models covering 55 object categories. Before pre-training, we apply Potts energy segmentation on the point cloud to complete the geometric partitioning. Geometric labels are stored in the dataset to speed up pre-training. + +Experimental details. We sample $N = 1024$ points with their corresponding geometric labels from the dataset using FPS and partition them into $L = 64$ patches. We employ the AdamW optimizer [20] with a weight decay of 0.04 for training. The learning rate follows a cosine decay schedule [29], starting with a 50-epoch linear warm-up phase and reaching a maximum learning rate of 0.001. $\tau_{t}$ is initialized at 0.07 and decay to 0.04 during training. $\tau_{s}$ remains fixed + +![](images/98a8f69b30cec1799303cf9b23206f39e92608b5591c024c063ea18bdcbe78a7.jpg) +Figure 3. Visualization comparison of codebook update frequency under different perturbation modes. Each pixel in the figure represents the update frequency of a single vector. + +at 0.1 throughout the entire training process. Following the practice in OBoW [12], the codebook size $K$ is set to 8192. Model architecture. The teacher and student encoders share the same structure, both composed of $n = 12$ transformer blocks. The student decoder consists of $m = 4$ standard transformer blocks. The hidden dimension of transformer blocks is $D = 384$ . + +# 4.1. Evaluations on Downstream Tasks + +Shape classification. We evaluate our method by freezing the pre-trained student encoder and training a linear SVM on ModelNet40 for shape classification. We also report results with and without the voting trick after finetuning on ModelNet40. As shown in Tab. 1, compared to other teacher-student models following the regression paradigm, such as Point2Vec [53] and RIMAE [42], our method achieves the best performance in the Linear SVM evaluation. Since regressing the teacher features requires an accurate matching of each feature value, which makes the optimization process more challenging. By aligning the cluster centers to which the features belong, we only need to focus on the similarity of the feature distributions, thus simplifying the optimization process. + +We further validate our model on the ScanObjectNN dataset, which contains around 15 000 real-world objects from 15 categories. We report results on three subsets: OBJ-BG (objects with background), OBJ-ONLY (objects only), and PB-T50-RS (objects with background and perturbations). To ensure fairness, each input point cloud is sampled to 2048 points. As shown in Tab. 1, PointGAC achieves competitive performance, particularly in challenging settings. Although the algorithm is pre-trained on the synthetic dataset, it generalizes well to real-world datasets and achieves the best performance. Also, on the OBJ_ONLY variant, our method shows significant performance improvement. Since the results of geometric partitioning remain unaffected by background noise. This property makes it advantageous for codebook vectors to serve as geometrically well-defined cluster centers. + +
MethodReferences#Params(M)ModelNet40ScanObjectNN
#PointsLinear SVMw/o Votew/ Vote#PointsOBJ-BGOBJ-ONLYPB_T50_RS
Point-BERT[52]CVPR 202222.11k points87.492.793.21k points87.488.183.1
PointMAE[34]ECCV 202222.11k points92.793.293.82k points90.088.385.2
PointM2AE[55]NeurIPS 202215.31k points92.993.494.02k points91.288.886.4
Point2Vec[53]GCPR 202323.21k points92.192.593.12k points91.290.487.5
PointGPT[7]NeurIPS 202319.51k points--94.02k points91.690.086.9
MAE3D[18]TMM 202323.41k points-93.4-2k points88.487.786.2
PointGame[28]TGRS 2023-1k points90.093.193.52k points89.089.085.8
MaskFeat3D[49]ICLR 2024-1k points91.193.393.72k points91.790.087.7
RIMAE[42]AAAI 202523.81k points92.893.193.92k points91.989.386.8
Ours-24.11k points93.594.394.62k points92.691.489.4
+ +Table 1. Classification accuracy on ModelNet40 and ScanObjectNN. #Params indicates model size. For ModelNet40, overall accuracy (%) is reported with and without voting. For ScanObjectNN, overall accuracy (%) is shown for three variants. + +
Method5-way10-way
10-shot20-shot10-shot20-shot
Point-BERT[52]94.6±3.693.9±3.186.4±5.491.3±4.6
MaskPoint[27]95.0±3.797.2±1.791.4±4.092.7±5.1
Point-MAE[34]96.3±2.597.8±1.892.6±4.193.4±3.5
Point-M2AE[55]96.8±1.898.3±1.492.3±4.595.0±3.0
PointGame[28]96.7±2.797.9±1.592.9±3.794.7±2.6
MAE3D[18]95.2±3.197.9±1.691.1±4.695.3±3.1
PointOTG[48]97.2±2.398.7±1.293.2±3.495.6±2.6
Ours97.4±2.098.9±1.393.7±3.195.9±2.4
+ +Table 2. Few-shot classification results on ModelNet40. The mean accuracy and standard deviation are calculated in each setting. + +
MethodSemantic segmentationPart segmentation
mAccmIoUmIoUCmIoUI
Transformer[47]68.660.083.484.7
Point-MAE[34]69.960.884.286.1
Point-BERT[52]69.760.584.185.6
PCP-MAE[56]70.461.184.986.1
Point-LGMask[44]70.361.384.486.1
PointMPP[9]69.861.484.786.1
RIMAEL[42]68.460.382.184.3
Ours70.961.885.186.7
+ +Few-shot classification. We perform few-shot experiments on the ModelNet40 dataset using the $m$ -way, $n$ -shot setting, where $m \in \{5, 10\}$ denotes the number of randomly selected categories and $n \in \{10, 20\}$ indicating the number of samples per category. During testing, we randomly selected 20 unseen samples from each category. In experiments, we performed 10 independent trials for each setting. The experimental results are shown in Tab. 2. It can be + +Table 3. Segmentation results on S3DIS and ShapeNetPart. For S3DIS, mean instance IoU (mIoU) and mean class accuracy (mAcc) are reported; for ShapeNetPart, category-level $(\mathrm{mIoU}_C)$ and instance-level $(\mathrm{mIoU}_I)$ mean IoU are provided. + +
MethodCD-SCD-MCD-HCD-AvgF1
Point-JEPA[41]0.831.232.061.370.34
Pos-Bert[10]0.911.272.251.480.32
3D-JEPA[17]0.711.222.021.320.35
Point2Vec[53]0.580.811.921.100.38
Point-MSD[43]0.650.831.871.120.37
PM-MAE[26]0.530.791.811.040.41
RIMAE[42]0.510.721.740.990.46
Ours0.520.691.630.950.49
+ +Table 4. Results of point cloud completion on ShapeNet55 dataset. We use CD-S, CD-M, and CD-H to denote CD results in the simple, moderate, and hard settings, respectively. + +observed that even with limited data, our method exhibits competitive performance compared to other methods, while showing minimal deviation in most cases. + +Semantic segmentation. We test the generalization of our method on the large-scale S3DIS dataset for semantic segmentation evaluations. The S3DIS dataset consists of 271 scenes from 6 indoor regions, with each point labeled into 13 categories. Following the common practice, we use Area 5 for testing and the remaining areas for training. The experimental results are shown in Tab. 3. Compared to other methods, PointGAC achieves the best performance in terms of mIoU and mAcc metrics. Meanwhile, we provide a qualitative comparison of semantic segmentation results on the S3DIS dataset. As illustrated in Fig. 4, the predictions of our algorithm are closer to the ground truth and less incorrectly segmented result than PointMPP and PCP-MAE. + +Part segmentation. We evaluate part segmentation performance of PointGAC on ShapeNetPart dataset, which consists of 16,881 samples across 16 categories. We partition the point cloud into 128 patches using our geometry-aware partitioning strategy. We use a trilinear interpolation algorithm [37] to up-sample the encoded features to all input points. The experimental results are shown in Tab. 3. + +![](images/ac9d874a29226d65b29a98b808a3cecbbb75bacad010c6b180b3f9e9a8a9a5a0.jpg) +Figure 4. Qualitative comparison on S3DIS semantic segmentation. The first column shows the original point cloud input, followed by columns 2-4, which display the segmentation results of PointMPP, PCP-MAE, and our method. The fifth column shows the ground truth. Regions with poor segmentation results are marked with red dashed boxes. + +![](images/e3a240b52e3a2001ab16c7d2bb5ea36961b0494c67645b41240b8c6b70a1b4e3.jpg) + +![](images/605fa71aceb2e49811d845b6dda81c46cdf5093aec7b2805419f3380d893e847.jpg) + +![](images/c386796d91ed87c2dbc3192ffb03046628bad1d7651398e241b9422f07ec018c.jpg) + +![](images/73ff1d1ed0f60c2ed5e5cce09891e838ab8f476ebf0974e34a9212851c1be9ae.jpg) + +![](images/d116d27a328c1fe3b52df72b5658a4564137965604b10243cd54a62c302bad9c.jpg) +Figure 5. Qualitative comparison of different algorithms on ShapeNetPart, with differences highlighted in red boxes. + +Our method achieves better results in terms of $\mathrm{mIoU}_C$ and $\mathrm{mIoU}_I$ . In our approach, the features are extracted from geometrically homogeneous patches, effectively capturing the distinctive properties of the local geometry. It is beneficial for recovering the features of the original input points. In Fig. 5, we visualize the segmentation results of different methods. PointGAC exhibits minimal segmentation errors. + +Point cloud completion. Finally, we further validate the effectiveness of PointGAC on the ShapeNet55 dataset for the point cloud completion task. Following Pointr [51], we randomly remove $25\%$ to $75\%$ of points, creating varying levels of incompleteness. The remaining points are then sampled to 2048 points, which are used as the input. We use the original object containing 8192 points as the ground truth. During testing, we set the number of deleted points to 2048, 4096, or 6144. These correspond to three difficulty levels: simple, moderate, and hard. We use the $\ell_2$ Chamfer Distance (CD) and F1-Score[45] as the evaluation metrics. + +In Tab. 4, we compare PointGAC with other self-supervised algorithms whose pretext tasks focus on regressing the mask features. It can be seen that PointGAC achieves the lowest CD in both moderate and hard settings. In terms of F1-Score, PointGAC also achieves the best performance, which further indicates that the features extracted by our method are more robust to geometric reconstruction. We also provide a qualitative comparison of the point + +![](images/94a92af350c15e93bd22980b07cd31c04b608ea2359c1780d0690a34f267900f.jpg) +Figure 6. Qualitative comparison of different algorithms on the point cloud completion task. + +cloud completion results between the proposed algorithm and other methods in the hard setting. As shown in Fig. 6, it can be observed that almost all geometric details are lost for the input target. While the results reconstructed by other algorithms remain unsatisfactory, PointGAC achieves significantly higher fidelity in the reconstructed outputs. + +# 4.2. Ablation Studies + +Effects of different components. To further validate the effectiveness of the main module design, we conduct extensive experiments on the ModelNet40 dataset. We adopt the Point2Vec[53] method as our baseline model. It employs a teacher-student framework, where the student network learns to regress the feature output from the teacher network. The experimental results are shown in Tab. 5. It can be observed that the performance of the baseline algorithm is not ideal since regression is a challenging task. For Model B, directly constructing the codebook to perform the MPM task via online k-means did not lead to an improvement. Since the codebook at this stage contains many dead vectors. As observed in Model C, the codebook maintenance mechanism addresses this issue, enabling efficient feature alignment on the codebook for the masked point cloud modeling task. According to Model D, the perfor + +
ModelsBaselineCodebook UpdateGAP-/+ Vote
OKCCMM
A✓92.5 / 93.1
B✓✓92.1 / 92.5
C✓✓✓93.7 / 94.2
D✓✓92.8 / 93.4
E✓✓✓✓94.3 / 94.6
+ +Table 5. Ablation study of the main modules in the proposed algorithm on ModelNet40. OKC: Online K-means Clustering. CMM: Codebook Maintenance Mechanism. GAP: Geometry-aware Partition Strategy. $- / +$ Vote: without or with the voting strategy. + +
Group StrategyMask Ratiow/o Votew/ Vote
0.70.80.9
KNN✓93.293.8
KNN✓93.794.2
KNN✓93.494.0
GAP✓93.994.4
GAP✓94.394.6
GAP✓93.694.2
+ +mance is enhanced when the geometric-aware partitioning strategy replaces the traditional KNN in Model A. Furthermore, the performance reaches its peak when the geometry-aware partitioning strategy is applied to Model C, as demonstrated in Model E. At this point, the geometry represented by the codebook vectors becomes more distinct, enabling them to better serve as cluster centers. + +Effect of different grouping strategies. We validate the impact of different grouping methods for constructing point cloud patches on ModelNet40. Specifically, we compare our method with conventional KNN algorithms under different masking ratios, as shown in Tab. 6. It can be seen that the performance of the KNN is not ideal under different masking ratios. It leads to information leakage among the obtained point cloud patches, which simplifies the pretext task and ultimately limits the model performance. Benefiting from geometric consistency, the proposed geometry-aware partitioning strategy improves accuracy compared to KNN. Also, appropriately increasing the masking rate can enhance the overall difficulty of the self-supervised pretext task, thus further improving the model performance. + +Effect of different codebook construction formats. We present the impact of different codebook construction formats using the ModelNet40 dataset. Considering that codebook vectors should be as active as possible, we adopt a queue-based method for codebook construction, following the approach of MoCo [14]. Inspired by SwAV [5], we also compare with an alternative implementation using the Sinkhorn-Knopp algorithm [8]. As shown in Tab. 7, the + +Table 6. Evaluation of the geometric-aware partitioning strategy under different mask ratios. + +
Codebook FormatPerturbed modew/o Votew/ Vote
Queue-basedNone93.794.1
Sinkhorn-basedNone93.193.4
Online k-meansNone92.793.2
Online k-meansRandom93.493.8
Online k-meansMeaningful94.394.6
+ +Table 7. Evaluation of the codebook construction format under different perturbed modes. + +queue-based codebook ensures all vectors remain active by continuously updating with the latest batch data. However, its vectors do not serve as true cluster centers. Although the Sinkhorn-Knopp algorithm mitigates this by enforcing uniform assignments to $K$ clusters, this assumption is often inconsistent with real-world data distributions, leading to suboptimal performance. The codebook constructed using online k-means can solve this problem. However, the performance does not improve if we simply replace it without further optimization. Because there are many dead vectors in the codebook that have not been updated. After adding meaningful perturbations to the vectors in the codebook as proposed in our design, the model achieves its best performance. It achieves much higher codebook utilization (see in Fig. 3(c)) which ensures the accuracy of the feature alignment over the codebook. + +# 5. Conclusion + +In this paper, we propose a novel online codebook-guided teacher-student framework that adopts a clustering-based paradigm to for the MPM task. Unlike traditional regression methods, our method focuses on identifying the cluster centers to which the masked features belong, enabling the model to learn more generalized features. Moreover, by incorporating a geometry-aware partitioning strategy, we ensure geometric consistency within local point cloud block, which enhances the quality of feature learning. To further improves the efficiency of masked feature alignment, we introduce a codebook maintenance mechanism that promotes the convergence of the codebook vectors towards the optimal cluster centroid. Extensive experiments on various downstream tasks validate the effectiveness of the proposed method. Our proposed pre-training framework provides a novel direction to advance point cloud processing. + +# 6. Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China under Grant 62271237, Grant U24A20220, and Grant 62132006, in part by the Science Foundation of the Jiangxi Province of China under Grant 20242BAB26014 and Grant 20223AEI91002, and in part by the PNRR FAIR - Future AI Research (PE00000013), funded by NextGeneration EU. + +# References + +[1] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Armand Joulin, Nicolas Ballas, and Michael Rabat. Semi-supervised learning of visual features by nonparametrically predicting view assignments with support samples. In ICCV, pages 8443-8452, 2021. 2 +[2] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. Masked siamese networks for label-efficient learning. In ECCV, pages 456-473. Springer, 2022. 2 +[3] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. 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, Youwei Lyu $^{1}$ , Si Li $^{1*}$ , Boxin Shi $^{3,4}$ , Yunpeng Jia $^{1}$ , Zhanyu Ma $^{1}$ + +$^{1}$ Beijing University of Posts and Telecommunications $^{2}$ Xiong'an Aerospace Information Research Institute +${}^{3}$ State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University +$^{4}$ National Engineering Research Center of Visual Technology, School of Computer Science, Peking University + +{hanyufei, tiebowen, guoheng, youweilv, lisi, mazhanyu}@bupt.edu.cn + +shiboxin@pku.edu.cn xibei156@163.com + +![](images/5f3ad852ac3e86f6936eb66068654f23e21bd28f4491ff64b6b5f27beaca087d.jpg) +Input 35 views + +![](images/c4231588e4807ed26d94c63aa1f4e724d28af8fdc2a25daf8cc42af92c1d1df8.jpg) +NeRO [23] 8 hours + +![](images/e8f90a1f7492830d01b61d10b7c510465b2531ef75dbaeb9ddb8e3bb2c17cd74.jpg) +PANDORA [8] 10 hours + +![](images/2e7098f01dea85d7491b69d81809775eb560a271ba03188f3e8412c04b114196.jpg) +3DGS-DR [44] 12 min + +![](images/9f63fd31e6d0b06911db9afa0859426e752144f0d814732a2d55c625ad204c01.jpg) +PolGS (Ours) 7 min + +![](images/b110b06a134a356b070a544ad9eb217dbccd7fd525e945079970712c3bf92e26.jpg) +Figure 1. Comparison of efficiency and accuracy on reflective surface reconstruction. Our method takes the shortest time while comparable shape reconstruction accuracy (measured by Chamfer Distance in millimeters) with the existing method based on neural implicit surface representation [23]. + +# Abstract + +Efficient shape reconstruction for surfaces with complex reflectance properties is crucial for real-time virtual reality. While 3D Gaussian Splatting (3DGS)-based methods offer fast novel view rendering by leveraging their explicit surface representation, their reconstruction quality lags behind that of implicit neural representations, particularly in the case of recovering surfaces with complex reflective reflectance. To address these problems, we propose PolGS, a Polarimetric Gaussian Splatting model allowing fast reflective surface reconstruction in 10 minutes. By integrating polarimetric constraints into the 3DGS framework, PolGS effectively separates specular and diffuse components, enhancing reconstruction quality for challenging reflective materials. Experimental results on the synthetic and real-world dataset validate the effectiveness of our method. Project page: https://yu-fei-han.github.io/polgs. + +# 1. Introduction + +Fast and accurate reconstruction of reflective surfaces is essential for applications like real-time virtual reality and in- + +verse rendering. Reflective surfaces meet unique challenges in 3D reconstruction as their specular properties require precise handling of light interactions to capture realistic surface details. It is desired to develop a fast and accurate reconstruction method for reflective surfaces. + +For reflective surface reconstruction, most existing methods rely on implicit neural representations [28], such as Ref-NeRF [34] and NeRO [23], which model complex surface details effectively but suffer from slow processing times due to their implicit neural network structure. While the signed distance function (SDF) offers a better geometry representation, the MLP network incurs significant time costs. In contrast, the recent 3D Gaussian Splatting (3DGS) [14] technique offers a promising approach for fast novel view rendering through explicit surface representation. However, this representation lacks the same level of detail as implicit methods due to limitations in representing fine geometry and surface normals. Additionally, 3DGS-based reconstruction methods primarily focus on diffuse surfaces, leaving reflective surfaces under-explored and resulting in lower quality reconstructions for these challenging materials. + +To address the challenge of reflective surface reconstruction, polarized images are often utilized to enhance shape representation [3, 8, 12, 17]. By decomposing the dif + +fuse and specular components according to the polarimetric bidirectional reflectance distribution function (pBRDF) model [2], the surface normal can be effectively constrained. However, existing polarization-based methods rely on implicit neural representations, which significantly slow down the reconstruction process. + +To achieve high efficiency in reflective surface reconstruction, we propose PolGS, a novel method that integrates polarimetric information into the 3DGS architecture for the first time. Unlike previous approaches, the explicit surface representation and splatting rendering in 3DGS present unique challenges for directly applying polarimetric constraints. To overcome this, we adopt an enhanced 3DGS-based method, Gaussian Surfels [7], as our baseline, which offers better surface representation capabilities. To ensure that each Gaussian kernel retains a view-independent diffuse color, we modify the spherical harmonics (SH) coefficients to zero-order. Next, we introduce a Cubemap Encoder module, inspired by 3DGS-DR [44], to extract the specular component. Finally, we use the polarimetric constraint during the separation of diffuse and specular components [2]. This approach resolves shape ambiguities that arise when relying solely on RGB inputs, enabling more accurate reconstruction of reflective surfaces, especially for texture-less object. + +As shown in the teaser Fig. 1 and Table 1, PolGS achieves reconstruction quality comparable with SDF-based methods but with over 80-times speed improvement (compared to the fastest and best neural-based reconstruction work in our experiment using RGB input [23]), making it highly suitable for virtual reality applications and real-time inverse rendering. + +In summary, we advance the reflective surface reconstruction by proposing: + +- PolGS, the first method to incorporate polarimetric information into 3DGS, accelerating the progress of surface reconstruction. +- A pBRDF module integrated into 3DGS, which effectively constrains the diffuse and specular components of reflective surfaces, enhancing the accuracy of surface reconstruction. +- Our method achieves reconstruction quality comparable with SDF-based approaches while significantly improving reconstruction time within $10\mathrm{min}$ . Compared to existing 3DGS methods, PolGS delivers enhancements in reconstruction quality. + +# 2. Related works + +Our PolGS aims to reconstruct reflective surface with 3DGS by using polarized images, so we summarize recent progresses in 3D reconstruction techniques, focusing on reflective surfaces through SDF-based methods, 3DGS methods, and polarized image-based reconstruction, respectively. + +Table 1. Comparison of different methods in reflective 3D reconstruction: the top four methods are SDF-based, while the bottom four methods are based on 3DGS. + +
InputMethodReflectiveAccuracytime (h)
RGB ImagesNeRO [23]✓high8
AzimuthsMVAS [3]✓high11
Pol. ImagesPANDORA [8]✓medium10
Pol. ImagesNeRSP [12]✓high10
RGB ImagesGaussian Surfels [7]Xlow0.2
RGB Images3DGS-DR [44]✓low0.2
RGB ImagesRe-3DGS [10]✓low0.4
Pol. ImagesPolGS (Ours)✓medium0.1
+ +3D reconstruction based on neural SDF representation Novel view synthesis has achieved great success using Neural Radiance Fields (NeRF [28]). Motivated by the structure of the multi-layer perceptron (MLP) network within NeRFs, numerous 3D reconstruction methods have emerged that leverage implicit neural representations to predict object surfaces. Some approaches [31, 42] proposed the signed distance field (SDF) into the neural radiance field, effectively representing the surface as an implicit function. Other works [22, 32, 37, 39, 40, 43] extend it by proposing efficient framework in detailed surface reconstruction. + +These methods based on SDF represent complex scenes implicitly, but they typically suffer from high computational demands and are not suitable for real-time applications. Although some methods [22, 40] utilize hash grids and instant-NGP [30] structure, it is still a challenge for them to reconstruct the mesh efficiently facing the reflective surface. + +Ref-NeRF [34] uses the Integrated Directional Encoding (IDE) structure to estimate the specular reflection components of the object surface by using predicted roughness, view direction, and surface normals. NeRO [23] improves it by generating the physically-based rendering (PBR) parameters, and NeP [36] can better deal with the glossy surface. TensoSDF [19] combines a novel tensorial representation [4] with the radiance and reflectance field for robust geometry reconstruction. However, these approaches can not avoid high optimization time. + +3D reconstruction based on 3DGS 3DGS [14] aims to address limitations of neural radiance fields by representing complex spatial points using 3D Gaussian ellipsoids. However, 3D ellipsoids cannot conform effectively to actual object surfaces, resulting in inaccuracies in shape representation when producing point clouds. + +To overcome these drawbacks, several extensions and modifications have been proposed. SuGaR [11] approximates 2D Gaussians with 3D Gaussians, NeuSG [6], GSDF [45] and 3DGSR [24] integrate an extra SDF network for representing surface normals to supervise the Gaussian Splatting geometry. 2D Gaussian Splatting [13] + +and Gaussian Surfels [7] have taken a different approach by transforming the 3D ellipsoids into 2D ellipses for modeling. This transformation allows for more refined constraints on depth and normal consistency, addressing the surface approximation issues more effectively. GOF [46] achieves more realistic mesh generation through its innovative opacity rendering strategy. However, these methods do not focus on reflective surface reconstruction. + +Re-3DGS [10] associates extra properties, including normal vectors, BRDF parameters, and incident lighting from various directions to make photo-realistic relighting. 3DGS-DR [44] presents a deferred shading method to effectively render specular reflection with Gaussian splatting. Despite these advancements, these methods still face challenges in many scenarios and cannot provide accurate geometric expression. + +3D reconstruction using polarized images Polarized images are widely used in Shape from Polarization (SfP) [1, 2, 9, 15, 16, 26, 27, 29, 33, 41], reflection removal [20, 25, 38], and some downstream tasks [21, 48] due to the strong physics-preliminary information in the Stokes field. The SfP task aims to predict the surface normal captured by the polarization camera under the single distant light [26, 33] or unknown ambient light [1, 15]. Multi-view 3D reconstruction works using polarized images [47] try to settle down the $\pi$ and $\pi /2$ ambiguities with the Angle of Polarization (AoP). PANDORA [8] first uses polarized images in neural 3D reconstruction work, following the relevant constraints of pBRDF [2]. MVAS [3] leverages multi-view AoP maps to generate tangent spaces for surface points during the optimization process, which can reconstruct mesh without rendering supervision. NeRSP [12] combines the photometric and geometric cues from polarized images and generates better results under sparse views for reflective surfaces. PISR [5] focuses on texture-less specular surface and integrates the multi-resolution hash grid for efficiency. NeISFs [17, 18] consider the inter-reflection and models multi-bounce polarized light paths during rendering. Despite these advancements, computational cost remains a significant limitation for many polarized-based 3D reconstruction methods. + +# 3. Preliminaries + +# 3.1. Gaussian surfels model + +Our PolGS selects Gaussian Surfels [7] as our base framework due to its stronger geometry expression ability. According to Gaussian Surfels [7], we use a set of unstructured Gaussian kernels $\{G_{i} = \{\mathbf{x}_{i},\mathbf{s}_{i},\mathbf{r}_{i},o_{i},C_{i}\} |i\in \mathcal{N}\}$ to represent the structure of 3DGS, where $\mathbf{x}_i\in \mathbb{R}^3$ denotes the center position of each Gaussian kernel, $\mathbf{s}_i = [s_i^x,s_i^y,0]^{\top}\in \mathbb{R}^{3}$ is the scaling factors of $x$ and $y$ axes after flattening the 3D Gaussians [14], $\mathbf{r}_i\in \mathbb{R}^4$ is the rotation quaternion, $o_i\in \mathbb{R}$ + +is the opacity, and $C_i \in \mathbb{R}^k$ represents the spherical harmonic coefficients of each Gaussian. And Gaussian distribution can be defined by the covariance matrix $\Sigma$ of a 3D Gaussian as: + +$$ +G (\mathbf {x}; \mathbf {x} _ {i}, \Sigma_ {i}) = \exp \left(- \frac {1}{2} \left(\mathbf {x} - \mathbf {x} _ {i}\right) ^ {\top} \Sigma_ {i} ^ {- 1} \left(\mathbf {x} - \mathbf {x} _ {i}\right)\right), \tag {1} +$$ + +where $\Sigma_{i}$ can be represented as: + +$$ +\begin{array}{l} \Sigma_ {i} = \mathbf {R} (\mathbf {r} _ {i}) \mathbf {s} _ {i} \mathbf {s} _ {i} ^ {\top} \mathbf {R} (\mathbf {r} _ {i}) ^ {\top} \tag {2} \\ = \mathbf {R} (\mathbf {r} _ {i}) \operatorname {D i a g} \left[ \left(s _ {i} ^ {x}\right) ^ {2}, \left(s _ {i} ^ {y}\right) ^ {2}, 0 \right] \mathbf {R} \left(\mathbf {r} _ {i}\right) ^ {\top}, \\ \end{array} +$$ + +where $\operatorname{Diag}[\cdot]$ indicates a diagonal matrix and $\mathbf{R}(\mathbf{r}_i)$ is a $3 \times 3$ rotation matrix represented by $\mathbf{r}_i$ . + +Gaussian splatting According to 3D GS [14], novel view rendering process can be represented as: + +$$ +C = \sum_ {i = 0} ^ {n} T _ {i} \alpha_ {i} c _ {i}, \tag {3} +$$ + +where $T_{i} = \prod_{j=0}^{i-1}(1 - \alpha_{j})$ is the transmittance, $\alpha_{i} = G'(\mathbf{u};\mathbf{u}_{i},\Sigma_{i}')o_{i}$ is alpha-blending weight, which is the product of opacity and the Gaussian weight based on pixel $\mathbf{u}$ . In order to speed up the rendering process, the 3D Gaussian in Eq. (2) is re-parameterized in 2D ray space [50] as $G'$ : + +$$ +G ^ {\prime} (\mathbf {u}; \mathbf {u} _ {i}, \Sigma_ {i} ^ {\prime}) = \exp \left(- \frac {1}{2} \left(\mathbf {u} - \mathbf {u} _ {i}\right) ^ {\top} \Sigma_ {i} ^ {\prime} ^ {- 1} \left(\mathbf {u} - \mathbf {u} _ {i}\right)\right), \tag {4} +$$ + +where $\Sigma_{i}^{\prime} = (\mathbf{J}_{k}\mathbf{W}_{k}\Sigma_{i}\mathbf{W}_{k}^{\top}\mathbf{J}_{k}^{\top})[:2,:2]$ . The $\mathbf{W}_k$ is a viewing transformation matrix for input image $k$ and $\mathbf{J}_k$ is the affine approximation of the projective transformation. $\Sigma_{i}^{\prime}$ represents the covariance matrix in the 2D ray space. + +The depth $\tilde{D}$ and normal $\tilde{N}$ for each pixel can also be calculated via Gaussian splatting and alpha-blending: + +$$ +\tilde {D} = \frac {1}{1 - T _ {n + 1}} \sum_ {i = 0} ^ {n} T _ {i} \alpha_ {i} d _ {i} (\mathbf {u}), \tag {5} +$$ + +$$ +\tilde {N} = \frac {1}{1 - T _ {n + 1}} \sum_ {i = 0} ^ {n} T _ {i} \alpha_ {i} \mathbf {R} _ {i} [:, 2 ]. \tag {6} +$$ + +Specifically, according to Gaussian Surfels [7], the depth of pixel $\mathbf{u}$ for each Gaussian kernel $i$ is computed by calculating the intersection of the ray cast through pixel $\mathbf{u}$ with the Gaussian ellipse during splatting. So $d_{i}(\mathbf{u})$ can be represented by Taylor expansion as: + +$$ +d _ {i} (\mathbf {u}) = d _ {i} \left(\mathbf {u} _ {i}\right) + \left(\mathbf {W} _ {k} \mathbf {R} _ {i}\right) [ 2,: ] \mathbf {J} _ {p r} ^ {- 1} \left(\mathbf {u} - \mathbf {u} _ {i}\right), \tag {7} +$$ + +where $\mathbf{J}_{pr}^{-1}$ is the Jacobian inverse mapping one pixel from image space to tangent plane of the Gaussian surfel as in [49], and $(\mathbf{W}_k\mathbf{R}_i)$ transforms the rotation matrix of a Gaussian surfel to the camera space. + +# 3.2. Polarimetric image formation model + +Polarization cameras can capture polarized images in a single shot, which can be represented as 4 different polarized angles of images $I = [I_0, I_{45}, I_{90}, I_{135}]$ . The Stokes vector $S = \{s_0, s_1, s_2, s_3\}$ can be calculated by: + +$$ +S = \left[ \begin{array}{c} \frac {1}{2} \left(I _ {0} + I _ {4 5} + I _ {9 0} + I _ {1 3 5}\right) \\ I _ {0} - I _ {9 0} \\ I _ {4 5} - I _ {1 3 5} \\ 0 \end{array} \right], \tag {8} +$$ + +where we assume the light source is no circularly polarized here, thus the $s_3$ is 0. + +According to PANDORA [8] and NeRSP [12], we assume the incident environmental illumination is unpolarized, the Stokes vector for the incident light direction $\omega$ can be expressed as: + +$$ +\mathbf {s} _ {i} (\boldsymbol {\omega}) = L (\boldsymbol {\omega}) [ 1, 0, 0, 0 ] ^ {\top}, \tag {9} +$$ + +where $L(\omega)$ represents the light intensity. The polarization camera captures outgoing light that becomes partially polarized due to reflection, which is modeled using a $4\times 4$ Muller matrix $\mathbf{H}$ . The outgoing Stokes vector $s$ then is formulated as the integral of the incident Stokes vector multiplied by this Mueller matrix: + +$$ +\mathbf {s} (\mathbf {v}) = \int_ {\Omega} \mathbf {H} \mathbf {s} _ {i} (\boldsymbol {\omega}) d \boldsymbol {\omega}, \tag {10} +$$ + +where $\mathbf{v}$ indicates the view direction and $\Omega$ is the integral domain. Following the polarized BRDF (pBRDF) model [2], the output Stokes vector can be divided into diffuse and specular components, represented by $\mathbf{H}_d$ and $\mathbf{H}_s$ respectively. $\mathbf{s}$ can be represented as: + +$$ +\mathbf {s} (\mathbf {v}) = \int_ {\Omega} \mathbf {H} _ {d} \mathbf {s} _ {i} (\boldsymbol {\omega}) d \boldsymbol {\omega} + \int_ {\Omega} \mathbf {H} _ {s} \mathbf {s} _ {i} (\boldsymbol {\omega}) d \boldsymbol {\omega}. \tag {11} +$$ + +Based on the derivations from PANDORA [8] and NeRSP [12], the output Stokes vector can be further specified as: + +$$ +\mathbf {s} (\mathbf {v}) = L _ {d} \left[ \begin{array}{c} T _ {o} ^ {+} \\ T _ {o} ^ {-} \cos (2 \phi_ {n}) \\ - T _ {o} ^ {-} \sin (2 \phi_ {n}) \\ 0 \end{array} \right] + L _ {s} \left[ \begin{array}{c} R ^ {+} \\ R ^ {-} \cos (2 \phi_ {h}) \\ - R ^ {-} \sin (2 \phi_ {h}) \\ 0 \end{array} \right], \tag {12} +$$ + +where $L_{d} = \int_{\Omega}\rho L(\omega)\pmb{\omega}^{\top}\mathbf{n}T_{i}^{+}T_{i}^{-}d\pmb{\omega}$ denotes the diffuse radiance associated with the surface normal $\mathbf{n}$ , Fresnel transmission coefficients [2] $T_{i,o}^{+}$ and $T_{i,o}^{-}$ . The diffuse albedo is represented by $\rho$ , and $\phi_{n}$ is the azimuth angle of the incident light. + +Similarly, $L_{s} = \int_{\Omega}L(\omega)\frac{DG}{4\mathbf{n}^{\top}\mathbf{v}} d\omega$ denotes the specular radiance, which involves Fresnel reflection coefficients [2] $R^{+}$ and $R^{-}$ , and the incident azimuth angle $\phi_h$ concerning + +![](images/bedefdb5d9c4429c4efd44f21d7faf514b05d02f2c4e1ac80726a032ecfea98b.jpg) + +![](images/17e525696b17a6bd5e66b8bce1ec0b90e333c5a8463cbf54f05a7cc4ae8092ea.jpg) +Figure 2. Comparison between SDF-based and 3DGS-based method on geometry representation. (Top) The surface normal of a point has a strong relationship with its opacity in NeuS [37]. (Bottom) The surface normal of a point is dependent on its opacity in Gaussian Surfels [7]. + +the half vector $\mathbf{h} = \frac{\boldsymbol{\omega} + \mathbf{v}}{\|\boldsymbol{\omega} + \mathbf{v}\|_2^2}$ . For the sake of simplification in our model, we assume that $\phi_h$ is equivalent to $\phi_n$ . The Microfacet model incorporates the normal distribution and shadowing terms represented by $D$ and $G$ [35]. + +# 4. Proposed method + +Our PolGS framework integrates multi-view polarized images, their corresponding masks, and camera pose information to produce a rich output that includes diffuse and specular components represented as Stokes vectors across various views, a reconstructed geometric mesh, and estimated environment light. In this section, we will analyze the surface normal representations employed in SDF-based approaches and 3DGS methods. Then we introduce a theoretical foundation for our polarization-guided reconstruction pipeline. + +# 4.1. Analysis of surface normal representation + +In implicit neural networks, they use signed distance to determine if points are on the surface and the surface normals are obtained by calculating gradients of the SDF. However, 3DGS methods often treat the surface normal as inherent properties typically. In this section, we analyze the differences between the surface normal representations in SDF-based methods and 3DGS, explaining the reason we use polarimetric cues in the Gaussian Splating method. + +![](images/3272bb09126093c738805a60c43383894fb09017c1f9f6a6b923bc532adfed43.jpg) +Figure 3. Pipeline of PolGS. We re-rendered Stokes vectors $\hat{s}$ by using the diffuse color $C$ from 3DGS and specular color $L_{r}$ from Cubemap encoder module, which is supervised by the ground truth Stokes information. + +SDF-based representation The implicit neural network approach, exemplified by NeuS [37], enhances the constraints on the reconstructed surface by incorporating a Signed Distance Function (SDF). As illustrated at the top of Fig. 2, the SDF value $f(\mathbf{x})$ , generated by the SDF Network, can be used to compute the normal vector $\mathbf{n}(\mathbf{x})$ at point $\mathbf{x}$ . According to the definition, the opacity $\rho(\mathbf{x})$ of a point $\mathbf{x}$ is given by: + +$$ +\rho (\mathbf {x}) = \max \left(\frac {- \frac {d \Phi_ {s}}{d x} (f (\mathbf {x}))}{\Phi_ {s} (f (\mathbf {x}))}, 0\right), \tag {13} +$$ + +where $\Phi_s$ is a sigmoid function. + +During optimization, the surface normal and the opacity at a given point influence each other. Consequently, after optimization, points farther from the surface tend to have lower opacity values, while the final normal vector is predominantly determined by points located on the surface. This mutual interaction results in a more precise and accurate representation of the surface. + +3DGS-based representation In the case of Gaussian Surfels [7], surface normal is derived from the vector perpendicular to the plane of a 2D ellipsoid. As shown at the bottom of Fig. 2, for a single Gaussian kernel, there is no inherent relationship between opacity and the surface normal. + +The pixel-level constraint in 3DGS creates a probabilistic representation where no single Gaussian kernel is definitively assigned to a surface. Consequently, multiple Gaussian kernel configurations can potentially represent equivalent surface geometries, introducing inherent reconstruction ambiguity. The optimization mechanism effectively blends contributions from multiple Gaussian points, which offers reconstruction adaptability but compromises the precision of individual point geometric characterizations. + +It is obvious that using the normal prediction model as a prior constraint in Gaussian Splatting benefits object reconstruction, as demonstrated by Gaussian Surfels [7]. However, the normal prediction model is not always reliable especially in reflective cases, highlighting the need for a more robust method to provide prior information. + +Polarimetric information for reflective surfaces Reflective surface reconstruction is challenging due to the view-dependent appearance. Unlike traditional RGB image inputs, polarimetric information can effectively constrain the surface normal during the rendering of Stokes Vectors with the pBDRF model [2]. Specifically, as demonstrated in Eq. (12), the diffuse and specular components of $s_1$ and $s_2$ exhibit a strong correlation with the object's surface normals. Leveraging this property, we incorporate polarimetric information as a prior in shape reconstruction and use the 3DGS-based method to accelerate this process. + +# 4.2. PolGS + +Network structure In this section, we introduce our proposed PolGS, which is a novel 3D reconstruction method that integrates the Gaussian Splatting method with polarimetric information. The network structure of PolGS is shown in Fig. 3. The framework comprises two primary components: the Gaussian Surfels module and the Cubemap Encoder module. Initially, the Gaussian Surfels module is employed to estimate the diffuse component of the object, seems like Gaussian Surfels [7]. Subsequently, we utilize the CubeMap Encoder to assess the specular component, akin to the approach taken in 3DGS-DR [44]. While the CubeMap Encoder does not provide the roughness component, it effectively handles reflective or rough surfaces and maintains high computational efficiency due to its CUDA-based implementation. To enhance the rendering process, we incorporate a pBRDF model into the rendering formulation. This addition introduces a polarimetric constraint that further refines the Gaussian Splatting method, enabling more accurate and realistic 3D reconstructions. The final rendering formulation model following Eq. (12) can be represented as: + +$$ +\hat {S} = C \left[ \begin{array}{c} T _ {o} ^ {+} \\ T _ {o} ^ {-} \cos (2 \phi_ {n}) \\ - T _ {o} ^ {-} \sin (2 \phi_ {n}) \\ 0 \end{array} \right] + L _ {r} \left[ \begin{array}{c} R ^ {+} \\ R ^ {-} \cos (2 \phi_ {h}) \\ - R ^ {-} \sin (2 \phi_ {h}) \\ 0 \end{array} \right], \tag {14} +$$ + +where $C$ is the diffuse color after Gaussian Surfels rendering according to Eq. (3) and $L_{r}$ is the specular color after CubeMap rendering $E(\cdot)$ , which can be represented as $L_{r} = E(2(\mathbf{v}\cdot \mathbf{n})\mathbf{n} - \mathbf{v})$ . + +Adjustment of spherical harmonic coefficients Due to Eq. (14), the diffuse color rendered by Gaussian Surfels must remain consistent across different viewing directions. To satisfy this constraint, we adjust the spherical harmonic (SH) coefficients of the Gaussian Surfels to zero-order, ensuring the splattering results are view-independent. + +# 4.3. Training + +The overall training loss in PolGS formulated as a comprehensive weighted sum of multiple loss components: + +$$ +\mathcal {L} = \mathcal {L} _ {r g b} + \lambda_ {1} \mathcal {L} _ {p o l} + \lambda_ {2} \mathcal {L} _ {m} + \lambda_ {3} \mathcal {L} _ {o} + \lambda_ {4} \mathcal {L} _ {d}, \tag {15} +$$ + +where we set $\lambda_1 = 1$ , $\lambda_2 = 0.1$ , $\lambda_3 = 0.01$ , $\lambda_4 = 0.01 + 0.1 \cdot (iteration / 15000)$ to balance the loss function. + +Rendering Stokes loss $\mathcal{L}_{rgb}$ and $\mathcal{L}_{pol}$ The rendering Stokes loss is combined with the $s_0$ (unpolarized image) rendering loss as 3DGS [14] and the $s_1$ , $s_2$ rendering loss as PANDORA [8] [2]. These two loss functions can be represented as: + +$$ +\mathcal {L} _ {r g b} = 0. 8 \cdot L _ {1} \left(s _ {0}, \hat {s} _ {0}\right) + 0. 2 \cdot L _ {D S S I M} \left(s _ {0}, \hat {s} _ {0}\right), \tag {16} +$$ + +$$ +\mathcal {L} _ {p o l} = L _ {1} \left(s _ {1}, \hat {s} _ {1}\right) + L _ {1} \left(s _ {2}, \hat {s} _ {2}\right). \tag {17} +$$ + +Mask loss $\mathcal{L}_m$ The mask loss is used to make the rendering results of the object more accurate, which can be represented as: + +$$ +\mathcal {L} _ {m} = \Sigma \mathrm {B C E} (\mathbf {M}, \hat {\mathbf {M}}). \tag {18} +$$ + +Opacity loss $\mathcal{L}_o$ The opacity loss follows Gaussian Surfels [7] to encourage the opacity of the Gaussian points to be close to 1 or 0. It can be represented as: + +$$ +\mathcal {L} _ {o} = \Sigma \exp \left(- 2 0 \left(o _ {i} - 0. 5\right) ^ {2}\right). \tag {19} +$$ + +Depth-normal consistency loss $\mathcal{L}_d$ The depth-normal consistency loss follows Gaussian Surfels [7] to make the rendered depth and normal of the object to be more consistent. It can be represented as: + +$$ +\mathcal {L} _ {d} = 1 - \hat {\mathbf {N}} \cdot N (V (\hat {\mathbf {D}})), \tag {20} +$$ + +where $V(\cdot)$ transforms each pixel and its depth to a 3D point and $N(\cdot)$ calculates the normal from neighboring points using the cross product. + +# 5. Experiments + +To evaluate the performance of our method, we conduct these experiments: 1) Shape reconstruction on synthetic dataset, 2) Shape reconstruction on real-world dataset, 3) Radiance decomposition and 4) Ablation study of polarimetric constraint adding. + +Dataset We use three datasets to evaluate our method: the synthetic dataset SMVP3D [12], the real-world dataset RMVP3D [12], PANDORA [8] and PISR [5], where PANDORA [8] can only be used for qualitative evaluation due to the lack of ground truth. + +Baselines We compare our method with state-of-the-art techniques, including SDF-based methods NeRO [23], MVAS [3], PANDORA [8], NeRSP [12], and 3DGS methods Gaussian Surfels [7], 3DGS-DR [44], and Re3DGS [10]. All of these methods, except Gaussian Surfels [7], can handle reflective surfaces. MVAS [3], PANDORA [8] and NeRSP [12] utilize polarimetric information to reconstruct shapes. Specifically, we do not add the normal prior in Gaussian Surfels [7] among the whole experiments. + +Evaluation metrics We use the Chamfer Distance (CD) to evaluate the shape recovery performance and the mean angular error (MAE) to evaluate the quality of surface normal estimations. 3DGS-based methods provide point cloud results and we use the Poisson surface reconstruction to generate the mesh for the evaluation. + +Implementation details We conduct the experiments on an NVIDIA RTX 4090 GPU with 24GB memory. The training of our model is implemented in PyTorch 1.12.1 using the Adam optimizer. The specific learning rates of different components in Gaussian kernels are set the same as Gaussian Surfels [7]. We use the warm-up strategy to train the model, where adding the polarimetric information and deferred rendering after 1000 iterations. + +# 5.1. Reconstruction results on synthetic dataset + +In Fig. 4 and Table 2, we compare the shape recovery performance of various methods on the SMVP3D [12] dataset, which contains five objects with spatially varying and reflective properties. However, it is worth noting that SDF-based methods, such as NeRO [23], MVAS [3], PAN-DORA [8], and NeRSP [12], outperform 3DGS methods in terms of surface representation. This advantage is largely due to their superior ability to model complex surface details. Among the 3DGS methods, Gaussian Surfels [7] struggles with reflective surfaces, while 3DGS-DR [44] and Re-3DGS [10] still has difficulty in representation of surface normal accurately. In contrast, PolGS effectively leverages polarimetric information, significantly improving geometric surface performance. Due to the inadequate point cloud generation by other 3DGS methods, they fail to produce reasonable mesh results using Poisson surface reconstruction. Our method, however, achieves the lowest mean Chamfer Distance across the synthetic SMVP3D [12] dataset, reinforcing the trends observed in surface normal estimations and confirming that our approach delivers the best performance among the 3DGS techniques. + +![](images/04af59a97931374a3969c1bc5aa0656f1de35b9028f2bfaebd9b93f5732d9f85.jpg) +Figure 4. Qualitative comparisons on surface normal estimation of SQUIRREL in SMVP3D [12], where our 3DGS-based method can outperform existing methods based on the same representation and achieves comparable results with SDF-based methods such as NeRSP [12] and PANDORA [8]. + +![](images/4211fd52084225f8a923dc3e38589cd04ce2e2ddc4ba8c1b85902ceb41808076.jpg) +Input + +![](images/ec85e78d5c605cc7313438724ecbf117ec7eabecc7e6de8a90bcc16c77e99f26.jpg) +NeRO [23] + +![](images/79f76f46f2e50d799eaea6872f8c0b39de2e9c3d38690a38515d43b73ee0a8dd.jpg) +MVAS [3] + +![](images/9b56c3a989b790e479543e545d8d9e56de95eb55b0d02b776bdf028310083e38.jpg) +PANDORA [8] + +![](images/c066511f68fd16dc744fc94c525355dbacc9f7c1138d63afd54051947d404b8b.jpg) +NeRSP [12] + +![](images/a8d59bc2af1a334b644c22e01ddddba619c44801b0b08d67e8c1fd4aa57ede80.jpg) + +![](images/12332342b900aaab33ba60304780b7f5fb1c56aca8fa074cc665f5222c5a27a6.jpg) +Gaussian Surfels [7] 3DGS-DR [44] + +![](images/98555040ed02e4bdea7dff7d6d90e9cf45b063baa512d2260e7c1cb216b2dbde.jpg) +Re-3DGS [10] + +![](images/bc93410cddb2c9ba27f0bb83a5bea288b0b0bc9582ef487e22c9431fc752323c.jpg) +PolGS (Ours) + +![](images/1e566a005c8a27ace94e6d46e6c69f4ee9437454a589bf02172ae3ee791893be.jpg) +Figure 5. Qualitative comparison shape on PANDORA [8] and RMVP3D [12], where PolGS (Ours) produces similar quality of reconstruction mesh compared to SDF-based methods. + +![](images/b136ca2fcd07514ce7b2ec0e298f6d0c3a9476213f01df137b9688f5e3699350.jpg) + +![](images/6d932823ce926e3787084d286807aaaab95fcf010a7a0e2e3e6a8194f1785fe8.jpg) + +![](images/adb75456707e4b9b5c6d206a4c7b259d2fe521dd143f158c5193d887ca8da58b.jpg) + +![](images/50ac09ee493d179d8b01132a7380ce9eafd601ac47f920eeccb50f99e4e634db.jpg) + +![](images/bfbf52f02ddec81de7e142303fc15a04645da54f5f839f1b2742c37870345886.jpg) + +![](images/5f1675a64be28317e0f83d3cd72f812a9d50e397a491b9fae18d141b0b0e7259.jpg) + +![](images/edd46827a7371d0d203841706d2941b2b93e48f7db8c1e274ec74fbcb2f4d649.jpg) + +![](images/c60cfc69fef3bba704cb59334701a64e0b4a0efc18fa5d2ae1bcbdf85a5edb82.jpg) + +# 5.2. Reconstruction results on real-world dataset + +We further evaluate the reconstruction performance on the RMVP3D [12] and PANDORA [8] datasets, with qualitative results illustrated in Fig. 5 and quantitative results detailed in Table 2. In real-world scenarios, our method produces reconstructions that align more closely with SDF-based approaches, while significantly outperforming other 3DGS-based methods in terms of reconstruction quality. For example, in the VASE case, our approach accurately estimates the shape of a ceramic surface in just 7 minutes, achieving results closer to those generated by SDF-based methods. Additionally, the FROG sample highlights our method's ability to reconstruct objects with rough glossy surfaces, showing the robustness and generalization capability of our method. These results collectively demonstrate the effectiveness of our approach in handling diverse realworld objects with varying surface properties. + +![](images/1acd5db5d283509bcd91590c6a3d605910ed1a3194db7fe79d4c5e57bcc1e3f5.jpg) +Figure 6. Separation of diffuse and specular components with PANDORA [8], 3DGS-DR [44] and PolGS (Ours). + +# 5.3. Comparison of radiance decomposition + +Figure 6 presents a comparison of diffuse and specular component decomposition generated by PANDORA [8], 3DGS-DR [44], and PolGS (Ours). Here, PANDORA [8] utilizes the IDE [34] structure to produce environment map results, whereas PolGS (Ours) adopts 3DGS-DR [44]'s methods by + +Table 2. Comparisons on SMVP3D [12] and RMVP3D [12] evaluated by mean angular error (MAE) (↓) with degree and Chamfer distance (CD) (↓) in millimeter (mm), respectively. Best and second results in SDF-based and 3DGS-based methods (except PolGS w/o $\mathcal{L}_{pol}$ ) are highlighted as 1st and 2nd. The time consumed is shown on the far right side of the table. + +
MethodSMVP3D [12]RMVP3D [12]Meantime
HEDGEHOGSQUIRRELSNAILDAVIDDRAGONSHISAFROGDOGMAECD
MAECDMAECDMAECDMAECDMAECDCDMAECDMAECDMAECDMAECD
PANDORA [8]9.419.5010.855.888.0810.9714.754.8816.334.7812.9311.2915.867.8820.1110.1913.548.1710 h
NeRSP [12]8.946.578.233.025.563.7215.384.1815.303.0110.797.3915.626.6816.578.5712.055.3910 h
MVAS [3]4.304.226.103.733.307.878.473.218.111.898.569.2817.637.0016.658.769.015.7411 h
NeRO [23]3.43.693.551.862.673.717.642.888.121.698.414.8815.295.3917.728.748.274.108 h
3DGS-DR [44]12.2812.6617.1811.2011.4220.720.567.9126.209.5619.5315.8717.0827.6724.8511.0019.7613.320.2 h
Re-3DGS [10]14.4019.8415.4118.979.0819.0415.4713.4717.6510.9616.6914.6617.8513.3521.5312.2415.8914.120.4 h
Gaussian Surfels [7]16.508.8221.659.5319.0514.0421.567.3921.416.9812.799.0916.197.0119.309.5618.5610.300.2 h
PolGS (Ours)10.837.6211.426.289.6410.8513.995.3024.237.6110.887.7615.037.4818.807.7114.357.570.1 h
PolGS w/o Lpol11.397.9711.836.399.8210.7515.445.9025.748.2210.957.9215.167.5618.867.7414.897.800.1 h
+ +![](images/cf673bacb86b8e2ee61a718b37788d4849a9639e04cab5f5224549085e2cebcb.jpg) +Figure 7. Ablation study on surface normal estimation with and without polarimetric information $\mathcal{L}_{pol}$ . The MAE values are displayed on the top of each image. + +employing a Cubemap encoder for the same purpose. Compared with 3DGS-DR [44], PolGS (Ours) leverages additional polarimetric information to effectively constrain and disambiguate diffuse and specular components. Notably, our results closely align with PANDORA [8]'s, demonstrating improved radiance decomposition ability. + +# 5.4. Ablation study + +In this section, we conduct an ablation study to evaluate the contribution of polarimetric information to surface reconstruction. As shown in Table 2 and Fig. 7, integrating $\mathcal{L}_{pol}$ consistently improves reconstruction accuracy across both synthetic and real-world datasets. The incorporation of $\mathcal{L}_{pol}$ particularly enhances geometric fidelity in challenging regions such as the HEDGEHOG's bottom and the SNAIL's back, where it effectively suppresses concave artifacts. + +However, for texture-rich surfaces captured under dense views ( $>30$ views), the existing photometric cues (RGB) provide sufficient constraints, leaving limited room for additional improvement from polarimetric information. This contrasts with texture-less surfaces like the DAVID statue, where $\mathcal{L}_{pol}$ contributes to reconstruction quality by providing additional geometric constraints. + +![](images/fb1e2c8d4f5dbb7186b613be20320373fae8dffa4a78fb9b29693b8d53d1bb58.jpg) +Figure 8. Stokes vectors can help surface normal reconstruction on texture-less surfaces. + +Boosting on texture-less surfaces recovery with $\mathcal{L}_{pol}$ To further validate the benefits of $\mathcal{L}_{pol}$ on texture-less surfaces, we conduct additional experiments using a real-world dataset from PISR [5], as shown in Fig. 8. While the RGB appearance lacks discernible texture, the polarization channels $s_1$ and $s_2$ exhibit meaningful variations that provide additional geometric cues for resolving shape ambiguities. The results show that both concave and convex surface distortions are more accurately reconstructed when $\mathcal{L}_{pol}$ is employed. Moreover, as the number of input views decreases, the advantages of incorporating polarization become even more evident. This demonstrates the unique value of polarimetric information in challenging scenarios where conventional RGB inputs offer limited constraints. + +# 6. Conclusion + +We propose PolGS, a novel Polarimetric Gaussian Splatting method for fast and accurate 3D reconstruction of reflective surfaces. PolGS leverages polarimetric information for separating the diffuse and specular components based on Stokes field, which can help to constrain the surface normal in the gaussian splatting representation and finally improve the reflective surface reconstruction results. Extensive experiments demonstrate that PolGS outperforms state-of-the-art 3DGS methods in terms of accuracy and efficiency. + +# Acknowledgments + +This work was supported by Hebei Natural Science Foundation Project No. 242Q0101Z, Beijing-Tianjin-Hebei Basic Research Funding Program No. F2024502017, National Natural Science Foundation of China (Grant No. 62472044, U24B20155, 62225601, U23B2052, 62136001), Beijing Natural Science Foundation Project No. L242025, BUPT Excellent Ph.D. Students Foundation. 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