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Our approach excels in reference-based edits, faithfully reproducing the copied reference parts with a single source and reference image. Leveraging 3D-aware triplanes, our edits are versatile and 3D consistent, allowing for rendering from various viewpoints. We show results on human faces, heads, bodies, and extending beyond to animal faces and class-agnostic samples. + +![](images/6138e01262f19e1701fe9c87e3d7fc714934a6e1b18c67ce85b15f8a0a3f5de6.jpg) + +![](images/66b6f37a12a62ecd40c0eddd58793612a54bfa35054e069cd95c4564089a1011.jpg) + +# Abstract + +Generative Adversarial Networks (GANs) have emerged as powerful tools for high-quality image generation and real image editing by manipulating their latent spaces. Recent advancements in GANs include 3D-aware models such as EG3D, which feature efficient triplane-based architectures capable of reconstructing 3D geometry from single images. However, limited attention has been given to providing an integrated framework for 3D-aware, high-quality, reference-based image editing. This study addresses this gap by exploring and demonstrating the effectiveness of the triplane space for advanced reference-based edits. Our novel approach integrates encoding, automatic localization, spatial disentanglement of triplane features, and fusion learning to achieve the desired edits. We demonstrate how our approach excels across diverse domains, including human faces, 360-degree heads, animal faces, partially stylized edits like cartoon faces, full-body clothing edits, and edits on class-agnostic samples. Our method shows state + +of-the-art performance over relevant latent direction, text, and image-guided 2D and 3D-aware diffusion and GAN methods, both qualitatively and quantitatively. $^{1}$ + +# 1. Introduction + +In recent years, the high-fidelity image synthesis performance has been profoundly transformed by the emergence of Generative Adversarial Networks (GANs) [24, 34, 35]. Through adversarial training, they learn to map random distributions to actual data observations, enabling the generation of photo-realistic images from latent codes. The evolution of GANs from 2D into 3D-aware [9, 10, 25, 51] has further boosted this capability, integrating hybrid 3D representations and Neural Radiance Fields (NeRF) [49] into style-based generators, yielding unparalleled success in crafting highly realistic 3D portraits. + +The application of GANs extends beyond generation, venturing into real image editing through GAN inversion [3, + +![](images/91d974f783ffedebafa564bb4c27cdd4981dc6c7d044c8808dafef6c17ee7587.jpg) +Figure 2. Current methods struggle with 3D consistency [63, 70, 85], faithfulness to the reference [8, 33, 69], and visual artifacts [69, 70]. Our method provides 3D-consistent, reference-based edits from single images, independent of camera poses. N/A indicates the model is incapable of such edits. + +56, 62, 74, 76] and manipulation of the latent space [59]. A critical challenge in reference-based image editing via this latent space is striking the optimal balance between retaining essential elements from the input image and incorporating desired attributes from the reference image. This balance is crucial to avoid overshadowing the input image's essence in the editing process, thereby maintaining its identity while still transferring the reference's attributes. This presents itself as a complex problem of disentanglement and fusion, requiring the identification and integration of relevant feature components from both the reference and input images within the latent space to produce the edited output. + +Despite the advancements in image editing, there is a noticeable gap in the development of reference-based, 3D-aware image editing techniques. Existing methods in 3D-aware image editing lack reference-based capabilities [23, 39, 76], while current GAN and diffusion reference-based editing approaches do not support 3D-awareness [63, 70, 85] and/or facilitate local editing [7, 8, 13, 53, 59] (Figs. 2 and 6). Addressing this gap, our work focuses on pioneering reference-based, 3D-aware image editing, where we learn spatial disentanglement and fusion within triplane latent spaces [10, 20]. Our primary motivation stems from discovering that triplanes can be manipulated for editing purposes akin to the 2D image domain but offer distinct advantages. Triplanes not only facilitate 3D editing but also alleviate alignment issues inherent in 2D image space. For example, transferring eyeglasses from one person to another in 2D necessitates precise alignment in the image space. Conversely, in the triplane space, stitching is facilitated as images with varying camera parameters can be projected onto the same canonical triplane space. However, ensuring seamless boundaries requires careful attention. To accomplish reference-based image editing, our framework localizes parts within triplanes using masked residual gradients and fuses them using the encoders we train. + +Our contributions span the following: + +1. We are at the forefront of conceptualizing reference-based 3D-aware image editing as an integrated framework by leveraging the power of triplanes. Our approach includes encoding triplane features, spatial disentangle- + +ment with automatic localization of features, and fusion learning for desired image editing. + +2. Our work establishes new benchmarks for quantitative and qualitative assessment in reference-based image editing and surpasses the 12 most recent and relevant baseline editing methods. This advancement is quantified by significant improvements in FID for quality and masked pixel-wise metrics for source preservation. +3. We extend our framework based on [10] towards 360-degree human heads [4], animal faces [10], cross-domain edits with cartoon portraits [60], full-body [20] clothing edits, and edits on class-agnostic samples [29, 37, 68], showcasing its versatility and robustness across different triplane domains as shown in Fig. 1. This not only proves the effectiveness of our method but also broadens its potential in creative editing contexts. + +# 2. Related Works + +StyleGAN inversion-based editing. It has been shown that well-trained GAN models organize their latent space in a semantically meaningful way that enables edits via latent vector arithmetic. Especially for StyleGAN models [35], many methods are proposed to find interpretable directions in unsupervised ways such as GANSpace [27], StyleFlow [2], StyleSpace [64], StyleCLIP [53] and supervised ways such as InterFaceGAN [59], and recently E3DGE [36], Barbershop [85], HairCLIPv2 [63], and SFE [7]. These methods are combined with real image inversion methods so that an image is projected onto StyleGAN's latent space $(\mathcal{W},\mathcal{W}^{+},\mathcal{F},$ etc.) and is edited [54, 56]. Recently, EG3D [10] augmented StyleGAN architecture with triplanes that provide efficient 3D-aware representations. For this new domain, new inversion methods are proposed [23, 67, 75, 76]; however, previous editing methods [53, 59] are re-used from 2D StyleGAN literature, which all lack reference-based editing. + +Reference-based image-to-image translation. We refer to the models that are end-to-end trained for editing applications as image-to-image translation methods. These methods are trained to change selected attributes of images while preserving the content [12, 21, 30, 40, 41, 47, 58, 66, 77], rather than using the latent codes of StyleGAN. Specifically, they include an encoder for the reference image and another encoder or shared one for the source image [12, 31, 40, 48, 71, 83, 84]. In these models, the reference style can be sampled from a normal distribution, or it can be encoded from a reference image [14, 15, 40]. One major limitation of these works is that they require labeled datasets for each attribute [45]; hence, models like VecGAN [15] and HisD [40] can only achieve a handful of edits (hair color, smile, eyeglasses, bangs, etc.). They also cannot provide editing using images taken from vastly different camera poses and lack faithfulness to the reference. + +Text and image-conditioned diffusion models for image editing. There is an abundance of diffusion-based image editing methods [8, 13, 19, 61, 69, 70], leveraging the prior of Stable Diffusion (SD) denoiser [57] and achieving diverse edits. Recently, methods like ControlNet [78], IP [73], and T2I [50] have made editing more controllable. Still, all these SD-based methods lack 3D-aware, faithful-to-reference image editing, especially in the face and body domain. LEDs++ [8] and InfEdit [69] utilize text prompts and are incapable of image reference-based editing. Paint by Example [70] fine-tunes the denoiser with masked images to carry information from reference images. Nevertheless, [70] is not capable of choosing which region to copy, harming the controllability - more noticeably when camera poses are different. NoiseCLR [13] attempts to find editing directions unsupervised but fails for fundamental face-edit attributes like hair color and style changes. There are 3D-aware denoisers [43, 44, 72] and edit methods [22, 52, 81], but they also become impractical in our context, as they are either fine-tuned with general object datasets [16, 17] failing to perform well in the face domain or lack faithful reference-based editing altogether. There are also methods fusing GAN & diffusion for adding stylization and diversity [5, 26, 39, 60], but controllable reference-based edits are not achieved in those, either. + +# 3. Method + +Our main motivation lies in that triplanes can be stitched and blended for editing like in the 2D image domain. However, achieving satisfying results requires carefully designed steps, which will be detailed in this section. + +# 3.1. Localizing parts in the triplane space + +![](images/fee9d2b6f7069898af7e7d064ea164cc94cd3ecba398cb6ed2c2ce55cadc1053.jpg) +Figure 3. Triplane part localization stage, where $\mathbf{E}$ , $\mathbf{G}$ , and $\mathcal{R}$ are encoder [6, 76], generator [10], and neural volumetric renderer, respectively. For the 2D segmentation model $S_{2\mathrm{D}}$ , we use state-of-the-art off-the-shelf segmentation models [1]. Images other than the input image are zoomed in for visualization purposes. + +The most direct way to perform a region transfer from reference to source image would be to mask and copy & paste the region of interest. However, this process becomes intricate in hybrid 3D representations like triplanes, due to the absence of a conventional method for identifying the regions to be masked. + +# Algorithm 1 Triplane localization and masking + +Require: Generator $\mathbf{G}$ , encoder $\mathbf{E}$ , renderer $\mathcal{R}$ , image $I$ , extrinsic matrices $\pi_{1,2,\dots,N}$ , segmentation net $S_{2D}$ , post-processing params $(\epsilon, \gamma)$ + +Ensure: Triplane mask M + +1: $\mathbf{T},\nabla_{\mathbf{T}},\leftarrow \mathbf{G}(\mathbf{E}(I)),0\quad \triangleright$ Initialize triplane and gradients +2: for each $\pi_i$ in $\pi_{1,2,\dots,N}$ do $\triangleright$ Triplane localization +3: $I_{\pi_i} \gets \mathcal{R}(\mathbf{T}, \pi_i)$ +4: $\nabla_{\mathcal{R}(\mathbf{T},\pi_i)}\gets S_{\mathrm{2D}}(I_{\pi_i},\mathbf{attr})$ +5: $\nabla_{\mathbf{T}} \gets \nabla_{\mathbf{T}} + \text{autograd}(\mathcal{R}, \nabla_{\mathcal{R}(\mathbf{T}, \pi_i)})$ +6: end for + +7: for each $c$ in $\nabla_{\mathbf{T}}\mathbf{d}\mathbf{o}$ Post-processing +8: $\nabla_{\mathbf{T}_c} \gets \{x \in \nabla_{\mathbf{T}_c} : |\nabla_{\mathbf{T}_c}(x) - \mu_c| \leq \epsilon\}$ +9: $\nabla_{\mathbf{T}_c} \gets (\nabla_{\mathbf{T}_c} - \min \nabla_{\mathbf{T}_c}) / (\max \nabla_{\mathbf{T}_c} - \min \nabla_{\mathbf{T}_c})$ +10: $\nabla_{\mathbf{T}_c} \gets \{x \in \nabla_{\mathbf{T}_c} : 1 \text{ if } \nabla_{\mathbf{T}_c}(x) \geq \gamma \text{ else } 0\}$ +11: end for + +12: return $\mathbf{M} \gets \nabla_{\mathbf{T}}$ + +To address this, we take advantage of the volumetric renderer used in [10] being fully differentiable, and backpropagate the 2D image domain masks to the 3D hybrid triplane domain to calculate gradients on triplanes (Fig. 3, triplane localization in Algorithm 1). First, input images are encoded using a pre-trained model [6, 76] to obtain triplane features $\mathbf{T}$ . These features are rendered with different camera poses $\pi_{1,2,\dots,N}$ to create multi-view 2D renderings $\mathcal{R}(\mathbf{T},\pi)$ . An off-the-shelf segmentation network $S_{2\mathrm{D}}$ identifies attributes [1] (e.g., hair, eyes, glasses) in each rendering. The segmentation outputs are assigned as output gradients $\nabla_{\mathcal{R}(\mathbf{T},\pi)}$ , and are back-propagated to the triplane domain to accumulate input gradients $\Sigma_{\pi}\nabla_{\mathbf{T}}$ , which localizes the triplane mask. + +To convert a gradient mask into a binarized one, we perform mean clipping, normalization, and thresholding with parameters $(\epsilon, \gamma)$ (post-processing in Algorithm 1). These parameters are set once and used across all experiments for each attribute and domain, and are in the Supplementary. This localization is done for source and reference images. + +For finer granularity and to avoid copying unwanted attributes, such as copying glasses and not the eyes, $\mathcal{W}^+$ directions [59] can be utilized in addition. By computing the difference between triplanes with and without the attribute, $\Delta \mathbf{T}_{\mathrm{attr}} = \mathbf{G}(w) - \mathbf{G}(w - w_{\mathrm{attr}})$ and multiplying with gradient mask $\mathbf{M}$ , a more precise mask can be created. + +# 3.2. Implicit fusion by encoding & decoding + +After finding suitable masks for reference and source triplanes, $\mathbf{M}_{\mathrm{ref}}$ and $\mathbf{M}_{\mathrm{src}}$ respectively, a naive approach would be to follow Eq. (1): + +$$ +\mathbf {T} _ {\text {t m p}} = \mathbf {M} _ {\text {r e f}} * \mathbf {T} _ {\text {r e f}} + \mathbf {M} _ {\text {s r c}} * \mathbf {T} _ {\text {s r c}} \tag {1} +$$ + +However, Fig. 8 (V1) reveals only using Eq. (1) distorts the geometry and color consistency, and creates stitching seams + +around the editing borders. In addition, in some cases, the contents in $\mathbf{T}_{\mathrm{ref}}$ and $\mathbf{T}_{\mathrm{src}}$ are not enough to ensure the editing looks natural around the region where two masks meet, necessitating the hallucination of additional content to complement the editing. For example, we may want to remove the long hair from the source image and replace it with the short hair from the reference image. In this case, the pixels that correspond to long hair regions need to be inpainted. + +Given the above observations and GAN's latent spaces embed natural images, we render the naively fused triplane with the canonical pose $\pi_{\mathrm{can}}$ , re-encode $\mathbf{E}_{\mathcal{W}^+}$ , and re-decode via the generator $\mathbf{G}$ to obtain an implicitly fused triplane, shown in Eq. (2): + +$$ +\mathbf {T} _ {\text {i m p}} = \mathbf {G} \left(\mathbf {E} _ {\mathcal {W} ^ {+}} \left(\mathcal {R} \left(\mathbf {T} _ {\text {t m p}}, \pi_ {\text {c a n}}\right)\right)\right) \tag {2} +$$ + +Note that state-of-the-art image inversion methods for EG3D [6, 76] employ both low-rate $\mathcal{W}^+$ and high-rate $\mathcal{F}$ features. The latter is crucial for reconstructing fine image details. However, our objective in this phase is not to achieve perfect image reconstruction. On the contrary, we aim for the encoder to map the image to a latent space with natural reconstructions. To achieve this, we disable the high-frequency restoration branch of $\mathbf{E}_{\mathcal{W}^+}$ to prevent encoding visible seams. This allows us to project the edited image onto its nearest representation on $\mathbf{G}$ 's manifold, implicitly fusing the masked triplanes. Fig. 4 showcases seamless boundaries across the stitches after this operation. + +Note that image details are compromised at this stage, as we solely depend on the low-rate $\mathcal{W}^+$ space. To bring the details back, we only employ $\mathbf{T}_{\mathrm{imp}}$ at the transition regions, as depicted in Eq. (3). For instance, when we transfer the mouth from reference to source, we aim for the triplane features outside the mouth to originate from $\mathbf{T}_{\mathrm{src}}$ , the mouth features from $\mathbf{T}_{\mathrm{ref}}$ , and features near mouth from $\mathbf{T}_{\mathrm{imp}}$ . + +$$ +\begin{array}{l} \mathbf {T} _ {\mathrm {f}} = \mathcal {E} (\mathbf {M} _ {\text {r e f}}) * \mathbf {T} _ {\text {r e f}} + \mathcal {E} (\mathbf {M} _ {\text {s r c}}) * \mathbf {T} _ {\text {s r c}} \tag {3} \\ + \left(\mathcal {E} \left(\mathbf {M} _ {\mathrm {s r c}}\right) - \mathcal {E} \left(\mathbf {M} _ {\mathrm {r e f}}\right)\right) * \mathbf {T} _ {\text {i m p}} \\ \end{array} +$$ + +Here, $\mathcal{E}$ denotes morphological erosion. We also apply Gaussian blurring with parameters $(\mu, \sigma)$ onto the masks to avoid sharp edges. This step is not illustrated in Fig. 4 for brevity, but $(\mu, \sigma)$ are provided in the Supplementary. + +Finally, $\mathbf{T}_{\mathrm{f}}$ is rendered from any desired pose $\pi_R$ , and the final image is obtained, as illustrated in Eq. (4). + +$$ +I _ {\text {e d i t e d}} = \mathcal {R} \left(\mathbf {T} _ {\mathrm {f}}, \pi_ {R}\right) \tag {4} +$$ + +# 3.3. Fine-tuning the image encoder + +Although $\mathbf{T}_{\mathrm{imp}}$ obtained in Sec. 3.2 helps tremendously even though a pre-trained encoder is used to obtain it, we notice in some cases where we have skin color inconsistencies, background leakages, and missing high-frequency details + +around the editing regions (Fig. 8 (V2)). Hence, we fine-tune implicit fusion encoder $\mathbf{E}_{\mathcal{W}^+}$ , jointly with the triplane editing pipeline to mitigate the aforementioned effects. + +During the fine-tuning phase, we generate renders as ground-truths from various viewpoints of the source and reference images corresponding to different attributes. Then, we employ masked losses to guide $\mathbf{E}_{\mathcal{W}^{+}}$ in encoding only the visible regions, illustrated in Fig. 5. For instance, if our objective is to transfer hair, we mask the reference renderings to exclude pixels that do not represent hair while doing the opposite for the source ground truth. To ensure that losses do not affect the boundaries, we dilate the segmentation masks. The objective function is provided in Eq. (5): + +$$ +\begin{array}{l} \min _ {\mathbf {E}} \lambda_ {\Phi} \mathcal {L} _ {\Phi} (\mathcal {D} (\tilde {\mathbf {M}} _ {\mathrm {r e f}}) * \mathcal {R} (\mathbf {T} _ {\mathrm {f}}, \pi_ {i}), \mathcal {D} (\tilde {\mathbf {M}} _ {\mathrm {r e f}}) * \mathcal {R} (\mathbf {T} _ {\mathrm {r e f}}, \pi_ {i})) \\ + \lambda_ {\mathrm {I D}} \mathcal {L} _ {\mathrm {I D}} \left(\mathcal {D} \left(\tilde {\mathbf {M}} _ {\mathrm {s r c}}\right) * \mathcal {R} \left(\mathbf {T} _ {\mathrm {f}}, \pi_ {i}\right), \mathcal {D} \left(\tilde {\mathbf {M}} _ {\mathrm {s r c}}\right) * \mathcal {R} \left(\mathbf {T} _ {\mathrm {s r c}}, \pi_ {i}\right)\right) \tag {5} \\ \end{array} +$$ + +where $\mathcal{L}_{\Phi}$ is the learned perceptual image patch similarity loss (LPIPS) [82], $\mathcal{L}_{\mathrm{ID}}$ is the identity similarity loss [18], $\mathcal{D}$ is dilation operation, and $\tilde{\mathbf{M}}_{\mathrm{src}}$ and $\tilde{\mathbf{M}}_{\mathrm{ref}}$ are the corresponding 2D segmentation masks for the rendered images $\mathcal{R}(\mathbf{T}_{\mathrm{src}},\pi_i)$ and $\mathcal{R}(\mathbf{T}_{\mathrm{ref}},\pi_i)$ with poses $\pi_{i}$ , respectively. + +To achieve identity preservation of the source image, we rely on the ID losses, and to copy the attribute with details, we rely on the LPIPS score from Eq. (5). We omit pixelwise losses like $\mathcal{L}_2$ since they are highly dependent on the quality of the off-the-shelf 2D segmentation network. During the fine-tuning, we use each subject tuple $(\mathbf{T}_{\mathrm{src}},\mathbf{T}_{\mathrm{ref}})$ multiple times, rendered from $N$ randomly chosen $\pi_i$ 's. + +Compliant with the common encoder training methodology, we use the same training datasets generators are trained with. We employ Ranger optimizer, which is a combination of Rectified Adam [42] with Lookahead [80]. The learning rate is set to $1e^{-4}$ , and fine-tuning is done for 1500 steps with a batch size of 2 on a single RTX 4090. + +# 4. Experiments + +Evaluation. We present metrics evaluating both the reconstruction and editing qualities of our approach. For editing assessment, we employ the Fréchet Inception Distance (FID) [28], which evaluates realism by comparing the distribution of target images with that of edited images. Specifically, we compute FIDs for adding eyeglasses and hair edits from black to blonde transition using the CelebA [45] dataset. For instance, leveraging ground-truth attribute labels, we add eyeglasses to images without them and compute FIDs between the edited and original images that already have eyeglasses. This procedure is similarly applied to hair edits. For reconstruction evaluation, we mask the edited areas and measure the L2 and Structural Similarity + +![](images/dcfcf24f784146d917dba8c90cd18e2a90c61f8a3625c831404a687f32f3f464.jpg) +Figure 4. Triplane localization and implicit fusion stages, where $\mathbf{E}^*$ denotes the fine-tuned image encoder that is described in Sec. 3.3. Straightforward stitching in the triplane results in color inconsistency across the boundaries, as shown in $I_{tmp}$ (zoom in for details). Leveraging $\mathbf{E}^*$ , we aim to attain seamless boundaries and produce outputs with a natural appearance. + +![](images/7257b31f9aeca07518ec88619c7d951b9e00f1cda12d13131d0846c84694ac6b.jpg) +Figure 5. Pipeline for the implicit fusion encoder fine-tuning. We generate masked ground truths for our task by utilizing 2D segmentation networks and via renderings from multiple views. We aim to carry the reference parts in great detail to our source image while preserving the source's identity. Triplane fusion corresponds to Eq. (3). + +Index (SSIM) between the input and edited images. For instance, in the eyeglasseses edit, we mask the eyeglasses and measure the alteration in the unedited regions. This dual assessment framework ensures a robust evaluation of both the fidelity and quality of our editing approach. + +Baselines. We conducted comprehensive comparisons by evaluating our method against a range of latent direction, text and image reference-based, 2D and 3D-aware, GAN, and diffusion-based editing methods. Notably, no existing reference-based editing methods achieve 3D consistency within a single framework. + +HiSD and VecGAN++ are reference-based 2D image-to-image methods. InterFaceGAN, StyleCLIP $(\mathcal{W}^{+})$ , SFE $(\mathcal{W}^{+} / \mathcal{F})$ , StyleFusion $(\mathcal{W})$ , Barbershop, and HairCLIPv2 $(\mathcal{F} / \mathcal{S})$ operate within the latent spaces of StyleGAN and can be adapted to 3D-aware GANs like EG3D. However, only the last three are reference-based, with two focusing on hair edits. E3DGE is a SDF-based generator, and editing is done via latent directions. For diffusion-based models, LEDs++ and InfEdit perform text-based editing, while NoiseCLR utilizes pretrained latent edit noise directions. Paint by Example inpaints the masked source image with the reference image but lacks control over which parts of + +Table 1. Quantitative scores on CelebA. $(\mathcal{X})$ indicates the method is not capable of such edits. First and second best method are given in bold and underlined. Time is measured on Tesla T4. + +
EyeglassesHairTime
FID ↓MSIM↑ML2↓FID ↓MSIM↑ML2↓(s)
HiSD [40]77.560.94710.009094.530.97430.00361.1
VecGAN++ [14]71.470.74830.063080.470.92960.00902.2
Barbershop [85]XXX62.800.87560.0182125
HairCLIPv2 [63]XXX85.750.87690.0173180
StyleFusion [33]XXX84.670.84350.01982.4
InterfaceGAN [59]88.130.93980.010480.930.78880.03870.6
StyleCLIP [53]80.130.84210.047692.600.87160.01960.6
SFE [7]106.10.93410.009989.490.93550.00505.1
E3DGE [36]XXX77.860.80830.02571.2
NoiseCLR [13]107.10.79580.0440XXX17.2
LEDSIIS++[8]115.20.96450.004796.560.97170.002525.9
InfEdit [69]90.330.83380.1042105.40.74250.06139.1
Paint by ex. [70]74.180.88280.025282.380.92290.01559.6
Ours66.680.98180.002164.590.97200.00296.0
+ +the reference are used. + +Results. We present quantitative and qualitative comparisons with competing methods in Tab. 1 and Fig. 6, respectively. From Tab. 1, it is evident that our method outperforms competing methods significantly in terms of FID and preserves identity better in the non-edited regions. + +Observing Fig. 6, our method demonstrates superior per + +![](images/76d5e8d5451bda54d3be201c1e24d65885ff1e16b987e5f1d44582bf14b6cbe7.jpg) +Figure 6. Comparisons with the competing editing methods for glasses addition and hair edits. Ours, HisD, VecGAN++, Barbershop, StyleFusion, HairCLIPv2, and Paint by Ex. use reference images for editing. InterFaceGAN, StyleCLIP, SFE, E3DGE, and NoiseCLR use previously calculated latent directions. LEDs++ and InfEdit use text prompts. N/A indicates the model is incapable of such edits. + +![](images/c56d37e4f01e7ffebdf06db4776a2aab585aee80d227a4c1b8a7f34d9e338b46.jpg) +Figure 7. Additional editing examples from the CelebA dataset showcasing our method's ability to seamlessly incorporate features such as lips, eyes, and nose from reference to source, despite pose differences and interference like eyeglasses. + +formance in hair and glasses edits compared to competing methods. HisD and VecGAN++ struggle with maintaining fidelity to the reference, particularly with glasses, due to their reliance on low-rate latent spaces. While InterFaceGAN, StyleCLIP, and SFE can add glasses and perform some hair transfers, they falter with uncommon edits like hat removal (row 5) and red hair (row 8) due to the limitations of their $\mathcal{W}^{+}/\mathcal{F}$ spaces and their non-reference-based approach. E3DGE's pre-trained editing directions yield unsatisfactory results. LEDITS++ and InfEdit, being text-conditioned, fail to accurately reflect the original + +reference in their edits. NoiseCLR does not effectively explore hairstyle directions, and its glasses modifications are entangled with makeup changes (rows 2 and 4). Paint by Example can transfer some features but often produces severe out-of-domain artifacts (rows 1, 5-8). Barbershop and HairCLIPv2, optimized for hairstyle edits, suffer from geometric inconsistencies (row 8) and fail in some hair edit cases (row 5). Finally, StyleFusion's feature transfer relies on $\mathcal{W} / \mathcal{W}^{+}$ directions, resulting in the loss of many high-rate details and outputs that do not fully reflect the original images, especially when the features cannot be well + +Table 2. Results of our user study where participants are asked to identify the edited image. Based on this study, we find that our edits are challenging to distinguish. + +
FFHQAFHQ
EyesNoseMouthOverallEyesNose+MouthOverall
Original40%29%34%34%40%42%41%
Ours (edited)49%59%40%49%49%43%46%
Undecided11%13%26%16%11%15%13%
+ +Table 3. Quantitative ablation study of our editing. V1 is the post-processing triplane gradients, V2 is the implicit fusion, and V3 fine-tunes the implicit fusion encoder. + +
EyeglassesHair
V1V2V3FID ↓MSSIM ↑ML2 ↓FID ↓MSSIM ↑
XXX79.500.84510.032382.420.8177
✓XX74.460.98140.002277.300.9674
✓✓X68.190.98220.002067.040.9691
✓✓✓66.680.98180.002164.590.9720
+ +![](images/b44f3f5bc2a68c9a8482f3b2f4fdcfe656368be66d020b9a2a8c2262343f270a.jpg) +Figure 8. Qualitative ablation study for glasses and hair edits, showing the effects of all fundamental stages of our pipeline. + +![](images/aa2fa440eebb0c525a0db9ec33933918ba45e283f203ac7d245b6c616f029c8a.jpg) +Figure 9. Cross-generator edits with stylizing. Our method achieves copying local parts from stylized images, such as cartoon portraits. + +represented in those domains (row 8). + +Next, we conduct a user study with 25 participants to evaluate our reference-based edits. Participants are shown original and edited images and asked to identify the edited ones. We utilize outputs of EG3D for both original and edited images to neutralize the influence of encoding on the results, and utilize the same angle for the source and edited + +![](images/3628a974546f56ad37aec4ea1624ab55af29efa6a03de8aff440f71fcdc36e78.jpg) +Figure 10. Additional editing examples from AFHQ dataset. The nose and mouth are handled as a single part. + +images with random ordering to minimize bias. Participants could also choose "undecided" if they find it difficult to distinguish. The study focus on edits to mouth, eyes, and nose on the FFHQ dataset, and eyes, nose & mouth on the AFHQ dataset. Some participants frequently chose "undecided", while others perform near random chance, in Tab. 2. + +Ablation study. We demonstrate the improvements during the development of our pipeline stages, both quantitatively and qualitatively, in Tab. 3 and Fig. 8, respectively. + +In our initial ablation study, we apply Eq. (1) to merge the triplanes using a mask calculated via autograd function without any post-processing (No V). Due to the intricate volumetric function affecting many pixels for each value in the triplane, the initial mask fails to stitch images effectively, resulting in blurry outputs. Following the introduction of post-processing (+V1), as described in Sec. 3.1, we successfully achieve clear stitching, as depicted in Fig. 8. This allows us to transfer the hair of one person to our input while aligning the features using the canonical representation of the triplane. However, the resulting output still lacks realism because it combines features from two different images with varying illuminations, identities, and skin colors (row 2). To address the issue of smoothness at stitch boundaries, we follow Sec. 3.2 and perform encoding and decoding via the pretrained encoder and decoder, respectively, on the fused triplane. Since these encoders are trained with real images, they know about real image priors. Despite the input image not being realistic, as shown in Fig. 8 (V1), the encoder successfully encodes its latent to the generator's natural latent space while attempting to preserve the identity in (+V2). However, a pretrained encoder optimized for projecting real images onto the generator's latent space is not optimal for our specific use case. Consequently, we replace the encoder with one trained specifically for this task, elaborated in Sec. 3.3. This specialized encoder (+V3) ensures color preservation (row 2) and enhances editing details, such as the coherence of eyeglass frames, as well as + +![](images/84aff018f6a436698cf8b5e5438dfcc75d2de876e2159ab0f48a9f6144ec8b43.jpg) +Figure 11. Extending our method on full-head hair edits on [4]. + +![](images/81b561ce828dd2aaf374581768467bd1de1abc7615d07a49b80c111d9efadc06.jpg) +Figure 12. Extending our method on try-on edits on [20]. + +reducing background leakage (rows 1 and 4). + +Cross-generator edits. We also provide novel edits in Fig. 9, where the reference and source triplanes are gathered from stylized and non-stylized generators, respectively. Specifically, we utilize [60] and fine-tune the EG3D backbones via different text prompts [55]. Then, we synthesize stylized triplanes $(\mathbf{T}_{\mathrm{ref}})$ and perform reference-based editing on the triplanes of default EG3D $(\mathbf{T}_{\mathrm{src}})$ . The rest of the steps are the same as before, using the original EG3D and encoder we train for EG3D. The results presented in Fig. 9 demonstrate our method's independence from backbones, showcasing its capability to achieve part-based attribute stylization. This differs from [60], which offers global stylization. + +Full body and 360-degree head edits. Fig. 7 demonstrates challenging human face reference-based edits on EG3D [10] like transferring lips, eyeglasses, and nose from one person to another. Fig. 10 shows edits on animal face parts for eyes, nose, and mouth. Fig. 12 demonstrates fashion edits on AG3D [20] trained with DeepFashion [46] dataset. Fig. 11 extends human face part edits to full 360-degree hair edits on PanoHead [4]. It is evident that our approach is generalizable to different triplane generators. + +While extending our method to different triplane-based generators and datasets, we only changed the 2D segmentation network and the encoder fine-tuning dataset to comply with the generator, when required. We also provide multiview image results and more examples in Supplementary. + +![](images/338a8dbdef73e1dbd0947a27f638fcf049d2893babb5df680137146d74f5e76f.jpg) +Figure 13. Simultaneous editing results. + +Generalizing to class-agnostic edits. Given the importance of large reconstruction models [11, 29, 32, 37, 38, 65, 68, 79], we extend our method to arbitrary object edits using the triplanes of LN3Diff and InstantMesh [37, 68] in Fig. 1, proving the potential capabilities of our method. + +# 5. Conclusion + +In conclusion, our work presents a comprehensive framework for reference-based, 3D-aware image editing, leveraging the unique capabilities of triplanes. Through spatial disentanglement and fusion learning, we achieve seamless integration of reference attributes while preserving the identity of the input image. We have shown our method's effectiveness through extensive qualitative and quantitative experiments. Our approach fills a crucial gap by offering a unified and generalizable solution. + +Limitations. Our approach relies on the capabilities of EG3D, AG3D, PanoHead, LN3Diff and InstantMesh, which may struggle with background generation and high-quality reconstruction. Consequently, in some instances, rich background details may not be fully presented (row 4 on Fig. 6). However, this can be mitigated by not relying on the generator for background generation. + +Future work. Extending our reference-based editing approach beyond triplanes using large reconstruction models [11, 32, 38, 65, 79] is an underexplored path. Specifically, on DiT-based approaches, we believe that the reference and source image tokens can be processed jointly, and the masks created via gradient accumulation can be applied onto self-attention layers for implicit fusion. We think that this can also eliminate the necessity for a canonical space where the source and reference features must be aligned, as the attention mechanism can handle misalignment easily. + +# References + +[1] zllrunning. face-parsing.pytorch. https://github.com/zllrunning/face-parsing.PyTorch/. Accessed: 2024-28-02. 3 +[2] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Styleflow: Attribute-conditioned exploration of stylegan-generated images using conditional continuous normalizing flows. ACM Transactions on Graphics (ToG), 40(3):1-21, 2021. 2 +[3] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. 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Our Ref-GS method generates photo-realistic renderings with view-dependent effects while also enabling accurate geometry recovery. The top row shows a comparison of renderings for a scene with specular reflections, along with the recovered normals and mesh. The bottom row demonstrates our successful reconstruction of the geometries of the 'reflective table center' in the 'Garden' scene [2] and the 'windshield' in the 'Truck' scene [13], which existing methods typically fail to handle. + +![](images/76792458e78b02459b514fd40216003079e9877f77a93891cd09a153c484a519.jpg) +Mesh + +![](images/417e07fa77d27ed5895ba822a4b9f01b995c71bddce23733813d24f8fadb1ae7.jpg) +Rendering + +![](images/4f85b6451fa8b6a5b84596bf6d53d8b9dad587616fe55309c15a4798c44089fd.jpg) +Mesh + +# Abstract + +In this paper, we introduce Ref-GS, a novel approach for directional light factorization in 2D Gaussian splatting [8], which enables photorealistic view-dependent appearance rendering and precise geometry recovery. Ref-GS builds upon the deferred rendering of Gaussian splatting and applies directional encoding to the deferred-rendered surface, effectively reducing the ambiguity between orientation and viewing angle. Next, we introduce a spherical Mip-grid to capture varying levels of surface roughness, enabling roughness-aware Gaussian shading. Additionally, we pro + +pose a simple yet efficient geometry-lighting factorization that connects geometry and lighting via the vector outer product, significantly reducing renderer overhead when integrating volumetric attributes. Our method achieves superior photorealistic rendering for a range of open-world scenes while also accurately recovering geometry. See our interactive project page. + +# 1. Introduction + +View-dependent effects are a key element in 3D reconstruction and rendering - capturing complex interactions of light in materials such as reflection and refraction - have + +been studied for decades in forward rendering for computer graphics to enhance realism and visual fidelity in simulations, animations, and visual effects. Recent advances in Neural Radiance Fields (NeRF [20], Mildenhall et al. in 2020) and Gaussian Splitting (GS [11], Kerbl et al. in 2023) have enabled high-fidelity 3D scene reconstruction and novel view synthesis. However, unlike forward rendering in computer graphics, light propagation such as reflection and refraction has received much less attention in neural fields, and significant artifacts in both geometry and rendered images can be observed when reconstructing scenes with complex materials. + +This is because NeRF and its follow-ups [1, 2, 31, 39] represent 3D scenes as a collection of emission radiance points and query view-dependent colors using viewing direction, without accounting for the bouncing and bending of light rays as they travel from the light source to the viewing cameras. To tackle this issue, Ref-NeRF [29] take advantage of surface light field rendering [4, 34] and replaces NeRF's directional parameterization with an integrated reflection encoding, achieving significant improvement in the realism and accuracy of specular reflections. Recent work [35] brings feature grid-based encoding to the directional domain to speed up the efficiency of directional encoding. In the context of 3DGS, directly applying the reflection of the view direction as the view-dependent color query for recent efficient GS representation is problematic, as it independently inherits model orientation and Spherical Harmonics (SH) color for each primitive, resulting in transforming viewing direction can easily be offset during parameter updating. To do so, recent work [33, 37, 40] incorporates smooth regularization and higher-order view-dependent color modeling into the rendering function, achieving promising quality on reflective surfaces. Despite the high rendering quality, they are struggling to provide accurate geometry. + +In this paper, we present Ref-GS, a new directional encoding method for 2D Gaussian splatting that leverages deferred rendering and lighting factorization to achieve photorealistic view-dependent effect reconstruction, while preserving accurate geometry. Unlike previous work that treats ray color as the integration of point radiance, we leverage deferred rendering techniques by postponing view-dependent color evaluation until after Gaussian attribute blending and performing directional encoding only on the estimated surface, which efficiently reduces the orientation-viewing ambiguity of Gaussian representations (see Section 4). In addition, we introduce a Mip-grid to capture varying levels of surface roughness, enabling roughness-aware Gaussian shading. Furthermore, spatially varying materials are crucial for modeling open-world scenes; therefore, we propose a simple yet efficient geometry-lighting factorization that connects the geometry and light- + +ing through the vector outer product, significantly lowering renderer overhead for volumetric attribute integration. + +Our Ref-GS achieves effective reconstruction of high-frequency reflection and fraction from multi-view images and enables faithful geometry recovery. An extensive evaluation of our approach with both synthetic and real-world scenes demonstrates that Ref-GS produces state-of-the-art renderings of novel views, even compared to implicit methods. Furthermore, our method maintains competitive training times and importantly allows high-quality real-time (> 45 FPS) novel view synthesis at $800 \times 800$ resolution with a novel deferred mechanism. + +# 2. Related Work + +Our work is closely related to research in novel view synthesis, and reflective and refractive object reconstruction and rendering. + +Novel View Synthesis. Novel view synthesis (NVS) focuses on generating novel views from a collection of posed images. A significant achievement in Neural Radiance Fields (NeRF) [20] has been made for realistic NVS, thanks to implicit representations and volumetric rendering. Which has inspired other scene representations, including those for bounded objects [5, 7, 21, 25], unbounded scenes [2, 19, 27, 43], and scenes with high specular reflections and reflective effects [29, 38, 45, 46]. Despite advancements, NeRF-based methods face challenges related to low training and rendering efficiency due to their implicit nature. Recently, 3D Gaussian Splatting (3DGS)[11] has emerged as an alternative 3D representation to NeRF. While 3DGS achieves high-quality novel view synthesis, the reconstructed surface is generally noisy. To address the multi-view geometric inconsistencies in 3DGS, Huang et al. [8] introduced 2D Gaussian Splatting (2DGS), where Gaussian disks are placed on object surfaces and smoothed locally. Our method extends 2DGS, significantly enhancing view-dependent effects and geometry quality. + +Reflective Scene Reconstruction and Rendering. Reflective scene reconstruction and rendering has been a challenging task, attracting significant attention. Directional encoding techniques have been explored to improve the modeling of reflections. Ref-NeRF [29] applies Integrated Directional Encoding (IDE) to enhance NeRF's view-dependent effects but struggles with modeling near-field lighting. To address this limitation, Spec-NeRF [18] introduces Gaussian Directional Encoding, improving the modeling of specular reflections under near-field lighting conditions. Wu et al. [35] proposes Neural Directional Encoding, simulating near-field inter-reflections by tracking light cones within the NeRF model and utilizing a global cubemap filtered by a GGX kernel [30] for reflection modeling. However, these methods rely on large multi-layer perceptrons (MLPs) to represent geometry, resulting in slower training and ren + +![](images/8fb7002a03f3e3b67b2e4c1481d05fdeb924686b845986086e3e2f8c6eeb3564.jpg) +Figure 2. Overview of Ref-GS. From left to right: the geometry pass renders the scene properties, including appearance feature $\mathbf{K}$ , roughness map $\mathbf{M}$ , and normal map $\mathbf{N}$ , into buffers via deferred rendering, the lighting pass projects the reflected direction $\omega_{r}$ onto spherical coordinates $(\theta, \phi)$ and featurized by Sph-Mip encoding for modeling far-field lighting, finally the rendering pass use tensor factorization $\mathbf{s} \circ \mathbf{k}$ to obtain spatially varying view-dependent effects and color each pixel $(u, v)$ . + +dering speeds compared to Gaussian-based representations. Other approaches [10, 15-17, 38, 42] incorporate indirect lighting. ENVIDR [16] uses a neural renderer to learn physical light interactions through ray tracing, without explicitly formulating the rendering equation. NeRO [17] introduces a lighting representation method using two MLPs and a split-sum approximation to model direct and indirect lighting, enabling high-quality reconstruction of reflective objects. However, NeRO requires extracting geometry from a pretrained Signed Distance Function (SDF), which takes over 3 hours, resulting in significant inefficiencies. In contrast, recent Gaussian-based methods [9, 28, 36, 40, 47] offer more efficient solutions. For instance, 3iGS [28] uses tensorial factorization [5] to optimize incident illumination, while GaussianShader [9] separately models view-dependent effects, and 3DGS-DR [40] incorporates deferred rendering for reflection modeling. While these methods excel in generating high-quality novel views, they still struggle to model near-field lighting, where environment maps change spatially. + +Moreover, concurrent work NU-NeRF [26] simulates reflection and refraction using physics-based ray tracing, improving the reconstruction of objects with fully transparent materials. To better demonstrate our method's capabilities, we evaluate reconstruction results on real-world scenes with transparent objects. + +# 3. Preliminaries + +# 3.1. Gaussian Splitting + +Gaussian Splatting is a recent advance for efficient 3D reconstruction and rendering built upon rasterization. 3DGS and 2DGS are point-based representations that each point + +associated with geometry attributes (i.e. $\pmb{\Sigma} \in \mathbb{R}^{3 \times 3}$ , position $\mu \in \mathbb{R}^3$ and opacity $\alpha$ ) and Spherical Harmonics (SH) appearance attributes $\mathbf{c}$ , and the Gaussians are defined in world space centered at $\mu$ : + +$$ +\mathcal {G} (\mathbf {x} | \boldsymbol {\mu}, \boldsymbol {\Sigma}) = \exp \left(- \frac {1}{2} (\mathbf {x} - \boldsymbol {\mu}) ^ {T} \boldsymbol {\Sigma} ^ {- 1} (\mathbf {x} - \boldsymbol {\mu})\right) \qquad (1) +$$ + +where the covariance matrix is factorized into a rotation matrix $\pmb{R}$ and a scaling matrix $S$ , to facilitate optimization: + +$$ +\boldsymbol {\Sigma} = \boldsymbol {R} \boldsymbol {S} \boldsymbol {S} ^ {T} \boldsymbol {R} ^ {T} \tag {2} +$$ + +Note that, the surface of the 3D Gaussian is not well defined, leading to noisy surface reconstruction. To address this issue, 2D Gaussian Splatting (2DGS [8]) takes advantage of standard surfel modeling [24, 41, 48] by adopting 2D oriented disks as surface elements and allows high-quality rendering with Gaussian splatting. Specifically, instead of evaluating a Gaussian's value at the intersection between a pixel ray and a 3D Gaussian [11], 2DGS evaluate Gaussian values at 2D disks and utilizes explicit ray-splat intersection, resulting in a perspective-correct splatting: + +$$ +\mathcal {G} (\mathbf {u}) = \exp \left(- \frac {u (\mathbf {r}) ^ {2} + v (\mathbf {r}) ^ {2}}{2}\right) \tag {3} +$$ + +where $\mathbf{u} = (u(\mathbf{r}), v(\mathbf{r}))$ is the intersection point between ray $\mathbf{r}$ and the primitive in UV space. Furthermore, each Gaussian primitive has its own view-dependent color $\mathbf{c}$ with SH coefficients. For rendering, Gaussians are sorted according to their centers and composed into pixels with front-to-back alpha blending: + +$$ +\mathbf {c} (\mathbf {r}) = \sum_ {i = 1} \mathbf {c} _ {i} \alpha_ {i} \mathcal {G} _ {i} (\mathbf {u}) T _ {i} \tag {4} +$$ + +where $T_{i}$ is approximated accumulated transmittances defined by $\prod_{j=1}^{i-1}(1 - \alpha_{j}\mathcal{G}_{j}(\mathbf{u}))$ . Note that both 3DGS and 2DGS are forward processes, where scenes are directly projected onto the image plane. Each Gaussian primitive is rendered and lighted in object space before being mapped to screen space. However, forward rendering generally tends to waste a lot of fragment Shader runs in scenes with a high depth complexity (multiple primitives cover the same screen pixel) as fragment Shader outputs are overwritten. + +# 3.2. Deferred Shading + +In 3D computer graphics, deferred shading [6] is a screen-space shading technique designed to significantly reduce the number of shading operations compared to the forward rendering process. + +Deferred shading is a technique that defers most intensive rendering operations, such as lighting calculations, to a later stage in the rendering pipeline. This technique involves two main passes. In the first pass, known as the geometry pass, the scene is rendered once to capture various types of geometric information from objects in the scene. These data are stored in a collection of textures called the G-buffer, which contains information such as position vectors, color vectors, normal vectors, and specular values. The G-buffer thus serves as a repository of scene geometry that can be utilized for subsequent, potentially complex, lighting calculations. + +In the second pass, referred to as the lighting pass, the G-buffer textures are used to calculate lighting across the scene. A screen-filled quad is rendered, and the lighting for each fragment is computed using the geometric information stored in the G-buffer, iterating over each pixel. This process decouples advanced fragment processing from the initial rendering of each object, allowing lighting calculations to draw directly from the G-buffer textures rather than the vertex Shader, with additional input from uniform variables as needed. This allows to maintain the same lighting calculations but optimizes the process by postponing them until after the G-buffer has been populated. + +# 4. Ambiguity in Directional Query + +In prior Gaussian Splatting methods, the diffusion, reflection and refraction components of each primitive are simplified using view-dependent emission radiance, which significantly accelerates the forward rendering process without the need for per-instance lighting evaluation. Then, they optimize the emission radiance together with the geometry jointly through an inverse rendering framework by backpropagating a multi-view photometric loss. + +We observe that this modeling suffers from serious representation ambiguities as illustrated in Fig. 3 shows an integration process of three primitives. Consider the integration processing used by vanilla 3D and 2D Gaussian Splatting + +a) +![](images/ea0743a14e75abc38b3dec232e7490ff28c787e17fa177170070f58d28c1249c.jpg) +directional query: 3 + +b) +![](images/836659d09fe089de323b60a4a8ea95f60c90c7769f7db8c1ef3de9b8c5ed088e.jpg) +$\mathbf{c}(\mathbf{r}) = \mathrm{SH}_1(\omega)W_1 + \mathrm{SH}_2(\omega)W_2 + \mathrm{SH}_3(\omega)W_3$ +directional query: 3 +$\mathbf{c}(\mathbf{r}) = \mathrm{SH}_1(\omega ,\mathbf{n}_1)W_1 + \mathrm{SH}_2(\omega ,\mathbf{n}_3)W_2 + \mathrm{SH}_3(\omega ,\mathbf{n}_3)W_3$ + +c) +Figure 3. Comparison of directional query in Gaussian Splat-ting. a) The original 3DGS [11] and 2DGS [8] methods query each primitive's SH coefficient using the viewing direction, then accumulate view-dependent radiance as the ray color. b) Ref-NeRF [29] and recent GaussianShader [9] utilize the reflection direction transformed by both the viewing and normal directions as the directional query. c) We introduce Gaussian deferred shading by first integrating the SH coefficient and normal as a surface point, then evaluating its view-dependent color. +![](images/50f3997b5f004cd3f284bdf22ec80784ec10df6f95973f15c3f52f39ac74863e.jpg) +directional query: 1 +$\mathbf{c}(\mathbf{r}) = \widehat{\mathrm{SH}} (\omega ,\widehat{\mathbf{n}})$ +$\widehat{\mathbf{n}} = \mathbf{n}_1W_1 + \mathbf{n}_2W_2 + \mathbf{n}_3W_3$ +$\widehat{\mathrm{SH}} = \mathrm{SH}_1W_1 + \mathrm{SH}_2W_2 + \mathrm{SH}_3W_3$ + +in (a), it queries view-dependent color using viewing direction, leading to strong bias to diffuse materials and high-frequency irradiance is generally fake by complex primitive overlaying; to handle strong reflection, Ref-NeRF [29] and its follow-ups [16, 17] utilize reflection direction as color query by considering point normal in (b). Unlike the continuous representation in NeRF that neighboring points' attributes are regularized to each other, Gaussian Splatting treats each point independently. Directly applying reflection direction provides limited gains due to the ambiguity between SH coefficients and the primitive orientation, i.e. transforming viewing direction to reflection direction can be eliminated by the changing in SH coefficient. In practice, since irradiance is independent across primitives and multiple primitives contribute to a target ray, this inherently introduces strong ambiguities, leading to noisy reconstructions. + +# 5. Ref-GS + +Our approach aims to reconstruct photorealistic view-dependent effect. The overview of our method is shown in Fig. 2. Specifically, we present a deferred Gaussian splating to generate a G-buffer (Section 5.1). We then introduce a directional factorization for representing spatially varying view-dependent effects (Section 5.2) and a multi-level spherical feature grid that models far-field lighting (Section 5.3). + +# 5.1. Deferred Gaussian + +We now introduce a novel deferred Gaussian Splatting method to address the ambiguity issue discussed in Section 4. Direct volume integration of Gaussian representations can result in blurry view-dependent effects and noisy surfaces due to ambiguity in directional queries. Our solution is to first blend Gaussian attributes, then apply shading, similar to deferred shading. To be specific, we perform alpha blending on primitive attributes (i.e., for the $i^{th}$ Gaussian include diffuse color $\mathbf{c}_{d_i} \in \mathbb{R}^3$ , feature $\mathbf{f}_i \in \mathbb{R}^D$ , roughness $\rho_i \in [0,1]$ ) along the rays and convert the attributes into color in image space, as described in Eq. 4 and (c) of Fig. 3. Additionally, the color of each pixel is decomposed into a diffuse component $\mathbf{I}_d$ and a specular component, queried by the reflected direction $\omega_r \in \mathbb{R}^3$ with surface normal $\mathbf{n} \in \mathbb{R}^3$ . We use the integrated diffuse color $\mathbf{I}_d$ directly as the ray's diffuse component and obtain view-dependent effects at each pixel through a shader $f_\Theta$ , conditioned on the spatial feature $\mathbf{K} \in \mathbb{R}^{H \times W \times D}$ and the directional feature $\mathbf{S} \in \mathbb{R}^{H \times W \times C}$ : + +$$ +\mathbf {I} = \mathbf {I} _ {d} + f _ {\Theta} (\mathbf {S}, \mathbf {K} \otimes \mathbf {S}) \tag {5} +$$ + +where $\otimes$ denotes the per-pixel outer product, obtaining the high-dimensional intermediate tensor with the shape of $H\times W\times (D\times C)$ + +Note that the feature $\mathbf{K}$ represents the expected feature of each pixel and is obtained by splatting per-primitive features $\mathbf{f}_i$ using Eq. 4. Similarly, we generate the roughness map $\mathbf{M}$ corresponding to $\rho_i$ and the normal map $\mathbf{N}$ . In practice, we treat $\mathbf{M}, \mathbf{N}, \mathbf{K}$ as a G-buffer and pass it a standard rasterization render for shading. + +# 5.2. Directional Factorization + +In essence, the key to modeling view-dependent effects is accurately capturing spatially varying near- and far-field inter-reflections. Prior methods [9, 22, 40] often rely on a global 2D environment map for far-field lighting, assuming all light sources are at an infinite distance. Other methods [28, 29] only model direct lighting. These assumptions are insufficient for reconstructing surfaces under near-field lighting, especially in scenes where light sources or objects are close to the target object. + +![](images/3ac7274a61967f757bcc765db872703eab487fd916005e3519c7c5b8f4e02f7f.jpg) +Figure 4. Visualized estimated surface normal results synthetic datasets [17, 29]. Compared to existing Gaussian-based methods, our method has more accurate surface reconstruction for shiny objects with inter-reflections, as depicted for this 'Toaster' and 'Bell' scenes. + +Inspired by TensoRF [5], we propose a low-rank tensor factorization $\mathbf{s} \circ \mathbf{k}$ to represent spatio-angular view-dependent effects, where $\circ$ denotes the outer product. As illustrated in Fig. 2, we connect the spatial feature vector $\mathbf{k} \in \mathbb{R}^D$ and directional feature vector $\mathbf{s} \in \mathbb{R}^C$ using a simple vector outer product to form a block matrix, which is then flattened into a 1D vector and fed into a lightweight MLP decoder for final color prediction. The outer product of spatial feature $\mathbf{k}$ and directional feature $\mathbf{s}$ enables decomposition of geometry and lighting, while effectively capturing essential information such as global lighting, shadows, and self-occlusion. + +Our factorization-based model is simple yet effective for representing spatially varying view-dependent effects in complex reflective scenes, enhancing both novel view synthesis and surface reconstruction. Additionally, this factorization reduces the feature channels for each Gaussian primitive, significantly lowering the computational overhead in volume rendering and scene representation. + +# 5.3. Far-field Lighting + +We now present a novel Sph-Mip encoding for modeling high-frequency far-field lighting, using a learnable multilevel spherical feature grid, named Sph-Mip grid. + +We utilize a longitude-latitude lattice (Long.-Lat.) to distribute feature points on a spherical surface and unfold them into a 2D feature grid for efficient indexing. Given the G-buffer $\{\mathbf{M},\mathbf{N},\mathbf{K}\}$ , the normal $\mathbf{n} = \mathbf{N}(u,v)$ , roughness $\rho = \mathbf{M}(u,v)$ for the pixel $(u,v)$ , we have: + +$$ +\mathbf {s} = \operatorname {S p h} - \operatorname {M i p} \left(\omega_ {r}, \rho , \mathcal {M}\right) \tag {6} +$$ + +where $\omega_{r}$ denotes the reflection direction reflected by the surface normal $\mathbf{n}$ and viewing direction $\omega_{i}$ . + +![](images/c37411e680e2de96cd37aca78a83cb3ab6bd1c7498e8c553c482f22f25ce5d71.jpg) +Figure 5. Qualitative comparisons of test-set views of real-world scenes. Notice the high-frequency reflections rendered by our model, including sharp details of the tree branches and buildings reflected in the sphere. + +Note that, as shown in Fig. 2, the Sph-Mip grid is three-dimensional, the directional coordinates $(\theta, \phi)$ correspond to the XY axes of the grid, while the Z-axis represents the roughness $\rho$ variance. Given rasterized buffers, we first calculate its corresponding spherical coordinates $(\theta, \phi)$ for each pixel by: + +$$ +\theta = \arccos \left(\frac {\omega_ {r} ^ {z}}{\sqrt {\omega_ {r} ^ {x 2} + \omega_ {r} ^ {y 2} + \omega_ {r} ^ {z 2}}}\right) \in [ 0, \pi ] \tag {7} +$$ + +$$ +\phi = \arctan 2 \left(\frac {\omega_ {r} ^ {y}}{\omega_ {r} ^ {x}}\right) \in [ - \pi , \pi ] +$$ + +Then, given the surface roughness $\rho$ , we interpolate features along the roughness dimension. In practice, we resize the grids at different levels to the same resolution during the feature query, facilitating efficient three-dimensional interpolation using trilinear interpolation with the coordinates $(\theta, \phi, \rho)$ in the fragment Shader. + +For the mipmap resolution, we define the base level $\mathcal{M}^{L_0}$ at the highest resolution of $H_{\mathcal{M}} \times W_{\mathcal{M}} \times C$ , where $H_{\mathcal{M}}, W_{\mathcal{M}}$ , and $C$ represent the height, width, and number of channels, respectively. While the resolution for other + +levels $(\mathcal{M}^{L_i},i = 1,2,\ldots ,N)$ is divided by $2\times$ along the height and width dimensions. + +# 6. Experiments and Results + +# 6.1. Datasets + +We evaluate our method on several synthetic and real-world datasets. For the synthetic datasets, we evaluate our model on NeRF Synthetic [20], which contains scenes of complex geometries with realistic non-Lambertian materials. Similarly, we evaluate our model on reflective objects using Shiny Blender [29] and Glossy Synthetic [17]. For the real-world datasets, we use Shiny Real dataset captured from [29], as well as scenes with reflections from MipNeRF360 [2] and Tanks & Temples [13]. Additionally, we use Glass & Ball [3], which contains refractive objects with unknown geometry, to show the generalization ability of our method for diverse materials. + +# 6.2. Baselines and metrics + +We compare our method with the following baselines: Ref-NeRF [29], a NeRF-based method focusing on reflec + +
Shiny BlenderShiny Real
CarBallHelmetTeapotToasterCoffeeAvg.GardenSedanToycarAvg.
PSNR†
Ref-NeRF [29]30.4129.1429.9245.1925.2933.9932.3222.0125.2123.6523.62
NeRO [17]25.5330.2629.2038.7026.4628.8929.84————
ENVIDR [16]28.4638.8932.7341.5926.1129.4832.8821.4724.6122.9223.00
3DGS [11]27.2427.6928.3245.6820.9932.3230.3721.7526.0323.7823.85
3GiS [28]27.5226.8228.0846.0522.7132.6430.6421.9626.5923.7524.10
3DGS-DR [40]30.4333.4431.4947.0026.6934.6133.9421.5226.3223.5723.80
Ours30.9436.1033.4046.6927.2834.3834.8022.4826.6324.2024.44
SSIM†
Ref-NeRF [29]0.9490.9560.9550.9950.9100.9720.9560.5840.7200.6330.646
NeRO [17]0.9490.9740.9710.9950.9290.9560.962————
ENVIDR [16]0.9610.9910.9800.9960.9390.9490.9690.5610.7070.5490.606
3DGS [11]0.9300.9370.9510.9960.8950.9710.9470.5710.7710.6370.660
GaussianShader [9]0.9300.9540.9550.9950.9000.9690.9510.5760.7280.6370.647
3GiS [28]0.9300.9330.9510.9960.9090.9720.9480.5570.7890.6260.657
3DGS-DR [40]0.9620.9790.9710.9970.9420.9760.9710.5700.7730.6350.659
Ours0.9610.9810.9750.9970.9500.9730.9730.6070.7830.6560.682
LPIPS↓
Ref-NeRF [29]0.0510.3070.0870.0130.1180.0820.1100.2510.2340.2310.239
NeRO [17]0.0740.0940.0500.0120.0890.1100.072————
ENVIDR [16]0.0490.0670.0510.0110.1160.1390.0720.2630.3870.3450.332
3DGS [11]0.0470.1610.0790.0070.1260.0780.0830.2480.2060.2370.230
GaussianShader [9]0.0450.1480.0880.0120.1110.0850.0820.2740.2590.2390.257
3GiS [28]0.0450.1660.0730.0060.0980.0770.0770.2520.1900.2510.231
3DGS-DR [40]0.0340.1040.0500.0060.0830.0760.0590.2510.2080.2490.236
Ours0.0340.0980.0450.0060.0700.0820.0560.2420.1960.2360.224
+ +![](images/7f6d702b8357e77c806dffc545426ae73d14d33b6f02991827292a18cef29d0e.jpg) +Figure 6. Comparison results on refractive scenes. Normal reconstruction and rendering results on real scenes from Glass & Ball [3]. Our method performs significantly better than 3DGS-DR [40] and 3iGS [28]. + +tive objects rendering; SDF-based methods including ENVIDR [16] and NeRO [17], top-performing implicit methods for reconstructing reflective objects; and Gaussian-based methods such as GaussianShader [9], 3iGS [28] and 3DGS-DR [40]. We trained these models based on their public codes and configurations. Evaluation metrics for rendering quality include PSNR, SSIM [32], and LPIPS [44]. Additionally, we use Mean Angular Error in degrees $(\mathrm{MAE}^{\circ})$ to evaluate the normal accuracy. + +# 6.3. Implementation Details + +All experiments are conducted on a single Tesla V100 GPU with 32GB of VRAM. The parameters to be optimized include the MLP $f_{\Theta}$ , the mipmap $\mathcal{M}$ and each 2D Gaussian's parameters (e.g. the feature $\mathbf{f}_i \in \mathbb{R}^4$ ). Following the approach in [8], we optimize these parameters using differ + +Table 1. Quantitative NVS comparisons on Shiny Blender and Shiny Real datasets [29]. Our method is comparable with both Gaussian-based methods and prior reflective object reconstruction methods. 'Gardenspheres' is abbreviated as 'Garden'. + +
NeRF SyntheticGlossy SyntheticShinyB
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓MAE°↓
Ref-NeRF [29]31.290.9470.05827.500.9270.10018.38
ENVIDR [16]28.130.9530.06829.580.9520.0574.61
3DGS [11]33.300.9690.03026.500.9170.092—
GShader [9]31.480.9600.04227.540.9220.08710.93
3iGS [28]33.600.9700.02926.390.9130.08915.47
3DGS-DR [40]31.020.9620.04729.780.9540.0572.43
GS-ROR [47]———29.700.956—7.23
Ours33.200.9660.03630.590.9570.0582.21
+ +Table 2. Quantitative NVS comparisons on NeRF Synthetic [20] and Glossy Synthetic [17] datasets. Normal reconstruction quality on the Shiny Blender (ShinyB) [29] dataset evaluated by MAE°. GaussianShader [9] is abbreviated as GShader. + +entiable splatting and gradient-based backpropagation. Optimization was performed over 30,000 iterations using the Adam optimizer [12]. We implement our Sph-Mip using PyTorch [23] framework, and employ the Nvdiffrast [14] library for efficient mipmap querying. The shape of the base level of the mipmap $\mathcal{M}^{L_0}$ in Sph-Mip encoding is empirically set to $H_{\mathcal{M}} = 512, W_{\mathcal{M}} = 1024, C = 16$ , and the number of levels is $N = 9$ . For our implicit representation of the specular color prediction, we use a lightweight MLP with 1 hidden layers of size 256. We use the ReLU activation function. We propose to train our model with the same loss function $\mathcal{L}$ as 2DGS [8]. + +# 6.4. Comparisons + +Quantitative results on synthetic datasets are reported in Tab. 1 and Tab. 2, where high-quality reflection modeling relies on accurate normal estimation, as shown in Fig. 4. Furthermore, we report the training and rendering speeds (tested) of our model on the same hardware in Tab. 4, comparing it with existing Gaussian-based methods. Our method achieves a balance between quality and training speed. Although the speed of our model is not as fast as 3DGS [11], it remains competitive and achieves real-time rendering speeds. + +To demonstrate the effectiveness of our method in real-world scenes, rather than just small objects, we evaluated our renderings on the Shiny Real dataset from Ref-NeRF [29] as shown in Tab. 1 and Fig. 5. Furthermore, the qualitative results in Fig. 6 show that for real-world scenes with refractive objects, our model outperforms 3iGS [28] and 3DGS-DR [40] on the Glass & Ball dataset from Eikonal Fields [3]. + +# 6.5. Ablation Studies + +We now perform ablation studies on the Shiny Blender [29] and NeRF Synthetic [20] datasets. Tab. 3 reports quantitative results for deferred shading, Sph-Mip encoding, and directional factorization. Fig. 7 shows ablation comparisons for novel view synthesis and surface reconstruction. + +![](images/9dd84c979f846a70bd1a6e0baac35ab59c52b3cd6090e4517e928813cec253a0.jpg) +Figure 7. Qualitative ablation on the 'Gardenspheres' scene [29]. Using the G-buffer instead of Sph-Mip (i.e., w/o Sph-Mip) or without deferred shading (i.e., w/o DS), sharp details, such as tree branches reflected in the sphere, are not accurately reconstructed. It is necessary to use multi-level spherical feature grid strategies (i.e., w/o mipmap), otherwise rough surfaces will fail to be reconstructed and artifacts will appear during rendering. Additionally, directional factorization (i.e., w/o $\mathbf{K} \otimes \mathbf{S}$ ) is essential for modeling near-field inter-reflections. + +
PSNR↑SSIM↑LPIPS↓MAE°↓
w/o Sph-Mip29.950.9430.0903.61
w/o mipmap30.120.9450.0915.12
w/o DS31.790.9570.0622.57
w/o K⊗S33.370.9660.0512.38
Ours34.000.9690.0462.21
+ +Sph-Mip. We first analyze the effect of the Sph-Mip by directly feeding G-buffer components to the decoding MLP: $f_{\Theta}(\mathbf{M}, \mathbf{N}, \mathbf{d})$ , where $\mathbf{d} \in \mathbb{R}^{H \times W \times 3}$ is the view directions. As shown in Fig. 7 and Tab. 3, compared to directly using the G-buffer as input, our Sph-Mip encoding effectively models high-frequency view-dependent appearance. + +Mipmap. To verify the effectiveness of the multi-level spherical feature grid strategies, we replace the mipmap $\mathcal{M}$ with a 2D feature map of the same shape as the base level of the mipmap $\mathcal{M}^{L_0}$ (i.e., w/o mipmap). Fig. 7 shows that the method without mipmap fails to recover accurate geometry and produces artifacts when rendering rough surfaces, primarily because real-world scenes typically do not consist of a single material. + +Deferred Shading. We ablate deferred shading (i.e., w/o DS) by applying the standard volume rendering. As shown in Fig. 7, deferred shading provides more accurate specular reflections and better surface reconstruction quality. + +Table 3. Ablation study of our model on the synthetic datasets. + +
Rendering SpeedTrain Time
3DGS [11]1.00×1.00×
GaussianShader [9]0.17×11.05×
3iGS [28]0.44×2.07×
3DGS-DR [40]0.93×3.25×
Ours0.37×2.63×
+ +Table 4. Comparisons on training and rendering (test) speed. We consider the 3DGS [11] as a baseline and normalise the speed. With our GPU device, 3DGS takes about $14.5\mathrm{min}$ for training, and achieves 125 FPS for rendering. + +Directional Factorization. We study the proposed directional factorization (i.e., w/o $\mathbf{K} \otimes \mathbf{S}$ ). We directly used the directional feature $\mathbf{S}$ as input to the shader: $f_{\Theta}(\mathbf{S})$ . As shown in Fig. 7, inter-reflections cannot be reconstructed using only the far-field feature $\mathbf{S}$ . + +# 7. Conclusion + +We have presented Ref-GS to address view-dependent effects in 2D Gaussian Splatting, enabling photorealistic rendering and precise geometry recovery for open-world scenes. Our technical contribution is a novel deferred Gaussian rendering pipeline that integrates a spherical Mip-grid to efficiently represent surface roughness and employs a geometry-lighting factorization to explicitly connect geometry and lighting through the vector outer product. + +# Acknowledgements + +This work is supported by the National Natural Science Foundation of China (NSFC No.62272184) and "Pioneer" and "Leading Goose" R&D Program of Zhejiang (No.2024C01161). The computation is completed in the HPC Platform of Huazhong University of Science and Technology. + +# References + +[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Proceedings of the IEEE/CVF international conference on computer vision, pages 5855–5864, 2021. 2 +[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. 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To tackle this issue, we propose RefPose, an innovative approach to object pose estimation that leverages a reference image and geometric correspondence as guidance. RefPose first predicts an initial pose by using object templates to render the reference image and establish the geometric correspondence needed for the refinement stage. During the refinement stage, RefPose estimates the geometric correspondence of the query based on the generated references and iteratively refines the pose through a render-and-compare approach. To enhance this estimation, we introduce a correlation volume-guided attention mechanism that effectively captures correlations between the query and reference images. Unlike traditional methods that depend on pre-defined object models, RefPose dynamically adapts to new object shapes by leveraging a reference image and geometric correspondence. This results in robust performance across previously unseen objects. Extensive evaluation on the BOP benchmark datasets shows that RefPose achieves state-of-the-art results while maintaining a competitive runtime. + +# 1. Introduction + +6D pose estimation is a key aspect of computer vision and robotics, focusing on accurately predicting an object's position (3D translation) and orientation (3D rotation) in a given scene. This task is essential for a range of applications, such as autonomous driving [5, 23], augmented reality (AR) [25, 38], and robotic manipulation [2, 36]. Despite significant research efforts in this field, estimating the 6D pose of previously unseen objects remains a considerable challenge. This challenge largely stems from the lack of prior knowledge and the limited generalization capabilities of existing models when faced with new objects [12]. + +![](images/81cf1590b2351797ec395fa45ae77256b5112c8089e77a600262a95c2a3c852d.jpg) +Figure 1. Comparison between conventional methods and proposed method (RefPose). In contrast to conventional methods, RefPose leverages a reference image and geometric correspondence generated from the estimated pose in the coarse pose estimation stage to guide the query's geometric correspondence and pose estimation. + +In instance-level object pose estimation, various methods rely on geometric correspondence as a crucial element for achieving accurate pose estimation [3, 7, 11, 19, 34, 35, 42, 45, 47]. Geometric correspondence refers to identifying the 3D model points that correspond to each pixel in a 2D image, which provides essential information for determining an object's pose. Typically, this correspondence is estimated using deep learning networks and is subsequently used to infer the object's pose through methods such as PnP/RANSAC [16] or neural network regression. However, these techniques face challenges in accurately estimating 2D-3D geometric correspondences for unseen objects, mainly due to their reliance on pre-defined object models and the limited generalization capabilities of the correspondence estimation network. + +To address these limitations, we propose RefPose, a + +novel approach to object pose estimation for unseen objects. As illustrated in Fig. 1, RefPose predicts the geometric correspondence of the query object by leveraging a reference image and geometric correspondence as guidance. This guidance provides crucial geometric information about the target object, allowing the network to avoid reliance on shape priors learned from a fixed set of objects during training. FoundPose [32] also estimates correspondences using pre-rendered templates through patch-wise matching, similar to our approach. However, these pre-rendered templates often lack proper alignment with the query image, leading to inaccurate matches and insufficient geometric information. To overcome this, we perform coarse pose estimation by processing the pre-rendered templates to obtain an initial pose, which is then used to render a reference image closely aligned with the query image, providing more reliable information. Additionally, rather than relying solely on direct matching, we carefully design a network that enhances correspondence estimation by integrating information from both the reference image and geometric correspondence guidance. + +Specifically, in the coarse pose estimation stage, we select multiple templates from a set of pre-rendered templates for the target object. This selection is based on the accuracy of optical flow predictions made by the optical flow network [43], which will later help us estimate the geometric correspondence for the query object. We then use these selected templates in a warping-based approach that employs medoid voting to enhance robustness against outliers, yielding a reliable coarse geometric correspondence for the query object. Subsequently, we obtain an initial pose using PnP/RANSAC and render references accordingly. With synthesized reference guidance, we estimate a more reliable and precise geometric correspondence for the query during the refinement stage. To improve this estimation, we introduce a novel attention mechanism that leverages a correlation volume from the optical flow network, effectively integrating reference information. The estimated geometric correspondence for the query then serves as a fixed basis for further refining the pose. We iteratively update the initial pose by estimating the relative pose in comparison to the reference geometric correspondence. At each iteration, we re-render the reference geometric correspondence using the updated pose and compare it to the fixed geometric correspondence of the query. This render-and-compare process is repeated until we achieve an accurate final pose. + +We assess our method on seven key datasets from the BOP benchmark [12]. Our findings indicate that RefPose achieves superior accuracy in both coarse pose estimation and final pose accuracy compared to state-of-the-art methods. By optimizing runtime in the pose refinement stage, RefPose not only delivers the highest accuracy across all methods but also maintains competitive speed. + +Our contributions are as follows: + +- We propose RefPose, a method that leverages a reference image and geometric correspondence to guide the estimation of the query's geometric correspondence and pose, eliminating the need for shape priors learned from predefined object sets. +- We present a classifier based on optical flow for improved template selection. Additionally, we introduce a warping-based geometry estimation method that utilizes medoid voting to enhance robustness against outliers, leading to more accurate coarse pose estimates. +- We propose a correlation volume-guided attention mechanism, improving the model's ability to focus on relevant regions in a reference image corresponding to the query image. +- We achieve state-of-the-art results on the BOP benchmark datasets while maintaining competitive runtime. + +# 2. Related work + +Geometric correspondence-based pose estimation. In instance-level object pose estimation, where training and testing are performed within a fixed set of objects, a common strategy is to utilize 2D-3D geometric correspondence. Most methods follow a two-step process: they first establish 2D-3D correspondences from an RGB image and then determine the pose using a RANSAC-based PnP algorithm or a neural network. Early studies [37, 44] employed the 3D bounding box corners of the object as keypoints, focusing on identifying the projected positions of these points in the image. For more robust and precise pose estimation, recent research [3, 7, 11, 19, 35, 45, 47] has shifted toward establishing dense correspondence maps rather than relying on sparse points. Consequently, designing and training deep learning networks that can accurately predict geometric correspondence maps is essential. However, these networks often struggle with generalization, especially when applied to unseen objects outside the fixed training set. Some models [20, 42] even require separate network models for each object. Therefore, to effectively estimate the geometric correspondence of the query object, we train the network using not only the query image but also a reference image and its geometric correspondence, providing reliable and valuable contextual information. + +Most methods use 3D coordinates as the geometric correspondence; however, some approaches modify these coordinates to achieve finer correspondence estimation. For example, [20, 42] adopts a binary code representation, while [34] applies positional encoding, as seen in NeRF [27], to improve performance. Inspired by these methods, we also employ a positionally encoded representation for geometric correspondence during the refinement stage. + +Unseen object pose estimation. Some studies focus on + +![](images/71855550a12ad08bdb55f57ecb634d4b27300d35b4f3581fb261e42ae12cbeff.jpg) +Figure 2. Overview of the RefPose pipeline. Given an input RGB image, the target object is first detected, cropped, and resized to create the query image, $I_{q}$ . In Stage 1: Coarse Pose Estimation, a set of templates, $S$ , is selected from the pre-rendered template set, $\mathcal{T}$ , to estimate an initial pose, $P_{0}$ , for the query object. In Stage 2: Pose Refinement, the query's geometric correspondence, $G_{q}^{pos}$ , is estimated using the rendered reference image, $I_{r}$ , and geometric correspondence, $G_{r}^{pos}$ . The initial pose, $P_{0}$ , is iteratively refined by estimating the relative pose, $\Delta P$ , between the query and reference. At each iteration, $G_{r}^{pos}$ is re-rendered to align with the updated pose, leading to an accurate final pose estimate. + +category-level pose estimation [6, 17, 24, 46], utilizing shared geometric traits within a category to broaden the range of identifiable target objects. However, these methods face generalization limitations, making it challenging to unseen object categories in real-world settings. To address these limitations, recent research has explored unseen object pose estimation, which aims to accurately predict poses for objects not encountered during training. + +MegaPose [15] combines a render-and-compare refiner with a classifier that assesses whether the refiner can correct given pose errors, achieving strong generalization by training on a large synthetic dataset. GigaPose [30] leverages discriminative templates to handle out-of-plane rotations and uses patch correspondences for estimating remaining pose parameters, resulting in improvements in both speed and segmentation robustness. GenFlow [28] addresses the accuracy-scalability trade-off by directly leveraging the target object's shape through optical flow prediction. GenFlow iteratively refines poses by leveraging a 3D shape constraint alongside a multi-scale, coarse-to-fine refinement process. FoundPose [32] establishes 2D-3D correspondences by matching patch descriptors from a self-supervised DINOv2 [31] model between the image and prerendered templates, integrating these descriptors into a bag-of-words model for more efficient template retrieval. + +FoundPose is particularly relevant to our approach in that it also aims to estimate correspondences to assist pose estimation. However, FoundPose derives correspondences by performing patch-wise matching with pre-rendered templates, which may result in inaccuracies due to misalignment with the query image. In contrast, our method begins with a coarse pose estimation to establish an initial + +pose, which we then refine using a rendered reference image closely aligned with the query object. Additionally, rather than relying solely on direct matching, we design a geometry estimation network that improves correspondence estimation by effectively integrating information from the reference image and geometric correspondence guidance. + +# 3. Method + +This section introduces RefPose, a novel approach to object pose estimation for unseen objects. We start with a brief overview (Sec. 3.1), followed by a detailed explanation of the initial pose estimation process used to generate a reference (Sec. 3.2). Finally, we describe how this reference information is leveraged to estimate the query's geometric correspondence and iteratively refine the pose to reach the final result (Sec. 3.3). + +# 3.1. Overview + +RefPose follows a multi-stage pipeline, similar to other recent methods [15, 28, 30, 32], comprising object detection/segmentation, coarse pose estimation, and pose refinement. Following these methods, we use an off-the-shelf model [29] for object detection and segmentation to preprocess the input image. + +Fig. 2 illustrates the overall pipeline of RefPose. Starting with an RGB image, the target object is detected, cropped, and resized to $256 \times 256$ to create the query image, $I_{q}$ . In the coarse pose estimation stage, a classification network selects a set of templates, $\mathcal{S} = \{S_1, S_2, \dots, S_k\}$ , from a pre-rendered template set, $\mathcal{T} = \{T_1, T_2, \dots, T_N\}$ . This selected set, $\mathcal{S}$ , is then used to estimate the geometric correspondence of the query, $G_{q}$ , providing an initial pose esti + +![](images/58f1c0b0651fac8a65214ad2ab3a1f100498294813cf0c4919d20a8afea0cbb6.jpg) +Figure 3. Templates selection using a classification network. The classification network scores pre-rendered templates based on how well optical flow can be estimated between each template and the query image. During inference, these scores are used to select the top- $k$ templates. The classifier leverages a frozen feature encoder from a pre-trained optical flow network, with only the classification head trained. + +mate, $P_0$ . Using $P_0$ , we render a reference image, $I_r$ , and a geometric correspondence, $G_r^{pos}$ , that are closely aligned with the query. Here, $G_r^{pos}$ represents the geometric correspondence with positional encoding applied. In the refinement stage, this reference information is then used to estimate a more accurate geometric correspondence for the query, $G_q^{pos}$ . Finally, the relative pose, $\Delta P$ , between the query and reference is iteratively refined through a render-and-compare approach to reach a final pose estimate. + +# 3.2. Coarse pose estimation + +Templates selection. We start by randomly sampling poses and rendering images along with geometric correspondences for each pose based on the given 3D model. The geometric correspondence $G \in \mathbb{R}^{h \times w \times 3}$ represents a dense map that indicates the corresponding 3D model point for each pixel. For simplicity, we refer to geometric correspondence as "geometry" throughout this paper. Inspired by MegaPose [15], we select a set of multiple templates, $S$ , using a classification network. However, unlike MegaPose, where the classifier is trained based on the refining capability of its refiner, we introduce a new training criterion. Since our subsequent pose estimation stage relies on optical flow, we train the classifier to assess the accuracy of optical + +![](images/6195ed730e949297d3d787048ae4074d9d8a2ed88adf3a395f24705b3cafecc9.jpg) +Figure 4. Warping-based geometry estimation process. The optical flow between each template image $I_{S}$ in the selected set $S$ and the query image $I_{q}$ is used to warp the corresponding template geometries $G_{S}$ , generating candidate geometries for the query, $G_{q}$ . A pixel-wise voting scheme refines these candidates, and the resulting 2D-3D correspondences in $G_{q}$ are then applied with PnP/RANSAC to estimate the initial pose $P_{0}$ . + +flow estimation between each template image, $I_{T}$ , and the query image, $I_{q}$ . + +During training, we utilize a pre-trained optical flow network [43] to estimate the optical flow between $I_{q}$ and each template image in $\mathcal{T}$ . Positive and negative pairs are identified by comparing the predicted flow with the ground truth flow, which serves as labels for training the classifier. Additionally, rather than designing and training a new feature encoder for the classification network, we leverage the feature encoder from the optical flow network to enhance both the classifier's performance and coherence with subsequent stages. Specifically, as in RAFT, we extract the correlation volume and context features, then attach a simple CNN as the classification head to complete the classifier. The classifier is trained using Binary Cross-Entropy (BCE) Loss [40]. During inference, the classifier ranks template images from the set $\mathcal{T}$ , and we select the top- $k$ templates based on the predicted scores. The classifier's structure and training and inference processes are illustrated in Fig. 3. + +Warping-based geometry estimation. To predict an initial pose $P_0$ , we estimate the query geometry $G_{q}$ based on a set of selected templates $S$ . First, we calculate the optical flow between each template image $I_{S}$ and the query image $I_{q}$ , then warp the template geometries $G_{S}$ accordingly. These warped geometries serve as candidates for $G_{q}$ . However, due to potential inconsistencies and inaccuracies in the optical flow estimated from each template, these candidates may indicate different 3D points for the same query pixel. To address this, we employ a voting scheme to select a single 3D point per pixel. PFA [13] follows a similar approach + +by aggregating multiple optical flows from different templates to estimate the 2D-3D correspondences. However, it performs this aggregation without explicitly addressing the inconsistencies and inaccuracies, which can lead to unreliable correspondences. In contrast, our method employs a more robust medoid-based voting scheme, where the most representative 3D point per pixel is selected rather than aggregating all candidates indiscriminately. This approach ensures that errors in optical flow estimation do not adversely affect the final result, leading to a more accurate and stable coarse pose estimation. Finally, based on the established 2D-3D correspondences in $G_{q}$ , we apply the PnP/RANSAC algorithm to estimate the pose $P_{0}$ . The overall process is illustrated in Fig. 4. + +# 3.3. Pose refinement + +Using the initial pose $P_0$ obtained from the coarse pose estimation stage, we render a single reference image $I_r$ and geometry $G_r^{pos}$ that are more closely aligned with the query image $I_q$ than the previously selected templates in $S$ . Rather than using raw 3D coordinates, we apply positional encoding to the 3D coordinates of $G$ to enrich the geometry representation, thereby improving estimation accuracy [34]. This encoding results in a representation $G^{pos} \in \mathbb{R}^{h \times w \times 6N_{freq}}$ , where $N_{freq}$ denotes the frequency bands used for encoding [27]. + +Correlation volume-guided attention mechanism. Accurately retrieving relevant geometric information from the reference geometry $G_{r}^{pos}$ requires precise pixel-level correspondence between the query image $I_{q}$ and the reference image $I_{r}$ . To achieve this, we introduce a correlation volume-guided attention mechanism. In this setup, the query image $I_{q}$ serves as the query, the reference image $I_{r}$ acts as the key, and the reference geometry $G_{r}^{pos}$ is treated as the value. The mechanism computes attention weights based on the similarity between the query $(I_{q})$ and the key $(I_{r})$ , enabling the extraction of relevant features from the value $(G_{r}^{pos})$ . + +In contrast to vanilla attention mechanisms that implicitly learn relevance, our approach uses explicit pixel-level correspondence information, as both the query image $I_{q}$ and reference image $I_{r}$ represent the same object from different viewpoints. We obtain the attention weights by applying a softmax operation to the correlation volume from the optical flow network, which encodes pixel-level similarities between $I_{q}$ and $I_{r}$ . By applying these weights to the reference geometry features $G_{r}^{pos}$ , we retrieve highly relevant geometric information, facilitating accurate correspondence estimation for improved pose refinement. + +Geometry estimation network. Our geometry estimation network processes the query image $I_{q}$ , reference image $I_{r}$ , and reference geometry $G_{r}^{pos}$ as inputs and outputs the query geometry $G_{q}^{pos}$ . To capture multi-scale features ef + +![](images/d59c7f2b86c3499f6d477ac858013c922f24777c62eab652fa5fe0d1e2007092.jpg) +Figure 5. Architecture of the geometry estimation network. The network takes the query image $I_{q}$ , reference image $I_{r}$ , and reference geometry $G_{r}^{pos}$ as inputs to estimate the query geometry $G_{q}^{pos}$ . A correlation volume-guided attention mechanism is applied at each level of the U-Net to effectively integrate these inputs. The geo head and mask head output a low-resolution geometry map and mask, which are then refined through convex upsampling to produce the final high-resolution geometry $G_{q}^{pos}$ . + +fectively, we employ a U-Net structure [39], with correlation volume-guided attention mechanisms applied at each level to incorporate reference information. As features are downsampled within the U-Net, the correlation volume is correspondingly downsampled. The U-Net concludes with two heads: a geo head, which estimates geometry at an 8x downsampled resolution, and a mask head, which predicts an up-mask for convex upsampling. Following RAFT [43], convex upsampling is applied to reconstruct $G_{q}^{pos}$ at the original resolution, providing higher fidelity than bilinear upsampling. The complete network architecture is illustrated in Fig. 5. + +The network is optimized by minimizing the $\mathcal{L}_1$ loss, which measures the difference between the predicted and ground truth geometry: + +$$ +\mathcal {L} _ {\text {g e o}} = \left\| \bar {G} _ {q} ^ {\text {p o s}} - G _ {q} ^ {\text {p o s}} \right\| _ {1}, \tag {1} +$$ + +where $\bar{G}_q^{pos}$ is the ground truth geometry and $G_{q}^{pos}$ is the predicted geometry. + +Iterative pose refinement. The estimated query geometry $G_{q}^{pos}$ enables iterative pose refinement through a render-and-compare approach [14, 18, 33]. Initially, a relative pose $\Delta P$ is estimated between $G_{q}^{pos}$ and the reference geometry $G_{r}^{pos}$ , updating the initial pose $P_{0}$ . With each update, a new reference geometry is rendered and compared to the fixed query geometry $G_{q}^{pos}$ , progressively refining the pose. This iterative process continues until the final pose is accurately determined. + +The relative pose estimator, based on a CNN, is trained using sequence loss [43], which is inspired by SCFlow [10], to improve learning efficiency and ensure consistent prediction quality across iterations. The sequence loss, $\mathcal{L}_{seq}$ , is defined as follows: + +$$ +\mathcal {L} _ {\text {s e q}} = \sum_ {m = 1} ^ {M} \gamma^ {M - m} \mathcal {L} _ {\text {p o s e}} ^ {(m)}, \tag {2} +$$ + +where $M$ denotes the total number of refinement iterations, $\gamma$ is an exponential weighting factor, and $\mathcal{L}_{\text{pose}}^{(m)}$ represents the pose loss at each iteration $m$ . + +After updating the reference pose, we compare it with the ground truth pose to assess the refinement strategy. The pose loss $\mathcal{L}_{\text {pose }}$ , which measures this alignment, combines grid-matching and grid-distance loss functions [33], formulated as follows: + +$$ +\mathcal {L} _ {\text {p o s e}} = \| \bar {\mathcal {G}} - \mathcal {G} \| _ {2} + \| \| \bar {t} \| _ {2} - \| t \| _ {2} \| _ {1}, \tag {3} +$$ + +where $\bar{\mathcal{G}}$ and $\bar{t}$ are the ground truth grid and translation vectors, respectively, while $\mathcal{G}$ and $t$ are derived from the estimated pose. + +# 4. Experiment + +# 4.1. Experimental Setup + +Datasets. We train our model on the synthetic dataset, Google Scanned Objects (GSO) [9], as provided by [15]. This dataset contains nearly 1 million images representing 1,000 different object types. Although [15] also includes data from approximately 50,000 ShapeNet [4] objects, we opted to use only the GSO dataset due to computational and memory constraints. This choice is further supported by the higher-quality mesh models in the GSO dataset, which, as noted in [15], contribute more critically to model performance than ShapeNet's. For evaluation, we test our approach on the seven primary datasets in the BOP benchmark [12], including YCB-V, LM-O, T-LESS, TUD-L, ICBIN, ITODD, and HB. Our method relies solely on RGB images and 3D object models, without leveraging any depth information. + +Evaluation metrics. We follow the standard BOP evaluation protocol [12], which employs three core metrics: Visible Surface Discrepancy (VSD), Maximum Symmetry-Aware Surface Distance (MSSD), and Maximum Symmetry-Aware Projection Distance (MSPD). Overall performance, referred to as Average Recall (AR), is calculated by averaging the individual recall scores for each metric across a range of error thresholds. + +Implementation details. Our model is trained with the AdamW optimizer [21], using a batch size of 8 and a learning rate of 0.0001 for a total of 400k training steps. A cosine annealing scheduler [22] with a 10k step period is employed + +![](images/e48ef7406dd939f54a0a52d43f4f0e8bf285543caf032a4d61c6fd2d0fc9bd42.jpg) + +![](images/c61b1f4bc856e03e50d9f66d67f7d7720e4a63c13087bb2aab4ad0c9c56d8ee1.jpg) + +![](images/224f83fbd6e0deeb9262e8658c8d80f605f4ca57190d5c26eebfb254449b7644.jpg) + +![](images/6928b1b22652849de98ad590f129dc105bb58c6d31eb08504434cf0d06558054.jpg) + +![](images/0fa95d1be87930aacde6e2cd39b59e2280f975acf01bfbd7813f657ea8eca4d1.jpg) + +![](images/da0e224cdc96d77ba260fc6c92a66480427cb2b77260f8f8427070e7b9bc7512.jpg) + +![](images/80a3dba78901f649a4baf1abc5b42aec96efb0b930a7f055dd02f914ee4f1f8c.jpg) + +![](images/3257339fb654acf4979266836eef1fb98691d5e1e0cd0c2c421ba75e511479e5.jpg) + +![](images/60222c57ffb16ab033bb417dd86b151ddde29f17feee3f73498a92b646ee1a54.jpg) + +![](images/dfb8dd1bd23f69dd78b5fb11b6dfd5823b52ff031692dcff1c3a240592b59f23.jpg) + +![](images/3272aff8acb613cfc22da5e0448054157240513427c43bfd5e8d929c3e457b2f.jpg) +Ours + +![](images/d85227e61ab6a069e5709c51b3b86376f71e693cb836607abd7f94d1bd258af0.jpg) +FoundPose + +![](images/4840c5abfbaba84231f5087102be447dc853a14224773f15c0f2f0611c0f2013.jpg) +GigaPose + +![](images/9cdf92fdad832c9a0f4ce621b545a86987b7ac144cbf885bc863fbae0b6ba9e0.jpg) +GenFlow + +![](images/098e3c49cea479203dbbd0033bb8c571e71d6b4aa0e7ffa0f8fe897d0a07a60a.jpg) +MegaPose +Figure 6. Qualitative comparison of pose estimation results. We present a qualitative comparison of our method against other approaches, with the projected contours from the ground-truth pose shown in green and those from the predicted pose in blue. + +to adjust the learning rate. Both training and evaluation are conducted on an RTX-3090 GPU. For the optical flow network in RefPose, we use the large model of RAFT [43], which is pre-trained on the FlyingChairs [8] and FlyingThings3D [26] datasets and then fine-tuned on the GSO dataset for our specific application. In the pose refinement stage, we generate the geometry $G^{pos}$ using sine and cosine positional encoding with five frequency bands, following the approach in [34]. The number of pose refinement iterations, $M$ , is set to 5, balancing accuracy and runtime efficiency. + +# 4.2. Comparison with state-of-the-art methods + +Tab. 1 presents the results of our method on the BOP benchmark datasets. Except for OSOP [41], which uses its own detection model, all methods employ CNOS [29] as the detection/segmentation model to ensure a fair comparison. Our method achieves the best performance in both the coarse pose estimation and the refined results following the refinement stage. While our approach slightly underperforms the current state-of-the-art methods on LM-O, T-LESS, and ITODD, it achieves state-of-the-art results on the other datasets, with particularly notable improvements on YCB-V and HB. Overall, our method demonstrates the best performance across all datasets. Fig. 6 provides qualitative comparisons with existing methods, further illustrating the robustness of our approach. + +Table 1. Evaluation results on BOP benchmark datasets. The table reports Average Recall (AR) scores across the seven datasets in the BOP challenge, where higher AR scores indicate better performance. The best-performing method is highlighted in bold, and the second-best is underlined. The top section presents results from coarse pose estimation alone, while the bottom section displays results after applying the refinement stage. "MH" denotes MegaPose and GenFlow versions that incorporate a multi-hypotheses strategy in the refinement stage, and "featuremetric" refers to the refinement method introduced in FoundPose. + +
MethodRefinementYCB-VLM-OT-LESSTUD-LIC-BINITODDHBMeanRun-time
OSOP [41]-29.627.440.3------
ZS6D [1]-32.429.821.0------
MegaPose [15]-28.122.917.725.815.210.825.120.815.5s
GenFlow [28]-27.725.021.530.016.815.428.323.3.8s
GigaPose [30]-27.829.626.430.022.317.534.126.80.4s
FoundPose [32]-45.239.633.846.723.920.450.837.21.7s
RefPose (Ours)-50.035.838.148.523.121.549.838.13.1s
MegaPose [15]MegaPose60.149.947.765.336.731.565.450.917.0s
MegaPose [15]MegaPose, MH62.156.050.768.441.433.870.454.721.9s
MegaPose [15]RefPose (Ours)65.356.052.866.445.341.173.657.216.4s
GenFlow [28]GenFlow, MH63.356.352.368.445.339.573.957.020.8s
GigaPose [30]MegaPose63.255.754.158.045.037.669.354.72.3s
GigaPose [30]GenFlow, MH65.263.158.266.449.845.375.660.510.6s
FoundPose [32]MegaPose, MH + Featuremetric69.061.057.069.447.940.772.359.620.5s
RefPose (Ours)MegaPose63.756.351.165.843.741.471.856.34.6s
RefPose (Ours)RefPose (Ours)72.759.657.869.751.243.876.261.43.9s
+ +The 10th and 15th rows of Tab. 1 report results where our proposed coarse pose estimation and refinement methods are independently combined with MegaPose to assess their standalone effectiveness. A comparison among the 8th, 12th, and 15th rows shows that our coarse pose estimation achieves better results even when using the same refinement method as MegaPose. Additionally, comparing the 8th and 10th rows demonstrates that our refinement method is more effective even when applied to the coarse poses estimated by MegaPose. + +The reported runtime represents the average speed for processing all objects within a single image. Though our method takes slightly longer in the coarse pose estimation stage, it significantly reduces refinement time by minimizing the number of renderings and using a lightweight model. As a result, our method achieves superior performance with runtime comparable to other state-of-the-art approaches. + +# 4.3. Ablation study + +Number of pre-rendered templates. The results of the ablation study on the number of pre-rendered templates in the set $\mathcal{T}$ , represented by $N$ , are shown in Tab. 2. With only 64 templates, the sampled poses are too sparse across the object's orientation space, leading to reduced performance in pose estimation due to insufficient coverage of various possible object poses. Increasing to 128 templates provides a denser sampling, significantly enhancing query-template matching and improving performance. Using more than 128 templates yields only marginal improvements while increasing both memory and computational overhead. Additionally, a larger template set results in longer inference times, as more templates must be evaluated. Therefore, using 128 templates achieves an optimal balance between ef + +Table 2. Ablation study on the number of pre-rendered templates. The table presents AR scores, illustrating the impact of varying numbers of pre-rendered templates, $\mathcal{T}$ , on coarse pose estimates. + +
NYCB-VLM-OT-LESSTUD-LIC-BINITODDHBMean
6445.229.836.543.720.118.843.533.9
12850.035.838.148.523.121.549.838.1
25648.837.239.545.824.323.149.838.3
+ +Table 3. Ablation study on the number of selected templates. The table presents AR scores, showing the impact of varying numbers of selected templates, $S$ , on coarse pose estimates. + +
kYCB-VLM-OT-LESSTUD-LIC-BINITODDHBMean
142.631.028.840.118.818.140.831.5
246.837.234.043.119.818.846.535.2
450.035.838.148.523.121.549.838.1
850.029.836.444.521.719.951.036.2
+ +ficiency and performance. + +Number of selected templates. The results of our ablation study on the number of selected templates $S$ , denoted by $k$ , are shown in Tab. 3. Selecting four templates from the prerendered set $\mathcal{T}$ yields the best results, achieving a balance between diversity and alignment accuracy. Using fewer templates limits diversity, increasing the risk of alignment errors during warping-based geometry estimation if a template is poorly selected or if the optical flow is inaccurately estimated potentially, leading to inaccurate pose estimation. Conversely, selecting more than four templates raises the likelihood of including misaligned templates, which may reduce the effectiveness of the medoid-based voting stage in handling outliers. With too many templates, the medoid's robustness can be compromised, as it becomes more challenging to filter out misaligned correspondence effectively. + +Table 4. Ablation study on components in coarse pose estimation stage. This table presents AR scores for the coarse pose estimates. + +
SettingYCB-VLM-OT-LESSTUD-LIC-BINITODDHBMean
w/o Flow features46.834.233.247.122.320.945.835.8
w/o Medoid49.629.636.845.921.318.850.236.0
Ours50.035.838.148.523.121.549.838.1
+ +Table 5. Ablation study on components of the geometry estimation network in the pose refinement stage. This table presents AR scores for the pose refinement results. + +
SettingYCB-VLM-OT-LESSTUD-LIC-BINITODDHBMean
w/o P.E.69.357.157.068.448.339.573.959.1
w/o Convex.70.056.858.268.447.943.175.660.0
w/o C.G. atm.68.861.052.866.047.341.974.858.9
Ours72.759.657.869.751.243.876.261.4
+ +Thus, selecting four templates provides an effective balance, ensuring sufficient diversity while minimizing alignment errors, which is crucial for accurate geometry and pose estimation. + +Components in the coarse pose estimation stage. Tab. 4 presents the results of our ablation study on key components used in the coarse pose estimation stage. The first row evaluates the impact of using the feature encoder from the optical flow network as the classifier's feature encoder. This feature encoder outputs flow features, including the correlation volume and context feature, which provide rich cues related to optical flow, enhancing the classifier's accuracy in selecting templates. By directly leveraging the same encoder applied in the warping-based geometry estimation stage, consistency across stages is maintained, contributing to superior results. + +The "w/o Medoid" variant represents a model in which, during pixel-wise voting in the warping-based geometry estimation, the medoid is replaced with a simple average for selecting correspondences. Using the medoid rather than averaging mitigates the impact of outliers that may arise from imperfect optical flow estimations, leading to a more robust correspondence selection. This robustness directly translates to greater accuracy of the coarse pose estimation. Components of the geometry estimation network in the pose refinement stage. Tab. 5 presents the ablation study results on key components of the geometry estimation network within the pose refinement stage. The first row shows that applying positional encoding to the 3D coordinates, inspired by [34], improves performance over using raw 3D coordinates as geometric correspondence. Specifically, the "w/o P.E." variant, which omits positional encoding and directly uses 3D coordinates, shows lower accuracy. + +Additionally, estimating an up-mask and utilizing convex upsampling yield superior performance compared to bilinear upsampling, as indicated by the "w/o Convex." variant. Convex upsampling more effectively preserves spatial detail at the original resolution, leading to a closer alignment between the estimated geometry and the true geome + +![](images/31fff34a5b365fba398767415c5899c51bc9a08fd6d08d27b0dcabbbcbffe8f6.jpg) + +![](images/bcd927068fcb6714c7e2e51c83b17b13ec7cc82f19a975cfd128a5073a260091.jpg) + +![](images/c2efaa3e4f11bcf1372ed31d5b033187b6828acaaaedbfed3f62fde615a1f05c.jpg) +$I_{q}$ + +![](images/1640575223e02f2fe17d6b115b409e4f064da35c39642b26685012926424df0d.jpg) + +![](images/4c02814d7ef57677b9cc9a18531b41e5d90cd387689d785c4ad0f2d911046e76.jpg) + +![](images/c0b89c1446195c0eca4d0caf34e03f7325809b63541e8f03bbccab658c956346.jpg) +$I_{r}$ + +![](images/6c3add3106f8db701431bf6ff19bee6e01072658cceafaae0c6ccf7af0b1966c.jpg) + +![](images/3875e8e9529a74f75aae60989248b1c45f3ef9296afe3bc81d5ed44bd7f6c9e6.jpg) + +![](images/41d0004200b58a06ed2217f6677fa81aeca2787cbb8ac884bc5849d6cc6fb769.jpg) +C.G. Attn. + +![](images/a2b4b3f18e8b79f2711cea674263088445f6a9ce4d87108c93bddb92b051b6ec.jpg) + +![](images/f32b4ff9324c7b01bf968a83d3fa16b0f35c74e25c0b1561a717568d546d80bc.jpg) + +![](images/bdaa359e1bc6e156668ecaa9ded251f4369c48a8c44f2419ae84563704785495.jpg) +Vanilla Attn. +Figure 7. Visual comparison of attention mechanisms in the geometry estimation network. Each row shows a query image $I_{q}$ with a yellow dot marking the point of interest, the corresponding reference image $I_{r}$ , and the attention maps produced by the correlation volume-guided (C.G.) attention and vanilla attention. The C.G. attention accurately focuses on relevant regions in $I_{q}$ and $I_{r}$ , while vanilla attention lacks this precision. + +try of the object. + +Finally, the proposed correlation volume-guided (C.G.) attention mechanism outperforms vanilla attention, as demonstrated by the "w/o C.G. attn." variant, which replaces C.G.attention with vanilla attention. This result underscores the effectiveness of C.G. attention in accurately capturing relevant correspondences between the query and reference images. As illustrated in Fig. 7, C.G. attention maps exhibit a sharper focus on relevant regions in the reference image that correspond to points of interest in the query, while vanilla attention maps appear less precise. This comparison highlights the effectiveness of C.G. attention in establishing accurate correlations between the query and reference images. + +# 5. Conclusion + +In this paper, we have proposed RefPose, a two-stage method designed for enhanced accuracy and generalization in unseen object pose estimation. Starting with a coarse pose estimation using template selection and medoid-based voting, RefPose builds an initial pose, which is then used to assist the geometry estimation through a correlation volume-guided attention mechanism. This refined geometry for the query supports an iterative render-and-compare process, producing a precise final pose. Extensive experiments on the BOP benchmark demonstrate RefPose's strong performance and generalization ability, while ablation studies confirm the effectiveness of each component. RefPose advances adaptable and efficient solutions for 6D pose estimation in complex, real-world scenarios. + +Acknowledgements This work was supported by Samsung Electronics Co., Ltd.(No. 0423-20240056), 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)], and in part by the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University in 2025. + +# References + +[1] Philipp Ausserlechner, David Haberger, Stefan Thalhammer, Jean-Baptiste Weibel, and Markus Vincze. 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Currently, transformer-based methods are gaining increasing attention due to their elegant pipelines and superior predictions. However, these methods primarily focus on modeling the external relationships between scene features and query features through mask attention. They lack effective modeling of the internal relationships among scene features as well as between query features. In light of these disadvantages, we propose Relation3D: Enhancing Relation Modeling for Point Cloud Instance Segmentation. Specifically, we introduce an adaptive superpoint aggregation module and a contrastive learning-guided superpoint refinement module to better represent superpoint features (scene features) and leverage contrastive learning to guide the updates of these features. Furthermore, our relation-aware self-attention mechanism enhances the capabilities of modeling relationships between queries by incorporating positional and geometric relationships into the self-attention mechanism. Extensive experiments on the ScanNetV2, ScanNet++, ScanNet200 and S3DIS datasets demonstrate the superior performance of Relation3D. Code is available at this website. + +# 1. Introduction + +Point cloud instance segmentation aims to identify and segment multiple instances of specific object categories in 3D space. With the rapid development of fields such as robotic grasping [1], augmented reality [2, 3], 3D/4D reconstruction [4-8], and autonomous driving [9, 10], as well as the widespread application of LiDAR and depth sensor technologies [11, 12], point cloud instance segmentation has become a core technology for achieving efficient and accurate scene understanding. However, the unordered, sparse, and irregular nature of point cloud data, combined with the complex + +![](images/ade4367d0b4829c122096783f72bd978f179d79da69cbfd64ef75709b983fd74.jpg) +Figure 1. T-SNE visualization of the superpoint-level feature distributions on ScanNetV2 validation set. Different colors represent different instances. Our method highlights better inter-object diversity and intra-object similarity. + +![](images/be611796b251de8d207827e8de42d640360d6eac7c767b616e98fae5dadfcd48.jpg) + +
Point feature variation (Maft)1.8603 (Excessive)
SettingMaftOurs (Stage 1)Ours (Stage 2)Ours (Stage 3)
Lcont1.0570.72550.58410.5739
+ +Table 1. Excessive feature variation among points within the same supepoint and comparison of $L_{cont}$ in different settings. The experiment is conducted on ScanNetV2 validation set. $L_{cont}$ measures the consistency of superpoint features within the same instance and the differences between features of different instances. Detailed information about $L_{cont}$ can be found in Equation 5. Stage 1 represents the features output by ASAM, while stages 2 and 3 represent the features after refinement by CLSR. + +distribution of objects and the numerous categories in real-world applications, presents unique challenges for effective point cloud analysis. To tackle these challenges, early approaches mainly concentrated on accurately generating 3D bounding boxes (top-down) [13-15] or effectively grouping the points into instances with clustering algorithms (bottom-up) [16-18]. However, these methods have limitations: they either heavily rely on high-quality 3D bounding boxes, or require manual selection of geometric attributes. + +Recently, researchers start to focus on the design of transformer-based methods [19-23]. These methods adopt an encoder-decoder framework (end-to-end), where each object instance is represented by an instance query. The encoder is responsible for learning the point cloud scene features, while the transformer decoder [24] iteratively at + +tends to the point cloud scene features to learn the instance queries. Ultimately, the instance queries can directly generate the masks for all instances in parallel. Current mainstream transformer-based methods commonly use mask-attention [25] to effectively model the external relationships between scene features and query features. However, they lack effective modeling for the internal relationships among scene features and between query features. As shown in Table 1 and the left panel of Figure 1, we observe insufficient consistency in superpoint features within the same instances, inadequate differentiation between features of different instances, and excessive feature variation among points within the same superpoint. These erroneous relationships between scene features undoubtedly increase the difficulty of instance segmentation. Besides, the effectiveness of self-attention lies in its establishment of relationships between query features. However, simply computing similarity between query features is too implicit and lacks adequate spatial and geometric relationship modeling, whose importance has been demonstrated in [26-28]. Although position embeddings are used to guide self-attention in transformer-based methods, the spatial information position embeddings provide is typically imprecise. For instance, SPFormer's [20] position embeddings are learnable and lack concrete spatial meaning, and in methods like Mask3D [19], Maft [22], and QueryFormer [21], discrepancies exist between the positions indicated by position embeddings and the actual spatial locations of each query's corresponding mask. This limitation in conventional self-attention prevents effective integration of implicit relationship modeling with spatial and geometric relationship modeling. + +Based on the above discussion, we summarize two core issues that need to be considered and addressed in point cloud instance segmentation: 1) How to effectively model the relationships between scene features? Most previous methods use pooling operations to obtain superpoint features [20, 22], but this pooling operation introduces unsuitable features and blurs distinctive features when there are large feature differences between points within a superpoint. Therefore, we need a new way to model superpoint features to emphasizing the distinctive point features. Additionally, considering the significant feature differences between superpoints within the same instance, we need to introduce scene feature relation priors to guide the superpoint features and model better superpoint relationships. 2) How to better model the relationships between queries? Current self-attention designs rely on a simple computation of similarity between queries, but this implicit relationship modeling often requires extensive data and prolonged training to capture meaningful information. Therefore, integrating explicit spatial and geometric relationships is crucial, as it can refine attention focus areas and accelerate convergence. This motivates us to introduce instance-related biases to enhance the modeling of spatial + +and geometric relationships effectively. + +Inspired by the above discussion, we propose Relation3D: Enhancing Relation Modeling for Point Cloud Instance Segmentation, which includes an adaptive superpoint aggregation module (ASAM), a contrastive learning-guided superpoint refinement module (CLSR), and relation-aware self-attention (RSA). To address the first issue, we propose an adaptive superpoint aggregation module and a contrastive learning-guided superpoint refinement module. In the adaptive superpoint aggregation module, we adaptively calculate weights for all points within each superpoint, emphasizing distinctive point features while diminishing the influence of unsuitable features. In the contrastive learning-guided superpoint refinement module, we first adopt a dual-path structure in the decoder, with bidirectional interaction and alternating updates between query features and superpoint features. This design enhances the representation ability of superpoint features. Furthermore, to optimize the update direction of superpoint features, we introduce contrastive learning [29-31] to provide contrastive supervision for superpoint features, reinforcing the consistency of superpoint features within instances and the differences between features of different instances, as is shown in Figure 1. To address the second issue, in relation-aware self-attention, we first model the explicit relationships between queries. By obtaining the mask and its bounding box corresponding to each query, we can model the positional and geometric relationships between queries. Next, we embed these relationships into self-attention as embeddings. Through this approach, we achieve an effective integration of implicit relationship modeling with spatial and geometric relationship modeling. + +The main contributions of this paper are as follows: (i) We propose Relation3D: Enhancing Relation Modeling for Point Cloud Instance Segmentation, which achieves accurate and efficient point cloud instance segmentation predictions. (ii) The adaptive superpoint aggregation module and the contrastive learning-guided superpoint refinement module effectively enhances the consistency of superpoint features within instances and the differences between features of different instances. The relation-aware self-attention improves the relationship modeling capability between queries by incorporating the positional and geometric relationships into self-attention. (iii) Extensive experimental results on four standard benchmarks, ScanNetV2 [32], ScanNet++ [33], ScanNet200 [34], and S3DIS [35], show that our proposed model achieves superior performance compared to other transformer-based methods. + +# 2. Related Work + +Proposal-based Methods. Existing proposal-based methods are heavily influenced by the success of Mask R-CNN [36] for 2D instance segmentation. The core idea of these methods is to first extract 3D bounding boxes and then use a + +mask learning branch to predict the mask of each object within the boxes. GSPN [13] adopts an analysis-by-synthesis strategy to generate high-quality 3D proposals, refined by a region-based PointNet [37]. 3D-BoNet [15] employs PointNet++[38] for feature extraction from point clouds and applies Hungarian Matching[39] to generate 3D bounding boxes. These methods set high expectations for proposal quality. + +Grouping-based Methods. Grouping-based methods follow a bottom-up processing flow, first generating predictions for each point (such as semantic mapping and geometric displacement), and then grouping the points into instances based on these predicted attributes. PointGroup [40] segments objects on original and offset-shifted point clouds and employs ScoreNet for instance score prediction. SoftGroup [18] groups on soft semantic scores and uses a top-down refinement stage to refine the positive samples and suppress false positives. ISBNet [41] introduces a cluster-free approach utilizing instance-wise kernels. Recently, Spherical Mask [42] has addressed the low-quality outcomes of coarse-to-fine strategies by introducing a new alternative instance representation based on spherical coordinates. + +Transformer-based Methods. Following 2D instance segmentation techniques [24, 43, 44], in the 3D field, each object instance is represented as an instance query, with query features learned through a vanilla transformer decoder. Transformer-based methods require the encoder to finely encode the point cloud structure in complex scenes and use the attention mechanism in the decoder to continuously update the features of the instance queries, aiming to learn the complete structure of the foreground objects as much as possible. Mask3D [19] and SPFormer [20] are pioneering works utilizing the transformer framework for 3D instance segmentation, employing FPS and learnable queries, respectively, for query initialization. QueryFormer [21] and Maft [22] build on Mask3D [19] and SPFormer [20] by improving query distribution. However, these works have not thoroughly explored the importance of internal relationships between scene features and between query features. Our method aims to enhance relation modeling for both scene features and query features to achieve better instance segmentation. + +Relation modeling. Many 2D methods have demonstrated the importance of relation modeling. CORE [26] first leverages a vanilla relation block to model the relations among all text proposals and further enhances relational reasoning through instance-level sub-text discrimination in a contrastive manner. RE-DETR [28] incorporates relation modeling into component detection by introducing a learnable relation matrix to model class correlations. Relation-DETR [27] explores incorporating positional relation priors as attention biases to augment object detection. Our method is the first to explore the significance of relation priors in 3D instance segmentation. Through the adaptive superpoint ag + +gregation module and the contrastive learning-guided superpoint refinement module, we progressively enhance the relationships among scene features. Additionally, relation-aware self-attention improves the relationships among queries. + +# 3. Method + +# 3.1. Overview + +The goal of 3D instance segmentation is to determine the categories and binary masks of all foreground objects in the scene. The architecture of our method is illustrated in Figure 2. Assuming that the input point cloud has $N$ points, each point contains position $(x,y,z)$ , color $(r,g,b)$ and normal $(n_x,n_y,n_z)$ information. Initially, we utilize a Sparse UNet [45] to extract point-level feature $F\in \mathbb{R}^{N\times C}$ . Next, we perform adaptive superpoint aggregation module (Section 3.3) to acquire the superpoint-level features $F_{\mathrm{super}}\in \mathbb{R}^{M\times C}$ . Subsequently, we initialize several instance queries $Q\in \mathbb{R}^{K\times C}$ and input $Q$ and $F_{\mathrm{super}}$ into the transformer decoder. To improve the relationship modeling capability between queries, we propose the relation-aware self-attention (Section 3.5). To update the features of $F_{\mathrm{super}}$ , we design a superpoint refinement module (Section 3.4) in the decoder, which is also a cross attention operation. However, unlike conventional cross-attention, the scene features $F_{\mathrm{super}}$ act as the $\mathcal{Q}$ , while the instance queries $Q$ serve as the $\mathcal{K}$ and $\mathcal{V}$ . To guide the update direction of the superpoint features $F_{\mathrm{super}}$ , we implement a contrastive learning approach, which enhances the consistency of superpoint features within instances and increases the differences between features of different instances. + +# 3.2. Backbone + +We employ Sparse UNet [45] as the backbone for feature extraction, yielding features $F$ , which is consistent with SPFormer [20] and Maft [22]. Next, we aggregate the point-level features $F$ into superpoint-level features $F_{\mathrm{super}}$ via adaptive superpoint aggregation module, which will be introduced in the subsequent section. + +# 3.3. Adaptive Superpoint Aggregation Module + +The purpose of this module is to aggregate point-level features into superpoint-level features. To emphasize distinctive and meaningful point features while diminishing the influence of unsuitable features, we design the adaptive superpoint aggregation module, as shown in Figure 2 (b). Specifically, we first perform max-pooling and mean-pooling on the point-level features $F$ according to the pre-obtained superpoints, resulting in $F_{\mathrm{max}}$ and $F_{\mathrm{mean}}$ respectively. Next, we calculate the difference between the superpoint-level features and the original point-level features $F$ . We then utilize two non-shared weight MLPs to predict the corresponding + +![](images/3eed8d78028460f2119fb9dfbf272b390dc1c8c776d46968e885511858255503.jpg) + +![](images/5761eced05fa324be6f7a0732aa737dfac22f26c3a6cd94b46d3b3b39b2f77eb.jpg) +Figure 2. (a) The overall framework of our method Relation3D. (b) The details of our proposed adaptive superpoint aggregation module. (c) The details of our proposed relation-aware self-attention. + +![](images/f6635b14e7797d5c26452b19b37e1b11653375aa345f16ca8b4c55a691c4c463.jpg) + +weights, + +$$ +\mathcal {W} _ {\max } = \operatorname {M L P} _ {1} \left(F _ {\max } - F\right), \tag {1} +$$ + +$$ +\mathcal {W} _ {\text {m e a n}} = \mathrm {M L P} _ {2} \left(F _ {\text {m e a n}} - F\right). \tag {2} +$$ + +Getting the corresponding weights $\mathcal{W}_{\mathrm{max}}$ and $\mathcal{W}_{\mathrm{mean}}$ , we apply a softmax operation to them in each superpoint. In this way, we can obtain the contribution of each point to its corresponding superpoint. We then use these weights, which sum to 1 in each superpoint, to perform feature weighting on $F$ , resulting in $F_{\mathrm{max}}^{\prime}$ and $F_{\mathrm{mean}}^{\prime}$ . It's worth noting that the computation for each superpoint can be parallelized with point-wise MLP and torch-scatter extension library [46], so this superpoint-level aggregation is actually efficient. Finally, we concatenate $F_{\mathrm{max}}^{\prime}$ and $F_{\mathrm{mean}}^{\prime}$ to $[F_{\mathrm{max}}^{\prime}, F_{\mathrm{min}}^{\prime}]$ and input them into an MLP to reduce the $2C$ channels to $C$ , obtaining the final superpoint-level features $F_{\mathrm{super}} \in \mathbb{R}^{M \times C}$ . + +# 3.4. Contrastive Learning-guided Superpoint Refinement Module + +In the previous section, we introduce the adaptive superpoint aggregation module to emphasize distinctive point features within superpoints. Next, to further enhance the expressiveness of superpoints, we will leverage query features to update superpoint features within the transformer decoder. This design, in conjunction with the original mask attention, forms a dual-path architecture, enabling direct communication between query and superpoint features. This approach accelerates the convergence speed of the iterative updates. + +Specifically, the superpoint refinement module employs a cross-attention mechanism for feature interaction. Here, we use the superpoint-level features $F_{\mathrm{super}}$ as the $\mathcal{Q}$ in the cross attention, while the instance queries $Q$ serve as the $\mathcal{K}$ and $\mathcal{V}$ . The specific structure is illustrated in Figure 3. To + +![](images/26d656b4df6fd30c311c1fe8c1777971011d8ac6cd2431184a1e46b6285a668d.jpg) +Figure 3. The superpoint refinement module. Superpoint-level features $F_{\mathrm{super}}$ serve as the $\mathcal{Q}$ in cross-attention, while the instance queries $Q$ serve as the $\mathcal{K}$ and $\mathcal{V}$ . + +reduce computational and memory costs, we do not perform self-attention for self-updating $F_{\mathrm{super}}$ . Furthermore, the superpoint refinement module is not applied at every decoder layer. Instead, we perform the refinement of $F_{\mathrm{super}}$ every $r$ layers to reduce computational resource consumption. + +Furthermore, to guide the update direction, we have designed a contrastive learning mechanism, which constrains the consistency of superpoint features within the same instance and enlarge the differences between features of different instances. First, we can obtain the superpoint's relation prior $R_{\mathrm{super}}^{\mathrm{GT}}$ based on instance annotations. If the current scene has $M$ superpoints, then $R_{\mathrm{super}}^{\mathrm{GT}}$ is an $M \times M$ binary matrix defined as follows, + +$$ +R _ {\text {s u p e r}} ^ {\mathrm {G T}} (i, j) = \left\{ \begin{array}{l l} 1, & \text {i f i a n d j a r e i n t h e s a m e i n s t a n c e ;} \\ 0, & \text {o t h e r w i s e ,} \end{array} \right. \tag {3} +$$ + +where $i$ and $j$ represent two different superpoints. Next, we will compute the similarity between $F_{\mathrm{super}}$ features, defined + +as follows, + +$$ +\mathcal {S} = \operatorname {N o r m} \left(F _ {\text {s u p e r}}\right) @ \operatorname {N o r m} \left(F _ {\text {s u p e r}}\right) ^ {\mathrm {T}}. \tag {4} +$$ + +Here, $S$ represents the similarity matrix where each element quantifies the relationship between pairs of superpoint features. Finally, we will apply contrastive learning by comparing $S$ and $R_{\mathrm{super}}^{\mathrm{GT}}$ as follows, + +$$ +L _ {\text {c o n t}} = \mathrm {B C E} \left(\frac {\mathcal {S} + 1}{2}, R _ {\text {s u p e r}} ^ {\mathrm {G T}}\right), \tag {5} +$$ + +where $L_{cont}$ is the contrastive loss computed using binary cross-entropy (BCE). This loss will encourage the model to enhance the consistency of superpoint features within the same instance while reinforcing the differences between features of different instances. Notably, we also add this loss function after the adaptive superpoint aggregation module, which can guide ASAM to focus on meaningful features within the superpoint that help enhance the consistency of superpoint features within the same instance. + +# 3.5. Relation-aware Self-attention + +Previous methods use traditional self-attention to model the relationships between queries, where each query contains a content embedding and a position embedding. They first add the position embedding to the content embedding before computing the attention map. However, in most methods [19-22], the position embedding does not accurately match the actual position of the mask predicted by the corresponding query, leading to imprecise implicit modeling of positional relationships. More explanation can be found in the supplemental materials. Inspired by Relation-DETR [27], to enhance the self-attention's ability to model positional relationships and to improve geometric relationship modeling, we propose a relation-aware self-attention (RSA). + +To be specific, we calculate the binary mask $\mathbb{M}$ for each instance query $Q$ . Next, we calculate the bounding box (bbox) corresponding to each mask, including its center point and scale: $x,y,z,l,w,h$ . With the_bbox calculated, we compute the relative relationships between queries as follows, + +i. Positional Relative Relationship: + +$$ +\left[ \log \left(\frac {\left| x _ {i} - x _ {j} \right|}{l _ {i}} + 1\right), \log \left(\frac {\left| y _ {i} - y _ {j} \right|}{w _ {i}} + 1\right), \log \left(\frac {\left| z _ {i} - z _ {j} \right|}{h _ {i}} + 1\right) \right]; +$$ + +ii. Geometric Relative Relationship: + +$$ +\left[ \log \left(\frac {l _ {i}}{l _ {j}}\right), \log \left(\frac {w _ {i}}{w _ {j}}\right), \log \left(\frac {h _ {i}}{h _ {j}}\right) \right], +$$ + +where $i,j$ represents two different queries. Next, we concatenate these two sets of relationships to form an embedding, denoted as $\mathfrak{T}\in \mathbb{R}^{K\times K\times 6}$ . Then, following past methods, we use conventional sine-cosine encoding to increase the dimensionality of $\mathfrak{T}\in \mathbb{R}^{K\times K\times 6d}$ , + +$$ +\mathfrak {T} ^ {\prime} = \sin \cos (\mathfrak {T}). \tag {6} +$$ + +Finally, the embedding $\mathfrak{T}'$ undergoes a linear transformation to obtain $R_q \in \mathbb{R}^{K \times K \times \mathcal{H}}$ , where $\mathcal{H}$ denotes the number of attention heads. + +After obtaining $R_{q}$ , we incorporate it into the traditional self-attention mechanism. The specific formula is as follows, + +$$ +\operatorname {R S A} (Q) = \operatorname {S o f t m a x} \left(\frac {\mathcal {Q} \mathcal {K} ^ {T}}{\sqrt {\mathcal {C}}} + R _ {q}\right) \mathcal {V}. \tag {7} +$$ + +In this formulation, we have $\mathcal{Q} = QW_{q}$ , $\mathcal{K} = QW_{k}$ , and $\mathcal{V} = QW_{v}$ , where $W_{q}, W_{k}$ , and $W_{v}$ denote the linear transformation matrices for query, key, and value respectively. + +# 3.6. Model Training and Inference + +Apart from Maft's losses [22], our method includes an additional contrastive loss $L_{cont}$ , + +$$ +\begin{array}{l} L _ {a l l} = \lambda_ {1} L _ {c e} + \lambda_ {2} L _ {b c e} + \lambda_ {3} L _ {d i c e} \\ + \lambda_ {4} L _ {\text {c e n t e r}} + \lambda_ {5} L _ {\text {s c o r e}} + \lambda_ {6} L _ {\text {c o n t}}, \tag {6} \\ \end{array} +$$ + +where $\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5, \lambda_6$ are hyperparameters. During the model inference phase, we use the predictions from the final layer as the final output. In addition to the normal forward pass through the network, we also employ NMS [47] on the final output as a post-processing operation. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and Metrics. We conduct our experiments on ScanNetV2 [32], ScanNet++ [33], ScanNet200 [34], and S3DIS [35] datasets. ScanNetV2 comprises 1,613 scenes with 18 instance categories, of which 1,201 scenes are used for training, 312 for validation, and 100 for testing. ScanNet++ contains 460 high-resolution (sub-millimeter) indoor scenes with dense instance annotations across 84 unique instance categories. ScanNet200 uses the same point cloud data, but it enhances annotation diversity, covering 200 classes, 198 of which are instance classes. S3DIS is a large-scale indoor dataset collected from six different areas, containing 272 scenes with 13 instance categories. Following previous works [22], we use the scenes in Area 5 for validation and the remaining areas for training. AP@25 and AP@50 represent the average precision scores with IoU thresholds of $25\%$ and $50\%$ , respectively. mAP is the mean of all AP scores, calculated with IoU thresholds ranging from $50\%$ to $95\%$ in $5\%$ increments. On ScanNetV2, we report mAP, AP@50, and AP@25. Additionally, we report Box AP@50 and AP@25 results, as done in SoftGroup [18] and Maft [22]. For ScanNet200 and ScanNet++, we report mAP, AP@50, and AP@25. On S3DIS, we report AP@50 and AP@25. + +Implementation Details. We build our model on PyTorch framework [46] and train our model on a single + +
MethodScanNetV2 validationScanNetV2 test
mAPAP@50AP@25BoxAP@50BoxAP@25mAP
3D-SIS [14]/18.735.722.540.216.138.255.8
3D-MPA [16]35.351.972.449.264.235.561.173.7
DyCo3D [49]40.661.0/45.358.939.564.176.1
PointGroup [40]34.856.971.348.961.540.763.677.8
MaskGroup [50]42.063.374.0//43.466.479.2
OccuSeg [51]44.260.7///48.667.274.2
HAIS [52]43.564.475.653.164.345.769.980.3
SSTNet [17]49.464.37452.762.550.669.878.9
SoftGroup [18]45.867.678.959.471.650.476.186.5
DKNet [53]50.866.976.959.067.453.271.881.5
ISBNet [41]54.573.182.562.078.155.975.783.5
Spherical Mask [42]62.379.988.2//61.681.287.5
Mask3D [19]55.273.782.956.671.056.678.087.0
QueryFormer [21]56.574.283.361.773.458.378.787.4
SPFormer [20]56.373.982.9//54.977.085.1
Maft [22]58.475.984.563.973.557.877.4/
Maft‡ [22]59.976.5///59.678.686.0
Ours62.580.287.066.775.362.281.690.1
+ +RTX4090 with a batch size of 6 for 512 epochs. We employ Maft [22] as the baseline. We employ AdamW [48] as the optimizer and PolyLR as the scheduler, with a maximum learning rate of 0.0002. Point clouds are voxelized with a size of $0.02\mathrm{m}$ . For hyperparameters, we tune $K,r$ as 400, 3 respectively. $\lambda_{1},\lambda_{2},\lambda_{3},\lambda_{4},\lambda_{5},\lambda_{6}$ in Equation 8 are set as 0.5, 1, 1, 0.5, 0.5, 1. Since ScanNet++ and ScanNet200 have more categories and instances, we set $K$ as 500. All the other hyperparameters are the same for all datasets. + +# 4.2. Comparison with existing methods. + +Results on ScanNetV2. Table 2 reports the results on ScanNetV2 validation and hidden test set. Due to our focus on modeling the internal relationships between the scene features and between the queries, our approach outperforms other transformer-based methods, achieving an increase in mAP by 2.6, AP@50 by 3.7, AP@25 by 2.5, Box AP@50 by 2.8 and Box AP@25 by 1.8 in the validation set, and a rise in mAP by 2.6, AP@50 by 3.0 and AP@25 by 4.1 in the hidden test set. To vividly illustrate the differences between our method and others, we visualize the qualitative results in Figure 4. From the regions highlighted in red boxes, it is evident that our method can generate more accurate predictions. + +Results on ScanNet++. Table 3 presents the results on ScanNet++ validation and hidden test set. The notable performance enhancement underscores the efficacy of our method in handling denser point cloud scenes. + +Results on ScanNet200. Table 4 reports the results on ScanNet200 validation set. The significant performance improvement demonstrates the effectiveness of our method in handling complex and challenging scenes with a broader range of categories. + +Results on S3DIS. We evaluate our method on S3DIS us + +![](images/a7987d52113f422e7044feee2c91179a284a772660e1f3e1beeb69f77d257702.jpg) +Figure 4. Visualization of instance segmentation results on ScanNetV2 and ScanNet++ validation set. The red boxes highlight the key regions. + +Table 2. Comparison on ScanNetV2 validation and hidden test set. The second and third rows are the non-transformer-based and transformer-based methods, respectively. $\ddagger$ denotes using surface normal. + +
MethodScanNet++ validationScanNet++ test
mAPAP@50AP@25mAPAP@50AP@25
PointGroup [40]///8.914.621.0
HAIS [52]///12.119.929.5
SoftGroup [18]///16.729.738.9
Maft [22]23.132.639.720.931.340.4
Ours28.239.346.124.235.544.0
+ +Table 3. Comparison on ScanNet++ validation and hidden test set. ScanNet++ contains denser point cloud scenes and wider instance classes than ScanNetV2, with 84 distinct instance classes. + +
MethodScanNet200 validation
mAPAP@50AP@25
SPFormer [20]25.233.839.6
Mask3D [19]27.437.042.3
QueryFormer [21]28.137.143.4
Maft [22]29.238.243.3
Ours31.641.245.6
+ +Table 4. Comparison on ScanNet200 validation set. ScanNet200 employs the same point cloud data as ScanNetV2 but enhances more annotation diversity, with 198 instance classes. + +
MethodAP@50AP@25
PointGroup [40]57.8/
MaskGroup [50]65.0/
SoftGroup [18]66.1/
SSTNet [17]59.3/
SPFormer [20]66.8/
Mask3D [19]68.475.2
QueryFormer [21]69.9/
Maft [22]69.175.7
Spherical Mask [42]72.3/
Ours72.578.5
+ +Table 5. Comparison on S3DIS Area5. S3DIS contains 13 instance categories. + +ing Area 5 in Table 5. Our proposed method achieves better performance compared to previous methods, with gains in both AP@50 and AP@25, demonstrating the effectiveness and generalization of our method. + +
ASAMCLSRRSAmAPAP@50AP@25
[A]XXX59.877.485.4
[B]✓XX60.177.985.6
[C]X✓X60.978.786.2
[D]✓✓X61.578.886.3
[E]XX✓61.078.586.0
[F]✓✓✓62.580.287.0
+ +# 4.3. Ablation Studies + +Evaluation of the model with different designs. To further study the effectiveness of our designs, we conduct ablation studies on ScanNetV2 validation set. As shown in Table 6, [A] represents the baseline of our method, which is Maft [22] using surface normals and NMS. [B] demonstrates that with the assistance of ASAM, which aims to better aggregate point-level features into superpoint-level features and emphasize distinctive and meaningful point features while diminishing the influence of unsuitable features, there is a performance improvement: mAP increases by 0.3, AP@50 by 0.5, and AP@25 by 0.2. However, due to the lack of guidance from contrastive loss (introduced in the CLSR), the aggregation direction of superpoints cannot be effectively controlled as expected, so the performance gain is limited. To validate this point, as shown in Table 7, adding contrastive loss to guide ASAM leads to further performance enhancement. + +[C] shows that with the help of CLSR, we can interactively update superpoint features, and the use of contrastive learning guides the update direction by enforcing consistency of superpoint features within the same instance and increasing the difference between features of different instances. Compared to the baseline [A], the performance improves significantly, with mAP increasing by 1.1, AP@50 by 1.3, and AP@25 by 0.8. [D] combines ASAM and CLSR. In this design, not only the contrastive learning embedded within CLSR provides ASAM with a clear direction for feature aggregation but also ASAM can offer better-initialized superpoint features to CLSR. This synergistic design cooperates well and results in a $0.6\mathrm{mAP}$ improvement. [E] demonstrates the effectiveness of RSA, which enhances the self-attention mechanism's ability to model positional relationships and improves geometric relationship modeling. Compared to [A], RSA leads to an improvement of $1.2\mathrm{mAP}$ and $1.1\mathrm{AP}@50$ . Finally, in [F], we present the performance of the complete model, underscoring the essential roles played by each module in 3D instance segmentation. + +Importance of different designs. I: RSA incorporates explicit relationship modeling between queries, which helps + +Table 6. Evaluation of the model with different designs on ScanNetV2 validation set. ASAM refers to the adaptive superpoint aggregation module. CLSR refers to the contrastive learning-guided superpoint refinement module. RSA refers to the relation-aware self-attention. + +
SettingmAPAP@50AP@25
W/o contrastive loss60.177.985.6
W contrastive loss60.578.485.9
+ +Table 7. Effectiveness of contrastive loss to ASAM. + +
SettingmAPAP@50AP@25
W max-pooling62.279.986.7
W mean-pooling62.379.786.7
W max-pooling & mean-pooling62.580.287.0
+ +Table 8. Ablation study on ASAM. + +the network learn and converge more easily by focusing on more relevant queries, compared to purely implicit modeling. II: ASAM and CLSR are essentially a unified entity (designed to solve the same problem: better modeling of scene relationships). We separated them only for clarity in description. Both I and II are equally important for instance segmentation, and their contributes comparably to the final performance. + +Ablation study on the adaptive superpoint aggregation module. In this section, we conduct experiments on the adaptive superpoint aggregation module (ASAM). First, we perform an ablation study on max-pooling and mean-pooling, as shown in Table 8, where "W max-pooling" indicates that ASAM includes only the max-pooling branch. The results show that both mean-pooling and max-pooling contribute to performance gains. Furthermore, to illustrate the characteristics of the learned weight distribution in ASAM, we present corresponding visualization in Figure 6. From the figure, it is evident that ASAM places greater emphasis on the edges and corner regions of objects—areas that are typically distinctive for each instance. Therefore, with the assistance of ASAM and contrastive learning, the model is able to aggregate more discriminative superpoint features. + +Effectiveness of the relation-aware self-attention. As shown in Figure 5, we compare the attention maps and attention weight distributions between traditional self-attention and relation-aware self-attention. From Figure 5(a), it can be observed that our proposed relation-aware self-attention has more high-weight focal points in its attention map, which is further supported by the data in Figure 5(b). Notably, we have excluded points with attention values ranging from 0 to 0.03 from our statistical analysis, as these account for the vast majority (approximately $99\%$ ) of the attention map and would otherwise obscure the meaningful patterns in our study. Furthermore, we substantiate this from a visualization perspective. As demonstrated in Figure 5(c), with the aid of RSA, the representative query can forge connections with a broader set of relevant queries, in contrast to traditional attention mechanisms that concentrate on a limited number of specific queries. This enhancement facilitates the generation of superior instance masks. These observations indicate + +![](images/fb68c0223c354e7e2d8650517699b6b3adaf725e31e63af4828fbfc085ea5784.jpg) +Figure 5. (a) Comparison of attention maps for traditional self-attention vs. relation-aware self-attention. We display the progression of attention maps from layer 1, 3, 5. (b) Comparison of attention weight distributions for traditional self-attention vs. relation-aware self-attention. The attention weight distributions are also shown from layer 1, 3, 5. (c) Query (yellow bbox) with its highly related queries. + +![](images/69014b5de019ec70ebb601026ba706563fcaf71fd545a5b49e37a495056d69ce.jpg) +Figure 6. Visualization of weights in the adaptive superpoint aggregation module. A deeper red color indicates a higher weight assigned to point feature during the "Softmax & Feature Weighting" stage (Figure 2 (b)). + +that relation-aware self-attention achieves a more focused attention when modeling position and geometric relationships. Unlike traditional self-attention, which has relatively dispersed attention without any specific focal query, relation-aware self-attention selectively emphasizes relevant queries, resulting in a more precise and meaningful representation. + +Contribution to the convergence speed. As shown in Figure 7, our method demonstrates a faster convergence speed compared to the baseline. This improvement can be attributed to the relation priors introduced by CLSR and RSA: contrastive learning provides relation priors for superpoints to guide feature aggregation, while RSA introduces + +position and geometric relation priors for query features, enhancing self-attention. Additionally, the superpoint refinement module in CLSR forms a dual-path architecture, enabling direct communication between query features and superpoint features, speeding up the convergence. + +![](images/28f8ec7d425cb07cebc13ba707e5565e4a634952038dc9dce0ceb77f5b64cadb.jpg) +Figure 7. The convergence curve on ScanNet-v2 validation set. + +# 5. Conclusion + +In this paper, we propose a novel 3D instance segmentation method called Relation3D. We focus on modeling the internal relationships among scene features as well as between query features, an aspect that past methods have not explored sufficiently. Specifically, we introduce an adaptive superpoint aggregation module to better represent superpoint features and a contrastive learning-guided superpoint refinement module that updates superpoint features in dual directions while guiding the direction of these updates with the help of contrastive learning. Additionally, our proposed relation-aware self-attention mechanism enhances the modeling of relationships between queries by improving the representation of positional and geometric relationships. Extensive experiments conducted on the several datasets demonstrate the effectiveness of Relation3D. + +# 6. Acknowledgements + +This work was partially supported by Wenfei Yang and Tianzhu Zhang. + +# References + +[1] Chungang Zhuang, Shaofei Li, and Han Ding. Instance segmentation based 6d pose estimation of industrial objects using point clouds for robotic bin-picking. 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Open-Vocabulary Relationship Understanding. We propose RelationField, the first framework to extract open-vocabulary inter-object relationships directly from neural radiance fields. RelationField can answer a wide variety of relationship queries, such as "composition", "compare", "spatial", "affordance" and "support" relationships. + +# Abstract + +Neural radiance fields are an emerging 3D scene representation and recently even been extended to learn features for scene understanding by distilling open-vocabulary features from vision-language models. However, current method primarily focuses on object-centric representations, supporting object segmentation or detection, while understanding semantic relationships between objects remains largely unexplored. To address this gap, we propose RelationField, the first method to extract inter-object relationships directly from neural radiance fields. RelationField represents relationships between objects as pairs of rays within a neural radiance field, effectively extending its formulation to include implicit relationship queries. To teach RelationField complex, open-vocabulary relationships, relationship knowledge is distilled from multi-modal LLMs. To evaluate RelationField, we solve open-vocabulary 3D scene graph generation tasks and relationship-guided instance segmentation, achieving state-of-the-art performance in both tasks. See the project website at relationfield.github.io. + +# 1. Introduction + +3D scene understanding bridges the gap between the physi + +cal and the digital world, by enabling machines to perceive environments in a way similar to humans. In robotics, 3D scene understanding is required to navigate complex environments, interact with objects, and perform tasks autonomously. In AR/VR it enables realistic and immersive experiences, e.g., by allowing accurate placing of and interacting with virtual content in the real world. Notably, many applications require a level of understanding that goes beyond just localizing and segmenting a known list of objects categories [8, 34, 37, 44] but are also able to segment novel entities beyond the closed-set class assumption [16, 36, 48]. + +True holistic and adaptable scene understanding needs to go a step further and not only reconstruct and identify individual objects within a scene but also understand complex inter-object relationships, functionalities, and the overall context of the environment. This aspect of scene understanding, particularly the ability to recognize and reason about relationships between objects, is often overlooked. Yet, it is essential to interact with the surroundings in a sophisticated, adaptive and natural manner. Significant progress has been made in understanding relationships in 2D images, mainly driven by the exploration of foundation models [4, 24, 39] and in particular by multi-modal LLMs [1, 12]. These mod + +els are extremely powerful, although they primarily operate on 2D representations and do not fully leverage the richness of 3D data. + +3D scenes provide more complete captures of the environment and are able to represent a high level of complexity, with overlapping objects and occlusions that make it difficult to consistently infer relationships with 2D models alone. 3D approaches have been shown to reduce per-frame noise and resolve occlusions. Despite this advantage, 3D foundation models have yet to emerge, as the data available in 3D remains limited compared to 2D. + +3D scene graphs on the other hand, are a promising and compact representation for scene understanding and capture not only scene objects but also inter-object relationships. However, several scene graph approaches either rely on a closed set of relationships [25, 50, 51, 53], depend on class-agnostic instance segmentation [27], and/or require an explicit 3D representation such as point clouds. + +A recent work, Open3DSG [27], distills relationship knowledge from foundation models [9, 39] into a 3D graph neural network, which can then predict open-vocabulary graphs. Capturing both objects and relationships with open-vocabulary features allows capturing a wide range of objects, functions, and relationships without prior training on specific object or relationship classes. This flexibility is crucial for handling the diversity and complexity of real-world scenes. However, Open3DSG still relies on given class-agnostic instance segmentation [27] and is bound by the quality of the explicit 3D mesh representation of the underlying dataset. These approaches furthermore require the availability of depth sensors. In contrast to 3D scene graphs, radiance fields are 3D representations that do not require 3D sensor data, but instead represent 3D scenes solely based on a set of posed 2D images [21, 33]. While they were first introduced for novel view synthesis and 3D reconstruction, they have since then been extended in several works to also capture semantic information [13, 22, 38, 45]. + +LERF [22], as well as a few follow-up works [13, 23, 38] present alternative approaches to distill features from 2D foundation models, such as CLIP [39], DINO [4] or SAM [24], into 3D by means of radiance fields. Yet, these approaches predominantly focus on object-centric semantic features, limiting their application in high-level scene reasoning tasks. + +To enable holistic and high-level scene reasoning tasks based on neural radiance fields, we propose RelationField, a rich radiance field representation that learns open-vocabulary features for objects and their relationships. This allows us to reason about complex scenes and object interactions such as compositional, spatial, support, or affordances, see Fig. 1. In summary, this work has the following contributions: + +- We present the first method for open-vocabulary scene + +segmentation enabling interactive and textual relationship queries by extending the semantic neural radiance formulation with inter-object relationships distilled from a foundation model into a dense and multi-view consistent 3D representation. + +- This novel representation not only facilitates relationship-based queries but also allows us to obtain state-of-the-art 3D scene graphs – making it the first time scene graphs have been inferred from neural radiance fields. +- Furthermore, we introduce a new task - relationship-guided instance segmentation - on ScanNet++ [59]. This task involves segmenting an instance based on an object-relationship search query, e.g., "picture standing on the shelf", providing a benchmarking for future research in this direction. + +# 2. Related Work + +Open-Vocabulary 3D Scene Understanding. Recent 3D scene understanding approaches for detection, semantic segmentation, or instance segmentation have moved from closed-set categories [8, 34, 37, 44] to open-vocabulary, removing the limitation to a pre-defined vocabulary. To do so, 2D features from vision-language models (VLMs) are lifted into 3D by either using feature distillation and feature lifting. The latter extract vision-language features directly on 2D images and then project these to 3D by utilizing depth or by separately training 2D and 3D feature encoders that are combined at inference time [10, 16, 18, 35, 48]. Feature distillation on the other hand, trains a 3D model using semantic features extracted from a VLM from posed 2D images [13, 27, 36] and does not assume the availability of 2D frames at test time. Both feature lifting and distillation methods require 2D and 3D data either for training or for inference. + +While open-vocabulary 3D scene understanding approaches have shown impressive progress in semantic object segmentation, they do not holistically capture the scene lacking knowledge about high-level compositions and/or interobject relationships. + +Relationships in 3D Scenes. Understanding the full 3D scene involves extracting compositional knowledge and relationships between objects and has been shown to improve object-centric predictions [28, 53]. 3D scene graphs [3, 50] have emerged as the predominant representation for modeling these relationships with applications in several different tasks such as place recognition [50], registration [43], change detection [30, 50], task planning [2, 29, 40], and navigation [52]. By representing objects as nodes into graphs and explicitly encoding their connections (spatial, semantic, etc.) as edges, 3D scene graphs offer an efficient representation of the environment. [3] proposes to represent buildings, rooms, objects, and cameras as 3D scene graphs and later works extended this idea by learning hierarchical 3D scene graphs directly from sensor data [19, 41, 42]. On the other + +![](images/97308228a4ab0c4eb10feb3f67072a0a1e4a069d8f33dbdb73ea848a2d582959.jpg) +Figure 2. RelationField Training. Left: RelationField learns a 3D feature field (a) that can be queried with a relationship query location (b) which changes the relationship field of the 3D volume depending on what position is selected. The relationship feature is sampled and rendered along a ray according to NeRF's rendering weights. The language loss maximizes the cosine similarity between the extracted sparse features from the 2D views and the rendered 3D relationship features. Right: We estimate 2D relationship proposals from a multi-model LLM prompted with SoM (e) for each training view and encode extracted textual relationship description into the image plane (d). A pair pixel sampler samples subject and object pixels (c) for which the relationship feature is distilled into the 3D volume. + +hand, [50] introduced semantic 3D scene graphs, focusing more on the semantic components of a scene including interobject relationships. Subsequent works have advanced this research area by refining semantic 3D scene graphs from point clouds using scene priors [61], pre-training [25, 26] and improved message passing in graphs [53, 54]. + +While all these works have a close-set assumption, only a few very recent works have investigated the use of VLMs and large language models (LLMs) to obtain open-vocabulary scene graphs which capture a more flexible representation of the environment [5, 6, 15, 27, 32]. However, these approaches often require depth data and a complete and explicit 3D representation of the scene e.g. in the form of a 3D mesh or point cloud [25, 27, 50] which often is not available or of poor quality. + +Radiance and Feature Fields. Radiance Fields [21, 33] were first introduced for novel view synthesis and have the benefit that they do not require explicit 3D supervision. Recently, radiance fields have been adapted for several different 3D scene understanding tasks such as segmentation [45, 62] or detection [17, 55]. Notably, some methods propose to extend radiance fields to predict features obtained from 2D foundation models in 3D. For instance, LERF [22] and OpenNeRF [13] learn vision-language features using a separate MLP-head in the NeRF model to produce CLIP [39] embeddings for open-vocabulary 3D segmentation. Similarly, GARField [23] learns instance embeddings using a contrastive formulation provided by SAM [24] using a separate MLP-head in their NeRF. Among others, LangSplat [38] and ClickGaussians [7] extend these ideas to Gaussian Splatting for faster training and rendering. While these works show impressive results, they mainly investigate object-centric semantics and also do not explore the composition of a scene or object relationships. + +Inspired by these works, our method learns open-vocabulary vision-language features directly from multiple posed + +2D views. Therefore, we similarly do not require any explicit 3D scene representation in the form of depth or point cloud data. Instead, our approach aims to obtain open-vocabulary scene understanding beyond objects by also encoding object relationships, creating a consistent and rich representation. This way, our approach – as the first of its kind – supports interactive relationship queries and allows to extract 3D semantic scene graphs directly from the radiance field. + +# 3. Method + +Given a set of posed RGB images, our goal is to build a queryable 3D representation of the scene that supports understanding object instances using open-vocabulary object and relationship descriptions. To achieve this, we introduce a novel approach, RelationField, as illustrated in Fig. 2. Our proposed approach is independent of the underlying radiance field, and can be adapted to NeRFs [33] as well as Gaussian Splatting [21], in the following section we demonstrate how our method incorporates implicit open-set relationship feature prediction into $\mathrm{NeRFs}^1$ [33], enabling the querying of arbitrary object and relationship concepts within a continuous volumetric 3D scene representation. To enhance NeRF with object-centric semantics, we distill CLIP-feature [39] prediction and SAM [24] supervision for instance grouping of each ray. Our method is the first to introduce an implicit open-set relationship feature prediction head as explained in Sec. 3.1. It is supervised by the embedded features of a multi-modal LLM using set-of-mark prompting (SoM) [57] (see Sec. 3.2). The learned RelationField then can be queried to retrieve relationships such as "the light switch turns on the lamp" by defining the predicate "turns on" as a pair of input rays within the feature field for all rays that hit the light switch and lamp (see Sec. 3.3). + +# 3.1. RelationField + +Radiance Field. A radiance field describes a function that models the color $\mathbf{c} \in [0,1]^3$ and density $\sigma \in [0,\infty)$ for a given 3D point $\mathbf{x} \in \mathbb{R}^3$ and ray direction $\mathbf{d} \in \mathbb{S}^2$ . Mildenhall et al. [33] first proposed to model this implicit function as a neural radiance field (NeRF) that implements a multilayer perceptron $f$ with the training objective of learning the parameters $\theta$ with supervision from multi-images of the scene + +$$ +f _ {\theta} (\mathbf {x}, \mathbf {d}) \mapsto (\mathbf {c}, \sigma). \tag {1} +$$ + +Object-level Semantics in Radiance Fields. To learn object-level open-vocabulary instances within the radiance field, we extend NeRF with two additional output embedding heads: one predicts open-vocabulary features $s$ in the CLIP embedding space, inspired by [13], and the other predicts a grouping embedding $i$ that co-locates rays of the same instance in the same region of the embedding space for easy instance clustering, similar to [23]. The open-vocabulary feature is therefore defined as a tuple $o = (s, i)$ of semantic and instance features. These object-level open-vocabulary features allow us to query object entities but do not capture relationships. Therefore, it is necessary to model relationships explicitly. + +Relationship Semantics in Radiance Fields. Unlike radiance fields, which only predict color and density for a point $\mathbf{x}$ , relationship modeling requires an additional point $\mathbf{z}$ to specify the relationship between $\mathbf{x}$ and $\mathbf{z}$ . Therefore, to capture relationships within the radiance field, we extend the input by an additional implicit query location $\mathbf{z} \in \mathbb{R}^3$ (Fig. 2b). With this query location, our approach implicitly models the relationship feature $\mathbf{r}$ between the ray $(\mathbf{x}, \mathbf{d})$ and the location $\mathbf{z}$ . The relationship feature $\mathbf{r}$ is located within the language embedding space and can be queried for arbitrary relationships based on the cosine similarity. + +The complete function $g_{\theta}$ that models the color, density, open-vocabulary instance feature as well as open-vocabulary relationships of the objects in the 3D scene is given by + +$$ +g _ {\theta} (\mathbf {x}, \mathbf {d}, \mathbf {z}) \mapsto (\mathbf {c}, \sigma , \mathbf {o}, \mathbf {r}). \tag {2} +$$ + +# 3.2. Relationship Supervision + +While vision-language models such as CLIP [39] excel at modeling individual objects and concepts, their understanding of relationships remains limited [60]. To address this, we distill relationship knowledge from multi-modal LLMs, which better represent complex relationships. However, a challenge arises because multi-modal LLMs produce textual descriptions, while models like CLIP generate pixel- or patch-level features that can be queried using various text encodings. Our goal is to transfer relationship features into the radiance field representation, enabling open-vocabulary + +querying similar to object-centric approaches with CLIP [13, 22]. The following paragraphs outline our approach for extracting such high-dimensional, pixel-aligned features from multi-modal LLMs, effectively bridging the gap between textual understanding and visual feature extraction. + +Set-of-Mark (SoM). To extract dense pixel-aligned visual relationship features, we utilize SoM prompting [58]. SoM is a visual prompting approach that enhances the visual grounding abilities of multi-modal LLMs by overlaying marks, masks, or bounding boxes to help the model answer fine-grained visual questions. By using SoM over a direct approach, it has been shown, that it improves the spatial reasoning of LLMs, such as GPT-4 [58]. + +Feature extraction. To generate sparse high-dimensional pixel-aligned visual relationship features, we use SAM [24] to extract $m$ segmentation masks each corresponding to a detected object in the image from a training view. Using these masks, we annotate the image with alphanumeric marks for each segmented object following the SoM prompting technique. Next, we prompt a multi-modal LLM to identify and extract inter-object relationships for closely positioned marked object pairs (Fig. 2e) $^2$ . The output text $t$ includes a textual description of the relationships between object pairs $(i,j)$ using the identifiers from the SoM annotations. Each textual relationship description $t_{ij}$ is then encoded to a high-dimensional feature representation $\phi_{t_{ij}}$ using an encoder-only language model such as [20], resulting in $d$ dimensional features for each relationship (Fig. 2d). These features are then projected onto the image plane using the SAM segmentation masks and the SoM marks as a reference to generate a high-dimensional feature representation of the extracted relationships that are aligned with the pixel locations of the objects in the image. + +Training. During training we randomly sample ray and query origins uniformly throughout the input views in a pairwise manner using a pair-pixel sampler (Fig. 2c). Using the density prediction of the radiance field, we estimate the query positions along the ray of the query origin. Ray and query samples are concatenated and fed together into an MLP-head that predicts the relationship feature along the sample ray. The feature is rendered onto the image plane using the radiance field's rendering weights. We minimize a loss + +$$ +\mathcal {L} = 1 - \frac {\mathbf {r}}{| | \mathbf {r} | | _ {2}} \cdot \frac {\hat {\mathbf {r}}}{| | \hat {\mathbf {r}} | | _ {2}}, \tag {3} +$$ + +that maximizes the cosine similarity between the rendered relationship feature $\mathbf{r}$ and the ground-truth relationship feature $\hat{\mathbf{r}}$ . Similarly, the rendered object-centric features, such as color and open-vocabulary semantics, as well as instance + +features for each ray, are supervised by their respective ray origin features. + +# 3.3. Querying RelationField + +To effectively explore and understand the relationships between objects in a scene, it is natural to first identify and query the objects themselves before investigating their interobject relationships. In this context, RelationField supports both object querying and subsequent relationship querying, providing a comprehensive framework for scene understanding. The querying process of RelationField consists of two steps. First, selecting a query location, which involves determining for which object in the scene to investigate relationships. This location can be specified directly by the user or chosen based on detected object instances. The second step requires to query a textual relationship for the selected object. Once a query location is chosen, users can specify a particular relationship they wish to investigate, such as "standing on" or "similar to" using a text query. Alternatively, a set of possible relationships for exploration can be provided, which is particularly useful for an open-ended investigation of the scene. + +To evaluate the response of a queried relationship, we assign a score to each ray in the radiance field by calculating the cosine similarity between the language encoding of the query $\phi_q$ , and the relationship embedding, $\mathbf{r}$ . However, since it is difficult to interpret the cosine similarity directly without context, we follow the approach introduced by [22] and output the pairwise softmax with regard to canonical phrase embeddings $\phi_{canon}$ such as "and", "next to" and "none". The relationship response is then + +$$ +\rho = \min _ {i} \frac {\exp (\phi_ {q} \cdot \mathbf {r})}{\exp (\phi_ {c a n o n} ^ {i} \cdot \mathbf {r}) + \exp (\phi_ {q} \cdot \mathbf {r})}. (4) +$$ + +Intuitively, this softmax probability represents how much the model favors a certain relationship query over no relationship. + +# 3.4. Implementation Details + +RelationField is built in Nerfstudio [49] on top of the Nerfaco model for color and density estimation of a given ray from posed training images with known intrinsic and optionally depth supervision. We define separate heads to estimate the open-vocabulary semantic object, instance, and relationship feature fields. The open-vocabulary segmentation head outputs 768-dimensional features in CLIP [39] / OpenSeg [14] embedding space for a given location vector without view-direction. Similarly, the instance head outputs a 256-dimensional grouping feature in the instance embedding space for a given location vector. Our relationship field encodes a pair of location vectors for the ray and query locations by concatenating them and outputs a language-aligned relationship feature of 512 dimensions in the jina- + +embeddings-v3 [47] embedding space. For relationship feature supervision, we use GPT-4o [1] to extract relationship features from the training image together with SoM [57] using numeric marks and semi-transparent masks. The language outputs are encoded using jina-embeddings-v3 [47]. + +# 4. Experiments + +In the following, we present both qualitative and quantitative results that highlight the capabilities of our method. To highlight the performance of our method in an in-the-wild setting, we provide a qualitative analysis of various relationship queries in different indoor environments in Sec. 4.1. To quantify RelationField performance, we leverage the task of 3D scene graph prediction in Sec. 4.2. Our approach outperforms several competitive baselines and establishes a new state-of-the-art on the 3DSSG benchmark. We then perform comprehensive ablation studies to demonstrate the importance of 3D consistency and knowledge distillation. Specifically, we compare our method against various 2D multimodal LLMs. Further ablation studies justify our choice of relationship encoders by comparing different multi-modal LLMs for this purpose. Furthermore, we demonstrate the capabilities of our model in Sec. 4.3 by reporting its performance on a new task - relationship-guided 3D instance segmentation - which leverages natural language prompts e.g., "picture standing on the shelf" for 3D segmentation. Notably, our method outperforms all recent open-vocabulary feature fields, demonstrating its ability to understand object relationships accurately. + +# 4.1. Relationship Segmentation + +Fig. 3, shows our method's ability to segment relationships. We visualize the model's response for a given textual relationship prompt together with the selected target location. Results are reported on 4 different scenes taken from three datasets: LERF [22], Scannet++ [59], and Replica [46]. The scenes consist of several complex object interactions such as compositional relationships like "the freezer being part of the refrigerator", support relationships such as "the pillow lying on the couch", comparative or similarity relationships like "one ottoman being the same as another ottoman", or even affordances such as "the light switch turns on the lamp". The colormap which shows the top $50\%$ confidence for each query respectively, shows that our model is able to segment these complex relationships. + +# 4.2.3D Scene Graph Prediction + +Our method's ability to estimate both open-vocabulary relationships as well as object instances enables the generation of 3D scene graphs. The following section details the extraction process of these graphs from our radiance field representation and presents quantitative comparisons against state-of-the-art open-vocabulary 3D scene graph prediction + +![](images/28063d0d493dab3b78d8152965a2f8a24b93d347bfb23d762924f68134a36b31.jpg) +Kitchen + +![](images/f5ef1054d3e5a9f76ebc977675663d69be44d7191d90b8ad6952d0e7f3505853.jpg) +"part of" + +![](images/e53a3b22edf29fec89a89f4b5010157128150bb15da849a93559987cdb57b71a.jpg) +"lying in" + +![](images/20f7c1699159562bb2f877d5d33b57c2e9d4070998ce79eb9f65210fc8e71c1c.jpg) +"hanging on" + +![](images/d629579f9ae25360e0940e96f90c8f315c62db2a8b344c7dab21458d2f967548.jpg) +Bedroom + +![](images/a6655a0490f2426a6e54e4a205911a3ae48280b2d7946229a8e32b009e37dc41.jpg) +"turns on" + +![](images/43097685f1f2e701d36099810b8037002480468fac3eeb38777ef6b5d8799e99.jpg) +"covers" + +![](images/7acc83240179d27d307baf74b964e893cd2f00876fecdf4c8c2de4da56c92f1a.jpg) +"standing on" + +![](images/96f7dbffd5744ba853159e06d8d673a494fd6da1f22a2e4356926b206675a66f.jpg) +Bathroom + +![](images/82fdcf10768dc56abea420f863c9f6e895215285931103aa7840375abaa34ecd.jpg) +"belongs to" + +![](images/cc313ce53b2b609b6f7fc4af8b526e839a60bcf308d8c252549bd0d189a6cafe.jpg) +"used with" + +![](images/7a5e41a57dc154ef711c60eab2d0fa3596308837a95069feeb474a4f70b79fa9.jpg) +"attached to" + +![](images/3ce77f8d8fbb2d9cbffaf65ccb80ce2c9df85e385c55e30a8a9b50a08a780260.jpg) +Living room + +![](images/b47c4fc4eb5992c41e11f51bb13832bf8a09523571d0652ff5c3723d63c87bfb.jpg) +"same as" + +![](images/cf12e639bebd75eaa929a633a699bf091b500be1164756ab834cea588e965f4c.jpg) +"lying on" +Figure 3. Results with RelationField in 4 in-the-wild scenes. Each image shows a rendering from RelationField, along with the relationship response for each query relationship. The relevancy score describes the answer of the model to the question: What is standing on/attached to/similar to etc.? For demonstration purposes, we highlight the click as well as the outline of the clicked object, which is not needed when querying the model. Our model is able to understand complex relationships, such as the functionality of light switches or uncommon support structures, such as "knives hanging on a magnetic mount". + +![](images/5423774a04209f02e737cce304c45a8c45b72d2d39509585b96344c026dc7512.jpg) +"standing on" + +models. Our proposed approach is not only able to predict open-vocabulary relationships but also open-vocabulary object instances. Combining both predictions enables the inference of open-vocabulary 3D scene graphs. + +3D Scene Graph Construction. To extract explicit 3D scene graphs from our implicit representation requires an automated querying process. For a fair comparison with point cloud-based methods, we query the radiance field directly on the provided 3D point cloud. This ensures alignment between the extracted graph and the provided point cloud. Please note that while our method is trained solely on RGB data, the 3D point cloud is utilized exclusively for evaluation. + +To do so, for each 3D point $\mathbf{p}$ in the point cloud $\mathcal{P}$ , we extract semantic and instance features by querying the radiance field at the given location. Since this process is viewpoint- + +independent, it does not require a ray direction $\mathbf{d}$ . We then identify instances by clustering the instance embeddings using DBSCAN [11]. For each instance $i\in \mathcal{I}$ , the open-vocabulary object embedding $S_{i}$ is obtained by aggregating the respective semantic features. + +To extract relationships, each instance $i$ , comprising of points $\mathcal{P}_i$ , serves as a query for the relationship field, which predicts relationship embeddings $\mathcal{R}$ for the remaining point cloud. The relationship embedding $R_{ij}$ is then obtained for each pair $(i,j)$ by aggregating the relationship embeddings $R_i$ for all other instances $j \in \mathcal{I}, j \neq i$ . + +Since the scene graph benchmark evaluates on a closed-set of object and relationship classes, we query with predefined benchmark labels. Object and relationship classes are encoded with CLIP [39] and Jina [47] respectively. We then compute the pair-wise cosine similarity between the + +
MethodObjectPredicateRelationship
R@5R@10R@3R@5R@50R@100
GPT-4 [1] (2D+depth)0.340.420.550.580.520.54
Llama 3.2 [12] (2D+depth)0.400.520.460.480.450.51
Open3DSG [27]0.560.610.580.650.550.56
ConceptGraphs [15]0.370.460.740.790.690.71
RelationField0.690.800.760.820.730.74
+ +Table 1. 3D Scene Graph Prediction on 3DSSG. RelationField outperforms existing open-vocabulary 3D scene graph approaches as well as 2D-only frontier models. RelationField can lift different frontier models into 3D with similarly strong performance. + +ground truth label encodings with the predicted embeddings. To evaluate the predictions, we use the top-k recall metric, selecting the top-k highest-scoring classes as introduced in [31]. For relationship prediction, we follow [56]; ranking our relationship predictions by multiplying the object and relationship scores. + +Implementation details on the 3D scene graph extraction can be found in the supplementary. + +Data. In the following, we report quantitative 3D scene graph evaluation results on the RIO10 subset of the 3DSSG dataset [50]. The 3DSSG dataset consists of semantic scene graphs for 3D point clouds and posed RGB-D frames obtained from a Google Tango device. It contains a closed vocabulary with 160 object classes and 27 relationship types. + +Baselines. We compare our approach against ConceptGraphs [15], which also uses GPT-4, but in combination with a SLAM pipeline that predicts image captions. Once, the scene is reconstructed, GPT-4 is used to provide scene-consistent object and relationship caption. Additionally, we compare against Open3DSG [27], which uses a combination of CLIP [39], and InstructBLIP [9] distilled into a 3D graph neural network. Furthermore, we propose additional 2D-based baselines for GPT-4 [1] and Llama 3.2 [12], which utilize recorded depth data to lift their 2D predictions to 3D. + +Results. A quantitative 3D scene graph comparisons is reported in Tab. 1. We query the 160 object and 27 relationship classes and obtain the embedding similarity of the language feature with the feature field and treat the extracted similarity as a label confidence. RelationField demonstrates state-of-the-art results compared to other recent open-vocabulary 3D scene graph approaches and compared to ConceptGraphs [15]. Our method demonstrates improved performance across all tasks: object, predicate as well as relationship prediction. Furthermore, 2D methods exhibit inferior performance compared to the 3D approaches, potentially due to occlusions and view-dependent challenges. Please note, our approach, compared to closed-set segmentation methods does not require any semantic labels for training and can be deployed on any dataset that provides posed RGB frames. + +Fig. 4 show a subset of extracted relationships with subject, predicate, and object labels, respectively, on a scene + +![](images/ea5d5693af93b2d95f499e12f45c80e275d4faced1b04073ac0757bd9ab72ec6.jpg) +Figure 4. 3D Scene Graph Prediction. Our open-vocabulary approach is able to predict complete 3D scene graph edges containing a subject-predicate-object relationship. + +from the 3DSSG dataset. For clarity, we omit the complete graph but show the most interesting relationships. More 3D scene graph results can be found in the supplementary. + +Ablation - Advantages of 3D relationship modeling over 2D inference. This paper demonstrates a process to distill knowledge from multi-modal LLMs such as GPT-4 into a 3D consistent representation. In Tab. 1 and Fig. 5, we analyze the benefit of a 3D representation over a 2D-only approach which directly utilizes our knowledge provider GPT-4. It can be seen that the 2D approach will always suffer from view-dependent effects. Fig. 5 shows how GPT-4 is missing the lying on relationship because some objects are only partially visible in the current frame. Meanwhile, when rendering the 3D prediction from RelationField, our model is able to predict the correct relationships since it relies on the underlying 3D representation. The quantitative results confirm this observation, see Tab. 1 where RelationField clearly outperforms the 2D-only GPT-4 model. This shows that our model generalizes beyond simple view-level supervision and, indeed, learns a consistent 3D representation, which improves over simple aggregated 2D inference. Ablation - Impact of multi-modal LLM choice on relationship understanding. While we utilize GPT-4 as our backbone model for extracting relationships, our approach is agnostic to the backbone model and can accommodate any LLM capable of reasoning about object relationships. In Fig. 6, we compare our approach which is using the latest version of GPT-4o against the popular open-source alternative Llama 3.2 [12] (90B). Llama 3.2, which is considerably smaller than GPT-4o, has only a minor recall drop for relationship prediction. This shows that our model can be trained with any sufficiently powerful multi-modal LLM. + +# 4.3. Relationship-guided 3D Instance Segmentation + +To highlight the advantages of understanding relationships, we propose a new evaluation task for quantitative relationship-guided 3D instance segmentation. In this task, + +SoM+GPT-4o (2D) Ours (3D) + +![](images/30a550b2bbb0a17d66175a01a9e66bdd9f7dd95ced327c473ac6ee74d1551951.jpg) + +![](images/40f537e747bd536fc091382f612ba27342d3e7ec856f09e332e9108b8fb86a3d.jpg) + +![](images/66b72f1c477cc34f31c7cc13825aa2201d1fe8aefd75f72a4ce2499a4765b0ff.jpg) + +![](images/9b41eb2368619eb0950389f7832c8da5bcbff36dc1a523a67a300eb73d615f55.jpg) +Figure 5. 3D Consistency Ablation. Left: Extracted SoM marks per image with query. Center: Existing relationship in GPT-4 caption. Right: Relationship response from RelationField rendered into image space. While GPT-4 struggles with partially visible objects, RelationField produces more robust results, independent of the view, because our volumetric rendering incorporates information from multiple views and models the underlying 3D relationship representation. + +![](images/032678240c741db8cc5790a596440ffeb444628d71ae8a20cc9f27799b3e92e2.jpg) + +![](images/b2646515bb92df800ff4b6ac8a0beca11fb446bad08e7229b5478cca440c4f35.jpg) + +![](images/a94d11102f3829eefcdd9cd8d25b98e8da1de88eee8bb4d85426f8b0bf0ddf41.jpg) +Figure 6. Language Model Ablation. We compare GPT-4 with Llama 3.2 as the relationship extractor of RelationField for 3D scene graph prediction. + +we want to highlight the benefit of understanding relationships from open-vocabulary textual descriptions for localizing objects of interest. + +Data. We label a small benchmark on Scannet++ [59] of language-based relationship queries across 8 scenes with instance annotations for $\sim 30$ relationship queries spanning $\sim 40$ unique object types and $\sim 10$ semantic predicates. More details can be found in the supplementary. + +Baselines. For a fair comparison, we compare RelationField against three state-of-the-art feature field methods for open-vocabulary object segmentation, LERF [22], OpenNeRF [13], and LangSplat [38] which all rely on posed RGB for training and inference. All approaches are able to process open-vocabulary queries in natural language and localize them in the 3D scene by associating the CLIP [39] embedding of the query with the learned features in the NeRF. The experiments show that our approach is the only capable method to reliably understand complex prompts such as "the picture standing on the shelf" explicitly. + +Localization. To localize target queries with RelationField, we split the language queries into nouns and verbs. First, the nouns are localized using the object field by computing the cosine-similarity to the nouns in the language query. Then, we refine the localization by combining the object prediction with the relationship embedding by rejecting all candidate predictions that do not have a relationship feature + +
MethodIoUAcc
LERF [22]0.250.50
OpenNeRF [13]0.450.83
LangSplat [38]0.490.87
RelationField0.530.96
+ +Table 2. Open-Vocabulary relationship-guided Instance Segmentation. Comparison of open-vocabulary radiance field-based methods on instance segmentation performance for challenging relationship queries. + +aligned with the verb from the query. For LERF, OpenNeRF and LangSplat, the full query is processed directly, as these models do not distinguish between verbs and nouns in their query parsing. + +Results. In Tab. 2, we report the segmentation accuracy and IoU for the set of target queries. The performance of LERF, OpenNeRF and LangSplat degrades in this specialized setting where all queries contain complex relationships. We observe most failure cases for duplicate objects where the bag-of-words representation of CLIP cannot differentiate these objects by their relationship. Meanwhile, RelationField clearly outperforms LangSplat, OpenNeRF and LERF since it is able to model the relationship feature directly. + +# 5. Limitations + +The experiments conducted in this paper demonstrate the potential and advantages of learning 3D relationships in radiance fields. However certain limitations remain. For instance, the relationship knowledge embedded in RelationField is highly dependent on the multi-modal LLM prompting and its output. Furthermore, while posed RGB recordings are easier to acquire than point clouds, RelationField requires known calibrated camera intrinsics and high-quality multi-view captures, which are not always available or easy to capture. In general, the quality of RelationField is bounded by the quality of the radiance field reconstruction. + +# 6. Conclusions + +In this paper, we present RelationField, the first 3D scene representation based on radiance fields that allow for open-vocabulary object and relationship queries. By distilling knowledge from 2D multi-modal LLMs into radiance fields, we are able to not only extract relationship information but also to obtain state-of-the-art open-vocabulary 3D scene graphs. We demonstrate that RelationField effectively learns a consistent 3D representation that surpasses the performance of simple aggregated 2D inference. Furthermore, we introduce a new task of relationship-guided 3D instance segmentation, to highlight the importance of understanding relationships for localizing objects of interest. We hope this work will encourage future 3D scene understanding techniques to not only focus on object-centric features but explicitly incorporate the relations between them. + +Acknowledgement. We sincerely thank Jonathan Francis for providing support in running Llama 3.2 experiments. Our appreciation extends to David Adrian for helpful discussions. We are also grateful to Timm Linder and Andrey Rudenko for their proofreading. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 3 \ No newline at end of file diff --git a/relationfieldrelateanythinginradiancefields/images.zip b/relationfieldrelateanythinginradiancefields/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7040e3aa1966b73f58b1f89ad5f1aa2d456aac46 --- /dev/null +++ b/relationfieldrelateanythinginradiancefields/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6e00c733a0ec22f86f7c82c584795426f7c4df391c32b813eb1bb2d9711b277b +size 483495 diff --git a/relationfieldrelateanythinginradiancefields/layout.json b/relationfieldrelateanythinginradiancefields/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..126fa3518840842408064a3698e5805e917fc3b2 --- /dev/null +++ b/relationfieldrelateanythinginradiancefields/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f25287ccaf92b19629dd1160d67bd59196517fd0a80abe77eb05330150fefdc9 +size 405217 diff --git a/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_content_list.json b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d93dcd2cf4b3ad16fbc2d1797c305cc895bb63b4 --- /dev/null +++ b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0ffc6e50589442f17e423377fa0c0d67b9b18c958fa3401ce742fdd877dc64e7 +size 79612 diff --git a/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_model.json b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_model.json new file mode 100644 index 0000000000000000000000000000000000000000..af8d4b92396dba390ef6b121f26d76f117530a10 --- /dev/null +++ b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:20fa9de2c9c0d51061993ac3d0bad6e228ff909a43e58ab4750716a58f372d8d +size 95932 diff --git a/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_origin.pdf b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8029dd5d18f196ad701484f75da4ddc28efebc60 --- /dev/null +++ b/relationrichvisualdocumentgeneratorforvisualinformationextraction/e752f7aa-0541-4e00-a977-a255e1fa7667_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a7a9c1391e793317c7b5eedf8df484b3522052b1ad7ba5add240aee948f156c1 +size 4099101 diff --git a/relationrichvisualdocumentgeneratorforvisualinformationextraction/full.md b/relationrichvisualdocumentgeneratorforvisualinformationextraction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..25c432958cb30a1fd592e03f23322c20f6caddc6 --- /dev/null +++ b/relationrichvisualdocumentgeneratorforvisualinformationextraction/full.md @@ -0,0 +1,330 @@ +# Relation-Rich Visual Document Generator for Visual Information Extraction + +Zi-Han Jiang $^{1}$ , Chien-Wei Lin $^{1}$ , Wei-Hua Li $^{1}$ , Hsuan-Tung Liu $^{2}$ , Yi-Ren Yeh $^{3}$ , Chu-Song Chen $^{1}$ $^{1}$ National Taiwan University, $^{2}$ E.SUN Financial Holding Co., Ltd., $^{3}$ National Kaohsiung Normal University + +{r12922082,r11922212,d12922009,chusong}@csie.ntu.edu.tw, + +ahare-18342@esunbank.com.tw, yryeh@nknu.edu.tw + +# Abstract + +Despite advances in Large Language Models (LLMs) and Multimodal LLMs (MLLMs) for visual document understanding (VDU), visual information extraction (VIE) from relation-rich documents remains challenging due to the layout diversity and limited training data. While existing synthetic document generators attempt to address data scarcity, they either rely on manually designed layouts and templates, or adopt rule-based approaches that limit layout diversity. Besides, current layout generation methods focus solely on topological patterns without considering textual content, making them impractical for generating documents with complex associations between the contents and layouts. In this paper, we propose a Relation-rIch visual Document GEnergator (RIDGE) that addresses these limitations through a two-stage approach: (1) Content Generation, which leverages LLMs to generate document content using a carefully designed Hierarchical Structure Text format which captures entity categories and relationships, and (2) Content-driven Layout Generation, which learns to create diverse, plausible document layouts solely from easily available Optical Character Recognition (OCR) results, requiring no human labeling or annotations efforts. Experimental results have demonstrated that our method significantly enhances the performance of document understanding models on various VIE benchmarks. + +# 1. Introduction + +VDU has attracted significant attention in knowledge-centric applications. While conventional document pretrained models [13, 16, 37, 41, 46, 47] have demonstrated outstanding performance on specific downstream tasks, their practical applicability is often constrained by the necessity of task- or dataset-specific fine-tuning. This has prompted a shift in research focus towards the utilization of LLMs and MLLMs. + +To perform document analysis, segmented text entities are the basic elements in a visual document. Entity Linking + +(link between entities) and Entity Category (attributes or semantic classification labels of entities) are the two main types of information that are critical to VIE. To learn a document-analysis model, a major difficulty is the lack of labeled training data, where the labels can be of unary relation (containing $n$ entities) or binary relation (containing $O(n^{2})$ links between entity pairs). However, the effort for labeling $O(n^{2})$ labels is huge, which hinders the development of learning effective models for a comprehensive understanding of the diverse forms of visual documents. + +LLMs and MLLMs possess generalization capability and emergent properties resulting from training on extensive corpora, allowing them to perform effectively on document-related tasks. Recent models have shown promising results in document-oriented visual question answering, such as Qwen2-VL [44] approaching human-level performance on DocVQA [34]. However, significant challenges persist in extracting information from relation-rich (e.g., forms of various formats) or semi-structured documents (e.g., invoices and receipts). The variability complicates the process of accurately identifying and linking key-value pairs. A general extraction rule cannot be easily established, affecting model accuracy and requiring extensive training data to enhance the generalization capabilities. + +In this paper, we introduce a method to synthesize relation-rich visual documents. The generated documents exhibit highly diverse layouts, arise not only from the document's content but also from the variability across different document sources. Our content-rich generative approach leverages LLMs in two steps. First, we use ChatGPT [38] to generate text with entity-category and entity-link information in a hierarchy. Second, we adopt self-supervised learning to build a model that can place the generated text into appropriate bounding box locations with reasonable layouts. Unlike traditional layout generation solutions focusing mainly on producing bounding boxes without relationally meaningful textual content [19, 23, 28, 40], our generated content-and-relation-rich documents can boost the performance of VDU. We demonstrate an overview of existing datasets and our approach as follows. + +
Open-setClosed-set
DatasetFUNSD [20]XFUND [48]CORD [35]EPHOIE [43]POIE [26]SROIE [17]DocILE [39]
#Img.199199 per lang.1000149430001000real: 6680 syn:100K*
#KeysFreeFree301021455
+ +Table 1. Dataset statistics of VIE tasks. * represents the synthetic data are generated by 100 templates. + +VIE Datasets. Existing datasets for VIE falls into two categories: open-set and closed-set. Open-set datasets provide annotations for entity-level categories and entity linking. For example, FUNSD [20], an English form-type document dataset, classifies entities into four categories (header, question, answer, and other), and also provides links between questions and answers. In contrast, closed-set datasets define a set of specific keys and extract corresponding values. For example, CORD [35], a consolidated receipt dataset, includes 30 categories, such as menu name and total price. Compared with closed-set datasets, the number of images in open-set datasets is quite limited, as shown in Tab. 1. For instance, FUNSD contains only 199 document images, while XFUND [48], a form-type document dataset covering 7 languages, also has only 199 document images per language. Additionally, data collection poses another challenge, as these types of documents may contain personal information, making them difficult to access publicly. This shortage further highlights the pressing need for a tool that can automatically generate large volumes of this type of data, complete with annotations and document images. + +Overview of Our Approach. We propose RIDGE, a relation-rich visual document generator capable of producing meaningful document content that inherits complex hierarchical relationships between entities, while maintaining a highly diverse layout. To achieve this, we introduce a two-stage generation pipeline. I. Content Generation. In this work, we primarily focus on synthesizing open-set VIE data to address its scarcity. We leverage LLMs to generate document content in our meticulously designed Hierarchical Structure Text (HST) format, where the generated output can be directly parsed into segmented text entities with their category and linking annotations. With content and annotations now prepared, we advance to the next stage. II. Content-driven Layout Generation. Research [6, 9, 31, 40] has shown that LLMs demonstrate layout planning abilities attributed to their training on layout-specific sources like HTML code of mobile app interfaces or websites. Inspired by this, we leverage LLMs to generate document layouts through self-supervised learning. Our training data requires only OCR results (segmented text entities and their bounding box coordinates) from documents that are readily obtainable through off-the-shelf OCR tools. Although we do not provide entity category or linking annotations to the model, it can independently learn content + +layout relationships through self-supervision, generating a reasonable layout that aligns with the annotations produced in the previous stage. Additionally, we introduce a training paradigm called Hierarchical Structure Learning that further leverages HST for reinforcing document understanding models' comprehension. Experimental results have shown that RIDGE significantly enhances the performance of document understanding models on various VIE benchmarks. + +# 2. Related Work + +Synthetic Document Generators. Due to the high cost of manual annotation and the limited availability of sensitive documents, recent research has focused on automatically synthesizing documents to meet the substantial demands of machine learning applications. DocSynth [2] uses a Generative Adversarial Network (GAN) to generate synthetic document images based on manually-designed layouts. Due to the low resolution $(128 \times 128)$ of the generated images, the method can generate only blurry shadows for text and fails to capture detailed document content, resulting the generated synthetic documents only suitable for document layout analysis. SynthDoG [25] aims to generate documents for OCR training by selecting text content from Wikipedia at random and rendering it onto a natural or document-textured image. Its layouts are generated with a rule-based algorithm that merely places random grids on the image, causing content to split across grids in ways that may appear unnatural. DocILE [39] generates realistic content with key information annotations; however, its synthetic method is rule-based, relying on only 100 annotated layout templates. It primarily alters content or applies style changes to font and borders, which limits its diversity and suitability for general training. Existing methods are limited in their ability to produce realistic content and diverse layouts, both of which are essential for robust VIE training. Document Layout Generation. Automatic layout generation has emerged as a crucial task across diverse application domains, spanning documents, natural images, user interfaces, and posters. Early studies [1, 22, 24, 28, 36] employ GANs and VAEs to learn layout generation through reconstruction, while Jiang et al. [23] reformulate this as a sequence-to-sequence problem using transformer architectures. Through advances in diffusion techniques, some studies [12, 18, 19] demonstrate the effectiveness of treating layout generation as a diffusion process. More recently, researchers [6, 9, 30, 31, 40] have begun to utilize LLMs for this task, harnessing their inherent layout understanding. While most methods focus on generating layout (bounding box and category) independent of content, some [4, 21, 27] have incorporated text content with layout planning, primarily focusing on visual design contexts such as posters and graphic designs. These approaches typically handle sparse text elements (keywords or short phrases) arranged around + +![](images/bf84a937b28f0aa944f1c87bce744461d236f3a0a41361209d3384838ddbf16d.jpg) +Figure 1. Overview of RIDGE, including (a) Content Generation and (b) Content-driven Layout Generation. In the visualized annotation, purple represents the header, red represents the key, blue represents the value, and green lines represent entity linking. + +![](images/67b67af8a4f8229d7ea5fe72ac721a399a2e5bdfa954bff25162e9ea73590e3b.jpg) + +visual components, rather than documents with dense textual content and complex structural relationships. Among document layout-related research, most studies predominantly concentrate on academic paper formats due to the accessibility of training data. These methods address solely layout generation, without considering the specific textual content to populate these layouts. Given that font sizes in documents typically follow certain alignment principles, applying such pre-generated layouts would restrict users to fixed-length text within each layout bounding box—a constraint that makes these methods impractical for generating documents with meaningful textual content. + +Consequently, existing studies can only be applied to training document layout analysis models, rather than directly supporting VIE tasks, as the latter requires models to develop robust comprehension of complex content-Layout relationships. Moreover, previous methods rely heavily on supervised training with layout element categories, which is impractical for relation-rich documents due to limited publicly available annotations. In contrast, our proposed self-supervised method requires only readily available OCR results for training, making it more practical and scalable for real-world applications. + +# 3. Method + +This section elaborates on RIDGE, a novel method for synthesizing documents with realistic content and diverse layouts. It employs a two-stage pipeline: content generation for text generation and annotation parsing, and content-driven layout generation for spatial arrangement of document entities, as shown in Fig. 1. + +In this work, we aim to generate open-set VIE dataset consisting of document images and their corresponding annotations, including entity categories and linking, similar to FUNSD. Formally, a document $D = \{e_i\}_{i=1}^N$ is composed of entities, where $N$ is the number of entities in the document. Each entity $e = (id, t, b, c, l)$ , where $id$ is + +the entity's unique identifier, $t$ denotes its textual content, $b = (x_{\text{left}}, y_{\text{top}}, x_{\text{right}}, y_{\text{bottom}})$ specifies its bounding box coordinates, $c \in \{\text{header}, \text{key}, \text{value}, \text{other}\}$ indicates its semantic category; and $l$ contains a list of links with other entities, where a link is represented as $[id_{\text{key}}, id_{\text{value}}}$ . + +# 3.1. Content Generation + +As shown in Fig. 1(a), given a document title, LLMs generate corresponding detailed content of the document in the format of Hierarchical Structure Text (HST). The format is structured as follows: (1) the entire document is wrapped within tags after the document title, (2) paragraphs are organized using header tags (

,

, etc.), where text immediately following each header tag is treated as the paragraph's title, and (3) the content is organized in a tree structure through two patterns—using colon ('') for direct key-value pairs in the same line (e.g., "Name: John"), and using different numbers of hyphens ('-') to indicate hierarchical nesting relationships. + +This structured format enables automatic extraction of entity text, categories, and linking relationships. To help LLMs get a more comprehensive understanding of HST, we give a detailed task instruction and an in-context one-shot exemplar for LLMs to reference. For detailed prompts, please refer to the supplementary material. + +# 3.2. Content-driven Layout Generation (CLGM) + +In this subsection, we introduce CLGM (see Fig. 2), which is capable of arranging text segments to proper bounding box positions. Instead of traditional category-driven layout generation methods [19, 40], our model is content-driven to tackle nuanced text content in diverse documents. CLGM consists of three parts: serializing the document layout, self-supervised layout learning, and document rendering. + +# 3.2.1. Document Layout Compilation + +Since LLMs accept only text input, we need to represent a document layout as a sequence. Previous studies [9, 31, 40] + +![](images/fecfbb4f3a46af17e9bce18a61dcf96a5214da02829f100bb54a18a9e4b86051.jpg) +Figure 2. Content-driven Layout Generation Model (CLGM). + +have demonstrated that LLMs exhibit strong comprehension in programming languages, due to the inclusion of code-based data in their training corpora. Thus, the layout of a document $D$ can be represented in JSON format as: + +```json +{"width":W,"height":H,"entities":[ {"text":t1,"box":[xleft1,ytop, $x_{\mathrm{right}_1}$ ,ybottom]}}，,...， {"text":tN,"box":[xleftN,ytopN,xrightN,ybottomN]}}] +``` + +where $W$ and $H$ indicate the width and height of the layout canvas, and "entities" consists of all entities $e_i$ that comprise document $D$ . Unlike previous methods [9, 31, 40] that use HTML or CSS for layout representation, we adopt JSON to reduce input sequence length by eliminating redundant attribute text. In HTML and CSS, an element's bounding box requires repeating attribute text. Our representation consolidates attributes into a single "box" field, which particularly reduces sequence length for complex document layouts containing hundreds of entities. + +# 3.2.2. Layout Self-Supervised Learning + +To generate layouts for documents with varying content, we formulate this task as predicting bounding box coordinates for each given text entity. Our approach is inspired by LayoutNUWA [40], a method purely for layout generation without text contents. Our method is content-driven and performs self-supervised learning in a more general way for placing the texts into suitable positions. We use a masking strategy where bounding box coordinates are replaced with + +special mask tokens $<\text{FILL\_i}>$ for each $e_i$ . Specifically, let $S(D_{\backslash M})$ denote the input masked sequence to model $f_{\theta}$ : + +```json +{"width":W,"height":H,"entities":[ {"text":t1,"box":["]},..., {"text":tN,"box":["]}] +``` + +where $S(\cdot)$ is a serialization function and $M$ denotes the masked bounding boxes. Model $f_{\theta}$ then output a JSON dictionary sequence $S(M)$ that directly maps each mask token to its corresponding coordinates: + +```latex +\[ +\begin{array}{l} +\{\text{"}": \text{"xleft_1, ytop_1, xright_1, ybottom_1", ..., }\} \\ +\text{"}": \text{"xleft_N, ytop_N, xright_N, ybottom_N"} +\end{array} +\] +``` + +Content-based layout generation can thus be written as + +$$ +S (M) = f _ {\theta} \left(S \left(D _ {\backslash M}\right)\right). \tag {1} +$$ + +Unlike LayoutNUWA which requires LLMs to complete a code template by repeating the entire input with predicted coordinates, our method streamlines this process by focusing solely on predicting bounding box coordinates. This reduces the output sequence length and enhances the efficiency for layout generation. Following the standard auto-regressive formulation, we optimize our model using the cross-entropy loss: + +$$ +\mathcal {L} = - \sum_ {k = 1} ^ {K} \log P (S (M) ^ {k} | S (M) ^ {< k}, S (D _ {\backslash M}), \theta), \tag {2} +$$ + +with $K$ the number of tokens in the output sequence $S(M)$ , $S(M)^k$ the $k^{th}$ token in $S(M)$ , and $\theta$ the model parameters. + +Considering the auto-regressive nature of LLMs, we randomly permute the order of input entities during training to prevent the model from learning a fixed layout order, as the document layout inherently has no natural sequence. This randomization strategy brings a crucial benefit—by exposing LLMs to highly unordered text content, which is even challenging for humans to reconstruct, the model learns to infer reasonable relationships between entities solely from their text. This allows our method to generate plausible layouts without requiring category and linking annotations, thus eliminating the need for human annotation effort. During inference, we maintain the order of entities as they appear in HST (i.e., human reading order) to facilitate the model's understanding of document content. + +Additionally, we train our model with non-normalized canvas sizes, enabling it to handle diverse layout dimensions directly. It enhances the model's adaptability in practice where documents can vary significantly in size. + +# 3.2.3. Document Rendering + +After obtaining the layout coordinates from CLGM, the document rendering module transforms the layout sequence into a visually coherent document image. First, we validate the LLM output to ensure proper text rendering within bounding boxes. Second, we enhance the visual appearance by various styling operations to create realistic documents. + +LLM output processing and Styling. When using LLMs to generate structured output, format validation is inevitable. We verify that CLGM's output conforms to valid JSON format and contains all expected mask tokens, excluding samples that fail these criteria. Subsequently, we render text from the left boundary of each bounding box, with font size determined by the box height generated by CLGM. Since different fonts may yield varying text widths, we adaptively extend the box width and shift subsequent entities in the same row when text exceeds its allocated bounds, preserving readability and CLGM's overall layout design. In addition, we enhance the visual appearance through changing fonts, applying bold formatting to text labeled as header, adding different background materials, and incorporating grid lines around entities. + +# 3.3. Hierarchical Structure Learning + +Our generated documents with annotations can be directly applied to any document understanding method for training. W.L.O.G., we use MLLMs [32, 44] for training due to their promising performance recently. To exploit our generated HST better, we propose a training paradigm that extensively utilizes HST to enhance models' comprehension. Existing LLM/MLLM-based methods employ text-Layout reconstruction learning to enhance models' understanding of document structure. For example, DocOwl-1.5 [14] requires + +![](images/94f702ec206491a952e041e3cf169e3574c24c42671790efab1f350199121d12.jpg) +Figure 3. Hierarchical Structure Learning + +![](images/6a912c388ca30e42597e47abefd263b6b310d5d0a4a40f3a659f30bc32f008ad.jpg) + +models to output the document text with newline characters ('\n') and white spaces inserted to mimic the layout of the document image. Additionally, LayoutLLM [33] requires models to reconstruct the document by generating a sequence of entities in the format of “<{box}, {text}>]”. While these tasks help models learn to associate text with its spatial positions, they may not capture the complex hierarchical relationships inherent in document layouts. To address this issue, we introduce Hierarchical Structure Learning using HST generated by RIDGE to strengthen models' comprehension of hierarchical relationships within document text and layout. + +Hierarchical Structure Parsing (HSP) requires models to parse the entire document content into our HST format. As shown in Fig. 3(a), given a document image, models need to identify paragraph boundaries, understand the hierarchical nesting relationships within its content, and output HST with proper tags and indentation levels. This task helps models understand both the overall structure and complex relationships of the document. + +HSP with Localization is built upon the basic HSP task. We introduce spatial awareness by requiring models to parse hierarchical structures within specific regions. As shown in Fig. 3(b), models are given a region represented by bounding box coordinates (normalized to 0-999), and are required to output HST for content within that region. This task maintains the localization ability of pre-trained models during downstream training while facilitating hierarchical structure learning by reducing the task to a smaller region. + +Visual Information Extraction with HSP combines HSP with VIE task. As shown in Fig. 3(c), when querying specific information (e.g., "Name:"), models first output the hierarchical structure of the relevant document section, then provide the answer after "########Answer:". Inspired by the idea of Chain-of-Thought [45], this approach encourages models to understand document context through its hierarchical structure before extracting information, potentially leading to more robust and interpretable results. + +
MethodsOpen-setClosed-set
FUNSD F1 %XFUND-ZH F1 %CORD F1 %CORD- ANLS %EPHOIE Acc %ANOLES %POIE Acc %SROIE- ANLS%
LayoutLLM [33] (CVPR'24)---63.10---72.12
Monkey [29] (CVPR'24)34.2728.0254.5469.4822.4430.9630.6443.95
DocOwl-1.5-Chat [14] (EMNLP'24)50.8810.1464.0163.154.858.2551.5761.35
LLaVA-NeXT-Mistral-7B [32]31.186.0246.5863.814.318.0249.8860.05
LLaVA-NeXT-Mistral-7B+33.4110.3352.3263.935.3912.0751.4662.13
Δ↑2.234.315.740.121.084.051.582.08
Qwen2-VL-7B [44]59.8962.0882.7180.4076.9186.5293.5196.01
Qwen2-VL-7B+66.4869.8484.4785.5377.8987.7994.0496.71
Δ↑6.597.761.765.130.981.270.530.70
+ +Table 2. Performance improvements in zero-shot VIE for MLLMs fine-tuned with RIDGE. "+" denotes that the model is extensively trained with RIDGE. $\Delta \uparrow$ represents performance gain. + +# 4. Experiments + +We present the experimental setups for RIDGE, including implementation details, evaluation setup, and results. + +# 4.1. Implementation Details + +Models. For the LLM in the content generation stage, we adapt GPT-4o-mini [38] to generate various document-related content with themes spanning business, education, government, and medical use in both English and Chinese. As for CLGM, we use LLaMA-3.1-8B [8] as our backbone and fine-tune it with LoRA [15]. The max sequence length is set as 8000 to accommodate the long layout sequence formed by hundreds of layout entities. Content generation prompts and more training setup are in the supplementary. Datasets. To develop CLGM's expertise in form-like document layout design, we collect approximately 100K document images with OCR annotations from publicly available VDU datasets. The majority of our training data originates from RVL-CDIP [11], a document classification dataset comprising 16 classes with $25\mathrm{K}$ images per class. We specifically select the "form", "specification", "resume", and "memo" classes for training due to their highly structured layouts. Additionally, we incorporate form-type VIE datasets, including FUNSD [20], XFUND [48] with 7 languages. We also utilize HUST-CELL [50] and manually select approximately 600 structurally complex document images from it. For FUNSD, XFUND, and HUST-CELL, only images from the official training sets are used. Regarding OCR annotations, we use the results provided by the datasets themselves; while RVL-CDIP does not provide OCR annotations, we use Google Vision API to obtain OCR results. Given that FUNSD and XFUND consist entirely of form documents, we treat them as high-quality data and apply 4 times up-sampling during training. + +# 4.2. Evaluation Setup + +Since RIDGE is the first work that can automatically generate relation-rich visual documents with annotations, and + +![](images/276cbed45882cf5b4729d521a4b416ae5520e0de6d8df4b2b624e201196c7a7a.jpg) +Figure 4. Example of generated documents. (a) General form-like images. (b) Right: SROIE-styled image; Left: real SROIE image. (c) Bottom: EPHOIE-styled image; Top: real EPHOIE image. + +the layout evaluation criteria used in previous studies [19, 23, 40] do not consider text content in the document, it is difficult to apply those metrics (such as FID) to evaluate our work. Thus, we conduct comprehensive experiments applying RIDGE on MLLMs as well as the widely used document pre-trained model, LayoutLMv3 [16]. We assess the performance gains brought by RIDGE on various VIE benchmarks, including FUNSD, XFUND-ZH, CORD, $\text{CORD}^-$ , EPHOIE, POIE, and SROIE $^-$ . Benchmarks $^-$ are the cleaned version used in LayoutLLM [33], where keys with multiple values are filtered out. The synthetic documents (referred to as RIDGE) used in the experiments comprise approximately 3K English and 3K Chinese documents, yielding 444K instruction samples, including 194K classical VIE and additional Hierarchical Structure Learning samples. Examples of generated images are shown in Fig. 4(a), with more in the supplementary material. + +# 4.3. Fine-tuning MLLMs with RIDGE + +In this subsection, we evaluate the performance gains of MLLMs after being extensively fine-tuned with RIDGE. + +
Dataset CombinationsFUNSD F1 %CORD F1 %CORD- ANLS %POIESROIE- ANLS %
Acc %ANLS %
Qwen2-VL-7B [44]59.8982.7180.4093.5196.0197.50
+RIDGE65.72 (+5.83)84.20 (+1.49)83.71 (+3.31)94.45 (+0.94)96.71 (+0.70)97.64 (+0.14)
+RIDGE+DocVQA66.21 (+6.32)84.06 (+1.35)85.66 (+5.26)94.08 (+0.57)96.67 (+0.66)97.72 (+0.22)
+RIDGE+DocVQA+FUNSD67.54 (+7.65)84.25 (+1.54)85.57 (+5.17)94.11 (+0.60)96.72 (+0.71)97.71 (+0.21)
+ +To strengthen the hierarchical structure understanding of relation-rich documents, we apply Hierarchical Structure Learning during training. Experiments are conducted on LLaVA-NeXT-Mistral-7B (referred to as LLaVA-NeXT) and Qwen2-VL-7B (referred to as Qwen2-VL). More details on training are provided in the supplementary material. + +Fine-tuning with RIDGE alone. As shown in Tab. 2, RIDGE consistently enhances model performance across all evaluation benchmarks, with the only exception being a marginal decrease of $0.01\%$ for LLaVA-NeXT on SROIE-. While LLaVA-NeXT initially scores behind DocOwl-1.5 [14] on some benchmarks, which is an MLLM mainly trained on VDU tasks, extensive training with RIDGE enables it to surpass DocOwl-1.5. Regarding Qwen2-VL, RIDGE successfully pushes its performance to a new state-of-the-art level compared with previous studies. + +Further analyzing the results across different benchmark types, we observe that the performance gains are more substantial in open-set VIE benchmarks (exceeding more than $6\%$ ) compared to closed-set benchmarks, particularly for Qwen2-VL. This aligns with our expectations, as RIDGE is mainly designed to generate documents that emphasize open-set scenarios, which promotes better generalization. Beyond its primary strength in open-set data, training on these generalized key-value pairs also yields performance improvements on closed-set data. This is significant because closed-set data often contains inherent biases due to domain-specific key definitions that typically require extensive context to interpret correctly. + +Fine-tuning with existing real-world datasets. To further validate the efficacy of RIDGE in diverse training scenarios, we conduct experiments using RIDGE independently and in combination with real-world datasets. For a comprehensive evaluation, we incorporate DocVQA, a widely used dataset containing human-annotated QA pairs for general VDU training, and FUNSD, an open-set VIE dataset with annotated form-type documents. We use RIDGE-generated English documents in this experiment and evaluate the performance gains on English benchmarks. The results of various dataset combinations—(1) RIDGE alone, (2) RIDGE + DocVQA, and (3) RIDGE + DocVQA + FUNSD—are presented in Tab. 3. Each experimental configuration independently initializes from the base Qwen2-VL-7B model. + +Table 3. Comparison of fine-tuning MLLMs with RIDGE and real-world datasets. The values in parentheses show the performance gains compared to the baseline Qwen2-VL-7B model. + +
MethodsSROIE-ANLS%EPHOIE
Acc%ANLS%
Qwen2-VL-7B [44]97.5076.9186.52
+RIDGE97.74 (+0.24)77.89 (+0.98)87.79 (+1.27)
+RIDGE+RIDGE-DS98.05 (+0.55)80.91 (+4.00)89.82 (+3.30)
+ +Table 4. Performance improvements in closed-set VIE after applying domain-specific document generation. "RIDGE" denotes the general open-set documents generated by RIDGE. "RIDGE-DS" denotes domain-specific documents generated by RIDGE. + +Training with RIDGE alone achieves substantial improvements across all benchmarks. While incorporating DocVQA and FUNSD brings additional gains in some cases, these improvements are relatively modest. The effectiveness of RIDGE is evident from its contribution: on FUNSD, RIDGE alone contributes to a $5.83\%$ improvement, and on CORD, it yields a $1.49\%$ improvement. Even with the addition of real-world datasets, the maximum gains only reach $7.65\%$ on FUNSD and $1.54\%$ on CORD. These results demonstrate that RIDGE can provide a strong foundation for VIE tasks. + +# 4.4. Domain-Specific Document Generation + +To address the challenges in closed-set VIE discussed in Sec. 4.3, we generate additional synthetic data that directly align with specific benchmark's pre-defined key sets. In this experiment, we focus on SROIE and EPHOIE. For these benchmarks, we prompt GPT-4o [38] to generate text content that mimics their respective domains: receipts and exam cover pages. More details can be found in the supplemental. Subsequently, our CLGM tackles the layout design. Examples of generated images are shown in Fig. 4(b)(c). + +We conduct experiments using Qwen2-VL, initializing from an enhanced version trained with RIDGE alone (as discussed in Sec. 4.3) for better comprehension of document structure. We perform separate training for each benchmark using approximately 700 SROIE-styled documents and 800 EPHOIE-styled documents respectively. The performance gains after training on these domain-specific documents are presented in Tab. 4. The results show significant performance improvements on both benchmarks. Notably, on EPHOIE, we observe substantial improvements with accuracy increasing by $4.00\%$ and ANLS rising by $3.30\%$ . These improvements demonstrate the ef + +
Pre-training DataFine-tuning Data0-shot1-shot5-shot10-shot
-FUNSD-45.4272.4571.03
RIDGE62.7771.0773.2574.79
-XFUND-ZH-52.0276.3981.18
RIDGE69.7570.9178.5783.02
+ +fectiveness of our domain-specific document generation and validate the reliability of data generated by RIDGE. + +# 4.5. Applied RIDGE on LayoutLMv3 + +In addition to analyzing entity relations, Semantic Entity Recognition (SER), which focuses on classifying entities into semantic categories, is also a common subtask of VIE. In this experiment, we utilize LayoutLMv3BASE [16], which has been widely adopted for VIE tasks, with few-shot learning to verify the quality of the semantic category annotations in RIDGE and its effectiveness on SER task. We discuss whether introducing RIDGE for pre-training prior to few-shot fine-tuning on real images can boost performance on real datasets. Following LayoutLMv3, a linear classifier is added to adapt the model for SER downstream task. + +We evaluate on FUNSD and XFUND-ZH, as RIDGE adheres to the same semantic category labels. We conduct experiments with and without RIDGE pre-training, followed by few-shot fine-tuning on the training set and evaluation on the testing set of each dataset. As shown in Tab. 5, the use of RIDGE consistently enhances model performance across all few-shot settings. Notably, RIDGE demonstrates effective zero-shot adaptation, suggesting the reliability of its semantic category labels for real-world document simulation. + +# 4.6. Ablation Study + +To assess the effectiveness of Hierarchical Structure Learning, we conduct an ablation study comparing model performance between training with classical VIE tasks alone and training with both VIE and Hierarchical Structure Learning. To ensure a fair comparison, we train both settings for the same number of iterations (800 steps) to evaluate the efficiency and effectiveness of performance gains. We conduct this study on FUNSD, XFUND-ZH, and CORD, with F1 scores reported in Tab. 6. The first row ( $r1$ ) presents the baseline performance of Qwen2-VL-7B without any additional training. While the majority of performance gains come from VIE data generated by RIDGE (as shown by the larger improvements from $r1$ to $r2$ than those from $r2$ to $r3$ ), incorporating Hierarchical Structure Learning further improves performance, yielding additional gains of $1.61\%$ on FUNSD, $2.52\%$ on XFUND-ZH, and $0.70\%$ on CORD. + +# 4.7. Interpretability + +Since we apply the VIE with HSP task during training, the fine-tuned Qwen2-VL acquires the ability to construct + +Table 5. Few-shot learning with LayoutLMv3 for SER task. $x$ -shot specifies the number of fine-tuning images. + +
Hierarchical Structure LearningFUNSDXFUND-ZHCORD
r1Qwen2-VL-7B [44]59.8962.0882.71
r264.8767.3283.77
r3✓66.4869.8484.47
+ +Table 6. Ablation study on Hierarchical Structure Learning. $r1$ represents the baseline model without additional training, $r2$ is trained solely on VIE, and $r3$ adopts both VIE and Hierarchical Structure Learning. + +
(a)MLM response: +<hs:Items: +-(TA) NASI UNG TERI MEDAN +-Quantity: 4 +-Price: 165,460 +-(TA) BHUN GORENG SEAFOOD +-Quantity: 1 +-Price: 40,456 +-(TA) KWETIAW SEAFOOD SIRAM +-Quantity: 1 +-Price: 42,274 +-(TA) NASI GORENG +-Quantity: 2 +-Price: 55,456 +<hz>
(b)MLM response: +<ht:Itemized Bill: +-3 Nasi Putih: 30.000 +-1 Nasi Tambah: 7.000 +-2 Ayam Pab: 40.000 +-1 Samabal SP: 11.000 +-1 Samabal Gabus Asin Cb: 18.000 +-1 Kerupak Kuch: 15.000 +-1 Ikan Bawah Besa: 28.500 +-1 Telur Dadar: 10.000 +-1 Teh Es: 7.000 +-1 Teh Manis: 9.000 +-1 Es Batu: 4.000 +<hz>
(c)3 Nasi Putih: 30.000 +1 Nasi Tjahat: 40.000 +2 Pasei Riai: 40.000 +3 Samabal Gobur Sinan +-1 Tanjib Gobur Sinan +-1 Kasikun Xian: 18.000 +-1 Ikan Basai Sinan +-1 Telur Sebar: 10.000 +-1 Ten Is: 9.000 +-1 Tanjib: 9.000 +Subtotal: 179.500 +Pajek Best ToT: 197.450 +Total: 197.450
(d)###Answer: 14
+ +Figure 5. Interpretability brought by VIE with Hierarchical Structure Parsing. + +related information from documents in a hierarchical format before responding with the final answer. As shown in Fig. 5(a), before extracting the "subtotal price," the model first outputs each item's quantity and price. Also, in Fig. 5(b), before extracting the "total count of quantit," the model lists each item's information first. The process of hierarchical structure parsing not only helps the model think clearly but also provides users with detailed information related to the target query in a highly structured format. + +# 5. Limitation + +In this work, we train RIDGE mainly on form-like images and demonstrate its adaptability. Nevertheless, the generalization of RIDGE to significantly distinct document types may require additional training to achieve optimal performance, which is also our future work. + +# 6. Conclusion + +We propose RIDGE, a novel relation-rich visual document generator that leverages the powerful content-Layout understanding of LLMs to generate meaningful synthetic document images. RIDGE is the first work that can automatically generate annotated relation-rich visual documents, which facilitates the training of visual document analysis models. Additionally, we introduce Hierarchical Structure Learning to enhance models' comprehension of the inherent hierarchical structure in document layouts. Through experiments on various VIE benchmarks, RIDGE can boost the performance of existing document understanding models and increase interpretability for practical applications. + +# Acknowledgements + +This work was supported in part by the National Science and Technology Council, Taiwan under Grants NSTC 111-2634-F-002-023, 112-2221-E-002-182-MY3 & 112-2221-E-002-132-MY3, NTU under grants 113L900902 & 114L893104, and E.SUN Bank. 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Many MDE models aim to predict affine-invariant relative depth from monocular images, while recent developments in large-scale training and vision foundation models enable reasonable estimation of metric (absolute) depth. However, effectively leveraging these predictions for geometric vision tasks, in particular relative pose estimation, remains relatively under explored. While depths provide rich constraints for cross-view image alignment, the intrinsic noise and ambiguity from the monocular depth priors present practical challenges to improving upon classic keypoint-based solutions. In this paper, we develop three solvers for relative pose estimation that explicitly account for independent affine (scale and shift) ambiguities, covering both calibrated and uncalibrated conditions. We further propose a hybrid estimation pipeline that combines our proposed solvers with classic point-based solvers and epipolar constraints. We find that the affine correction modeling is beneficial to not only the relative depth priors but also, surprisingly, the "metric" ones. Results across multiple datasets demonstrate large improvements of our approach over classic keypoint-based baselines and PnP-based solutions, under both calibrated and uncalibrated setups. We also show that our method improves consistently with different feature matchers and MDE models, and can further benefit from very recent advances on both modules. Code is available at https://github.com/MarkYu98/madpose. + +# 1. Introduction + +Recently, deep learning based monocular depth estimation (MDE) has made remarkable progress [9, 31, 32, 69, 74, 75], offering increasingly accurate 3D information from single 2D images. These advancements have opened up new possibilities for enriching traditional geometric computer vision tasks with 3D priors. The ability to infer depth information from a single image has been shown to have useful implications in various applications [14, 28, 61]. + +![](images/bf97df5213f7e20a9278114e97927680e81ef13ac714d4a752d3ab8b435e9236.jpg) +Figure 1. Our method jointly estimates affine corrections of monocular depth maps $D_{1} + \beta_{1}$ and $\alpha (D_2 + \beta_2)$ together with relative pose $R, t$ (Right), whereas the classic way of aligning the depth maps with only scale modeling $(\alpha)$ leads to wrong and distorted alignments (Left). + +Despite the significant progress in monocular depth estimation, the integration of these depth priors in fundamental geometric computer vision tasks, particularly camera pose estimation, remains under-studied. While incorporating depth information would be beneficial intuitively, effectively leveraging these priors to find geometric relationships between multiple views presents unique challenges that have not been fully addressed by existing works [4, 17, 41]. + +A critical limitation of existing approaches is the common assumption that the predicted depth maps from different views can be related by a single scale factor. This assumption, however, fails to account for the intrinsic properties of existing monocular depth estimation models, as state-of-the-art MDE models [32, 69, 75] are typically trained to predict relative depth or disparity (inverse-depth) that are invariant to both scale and shift (affine) transformations. While there have been recent progress in developing models for metric depth estimation [8, 48, 75, 76], we find that surprisingly, they also benefit from modeling the affine corrections as they are not perfectly consistent with the actual metric depth (See Figure 6, Table 1, and Sec. 5.3). + +In this paper, we propose three solvers specialized for solving relative pose under calibrated or uncalibrated camera setups. These solvers use pixel correspondences along with their depth priors from MDE models as input, and incorporate explicit modeling of both scale and shift varia + +tions in the depth predictions. Specifically, the solvers introduced are as follows (with only the calibrated solver being minimal and the two others being over-constrained): + +- Calibrated 3-point solver: for calibrated image pairs. +- Shared-focal 4-point solver: for uncalibrated image pairs with a common unknown focal length. +- Two-focal 4-point solver: for uncalibrated image pairs. +In addition, we integrate these new solvers into a flexible hybrid robust estimation pipeline that combines our depth-aware solvers with classic point-based solvers [29, 46, 63]. We also develop hybrid solutions for scoring and local optimization, where we optimize both the classic Sampson error [53] and depth-induced reprojection error using depth and the solved affine corrections. This enables combining the advantages of both worlds and results in a robust relative pose estimator that achieves consistent improvement across datasets. Our key contributions are summarized as follows: +- We propose to solve relative pose with explicit affine (scale and shift) corrections on monocular depth predictions, addressing a limitation in existing methods. +- We develop 3 new solvers tailored to different calibration setups: calibrated, uncalibrated with common focal length, and fully uncalibrated image pairs. +- Our hybrid estimation pipeline integrates depth-aware and classic point-based solvers, scoring and local optimization, leading to largely improved accuracy and robustness in relative pose estimation. +- Our framework is compatible with a wide range of image matchers and MDE models with consistent improvement, making it easy to integrate in existing pipelines. + +# 2. Related Work + +Monocular Depth Estimation: Recovering depth information from a single image is a fundamental problem in 3D computer vision. Early methods [56, 57] resort to probabilistic modeling, and the advent of deep learning enables a variety of robust monocular depth estimators [23, 25, 27, 38, 51, 52, 69, 74, 75, 80] in the past decade. While most of them learn monocular depth with an error that is invariant to scale or affine transformation, thanks to large-scale data and vision foundation models in recent years, researchers have also developed models [7, 8, 10, 39, 48, 74-76] that aim to predict absolute (metric) depth from images. Recently, there have also been works [26, 32, 47, 58, 78] that demonstrate the benefits of repurposing generative models for monocular depth estimation. With such rapid and active developments, the latest state-of-the-art models [69, 75] have started to show foundation model level performance on open-domain images. This raises increasing attention and demand on studying how the off-the-shelf monocular depth models can best benefit geometric vision tasks. Our proposed method works with any monocular depth models and achieves improvement on relative pose estimation with + +both relative and metric depth priors. + +Relative Pose Estimation: Classic relative pose estimators mainly rely on cross-image point correspondences, which either comes from the detection [16, 18, 43, 67, 81] and matching [5, 40, 54] of salient keypoints, or direct dense / semi-dense matching [19, 20, 64, 66, 68]. While minimal solvers for point correspondences have been well studied in the two-view case under calibrated [46] and uncalibrated conditions [29, 63], researchers have been making continuous efforts on improving relative pose estimation with the help of data-driven machine learning, including differentiable robust estimation [50, 71], relative pose regression [82], and advanced proposal scoring [6]. However, they have not yet achieved the same generalization ability as classic methods in practice, with the LO-RANSAC [13, 36] in PoseLib [33] remaining the best practical solutions. Very recently, DUSt3R [70] introduced a 3D foundation model for two-view geometry that benefits from large-scale training, which is further improved by MAST3R [37] with better matching. In this paper, we present a relative pose estimator that consistently improves over PoseLib [33] with off-the-shelf monocular depth models, and further show that the improvements are orthogonal and can be combined with the recent advances from MAST3R [37]. + +Monocular Depth Priors for Geometric Tasks: As monocular depth estimation become increasingly robust, there has been growing interests on using the dense depth predictions to benefit downstream geometric tasks, including visual odometry/SLAM [14, 41, 42, 65], dense reconstruction [44, 49, 72, 77], and novel view synthesis [62, 73]. However, only a few works have attempted employing monocular depth priors to enhance relative pose estimation. Barath et al. [4] propose a $2\mathrm{pt} + \mathrm{D}$ solver and also attempt to incorporate affine correspondence [22]. However, the 2-point solver is intrinsically degenerate for rigid alignment due to rank deficiency. In [41], PnP-RANSAC is directly applied on top of monocular depths for small-baseline image pairs. Most recently, Ding et al. [17] develop fundamental matrix solvers for relative depths, and fCOP [79] relates monocular depth estimation with canonical object priors for focal length estimation. While all prior works assume the depth priors are up to scale, we show that modeling additional shifts are extremely beneficial in practice, even for off-the-shelf metric depth models. + +# 3. Problem Formulation + +Given two images $I_{1}$ and $I_{2}$ , relative pose estimation aims to estimate the rotation $\pmb{R}$ and translation $\pmb{t}$ transforming the coordinate frame of the first camera to the second one. The classic approach to solve this problem is to establish a set of corresponding pixel matches between the two images through either sparse feature matching (e.g., Super + +![](images/08da991f279c039242825466fbc796cabbbdd12020c5033bb6236473b8b97cd4.jpg) +Figure 2. Pipeline overview: Our method takes a pair of images as input, runs off-the-shelf feature matching and monocular depth estimation, then jointly estimates the relative pose, scale and shift parameters of the two depth maps, and optionally the focal lengths. Our method incorporates monocular depth priors in all stages (in green) of hybrid LO-MSAC [12, 35], including 3 new depth-aware solvers, while still being able to leverage traditional point-based solvers [29, 46, 63] (in blue). + +Point [16] + LightGlue [40]) or dense correspondence techniques (e.g., RoMa [20]), then solve for the essential matrix relating these point matches. + +In addition to the 2D correspondences, we aim to leverage depth maps $D_{1}$ and $D_{2}$ predicted by some off-the-shelf monocular depth estimation (MDE) model for each image. These depth maps provide valuable 3D priors but come with inherent ambiguities due to the nature of monocular depth estimation. State-of-the-art MDE models [9, 21, 32, 75] are often trained with scale- and shift-invariant loss [51]. They predict either disparity [9, 51, 75] or relative depth [21, 32, 75] that are related to the actual value with an unknown linear (affine) transformation. In our formulation, we focus on affine-invariant relative depth and model this transformation as: + +$$ +\widehat {D} _ {i} = a _ {i} D _ {i} + b _ {i}, \quad i \in \{1, 2 \} \tag {1} +$$ + +where $a_{i}$ and $b_{i}$ are unknown scalar values of the scale and shift of both depth maps. + +For a pair of image correspondences $(\mathbf{p}_{1j},\mathbf{p}_{2j})$ , and their corresponding predicted depth values after the unknown linear transformation $\widehat{d}_{1j}$ and $\widehat{d}_{2j}$ , we can lift the 2D points to 3D from both camera views: + +$$ +\mathbf {P} _ {i j} = \boldsymbol {K} _ {i} ^ {- 1} \left[ \begin{array}{l} \mathbf {p} _ {i j} \\ 1 \end{array} \right] \cdot \widehat {d} _ {i j}, \quad i \in \{1, 2 \} \tag {2} +$$ + +where $\pmb{K}_i$ is the camera intrinsic matrix of the $i$ -th image. + +The two 3D points $\mathbf{P}_{1j}$ and $\mathbf{P}_{2j}$ are related by the rotation $\pmb{R}$ and translation $\pmb{t}$ of the relative pose: + +$$ +\mathbf {P} _ {2 j} = \boldsymbol {R} \mathbf {P} _ {1 j} + \boldsymbol {t}. \tag {3} +$$ + +Thus, the monocular depth maps could provide additional constraints on the relative pose. However, explicitly modeling the scales and shifts for both views is necessary to obtain + +such constraint. In relative pose estimation, the actual scale of the scene is inherently ambiguous, so estimating the relative scale ratio $\alpha = a_{2} / a_{1}$ is sufficient. Therefore, in addition to the relative rotation $\pmb{R}$ and translation $\pmb{t}$ , we also explicitly estimate two scalar shifts $\beta_{1} = b_{1} / a_{1}$ , $\beta_{2} = b_{2} / a_{2}$ , and one scale $\alpha$ , which transforms the two depth maps: + +$$ +\widehat {D} _ {1} = D _ {1} + \beta_ {1}, \quad \widehat {D} _ {2} = \alpha (D _ {2} + \beta_ {2}). \tag {4} +$$ + +While this formulation assumes the depth priors are affine-invariant relative depth, using our method with metric depth predictions can also lead to more accurate and robust relative pose as we will show empirically in the experiments. This formulation is also illustrated in Fig. 1. + +# 4. Method + +We propose three solvers that solve for the relative pose $\mathbf{R}, t$ as well as the shifts $\beta_{1}, \beta_{2}$ and scale $\alpha$ using the feature correspondences and depth priors: + +1. Calibrated solver when all camera intrinsics are known; +2. Shared-focal solver when both images are captured by camera with a shared unknown focal length; +3. Two-focal solver when focal lengths are unknown for both cameras. + +The solvers work in a 2-step manner. First, find all possible values for the depth scale and shifts $\alpha, \beta_{1}, \beta_{2}$ , as well as the focal lengths if unknown. Then, solve for the rotation and translation for each set of the possible scales and shifts. + +# 4.1. Solving Depth Scale, Shifts, and Focal Lengths + +Given a sampled set of $M$ pixel correspondences $\{(\mathbf{p}_{11},\mathbf{p}_{21}),\ldots ,(\mathbf{p}_{1M},\mathbf{p}_{2M})\}$ , and the corresponding depth priors from the predicted depth maps $d_{ij} = D_i(\mathbf{p}_{ij})$ , the solvers rely on the assumption that the corresponding + +pair-wise distances $\delta$ among the lifted 3D points should be equal in the two camera frames. Formally, let us define + +$$ +\boldsymbol {\delta} _ {j k} ^ {(i)} = \mathbf {P} _ {i j} - \mathbf {P} _ {i k}, \text {w h e r e} i \in \{1, 2 \} \text {a n d} j \neq k. +$$ + +Because the rotation and translation transformation in (3) is length-preserving, the following equality constraint must hold for all pairs $(j,k)$ of the 3D points: + +$$ +\left\| \boldsymbol {\delta} _ {j k} ^ {(1)} \right\| ^ {2} = \left\| \boldsymbol {\delta} _ {j k} ^ {(2)} \right\| ^ {2}. \tag {5} +$$ + +We can thus obtain a system of $\binom{M}{2}$ equations where the rotation and translation have been eliminated. The three solvers require different numbers of correspondences to solve these equations due to the different numbers of unknowns. In addition to the three values $\alpha, \beta_1, \beta_2$ , the shared-focal solver also solves for the shared focal $f$ , and the two-focal solver solves for the two focals $f_1, f_2$ . + +Calibrated Solver: The calibrated solver addresses the scenario where both cameras have known intrinsic parameters. In this case the problem is minimal with $M = 3$ points (along with their associated depth priors), as we get $\binom{3}{2} = 3$ equations in (5) in the three unknowns $\alpha, \beta_{1}$ and $\beta_{2}$ . + +Since the intrinsics $K_{1}$ and $K_{2}$ are known, let $\tilde{\mathbf{P}}_{ij} = K_{i}^{-1}\begin{bmatrix} \mathbf{p}_{ij}\\ 1 \end{bmatrix} = (\widetilde{x}_{ij},\widetilde{y}_{ij},1)^{\top}$ . We have: + +$$ +\begin{array}{l} \left\| \boldsymbol {\delta} _ {j k} ^ {(i)} \right\| ^ {2} = \left\| \widehat {d} _ {i j} \widetilde {\mathbf {P}} _ {i j} - \widehat {d} _ {i k} \widetilde {\mathbf {P}} _ {i k} \right\| ^ {2} \\ = \left\| \widehat {d} _ {i j} (\widetilde {x} _ {i j}, \widetilde {y} _ {i j}, 1) ^ {\top} - \widehat {d} _ {i k} (\widetilde {x} _ {i k}, \widetilde {y} _ {i k}, 1) ^ {\top} \right\| ^ {2} \\ = \left(\widehat {d} _ {i j} \widetilde {x} _ {i j} - \widehat {d} _ {i k} \widetilde {x} _ {i k}\right) ^ {2} + \left(\widehat {d} _ {i j} \widetilde {y} _ {i j} - \widehat {d} _ {i k} \widetilde {y} _ {i k}\right) ^ {2} + \left(\widehat {d} _ {i j} - \widehat {d} _ {i k}\right) ^ {2}. \\ \end{array} +$$ + +This yields three quartic equations of $\alpha, \beta_{1}$ and $\beta_{2}$ . In the equations, $\alpha$ only appears as squares, so we re-parameterize with $\gamma = \alpha^{2}$ to make the equations cubic and reduce the number of solutions. Using the method from Larsson et al. [34] we find that the system of polynomials have at most 4 solutions and create a Gröbner basis solver. The solver performs linear elimination on a $12\mathrm{x}12$ matrix followed by a $4\mathrm{x}4$ eigenvalue problem. + +Shared-Focal Solver: The shared-focal solver is designed for scenarios where both images are captured by camera with an unknown shared focal length $f$ . This situation is common in applications such as visual odometry or structure-from-motion with a single moving camera. We assume that the focal length is the only unknown intrinsic parameter, and thus we can assume without loss of generality that $K = \mathrm{diag}(f, f, 1)$ . We then have + +$$ +\widetilde {\mathbf {P}} _ {i j} = \boldsymbol {K} ^ {- 1} \left[ \begin{array}{l} \mathbf {p} _ {i j} \\ 1 \end{array} \right] = \left(\frac {x _ {i j}}{f}, \frac {y _ {i j}}{f}, 1\right) ^ {\top}. \tag {6} +$$ + +As we now have an additional unknown, one more correspondence is needed to solve for $\alpha, \beta_1, \beta_2$ , and $f$ . However, + +taking all equations (5) from $M = 4$ matches will give an overdetermined system. We therefore only select 4 out of the 6 possible equations from inserting (6) into (5). Similar to the $\alpha$ reparametrization in the calibrated case, we additionally perform substitution $\omega = 1 / f^2$ . After these two substitutions we get four equations of degree 4. Again applying the method from Larsson et al. [34] we find that the problem has 8 solutions and we generate a solver with template size 36x36. + +Two-Focal Solver: Last but not least, the two-focal solver addresses the most general case where the two images are captured by cameras with potentially different, unknown focal lengths. This scenario is particularly relevant for applications involving crowd-sourced imagery. + +This case can also be solved with $M = 4$ correspondences, but now requires using 5 out of the 6 equations they generate. The derivation is similar to the shared focal length case, except that we now have independent calibration matrices $K_{1} = \mathrm{diag}(f_{1}, f_{1}, 1)$ and $K_{2} = \mathrm{diag}(f_{2}, f_{2}, 1)$ for each camera. In the equations we now introduce $\omega_{1} = 1 / f_{1}^{2}$ and $\omega_{2} = 1 / f_{2}^{2}$ . Applying the method from Larsson et al. [34] we surprisingly find that the problem only has 4 solutions, fewer than in the shared focal length case. The solver however requires linear elimination on a 40x40 matrix followed by solving a 4x4 eigenvalue problem. + +# 4.2. Finding Rotation and Translation + +Only real solutions of $\alpha, \beta_1, \beta_2$ that result in positive depth values in (4) are kept as valid solutions (and similarly for the focal lengths). For each possible solution, we estimate a rigid transformation (a rotation $R$ and a translation $t$ ), which can be easily retrieved using the SVD method [60] aligning the back-projected 3D points from both views which satisfy (3). Since relative poses are inherently up to scale, $R$ and $t$ are the final outputs of our proposed solvers. + +# 4.3. Evaluating Solutions + +The solutions $\Theta = (R, t, \alpha, \beta_1, \beta_2)$ (optionally also include $f$ or $f_1, f_2$ ) need to be evaluated on all correspondences with their depth priors. To do so, we compute the depth-induced reprojection errors: + +$$ +E _ {r (1 \rightarrow 2)} (\Theta) = \| \boldsymbol {\Pi} _ {2} (\boldsymbol {R} \mathbf {P} _ {1} + \boldsymbol {t}) - \mathbf {p} _ {2} \| ^ {2} \tag {7} +$$ + +$$ +E _ {r (2 \rightarrow 1)} (\Theta) = \left\| \boldsymbol {\Pi} _ {1} \left(\boldsymbol {R} ^ {- 1} \mathbf {P} _ {2} - R ^ {- 1} \boldsymbol {t}\right) - \mathbf {p} _ {1} \right\| ^ {2}, +$$ + +where $\mathbf{P}_1, \mathbf{P}_2$ are the lifted 3D points of a pair of correspondences using the shift-and-scaled depth priors $\widehat{d}_1 = d_1 + \beta_1$ , $\widehat{d}_2 = \alpha (d_2 + \beta_2)$ , and $\Pi_i(\mathbf{P})$ is the camera projection using $\pmb{K}_i$ . $\pmb{K}_i$ is either known with calibrated cameras, or assembled using the estimated focal lengths solved by solvers. Note that the errors are computed separately for + +two directions. This is designed to be robust against inconsistencies between the depth maps when combining into a MSAC score with a squared inlier threshold $\tau_{r}$ : + +$$ +\overline {{E}} _ {r} (\Theta) = \min \left(E _ {r (1 \rightarrow 2)}, \tau_ {r}\right) + \min \left(E _ {r (2 \rightarrow 1)}, \tau_ {r}\right). \tag {8} +$$ + +# 4.4. Hybrid Estimation + +While monocular depth estimation models can provide useful geometric cues, solely relying on the depth priors can be prone to erroneous results when the priors are unreliable. We further propose to jointly use our depth-aware solvers and reprojection errors together with the classic point-based solvers and epipolar (Sampson) error $E_{s}$ [45, 53] in a hybrid LO-MSAC [12, 35] framework. For the calibrated case, the Sampson error is rescaled with the focal lengths to ensure both errors are in pixels. + +This approach enhances the estimation with good depth priors but can also utilize 2D correspondences when the priors are unsatisfactory. As shown in Fig. 2, each iteration of the hybrid LO-MSAC pipeline starts by selecting a solver between a depth-aware and a point-based solver depending on the setting: + +- Calibrated: calibrated solver & 5-pt essential matrix solver [46]; +- Shared-focal: shared-focal solver & 6-pt shared focal relative pose solver [63]; +- Two-focal: two-focal solver & 7-pt fundamental matrix solver [29]. + +For point-based solvers, we also need to estimate $\alpha, \beta_{1}, \beta_{2}$ consistent with the estimated pose and potentially focal lengths. This is done by triangulating 3D points from the $M$ correspondences, and fitting the depth priors to the projected depth to find the scale and shift in least-squares manner. For the 7-pt fundamental matrix solver, the possible focal lengths are retrieved using Bougnoux formula[11]. + +The two solvers are initially randomly selected with equal probabilities, and are later chosen using the inlier ratios of the data types following [12]. Specifically, we view each correspondences as three different data types: $(\mathbf{p}_1,\mathbf{p}_2,d_1)$ , $(\mathbf{p}_1,\mathbf{p}_2,d_2)$ , and $(\mathbf{p}_1,\mathbf{p}_2)$ . The first two are evaluated using $E_{r(1\rightarrow 2)}$ and $E_{r(2\rightarrow 1)}$ respectively, and the third using $E_{s}$ . Inliers are defined as correspondences (in each data type) with error within the squared thresholds: $E_{r} < \tau_{r}$ or $E_{s} < \tau_{s}$ . The local optimization runs on the inliers with least square optimizer that jointly optimizes all parameters of $\Theta$ to minimize the cost function + +$$ +E (\Theta) = \sum_ {i \in I _ {1}} E _ {r (1 \rightarrow 2)} + \sum_ {i \in I _ {2}} E _ {r (2 \rightarrow 1)} + 2 \lambda_ {s} \frac {\tau_ {r}}{\tau_ {s}} \sum_ {i \in I _ {3}} E _ {s}. \tag {9} +$$ + +with $I_1, I_2, I_3$ being the inlier sets of the three data types, and $\lambda_s$ is the Sampson error weight (tunable, empirically set to 1 in our experiments). + +With $\overline{E}_s = \min (E_s,\tau_s)$ , the combined hybrid MSAC score of all correspondences is then + +$$ +\overline {{E}} (\Theta ; \mathbf {p} _ {1}, \mathbf {p} _ {2}) = \overline {{E}} _ {r} + 2 \lambda_ {s} \frac {\tau_ {r}}{\tau_ {s}} \overline {{E}} _ {s}, \tag {10} +$$ + +which is used to select the best solution with minimal $\overline{E}$ summed over all correspondences. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets: We evaluate our method across multiple datasets: ScanNet-1500 [15] and MegaDepth-1500 [38] are used to evaluate relative pose estimation performance with calibrated cameras on indoor and outdoor images. ScanNet-1500 is also used for the unknown shared-focal case, and MegaDepth-1500 for the two unknown focal case. To also evaluate the relative pose estimation with unknown, different focal lengths on indoor images, we sample 1064 image pairs from the Stanford 2D-3D-S panoramic dataset [2] with random focal lengths using the procedure detailed in Supp. Sec. A. In addition, we also sampled 1451 image pairs from the 7 indoor scenes1 of ETH3D [59] dataset. These include all covisible image pairs with a minimum of 50 covisible ground-truth (GT) 3D points. Having these GT 3D points allows us to analyze the performance of our framework especially in hard cases where the image pair has a low可视ibility (Fig. 3). + +Baselines: We compare against the three classic point-based methods for the three settings. We use the PoseLib [33] RANSAC implementation of each point-based baseline. We also compare with previous methods in their corresponding settings: the Perspective-n-Points (PnP) method [24] used in [41] and the solvers proposed in [4] for the calibrated setting; the 3p3d solver [17] for the unknown shared-focal setting; and the 4p4d solver [17] for the two-focal setting. The solvers from [4] and [17] are run using the implementation obtained from the authors within GC-RANSAC [3] as in the original papers. We also compare with two recent two-view dense reconstruction methods: DUSt3R [70] and MASt3R [37], in the shared-focal and two-focal settings. DUSt3R and MASt3R are evaluated using the direct output two-view pointmaps from the models without global alignment [70]. + +Feature Matchers and MDE Models: Our framework can work with off-the-shelf feature matchers and MDE models that produce affine-invariant depth priors. We test our method with sparse matchings Superpoint [16] $^+$ LightGlue [40], as well as the state-of-the-art (SOTA) dense matcher + +
MatchesMethodMD ModelMed. Err. ↓Pose Error AUC (%) ↑
εR(°)εt(°)@5°@10°@20°
SP+LGPoseLib-5pt-1.865.5321.5539.1155.60
PoseLib-PnPDA-met.2.036.4415.0534.1653.97
PoseLib-PnPMoGe1.725.3719.6940.2158.73
2PT+D&5pt [4]DA-met.1.905.6720.6238.4554.94
2PT+D&5pt [4]MoGe1.885.6620.7438.5354.98
Ours-calibDA-met.1.684.9722.4142.1859.96
Ours-calibMoGe1.574.7723.3643.3961.08
RoMaPoseLib-5pt-1.293.1833.4055.3472.41
PoseLib-PnPDA-met.1.634.4622.8347.0468.12
PoseLib-PnPMoGe1.383.7528.3852.6271.61
2PT+D&5pt [4]DA-met.1.323.2732.2754.3471.72
2PT+D&5pt [4]MoGe1.333.2932.2154.2971.62
Ours-calibDA-met.1.263.1434.2156.5573.55
Ours-calibMoGe1.243.1234.2656.7773.67
+ +Table 1. Results of relative pose estimation with known camera intrinsics on ScanNet-1500 [15]. The reported metrics are median rotation and translation direction errors $\varepsilon_{R}$ , $\varepsilon_{t}$ , as well as pose error AUCs under $5^{\circ}$ , $10^{\circ}$ , and $20^{\circ}$ thresholds. Best results with each type of matches are bolded and second best underlined. + +
MatchesMethodMD ModelMed. Err. ↓Pose Error AUC (%) ↑
εR(°)εt(°)@5°@10°@20°
SP+LGPoseLib-5pt-0.461.2360.1674.2584.34
PoseLib-PnPDA-met.0.993.2934.7954.5572.32
PoseLib-PnPMoGe0.561.8052.4671.0583.80
2PT+D&5pt [4]DA-met.0.521.3757.8372.8583.73
2PT+D&5pt [4]MoGe0.541.4455.8670.9782.20
Ours-calibDA-met.0.471.2659.8074.7785.47
Ours-calibMoGe0.411.1663.4877.7987.18
+ +RoMa [20]. Several MDE models predicting affine-invariant depths are used: Omnidata [31], Marigold [32], the metric depth models of Depth-Anything v1 [74] and v2 [75], and MoGe [69]. Due to limited space, we report results with best performing models in the main paper and put the others in Supp. Sec. B. Note that while the Depth-Anything metric models are trained to predict metric depth, Tab. 6 show that modeling the scale and shift is still beneficial. + +Implementation Details: We implement our solvers and hybrid estimation pipeline in $\mathrm{C + + }$ . Our hybrid LO-MSAC is based on the hybrid-RANSAC implementation from RansacLib [55], with non-minimal solver and least square optimization implemented using automatic differentiation from Ceres solver [1]. We further export Python bindings using pybind11 [30] to conveniently use our framework in Python scripts. For all experiments, ScanNet images are resized to $640\times 480$ , ETH3D images to $720\times 480$ , and other images are used with their original resolution. + +# 5.2. Results and Analysis + +Calibrated Cameras: Tab. 1 shows the median rotation error $\varepsilon_{R}$ and translation error $\varepsilon_{t}$ , as well as the Area Under the Curve (AUC) of the pose error (max of $\varepsilon_{R}$ and $\varepsilon_{t}$ ) for various thresholds on ScanNet-1500 [15]. With sparse feature + +Table 2. Relative pose estimation results with known intrinsics on MegaDepth-1500 [38]. + +
MatchesMethodMD ModelMed. Err. ↓Pose Err. AUC (%) ↑
εR(°)εt(°)εf(%)@5°@10°@20°
SP+LGPoseLib-6pt-2.718.0510.9414.1929.4945.47
3p3d [17]DAv23.279.3713.6612.0926.0941.88
Ours-sfDA-met.1.935.786.9917.7436.7155.12
RoMaPoseLib-6pt-1.523.854.4927.1749.2467.42
3p3d [17]DAv21.644.155.3025.4647.1765.47
Ours-sfDA-met.1.373.543.7129.8153.1171.15
MASt3RPoseLib-6pt-1.443.314.1830.2854.1672.87
3p3d [17]DAv21.513.404.5429.1752.2871.08
Ours-sfDA-met.1.353.093.7331.8756.2074.51
MASt3R1.323.063.7932.5856.9974.91
Reference entry - DUSt3R1.294.023.8025.9048.4568.03
Reference entry - MAST3R1.534.225.7223.9446.4466.18
+ +Table 3. Uncalibrated shared-focal relative pose estimation results on ScanNet-1500 [15]. In addition to $\varepsilon_{R}$ and $\varepsilon_{t}$ and pose error AUCs, the median relative focal error $\varepsilon_{f}$ is also reported. + +matching (SP+SG or SP+LG) as well as dense matching (RoMa), our method consistently improves over the baselines across all metrics using priors from both the Depth-Anything-v1 [74] metric model (DA-met.) and the nonmetric affine-invariant depth model MoGe [69]. Compared to the PnP baseline, even when the MDE model is trained to predict metric depth, our affine-invariant modeling of the depth priors is still beneficial. Comparisons with other solver combinations from [4] can be found in Supp. Sec. B. + +We also evaluate on the outdoor image pairs of MegaDepth-1500 [38]. Due to the larger and more varied scene scales, MDE models often perform poorly on outdoor data compared to indoor. However, as the results in Tab. 2 show, our method can still improve over the baselines on outdoor images with the latest MoGe [69] model. While DA-met. depth estimations become less reliable outdoor, our method still outperforms RANSAC PnP using the same depth priors and is reasonably close to the point-based baseline thanks to the hybrid estimation. + +Shared-focal Cameras: For the shared-focal case, we again use the ScanNet-1500 image pairs but ignore the GT intrinsics. We additionally report the median $\varepsilon_{f}$ of relative focal errors which are computed as $|f - f_{gt}| / f_{gt}$ . Tab. 3 shows the results. Note that the 3p3d solver [17] takes disparity values as input, so we use the disparity priors predicted by Depth-Anything-v2 [75] (as in [17]). Our results are reported with the best performing DA-met. model. MoGe is not used for shared-focal or uncalibrated case because it also estimates focal lengths and can therefore benefit directly from using calibrated hybrid estimation. + +With all tested matches, our method improves over the baselines consistently and significantly. 3p3d solver only models the depth priors as scale-invariant but does not consider the shift, so it is sensitive to noise in the priors [17] and therefore fails to improve over point-based baseline. The recent works DUSt3R [70] and MASt3R [37] produce good image matching, two-view depth maps, and relative + +
MatchesMethodMD ModelMed. Err. ↓Pose Err. AUC (%) ↑
εR(°)εt(°)εf(%)@2°@5°@10°@20°
SP+LGPoseLib-7pt-16.8321.5759.885.8513.9521.9430.71
4p4d [17]DAv219.2721.6466.575.3113.6621.7830.22
Ours-tfDAv2-met.5.669.2629.069.1522.2232.8043.26
RoMaPoseLib-7pt-7.998.7737.728.7320.3130.4541.48
4p4d [17]DAv210.9411.3544.947.2316.5025.3136.26
Ours-tfDAv2-met.3.334.3217.2913.5029.1942.1854.42
MASt3RPoseLib-7pt-3.213.3419.9512.5830.2745.5759.85
4p4d [17]DAv23.213.2820.0712.1329.8245.3060.05
Ours-tfDAv2-met.1.982.2211.2718.0539.9256.6470.86
MASt3R1.331.667.9322.4448.0264.7976.55
Reference entry - DUS3R2.654.657.416.4324.4742.3958.36
Reference entry - MAST3R1.712.492.9113.3938.4157.9271.91
+ +Table 4. Uncalibrated results on our generated image pairs with different focal lengths from Stanford 2D-3D-S [2] dataset. $\varepsilon_{f}$ is the maximum of the two relative focal errors per image pair. + +
MethodMD ModelMed. Err. ↓Pose Err. AUC (%) ↑
εR(°)εt(°)εf(%)@5°@10°@20°
PoseLib-7pt-1.975.7223.6421.2336.8054.89
4p4d [17]DAv23.488.7039.9214.0426.7044.08
Ours-tfDA-met.1.254.8115.9925.7042.9061.79
+ +Table 5. Uncalibrated results on MegaDepth-1500 [38]. + +pose by directly regressing aligned point maps from two views, so we report their relative pose estimation results for reference and also evaluate our method with MAST3R matches and depth. By using the shared-focal constraint which they do not model, our method performs better than these two-view methods with RoMa matches and DA-met. depth priors, and can be further improved with better matches and depth from MAST3R. + +Unknown focal cameras: For the most general case with two uncalibrated cameras, we define the focal error as the max of the two relative focal errors of the two cameras and again report the median $\varepsilon_{f}$ . Significant improvements can be observed in Tab. 4 on the uncalibrated image pairs from our sampled 2D-3D-S dataset. Our method achieves less than $50\%$ in the median errors of the point-based baseline and significant improvements in pose error AUCs. + +Similar to the 3p3d solver, the 4p4d solver [17] is tested with Depth Anything v2 [75] depth priors and again fails to improve over point-based baseline. Using better matches from MAST3R [37], our method is able to achieve on-par results using monocular depth priors (Depth-Anything-v2 metric model), with significantly better accuracy on small threshold AUCs. Our method further outperforms MAST3R if using the depth from MAST3R as priors. + +We also evaluate with the uncalibrated camera setting on outdoor MegaDepth-1500 [38] images (Tab. 5). Compared with the calibrated results in Tab. 2, our method (with DA-met. model) now shows significant improvements over the point-based fundamental matrix estimator. + +![](images/4d9509e7da458359b2c212815ee7edfbe1ba9a70cba57b455d5c1770e761eded.jpg) + +![](images/74dfe06d7727b9c50f1e4d5511cbd4277e2352ace411fbe46fbf0b32a725daf4.jpg) + +![](images/b2107671c8183496f57532be4c8c0cb7f5ee369af2e73a40afc3ca6107b8a06b.jpg) +Figure 3. Pose error AUCs on sampled indoor ETH3D [59] image pairs with covisible GT points less than the thresholds on X-axis. Left: calibrated, SP+LG, and MoGe [69] priors; Right: shared-focal, SP+LG, and DAv2-met.[75] metric priors. +Figure 4. Visualization on ETH3D [59]. Left: back-projected GT depth with pose found by point-based method (translation rescaled to match GT); Middle: back-projected depth priors from Marigold [32] aligned using the scale, shifts, pose, and focal length from our method; Right: GT depth with GT pose. + +Limited Covisibility: We further analyze the pose errors under different levels of covisibility between image pairs on the indoor ETH3D [59] pairs and the results are shown in Fig. 3. Comparing the gap between our method and point-based baselines, incorporating the depth priors can particularly improve the relative pose estimation results on difficult image pairs with limited covisibility. + +Visual examples: In Fig. 4 we show visualizations of point clouds reconstructed with relative pose estimated by point-based baseline and ground-truth (GT) depth, and results from our method with scale-and-shifted monocular depth priors. The visualizations demonstrate that by incorporating depth priors and by explicit modeling of the affine transformation, our method is able to find a better pose or to avoid failure cases with better depth alignment. + +Runtime: While the added considerations for depth priors introduces additional computations, our method achieves good performance while maintaining efficiency. By tuning LO and RANSAC parameters to balance performance and speed (with only marginal accuracy loss), our pipeline can achieve the following typical (median) solution times per image pair: 31ms for calibrated case, 65ms for shared-focal case on ScanNet-1500; and 129ms for uncalibrated case on 2D-3D-S image pairs. The numbers are measured on Intel Core i7-10700K CPU, with SP+LG matches. The speed can be further improved by replacing the Ceres autodifferentiated Jacobians with analytic expressions, further + +
DatasetMD ModelHybridShiftMed. ER↓Pose Error AUC (%)↑
εR(°)εt(°)@5°@10°@20°
ScanNet -1500DA-met.✓✓1.744.7323.1243.3762.26
✓1.805.0919.9641.4561.58
✓1.885.3319.1340.2160.65
2.005.8516.6337.2459.37
Marigold✓✓1.875.0520.6840.7159.92
✓2.859.1712.3426.6444.53
✓2.196.4114.7033.7354.75
6.2420.441.094.8417.15
MegaDepth -1500MoGe✓✓0.421.1663.4877.4486.85
✓0.631.9051.3270.0983.02
✓0.551.5656.8773.8085.11
0.742.4544.1564.9079.84
+ +tuning, and better multi-threading in the pipeline. When running on a RTX 3080 GPU, the typical runtime of matchers and MDE models are: SP+LG 16ms/pair; DAv2-met. (ViT-L) 0.16s/image; MoGe (ViT-L) 3ms/image. All models are run with default settings. + +# 5.3. Ablation Studies + +Modeling scale and shift: To further demonstrate the effectiveness of our affine correction modeling, we compare with an ablated scale-only baseline that removes the shift modeling in the calibrated solver and scoring. A visual example is shown in Teaser Fig. 1. Without the unknown $\beta_{1},\beta_{2}$ , the scale and pose can be together solved by finding the rigid transformation using the 3 point matches and depth priors. For scoring, the reprojection error also removes $\beta_{1},\beta_{2}$ and only lift the 2D points with $\alpha$ . + +Tab. 6 shows the comparison with the ablated baselines. The non-hybrid version uses only the depth-aware calibrated solver, and only reprojection errors in LO and scoring. The results show that the shift modeling especially makes a difference for non-metric monocular depth models like Marigold [32] and for outdoor images due to the larger and more varied scale. With depth priors targeting metric depth, modeling the shift is again proven beneficial. + +We further analyze when modeling the shift starts making a difference with a synthetic experiment. We add a shift value ranging from 0 to the median of GT depth for each image and use this shifted GT depth as "depth priors". We compare the median rotation and translation errors on ScanNet-1500 [15] with $\mathrm{SP + SG}$ matches. As shown in Fig. 5, modeling the shift is beneficial as long as the magnitude of $\beta$ is greater than $10\%$ of the median depth priors, and our method is not influenced by the increased shift magnitude while the errors of the PnP and scale-only baselines increase. In Fig. 6 we show the computed shift values by fitting depth priors to GT depth with metric [74] and nonmetric [32] models on indoor [15] and outdoor [38] images. Shift values larger than $10\%$ of the median of the priors are common even with metric depth models on indoor data, jus + +![](images/f42944614890806379aad8958d293353cbf4213043d5af7892c81141b1b9aa22.jpg) +Figure 5. Rotation and translation error by adding shift values to GT depth as "depth priors" on ScanNet-1500 [15]. + +![](images/7d79f5b84c3d4d9c9ccd82fc3b94d385e625b35817cf2e35e94ad9ced7853d64.jpg) +Figure 6. Distribution (probabilistic density) of GT shift values $(\beta_{1},\beta_{2})$ after fitting MDE depth priors to the GT depth. Red lines indicate $\beta = 10\% = 0.1$ (refer to Fig. 5). Even with metric depth priors on indoor data, modeling the shift is crucial. + +![](images/fc8dce5d7cda49cd407045034f121a555fc18af7139c2e9234196bbe9a54c271.jpg) + +![](images/af14e51b76e72f39c4b84bc8d746e6d665d8e006479eeb92a545d691653186c4.jpg) + +![](images/40c9480ebcd355d23fa530bb5bda12a4b280ca28857cb525b080edb5053fce7b.jpg) + +Table 6. Ablation of shift modeling with calibrated cameras. All results are with SP+LG correspondences. + +
SolverLOScoreMed. Err. ↓Pose Error AUC (%) ↑
εR(°)εt(°)εf(%)@5°@10°@20°
HHH2.005.706.8418.3537.5457.58
DHH2.205.897.4217.1736.1756.03
PHH2.206.107.3616.6035.3355.26
DDH2.226.337.9515.4234.3955.14
PPH2.426.689.0915.0632.3251.00
DDD2.216.838.1813.8532.1153.50
PPP2.847.4511.3014.0629.8648.13
+ +Table 7. Ablation of different components of hybrid LO-MSAC on ScanNet-1500 [15] with shared-focal setting, SP+SG matches and DA-met. depth priors. H - Hybrid; D - Depth solver and reprojection score; P - Point-based solver and Sampson score. + +tifying the gains of our method. + +Ablation of hybrid estimation: Tab. 7 shows ablation on different components of our hybrid estimation. While the hybrid scoring brings the largest improvements, all components contribute to the success of our hybrid estimation. + +# 6. Conclusion + +In this paper, we present a relative pose estimator that benefits from explicit modeling of affine variants of monocular depth priors. We propose solvers for calibrated and uncalibrated camera setups, and combine them with classic methods to achieve consistent improvements across multiple datasets. The proposed method can further benefit from latest advances on image matching and monocular depth estimation. + +Acknowledgements. We sincerely thank Philipp Lindenberger for insightful ideas, as well as Lei Li, Chong Bao, Yiming Zhao, and Zihan Zhu for their support and helpful discussions. Viktor Larsson was supported by ELLIIT and the Swedish Research Council (Grant No. 2023-05424). + +# References + +[1] Sameer Agarwal, Keir Mierle, and The Ceres Solver Team. Ceres Solver, 2023. 6 +[2] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. Joint 2d-3d-semantic data for indoor scene understanding. arXiv:1702.01105, 2017. 5, 7, 12, 13, 15 +[3] Daniel Barath and Jiri Matas. Graph-cut RANSAC. In CVPR, 2018. 5, 12, 13 +[4] Daniel Barath and Chris Sweeney. Relative pose solvers using monocular depth. In ICPR, 2022. 1, 2, 5, 6, 13 +[5] Daniel Barath, Dmytro Mishkin, Luca Cavalli, Paul-Edouard Sarlin, Petr Hruby, and Marc Pollefeys. Stereoglue: Robust estimation with single-point solvers. 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In recent years, deep neural networks that directly regress camera poses have gained popularity due to their fast inference capabilities. However, existing methods struggle to either generalize well to new scenes or provide accurate camera pose estimates. To address these issues, we present Reloc3r, a simple yet effective visual localization framework. It consists of an elegantly designed relative pose regression network, and a minimalist motion averaging module for absolute pose estimation. Trained on approximately eight million posed image pairs, Reloc3r achieves surprisingly good performance and generalization ability. We conduct extensive experiments on six public datasets, consistently demonstrating the effectiveness and efficiency of the proposed method. It provides high-quality camera pose estimates in real time and generalizes to novel scenes. Code: https://github.com/ffrivera0/reloc3r. + +# 1. Introduction + +Visual localization, also known as camera re-localization, is a key challenge in computer vision, robotics, and graphics. It's crucial for many applications, including augmented reality and robot navigation. The process involves registering new query images to a database of posed images or 3D models. This is typically done by estimating 6-degree-of-freedom (6-DoF) camera poses within a world coordinate system defined by the database. + +Traditional visual localization approaches rely on structure-from-motion (SfM) techniques [27, 80, 88] to reconstruct 3D models. These methods [33, 37, 60, 72, 76, 80, 84, 95, 109, 112] match pixels from query images to 3D scene points, then use geometric optimization [36, 38, 47, 79, 81] to solve camera poses. While renowned for their + +![](images/f4de6f27553b5dcb3030ce08b036dd7e34a22995c9539bc4ed89ce66b999280a.jpg) +Figure 1. Comparison of pose accuracy and runtime efficiency. We report the AUC@5 and image pairs per second (FPS) on the ScanNet1500 [26, 80] dataset. We provide two versions of Reloc3r: one trained and tested on image widths of 512, and another on 224. The proposed Reloc3r-512 outperforms all other methods, achieving the best AUC@5 while maintaining an efficiency of 24 FPS. Remarkably, even at 224 resolution, our method matches ROMA [34] in accuracy while being $20 \times$ faster. + +high localization accuracy, these approaches often struggle with inefficiencies at test time, which limits their scalability for real-time applications. Scene coordinate regression approaches [13-16, 30, 53, 54] provide an alternative perspective on pixel-to-point correspondences. These methods use neural networks to learn implicit scene representations, which are then used to infer dense correspondences. However, most of them face limitations in generalization. Moreover, these methods often require intensive supervision, such as ground-truth keypoint matches or 3D point maps, making it challenging to scale up the training data. + +Absolute pose regression (APR) approaches [18, 42, 43, 66, 70, 89, 90, 103, 104, 117, 124] directly regress camera poses from images, offering much faster inference times and high accuracy. However, most of these methods are inherently scene-specific and typically require dense viewpoint coverage during training, limiting their real-world applicability. Recent attempts [20-22, 58, 69] to enhance ac + +curacy through synthetic data generation introduce significant computational overhead, hampering widespread deployment. In contrast, relative pose regression (RPR) approaches [1, 4, 7, 35, 49, 49, 116, 129] estimate relative poses between database-query image pairs. These methods mitigate the need for per-scene training while maintaining the test-time efficiency of APR models. However, even the most advanced RPR methods [4, 29, 101, 116] have not yet matched APR approaches in localization accuracy. While several RPR methods [4, 49, 101, 116] have shown the ability to generalize across different datasets, this often results in further reduced camera pose accuracy. Therefore, most of the aforementioned approaches struggle with one of the following three criteria: novel-scene generalization, test-time efficiency, and camera pose accuracy. + +To address these challenges, we present Reloc3r (pronounced "rr'loʊkər"), a simple yet surprisingly effective visual localization framework. It draws inspiration from recent foundation models [6, 46, 51, 63, 73, 98, 108, 111]. These models, utilizing scalable network architectures (such as Transformers [32, 40]) and large-scale training, demonstrate strong performance and exceptional generalization across various tasks. This success motivates our exploration of a similar methodology for pose estimation. We adopt architecture from DUSt3R [111] as the backbone, applying parsimonious and elegant modifications to build a relative pose regression network. The network is designed to be fully symmetric and disregards the metric scale of relative poses during training. We then integrate this with a minimalist motion averaging module to estimate absolute poses, resulting in the Reloc3r framework. To unleash the power of large-scale training, we processed around eight million image pairs from diverse public sources, spanning object-centric, indoor, and outdoor scenes. Experimentally, Reloc3r demonstrates superior performance across six well-known pose estimation datasets, benefiting from its simple architecture and large-scale training. Our key contributions can be summarized as follows: + +- We introduce Reloc3r, a simple yet surprisingly effective visual localization framework. It enables excellent generalization to novel scenes, fast test-time efficiency, and high camera pose accuracy. +- Both the proposed fully symmetric relative pose regression network and the motion averaging module follow the principle of parsimony. This streamlined approach enables efficient large-scale training. +- Comprehensive experiments across six popular evaluation datasets consistently demonstrate the effectiveness of our proposed approach. + +# 2. Related Work + +Structure-based visual localization. The structure-based localization pipeline is a well-established approach to solv + +ing camera pose via multi-view geometry [38]. Modern methods [37, 41, 55, 64, 72, 81-86, 96, 109, 120, 125, 129] typically consist of two main steps: 1) establishing correspondences either between images or between pixels and a pre-built 3D model, and 2) robustly solving the camera pose from noisy correspondences. These correspondences are obtained through keypoint matching [2, 27, 33, 34, 51, 60, 65, 76, 80, 95, 112] or scene coordinate regression [13-16, 30, 53, 54, 97, 110, 119]. Robust estimators [8-11, 25, 36, 48, 50] are then applied to estimate the final camera pose. Though effective, these methods often have slow inference times, which limits their use in real-time applications. Recent efficiency-oriented variants [60, 112] have been proposed to speed up the matching process. However, the complex system design and high computational cost of robust estimation remain bottlenecks. These methods typically require ground-truth correspondences or 3D point maps for supervision, limiting their scalability for large-scale training. To address these challenges, we choose a straightforward camera pose regression approach. This method allows for efficient large-scale training while simplifying the system, resulting in a faster and more scalable visual localization solution. + +Camera pose regression. End-to-end pose regression [1, 4, 7, 18, 20-23, 29, 35, 42-44, 49, 58, 66, 69, 70, 78, 87, 89, 90, 101, 103, 104, 116, 117, 124, 129] has gained popularity due to its real-time inference capabilities. These methods fall into two broad categories: absolute pose regression (APR) and relative pose regression (RPR). + +APR approaches directly regress camera positions and orientations in the world coordinate system from images within milliseconds. Despite their simplicity, these methods fall short of the localization accuracy achieved by structure-based approaches and often resemble pose approximation through image retrieval [87]. To improve the accuracy of APR, some methods [21, 22, 58, 69] resort to novel view synthesis [67] to create dense viewpoints for training. While being effective, this strategy introduces significant computational costs, with training taking hours or days for each specific scene. More recent approach [23] attempts to reduce training time to minutes by building the connection between pose regressor and scene-specific maps. However, it is still limited to per-scene training and evaluation. + +RPR approaches aim to generalize across different scenes by learning the relative pose between image pairs. Localization is achieved by regressing the relative pose between the query image and the most similar (or top- $K$ ) database images. The metric scale of the relative translation can be estimated approximately from a single database-query pair [1, 4, 7, 35], while more precise absolute positioning is possible through multi-view triangulation [31, 49, 116, 129]. Despite this capability, the best RPR methods [4, 29, 45, 116, 129] lag significantly behind APR meth + +ods. Furthermore, the generalization ability of existing RPR models remains limited. For instance, methods like Relative PN [49] and Relpose-GNN [101] can adapt to new datasets and scenes, but their localization errors nearly double in these scenarios. Map-free [4], despite being trained on large datasets (about 523K samples), still relies on separate models for indoor and outdoor settings. Other approaches explore multi-view pose estimation [57, 106, 118, 127, 128], as well as wide-baseline [77] and panoramic methods [100]. However, they remain dataset-specific training, which limits their scalability. + +Previous methods have largely focused on technical design rather than scaling training on larger and more diverse datasets. In this paper, we present the first pose regression approach trained on a diverse mixture of object-centric, indoor, and outdoor datasets. Contrary to prior work [129] suggesting that pose regression inaccuracies stem from coarse feature localization, we find that a well-trained patch-level regression network can achieve, and sometimes even surpass the performance of pixel-level feature matching. + +Foundation Models. Large neural network models have advanced significantly due to the scalability of the Transformer architecture [102]. This architecture underpins both large language models [5, 24, 28, 68, 71, 99] and large vision models [6, 32, 46, 63, 73, 74, 98]. These foundation models, trained on large-scale datasets, have proven effective and demonstrate strong generalization capabilities across diverse tasks. Recently, DUSt3R [111] introduces the first 3D foundation model capable of addressing nearly all tasks related to two-view geometry. Its architecture has been adapted and fine-tuned in numerous follow-up works [51, 92, 105, 122, 126] to enhance performance in various downstream tasks. In our work, we adopt DUSt3R's Transformer backbone to develop Reloc3r, but featuring a fully symmetric design. We will discuss the benefits of this symmetric architecture in the following section. + +# 3. Method + +Problem statement. Given a database $\mathbf{D} = \{I_{d_n}\in$ $\mathbb{R}^{H\times W\times 3}\mid n = 1,\dots,N\}$ of posed images from a scene, and a query image $I_{q}$ from the same scene, the task of visual localization is to estimate the 6-DoF camera pose $P\in \mathbb{R}^{3\times 4}$ that can register $I_{q}$ to the world coordinate system defined by the database images. $P$ is represented by camera rotation $R\in \mathbb{R}^{3\times 3}$ and translation $t\in \mathbb{R}^3$ + +Method overview. Figure 2 illustrates an overview of the proposed visual localization method. It comprises two main components: a relative pose regression network, and a motion averaging module. The query image $I_{q}$ is paired with the top- $K$ database images using an off-the-shelf image retrieval approach [3], creating a set of image pairs $\mathbf{Q} = \{(I_{d_k}, I_q) \mid k = 1, \dots, K\}$ . The relative pose re + +gression network processes each image pair from $\mathbf{Q}$ independently to determine their relative poses $P_{d,q}$ and $P_{q,d}$ . With known poses of database images $\{\hat{P} d_1,\dots,\hat{P} d_K\}$ , it is possible to infer the query image's absolute rotation from a single pair. However, these estimates can be noisy, and the translation vector's metric scale remains uncertain. To tackle these issues, a motion averaging module performs rotation averaging and camera center triangulation, eventually producing the absolute metric pose of the query image. + +In Sec. 3.1, we provide a detailed description of the pose regression model. This model leverages a unified Vision Transformer (ViT) [32] architecture with minimal modifications. The motion averaging module discussed in Sec. 3.2 also takes a minimalist approach. It performs simple rotation averaging and camera center triangulation, without any trainable parameters involved. + +# 3.1. Relative Camera Pose Regression + +The proposed relative camera pose regression network, inspired by DUSt3R [111], takes an image pair $I_1, I_2$ as input. While we assume the images have the same resolution (consistent with DUSt3R), their resolutions may differ in practice. The network divides the images into patches and processes them as tokens through a Vision Transformer (ViT) encoder. A ViT decoder [113, 114] then uses a cross-attention mechanism to exchange information between tokens from both branches. This is followed by regression heads that predict the relative poses $\hat{P}_{I_1, I_2}$ and $\hat{P}_{I_2, I_1}$ . The two branches are fully symmetrical with shared weights. + +ViT encoder-decoder architecture. The two modules re-semble those of DUSt3R and gain substantial benefits from pre-training. We begin by dividing each input image $I_{i}$ into a sequence of $T$ tokens, each with dimension $d$ . Next, we compute RoPE positional embeddings [94] for each token to encode their relative spatial positions within the image. Then, we process the tokens through $m$ ViT encoder blocks, each comprising self-attention and feed-forward layers, to produce encoded feature tokens $F_{1}$ and $F_{2}$ : + +$$ +F _ {i} ^ {(T \times d)} = \operatorname {E n c o d e r} \left(\operatorname {P a t c h i f y} \left(I _ {i} ^ {(H \times W \times 3)}\right)\right), \text {w h e r e} i = 1, 2. +$$ + +The decoder comprises $n$ ViT decoder blocks, each using the same RoPE position embedding. Unlike the encoder block, each decoder block incorporates an additional cross-attention layer between its self-attention and feed-forward layers. This structure enables the model to reason the spatial relationship between two sets of feature tokens. We obtain decoded tokens as: + +$$ +G _ {1} ^ {(T \times d)} = \operatorname {D e c o d e r} \left(F _ {1} ^ {(T \times d)}, F _ {2} ^ {(T \times d)}\right), +$$ + +$$ +G _ {2} ^ {(T \times d)} = \operatorname {D e c o d e r} \left(F _ {2} ^ {(T \times d)}, F _ {1} ^ {(T \times d)}\right). +$$ + +Pose regression head. Following recent research [23], our pose regression head comprises $h$ feed-forward layers followed by average pooling, with additional layers to regress + +![](images/87bf9ef524ff43fbdc332e53e6da9e110bb6cd920b86bcd193952d3aa7036865.jpg) +Figure 2. Reloc3r consists of two modules: a relative camera pose regression network (Sec. 3.1) and a motion averaging module (Sec. 3.2). Given a pair of input images, the network module infers the relative camera pose (at an unknown scale) between them. This module consists of a two-branch Vision Transformer (ViT) with shared weights. The images are divided into patches, converted to tokens, and embedded as latent features through separate encoders. Decoders then exchange information between the two sets of latent features. Each head aggregates its latent features to estimate a relative camera pose. To determine the absolute camera pose of a query image relative to a database, we retrieve at least two database-query pairs. These pairs are first processed by the network for relative pose estimation. Subsequently, the motion averaging module computes the absolute metric pose by aggregating the relative estimates. + +relative rotation and translation. The rotation is initially represented using a 9D representation [52]. It is then converted into a $3 \times 3$ rotation matrix using SVD orthogonalization. This matrix is concatenated with the 3D translation vector to form the final transformation matrix. The final output for the relative pose is: + +$$ +\hat {P} _ {I _ {1}, I _ {2}} ^ {(3 \times 4)} = \operatorname {H e a d} (G _ {1} ^ {(T \times d)}), \quad \hat {P} _ {I _ {2}, I _ {1}} ^ {(3 \times 4)} = \operatorname {H e a d} (G _ {2} ^ {(T \times d)}). +$$ + +Supervision signal. The predicted pose by our network conveys two pieces of information: 1) rotation, which measures the relative change in orientation, and 2) translation, which indicates the relative direction of camera center movement. Both of these quantities can be expressed as relative angles. Consequently, we train the network by minimizing the difference between these predicted relative angles and their ground-truth: $\mathcal{L} = \ell_R + \ell_t$ , where + +$$ +\ell_ {R} = \operatorname {a r c c o s} (\frac {\operatorname {t r} (\hat {R} ^ {- 1} R) - 1}{2}), \ell_ {t} = \operatorname {a r c c o s} (\frac {\hat {t} \cdot t}{\| \hat {t} \| \| t \|}). +$$ + +Here, $\operatorname{tr}(\cdot)$ denotes the trace of a matrix. $\hat{R}$ and $\hat{t}$ represent the predicted rotation and translation, while $R$ and $t$ represent their respective ground-truth values. + +Discussion. Unlike DUSt3R's asymmetric branches for coordinate alignment, we use a fully symmetric architecture, which is inherently more suitable for relative pose estimation. This design eliminates biases from image ordering, thereby simplifying training. It also allows weight sharing across branches, reducing computational complexity and storage requirements. + +Recent works [4, 116] on relative pose regression prefer learning a metric pose. In contrast, we choose to learn only the direction of translation, as motion averaging can effectively solve the metric scale (discussed in the next section). This approach represents translations as angles in the same dimension as rotations, eliminating the need to weight ro + +tation and translation values during training. It also avoids the challenge of balancing different dataset metric scales. + +# 3.2. Motion Averaging + +To maintain efficiency and simplicity, we integrate our pose regression network with a minimalist motion averaging module. Given the high accuracy of the network's predictions, we don't apply any robust estimation [19, 31, 36, 115, 131]. For each image pair, the regression network produces two relative poses: $\hat{P}_{I_1,I_2}$ and $\hat{P}_{I_2,I_1}$ , which ideally should be inverses of each other. Empirically, we observe similar accuracy for both poses. By default, we use the transformation that maps the query to the database as input for motion averaging. The module processes rotation and translation separately, as detailed below. + +Rotation averaging. Given a relative rotation estimation $\hat{R}_{q,d_i}$ from a database-query pair, the absolute rotation is computed as $\hat{R}_q = R_{d_i}\hat{R}_{q,d_i}$ . The motion averaging module reduces prediction noise by aggregating absolute rotation estimates from all available pairs. This aggregation is efficiently performed by calculating the mean rotation using quaternion representations [129]. We have observed that calculating the median rotation can further enhance robustness against noise, with minimal additional computational cost. Consequently, we use the median rotation as our final rotation estimation. + +Camera center triangulation. The absolute camera center can be triangulated [39] from two database-query pairs. Similar to rotation averaging, we calculate an average intersection using all valid pairs. While the geometric median of the intersection is not analytically solvable and typically requires iterative optimization, we opt for a more efficient approach. We use a simple least-squares method that minimizes the sum of squared distances from the camera center to each translation direction derived from relative pose estimates. The solution is obtained through Singular Value + +Decomposition (SVD). + +# 4. Experiments + +In this section, we first introduce our training data and implementation details, then evaluate our method across multiple datasets. In Sec. 4.1, we verify our network's performance on the relative pose estimation task. In Sec. 4.2, we evaluate our full method on the visual localization task. Finally, we conduct ablation studies and analyses in Sec. 4.3. It's worth noting that our method is trained once for all experiments, meaning all evaluations use the same model, except for the ablation studies. + +Training data. To build up-to-scale training pairs with ground-truth relative poses, similar to DUSt3R [111], we process around eight million image pairs from seven public datasets. The statistics are reported in Table 1. We convert the ground-truth relative poses to a unified format: relative coordinate transformation aligned with the OpenCV [17] definition. Each image is center-cropped based on its principal points and resized to a width of 512 pixels. + +
DatasetsScene typeNumber of image pairs
CO3Dv2 [75]Object-centric~1M
ScanNet++ [123]Indoor~850K
ARKitScenes [12]Indoor~2.1M
BlendedMVS [121]Outdoor~1M
MegaDepth [56]Outdoor~1.8M
DL3DV [61]Indoor & outdoor~1.1M
RealEstate10K [130]Indoor & outdoor~100K
+ +Implementation details. By default, the proposed Reloc3r uses $m = 24$ encoder blocks, $n = 12$ decoder blocks, followed by the pose regression head with $h = 2$ convolutional layers. To improve memory usage and speed in self and cross-attention, we employ memory-efficient attention. This design achieves approximately a $14\%$ speed increase while saving $25\%$ of GPU memory during training. We initialize Reloc3r with DUSt3R's pre-trained 512-DPT weights. For decoder initialization, we use the weights from DUSt3R decoder2, as it's pre-trained to perform coordinate transformation. The full model is trained on 8 AMD MI250x-40G GPUs with a batch size of 8 and a learning rate starting at 1e-5, decaying to 1e-7. + +For the visual localization task, following the literature [79, 101], we apply NetVLAD [3] for image retrieval and use the top 10 similar image pairs. We directly use these retrieved image pairs without distance-based clustering, filtering, or other heuristics to enhance their spatial distribution. All evaluations are conducted on a 24GB NVIDIA GeForce RTX 4090 GPU and we use mixed precision fp16 + +Table 1. Training data of Reloc3r. It comprises about eight million image pairs from seven public sources, covering a wide range of scenes from object-centric to indoor and outdoor environments. + +
MethodsRRA@15RTA@15mAA@30
Non-PRPixSfM [59]33.732.930.1
RelPose [127]57.1--
PoseDiffusion [106]80.579.866.5
RelPose++ [57]82.377.265.1
RayDiffusion* [128]93.3--
VGGSfM [107]92.188.374.0
DUSt3R (w/ PnP) [111]94.388.477.2
MASt3R [51]94.691.981.1
PRPoseReg [106]53.249.145.0
RayReg* [128]89.2--
Reloc3r-224 (Ours)93.691.979.1
Reloc3r-512 (Ours)95.893.782.9
+ +Table 2. Relative pose evaluation (multi-view) on the CO3Dv2 dataset [75]. The best results for each method category are highlighted in bold. The underlined numbers indicate that our method achieves the best performance among all competitors. The methods marked with * donate evaluation on 8 frames. + +/ fp32 to improve speed and memory efficiency without sacrificing accuracy. + +# 4.1. Relative Camera Pose Estimation + +In this section, we evaluate Reloc3r's relative pose regression module. Our evaluation covers two scenarios: pair-wise relative pose on ScanNet1500 [26, 80], RealEstate10K [130], and ACID [62] datasets, as well as multi-view relative pose on Co3dv2 [75] dataset. + +Pair-wise relative pose. Following recent research [122], we evaluate pair-wise relative pose on three datasets: ScanNet1500 [26, 80], RealEstate10K [130], and ACID [62]. These datasets showcase a variety of indoor and outdoor scenes captured with diverse camera trajectories. ScanNet1500 [26, 80] focuses on indoor scenes, RealEstate10K [130] covers both indoor and outdoor environments, and ACID [62] is an aerial outdoor dataset. Importantly, our evaluation test sets do not overlap with scenes in our training data, and ACID remains entirely unseen by Reloc3r during training. Following previous research [80, 95, 112], we employ three metrics: AUC@5/10/20. These metrics calculate the area under the curve of pose accuracy using thresholds of $\tau = 5 / 10 / 20$ degrees for the minimum of rotation and translation angular errors. + +Since no existing pose regression (PR) methods have been specifically designed for these datasets, we primarily compare our approach with non-PR methods. Additionally, we evaluate the current state-of-the-art relative pose regression methods, ExReNet [93, 116] and Map-free [4], on these datasets. The results are presented in Table 3. Reloc3r outperforms other PR methods by a significant margin across all three datasets. When compared to non-PR methods, Reloc3r also achieves SoTA performance. Specifically, on the ScanNet1500 dataset, Reloc3r delivers top + +
MethodsScanNet1500RealEstate10KACIDInference time
AUC@5AUC@10AUC@20AUC@5AUC@10AUC@20AUC@5AUC@10AUC@20
Non-PREfficient LoFTR [112]19.2037.0053.60------40 ms
ROMA [34]28.9050.4068.3054.6069.8079.7046.3058.8068.90300 ms
DUSt3R [111]23.8145.9165.5739.7056.8870.4321.5035.9549.70441 ms
MASt3R [51]28.0150.2468.8363.5476.3984.5052.1264.5473.61294 ms
NoPoSplat [122]31.8053.8071.7069.1080.6087.7048.6061.7072.80>2000 ms
PRMap-free (Regress-SN) [4]1.848.7525.330.834.0613.971.325.8216.2810 ms
Map-free (Regress-MF) [4]0.503.4813.151.616.7418.382.579.9624.5010 ms
ExReNet (SN) [116]2.3010.7126.132.177.9420.431.907.5318.6917 ms
ExReNet (SUNCG) [116]1.617.0018.033.2712.0627.854.1413.4327.7017 ms
Reloc3r-224 (Ours)28.3452.6071.5659.7075.0584.7128.2547.3462.5415 ms
Reloc3r-512 (Ours)34.7958.3775.5666.7080.2088.3938.1856.3970.3425 ms
+ +Table 3. Relative camera pose evaluation on the ScanNet1500 [26, 80], RealEstate10K [130] and ACID [62] datasets. The best results for each method category are highlighted in bold. Our method outperforms all the pose regression competitors. Moreover, it achieves the best results (underlined) among all the competitors on several datasets and metrics. Notably, our method runs in real-time, which is over $50\times$ faster than the state-of-the-art Non-PR method. Please refer to Figure 1 for an intuitive comparison with representative methods. + +
MethodsChessFireHeadsOfficePumpkinRedKitchenStairsAverageDataset-specific training time
APRLENS [69]0.03 / 1.300.10 / 3.700.07 / 5.800.07 / 1.900.08 / 2.200.09 / 2.200.14 / 3.600.08 / 3.00Days / scene
PMNet [58]0.03 / 1.260.04 / 1.760.02 / 1.680.06 / 1.690.07 / 1.960.08 / 2.230.11 / 2.970.06 / 1.93Days / scene
DFNet [21]+NeFeS [22]0.02 / 0.570.02 / 0.740.02 / 1.280.02 / 0.560.02 / 0.550.02 / 0.570.05 / 1.280.02 / 0.79Days / scene
Marepo [23]0.02 / 1.240.02 / 1.390.02 / 2.030.03 / 1.260.04 / 1.480.04 / 1.710.06 / 1.670.03 / 1.5415min / scene
RPR (Seen)EssNet (7S) [129]-------0.22 / 8.03Hours
Relative PN (7S) [49]0.13 / 6.460.26 / 12.720.14 / 12.340.21 / 7.350.24 / 6.350.24 / 8.030.27 / 11.820.21 / 9.30Hours
NC-EssNet (7S) [129]-------0.21 / 7.50Hours
RelocNet (7S) [7]0.12 / 4.140.26 / 10.40.14 / 10.50.18 / 5.320.26 / 4.170.23 / 5.080.28 / 7.530.21 / 6.73Hours
Relpose-GNN [101]0.08 / 2.700.21 / 7.500.13 / 8.700.15 / 4.100.15 / 3.500.19 / 3.700.22 / 6.500.16 / 5.20Hours
AnchorNet [78]0.06 / 3.890.15 / 10.30.08 / 10.90.09 / 5.150.10 / 2.970.08 / 4.680.10 / 9.260.09 / 6.74Hours
CamNet [29]0.04 / 1.730.03 / 1.740.05 / 1.980.04 / 1.620.04 / 1.640.04 / 1.630.04 / 1.510.04 / 1.69Hours
RPR (Unseen)EssNet (CL) [129]-------0.57 / 80.06None
NC-EssNet (CL) [129]-------0.48 / 32.97None
Relative PN (U) [49]0.31 / 15.050.40 / 19.000.24 / 22.150.38 / 14.140.44 / 18.240.41 / 16.510.35 / 23.550.36 / 18.38None
RelocNet (SN) [7]0.21 / 10.90.32 / 11.80.15 / 13.40.31 / 10.30.40 / 10.90.33 / 10.30.33 / 11.40.29 / 11.3None
ImageNet+NCM [129]†-------0.19 / 4.30None
Map-free (Match) [4]†0.10 / 2.930.12 / 4.950.11 / 5.400.12 / 3.010.16 / 3.190.14 / 3.450.21 / 4.500.14 / 3.92None
Map-free (Regress) [4]0.09 / 2.660.13 / 4.540.11 / 4.810.11 / 2.770.16 / 3.110.14 / 3.480.18 / 4.700.13 / 3.72None
ExReNet (SN) [116]0.06 / 2.150.09 / 3.200.04 / 3.300.07 / 2.170.11 / 2.650.09 / 2.570.33 / 7.340.11 / 3.34None
ExReNet (SUNCG) [116]0.05 / 1.630.07 / 2.540.03 / 2.710.06 / 1.750.07 / 2.040.07 / 2.100.19 / 4.870.08 / 2.52None
Reloc3r-224 (Ours)0.03 / 0.990.04 / 1.130.02 / 1.230.05 / 0.880.07 / 1.140.05 / 1.230.12 / 2.250.05 / 1.26None
Reloc3r-512 (Ours)0.03 / 0.880.03 / 0.810.01 / 0.950.04 / 0.880.06 / 1.100.04 / 1.260.07 / 1.260.04 / 1.02None
+ +Table 4. Visual localization results on the 7 Scenes dataset [91]. We report median pose errors in meters and degrees. The best results for each method category are highlighted in bold. The underlined numbers indicate where Reloc3r outperforms all competitors. The methods marked with $\dagger$ indicate hybrid pose estimation, which combines additional geometric solvers with feature matching. + +![](images/b5175dfcfb638cc4a4d366a01992eb8162a3cf6970c3813fa5460af15395968d.jpg) +Figure 3. We visualize pose estimates for two scenes: Chess from the 7 Scenes dataset [91] and KingsCollege from Cambridge Landmarks [44]. We compare Reloc3r's results with those of the most closely related RPR methods: ExReNet [116] and Map-free [4]. We can observe that Reloc3r's pose estimates align more closely with the ground-truth poses. + +
MethodsGreatCourtKingsCollegeOldHospitalShopFacadeStMarysChurchAverage (4)AverageDataset-specific training time
APRLENS [69]-0.33 / 0.500.44 / 0.900.27 / 1.600.53 / 1.600.39 / 1.20-Days / scene
PMNet [58]-0.31 / 0.550.44 / 0.790.17 / 0.860.31 / 0.960.31 / 0.79-Days / scene
DFNet [21]+NeFeS [22]-0.37 / 0.540.52 / 0.880.15 / 0.530.37 / 1.140.35 / 0.77-Days / scene
RPR (Seen)EssNet (CL) [129]-----1.08 / 3.41-Hours
Relpose-GNN [101]3.20 / 2.200.48 / 1.001.14 / 2.500.48 / 2.501.52 / 3.200.91 / 2.301.37 / 2.30Hours
NC-EssNet (CL) [129]-----0.85 / 2.82-Hours
AnchorNet [78]-0.57 / 0.881.21 / 2.550.52 / 2.271.04 / 2.690.84 / 2.10-Hours
RPR (Unseen)EssNet (7S) [129]-----10.36 / 85.75-None
NC-EssNet (7S) [129]-----7.98 / 24.35-None
Map-free (Match) [4]†9.09 / 5.332.51 / 3.113.89 / 6.441.04 / 3.613.00 / 6.142.61 / 4.833.90 / 4.93None
Map-free (Regress) [4]8.40 / 4.562.44 / 2.543.73 / 5.230.97 / 3.172.91 / 5.102.51 / 4.013.69 / 4.12None
ExReNet (SN) [116]10.97 / 6.522.48 / 2.923.47 / 3.900.90 / 3.272.60 / 4.982.36 / 3.774.08 / 4.32None
ExReNet (SUNCG) [116]9.79 / 4.462.33 / 2.483.54 / 3.490.72 / 2.412.30 / 3.722.22 / 3.033.74 / 3.31None
ImageNet+NCM [129]†-----0.83 / 1.36-None
Reloc3r-224 (Ours)1.71 / 0.940.47 / 0.410.87 / 0.660.18 / 0.530.41 / 0.730.48 / 0.580.73 / 0.65None
Reloc3r-512 (Ours)1.22 / 0.730.42 / 0.360.62 / 0.550.13 / 0.580.34 / 0.580.38 / 0.520.55 / 0.56None
+ +Table 5. Visual localization results on the Cambridge Landmarks [44]. We report median pose errors in meters and degrees. The best results for each method category are highlighted in bold. The underlined numbers indicate where Reloc3r outperforms all competitors. The methods marked with $\dagger$ indicate hybrid pose estimation, which combines additional geometric solvers with feature matching. + +performance with AUC at all thresholds, outperforming its baseline DUSt3R [111] by around $13\%$ on AUC@20. On the RealEstate10K dataset, Reloc3r achieves performance comparable to NoPoSplat [122], with AUC values of 66.70 / 80.20 / 88.39% at thresholds of 5, 10, and 20, respectively. Similarly, on the ACID dataset, Reloc3r achieves high accuracy (AUC@20 = 70.34%), demonstrating its generalization ability to unseen datasets. Furthermore, Reloc3r runs at an inference time of just 42 ms at an image resolution of 512 in width. This is significantly faster than many non-PR methods such as NoPoSplat [122] (>2000 ms) and ROMA [34] (300 ms), and on par with PR methods. Such speed makes Reloc3r ideal for real-time applications. + +Multi-view relative pose. We evaluate the multi-view relative pose on the Co3dv2 [75] dataset. This dataset consists of object-level scenes captured with inward-facing camera trajectories. The main challenges of this dataset include visual symmetries, textureless objects, and wide baselines between images. Following the evaluation protocol in [106, 111], we evaluate Reloc3r on the test sets of 41 categories. For each sequence, we randomly sample 10 frames and formulate all 45 pairs for the evaluation. These relative poses are evaluated with three metrics: the relative rotation accuracy within 15 degrees (RRA@15), the relative translation accuracy within 15 degrees (RTA@15), and the mean average accuracy (mAA@30, also called AUC@30). + +We compare Reloc3r with recent SfM-based approaches, PixSfM [59] and VGGSfM [107], as well as data-driven methods including RelPose [127], RelPose++ [57], PoseDiffusion [106], RayDiffusion [128], DUSt3R (with PnP) [111], and MASTR [51]. In addition, we also compare the regression-based methods PoseReg [106] and RayReg [128]. Note that while we refer to our evaluation as multi-view, we actually only use pair-wise evaluation, + +similar to DUSt3R (w/ PnP) and MASt3R. In contrast, all other methods (excluding RayDiffusion and RayReg use 8 frames) use all 10 frames simultaneously, thus having more contextual information for evaluation. + +The quantitative results are reported in Table 2. Compared to existing approaches, the proposed Reloc3r achieves SoTA performance across multiple metrics, demonstrating significant improvements over competing methods. Specifically, Reloc3r achieves the best scores in terms of RRA@15 (95.8%), RTA@15 (93.7%), and mAA@30 (82.9%), surpassing both Non-PR and PR methods. This highlights Reloc3r's ability to robustly and accurately localize images in multi-view settings and wide baselines. + +# 4.2. Visual Localization + +In this section, we evaluate Reloc3r's absolute pose estimation for visual localization. We conduct experiments using two public datasets: the 7 Scenes dataset [91] and Cambridge Landmarks [44]. The 7 Scenes dataset comprises seven indoor room scenes, each containing several video sequences captured from different moving trajectories. Cambridge Landmarks is a suburban-scale outdoor dataset featuring six scenes. Following prior approaches [15, 54, 101], we use five of these scenes for evaluation. For each scene, we report the median translation and rotation errors (in meters and degrees, respectively). It's worth noting that both datasets were entirely unseen by Reloc3r during training. + +Indoor visual localization. We compare Reloc3r with state-of-the-art absolute pose regression (APR) and relative pose regression (RPR) methods on the 7 Scenes [91] dataset. The results are shown in Table 4. For RPR methods, we categorize them into two groups: seen, where the model is trained and evaluated on the same dataset, and unseen, where the dataset is entirely new to the model during + +
MethodsScanNet1500
AUC@5AUC@10AUC@20
Reloc3r-512 asymmetric32.7156.8474.63
Reloc3r-512 metric pose25.7050.2070.07
Reloc3r-512 (default)34.7958.3775.56
+ +Table 6. Ablation studies examining asymmetric network architecture and pose prediction with metric scales. + +evaluation. The table shows that methods like EssNet [129], Relative PN [49], and RelocNet [7] experience significant performance drops when evaluated on unseen datasets, revealing their limitations in scene generalizability. In contrast, our method consistently outperforms all RPR methods, even those trained on the same dataset, achieving an average median error of $0.04m / 1.02^{\circ}$ . Moreover, when compared with APR methods, our approach demonstrates comparable performance without requiring scene-specific training, further highlighting Reloc3r's robustness and adaptability across diverse scenes. + +Outdoor visual localization. For the Cambridge [44] dataset, a widely used benchmark for regression-based localization, all RPR methods (both seen and unseen) face challenges in this outdoor setting. Our proposed Reloc3r, as shown in Table 5, surpasses all previous RPR methods without any retraining or fine-tuning on specific scenes, achieving consistent improvements across all evaluated scenes. Notably, in unseen conditions, Reloc3r demonstrates an average halving of the pose error compared to the previous state-of-the-art RPR method, ImageNet+NCM [129], with average errors of $0.38m / 0.52^{\circ}$ across the last four scenes. Furthermore, our method shows a better average rotation error than all APR-based methods. This supports our motivation that leveraging a simple architectural design, coupled with scaled-up training, can effectively achieve good performance. Visual comparisons are shown in Figure 3. + +# 4.3. Analyses + +We summarize most insights here and refer the reader to the supplementary material for more details and discussions. + +Image resolutions. We train and evaluate Reloc3r at two image resolutions: widths of 224 and 512 pixels. The results are shown in the tables in Sec. 4.1 and Sec. 4.2. Similar to DUSt3R [111], the higher resolution improves accuracy but increases runtime due to processing more tokens. + +Comparison with asymmetric network architecture. We train an asymmetric version of Reloc3r-512 that uses separate decoders and heads for each branch. As shown in Table 6, this version performs even worse than the default Reloc3r while requiring more computational resources. + +Comparison with pose prediction with metric scale. We train a version of Reloc3r-512 with metric poses as output. The lower accuracy results reported in Table 6 validate the + +![](images/764b36f4128e2a758baa1ebc841ad13d5821eee875a25593eeea908a8fb35e36.jpg) + +![](images/48e9b317778341298fc8ca411c51ed797691cf985bafb2a5687eb4c46b98336f.jpg) +Figure 4. The top row showcases matches from Efficient LoFTR, while the bottom row displays the top-3 cross-attention responses from Reloc3r's decoder. We observe that the correlated regions in Reloc3r are superior to those of Efficient LoFTR, even though Reloc3r is trained solely with pose supervision. + +effectiveness of our default design without metric scales. + +Interesting findings. We visualize the cross-attention responses in some blocks from Reloc3r's decoder. Interestingly, we find that several layers have developed the ability to match patch correspondences, as illustrated in Figure 4. + +Limitations. A failure case of Reloc3r occurs when the query image and all the retrieved database images are perfectly collinear, leading to a degeneracy issue that makes the metric scale unsolvable using motion averaging methods. + +# 5. Conclusion + +In this paper, we present Reloc3r, a simple yet effective visual localization framework. It consists of an elegantly designed relative pose regression network with a minimalist motion averaging module. Leveraging large-scale training on around eight million image pairs, Reloc3r demonstrates strong generalization capability, high efficiency, and accurate pose estimation performance across multiple datasets, while remaining parsimonious. We hope it will advance research on data scale and diversity in visual localization. + +Acknowledgements. This work is supported by the Early Career Scheme of the Research Grants Council (grant # 27207224), the HKU-100 Award, a donation from the Musketeers Foundation, and in part by the JC STEM Lab of Autonomous Intelligent Systems funded by The Hong Kong Jockey Club Charities Trust. This work is also supported in part by the Research Council of Finland for funding the projects (grants No. 353138, No. 362407, and No. 352788). We acknowledge the computational resources provided by the CSC-IT Center for Science, Finland and the HKU-Shanghai ICRC. We thank the reviewers for their valuable feedback. 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While they are barely observable to our eyes, computer vision manners can, and the derived remote photoplethysmography (rPPG) has shown considerable promise. However, existing studies mainly rely on spatial skin recognition and temporal rhythmic interactions, so they focus on identifying explicit features under ideal light conditions, but perform poorly in-the-wild with intricate obstacles and extreme illumination exposure. In this paper, we propose an end-to-end video transformer model for rPPG. It strives to eliminate complex and unknown external time-varying interferences, whether they are sufficient to occupy subtle biosignal amplitudes or exist as periodic perturbations that hinder network training. In the specific implementation, we utilize global interference sharing, subject background reference, and self-supervised disentanglement to eliminate interference, and further guide learning based on spatiotemporal filtering, reconstruction guidance, and frequency domain and biological prior constraints to achieve effective rPPG. To the best of our knowledge, this is the first robust rPPG model for real outdoor scenarios based on natural face videos, and is lightweight to deploy. Extensive experiments show the competitiveness and performance of our model in rPPG prediction across datasets and scenes. + +# 1. Introduction + +Heart rate (HR), heart rate variability, respiratory rate, blood pressure, and blood oxygen saturation are significant vital parameters, and their remote sensing can provide important evidence for many tasks for clinical purposes and intelligent applications. Remote photoplethysmography (rPPG) aims to capture blood volume pulse (BVP) signals containing the above bio-indicators based on facial videos [1, 2]. With the popularization of commercial cameras and mobile communication devices, rPPG technique will play an irreplaceable + +![](images/63f8f900bb0961f0960863fd2d49e14e53e0f9882952f845ec2f51bed47222aa.jpg) +Figure 1. Existing learning-based rPPGs have shown promise under static illuminations (a), but they are not effective in real-world scenarios (b). Performances of different methods can be compared intuitively (under the MR-NIRP-DRV [20] dataset). + +role in health self-examination, anti-spoofing, driver fatigue diagnosis, and DeepFake in the foreseeable future. + +The contraction and relaxation of cardiac alter the instantaneous flow and velocity of red blood cells in subcutaneous capillaries, thereby changing facial skin imaging. Although these contents are difficult to be directly perceived by naked eyes, camera can capture the absorption and scattering of incident light caused by variations in superficial living tissues [3, 4]. On these bases, rPPG summarizes biosignal clues by comparing skin color between frames. Early related studies implemented rPPG based on manual features [5, 6]. Subsequently, deep learning-based methods showed stronger robustness in motion and heterogeneous videos [7, 8]. + +However, similar to the bottleneck of the traditional blind source separation methods which can demodulate as long as biosignal meets certain conditions, existing learning-based rPPG methods are also vulnerable in many cases, especially in the following aspects: 1) Insufficient ability to remove extreme light interference. Facial color changes caused by heart activity are relatively asthenic. When external light interference is sufficient to mask such changes, existing rPPG methods that mine clues from skin region-of-interest (ROI) can easily fail [9, 10]. 2) Weak ability to resist periodic interference. Cardiac signals have quasi-periodic character + +istics, and many existing long-term BVP perception models are developed based on this. However, when the external interference also shows a certain time-varying and rhythmicity, it is more difficult to unravel [11, 12]. 3) Still need to employ additional expensive equipment in practice. For the unknown complex interference, some studies choose to introduce near-infrared (NIR) imaging as multimodal input, but this leads to the community return to the old routine of complicated devices and high costs [13, 14]. 4) Difficulty in model deployment. Existing rPPG networks, especially those for the noise disentanglement, continue to accumulate heavy modules and complex pipelines, making them difficult to deploy on flexible hardware [15, 16]. In summary, in the real-world (such as driving scenarios) where the above challenges coexist, operating learning-based rPPG models rarely perform satisfactorily (as shown in Fig. 1). + +In this paper, we propose a novel rPPG framework based on vision transformer, which can be applied to a variety of application scenes with drastic illumination and complex inthe-wild interference, and can be better adapted to terminals due to its lightweight layout. Specifically, to prevent rPPG waveforms from being overwhelmed by external interference, our model exploits the common property of facial skin and subject background disturbances, takes the background interference as a reference, discouples it in a self-supervised manner, and eliminates its influence in the foreground. In this process, we increase the frame window length to make full utilize of BVP quasi-periodic features that are different from extreme lighting obstructions. Meanwhile, we use the biosignal frequency domain and biological prior constraints to prevent the influence of interference with rhythmic characteristics that are hidden in too long a temporal period, and use spatiotemporal filtering and reconstruction to eliminate sensitive noise and better guide network training. It is worth noting that all our learning support is based on facial optical reflectance model and feature mapping correlation calculation, without introducing additional imaging modalities and too many branch modules, so the deployment cost is lower. We conduct experiments on multiple mainstream datasets, including BUAA-MIHR (illuminance state variation [17]), VIPL-HR (indoor real state [18]), MR-NIRP-IND (motion [19]), and MR-NIRP-DRV (outdoor driving moment [20]). Sufficient verification results demonstrate that our approach shows significant advantages in actual open and challenging scenarios. In summary, the main contributions include: + +- We pioneer rPPG learning from facial videos in outdoor variable illumination, and propose a targeted paradigm. It relies merely on RGB imaging instead of various infrared spectra, aiming to extend rPPG to more realistic domains. +- Our model is guided by global interference sharing, background perturbation reference, self-supervised disentanglement, and long-term frequency and physiological prior constraint strategies, which can provide a robust solution + +for resisting unknown complex obstructions. + +- Our model is lighter than existing noise disentanglement methods, can be deployed more flexibly, and is more suitable for in-the-wild platforms and real-world tasks. +- We compare with the latest representative rPPG methods and demonstrate that our model achieves the state-of-the-art results in both extreme lighting and static scenes. + +# 2. Related works + +# 2.1. Learning-based rPPG in daily life + +Recently, researchers have developed many learning-based visual rPPG networks, which have continuously improved task-oriented performances in facial ROI attention [9, 21], spatiotemporal enhancement [22, 23], and long-term time perception [24, 25]. However, capabilities of these methods in open conditions are worrying. Currently, rPPG for actual scenes mainly solves the problems of subject motion robustness [26, 27] and shallow denoising [28-30], and rarely involves extreme real-time changes in illumination. Even the most widely used VIPL-HR dataset [18], which is generally considered to be the closest to real states, is not exception. Although some works have begun to focus on outdoor lighting, they all require the exploit of auxiliary infrared devices and have limited surface feature abilities [31, 32]. Infrared imaging with a specific wavelength has advantages in counteracting visible light variations with a wide wavelength distribution, but according to the skin optical reflection model, facial imaging caused by biological activities is mainly due to the reflection of light by red blood cells and the absorption of melanin. At the cellular level, short-wave reflection is more effective. Therefore, its effectiveness in rPPG imaging demands to be in-depth evaluated [33]. Meanwhile, narrowband waves contain less content, and the involvement of their equipment will make the deployment cost of detection more expensive. Therefore, rPPG in this field demands to be solved urgently to further serve downstream tasks [34, 35]. + +# 2.2. Self-supervised learning for rPPG + +Self-supervised learning is crucial for eliminating unknown interferences that affect rPPG. Initially, related approaches were mainly used to segment unlabeled skin [36] and solve annotation scarcity and misalignment [37]. Gideon et al. [38] used the quasi-periodicity of BVP to improve the network's ability to mine biosignal by learning its power spectral density (PSD). Shao et al. [39] used the masked autoencoding paradigm to avoid the distortion of rPPG fragile amplitude by redundant spatial information. Liu et al. [40] improved it to the multi-mapping parallelism. For unseen distributions, Sun et al. [8] explored conflict domains between different subjects through harmonic phase and hyperplane optimization, thereby improving the model generalization. Lu et al. [41] aligned the spatiotemporal mapping of source + +and target domains based on maximizing the coverage and diversity of neural structures to avoid the abnormal activation caused by sample inhomogeneity [42]. Liu et al. [16, 43] used adversarial canonical correlation analysis to separate background noise from original cardiac features. Moreover, researchers have proposed approaches such as frequency reconstruction [44, 45], conductive inference [46-49], multimodality fusion [50], and pseudo-label recombination [51, 52]. However, they often ignore the impact of environmental changes on facial color imaging, especially when these disturbances also show certain rhythmic characterizations. + +# 3. Methodology + +There are many challenges to overcome in order to make a learning-based rPPG framework work effectively outdoors. Therefore, when designing the end-to-end network, we had to account for interference from motion and general noise, as well as extremely complex lighting variations. + +# 3.1. Basic general interference elimination + +We follow the boosting design. First, to remove the general noise and for the sake of subsequent lightweight layout and efficient training, we transform the input RGB video into a YUV spatiotemporal map (STMap) [18] in the color space. This operation converts single frame into a one-dimensional array within the color channel, and constructs a new image based on the temporal length of video clips. Although there have been many works exploring the benefits of such multiscale pooling style ideas for the biosignal denoising [53, 54] and their contributions to embedding the latest frameworks into rPPG [41, 49], their latent is easily distorted when dealing with movements. Therefore, we improve that to a node graph manner based on facial landmarks. We split and divide the face skin into multiple non-overlapping regions according to its landmarks, which are consistent with the distribution of subcutaneous tissue units rather than shallow rectangle sub-patches. We calculate the average pixel value in each independent region. For an input natural video sequence $\mathbf{V}_{\mathrm{in}} \in \mathbb{R}^{3 \times T \times H \times W}$ with $T$ frames, its facial STMap can be expressed as: $\mathbf{V}_{\mathrm{face}} \in \mathbb{R}^{3 \times L \times T}$ , where $H$ and $W$ are the height and width of frames, and $L$ is the number of landmark points. As shown in Fig. 2, this can make our STMap immune to motion and behavior interference. + +HR transitions smoothly in the most cases. Therefore, in a short time period, rPPG fragments manifest similarity and quasi-periodicity, specifically in BVP frequency, amplitude, systolic point, diastolic point, and dicrotic notch. Based on these features, increasing the temporal dimension of STMap is conducive to strengthen long-term contextual interaction of biosignals, thereby improving the trained model robustness. The very recently produced vision transformer framework is also developed for related linear complexity. Therefore, we chose the Swin video transformer [55] with strong + +![](images/bb95c313684cb89625bbd5f320edcc9e434305261e6ba003772a00aac30a9ab4.jpg) +Figure 2. Our facial skin feature extraction method and the STMap built on it can enhance subtle color changes and spikes more finely than traditional sub-patch sliding window denoising algorithms. + +![](images/e977a81e0154d0bfd65ce38acc686a5c4b0bfc130044ba216756344cf8f123bc.jpg) + +![](images/0d882ae7ab48b0c35d6940349f3a4cbd68de1b1b79bded44ae8ce9e4907313b3.jpg) + +![](images/4ea483647dacc63e02f11cdf51c602b7d70771a3fb2aea3b8781b9aee7a42924.jpg) + +long-term capabilities as our backbone architecture. + +However, blindly increasing the temporal dimension will cause the preprocessing of STMap to fall into many uncertain factors. Especially when facing severe disturbance with an amplitude much greater than skin color changes, existing normalization methods of STMap will further magnify the interference [37]. To this end, we propose a novel augmentation algorithm. The camera frame rate available for rPPG is usually 20 to 30 frames per second (fps), and HR is generally in the range of 40 to 240 beats per minute (bpm) [56]. In view of this important physiological knowledge, we perform a biological prior-based sliding window enhancement (BioSE) on the raw STMap. Specifically, 1) To increase the independent representation of each organ unit, we calculate the color variations over time in each node region based on face landmarks. 2) To avoid the global normalization weakening in BVP imaging, we calculate sliding within the preset window length based on the biological prior to amplify subtle color differences and spike features. 3) To make the edges of windowed signal continuous and smooth, we adopt a parallel manner with multiple different starting positions. The imaging $v^{\mathrm{face}}$ in each independent unit is expressed: + +$$ +\operatorname {B i o S E} v _ {t, n - t + s _ {\text {n o r m}}} ^ {\text {f a c e}} = \left(v _ {n} ^ {\text {f a c e}} - \min _ {t}\right) / \left(\max _ {t} - \min _ {t}\right), \tag {1} +$$ + +where $t - s_{\mathrm{norm}} < n \leq t$ , $t$ is the current discrete time, $s_{\mathrm{norm}}$ is the span of the sliding window, $n$ is the discrete time numbers in the sliding window, $v_{i}^{\mathrm{face}}$ is the $i$ -th processed $v_{i}^{\mathrm{face}}$ , BioSE $v_{t,n-t+s_{\mathrm{norm}}}^{\mathrm{face}}$ is the skin imaging variation to which the $(n-t+s_{\mathrm{norm}})$ -th proposed method (BioSE) is applied at the $t$ -th, $\max_{t}$ and $\min_{t}$ are the max and min deviations on the $t$ -th sliding window. According to the facial skin optical feedback [9], to prevent implicit relations between the epidermal specular reflection and the subcutaneous tissue diffuse one from being destroyed in the above processes, we connect the map through BioSE with the raw facial STMap. That is also because R, G, and B act differently on the face. While the G channel performs well under the indoor LED lamps, its effect on real outdoor sunlight remains to be studied. Then, a new STMap $(\mathbf{S}_{\mathrm{face}} \in \mathbb{R}^{6 \times L \times T})$ with raw details and light-insensitive biosignals can be obtained: + +$$ +\mathbf {S} _ {\mathrm {f a c e}} = \operatorname {C o n c a t e} \left(\mathbf {V} _ {\mathrm {f a c e}}, \frac {2 5 5}{N} \sum_ {i = 1} ^ {N} \operatorname {B i o S E} \left(\mathbf {V} _ {\mathrm {f a c e} _ {i}}\right)\right), \tag {2} +$$ + +where $N$ is the number of BioSE performed with different starting frames, and Concate is the concatenate in NumPy. + +# 3.2. Boosted complex interference disentanglement + +To further improve the advantages of our model under complex conditions, which is also the core distinguish from current rPPGs, we make full use of the theory of global intraframe interference sharing. For example, in a driving scene, when a vehicle travels through a city, the entering light will change at any time due to car turns, building occlusions, etc. However, the interference of the main object of the person, the kernel skin ROI of the face, and the background is consistent. Therefore, on the basis of remapping the enhanced STMap based on the facial skin node set, we also construct a background STMap $(\mathbf{S}_{\mathrm{back}})$ , which is the region outside the bounding box formed by the facial landmarks. To ensure the subsequent linear embedding and patch merging, we project the face background STMap in the same way as $\mathbf{V}_{\mathrm{face}}$ , except that each frame is average pooled in $L$ rectangular windows so that $\mathbf{S}_{\mathrm{back}}$ and $\mathbf{S}_{\mathrm{face}}$ have the same tensor shape. + +Subsequently, we use the background perturbation as the reference and mine the potential temporal similarity in $\mathbf{S}_{\mathrm{face}}$ and $\mathbf{S}_{\mathrm{back}}$ to disentangle strong interference. Based on this, we hope to embed them into a unified framework to capture their commonalities while not ignoring their individuality. Therefore, we need to enable our model pre-form a concept of the calculated features in advance, but not to make them too significant to avoid overfitting. Based on the above discussions, we additionally construct a global STMap ( $\mathbf{S}_{\mathrm{glob}}$ , shaped like $\mathbf{S}_{\mathrm{face}}$ ), which is obtained by dividing the overall input video frame into $L$ blocks and computing their means. Using the global map as the initial input of learning pipeline can be regarded as training in a way that actively reduces the signal-to-noise ratio of the modeling subject, avoiding premature fitting of fine-grained concepts. Meanwhile, we improve the traditional one-dimensional BVP regression to the spatiotemporal reconstruction of the STMap by the stacked BVP signals to increase the temporal interaction of different STMap sub-blocks, and design the model as a U-shaped structure. As far as we know, it is also the front explorations of U-shaped transformer in biosignal measurement. In addition, the expansion of mapping relations enables our model to be trained directly from scratch on rPPG datasets. + +While reconstructing the global frame map $\mathbf{S}_{\mathrm{glob}}$ at the spatiotemporal level using the U-shaped video transformer, we extract the corresponding implicit feature from the middle layer of the architecture. Since this feature comes from the overall video with unknown noise, we let it as a coarse-grained feature $\mathbf{F}_{\mathrm{coar}}$ . Correspondingly, we feed $\mathbf{S}_{\mathrm{face}}$ and + +![](images/d0992ab48287c6890334288218b9ffa235890350a1097458d7fdfa5de05f57b0.jpg) +Figure 3. Comparison of our method with existing rPPG interference disentanglement models that are representative in paradigm. + +$\mathbf{S}_{\mathrm{back}}$ together into the encoder of the U-shaped backbone to obtain foreground feature $\mathbf{F}_{\mathrm{fore}}$ and background one $\mathbf{F}_{\mathrm{back}}$ . They satisfy: $\mathbb{R}^{C\times L^{\prime}\times T^{\prime}}$ , where $C$ , $L^{\prime}$ , and $T^{\prime}$ are the new dimensions after channel excitation and STMap downsampling. Since reflectance and material of diverse body background regions are not the same, we do not know the distribution of background variations and cannot pre-define or assume them. Therefore, we employ a self-supervised manner to query the foreground feature $\mathbf{F}_{\mathrm{fore}}$ for its response using the background tensor $\mathbf{F}_{\mathrm{back}}$ as a reference to capture sub-blocks with similar temporal representations in foreground and background maps. To make our architecture compatible with general rPPG tasks, after obtaining the similarity score mapping, we do not adopt the strategy of setting hyperparameters and selecting the first few high-scoring blocks as interference removal. In response, global adaptive computation is utilized instead. Specifically, we construct a newly fine-grained tensor $\mathbf{F}_{\mathrm{fine}}$ , which considers the influence and weights of all sub-regions within the face: + +$$ +\mathbf {F} _ {\mathrm {f i n e}} = \left(1 - \operatorname {S o f t m a x} \big (\mathbf {F} _ {\mathrm {b a c k}} \cdot (\mathbf {F} _ {\mathrm {f o r e}}) ^ {\mathsf {T}} \big)\right) \cdot \mathbf {F} _ {\mathrm {f o r e}}. (3) +$$ + +After that, we guide interference disentanglement by latent contrastive learning. We construct a contrast constraint function $\mathcal{L}_{\mathrm{c}}$ to calculate the temporal relation between different facial sub-regions and background sub-patches. According to the irrelevance coefficient, the facial sub-regions that are irrelevant to the background pattern are pulled away, and the relevant ones are pushed away: + +$$ +\mathcal {L} _ {\mathrm {c}} = \log \left(\frac {\sum_ {i _ {1} = 1} ^ {L ^ {\prime}} \sum_ {i _ {2} = 1} ^ {L ^ {\prime}} \exp \left(D \left(\mathbf {F} _ {\text {f i n e} i _ {1}} ^ {\prime} , \mathbf {F} _ {\text {f i n e} i _ {2}} ^ {\prime}\right) / \tau\right)}{\sum_ {i = 1} ^ {L ^ {\prime}} \sum_ {j = 1} ^ {L ^ {\prime}} \exp \left(D \left(\mathbf {F} _ {\text {f i n e} i _ {1}} ^ {\prime} , \mathbf {F} _ {\text {b a c k} j} ^ {\prime}\right) / \tau\right)} + 1\right), \tag {4} +$$ + +where $D$ is the mean square error of two tensors with respect to time, $\mathbf{F}_{\mathrm{fine}_i}^{\prime}$ and $\mathbf{F}_{\mathrm{back}_i}^{\prime}$ are the tensors of $\mathbf{F}_{\mathrm{fine}}$ and + +![](images/9d9eb29be34aa1e8e332b840f6518cd954e16b67f341707f79a12a18b0e7c8ab.jpg) +Figure 4. The framework of our end-to-end time-varying interference disentanglement network, which consists of a U-shaped transformer module for coarse-grained spatiotemporal reconstruction and an rPPG prediction module for fine-grained BVP waveform regression. + +$\mathbf{F}_{\mathrm{back}}$ at the $i$ -th sub-block, and $\tau$ is the temperature hyperparameter which is set to 0.08 following [44]. Besides, the global reconstruction features do not participate in the disentanglement calculation. Their purpose is to continuously iterate network parameters, increase the model's abilities to express fine-grained and background features, and prevent the encoder from overfitting fine-grained features or fitting noise. At this point, still taking the city driving scenario as an example, the regularity of street lights and roadside trees will make the external interference periodic when the vehicle passes by. Studies have proven that rPPG biosignals obtained from different facial sub-regions often show similar power spectrum [57]. Therefore, to avoid above influences, we adopt power spectral density (PSD) of imaging features as the target of the distance metric for $D$ calculation. + +It is worth mentioning that the current methods that consider illumination changes usually require the assistance of infrared rays, but according to the surface optical reflection theory, the feedback of cardiac activity is the variation that occurs when natural light passes through the pulsating cell flow in the capillaries, not thermal radiation, and there is an essential difference between the two. Therefore, decoupling based on visible light is the key to solving this problem. In addition, it can be seen that our computing is mainly based on the facial reflectance and feature correlation calculation, unlike existing disentanglement methods that rely on generative networks [28, 58-60] or adversarial learning [16, 61], which requires the introduction of too many heavy modules. Therefore, it is more lightweight. Furthermore, we present differences between ours and existing modules (Dual-GAN [28], PFDNet [62], ND-DeepPrPG [16]) in Fig. 3. Specifically, although PFDNet is based on rPPG for atrial fibrillation screening, its core is still the purification of BVP waveforms. As for ND-DeepPrPG, its core is to equip a shallow model with a noise disentanglement module. The similarity between our algorithm and it is that we both take advantage + +of the consistency of skin (foreground)-environment (background) noise. The main difference is that it needs to build an external discriminator to judge the HR counted by the environment as false and the value counted by the skin as true. We directly adopt BVP with the same time dimension as the video for spectrum consistency comparison, which is more in line with the requirements of long sequence regression. + +# 3.3. Overall rPPG prediction and optimization + +For the global $\mathbf{F}_{\mathrm{coar}}$ which dose not participate in disentanglement, it is then reconstructed by the U-shaped decoder, and the spatiotemporal reconstruction loss $\mathcal{L}_{\mathrm{r}}$ is counted by stacking the ground truth (GT) biological signal $B_{\mathrm{g}}$ , so that our model can increase the perception of BVP from coarse to fine: $\mathcal{L}_{\mathrm{r}} = ||\mathbf{F}_{\mathrm{coar}}^{\prime} - \mathbf{F}_{\mathrm{bvp}}||_2$ , where $\mathbf{F}_{\mathrm{coar}}^{\prime}$ is the feature of $\mathbf{F}_{\mathrm{coar}}$ expanded by the decoder projection, and $\mathbf{F}_{\mathrm{bvp}}$ is the single channel STMap stacked by $B_{\mathrm{g}}$ . For $\mathbf{F}_{\mathrm{fine}}$ after eliminating the interference, we construct a separate regression module based on temporal deconvolution in addition to the spatiotemporal reconstruction to predict the remote biosignal $B_{\mathrm{p}}$ . Specifically, it consists of six groups of blocks including convolutional layers, activation, and batch normalization. Without varying the node scale of $L^{\prime}$ , the downsampled time dimension is transposed to the input level layer by layer. The loss function $\mathcal{L}_{\mathrm{p}}$ that focuses on temporal series regression and spike protection at this stage is: + +$$ +\mathcal {L} _ {\mathrm {p}} = 1 - \frac {T \sum_ {i = 1} ^ {T} B _ {\mathrm {p} _ {i}} B _ {\mathrm {g} _ {i}} - \sum_ {i = 1} ^ {T} B _ {\mathrm {p} _ {i}} \sum_ {i = 1} ^ {T} B _ {\mathrm {g} _ {i}}}{\sqrt {\left(T \sum_ {i = 1} ^ {T} B _ {\mathrm {p} _ {i}} ^ {2} - \left(\sum_ {i = 1} ^ {T} B _ {\mathrm {p} _ {i}}\right) ^ {2}\right) \left(T \sum_ {i = 1} ^ {T} B _ {\mathrm {g} _ {i}} ^ {2} - \left(\sum_ {i = 1} ^ {T} B _ {\mathrm {g} _ {i}}\right) ^ {2}\right)}}. \tag {5} +$$ + +Furthermore, in terms of biological priors, based on the rule of 40 to 240 heartbeats per minute, we focus on the PSD frequency between 0.66 to $4\mathrm{Hz}$ in $\mathbf{F}_{\mathrm{fine}}$ in the calculation of $\mathcal{L}_{\mathrm{c}}$ . In terms of further spatiotemporal context interaction, + +Table 1. Comparative results (bpm) of remote HR estimation on MR-NIRP-IND, MR-NIRP-DRV, VIPL-HR, and BUAA-MIHR datasets, where $\downarrow$ means the smaller the better, $\uparrow$ is the bigger the better, the best result is bolded, and the second best is underlined (the same below). + +
rPPG Methods / VenuesTest TrainMR-NIRP-IND [19]MR-NIRP-DRV [20]VIPL-HR [18]BUAA-MIHR [17]
MAE↓RMSE↓ρ↑MAE↓RMSE↓ρ↑MAE↓RMSE↓ρ↑MAE↓RMSE↓ρ↑
CHROM[3] / IEEE TBME 2013n/a6.848.410.3214.5217.410.1811.0717.990.276.098.290.51
POS[1] / IEEE TBME 2017n/a5.526.850.4012.7515.360.3411.5017.200.305.047.120.63
LGI[6] / CVPR 2018n/a8.9511.010.3912.9015.510.3112.8419.020.296.9711.330.42
CNN-Based rPPG MethodsDeepPhys [33]MR-NIRP3.114.440.7413.2218.390.4315.5317.480.414.786.740.69
ECCV 2018VIPL-HR6.589.160.5210.5112.710.5611.0013.800.11
TS-CAN [9]MR-NIRP2.493.890.7512.7018.030.4712.0415.120.454.846.890.68
NeurIPS 2020VIPL-HR6.579.250.5710.3712.650.619.3914.590.21
Dual-GAN [28]MR-NIRP2.473.620.848.0012.180.719.4811.660.493.415.230.84
CVPR 2021VIPL-HR4.046.070.739.2311.340.624.937.680.81
PFE-TFA [26]MR-NIRP2.814.570.845.348.920.738.2011.220.641.292.650.91
AAAI 2023VIPL-HR1.873.670.777.829.990.646.918.650.65
NEST [41]MR-NIRP1.082.260.893.617.320.825.158.780.722.884.690.89
CVPR 2023VIPL-HR2.784.630.786.278.450.655.527.960.80
ND-DeeprPPG [16]MR-NIRP0.661.450.893.476.540.855.087.920.750.581.810.95
IEEE TIP 2024VIPL-HR1.743.280.816.187.750.685.157.520.78
TransformersEfficientPhys [21]MR-NIRP1.374.810.813.6712.280.815.2511.810.711.434.980.93
WACV 2023VIPL-HR1.806.190.766.0711.530.645.238.250.72
PhysFormer++ [24]MR-NIRP0.641.390.893.567.590.835.098.970.710.931.660.94
IJCV 2023VIPL-HR1.793.770.815.788.650.664.887.620.80
RhythmFormer [25]MR-NIRP0.521.100.913.446.720.824.838.050.750.671.570.94
arXiv 2024VIPL-HR1.703.430.835.407.930.724.757.490.82
OursMR-NIRP0.450.910.922.696.030.874.137.610.760.531.200.95
VIPL-HR1.433.050.884.977.230.744.527.090.85
+ +Table 2. Results for different lights and modalities involving NIR. + +
rPPG MethodsRGB Mode (RMSE↓)NIR Mode (RMSE↓)
Mo.DayNightGa.DayNightGa.
TURNIP [63]n/an/an/an/a11.4011.274.60
AutoSparsePPG [20]17.6915.9216.232.9011.8011.205.10
Wu et al. [64]15.4110.8714.465.949.889.583.93
Chiu et al. [13]9.717.6010.114.468.829.954.09
Ours7.305.457.512.157.5210.933.84
+ +after $\mathbf{F}_{\mathrm{coar}}$ passes through U-shaped model, it provides hierarchical information by multi-scale skip-layer connection to guide reconstruction. At this time, the traditional window shifting of the Swin mechanism destroys skin temporal continuities. Therefore, we modify it to the spatial shifting. We use a random spatial transformation for the Swin unit composed of two transformer blocks instead of utilizing a mask, randomly reorganizing its $L$ dimension in the first block and vice versa in the another. Since capillaries in different facial sub-regions are relatively independent, this can increase the diversity of spatial topology and improve the generalization of our model. In summary, our overall loss $\mathcal{L}_{\mathrm{total}}$ is: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \mathcal {L} _ {\mathrm {r}} + \beta \mathcal {L} _ {\mathrm {c}} + \gamma \mathcal {L} _ {\mathrm {p}}, \tag {6} +$$ + +where $\alpha = 0.5$ , $\beta = 0.5$ , and $\gamma = 1$ in our setting studies. Moreover, we can make our model compatible with existing common pathways through rPPG by controlling the coefficients of $\beta$ and the Hadamard product in $\mathcal{L}_{\mathrm{c}}$ as a score map. + +Our total workflow is shown in Fig. 4. We mark the spa + +tiotemporal reconstruction module and the spatiotemporal regression module with different color, visualize the temporal representation of different facial patterns and the map of PSD, and highlight the constraints of PSD contrast, coarse-grained reconstruction, and fine-grained rPPG. In addition, to demonstrate our disentanglement logic more intuitively, we represent $\mathbf{F}_{\mathrm{fore}}$ (Key, K), $\mathbf{F}_{\mathrm{back}}$ (Query, Q), and $\mathbf{F}_{\mathrm{fine}}$ (Score) and their attraction and repulsion, respectively. + +# 4. Experiments + +We conduct the experiments based on BUAA-MIHR [17], VIPL-HR [18], MR-NIRP-IND [19], and -DRV [20], which are important public datasets focusing on complex scenes in rPPG. Among them, BUAA-MIHR is divided into 11 light modes with fine span. VIPL-HR is the largest actual indoor dataset, including 3 natural lighting acquisitions and 9 dynamic types. MR-NIRP-IND is a studio dataset with object motion, and its extension MR-NIRP-DRV is the largest outdoor dataset involving real-world driving, extreme illumination, and day-night variations. More details and samples are shown in the Supplementary Materials (Supp). + +Since the video frame rate and label frequency of different datasets vary, we uniformly interpolate them to 25 fps. Accordingly, the sliding window length based on BioSE is 100 frames. We annotate facial landmarks based on the face recognition module involved in the publicly available code1, and build the facial skin STMap based on the first 64 non + +![](images/ba7d2efe41865dea3999f0518d93e0608ed510c6a5345e20543fe2bf914163d1.jpg) +Figure 5. Our method improves upon the state-of-the-art interference disentanglement baseline in both indoor and outdoor scenes. + +![](images/2106d56884fa71fbdc716a899a3dda5e42874bd2c777e9969921b3ed91e3b0dc.jpg) +Figure 6. Anchor patch (white) and its dynamic correlations with foreground (yellow) and background (blue) frame sub-blocks. + +overlapping areas $(L)$ enclosed by the 68 landmark nodes. On these bases, after spatial scale sampling and unification, the temporal dimension $(T)$ of STMap of $\mathbf{S}_{\mathrm{face}}$ , $\mathbf{S}_{\mathrm{back}}$ , and $\mathbf{S}_{\mathrm{glob}}$ is 320. Our model is based on the PyTorch framework and runs on a device with 4 RTX 4090 GPUs. The optimizer is AdamW, the initial learning rate is $1 \times 10^{-5}$ , 3/4 sample maps in each dataset are randomly utilized as training set, and another 1/4 is tested. They have 100 training epochs and adjust the learning rate to $0.5 \times 10^{-5}$ after the 50th epoch. + +# 4.1. Comparison with the state-of-the-art methods + +We train models independently in BUAA-MIHR and VIPL-HR, and jointly in MR-NIRP-IND and -DRV (MR-NIRP). Afterwards, we validate them across the datasets opposite to each other based on the training weights of MR-NIRP and VIPL-HR. We use the open source rPPG toolbox² to count and statistically analyze the prediction results, and evaluate them using mean absolute error (MAE), root mean square error (RMSE), and Pearson's correlation coefficient $(\rho)$ indicators. On this basis, we compare our measurements with current representative rPPG methods, including traditional chrominance-based methods [1, 3, 6], latest CNN models [9, 16, 26, 28, 33, 41], and highly competitive transformers [21, 24, 25], which are listed in Tab. 1. As can be observed that our approach has obvious improvements, especially in MR-NIRP-DRV with extreme time-varying interferences. + +In-the-wild driving scene is the most challenging aspect + +Table 3. Computational cost and rPPG performance comparison. + +
rPPG MethodsParameterFLOPsRTX 4090RMSE↓
TS-CAN [9]3.91 M110.15 G5.52 ms14.59
ND-DeeprPPG [16]6.05 M320.08 G29.87 ms7.52
PhysFormer++ [24]9.79 M49.85 G217.07 ms7.62
RhythmFormer [25]3.25 M38.49 G29.49 ms7.49
Ours6.03 M53.04 G24.64 ms7.09
+ +of rPPG, and the existing advanced methods [13, 20, 63, 64] based on existing MR-NIRP-DRV dataset all need infrared data (e.g., NIR). Based on this, Tab. 2 shows the comparison between our network and theirs, and distinguishes subject and light source interferences such as head motion (Mo.), day driving, night driving, and garage acquisition (Ga.). It can be observed that our model can achieve significant advantages when using only RGB. Meanwhile, since the limited feedback of NIR thermal drive on facial color changes, the effect achieved is mediocre. This also proves that rPPG based on visible light video should be the main focus direction. It is important to note that there is no intersection between Tab. 1 and Tab. 2. This is because Tab. 1 contains the strongest rPPG models based on natural light, while Tab. 2 is only a specific outdoor study using NIR. We have already verified the outdoor study in Tab. 1 by MR-NIRP-DRV. Furthermore, in Fig. 1, the scene comparison we conducted for methods [16, 24–26, 41] is based on weights trained on MR-NIRP. The scenario (a) corresponds on ideal pattern, and (b) matches the combination of daytime and night with motion. + +# 4.2. Visualization and effectiveness analysis + +To show our model's efforts in real-world interference filtering, we compare it with the most valuable noise disentanglement design: ND-DeepPrPPG [16]. We train corresponding models based on MR-NIRP and draw HR estimation results for 2,000 random periods as scatters. Fig. 5 left plot is the garage results, and its right plot is the outdoor HRs following Sec. 4.1. It can be clearly found that compared with the adversarial-based baseline, the paradigm we proposed can make predicted values more consistent with GT. It can make more points fall within confidence interval areas of $\mathrm{GT} \pm 6$ bpm, as well as its achievements in overcoming overfitting at marginal HR points. Comparative scatters with the latest transformer-based rPPGs [24, 25] are shown in the Supp. + +To intuitively demonstrate that our learned features can effectively avoid interference, we select a set of video segment from MR-NIRP-DRV and display them in Fig. 6. We use the white patch in the first row as the query anchor. The second row is the spatial similarity between the anchor and each sub-block in the foreground (yellow) and background (blue) of a single frame. The greater the similarity, the more saturated the color. The third row is the temporal correlation between captured sequence frames. For ease of visualiza + +Table 4. Comparison of the latest rPPG towards disentanglement. + +
Models1×Temporal SamplingTemporal Frequency
801606402×4×8×
DeeprPPG [43]11.2712.7710.4614.9013.2015.1417.39
ND-DeeprPPG [16]6.548.076.769.097.668.7810.09
Ours w/o ND8.129.508.999.809.2911.3913.09
Ours6.037.166.807.466.688.099.12
+ +![](images/4ddbfc4661ce95652339c9bf6349133a6a9607a5844e885e4687817776508f14.jpg) +Figure 7. Comparison with and without disentanglement module. + +tion, we utilize window blocks and $4 \times 4$ frame scale instead of node STMap. It can be seen that the learned inter-frame correlation obviously tends to the overall temporal distribution. Therefore, for the drastic interference caused by time-varying illumination, we can still stably mine the temporal correlation between different sub-blocks and get rid of the limitations of spatial texture and color. In addition, we draw the actual predicted BVP signals and HR values in the Supp. + +Tab. 3 presents the advantage of our network in computational complexity. Letting RMSE results under VIPL-HR as example evidence, due to our lightweight layout, we can achieve the best performance without significantly increasing the number of parameters and floating point operations per second (FLOPs), even lower than the cost of the latest rPPG methods. More comparisons are shown in the Supp. + +# 4.3. Ablation studies + +To investigate the effect of the core component of our architecture, the interference disentanglement module. We compare our whole model with the learning results of VIPL-HR without the disentanglement mechanism (w/o ND), and the continuous one-minute HR estimation results are plotted in Fig. 7. At this point, to simultaneously discuss the impact of the time window length on the prediction, we set the STMap time dimension of the undisentangled input size to 300, 280, 260, 240, 220, 200, 180, 160, and 140 (corresponding light-colored lines). As can be seen that although increasing the temporal length can improve the model's fit to BVP and thus calculate HR values, it still performs poorly. In addition, we present more exhibits and scatters in the Supp, including the ablation studies on the disentanglement module and BioSE. + +Based on the above studies on unwrapping and window, we further compare with ND-DeepPrPPG [16] in MR-NIRP-DRV. Similar to it with or without ND module (DeepPrPPG [43]), our configuration follows: We apply varying time dimensions (80, 160, 320, 640 frames) and readjust frequen + +![](images/693562255ab277ad293fcb711f76d6319f1c9237a949df5c838d1f1f9aeb8aed.jpg) +Figure 8. Results of four different structures on validation datasets. + +![](images/daf84da3c4df0801a6e38a41aa60cd779ec717721860945d90a85c6f692bef98.jpg) +Figure 9. Representation of the learned map corresponding to BVP peaks for daytime and night real-world driving scenarios. + +cies $(2\times, 4\times, 8\times)$ of STMap as training and testing samples. Specifically, temporal sampling is to training the models with different video clip lengths, and temporal frequency refers to testing the corresponding sets at different frequencies. RMSE results are listed in Tab. 4, which illustrates the reasons for our choice of window and the advantages of our manner over existing rPPG disentanglement strategies. + +While building the framework based on transformer, we discuss the perception of our disentanglement in CNN. This fully verifies that the improvement comes from architecture design rather than the inherent self-attention of transformer. We show the effects on four datasets based on CNN (Conv) and transformer. RMSE results in Fig. 8 can be adopted as a test of the rationality of our design. In addition, we compare the efficiency of CNN based on our strategy in the Supp. + +Finally, for the pure outdoor environments and complex time-varying lighting, we calculate the representation of the learned features corresponding to the pulsing spike points on the disentangled and undisentangled maps of MR-NIRP-DRV in day (left) and night (right) driving scenes, and count their normalized representations. Fig. 9 shows that the peak distribution learned by our overall structure is closer to 1.0, which means that its sensing has a higher overlap with GT. + +# 5. Conclusion + +Focusing on remote HR prediction and analysis has a wide range of practical applications. This paper proposes a novel rPPG framework to overcome the complex environment and eliminate the extreme interference that are difficult to solve with current approaches. 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Results of our reflection removal system. We use linear (RAW) images with an optional contextual photo, and output the clean and reflection images in linear color for editing, at full resolution (shown at 2K). Prior works use tone-mapped images at $\approx 256\mathrm{p}$ , yielding lower quality and inaccurate color. Brightness/contrast changes relative to captured photos arise from reflection removal, and are correct. + +![](images/d5218a0f09e5a5b3574f728937f9a947d42602726a8cbd46807073cc64f1bb02.jpg) + +![](images/1b4733a2dc5e26f9345fd02b2c4181da03ab3f3801215237112e09d6a21f0c36.jpg) + +![](images/df33fea139f9991ecef78fa6d914849934a768fd9c009e737218f1e0e082e3a8.jpg) + +![](images/97575bb87a92ea316ebcb1741f640b64ea05c068df621dc7309e0d795df17ae9.jpg) + +![](images/512bc09b48286ecf7770317ac152e8e4a6014eebdbcc98ee2555a93c4dd081c0.jpg) + +![](images/a1791ef09e969aaea798cad8987cfa555afee5a484c6ab29d4128338f54edf90.jpg) + +# Abstract + +We describe a system to remove real-world reflections from images for consumer photography. Our system operates on linear (RAW) photos, and accepts an optional contextual photo looking in the opposite direction (e.g. the "selfie" camera on a mobile device). This optional photo disambiguates what should be considered the reflection. The system is trained solely on synthetic mixtures of real RAW photos, which we combine using a reflection simulation that is photometrically and geometrically accurate. Our system comprises a base model that accepts the captured photo and optional context photo as input, and runs at 256p, followed by an up-sampling model that transforms 256p images to full resolution. The system produces preview images at 1K in 4.5-6.5s on a MacBook or iPhone 14 Pro. We show SOTA results on RAW photos that were captured in the field to embody typical consumer photos, and show that training on RAW simulation data improves performance more than the architectural variations among prior works. + +# 1. Introduction + +Taking pictures through glass is difficult. Light reflects off of the glass and linearly mixes with the subject, creating a distraction. Photos from cars and airplanes show the cabin, photos from buildings include the ceiling lights, paintings are covered by haze, and window shopping shots are photobombed by the photographer—to name just a few cases. + +Removing unwanted reflections is difficult because they occur in a diverse range of locations and situations. Locations include shopping spots, traveling (cars, planes), buildings, museums, and special cases (eyeglasses, screens). Reflections depend on the time, lighting (e.g. incandescent), scene (trees, streets), illuminant power, and appearance (complex textures or simple shapes). These factors create priors because glass is placed carefully in the world. + +One way to remove reflections involves capturing a second photo with a black material placed behind the glass to allow only reflected light to reach the camera. If this reflection image, and the original mixture image, are stored in a + +format that preserves the linear relationship between pixel values and the scene luminance (e.g., RAW), then these two scene-referred images can be subtracted to obtain the image that transmitted through the glass. This transmission image can be recovered because light mixes by addition in photosites on the sensor. Subtraction has been used for datasets [28, 48], but fails under motion or lighting changes; this severely restricts data collection. Alternatively one can place glass panes in the scene, but the scene and lighting are typically similar on both sides. Training and evaluating on such unrealistic data can be unhelpful and misleading. + +This paper presents a reflection removal system for consumer photography that targets the following requirements: + +1. Handle typical reflections in consumer photography. +2. Minimize user interactions (steps, taps, strokes). +3. Allow photo capture in a typical amount of time. +4. Produce results on-screen for review in about 5 seconds. +5. Produce results at the input image resolution. +6. Facilitate editing for error correction and aesthetics. + +Few prior works satisfy these, which affect design and evaluation. In particular, data should match how the system will be used. For req. 1, one needs a large dataset of realistic photos. Prior works require ground truth photos, but capturing them restricts the dataset size and diversity. We synthesize realistic and diverse photos in large quantities. + +We synthesize reflections by combining, for example, an image looking at a storefront with one of sunlit buildings presumed to be behind the photographer. To make the synthesis accurate, we use linear scene-referred images with known photometric and colorimetric calibration, and combine them in a physically correct way. For example, the reflected buildings are typically brighter and bluer than the storefront, but will be attenuated by reflection off the glass. + +To address req. 2 (capture time) and 4 (processing time), we avoid asking the user to capture video, bursts of frames, or stereo photos. These help identify what created the reflection, but they slow down processing. Instead, we allow the user to capture an optional, contextual photo. This photo does not need to be captured simultaneously, or registered with the original photo. In fact, it could be captured by quickly turning around and looking away from the window. + +To address req. 5, we use a novel upsampler with a flexible output resolution. Note that upsampling is imperative and non-trivial, but mostly disregarded in the literature. To meet req. 6 we output reflection and transmission images so users can remix them to fix the long tail of practical failures. + +# Contributions. In this work, we + +1. show how to synthesize training data such that models do not need to be fine-tuned on real images; +2. show that training/testing on RAW improves performance significantly—more than prior model variations; +3. use a contextual photo to help identify the reflection; +4. significantly reduce upsampling artifacts while produc + +ing output at 1K in 5s for review, and at full resolution. This paper is best read with hyperlinks into the supplement. See arXiv or the project website for a complete version. Prior work is outlined in Sec. 2, reflection synthesis (Sec. 3), removal (Sec. 4), and results (Sec. 5). In supplemental sections we discuss simulation (Sec. A-C), data collection (Sec. D), modeling (Sec. E), and results (Sec. F). + +# 2. Prior work + +Removing reflections is a long-standing problem. Prior works have used multi-image capture and machine learning. Among the latter, upsampling low-resolution results is an important sub-problem. We survey each category. + +Multiple input images. Prior methods use video [5, 16], image sequences [17, 30, 33, 37, 38, 41, 42, 55], flash [4, 26], near infrared [19], polarization [12, 25, 27, 34, 53], and dual pixel images [36], as well as light fields [49]. We use an optional and additional photo of the reflected scene (not of the glass) to identify the reflection. This contextual photo is any for which the camera is pointed at the reflected scene (e.g., the camera is turned $180^{\circ}$ as in a "selfie" camera). + +Reflection synthesis. Prior methods are trained with heuristically mixed pairs of tone-mapped images [6, 9, 11, 16, 20, 21, 31, 47, 56, 57]. Such mixing is inaccurate, so non-linear methods have been used [24, 52]. Physically based methods nonetheless use tone-mapped images [24]. Successful methods however require ground truth images to train models that generalize [28], typically at approximately a 10:1 ratio of synthetic and real [20, 28, 29, 32, 35, 47, 51, 59]. This ratio raises issues of dataset scale and diversity because ground truth capture is tedious and restrictive. The largest dataset of real images to-date [60] has 14,952 pairs $(10^{4})$ , but methods like [20, 47, 59] require pre-training on datasets larger than $10^{6}$ (e.g., ImageNet [40]). We synthesize photometrically accurate images to obviate ground truth training images, and train models from scratch on more than 1M examples, which improves performance. + +Removing high resolution reflections. Most methods operate at $\approx 256^2$ pixels, and cannot be trivially scaled up. Useful systems must create preview images at $\approx 1\mathrm{K}$ pixels, and final outputs beyond $4\mathrm{K}$ . Prasad [35] use a base model at $256^2$ pixels, and an upsampler that yields $\geq 4\mathrm{K}$ pixels. Their fast upsampler re-introduces sharp reflections. Our upsampler is similarly fast, but removes sharp reflections. + +Inference on RAW images. Most prior methods apply reflection removal to 8-bit display-referred images, such as internet JPEGs. Such images have been white-balanced, tone-mapped, denoised, sharpened, and compressed. We reframe dereflection to operate on scene-referred (RAW) images. Lei [26] subtract pairs of RAW images to suppress the reflection before converting to 8-bit for full removal. We operate on RAW end-to-end. RAW inputs improve prior methods, but our system outperforms them. + +# 3. Reflection synthesis + +Our pipeline for removing reflections uses a base model and an upsampler that are trained solely on simulated images (Sec. 4), which overcomes the scaling bottleneck of needing to capture real reflections. We simulate reflections photometrically by summing pairs of scene-referred images, which are linear with respect to scene luminance. In contrast, images in most 8-bit formats are display-referred—non-linearly related to luminance. Scene-referred images originate from sensor data stored in RAW format, such as Adobe Digital Negative (DNG). The transformation of RAW data into display-referred images is described by Adobe Camera RAW (ACR), the DNG spec. [1] pp.99-104, and the DNG SDK [1] as follows: + +1. Linearize (e.g. remove vignetting and black levels) +2. Demosaic +3. Subtract the scalar black level +4. Convert to XYZ color +5. White balance +6. Convert to RGB color +7. Dehaze, tone map (spatial adaptive highlights, shadows, clarity); enhance texture; adjust local contrast, hue, color tone, whites, and blacks. +8. Gamma compress + +Step 8 yields an 8-bit finished image for storage, but its pixel values are non-linearly related to scene luminance because Step 7 performs proprietary, non-linear, and spatially varying effects that cannot be modeled with a gamma curve as is often done [29, 53, 59]. Realistic reflections therefore cannot be simulated by summing pairs of finished images. + +Which earlier step is most appropriate for simulation? The outputs of Steps 5 and 6 are linear, but the illuminant color has been removed by white balancing—accurate reflections cannot be simulated here because scenes that reflect from and transmit through glass are often illuminated by light sources with differing colors, and those colors mix before white balancing. The output of Step 3 is linear, preserves the illuminant color, and has been demosaicked, but its colors are with respect to a sensor-specific spectral basis—images from different sensors cannot be summed here. The output of Step 4 is however ideal: the XYZ + +color space is sensor-independent, the illuminant color is preserved (unlike prior works [3]), and pixels are linear with respect to luminance. We therefore select Step 4 and XYZ color space to simulate photometrically accurate reflections. + +# 3.1. Photometric reflection synthesis + +Our most fundamental simulation principle is the additive property of light: glass superimposes the light fields from a reflection and transmission scene to form a mixture. The resulting mixture image $m = t + r$ accumulates (with equal weight) photons from the two scenes into a transmission image $t$ and a reflection image $r$ . We simulate $t$ and $r$ from images in linear XYZ color (ACR Step 4). + +The first photometric property is the illuminant color, which often differs between $t$ and $r$ because the glass in consumer photographs typically separates indoor and outdoor spaces. Otherwise, the photographer could walk around the glass to take their photo. Even in specialized scenes like museum display cases, the case is often internally illuminated, making its illuminant color different than in the gallery at large. By representing $t$ and $r$ in XYZ color before white balancing, the illuminant colors are mixed. + +The second property is the illuminant power. In typical scenes, this power differs on either side of the glass ( $t$ and $r$ differ in brightness). The number of captured photons is scaled by the exposure $e = s \cdot g / n^2$ , for shutter speed $s$ , aperture $n$ , and gain $g$ (ISO). We normalize the exposures of $t$ and $r$ by $e$ so pixels are proportional to scene luminance up to a shared constant. This un-exposed mixture is $m' = t' + r'$ , $t' = t / e_t$ , and $r' = r / e_r$ , for exposures $e_t$ and $e_r$ . We simulate a capture function $\mathcal{C}$ that re-exposes and re-white balances $m'$ by exposing the mean pixel to a target value $\tau$ , $m = \mathcal{C}(m') = We'm'$ , and $e' = \tau / \mathbb{E}[m']$ , where $W$ is a $3 \times 3$ matrix that white balances in XYZ (Func. S2, Sec. A.1). If pixels in $t$ or $r$ are saturated, $e' = 1 / \min(\max(t'), \max(r'))$ , to ensure they remain so. Lastly, $m$ is converted to scene-referred, linear RGB to train models. + +The full simulation is described in Func. 1 and Sec. A. This function produces mixtures $m$ are photometrically accurate, but they aren't always useful. When saturation dictates the re-exposure $e'$ , pixels can be clipped, modeling over-exposed $m$ . Images $t'$ or $r'$ can also be so dark that they are invisible, or so mutually destructive that one would struggle to identify the subject. These photos do not model $m$ that photographers care about. We therefore collect a large dataset of images and search for well exposed and well mixed $m$ . This search introduces photometric and semantic priors on $m$ , $t$ , and $r$ (e.g., skies often reflect). See Sec. D. + +# 3.2. Geometric reflection synthesis + +Our second fundamental simulation principle is that mixtures must be geometrically valid. Denoting the images to + +Function 1 Simulate reflection examples $(m, t, r, c)$ . +Input: A random pair of XYZ images $(i,j)$ +Output: Simulated components and context image. +1: Split $j$ into non-overlapping reflection and context parts $(r,c)$ +2: Split $i$ similarly: randomly select a transmission part $t$ +3: Unexpose $t$ and $r$ by using their exposure metadata. +4: Apply the geometric simulation to $(t,r)$ +5: Composite $m = t + r$ +6: Compute a new exposure $e$ for $m$ {Func.S1} +7: Compute WB matrix XYZ-to_XYZ_awb. {Func.S2} +8: White balance (WB) $m$ by applyingXYZ-to_XYZ_awb. +9: Apply the same white balance to $(t,r,c)$ +10: Get the transform XYZ-D50-to_sRGB.{SDK Func.S12} +11: Transform $(m,t,r,c)$ to linear sRGB. +12: return $(m,t,r,c)$ + +be summed as $t$ and $r$ , and our source image pairs as $(i,j)$ , we synthesize $t = T(i)$ and $r = R(j)$ by modeling spatially varying Fresnel attenuation, perspective, double reflection, and defocus. We omit from $T$ the effects of global color, dirt, and scratches; editing tools can correct them. We model a physically calibrated amount of defocus blur; most reflections are sharp as also noted in [28]. See Sec. B. + +# 3.3. The contextual photo + +We accept an optional contextual photo $c$ that directly captures the reflection scene to help identify the reflection $r$ . Capture of $c$ can be simultaneous with the secondary front camera (selfie) on a mobile device, or briefly later. We make three observations about the views of $c$ and $r$ (see Fig. S3): + +1. Even if the cameras are collocated, the viewpoints of $c$ and $r$ will be translated by twice the distance to the glass. +2. If the mixture is captured obliquely to the glass, rotating the contextual view $180^{\circ}$ yields little common content. +3. If the selfie camera is used, the reflection scene might be partially occluded by the photographer. + +Image $c$ will therefore often contain little content that matches with $r$ unless it is captured carefully. We avoid placing such a large burden on the user, and allow them to capture any view, $c$ , of the reflection scene. Crucially, this relaxation also facilitates the geometric simulation. We scalably model $c$ by cropping source images into a disjoint left/right half (or top/bottom). The context image encodes information about the lighting and scene because we use a capture function $\mathcal{C}$ with the same white balance as $(m, t, r)$ . See Sec. 3.1, Func. 1, and Sec. C for details. + +# 4. Reflection removal + +Our system removes reflections from RAW images, $m$ , in linear RGB color (ACR Step 6) with an optional context image $c$ that is white balanced like $m$ (see Func. 1). Both $m$ and $c$ share a scene-referred color space, which aids removal; RGB supports pre-trained perceptual losses. We predict $t$ and $r$ in linear RGB, and store inference outputs by inverting ACR steps 3-6 to produce new RAW images. + +Our system uses two models, Fig. 2. A base model uses $m, c$ at $256^2$ pixels to predict $t, r$ (rectangular images are tiled); $t, r$ are then upsampled using a Gaussian pyramid. + +# 4.1. Base model + +The base model is in Fig. S4 due to space limits. A multi-scale backbone projects $m$ into a high dimensional space and computes semantic features (labeled $P$ -Net). These features are + +![](images/19fd55b8e18428121a89a77abfd5225df84d57fe4878d744b45faac559af152b.jpg) +Figure 2. System + +fused (labeled $F$ -Net) with a feature pyramid network (FPN) at the input resolution. The backbone is EfficientNet [43] at $256^2$ pixels, and fusion uses a BiFPN pyramid [44, 54]. + +The context image $c$ , is processed identically to $m$ . Its low-resolution FPN features are used to predict affines that modify the FPN features of $m$ using conv-mod-deconv operations ala StyleGAN [23]. Modulation is per-channel because $c$ does not share identical content with $m$ . Conceptually, modulation gives the model additional capacity to identify $r$ within the features of $m$ . A finishing module further identifies and renders $t, r$ (it's the head in [59]). We predict $(t, r)$ independently, rather than enforcing $t + r = m$ , to decouple failures. Training uses the losses of [59] with improvements to the adversary and gradient terms. Crucially, training is end-to-end from random weights. See Sec. E.1. + +# 4.2. Upsampler + +The upsampler is shown in Fig. S5 due to space limits. Upsampling is performed iteratively over a Gaussian pyramid (see Fig. 2), as summarized below. Details are in Sec. E.2. + +Briefly, the upsampler first projects the low- and high-resolution images $(m,r,t)$ , and $M$ into a high dimensional space $\phi$ using a convolutional backbone. The upsampler then matches low resolution features $\phi_t$ , $\phi_r$ to $\phi_m$ to create masks that identify the features of $t$ , $r$ within $m$ . This matching process uses products of features: when features match, their product can be large regardless of sign, whereas summation yields large activations if either input is large. We generalize this idea by predicting affine transforms that are applied to the features of $t$ and $r$ , followed by a sigmoid; see Fig. S5 (bottom). Two per-pixel, per-channel masks are thus predicted, $\mathbb{I}_t$ , $\mathbb{I}_r$ . Errors are corrected by a joint mask predictor that inspects both $\mathbb{I}_t$ , $\mathbb{I}_r$ (see Sec. E.2). Masks $\mathbb{I}_t$ and $\mathbb{I}_r$ are resampled $2\times$ and multiplied with $\phi_M$ to project its features into subspaces for $T$ , $R$ . This key step assumes that the identity $\mathbb{I}_t$ , $\mathbb{I}_r$ of the component to which each feature belongs is low in spatial frequency. By resampling masks, not features, sharp features are preserved. Errors are corrected with finishing convolutions, which render $T$ , $R$ . + +Training uses a cycle-consistency loss, losses similar to [35], and begins from scratch. See Sec. E.2 for details. + +# 5. Results + +We evaluate the simulation, base model, and upsampler; extensive results are added in the supplement. We make four contributions. First, we show that dereflection models that are trained solely on simulated reflections can generalize to real images without fine-tuning on real images, provided that the simulation uses RAW images in a photometrically accurate way. Second, training and testing on RAW images improves results significantly, and more than prior model variations. Third, a context image can disambiguate the reflection content if it is captured in another direction (e.g., the selfie). Fourth, upsampling low-res results, which is imperative but largely neglected in the literature, works better if one explicitly matches features in the low-res outputs $t$ , $r$ to the low-res mixture, and masks them from the high-res mixture to recover the high-res transmission and reflection. + +# 5.1. Reflection simulation + +Source images were drawn from MIT5K [8], RAISE [10], and Laval Indoors [14], totaling 12,803 RAWs and 2,233 scene-referred Image-Based Lighting (IBL) panoramas. The $360^{\circ}$ IBLs are equivalent to about 12,367 indoor RAW images because we simulate random cameras with an average FOV of $65^{\circ}$ , Sec. B.2, B.4. Images are grouped into 10,547 outdoor and 14,623 indoor to create pairs $(i,j)$ , Sec. D.2. The groups are split into train, validation, and test sets $(80\%, 15\%, 5\%)$ before simulation. + +The number of examples $(m, t, r)$ is amplified by randomization in the geometric simulation (Sec. B, D). We search $10^{8}$ examples for useful $m$ . After culling, about $10^{7}$ mixtures remain, and we rendered $10\%$ at $256^{2}$ and $2048^{2}$ pixels to train the models. The $256^{2}$ pixel dataset has 1,241,091 for training, 46,121 for test, and 8,991 for validation; the $2048^{2}$ dataset has 1,079,631; 39,916; and 7,448. + +Fig. 3 shows results of mixing scene-referred images: (a) correct illuminant colors and (b) correct reflection visibility. We linearly blended 8-bit tone-mapped images for comparison, and compare to prior works (see caption). Fig. S2 shows an overview of the dataset, and is discussed below. + +In Tab. 1 we ablate each simulation component. We (gamma) compressed $t$ , $r$ before compositing; separately exposed them (exposure); did not constrain their inclination or field-of-view (pose); removed spatially varying attenuation by making all camera rays normal to the glass (fresnel); separately white balanced (WB); removed depth-of-field blur and double reflection (blur); and removed all. We trained our base model on each dataset, and evaluated on the full-simulation test set. Each feature affects performance (all differences are significant), and omitting them all $(All \pm G)$ decreases performance dramatically compared to the average degradation to $t$ , $r$ (control). + +Discussion. Prior works mix 8-bit tone-mapped images, and the results are qualitatively unrealistic. Their simulated + +reflections overpower the highlights, and are not powerful enough in the shadows, which are boosted by tone mapping. In our accurate simulations, light from two scenes is mixed linearly and equally without tone-mapping. This accurate mixing allows our models to generalize better to new scenes, and yields SOTA performance without training on real images (Sec. 5.2). Furthermore, by synthesizing physically accurate reflections and searching for visible ones, we introduce natural priors on their appearance. Indoor light is weak, so reflections of the indoors are typically of regions near light sources or windows; see Fig. S2, examples 1, 2, 5, 11, 14, 19, 24, 25. Indoor lights create small reflections that often look yellow atop outdoor scenes, due to typical illuminant colors, whereas outdoor light can bounce off diffuse objects with enough strength to create colorful reflections of whole scenes that can be blue in white balance due to the outdoor illuminant color; see Fig. S2, examples 4, 8, 10, 12, 15, 16, 17, 18, 21. At dusk, whole indoor scenes can reflect over cityscapes, etc. (examples 3, 13). Such priors are apparent in consumer photos (see Figs. 1, 7, 8, S6, S7, S8). Lastly, like prior works we pair indoor/outdoor photos, which permits pairings such as bathrooms and beaches. Such pairs can be removed if they prove unhelpful. + +# 5.2. Base reflection removal + +Base models were trained end-to-end from random weights at $256^2$ pixels using an Adam optimizer with $l_r = 1e - 4$ , discriminator $l_r = 5e - 5$ , and batch size 32 over 16 GPUs for 20 epochs. Adversarial training begins after one epoch. + +We trained three base models, one with and two without context $c$ . To omit $c$ , we removed the modulated merges (Fig. S4), which decreases model capacity. As a second option, we left the model unchanged, and trained/tested with random $c$ . We used this second approach for ablation. + +Our system uses RAW images end-to-end, but public datasets do not provide RAW images: Real20, Real45, Nature, SIR2, $\mathrm{SIR2^{+}}$ , $\mathrm{CDR},^2$ and RRW all use JPG/PNG formats [11, 28, 29, 46, 48, 59, 60]. We tabulate results using our simulation test sets, and show visual results using RAW photos that were captured in-the-wild. See also Sec. F.2. + +In Tab. 2 we compare to Zhang et al. [59], DSRNet [20], Zhu et al. [60], and CoRRN [47] by retraining their models on our RAW dataset. Recall that our model uses the same losses and network head as Zhang et al. This simplifies comparison to prior work. Tab. 2 (RAW Train) shows that, when training with RAW, all methods improve images relative to the average degradation to $t$ , $r$ (control). Our models however outperform prior works (ours +ctx, ours). + +To show the benefit of RAW simulation and inference, we ran the previously published 8-bit models on an 8-bit + +![](images/4736bc86726df03336f4ca8a8c9bf13a71730cef2ae9f2c92db2fa44a6967792.jpg) +Figure 3. The importance of synthesizing training data (top row) from linear images (middle row), compared to prior work. (a) Photometrically accurate illuminant colors are simulated by mixing before white balancing; mixing 8-bit white balanced images is much different. (b) Mixing in scene-referred linear units produces reflections that are strong in the shadows, but transparent in the highlights. (prior work) Such effects are visibly incorrect in prior work, which blend 8-bit tone mapped images [11, 52]. (bottom) Real and simulated examples are shuffled together. For each real image, a similar synthetic reflection was manually found in the dataset. Real images were not captured to match known examples; these qualitative matches exist because the dataset size exceeds $10^{6}$ ( $0\text{m} \times \text{m} \times \text{m}$ ) + +
MethodSSIMt%↑SSIMr%↑
Control85.849.0
Full Sim.95.77088.277
Ablate(G)amma88.82177.0
Exposure94.25986.1
Pose95.06585.4
Fresnel95.36787.3
WB95.56887.6
Blur95.56887.9
All - G90.23171.3
All + G89.22458.5
+ +Table 1. Ablated datasets were created, 1.2M examples each. Model ours+ctx was trained on these, and tested on the full-simulation test set. $\% \uparrow$ is w.r.t. control (see Tab. 2). SSIM values are shown as percentages. + +
MethodPSNRtSSIMt%↑PSNRrSSIMr%↑
RAW TrainControl21.7485.812.4849.0
Ours+ctx33.2395.7+7030.1788.2+77
Ours32.1595.2+6629.1886.7+74
Zhu [60]29.8492.8+49
DSRNet [20]28.9892.6+4823.9975.5+52
Zhang [59]26.2389.9+2822.7861.5+25
CoRRN [47]22.7586.7+618.3160.4+22
8-bit PubControl18.6278.49.7937.4
DSRNet [20]19.9980.0+816.9849.3+19
Zhu [60]19.8479.7+6
Zhang [59]18.6575.9-1117.3751.0+22
CoRRN [47]18.9574.7-1715.9923.8-22
Abl.Ours+rac33.2095.7+7030.2088.3+77
Ours+rnd32.4295.1+6629.2986.7+74
+ +Table 2. Base models: (control) compares $m$ to $t,r$ . 8-bit models use published weights. %↑ is w.r.t. SSIM control. Ablations: (rac) GT $r$ is used as context; (rnd) random $c$ . Ours+ctx beats Ours+rnd $\left( {p < {1.7e} - {11}}\right)$ . +Figure 5. Upsampling GT images 256p to 2048p. V-DESIRR [35] adds artifacts. + +
MethodPSNRtSSIMtPSNRrSSIMr
GTControl19.5086.313.1364.5
Ours47.7798.845.9398.2
Ours-NM43.2998.143.9996.9
VDSR+C [35]42.2497.938.3293.8
VDSR [35]40.7497.438.3093.9
Bicubic31.9885.141.5896.0
SUPIR [58]28.0964.628.2956.8
RESRGan [50]23.7265.623.1153.6
E2EOurs30.6295.228.5390.7
VDSR+C [35]30.2794.527.7488.7
+ +Table 3. Upsampling ground truth (GT), and using the base model for end-to-end results (E2E). Usampling is from 256p to 2048p using our method and V-DESIRR with and without cycle consistency (+C), which improves VDSR for T $(p < 1e - 12)$ + +version of our test set, $^{4}$ and compared the percent improvement to that of using RAW (Tab. 2, 8-bit Pub.). DSRNet and Zhu improve images modestly; Zhang and CoRRN distort the color (e.g. Fig. 1). Retraining DSRNet, Zhu, and Zhang on RAW improves their performance by $\approx 40$ pct. points (pp) $\mathrm{SSIM}_{\mathrm{t}}$ , whereas the performance differences among them are only $\approx 20$ pp. Training on RAW simulation data therefore improved performance more than the architectural variations among prior works. Fur + +thermore, abating the simulation (Tab. 1, $All + G$ ) degrades performance -46pp, which conversely matches the +40pp benefit of RAW retraining, and exceeds even the benefit of the contextual photo (+4pp). + +In Tab. 2 (Abl.) we ablate our contextual model by training/testing with random $c$ (ours+rnd), which degrades performance compared to (ours+ctx)—this is statistically significant. Removing operations that use $c$ (ours) did not degrade performance compared to ours+rnd ( $p < 1.7e-11$ ), which suggests that ours+rnd does not learn dataset priors + +with its additional capacity, and conversely that $\text{ours} + \text{ctx}$ leverages the content of $c$ . Ablating further, using the reflection as the context ( $c = r$ ) at test time only does not improve the contextual model results ( $\text{ours} + \text{rac}$ ), which suggests that $c$ and $r$ need not match; the model is robust to their differences since it is trained with disjoint crops ( $c, r$ ). + +For visual comparison, in Fig. 7 and Fig. S6 we captured ground truth reflections in common cases: looking outdoors, into a display case, and at artwork. We dereflected with Zhang, DSRNet (retrained, $RT$ ), and our models at $256 \times 384$ (inset images) and upsampled to $2048 \times 2731$ (next section). The empirical SSIM values (lowercase t, r) are commensurate with test performance (Tab. 2). In Fig. 7 our contextual model separates the reflection, but without context our model attributes the colors in the umbrella with a reflected object. Prior works perform quantitatively worse. + +In Figs. 1, 4, 8, S7, S8, and S9 we show results on photos in-the-wild from cameras that were not used to construct the training data. We also compare the 8-bit models of Zhang and DSRNet. The bottom two rows of Figs. 8, S7, S8 show that these prior 8-bit models perform qualitatively worse than when they are re-trained/evaluated on RAW (the top rows). They do not however recover $r$ well, which is needed for aesthetics and error correction (Sec. 5.4, Sec. F.4). + +Discussion. Our models recover $t, r$ in diverse real-world cases including museums, nature, shopping, a mid-day city, artwork, etc. (Figs. 1, 4, 7, 8, S6, S7, S8, S9). In Fig. 1, using the context photo yields more correct and uniform color on the Egyptian tablet because there is less ambiguity about the color of the reflection scene (compare to inset w/o context). Failures occur when $t$ or $r$ is bright, and pushes the other into the noise floor, saturating it to black—the problem becomes hole filling. When a single color channel saturates, the content can sometimes be recovered. But, systems must address hole filling because users typically cannot control the strength of reflections. + +Errors can occur when textured regions of $t$ and $r$ overlap, as in Fig. 1 where a stone wall overlaps the subject's dress. Color differences help: in Fig. 7 the reflected painting is separated from the tree. Without such differences, models must repair or hallucinate content in the corrupted $t$ . Saturated reflections pose a similar challenge. See Sec. F for more discussion of errors and additional results. + +# 5.3. Upsampling + +Our upsampler is trained using Adam with $l_r = 4e - 4$ , batch size 64 over 32 A100 GPUs, and converges after about 40 epochs. For end-to-end operation (E2E), we tune with the base model outputs for 19K examples at $l_r = 2e - 4$ . + +We compare to V-DESIRR [35] in Tab. 3 by upsampling the ground truth (GT) and using the base model (E2E). For + +best E2E performance, we fine tuned our upsampler and V-DESIRR with the base model. Our method performs best (ours). Cycle consistency loss improves V-DESIRR $(+C)$ so we used this for E2E. We ablated the upsampler masking operations by using only the finisher head (Ours-NM); performance degraded almost to match V-DESIRR. + +Comparing on GT images, Fig. 5 and Fig. S11, V-DESIRR produces strong artifacts, even after fine tuning (adding cycle-consistency losses did not help). + +Discussion. V-DESIRR amplifies errors at low resolutions by repeatedly upsampling its previous output images. Instead, our model masks and copies the high-res mixture features $\phi_{M}$ to the output $T,R$ . This direct copy reduces error propagation. Errors can still occur when features that are not present in the low resolution inputs become visible at the next level upward (e.g. Fig. S14) because the low resolution $t,r$ cannot guide upsampling of such features, and the + +upsampler must infer the high resolution image to which the features belong. + +# 5.4. Reflection editing + +In Fig. 6 and Fig. S15 we show that the predicted reflection facilitates aesthetic editing and error correction. In Fig. 6, the reflection color and spatial arrangement is modified. Error correction is shown in Fig. S15, Sec. F.4. Edits were made in Photo + +![](images/371ac3306ccd0bc654f79bc11e76f79baf10f79c6f95ed62a5194a4bbebabdfe.jpg) + +![](images/9b8096a0cd62f7c573b1b57bf5c656fee8af25a8682eeff62039f1e14e00128d.jpg) +Figure 6. Reflection editing. + +shop using the tone-mapped $t$ and $r$ images, and "Linear Dodge" blend mode (but linear blending would be ideal). + +# 6. Conclusion + +We have described a de-reflection system that is trained solely on images from a photometrically and geometrically accurate simulation. Moreover, we have imbued these images with natural priors by searching among millions of them for well-exposed and visually interpretable cases. This RAW simulation dramatically improves results, more than prior model variations, and enables our models to perform well on real images without training on them. + +Since Farid and Adelson [12], many cues have been used for de-reflection. We add illuminant color and context photos, and use RAW images end-to-end. Our models are thus sensitive and can uncover hidden reflections, Fig. S9; privacy should be protected. Our system can also remove lens flares, though they are not in the dataset, Fig. S10. Flare removal systems might therefore be pre-trained to remove reflections, since it is difficult to capture real lens flares. + +![](images/3b0b24d113f1f3fe371a75f751265aba702f3663104939e033afbc2f4aff769d.jpg) + +![](images/a7aec714be00fd11fea62d0a0b65856ff1357fa902a4b52bc18c0fae8ac49fd3.jpg) + +![](images/0a2fc8875c4bcc4101ff7fdb4ccd42db75a964f49f31921b6ba774148dc5dc21.jpg) + +![](images/a5303b0e5c3b0f289917bb514e65a7c0405f82d25fbc0cf9beb2b141826ddf20.jpg) + +![](images/fcaae6124bed8c0bdfb7789d5e6b4de7f9d4fc3ee24b5d307725b34949dc2495.jpg) + +![](images/e2b6718c9f3ac2b2c873528b87efaf08ad8d5f150b6fd37a44c3dc477e6282df.jpg) +Figure 7. Comparisons to ground truth (GT) at $256 \times 384$ (inset) and $2048 \times 3072$ . Methods are retrained for RAW (RT). SSIMs are relative to GT. + +![](images/69d40768d8a59adc67c404fe1b2af6b69ea46cc198477fc53ce94b30509d5c7b.jpg) + +![](images/7774b9ac785471bc47e67d610658fee4e5b18827fbadf062dfd6ad9b2c0f03a2.jpg) + +![](images/cfc8162b06d32ada5690927699e8353b0a8e55c31f61c5bfd7fa2b2d2a2503dc.jpg) + +![](images/ce54fc3d7593e833e40ec1d528142971cee9b32571cb4296a80b3a7d1feaa6c0.jpg) + +![](images/9f520cdfd69ffa7101c2f5e9379e92f0443e861244362c44628fbf1141c412dc.jpg) + +![](images/b7eca43318cf70b75569b299c455c59f050ded5cfad939d4f94527df2326e45d.jpg) + +![](images/eed08cfd3a0470c32d8d67dbd4d913f518559071cf36307821d2c39fe419d91f.jpg) +Figure 8. Comparisons to models trained on 8-bit images (bottom), with results at $256^{2}$ pixels. + +# References + +[1] Adobe. Adobe DNG specification. https://helpx.adobe.com/camera-raw/digital-negative.html, 2024. Accessed 2024-03-01. 3, 16, 17 +[2] Mahmoud Affifi, Jonathan T. Barron, Chloe LeGendre, Yun-Ta Tsai, and Francois Bleibel. 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While existing studies limited in the scope of pre-training knowledge, hardly underpinned its generalization to countless open-world concepts absent from the pre-training regime. This paper dives into such Out-of-Pre-training (OOP) generalization problem from a holistic perspective. We propose LAION-Beyond benchmark to isolate the evaluation of OOP concepts from pre-training knowledge, with regards to OpenCLIP and its reproducible variants derived from LAION datasets. Empirical analysis evidences that despite image features of OOP concepts born with significant category margins, their zero-shot transfer significantly fails due to the poor image-text alignment. To this, we elaborate the "name-tuning" methodology with its theoretical merits in terms of OOP generalization, then propose few-shot name learning (FSNL) and zero-shot name learning (ZSNL) algorithms to achieve OOP generalization in a data-efficient manner. LAION-Beyond dataset and codes: http://m-huangx.github.io/laion_beyond/. + +# 1. Introduction + +In recent years, pre-training vision models with language supervision by contrastive learning schemes becomes a focal point of interest [12, 23, 25]. The so-called CLIPs and its variants, forging a synergy between images and natural language, are pre-trained by aligning visual and textual information with a vast trove of image-text pairs using coupled encoders. The success of image-text matching is quantified by classifying images into the classes with their names in a vocabulary, which are fed into the text encoder with its prompt template (e.g., "a photo of a {class}") to generate their classification weights. Constructing Softmax classifier by the cosine similarity between normalized image features and weights, CLIP exhibits stellar few-shot / zero-shot + +![](images/24b8318c748c0ad5dfd565409dcc188d006a955a7c16790e8f1a0b38f7e62c45.jpg) +Visual concepts included for an open-vocabulary prediction +(a) In-Pretraining (IP) Generalization + +![](images/f3a5b676aa3c67b87d323cbfdec90d3609456f103c93a005b7f7fc3c31eb6c6f.jpg) +Visual concepts included for pre-training OpenCLIP +Visual concepts Beyond the scope of pre-training OpenCLIP +(b) Out-of-Pretraining (OOP) Generalization +Figure 1. Comparison between IP and OOP generalization. The former evaluate OpenCLIP's generalization with visual concepts seen in pre-training phases, whereas the latter justifies its generalization through the concepts absent during pre-training. + +learning on behave of its out-of-distribution (OOD) generalizability [10, 11, 41]. + +Leading studies investigated the CLIP family from diverse aspects of OOD generalization, while visual concepts employed in their evaluations were almost expected to have been encountered during pre-training (Fig.1.a). In contrast of these In-Pre-training (IP) concepts, Out-of-Pre-training (OOP) concepts never shown previously yet might predominant in the majority of open-world cases, remain questionable (Fig.1.b). This limitation stems from the scarcity of available evaluation data: existing benchmarks mainly consist of visual concepts well-represented in large-scale pretraining datasets such as LAION [26]. This category overlap between evaluation and pre-training distributions potentially masks the CLIP's true OOD generalization evaluation beyond commonly encountered concepts. + +To demystify the underlying capability of CLIP in OOP concepts, we propose LAION-Beyond benchmark with the counterpart classes absent in LAION datasets used to build OpenCLIP, the reproducible variants of CLIP. It derives LAION-Beyond's construction with 324 IP and 674 OOP classes under the rubric of 9 domains, which are tractably crawled from web to prevent the category-set contamination from the vocabulary of LAION. Combining LAION series and their OpenCLIP-derived models helps rigorously identify whether a concept joined contrastive pre-training. + +It facilitates the fair comparison between the IP and OOP concepts given their images recognized by OpenCLIP. + +Remarkable insights are found in the image features extracted from OOP concepts by the OpenCLIP encoder, illustrating significant clustering margins across arbitrary IP and OOP classes through visualization and clustering indexes. This phenomenon suggests that visual concepts are potentially categorized regardless of whether they were included in the pre-training dataset. However, in contrast with previous observations in IP classes, the zero-shot learning performance of OpenCLIP exhibits a tremendous deficit in OOP classes. It showcases the cross-modal alignment failure of the text encoder when OOP concepts appear in images. + +In the realm of open-vocabulary classification in LAION-Beyond, the alignment failure can be solved via fine-tuning the name embeddings of OOP concepts. We analyze the OOP generalization from a principled view, verifying the merit of fine-tuning OOP name embeddings and the potential risk when we take prompt-tuning or adapter in this problem. Derived from this, we propose few-shot name learning (FSNL) algorithm, then extend it to suit the situations without image-text pairs available in OOP concepts, which leads to zero-shot name learning (ZSNL) algorithm. FSNL fine-tunes name embedding of OOP concepts by shuffling contexts across similar concept pairs; ZSNL combines the name-tuning with bipartite graph matching algorithms to align proper OOP-class image-cluster centers. They are evaluated via LAION-Beyond in the comparison with prevalent prompt-tuning and adapter baselines, which justify our theoretical claims and the superiority of our methodology. + +# 2. Related Work + +Vision-Language Models (VLMs). VisualBERT is a pioneer in pre-trained VLMs, adapting BERT for multimodal inputs that shed a light to the follow-up pre-training models and techniques [3, 13, 14, 27, 29]. CLIP [9, 24] and its variants [4, 28, 42] revolutionized multimodal learning by pre-training to align large-scale images and texts in a uniform embedding space. The paradigm shift owes the broad employment of their pre-trained image encoders in most existing visual large language models (vLLMs) [1, 2, 37], which capably fast adapts to new visual concepts without extensively re-training their image-encoding pipelines. It is hardly coordinated with the existing CLIP-based empirical studies without the concerns of clarifying the concepts in or beyond the scope of pre-training. + +Generalization mechanism in VLM. Impressed by CLIP's capability, attentions were gradually paid to unveil its generalization mechanism behind. Some work are interested in its robustness [20, 30, 38] and its adaptation to long-tailed distribution bias [34, 49], while others examine train-test similarity [17] and compositionality understanding [40]. + +While Udandarao et al [31] reveal that CLIP requires exponentially more data for linear performance gains, these studies leave unexplored a critical question: how does CLIP handle cross-modal alignment for concepts absent from pretraining? Our work proposes LAION-beyond benchmark to formally investigate this OOP generalization problem. + +Data-Efficient Fine-tuning of VLM. Remarked by the extraordinary generalization, CLIP-based VLMs are primarily evaluated through open-vocabulary prediction with textual input as task-oriented prompt templates. Many studies aim for data-efficient fine-tuning CLIP to adapt downstream tasks. [8, 43] prefer a adapter layer inserted between CLIP's pre-training pipeline and the output, then fine-tuned to encourage the downstream-task adaptation. More recently, prompt-tuning approaches [15, 46-48] directly seek for optimizing the embedding parts behind task-specific context templates. The methodology is more flexible and broadly adopted in CLIP-based research. Distinct from conventional zero-shot learning settings [6, 7, 18], CLIP have observed large-scale vision-language pairs during pretraining so its zero-shot transfer inference heavily relies on the extensive supervision available in pretraining. How do the concepts unseen in pre-training influence CLIP's fine-tuning strategies? It remains a mystery. + +# 3. Preliminary + +As a reproducible variant of CLIP, OpenCLIP [4] consists of an image encoder $f$ and a text encoder $g$ jointly pretrained with massive image-text pairs $\{I_i, T_i\}_{i=1}^N$ drawn from open-source pre-training sets LAION [26], where normalized features $f(I^{(j)})$ , $g(T^{(j)})$ are extracted to train the encoders via closing their consine similarity gap with InfoNCE [21]. Well-trained encoders serve the prompt-based open-vocabulary classification principle: + +$$ +P _ {V} ^ {(f, g)} (\boldsymbol {y} | \boldsymbol {I}) = \frac {\exp \left(\frac {\operatorname* {s i m} (f (\boldsymbol {I}) , g (\boldsymbol {T} (\boldsymbol {y})))}{\gamma}\right)}{\sum_ {\boldsymbol {y} _ {i} \in V} \exp \left(\frac {\operatorname* {s i m} (f (\boldsymbol {I}) , g (\boldsymbol {T} (\boldsymbol {y} _ {i}))}{\gamma}\right)}, \tag {1} +$$ + +where $T(\boldsymbol{y})$ indicates a text with the class name $\boldsymbol{y}$ . It is also well-known as prompt if $T(\cdot)$ takes a task-specific template, e.g., $T(-) =$ "a photo of [−]" for few-shot/zero-shot learning paradigm. $V$ denotes the vocabulary to identify the range of predicted classes. + +Motivation. Given classes with respect to a vocabulary $V$ , we may fine-tune a lightweight adaptation layer [8] or the context embedding of prompt [45] to classify their images. In this case, OOD generalization is measured via the performance balance between the classes in $V$ or beyond. But no matter which, the success rises from vision-language alignment achieved during pre-training phase. Instead of constructing classifiers with pre-training words and phrases, the vocabulary $V$ in this work also permits the class names beyond the textual scope of $\{T_i\}_{i=1}^N$ . + +![](images/243e4d6162491195b18795ece4ddeb6a668b1364c1bb61e06dca64af3bb602b8.jpg) +Figure 2. The statistics of OOP and IP concepts and their images in LAION-Beyond (400M), (2B), and (5B). + +# 4. Unveiling OpenCLIP by Out-of-Pretraining (OOP) Concepts + +As discussed, our study needs to examine the performances of OpenCLIP when evaluating visual concepts absent in the pre-training dataset $\{I_i, T_i\}_{i=1}^N$ , whereas to the best of our knowledge, there is no proper identification of OOP concepts in existing benchmarks. Towards this end, we propose a evaluation benchmark LAION-Beyond. + +# 4.1. LAION-Beyond Benchmark + +Construction and statistic. LAION-Beyond consists of 106,052 images in 674 OOP concepts and 51,330 images in 324 IP concepts in terms of words and phrases in LAION-400M, distributed across 9 domains, i.e., Plants_Fungi, Insects_Spiders, Animals, Pokemon, FolkArt, Landmark, Attire, Food, and Architecture. Each domain represented as a categorical ancient branches in a hierarchy, simultaneously contains OOP concepts and IP concepts under the rubric of its categorical branch. The IP-class names are found in LAION-400M while the OOP-class names stays beyond the lexical scope of LAION-400M vocabulary. Images with texts associated with the OOP concepts are divided into train, val, test sets to facilitate our OOP generalization experiments (Sec.6), instead, IP concepts solely contain their images to evaluate the generalization of OpenCLIP. Our construction promises both OOP and IP concepts visually perceptible and long-tail distributed, to ensure their fair comparison. + +Scaling OOP concepts beyond LAION-2B and 5B. Despite LAION-Beyond drawn from concepts beyond LAION-400M, we further derive subsets to identify OOP concepts out of the scopes of LAION-2B and 5B, respectively. Specifically, we construct the word-and-phrase list of LAION-2B and 5B, as what was done previously, then screen the OOP concepts in LAION-Beyond (400M) to generate the image-text subsets drawn from OOP concepts + +Table 1. The normalized clustering accuracy across features extracted from OOP-class test images and IP-class test images across 9 domains, respectively. + +
AniumArchArtiFolkFoodInsectLadmkPlantPokemAvg
IP classes40.2791.0482.0978.0281.7250.4493.0155.7134.0768.15
OOP classes37.2781.0668.9276.6080.6548.3086.3953.1735.8063.13
IP-OOP gap3.0010.0213.831.421.072.146.622.541.735.02
+ +![](images/3bd026c43a0bb01590b64bbb40bef9cd86b70e1305af7ae4b318f76249727d16.jpg) +(a). Image features of OOP concepts + +![](images/01620b91b0048b430f38cf1e69747e65917c101f18f78e883a25b93ad374d813.jpg) +(b). Image features of OOP and IP concepts +Figure 3. The t-SNE visualization for (a).image features from 20 OOP classes drawn from Plants_Fungi; (b).image features from 10 OOP classes and 10 IP classes. Colors indicate the image features extracted from corresponding OOP classes. The gray spots in (b) indicate the image features extracted from arbitrary IP classes. + +excluded by LAION-2B and 5B. LAION-Beyond with 400M, 2B, and 5B splits, enable comprehensive evaluation of CLIP models pre-trained on their corresponding LAION datasets. This stratification encourages OOP-concept examination based upon the CLIP-based neural scaling law. + +Details of construction and statistic of (400M), (2B), and (5B) versions in LAION-Beyond refer to our Appendix.A. + +# 4.2. Generalization of CLIP: IP v.s. OOP Concepts + +Providing LAION-Beyond with concepts beyond LAION-400M, we evaluate OpenCLIP across the OOP and IP concepts, with the same categorical ancients for a fair comparison. It results in remarkable insights to better understand CLIP-derived systems in the realm of open-world concepts. + +Finding 1: clustering margins of OOP concepts. We first investigate the OOP image features through their t-SNE embeddings [32]. The features in Fig.3.a are illustrated with significant clustering gaps across different OOP categories and what's more, these clusters would not be overlapped by category clusters with respect to IP concepts (Fig.3.b) (Full t-SNE-based observations across 9 domains can be found in Appendix.A and corroborate our finding). The report of clustering accuracy across different OOP and IP classes (Table.1) further confirm this finding. In particular, we observe both IP and OOP classes with high normalized clustering accuracy in 7 domains, and the performance gaps in 6 domains less than $3\%$ . The digits coincide with the illustration in Fig.3, which jointly implies that image features extracted by the vision encoder of CLIP conceive the + +![](images/f9c8294ea6cfd24dd8fb5695c00e67ff71392acacbedee169ecc5f43d3814712.jpg) +Figure 4. The zero-shot inference performances of OpenCLIP and EvaCLIP on OOP and IP classes in LAION-Beyond (400M), (2B), and (5B), respectively. IP (cls-balance) and OOP (cls-balance) indicate the class-balanced accuracy $ACC_{\mathrm{cls - bal}}$ : Suppose that $N_{\mathrm{IP}}^c, N_{\mathrm{OOP}}^c$ denote the number of IP, OOP classes, then $ACC_{\mathrm{cls - bal}}(x) = \frac{N_{\mathrm{IP}}^cACC(x)}{N_{\mathrm{IP}}^c + N_{\mathrm{OOP}}^c}$ if $x \in D_{\mathrm{IP}}; ACC_{\mathrm{cls - bal}}(x) = \frac{N_{\mathrm{OOP}}^cACC(x)}{N_{\mathrm{IP}}^c + N_{\mathrm{OOP}}^c}$ if $x \in D_{\mathrm{OOP}}$ . The class-balanced accuracy debiases the performances with different numbers between IP and OOP classes for a fair evaluation. + +![](images/fcce9fb5f6c8f28ebad7597163521fa5682d37258147b198b8f27ec94f97a91c.jpg) + +![](images/ac3303f5cb5fff1a1eae31d393d8687030d3f0926196da2966dbca6f263169d1.jpg) + +![](images/bb28771c663b9db6b36a72c8f19a8b7f6a50e13fec36598e90d15b15954a51f5.jpg) + +![](images/a1dc57a3b0d07e353508f41020889eb51ec6a1d2c3379bc775f36605f40b7496.jpg) + +![](images/c54620dde4ca68e9ddca31e20f96f827da4ebfecd217ac8d64ceab31da683dba.jpg) + +discriminability across arbitrary classes, even if they have never shown the names in pre-training. + +Finding 2: image-text alignment failure. Though OpenCLIP born with the promising discriminability in OOP concepts with its image encoder, the text encoder fails to achieve the cross-modal alignment. To justify this, we compare zero-shot learning performances on IP and OOP concepts with neural scaling law. As illustrated in Fig.4, compared with the accuracy in IP classes, OOP-class zero-shot learning results drop with huge gaps in LAION-Beyond (400M), while the gaps are narrower while considering the class-balance accuracy between the images in OOP and IP classes, which demonstrates the class imbalance also contributes the gap. In the cases in LAION-Beyond (2B), IP and OOP results are close, however, balancing the classes leads to a larger gap. To this, the image-text misalignment in LAION-Beyond (2B) become more serious. In LAION-Beyond (5B), no matter class balance or not, OOP-class zero-shot learning significantly outperforms IP-class zero-shot learning. Summarize them and we found, despite OpenCLIP pre-trained with more image-text pairs (LAION-400M v.s. LAION-5B), as long as the concepts absent from pre-training, there is no promise to solve the image-text misalignment by neural scaling law. + +Opposed with image features, the disaster performances across OOP domains in OpenCLIP may owe to the text encoder fails to generate OOP classification weights. It stems from the absence of alignment between prompts with OOP concepts and their corresponding visual features, because of token embeddings of OOP concepts not initialized with any image-text alignment in pre-training. Since OOP concepts typically refer to rare classes, optimizing their embeddings in an efficient manner is supposed to be the key that achieves OOP image-text alignment. + +# 5. Methodology + +In this section, we first elaborate fine-tuning the name embeddings of OOP concepts along with its theoretical merits, then propose the derived algorithms in the open-vocabulary + +few-shot and zero-shot learning setups, respectively. + +# 5.1. Fine-Tuning Names of OOP Concepts + +Distinct from pretraining and prompt-tuning, name-tuning only optimizes the token embedding with regards to words and phrases of OOP concepts, while keeps the rest words' embeddings as usual. Suppose that we have OOP imagetext pairs $\left\{\left\langle \hat{I} (y),\hat{T} (e(y))\right\rangle \right\}$ , where $\pmb{y}$ indicates a word or a phrase with respect to a specific concept drawn from an OOP list $Y_{\mathrm{OOP}}$ . $\left\langle \hat{I} (y),\hat{T} (e(y))\right\rangle$ presents as a imagetext pair with the concept $\pmb{y}$ and its name tokenized into the embedding $e(y)$ , is included by caption $\hat{T} (e(y))$ . To this, tuning embeddings of OOP concepts is formulated + +$$ +\min _ {e (\boldsymbol {y}) \in e \left(\boldsymbol {Y} _ {\text {O O P}}\right)} \hat {\mathcal {R}} _ {\boldsymbol {Y} _ {\text {O O P}}} = \mathcal {L} _ {\text {I n f o N C E}} \left(\left\langle \hat {\boldsymbol {I}} (\boldsymbol {y}), \hat {\boldsymbol {T}} (e (\boldsymbol {y})) \right\rangle\right), \tag {2} +$$ + +where $\mathcal{L}_{\mathrm{InfoNCE}}$ denotes the optimization derived from InfoNCE whereas the image and text encoders are frozen to tune OOP word or phrase embeddings ahead of the text encoder input. $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{OOP}}}$ denotes the empirical risk minimization (ERM) with respect to the list of OOP concepts. + +OOP Generalization analysis. To show the necessity of name-tuning, we consider the population risk $\mathcal{R}_{\mathbf{Y}_{\mathrm{IP}} \cup \mathbf{Y}_{\mathrm{OOP}}}^{(f^*, g^*)}$ that denotes the ideal pre-training with $f, g$ and word embeddings in lists of IP and OOP concepts, and the practical pre-training ERM $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{IP}}}^{(\hat{f}, \hat{g})}$ only with IP concepts1. Obviously, minimizing $\mathcal{R}_{\mathbf{Y}_{\mathrm{IP}} \cup \mathbf{Y}_{\mathrm{OOP}}}^{(\hat{f}, \hat{g})}$ is perfect yet impossible since we are unable to go through the countless samples and the concepts newly up-coming, but combing $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{IP}}}^{(\hat{f}, \hat{g})}$ and $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{OOP}}}^{(\hat{f}, \hat{g})}$ leads to the generalization bound below + +Proposition 1. (Informal) Suppose that $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{OOP}}}$ denotes the ERM of fine-tuning the name embeddings of OOP concepts on top of frozen $\hat{f}, \hat{g}$ , which are pre-trained along with the + +name embeddings of IP concepts. Suppose $D_{\mathrm{IP}}$ , $D_{\mathrm{OOP}}$ as the distributions with IP and OOP concepts, respectively; and $N_{\mathrm{IP}}$ and $N_{\mathrm{OOP}}$ denote the number of samples drawn from $D_{\mathrm{IP}}$ , $D_{\mathrm{OOP}}$ for pre-training and fine-tuning, respectively. $\forall \epsilon > 0$ , it holds the probability $1 - \epsilon$ with + +$$ +\begin{array}{l} \mathcal {R} _ {\boldsymbol {Y} _ {\mathrm {I P}} \cup \boldsymbol {Y} _ {\mathrm {O O P}}} ^ {(f ^ {*}, g ^ {*})} \leq \hat {\mathcal {R}} _ {\boldsymbol {Y} _ {\mathrm {I P}}} ^ {(\hat {f}, \hat {g})} + \hat {\mathcal {R}} _ {\boldsymbol {Y} _ {\mathrm {O O P}}} + \frac {1}{2} \gamma (D _ {\mathrm {I P}}, D _ {\mathrm {O O P}}) \\ + d _ {p} (\hat {f}, f ^ {*}) + d _ {p} (\hat {g}, g ^ {*}) + \Re_ {D _ {\mathrm {I P}}} (\mathcal {F}, \mathcal {G}, \mathcal {E} _ {\mathrm {I P}}) + \Re_ {D _ {\mathrm {O O P}}} (\mathcal {E} _ {\mathrm {O O P}}) \\ + \frac {3}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {\mathrm {I P}}}} + \frac {3}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {\mathrm {O O P}}}} + \frac {1}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2}} \left(\frac {1}{N _ {\mathrm {I P}}} + \frac {1}{N _ {\mathrm {O O P}}}\right), \tag {3} \\ \end{array} +$$ + +where $\gamma (D_{\mathrm{IP}},D_{\mathrm{OOP}})$ indicates the distribution gap, $d_p(\cdot ,\cdot)$ indicates the approximation error via a $p$ -norm (entry-wise) to measure the difference between functions, $\Re_{D_{\mathrm{IP}}}$ and $\Re_{D_{\mathrm{OOP}}}$ denote the Rademacher complexity for pre-training and fine-tuning, with $\mathcal{F},\mathcal{G},\mathcal{E}_{\mathrm{IP}}$ and $\mathcal{E}_{\mathrm{OOP}}$ denote the functional spaces of $f,g,e(Y_{\mathrm{IP}}),e(Y_{\mathrm{OOP}})$ + +The insight of Eq.3 is that despite $\mathbf{Y}_{\mathrm{OOP}}$ has never seen before, as long as some semantic connected between $\mathbf{Y}_{\mathrm{IP}}$ and $\mathbf{Y}_{\mathrm{OOP}}$ hold in $\gamma(D_{\mathrm{IP}}, D_{\mathrm{OOP}})$ , tuning the name embeddings of OOP concepts after pre-training with $\hat{\mathcal{R}}_{\mathbf{Y}_{\mathrm{IP}}}^{(\hat{f}, \hat{g})}$ can control the ideal population risk $\mathcal{R}_{\mathbf{Y}_{\mathrm{IP}} \cup \mathbf{Y}_{\mathrm{OOP}}}^{(f^*, g^*)}$ . + +But why not prompt-tuning or adapter approaches? The following result unveils that the arbitrary initialization of OOP embeddings may lead to the risk of non-identification between IP and OOP concepts, regardless of what prompts or adapters used in open-vocabulary prediction in Eq.1: + +Proposition 2. (Informal) $\forall \pmb{y}_1\in \pmb{Y}_{\mathrm{IP}}$ and $\forall \pmb{y}_2\in \pmb{Y}_{\mathrm{OOP}}$ if the embeddings $e(Y_{\mathrm{OOP}})$ can be arbitrarily initialized, then given $\forall \epsilon >0$ and an image $\pmb{I}$ with label $\pmb{y}_2$ , for any prompt-tuning and adapter layer of CLIP behind $f$ and $g$ it holds $d_p\bigl (\log P_V^{(f,g)}(\pmb {y}_1|\pmb {I}),\log P_V^{(f,g)}(\pmb {y}_2|\pmb {I})\bigr)\leq \epsilon .$ + +The theory is formalized in Appendix.B along with the further empirical study for better understanding. The aforementioned analysis motivates learning OOP name embedding in the data-efficient manner. + +# 5.2. Few-Shot Name Learning + +In the few-shot learning setup, we have the access of image-text pairs in OOP concepts, whereas the amount is very limited. Our first trick to address the training-data eager is to initialize OOP-class name embedding using language models. Our implementation inherits the tokenized input ahead of BERT [6] to initialize the OOP word embeddings. Given OOP phrases composed of old words, their embeddings are independently learnt by deploying the new tokens without the disturbance to IP word embeddings. + +Augmentation by contexts of similar concepts. Given each OOP image-text pair $\left\langle \hat{I} (y),\hat{T} (e(y))\right\rangle$ , we further augment few-shot image-text matching by simply shuffling + +context $\hat{T}$ with arbitrary contexts presented in the other pairs with the similar OOP concepts (e.g., under the same categorical ancient). For instance, given a caption $\hat{T}(e(y)) = \text{"A women in a cheongsam"}$ , the augmentation may switch the context "A women in a [-]" by "People are dressed in [-]" rather than "This animal is [-]", etc. It derives to the formulation: + +$$ +\min _ {e (\boldsymbol {y}), \forall \boldsymbol {y} \sim \boldsymbol {Y} _ {\mathrm {O O P}}} \sum_ {\hat {\boldsymbol {T}} _ {j} \sim P _ {\mathrm {C S}}} \mathcal {L} _ {\text {I n f o N C E}} \left(\sum_ {\hat {\boldsymbol {T}} _ {j} \sim P _ {\mathrm {C S}}} \left\langle \hat {\boldsymbol {I}} (\boldsymbol {y}), \hat {\boldsymbol {T}} _ {\boldsymbol {j}} (\boldsymbol {e} (\boldsymbol {y})) \right\rangle\right), \tag {4} +$$ + +where $P_{\mathrm{CS}}$ denote the prompts generated with the shuffled contexts, then Eq.4 and Eq.2 are jointly optimized to fine-tune the OOP-name embedding. Similar with compositional prompts [19, 40] that we are inspired from, the augmentation may lead to noisy contexts with inevitable incorrect fine-grained information. While under the same umbrella of categorical ancient, our strategy promises the semantic is convincing in open-vocabulary prediction tasks. + +# 5.3. Zero-Shot Name Learning + +Few-shot learning permits an access of image-text pair for OOP concepts. To take a step further, we prescribe that the image set $\left\{\hat{I}(\boldsymbol{y})\right\}$ does not have the text set $\left\{\hat{T}(e(\boldsymbol{y}))\right\}$ in OOP concepts to align with, which literally refers to a zero-shot learning setup since images in $\left\{\hat{I}(\boldsymbol{y})\right\}$ were never labeled by any concept names. To classify them into $Y_{\mathrm{OOP}}$ , we propose a bipartite-graph matching strategy to estimate the names of image in $\left\{\hat{I}(\boldsymbol{y})\right\}$ with regards to $Y_{\mathrm{OOP}}$ , then learning to classify them by name-tuning the label. + +Cluster initialization by novel-class discovery. As discussed previously, despite images in OOP class not aligned with their names, those in the same OOP class tend to converge into a cluster. However, unsupervised clustering always suffers from the ambiguity in cluster granularity due to no explicit category information provided. To this, we follow the spirit of novel class discovery (NCD) [5], which guides the clustering of OOP-class images by the supervision from the images in IP classes, thus, obtained by low cost. In our methodology, we limit the training scope of the NCD model to the classification head while its backbone is frozen by the image encoder $f(\cdot)$ . This strategy injects the OpenCLIP's pre-training knowledge to ensure the performance transfer from IP classes to OOP classes. + +Image-text bipartite-graph matching. With category-aware image clusters obtained in OOP classes, we attempt to find the optimal bipartite-graph matching across the cluster centers and prompt embedding with the names in OOP classes. Specifically, we obtained the normalized average of each cluster to represent the OOP-class centers, then compute their cosine similarities with the prompt embedding representing each concept in OOP classes. Given this, we have a bipartite graph between the image-cluster centers and + +![](images/b3d4ff9fa264849e26cc6aa45fa132e95d761cedea803a9f7ae12f547983eb3a.jpg) + +![](images/8cbdf8353496d31d6cd9347764047089fc00cbbe7ae5adb332cf05cf1a1ee0aa.jpg) + +![](images/1edf0a3ed02ab4a665a545593354cda7fee644c30714fe96c5e73446edb8ffd4.jpg) + +![](images/c502bbd6689ef5ec601a7dd3e6af0575caa0be5dc8da267aa49a55823989308a.jpg) + +![](images/f479f6b6178fdf6626212e772ff24187b88d31f2db2b1d7d7a76ea0c81eb7417.jpg) + +![](images/30df7cad0b38b5ec8b331424c6e965074214baa8b6c332af5f5a3b1aca513ad9.jpg) + +![](images/d1a1f20f8c9e9498896bf442da01cd2683342212f50b2f3794ca397f45445c9c.jpg) +Figure 5. OOP few-shot learning performances (1,2,4,8,16 shots) of different baselines in the test sets of Animals, Landmark, and Pokemon across 9 domains in LAION-Beyond (400M). + +![](images/d559f59491522232cb28cf5724363ac674c7160564aff9e09c5f46662d2ef35e.jpg) + +![](images/83107aa1dd7192e9bdbe9879fea6368976c0673f2137b7267236555d3b7e37b1.jpg) + +the OOP-class prompt embeddings, then we assign pseudo OOP names to each cluster by executing the Hungarian algorithm to the bipartite graph. Fine-tune name embeddings by Eq.(2) with high-confidence samples drawn from OOP-class clusters, leading to our zero-shot learning algorithm with regards to OOP concepts for OpenCLIP. + +The implementation details of FSNL and ZSNL, along with their codes, have been elaborated in SM. + +# 6. Experiment + +In this section, we provide extensive empirical evaluation for FSNL, ZSNL in OOP concepts, to justify their abilities to alleviate the image-text alignment failure. Codes and implementation details of our algorithms are found in SM. + +# 6.1. Few-shot Learning for OOP Classes + +Benchmark. We employed LAION-Beyond (400M) as our evaluation benchmark for few-shot classifying OOP concepts, since it contains the most concepts in our three splits + +of LAION-Beyond. In order to verify the open-vocabulary prediction on data with OOP concepts, we only employed OOP image-text pairs for training and validation, then incorporated the images drawn from OOP test set and the images drawn from IP classes to serve our evaluation. + +Baselines To answer the first question in Sec.5.2, we compare FSNL with existing adapter-based and prompt-based tuning baselines, i.e., CoOp [45], CoCoOp [44], ClipAdapter (Clip-Ada) [8], TaskRes [39], and Linear Probe [24]. Note that their original implementations solely promote fine-tuning with vanilla CLIP's backbone, which may violate the premise of OOP classes in this paper. Hence we reproduced their implementations by importing OpenCLIP as their backbone models, then further verified the results with their digits reported in their original papers. It promotes the reproducibility in LAION-Beyond + +OOP-class few-shot learning setup. This task refers to the primary goal in this experiment. It requires the evaluated baselines to fine-tune their OpenCLIP backbones, in partic- + +Table 2. OOP-to-IP open-vocabulary prediction. OOP, IP, and H-mean represent the accuracies of the models trained for OOP few-shot learning (4-shot), their accuracies in IP image dataset, and their compound Harmonic mean score [35], respectively (best viewed in color). + +
BaslinesMetricDomainsExtra subnet
AnimalsArchitectureAttireFolkArtFoodInsects_SpiderLandmarkPlants_FungiPokemonAvg
OpenCLIPOOP19.7022.4916.1827.078.8816.8625.6515.7115.4718.67No
IP41.6648.6064.5749.6756.9333.2893.4133.7158.5853.38
H-mean26.7530.7525.8835.0415.3622.3840.2521.4324.4826.92
CoOpOOP38.3176.5460.2868.3561.6747.1885.2448.2539.2458.34No
IP26.5646.4343.2942.0432.4817.6986.5416.6732.4538.24
H-mean31.3757.850.3952.0642.5525.7385.8924.7835.5245.12
CoCoOpOOP23.8238.5329.5831.2919.9423.1645.8120.3518.1027.84Yes
IP36.8241.3039.4033.1936.1530.7685.2728.2937.2240.93
H-mean28.9339.8733.7932.2125.726.4259.623.6724.3632.73
CLIP-AdapterOOP42.8081.4073.7278.2083.4851.0092.0354.1763.8268.69Yes
IP35.7846.6057.4344.0152.3123.8689.6422.6848.3046.73
H-mean38.9859.2764.5656.3264.3232.5190.8231.9754.9954.86
Learning-to-NameOOP26.1841.6443.2454.1144.1831.2150.1324.7637.9939.27Yes
IP32.8640.1651.2439.8942.1728.9088.2126.0545.1143.84
H-mean29.1440.8946.9045.9243.1530.0163.9325.3941.2540.73
FSNL(ours)OOP51.7788.0380.4786.2390.8565.0395.5763.8577.8877.74No
IP41.6648.6064.5749.6756.9333.2893.4133.7158.5853.38
H-mean46.1762.6371.6563.0370.044.0394.4844.1268.8762.55
+ +ular, using the random shots drawn from the training set that contains OOP image-text pairs. The number of shots is ranged from $\{1,2,4,8,16\}$ , which follows the efficient-tuning setup broadly employed to evaluate IP generalization [45]. Then well-trained models would be evaluated to classify the OOP test-set images into their OOP classes. + +Table 3. The open-world transfer results (ACC across all OOP-class test images and IP-class images) across 9 domains. Linear Probe and TaskRes have been excluded due to their failure to transfer the training vocabulary. $\Delta$ indicates the absolute ratio that FSNL exceeds the second best. + +
AnimArchAttiFolkFoodInsectLadmkPlantPokemAvg
OpenCLIP19.4025.2125.2327.7518.8616.4346.1016.4726.8924.7
CoOp23.9957.9343.8552.3332.6326.3780.0727.2122.7840.8
CoCoOp18.8629.4023.7822.5417.0917.7850.1416.9318.3823.88
CLIP-Adap29.5164.6058.9259.9864.1429.2385.0532.8954.4753.2
L2Name21.7833.0225.2627.0925.1421.1367.0522.8926.4729.98
FSNL(ours)36.3571.0063.7569.2768.0939.7092.5440.5365.2960.72
Δ+6.84+6.40+5.42+9.29+3.95+10.47+7.49+7.64+10.82+7.52
+ +Results. The main results across baselines with 3 random seeds for their fine-tuning, have been comprehensively illustrated in Appendix.C (some scenarios shown in Fig.5). Their findings yield crucial insights into the OOP generalization issue. Firstly, FSNL excels as the state of the arts across 8 domains except Food, achieving the optimal image + +text alignment with the upperbound curve ranged from 1 to 16 shots. Second, perhaps surprising, the basic linear probe without the text-encoder assistance, rivals FSNL's performance in 4 domains. Its superiority verifies our claim to the image-feature distribution in Sec.4.3. Finally, despite surpassing OpenCLIP's zero-shot results, neither prompt-tuning nor structural adaptation are even close to linear probes'. This suggests that these CLIP-adaptive algorithms basically fail to align their textual modalities with image features. It justifies the wisdom of name-tuning. + +While the linear probe and TaskRes improve OpenCLIP, their class prediction are limited to a fixed vocabulary. Such design renders them unavailable in the open world. + +OOP v.s. IP few-shot learning. Open-vocabulary prediction is defined to switch their word and phrase list to facilitate the categorization to images with class name beyond the existing vocabulary. In this regards, it is significant to justify whether FSNL maintains the open-vocabulary learning behind OpenCLIP. We consider the few-shot learning trade-off between OOP and IP classes, the evaluation setup inspired from existing base-to-new setup for prompt-tuning approaches [44]. Given each domain, we simultaneously evaluated a model's few-shot learning in the domain-specific OOP test set and its IP-class prediction in the domain-specific IP counterpart dataset, then take their Harmonic means to judge the model's performance of balancing OOP and IP class predictions. All models are fine-tuned with 4-shot samples repeated by 3 random seeds. + +Table 4. Zero-shot learning ACC $(\%)$ in OOP classes drawn from domains in LAION-Beyond (400M) and (5B). $\Delta$ indicates the absolute ratio that ZSNL exceeds the second best. + +
SplitsAnimArchAttiFolkFoodInsectLadmkPlantPokem
OpenCLIP(400M)19.722.516.227.18.916.925.715.715.5
TransCLIP21.825.219.129.310.117.329.516.819.6
ZSNL(ours)25.739.934.927.629.424.243.926.462.7
Δ+3.9+14.7+15.8-1.7+19.3+6.9+14.4+9.6+43.1
OpenCLIP(5B)25.9----32.2-34.321.7
TransCLIP31.1----35.1-35.128.1
ZSNL(ours)45.6----59.8-70.772.5
Δ+14.5---+24.7+35.6+42.4
+ +Results. As the task requires models to change their vocabulary to adapt IP classes, linear probe and TaskRes are unavailable. To this, we compare our FSNL algorithm with OpenCLIP, CoOp, CoCoOp, CLIP-adapter, and Learning-to-Name (NTL) [22], another name-learning baseline that depends on an extra subnet to model the diverse semantic behind fixed name embeddings. As observed in Tab.2, we found that despite OpenCLIP's failure in OOP-class prediction, it remains the state-of-the-art in IP classes compared with prompt-tuning and CLIP-adapters. It implies CLIP's generalizability underestimated in many existing work. Besides, NTL fails in OOP classes because its extra subnet depends on the original OOP embedding, which is unreliable in cross-modal alignment. Thanks to tuning the embedding instead of the subnet, FSNL optimizes OOP-class embeddings without altering their IP embeddings in OpenCLIP. The merit makes FSNL to reap the best of both worlds. + +Open-world vocabulary transfer. In the open world, the boundary between OOP and IP classes is rather obscure in the sense of general AI. In term of this concern, we propose the task open-world vocabulary transfer to judge whether the OOP few-shot learning models could classify arbitrary images drawn from OOP and IP classes. It is distinct from OOP-to-IP since the test vocabulary should simultaneously include OOP and IP classes for each domain. So we only need to evaluate in the average across images. + +Results. TaskRes and Linear Probe are not available in this task either therefore we report the performances of the rest in Tab.3. FSNL still significantly outperform the other baselines with the least $+7.52$ leap to the second-best. We even found that CoCoOp underperform OpenCLIP. + +# 6.2. Zero-shot Learning for OOP Classes + +As previously discussed about Fig.4.b, zero-shot learning OOP classes is significantly challenging due to no available OOP concepts with their names to align image features during fine-tuning. As a alternative, we allow the usage of image-text training pairs in IP concepts, and the number of classes can be observed. It aims to justify the motivation be + +![](images/72fa749e67d56dc600bb15f9490316b4d69a737186e9a4a78122609fdccb6e61.jpg) +Figure 6. The FSNL ablation in Animals (viewed in colors). + +hind ZSNL algorithm, i.e., whether the IP-concept knowledge helps zero-shot learning OOP concepts. + +Benchmark. LAION-Beyond (400M),(5B) are employed as our training-evaluation sets, which contains 16-shot samples for training in each OOP class yet their labels and names in OOP concepts are masked, and the rest images in OOP classes are evaluated. It leads to 13 train-test domain splits to thoroughly justify the zero-shot results. We compare our algorithm with OpenCLIP and TransCLIP [16], a strong baseline derived from CLIP's IP ability. + +Results. OOP-class zero-shot learning results across 13 train-test splits are illustrated in Table.4. We observe that despite TransCLIP with positive transfer influence to OpenCLIP, the trivial zero-shot benefit in OOP concepts implies that it is not able to address the image-text misalignment. It is probably due to its methodology regardless of unreliable name embeddings in OOP concepts. In contrast, our ZSNL algorithm encourages the name-embedding tuning strategy based on image-text bipartite graph, whose matching also incorporates IP knowledge via NCD to increase the reliability of clustering centers. Across 13 domains, ZSNL significantly reaps the improvement to OpenCLIP with huge gaps in OOP-concept zero-shot learning. Some even outperform the 1-shot learning results by our FSNL algorithm. + +# 6.3. Ablation + +We ablate FSNL by different concept similarity strategies (categorical ancient branching, $k$ -means, and nearest neighbors, their details in Appendix.C) for context augmentation, along with the pure embedding fine-tuning in Eq.(2) and the original OpenCLIP. Fig.6 demonstrates that FSNL performs robustly across concept similarity strategies, and purely learning OOP concept embeddings indeed improves the text alignment with OOP image features, whereas the benefit is relatively marginal due to the shortage of training data augmentation. Context augmentation remedies the issue to yield the state of the art in OOP-class generalization. + +# 7. Conclusion + +This research proposes LAION-Beyond, not only illuminating the abilities and limitations of vision-language models in OOP concepts but also enlightens few-shot and zero-shot learning strategies to OOP generalization, contributing to the advancement of more adaptable multimodal systems. + +# Acknowledgment + +This work was supported in part by The Major Key Project of PCL (No. PCL2024A04, PCL2024AS204); National Key R&D Program of China under Grant (2021ZD0111601,2022YFC3303603); in part by National Natural Science Foundation of China (NSFC) under Grant No.61836012, U21A20470, 62206110, and 62077028; the Science and Technology Planning Project of Guangdong (No.2020ZDZX3013), the Science and Technology Planning Project of Guangzhou (No.202206030007) and the Opening Project of Key Laboratory of Safety of Intelligent Robots for State Market Regulation (No.GQIKFKT202205); Fundamental Research Funds for the Central Universities, Sun Yat-sen University under Grant 23hytd006; in part by GuangDong Basic and Applied Basic Research Foundation under Grant No.2023A1515012845 and 2023A1515011374. Liang Lin is also leading the GuangDong Province Key Laboratory of Information Security Technology. + +We particularly thank Yulu Li for her valuable contributions in collecting data from the LAION-Beyond dataset and running essential experiments that supported our findings. Their diligent work significantly enhanced the empirical foundation of this research. + +# 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. arXiv preprint arXiv:2303.08774, 2023. 2 +[2] Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al. Qwen technical report. arXiv preprint arXiv:2309.16609, 2023. 2 +[3] Yen-Chun Chen, Linjie Li, Licheng Yu, Ahmed El Kholy, Faisal Ahmed, Zhe Gan, Yu Cheng, and Jingjing Liu. Uniter: Universal image-text representation learning. 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Feng $^{2}$ , Haoming Cai $^{1}$ , Tianfu Wang $^{1}$ , Levi Burner $^{1}$ , Dehao Yuan $^{1}$ , Cornelia Fermüller $^{1}$ , Christopher A. Metzler $^{1}$ , Yiannis Aloimonos $^{1}$ $^{1}$ University of Maryland, College Park $^{2}$ Massachusetts Institute of Technology https://vdm-evfi.github.io/ + +![](images/608a14e07dc875c2cfbac22856334e91a2109fdcea679c367a32bdf6a49cc22c.jpg) +Reference +Figure 1. We compare our proposed approach RE-VDM, which adapts a pre-trained video diffusion model for event-based video frame interpolation on unseen real-world data, with three baselines: frame-only interpolation method GIMM-VFI-R-P [14], test-time optimization of a pre-trained video diffusion model via Time Reversal [11], and event-based interpolation method CBMNet-Large [21], trained on the same dataset as our method. The left-most column shows the start frame, end frame, and reference interpolation frames overlaid with events. Leveraging data priors in the pre-trained video diffusion model and the diffusion process, along with motion guidance controlled by input events, our approach demonstrates superior generalization performance on unseen real-world frames with substantial motion. + +![](images/4b1b2ce29471d58fca2a4a2aed3aed10623a1e9bf6d987225cdffa053e1a014c.jpg) +(a) Frame-only Video Frame Interpolation + +![](images/37c5477d9ba523e81f5ed5ae4576630f995d068ddbb6b6230c995c496a924263.jpg) + +![](images/89b585f023aff6b2c03196c480d2b87945b70d5e6ce931d07d6530564f099e5d.jpg) +(b) Pre-trained Video Diffusion Model + +![](images/e4dd7d64ecc754dce965b8eb6aa7b32d4eab333b43133631fdf6ac39b25d88ba.jpg) + +![](images/ed719b0773b9432efc9d552430983ef84734692a6c28b55711d8e9a58b8dbd64.jpg) +(c) Event-based Video Frame Interpolation + +![](images/db607f644c2981c8a8b20f684d98ed43a78c97f1dc1167c914763a3554ddf395.jpg) + +![](images/40849f5fbb9e3267ad460c1e8c5a168e94f63507ab6eb5ce59c381e8008bc403.jpg) +(d) Ours + +![](images/912b95e6cad1897aae0579990d6983e93e4a44e4a37cd92db1bbeea8b9a96fc6.jpg) + +# Abstract + +Video Frame Interpolation aims to recover realistic missing frames between observed frames, generating a high-frame-rate video from a low-frame-rate video. However, without additional guidance, the large motion between frames makes this problem ill-posed. Event-based Video Frame Interpolation (EVFI) addresses this challenge by using sparse, high-temporal-resolution event measurements as motion guidance. This guidance allows EVFI methods to significantly outperform frame-only methods. However, to date, + +EVFI methods have relied on a limited set of paired event-frame training data, severely limiting their performance and generalization capabilities. In this work, we overcome the limited data challenge by adapting pre-trained video diffusion models trained on internet-scale datasets to EVFI. We experimentally validate our approach on real-world EVFI datasets, including a new one that we introduce. Our method outperforms existing methods and generalizes across cameras far better than existing approaches. + +# 1. Introduction + +Event cameras are a novel class of neuromorphic sensors offering unique advantages, including high dynamic range and high temporal resolution [12]. One significant application of event cameras is Event-based Video Frame Interpolation (EVFI) [21, 27, 39-41, 50]. By capturing traditional frames alongside high temporal resolution events, event data can fill in missing motion information between frames, aiding in interpolation. This approach avoids the ill-posed problem of frame-only interpolation, where large motion between frames introduces excessive degrees of freedom, making the interpolation of frames infeasible. + +Current state-of-the-art (SOTA) EVFI methods achieve impressive performance when trained and tested on the same dataset. However, when the test set differs from the training set with changes in data and motion distribution, these methods experience significant performance degradation, as we can see in Fig. 1. This issue arises from two main factors. First, compared to broader fields like video generation, the EVFI field is much smaller, with limited data quantity and quality. Second, the models used in EVFI are highly specialized, with constrained representational power. + +Recent advances in generative AI, particularly in video generation, have spurred significant progress in the field. Leading companies have invested substantial resources into building massive, high-quality datasets [8] and developing foundation models for video generation [8, 17]. Most of these foundation models are video diffusion models. By leveraging millions of high-quality commercial video clips and billions of parameters, these diffusion models achieve impressive generalization performance compared to previous approaches. A comparison between video generation and EVFI fields is presented in Table 1. The primary differences between these fields lie in dataset quality/size and model parameter scale, the EVFI field lacks the extensive commercial datasets and large model sizes found in video generation, impacting its models' generalization and representational power. + +This raises a natural question: Can we adapt pre-trained video diffusion foundation models for EVFI to leverage their learned data priors and model design advantages? + +In this work, we introduce the first approach, RE-VDM, for adapting pre-trained video diffusion foundation models to the EVFI task, aiming to bridge EVFI with generative AI by leveraging robust data priors and foundation models. To achieve this, we address key technical challenges. First, for data-efficient adaptation, we train an additional subset of the model with event-based control on small EVFI datasets inspired by [48], while keeping the original weights frozen to avoid catastrophic forgetting of learned data priors as explained in Section 3.2. Second, while video generation aims to produce diverse videos without strict realism constraints, EVFI requires ground-truth fidelity to accurately + +
FeatureVideo GenerationEVFI
Dataset Size [7, 23, 31]10^710^2
Dataset Quality [7, 21, 23, 31, 38, 41]CommercialCustom
Model Type [7, 21, 27, 39, 41]Video Diffusion (Foundation) ModelsCustom Models
Model Size [7, 21, 27, 31, 39, 41]10^1010^8
Video Generation Type [7, 21, 27, 39, 41]ExtrapolationInterpolation
+ +Table 1. Comparison between video generation and event-based video frame interpolation (EVFI) fields reveals major differences in dataset size, quality, and model design. Video generation datasets are orders of magnitude larger than EVFI datasets and are of commercial-level quality. Models for video generation are typically foundation models with billions of parameters. With abundant training data and large-scale foundation models, video diffusion models are well-suited for generalized video generation tasks. + +recover missing frames. To preserve motion and appearance fidelity, we employ upsampling and Per-tile Denoising and Fusion as explained in Section 3.4 as the test-time optimization for video generation with high-fidelity appearance and event-based motion control. Finally, unlike video generation, which is an extrapolation task based on an image or text prompt, EVFI requires interpolation between the start and end frames. To address this, we develop a test-time optimization approach that generates event-based video latents from both the start and end frames at each denoising step, fusing them for a consistent, interpolated result that incorporates information from both frames, as explained in Section 3.5 + +For a robust evaluation, we compare the generalization performance of our approach against representative frame-only, event-based, and pre-trained video diffusion models for frame interpolation across multiple datasets, including self-collected Clear-Motion test sequences. The results demonstrate the potential and advantages of this adaptation. We also discuss the limitations observed, highlighting the exploratory nature of our work. To summarize, our contributions are + +- We present the first approach for adapting pre-trained video diffusion foundation models to the Event-based Video Frame Interpolation task, leveraging the strong data priors learned from large video generation datasets and the inherent advantages of video diffusion models. +- Experimental results demonstrate the strong potential of the adapted video diffusion model for the EVFI task, showing excellent generalization on unseen real-world data and consistency in reconstructed frames. + +# 2. Related Work + +# 2.1. Event Camera and Video Frame Interpolation + +Event cameras are neuromorphic sensors that capture the brightness changes in the scene, and the brightness changes are primarily due to the camera's motion and object motion in the scene. For this reason, events captured by event cameras can be used to compute motion-related information, for example, optical flow, motion segmentation, and ego-motion + +[3-6, 15, 28, 36, 46, 53, 54]. Various methods have been proposed to reconstruct intensity videos from event streams alone, demonstrating that while feasible, the quality of such reconstructions is significantly limited by camera and object motion [9, 32]. Combining events with images extends beyond event-only applications, offering powerful capabilities for tasks like image deblurring and video frame interpolation/extrapolation [10, 39-41, 50]. This approach leverages events as cues to bridge the gap between frames, thus avoiding the ill-posed challenges faced by frame-only methods [1, 14, 18, 20, 22, 24, 30, 44, 47, 52] when interpolating between frames with substantial motion. + +# 2.2. Diffusion and Video Diffusion Models + +Diffusion models [16, 37] is an emerging class of image generative models that model the reverse diffusion process of recovering data from noise. Starting from data $\mathbf{x}_0$ from the data distribution $p_{data}(\mathbf{x})$ , The diffusion model tries to reverse the forward diffusion process as an $N$ step Markov chain $\{\mathbf{x_i}\}, i \in [0, N]$ that satisfies the marginal distribution + +$$ +p _ {\alpha_ {i}} \left(\mathbf {x} _ {i} \mid \mathbf {x} _ {0}\right) = \mathcal {N} \left(\mathbf {x} _ {i}; \alpha (t) \mathbf {x} _ {0}, \sigma (t) ^ {2} \mathbf {I}\right). \tag {1} +$$ + +Here, $\alpha(t)$ , $\sigma(t)$ represents a noise schedule. Diffusion models have demonstrated remarkable image generation quality and diversity. Stable Diffusion [33] shifts the generation process to a low-dimensional latent space, greatly reducing computational cost. Trained on massive online text-image pair datasets [35], Stable Diffusion exhibits strong image generation capabilities. Video diffusion models [8, 17] add temporal layers on top of existing image diffusion models to jointly denoise multiple consistent image frames. Stable Video Diffusion (SVD) [8] is built on top of latent diffusion model and trained on massive video datasets, serving as a strong foundational model for video generation tasks. + +# 2.3. Controllable Diffusion Generation Through Fine-Tuning + +There have been numerous works on generation conditioned on additional user inputs or control [33, 34, 45, 48]. Stable Diffusion [33] uses cross-attention layers in the diffusion U-Net to inject text control. Dreambooth [34] showed that a diffusion model can be fine-tuned for conditional control. ControlNet [48] modifies a trainable copy of the original diffusion U-Net for conditional control. In addition to fine-tuning diffusion models for added controllability, various training-free methods have been proposed to alter the sampling process of image and video diffusion models for more flexible and generalized content synthesis [2, 11, 26, 51]. Latent diffusion models have limitations on generating a limited set of resolutions in a downsampled latent space. MultiDiffusion [2] provides a solution for resolution-agnostic generation by tile-based denoising. When combined with + +![](images/eec3492e845a02d729a2a3808eb259d1210edf32d1f6f5fc972e09429be0682b.jpg) + +![](images/8c26253cc74ff43615a8045939e13594dbaf1226dd4b892ae62c7c026a598f09.jpg) +Figure 2. The overview of our proposed approach RE-VDM: for adapting pre-trained video diffusion models includes two tasks: event-based video generation and interpolation. For video generation, the method utilizes the start frame $I_{s}$ and forward-time events $E_{s}$ . For interpolation, it incorporates both the start frame $I_{s}$ and forward-time events $E_{s}$ , as well as the end frame $I_{e}$ and backward-time events $E_{e}$ to achieve consistent results. Unlike video generation, for interpolation, a denoising step $t$ concludes with Two-side Fusion instead of EVDS. + +![](images/a52cf916c7b3762f6d632dcf93cc6c5b7843b52bb4cfcee44ff7489c40a0a227.jpg) + +conditional control, MultiDiffusion [2] has shown to be effective in generating synthetic detailed images under the condition of fine-grained condition control [19, 42]. On the video generation side, [11] proposes a test-time sampling method that empowers video diffusion models to control camera and object motion. [51] enables consistent long-frame generation outside of the trained frame length of a video diffusion model. + +# 3. Proposed Approach + +# 3.1. Pipeline Overview + +Figure 2 presents an overview of our pipeline RE-VDM, for adapting pre-trained video diffusion models to event-based video generation and interpolation tasks. The key difference is that interpolation applies our EVDS on both the start frame $I_{s}$ for forward-time video denoising/generation and the end frame $I_{e}$ for backward-time video denosing/generation. At each denoising step, forward-backward consistency is enforced to achieve accurate interpolation. + +In this work, without loss of generality, we assume that the pre-trained video diffusion model used is a Latent Diffusion Model, as is common in most video diffusion models. + +# 3.2. Data-Efficient Adaptation of Pre-trained Video Diffusion Models + +In this section we will explain the details for introducing the additional event-based motion control to pre-trained video + +![](images/263f645fc108540678a60d92ea662026e8845e06c9c749cfb571ce243ce8ce8f.jpg) +With a Uniform Random Choice of Denoising Step t +Figure 3. The illustration depicts our training scheme for adapting a pre-trained video diffusion model to event-based video denoising. Our approach uses a frozen denoiser network from the pre-trained model, augmented with a trainable subset of blocks copied from the frozen denoiser. + +diffusion models. As discussed in Section 1 and shown in Table 1, the large training datasets and model size of pre-trained video diffusion foundation models provide impressive generalization power for video generation tasks. However, these factors also limit the fine-tuning flexibility of the pre-trained model weights on existing EVFI datasets due to the risk of catastrophic forgetting, stemming from significant differences in data size and quality. + +To prevent catastrophic forgetting of the learned data priors in pre-trained video diffusion foundation models, we drew inspiration from the [48] approach for controllable image diffusion models, known for its impressive performance with small data adaptation. In our design, we keep the original weights of the video diffusion models frozen during training. Event-based control is introduced by training only a subset of blocks, copied from the original denoiser network, to serve as additional residuals to corresponding block outputs in the frozen denoiser network. A detailed illustration is provided in Figure 3. + +The added event encoder and trainable copy aim to learn the correct encoding for events as the control condition, $E_{cond}$ , as well as the block output residuals for the frozen pre-trained denoiser network by optimizing the trainable copy. We use the standard diffusion objective, which minimizes the mean squared error loss between the predicted noise $\epsilon'$ and the ground truth noise $\epsilon$ added to the video latent for a uniformly randomly sampled denoising time $t$ . + +During inference, the only difference from the training scheme is the absence of a given video latent $Z_{t}$ and noise $\epsilon$ for a sampled denoising time $t$ . Instead, the initial noisy + +![](images/5c6a397058df512214d30d48587211ff35594092db355f571c6660dc0a8765ea.jpg) +Figure 4. Our multi-stack event representation is illustrated as follows. The stack begins from the target frame at $t_i$ and expands backward in time to the previous frame $t_{i-1}$ . Within each stack, the number of events accumulated from $t_i$ is halved from the previous stack. In the long stack ( $m = 0$ ), the slowest-moving objects, such as around the human head, appear sharp; in the middle stack ( $m = 1$ ), slower-moving objects, like the human arm, are clear; and in the short stack ( $m = 2$ ), the fastest-moving objects, such as the ball, are sharp. This approach ensures that the event data provides adequate control information for generating frame $t_i$ . + +latent $Z_{T}$ is generated from standard Gaussian noise $N(0,1)$ at the beginning of the denoising process. + +# 3.3. Events as the Control Condition + +To introduce events as the control condition for the video generation process, we incorporate two main components: 1) Event Representation and 2) Event Encoder. For event representation, we adopt a multi-stack approach, inspired by [25, 29], which captures both fast- and slow-moving objects within a multi-channel, frame-like format. An example of this multi-stack event representation is illustrated in Figure 4. Based on this representation, our event encoder consists of a series of convolutional layers with stride to downsample the input event representation into the event latent $E_{cond}$ , matching the dimension of the image latent $I_{cond}$ . + +# 3.4. Per-tile Denoising and Fusion + +Due to the substantial memory demands of training and generating high-resolution video, most existing video diffusion models, such as Stable Video Diffusion (SVD) [7], are Latent Diffusion Models, meaning they operate in the latent space with downsampled spatial resolution rather than in the original pixel space. As illustrated in Figure 3, for an input RGB image/video of shape $[B,F,3,H,W]$ , where $B$ is the batch size, $F$ is the number of frames, $W$ is the width, and $H$ is the height, a latent encoder $(\mathcal{E})$ and decoder $(\mathcal{D})$ , typically based on a Variational Autoencoder (VAE), convert the input into image latents of shape $[B,F,C_{\text{latent}},\frac{H}{d},\frac{W}{d}]$ + +![](images/ffb7988b86be30a194cf706f70d5f147a8425e6da8cf21ef8768eab8ee1b4498.jpg) +Figure 5. The VAE encoding/decoding loss of small details in the original input image. In (a), we show the original image, sized 970 x 625. In (b), we pad the image to the nearest multiple of 8, then encode and decode it back. After decoding, the PSNR drops to 21.50, with noticeable detail loss in the zoomed-in view. In (c), we pad to the nearest multiple of 8, upsample to twice the original width and height, then encode and decode. After decoding, the PSNR increases to around 24.92, with no significant loss of details in the zoomed-in view. + +and decode it back. + +The Latent VAE encoder/decoder approach is effective for video generation, where realism is less critical, as the task often involves stylized animation rather than high-detail photorealism. However, for EVFI, minimizing the loss from downsampled encoding/decoding is essential, as our goal is to recover realistic missing frames between keyframes. A key observation is that small details can be lost after VAE encoding/decoding. Upsampling the input mitigates this loss, as shown in Figure 5, where increasing input upsampling effectively reduces encoding/decoding loss on fine details. + +Additionally, as illustrated in Figure 3, spatial downsampling of the input image to create image latents can also reduce event control accuracy, since the trainable copy's input consists of combined image latents $I_{cond}$ and event latents $E_{cond}$ of the same dimensions. However, upsampling input videos substantially increases computational costs for both training and testing. To address this, we divide the upsampled input video into overlapping cropped tiles of fixed width and height, applying EVDS to each tile independently. We then fuse the denoised latents of tiles to achieve consistent latents for each image and video, preserving shared context across overlapping regions + +Our Per-tile Denoising and Fusion process is illustrated in Figure 6. We employ tiled diffusion [2] by first dividing the latent canvas into $n$ overlapping tiles. For the denoised tile latents at tile $i$ at denoising step $t$ , we use an accumulation process to fuse them into the denoised latent for the entire + +![](images/502fbe099f2fcf817b6db98aee71840948aa177c2a10ea9b495566ebacd44a36.jpg) +Figure 6. The Per-tile Denoising and Fusion process is a test-time optimization applied during inference to enhance the fidelity of video generation appearance and improve event-based motion control accuracy. During each denoising step, our model operates on upsampled tiles of the input image and event representations to predict denoised latents for each tile $i$ at a denoising time $t$ ( $Z_{t-1}^{i}$ ). These denoised tile latents are then accumulated to obtain the predicted denoised latents for the entire video ( $\tilde{Z}_{t-1}$ ) at that denoising step $t$ . + +upsampled video. The accumulation process takes in $n$ tile latents and outputs the fused latent: + +$$ +\tilde {Z} _ {t - 1} = \sum_ {i = 1} ^ {n} \frac {W _ {i}}{\sum_ {j = 1} ^ {n} W _ {j}} \otimes Z _ {t - 1} ^ {i}, \tag {2} +$$ + +where $\tilde{Z}_{t-1} \in \mathbb{R}^{F \times H \times W \times d}$ , with $F$ representing the number of frames, $H$ and $W$ the height and width of the upsampled latent canvas, and $d$ the latent dimension. $Z_{t-1}^i$ contains the denoised latents of the $i$ -th grid tile, $Z_{t-1}^i \in \mathbb{R}^{F \times h \times w \times d}$ where $h$ and $w$ denote the height and width of each latent tile. $W_i \in \mathbb{R}^{F \times h \times w}$ represents pixel-wise weights for the $i$ -th tile. In our implementation, we assign equal weights, averaging the denoised latents across overlapping tiles. + +# 3.5. From Video Generation to Frame Interpolation + +Our approach thus far is designed to generate realistic video controlled by events from the start frame, suited for event-based video generation (extrapolation). However, the EVFI task requires frame interpolation, which involves utilizing information from both the start and end frames. + +The most straightforward approach to achieve frame interpolation would be to fine-tune base video diffusion models to accept an additional channel for the second image. However, as previously discussed, fine-tuning pre-trained video diffusion foundation models on the EVFI dataset risks catastrophic forgetting of the learned data priors, undermining the purpose of adaptation. + +To address this, we opted for a test-time optimization approach that avoids further training, enabling our video generation model to perform EVFI. As shown in Figure 2, + +
MethodCategoryBS-ERGB (3 skips)HQF (3 skips)Clear-Motion (15 skips)
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Time Reversal [11] (ECCV'24)Video Diffusion17.860.590.2717.920.530.1813.710.700.44
DynamiCrafter [45] (ECCV'24)Video Diffusion15.470.540.4015.990.560.3511.420.620.52
RIFE [18] (ECCV'22)Frame-only VFI23.300.830.0925.340.760.0516.930.760.35
PerVFI [44] (CVPR'24)Frame-only VFI23.530.790.1127.130.810.0416.740.750.30
InterAny-Clearer [52] (ECCV'24)Frame-only VFI25.510.850.1427.930.830.0617.210.770.32
EMA-VFI [47] (CVPR'23)Frame-only VFI26.010.860.1828.310.840.1017.790.780.44
GIMM-VFI-R-P [14] (NeurIPS'24)Frame-only VFI25.560.840.0827.960.830.0417.770.770.26
CBMNet-Large [21] (CVPR'23)EVFI26.240.790.2228.730.840.0922.260.860.39
RE-VDM (Ours)EVFI + Video Diffusion27.740.880.1229.040.890.0622.940.880.37
+ +Table 2. We compare our method on real-world EVFI datasets against representative and SOTA methods, including the pre-trained video diffusion model (Video Diffusion), frame-only methods (Frame-only VFI), and event-based video frame interpolation method (EVFI), where red indicates the best metric and blue indicates the second-best. For CBMNet-Large, we use publicly available model checkpoints trained on the same BS-ERGB dataset as our approach. For the BS-ERGB and HQF datasets, we use a skip number of 3 as in the EVFI papers, we evaluate all interpolated frames. For our Clear-Motion test sequences, we use a skip number of 15 for evaluation on large motion scenarios, we evaluate the 4th, 8th, and 12th interpolated frames. To control for VAE encoding/decoding loss, as discussed in Section 4.2, we apply VAE encoding/decoding to all model outputs. + +inspired by [11], our key idea is to run the EVDS at each denoising step from both the start frame $I_{s}$ and the end frame $I_{e}$ , producing two sets of predicted denoised video latents. We then apply a Two-side Fusion of these denoised latents to obtain consistent results. This approach allows us to achieve frame interpolation, effectively leveraging information from both frames. The details of the Two-Side Fusion algorithm are as follows: For a denoising time $t$ , the forward denoised video latents from the start frame $I_{s}$ and forward-time events $E_{s}$ are $Z_{t - 1}^{s} = EVDS(I_{s},E_{s})$ , and the backward denoised video latents from the end frame $I_{e}$ and backward-time events are $Z_{t - 1}^{e} = EVDS(I_{e},E_{e})$ with $Z_{t - 1}^{s},Z_{t - 1}^{e}\in \mathbb{R}^{F\times H\times W\times d}$ . To make the final denoised video latent $\tilde{Z}_{t - 1}$ consistent with information from both the start and end frames, we assign linearly increasing weights, $W_{f}\in \mathbb{R}^{F}$ , where $W_{0} = 0$ and $W_{1} = 1$ . This allows us to fuse the final video latents $\tilde{Z}_{t - 1}$ as follows: + +$$ +\tilde {Z} _ {t - 1} = W _ {f} \otimes Z _ {t - 1} ^ {s} + (1 - W _ {f}) \otimes f l i p \left(Z _ {t - 1} ^ {e}\right) \tag {3} +$$ + +where $flip$ denotes reversing the temporal order of the frames in $Z_{t-1}^{e}$ . The intuition behind this approach is that frames near the start frame rely more heavily on information from the start frame and forward-time events, while frames near the end rely more on the end frame and backward-time events, in the middle, they balance information from both. + +# 4. Experimental Results + +# 4.1. Datasets and Implementation Details + +To robustly evaluate the generalized frame interpolation performance of our approach, we select several real-world event camera datasets. The BS-ERGB dataset [40], the most cited for EVFI, provides aligned RGB and event video with large + +motion between frames, mainly featuring static cameras capturing dynamic objects. The HQF dataset [38] includes grayscale video aligned with events, with more sequences involving a moving event camera. In addition to existing datasets, we include our self-collected Clear-Motion test sequences, capturing both object and camera motion. Detailed information is provided in the Supplementary Material. Clear-Motion is a self-collected dataset used solely for testing, eliminating the possibility of data leakage. This makes it ideal for robustly evaluating the zero-shot generalization performance of all models. The pre-trained video diffusion model we used is Stable Video Diffusion [7] for 14-frame image-to-video generation. We provide detailed training information in the supplementary material. + +# 4.2. Evaluation Strategy + +To evaluate generalized frame interpolation performance, we compare our approach with representative methods from three categories: frame-only interpolation, pre-trained video diffusion models, and event-based interpolation. We use publicly available CBMNet checkpoints trained on the BS-ERGB dataset for evaluation. For Per-tile Denoising and Fusion in our method, which uses upsampled tiles to reduce detail loss and enhance event control accuracy, we apply an upsample factor of 2 for the BS-ERGB and Clear-Motion datasets and 3 for the HQF dataset. + +For evaluation metrics, we use average frame PSNR [13], SSIM [43], and LPIPS [49] for the interpolated frames. Since SVD is a latent diffusion model that uses a VAE to encode and decode between latent and pixel space, we apply VAE encoding and decoding to all model outputs. This eliminates the impact of discrepancies between the VAE-decoded frame distribution and the ground truth frame distribution, accounting for differences in small details and tone mapping. + +# 4.3. Evaluation on Video Frame Interpolation + +In this section, we present both quantitative and qualitative results demonstrating the effectiveness of our method compared to representative video frame interpolation approaches, as shown in Table 2. Our method outperforms all recent SOTA VFI baselines in terms of PSNR and SSIM. Qualitative comparisons in Figures 7 and 8 further show that recent frame-only VFI methods struggle with large and complex motion due to the ill-posed nature of the task. This limitation also affects pre-trained video diffusion models, which often exhibit a bias toward animation-style generation and suffer from spatial-temporal detail loss. + +In contrast, the SOTA event-based interpolation method, CBMNet-Large, can handle large motions by leveraging cues from events, similar to our approach. However, its performance on both the test set from the training dataset and unseen datasets is consistently lower than ours across all metrics. This difference is due to two factors: 1) as discussed in Section 1 and Table 1, the pre-trained video diffusion foundation model in our approach offers a superior data prior from its extensive training on large video generation datasets, and 2) our model's backbone, a highly representative pretrained video diffusion model, provides advantages over custom models typically used in EVFI. + +The effectiveness of our approach on real-world, unseen data for video frame interpolation is clearly demonstrated in the qualitative comparisons in Figure 7. Due to the ill-posed nature of interpolating frames with large motion, frame-only methods, despite often achieving better LPIPS scores, struggle to accurately reconstruct object locations and appearance. While CBMNet-Large uses event data to guide interpolation and achieves similar object and texture placements, it lacks generalization on unseen object and camera motion compared to our method, as shown in Figure 7, despite being trained on the same dataset. Additionally, CBMNet-Large suffers from frame-to-frame inconsistencies due to its frame-by-frame inference design, evident in Figure 8. CBMNet-Large produces frames with inconsistent textures and shapes on the ball and hand, whereas our method accurately reconstructs the challenging, regular shapes of both. This advantage is due to the strong data priors and foundational design of the pre-trained video diffusion model, allowing for consistent reconstruction across frames. These results support our unique contributions and motivation in adapting pre-trained video diffusion models for EVFI. + +# 4.4. Ablation Study + +In the Supplementary Material, we provide quantitative and qualitative ablation studies on two key components for adapting pre-trained VDMs to EVFI: 1) Comparing video generation and video interpolation using Two-Side Fusion. 2) Ablating the effect of upsampling in Per-tile Denoising and Fusion. Both quantitative and qualitative results demon + +strate the effectiveness of the two main components in our approach for adapting pre-trained VDMs to the EVFI task. + +# 5. Limitations + +Despite the promising results, adapting pre-trained video diffusion models to the EVFI task presents several limitations. First, the pre-trained VAE encoder and decoder, used for conversion between pixel space and latent space, have limited representational power, often resulting in color shifts and loss of small details. Second, the adapted video diffusion model tends to smooth out certain regions, likely due to its difficulty in preserving fine textures within the downsampled latent space or the need for a prohibitively high upsampling factor to prevent smoothing. Finally, the diffusion-based methods are more memory-intensive and time-consuming than other methods, we provide the detailed model run time, memory comparison in the Supplementary Material. These limitations stem from the current state of pre-trained video diffusion foundation models. However, as the field of video generation evolves rapidly, we anticipate that many of these issues could be mitigated or resolved with newer, more advanced pre-trained models in the near future. + +# 6. Conclusion + +In this work, we explore, for the first time, the adaptation of pre-trained video diffusion foundation models for the event-based video frame interpolation (EVFI) task, as a foundational step toward integrating event camera technology with the era of Generative AI. We present an approach to address the key challenges in adapting video diffusion models to EVFI. We use data-efficient adaptation to bridge the gap in data quality and size between large-scale video generation datasets and smaller EVFI datasets, minimizing the risk of catastrophic forgetting. Our method also includes test-time optimization techniques: Per-tile Denoising and Fusion to reduce encoding/decoding losses between pixel and latent spaces, preserving high-fidelity appearance and accurate event-based motion control, and Two-side Fusion, which incorporates both start and end frame information at each denoising step for improved interpolation consistency. We also discuss current limitations in pre-trained video diffusion models for EVFI. Lastly, we demonstrate our model's superior generalization and frame consistency on unseen real-world data, highlighting the motivation and potential of our approach. + +# 7. Acknowledgment + +We greatly acknowledge NSF's support under awards OISE 2020624 and BCS 2318255 + +![](images/f35f68a5f2452d3c6b068af2795de0192245c69a90ec429c8d2c5f0bb2513668.jpg) +(a) Illustration of start frame, end frame and events in-between overlayed with reference frames + +![](images/6e70fb6c7d2bf7ac549b9d2db4f466883376c3c92fab69c9a8e2bc2f5ec979a7.jpg) +(b) EMA-VFI + +![](images/f6fd5f26e9ea313ab9d17cb3576f2fed49b5f9b09a3e8501313fa26bd4b64f05.jpg) +(c) Time Reversal + +![](images/1f169f1d9289ec042fe4ad5adf0df1c3024f0bbbdf280c4022ef5c0e8a64158b.jpg) +(d) CBMNet-Large + +![](images/9aee880c22410286a5d011686e0b6366b1016a541d6492ddd65b8960b0daa5d7.jpg) +(e) Ours + +![](images/ec52faffcb3ae118eb071ae7fdf75f38464c444495029dd217cb796367f870a2.jpg) +Figure 7. The qualitative comparison on the Clear-Motion sequence Texture Boxes, featuring translation and rotation of a textured box, demonstrates that our method achieves the most consistent and accurate frame reconstruction. Other methods experience significant detail loss, artifacts, and difficulty maintaining regular object shapes, particularly in the characters and the bottom-right coconut. + +![](images/4aed70723b0fe696580ba29fd1bea60bb21243eaf66375bc3a1bb5ba5c3951bf.jpg) +(a) Illustration of start frame, end frame and events in-between overlayed with reference frames + +![](images/ec8d035f1c054e0a045e78c457fd4d9b9c8a8e55760624fa21f650e4411c10a5.jpg) + +![](images/01f8eca90ef84b1be75489c8eed52e093561eabc71bbeb96e2dc2c916a498f65.jpg) + +![](images/828fd00e274739e0590c5ce9ed3b06c108f31140443b657eb189fd8593ee0184.jpg) + +![](images/ff8471b2b2a937068c79a9c9ae804d55bf7000d08af8a7380cc9d49d73bef46a.jpg) +(b) GIMM-VFI + +![](images/4620191b0dd1c212811990c355f1b472d3c73cecf01fd216c04daf59a2e1199b.jpg) +(c) Time Reversal + +![](images/ddd32393950e243dc3f75487cd62e495cf648e6eedd4c04afc3567d295fae026.jpg) +(d) CBMNet-Large +Figure 8. The qualitative comparison on the BS-ERGB test sequences, featuring fast motion of a hand and a rising, spinning ball, shows that our method is the only approach capable of maintaining the regular texture shapes on both the ball and hand in this challenging scenario. + +![](images/25e0900824fdbfd3d90f0722e8d0591cc1bed56aacde34a1a79b8a03dcd603c9.jpg) +(e) Ours + +# References + +[1] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. Depth-aware video frame interpolation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3703-3712, 2019. 3 +[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. Multidiffusion: Fusing diffusion paths for controlled image generation. In ICML. PMLR, 2023. 3, 5 +[3] Patrick Bardow, Andrew J Davison, and Stefan Leutenegger. Simultaneous optical flow and intensity estimation from an event camera. 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We introduce M2N2, an unsupervised training-free point prompt based segmentation framework. We enhance the semantic information present in the self-attention of Stable Diffusion 2 by using a Markov process to generate semantically rich Markov-maps. We then perform a truncated nearest neighbor of each point's Markov-map to obtain a final segmentation. + +# Abstract + +Recent progress in interactive point prompt based Image Segmentation allows to significantly reduce the manual effort to obtain high quality semantic labels. State-of-the-art unsupervised methods use self-supervised pre-trained models to obtain pseudo-labels which are used in training a prompt-based segmentation model. In this paper, we propose a novel unsupervised and training-free approach based solely on the self-attention of Stable Diffusion. We interpret the self-attention tensor as a Markov transition operator, which enables us to iteratively construct a Markov chain. Pixel-wise counting of the required number of iterations along the Markov chain to reach a relative probability threshold yields a Markov-iteration-map, which we simply call a Markov-map. Compared to the raw attention maps, we show that our proposed Markov-map has less noise, sharper semantic boundaries and more uniform values within semantically similar regions. We integrate the Markov-map in a simple yet effective truncated near + +est neighbor framework to obtain interactive point prompt based segmentation. Despite being training-free, we experimentally show that our approach yields excellent results in terms of Number of Clicks (NoC), even outperforming state-of-the-art training based unsupervised methods in most of the datasets. Code is available at https://github.com/mkarmann/m2n2. + +# 1. Introduction + +The goal of point prompt based interactive image segmentation is to obtain a high-quality segmentation from limited user interaction in the form of clicking. Prompt-based image segmentation gained popularity lately due to large supervised foundation models [18, 35]. In this paper, we focus on unsupervised methods, where no segmentation labels are used at all in the design and/or training of the models. Most recent approaches rely on self supervised backbones like ViT [7], trained either by DINO [4] or MAE [13] based self- + +supervised techniques. On the other hand, Stable Diffusion (SD) [36] has been used for many different computer vision applications such as monocular depth estimation [16], semantic segmentation [45], object detection [5] and image classification [20], often resulting in state-of-the-art solutions. + +Inspired by DiffSeg [45], we investigate the potential of SD's self-attention maps for training-free interactive segmentation. Generally, for all self-supervised backbones, the main challenges are that attention maps don't distinguish between instances, exhibit noise and are typically of low resolution. We choose SD, particularly version 2 (SD2), as the backbone of our approach, as it provides the highest attention resolution (Sec. 14). To overcome the mentioned challenges, we interpret the self-attention tensors as a Markov transition operator, where the repeated application of the transition forms a Markov chain. We propose a novel Markov-iteration-map or simply Markov-map, where each pixel counts the number of iterations required to obtain a specific probability value. We show that the proposed Markov-map has less noise, the semantic boundaries are sharper and the semantic regions within Markov-maps are more uniformly distributed. Native Markov-maps do not distinguish between instances. Therefore, we further improve Markov-maps with a flood fill approach, which suppresses local minima, to enable instance based segmentation. Finally, we obtain Markov-maps of each prompt point and combine them with a truncated nearest neighbor approach to enable multi-prompt point interactive segmentation. Surprisingly, despite being training-free, we significantly improve the state-of-the-art in terms of Number of Clicks (NoC) and even surpass training-based unsupervised approaches in most of the datasets. Our main contributions are: + +- We introduce Markov-Map Nearest Neighbor (M2N2), the first attention-based unsupervised training-free multipoint prompt segmentation framework. +- We propose a novel method to refine semantic information in attention maps, which we call Markov-maps. +- We enable instance aware Markov-maps by utilizing a modified flood fill approach. +- We introduce a truncated nearest neighbor approach to combine multiple point prompts. +- We conduct extensive experiments with multiple backbones and achieve state-of-the-art results, surpassing even unsupervised training-based methods. + +# 2. Related Work + +Point prompt based interactive image segmentation has been approached from multiple perspectives. In this paper, we distinguish between supervised and unsupervised methods. + +# 2.1. Supervised Methods + +In [52] a click map and click sampling strategies are used in combination with FCN [29], creating the foundation for many follow-up methods. More recent approaches include [43], [24], [17, 18], [34], [15, 42], [27], [54], [6, 25], [26], [44], [28], [14], [46], either deploying dense fusion, where prompts are encoded as prompt maps, or sparse fusion, where prompts are transformed into embedding space to be fused with image and other related embeddings. + +Although the supervised approaches achieve good performance and efficiency, they require large-scale pixel-level annotations to train, which are expensive and laborious to obtain. While many supervised methods are tested on additional domains like medical images, it is unclear if there are other domains where the trained models would have a domain gap. + +# 2.2. Unsupervised methods + +Classical, unsupervised methods not based on Deep Learning like GraphCut [38], Random Walk [8], Geodesic Matting [2], GSC [9] and ESC [9] have been proposed. However, recently Deep Learning based approaches show great potential. Especially, methods utilizing self-supervised learning achieve impressive results. Such methods rely on pre-trained models (e.g., DenseCL [47], DINO [4]) to extract segments from their features. In [40] some heuristics are proposed to choose pixels belonging to the same object according to their feature similarity. [50] introduces normalized cuts [39] on the affinity graph constructed by pixel-level representations from DINO to divide the foreground and background of an image. In [11] a segmentation head is trained by distilling the feature correspondences from DINO. [31] adopts spectral decomposition on the affinity graph to discover meaningful parts in an image. FreeSOLO [48] designs pseudo instance mask generation based on multi-scale feature correspondences from densely pre-trained models and trains an instance segmentation model with these pseudo masks. + +Recently, several papers used Stable Diffusion (SD) [36] for various kinds of applications targeting unsupervised Semantic Segmentation. In [45] the self-attention maps of SD were used with KL-Divergence based similarity measures to merge semantically similar regions in order to extract segments. MIS [21] and UnSAM [49] use methods to capture the semantic hierarchy and create pseudo labels, which are used in a follow-up training process to obtain a model for promptable segmentation. UnSAM additionally allows automatic whole-image segmentation, but does not report NoC values on any dataset. In [5] object detection is formulated as a denoising diffusion process from noisy boxes to object boxes, and [22] proposes training-free unsupervised segmentation using a pre-trained diffusion model by iteratively contrasting the original image and a painted image + +![](images/44e83db001c30cde8080b57900bc2fc4a0f65c2bf8f8d45af3afde00565fae7a.jpg) +Figure 2. M2N2 framework overview. We perform a single denoising step of the input image with Stable Diffusion 2 to obtain attention tensors. The tensors are aggregated and utilized to obtain a Markov-map $M_{i}$ for each prompt point. The final segmentation is the result of a truncated nearest neighbor of scaled Markov-maps $M_{i}$ as a measure of semantic distance for each prompt point. The green and red areas in the scaled Markov-maps denote regions where the distance is less or equal to the global background threshold. In this visualization, components in blue contain adjustable hyperparameters. + +in which a masked area is re-painted. While this method obtains good results, it does not provide multi-prompt interactive segmentation. + +Inspired by [45], we focus on SD's self-attention maps as an initial semantic feature map. Our proposed Markov-map improves the semantic features, resulting in an excellent, unsupervised point prompt based interactive segmentation solution. + +# 3. Method + +In this section, we introduce our Markov-Map Nearest Neighbor (M2N2) framework in full detail. We design our interactive process similar to [27][18] where the user is shown an image with a suggested (initially empty) segmentation and allowing them to place a foreground or background point on objects they want to either include or exclude from the segmentation. Once a new point is set, M2N2 uses the entire set of points to predict a new segmentation. This interactive process continues until a satisfactory segmentation is achieved. Fig. 2 shows the three main stages of M2N2 applied on an example in which three points have already been set. In the first stage, we obtain an attention tensor of the input image by aggregating SD's self-attentions. The second stage extracts and enhances the semantic information of the attention tensor by creating a + +Markov-map for each prompt point. The semantically rich Markov-maps are then utilized in a truncated nearest neighbor algorithm to obtain a training-free unsupervised segmentation. In the following subsections, we first formulate the problem in the context of a nearest neighbor algorithm in Sec. 3.1, followed by an explanation of the acquisition of the attention tensor in Sec. 3.2 and extraction of the Markov-maps including the flood fill approach in Sec. 3.3. Finally, we introduce the full M2N2 algorithm Sec. 3.4. + +# 3.1. Truncated Nearest Neighbor + +In point prompt based segmentation we are given an image $I \in \mathbb{R}^{H \times W \times 3}$ of width $W$ and height $H$ and a set of labeled prompt points $D = \{(x_{1},y_{1}),(x_{2},y_{2}),\dots,(x_{N},y_{N})\}$ where $x_{i} \in \mathbb{R}^{2}$ are the 2D spatial coordinates of each prompt point in image pixel space and the labels $y_{i} \in \{0,1\}$ denote whether a point $x_{i}$ belongs to the background $y_{i} = 0$ or foreground $y_{i} = 1$ . To perform k-NN segmentation with $k = 1$ , we assign each query pixel $x_{q}$ of our output segmentation the class of its nearest neighbor $x_{i^{*}}$ : + +$$ +i ^ {*} = \underset {i} {\arg \min } d (x _ {i}, x _ {q}), \quad y _ {q} = y _ {i ^ {*}} \tag {1} +$$ + +where $d(\cdot, \cdot): \mathbb{R}^2 \times \mathbb{R}^2 \to \mathbb{R}_{\geq 0}$ is a semantic distance function measuring the semantic similarity between the query pixel $x_q$ and prompt point $x_i$ . In our case, we allow $d(\cdot, \cdot)$ + +to be asymmetric, meaning that $d(x_{i},x_{q})$ may, but does not have to, equal $d(x_{q},x_{i})$ . Using a canonical 1-NN, a single foreground prompt point would always segment the entire image as foreground, requiring a minimum of two prompts, one foreground and one background prompt, to get a useful segmentation. To mitigate this limitation and reduce NoC, we further extend the 1-NN algorithm with a distance threshold of 1 and define $\hat{y}_q$ as: + +$$ +\hat {y} _ {q} = \left\{ \begin{array}{l l} y _ {i ^ {*}} & \text {i f} d \left(x _ {i ^ {*}}, x _ {q}\right) \leq 1 \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {2} +$$ + +If the distance between a query pixel $x_{q}$ and its nearest neighbor $x_{i^{*}}$ exceeds the threshold of 1, it is classified as background $\hat{y}_{q} = 0$ , independent of its nearest neighbor's class $y_{i^{*}}$ . The main challenge is to find a good distance function $d(\cdot, \cdot)$ which measures the semantic dissimilarity of a prompt point $x_{i}$ and a query pixel $x_{q}$ . + +# 3.2. Attention Aggregation + +In this paper, we use the pre-trained SD 2. Given an image $I$ , we perform a single denoising step by computing a forward pass through the denoising U-Net and extract the multi-head self-attention $S_{j}$ of each transformer block $j$ . Each tensor $S_{j}$ is of the shape $N_{\text{heads}} \times h \times w \times h \times w$ . $N_{\text{heads}}$ denotes the number of attention heads and $h$ and $w$ are the height and width of the attention maps respectively. Each attention map $S_{j}[n,k,l,:;]$ of the tensor $S_{j}$ is a probability distribution, meaning the sum of each map's elements is equal to 1. We define the aggregated tensor $\mathbf{A} \in \mathbb{R}^{h \times w \times h \times w}$ as follows: + +$$ +\boldsymbol {A} [:,:,:,: ] = \sum_ {j \in \text {A t t n B l o c k s}} w _ {j} \sum_ {n} ^ {N _ {\text {h e a d s}}} \boldsymbol {S} _ {j} [ n,:,:,:,: ] \tag {3} +$$ + +Ensuring that the sum of weights $w_{j} \in [0,1]$ is 1, the result is a single attention tensor $\mathbf{A}$ of which each 2D-map $\mathbf{A}[k,l,:,:]$ is a probability distribution. + +# 3.3. From Attention Tensor to Markov-Maps + +First, we flatten the attention tensor $A \in \mathbb{R}^{h \times w \times h \times w}$ to obtain a matrix $A \in \mathbb{R}^{(h \cdot w) \times (h \cdot w)}$ . Since $A$ is a right stochastic matrix $^2$ , we can use it as a transition matrix in a Markov chain: + +$$ +p _ {t} = p _ {0} \cdot A ^ {t} \quad \text {w i t h} \quad p _ {0} = \operatorname {o n e h o t} (x) \tag {4} +$$ + +where the probability distribution row vector $p_0 \in \mathbb{R}^{1 \times (h \cdot w)}$ is the start state and $p_t \in \mathbb{R}^{1 \times (h \cdot w)}$ is the state after $t \in \mathbb{Z}_{\geq 0}$ iterations. The start state $p_0$ is the one-hot encoded vector of a prompt point $x$ . $A$ is strictly positive and generally irreducible, aperiodic stochastic matrix. Therefore, for $t \to \infty$ , each $p_0$ converges to a stationary distribution $p_\infty$ of the Markov chain [37]. The state $p_\infty$ depends on the attention matrix $A$ and is therefore different for each image. In order to be image agnostic, we remove the per-image bias in $p_\infty$ , by applying iterative proportional fitting (IPF) to the matrix $A$ . This converts $A$ to a doubly stochastic matrix. For all images, $A$ has therefore the property that each start state $p_0$ converges to a uniform distribution $p_\infty = \frac{1}{h \cdot w} \mathbf{1}$ for $t \to \infty$ [41]. As a result, the Markov chain describes the process from the lowest possible entropy in $p_0$ to the highest possible entropy in $p_\infty^3$ . Importantly, we are able to control the rate of convergence by changing the entropy of the attention maps $A[k,:]$ by modifying the temperature $T \in \mathbb{R}_{>0}$ : + +$$ +A _ {n e w} [ k, l ] = \frac {\exp \left(\frac {1}{T} \log \left(A _ {p r e v} [ k , l ]\right)\right)}{\sum_ {j} \exp \left(\frac {1}{T} \log \left(A _ {p r e v} [ k , j ]\right)\right)} \tag {5} +$$ + +Eq. (5) is applied before the IPF to ensure that the transition matrix $A$ is doubly stochastic. Temperatures $T$ higher than 1 increase the overall entropy of $A$ and therefore require fewer time steps $t$ to reach a uniform distribution in $p_t$ . The key idea is to measure the time $t$ it takes for each element $k$ in $p_0$ to converge to the uniform distribution: + +$$ +m [ k ] = \min \left\{t \in \mathbb {Z} _ {\geq 0} \mid \frac {p _ {t} [ k ]}{\max p _ {t}} > \tau \right\} \tag {6} +$$ + +Here $\max p_t$ returns the maximum element of the vector $p_t$ and the vector $m \in \mathbb{Z}_{\geq 0}^{1 \times (h \cdot w)}$ stores the minimal time required of each element $\bar{k}$ to saturate, i.e., to reach the relative probability threshold $\tau$ . As a result, the hyperparameter $\tau$ allows us to control how quickly the element $k$ saturates. Since $m$ only contains integers, we also perform a linear interpolation between consecutive time frames to obtain a smoother result. We then reshape $m$ into a matrix of the shape $h \times w$ and upscale it with JBU [19] to the input image resolution of $H \times W$ , resulting in $M \in \mathbb{R}^{H \times W}$ . Since $M$ measures the number of iterations of the Markov chain, we call the resulting map the Markov-iteration-map or in short Markov-map. + +Flood Fill. The task of point prompt based segmentation typically requires instance segmentation. This proves to be challenging for the proposed Markov-maps, since self-attention do not take object instances into account. + +
Attention Aggregation WeightsDAVIS
\(w_{\text{down0}}\)\(w_{\text{down1}}\)\(w_{\text{up0}}\)\(w_{\text{up1}}\)\(w_{\text{up2}}\)NoC85↓NoC90↓
1000011.3415.25
010009.3813.18
001004.866.90
000104.797.10
000016.009.02
000.50.504.606.72
+ +Therefore, we propose a modified flood fill approach. Given a prompt point $x$ and its corresponding Markov-map $M$ , we perform a flood fill on $M$ , using the pixel at $x$ as the starting pixel. In contrast to classical flood fill, we do not set each pixel to a desired color. Instead, we store the minimum required flood threshold to reach each pixel. This simple yet effective approach suppresses local minima and ensures a global minimum at the prompt point $x$ . Our approach requires that the instances do not overlap4. After applying our modified flood fill we obtain the final Markov-map. + +# 3.4. M2N2: Markov-Map Nearest Neighbor + +Using the one-hot encoded coordinates of each prompt point $x_{i}$ as start states, we generate a Markov-map $M_{i}$ for each prompt point $x_{i}$ . This allows us to construct the following distance function for the truncated nearest neighbor: + +$$ +d \left(x _ {i}, x _ {q}\right) = \frac {M _ {i} \left[ x _ {q} \right]}{\lambda_ {i}} \tag {7} +$$ + +where $M_{i}[x_{q}]$ denotes the value of the Markov-map $M_{i}$ at the pixel $x_{q}$ . Since every distance greater than 1 is assigned as background, we can use the scalar $\lambda_{i}$ as a threshold to truncate the Markov-map $M_{i}$ . Choosing a good threshold $\lambda_{i}$ is crucial to reduce the NoC. Therefore, we introduce a heuristic to adaptively determine an optimal $\lambda_{i}$ : + +$$ +\lambda_ {i} = \underset {\lambda} {\arg \max } s _ {i} (\lambda) \tag {8} +$$ + +Given a threshold $\lambda$ , we define the total score function $s_i(\lambda)$ as a product of four specific score functions, taking into account a prior, semantic edges and prompt point consistencies: + +$$ +s _ {i} (\lambda) = s _ {i, \mathrm {p r i o r}} (\lambda) \cdot s _ {i, \mathrm {e d g e}} (\lambda) \cdot s _ {i, \mathrm {p o s}} (\lambda) \cdot s _ {i, \mathrm {n e g}} (\lambda) (9) +$$ + +Each specific score $s_{i, \cdot}(\lambda)$ is based on the individual segmentation at the threshold $\lambda$ of a single prompt point $x_{i}$ : + +Table 1. Ablation study of the attention blocks on DAVIS. The blocks up0 and up1 achieve the lowest individual NoC. + +
Score Functions si,(λ)DAVIS
si,priorsi,edgesi,possi,negNoC85↓NoC90↓
××××6.4710.29
×✓✓✓4.676.81
✓×✓✓7.209.99
✓✓×✓4.926.87
✓✓✓×5.468.66
✓✓✓✓4.606.72
+ +Table 2. Ablation study of threshold score functions $s_{i,\cdot}(\lambda)$ on DAVIS. The first row utilizes no score with $\lambda_i = 0.5$ . + +- $s_{i,\text{prior}}(\lambda) = 1$ if the segment size relative to the image size is less than $40\%$ , 0 otherwise +- $s_{i,\mathrm{edge}}(\lambda)$ is the average Sobel gradient of $M_i$ computed along the segment boundary pixels +- $s_{i,\mathrm{pos}}(\lambda)$ is the percentage of all prompt points $x_{j}$ having the same class $y_{i} = y_{j}$ inside the segment +- $s_{i,\mathrm{neg}}(\lambda) = 0$ if any other prompt point $x_{j}$ of wrong class $y_{i} \neq y_{j}$ is inside the segment, 1 otherwise. + +By inserting Eq. (7) into Eq. (1) and Eq. (2), we arrive at the final M2N2 equations: + +$$ +i ^ {*} = \arg \min _ {i} \frac {M _ {i} \left[ x _ {q} \right]}{\underset {\lambda} {\operatorname {a r g m a x}} s _ {i} (\lambda)} \tag {10} +$$ + +$$ +\hat {y} _ {q} = \left\{ \begin{array}{l l} y _ {i ^ {*}} & \text {i f} \frac {M _ {i ^ {*} [ x _ {q} ]}}{\arg \max _ {\lambda} s _ {i ^ {*} (\lambda)}} \leq 1 \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {11} +$$ + +# 4. Experiments + +Datasets. We evaluate M2N2 on 4 public datasets: + +- GrabCut [38]: 50 images; 50 instances. +- Berkeley [30]: 96 images; 100 instances. Some of the images are shared with the GrabCut dataset. +- SBD [12]: 2857 images; 6671 instances (validation set). +- DAVIS [33]: 345 images; 345 instances. The segmentation is of very high-quality and instances include many objects with fine details and small structures. We use the same 345 images as used in [21, 27]. + +Evaluation Metrics. Following previous work [21, 27], we evaluate our approach by simulating user interaction, in which we place the next click in the center of the largest error region. The maximum number of clicks for each instance is 20 and we provide two metrics, the average number of clicks required to reach an IoU of $85\%$ as NoC85 and an IoU of $90\%$ as NoC90. + +Comparison with Previous Work. Tab. 3 compares our approach M2N2 with previous supervised and unsupervised approaches. To the best of our knowledge, M2N2 is + +
MethodBackboneGrabCut [38]Berkeley [30]SBD [12]DAVIS [33]
NoC85↓NoC90↓NoC85↓NoC90↓NoC85↓NoC90↓NoC85↓NoC90↓
Supervised: Trained on Ground Truth Labels
SimpleClick [27]ViT-B1.401.541.442.463.285.244.105.48
SimpleClickViT-H1.321.441.362.092.514.154.205.34
CPilot [26]ViT-B1.341.481.402.183.054.954.005.29
CFR-ICL [44]ViT-H-1.42-1.74-4.45-4.77
FocalClick [6]SegFormerB0-S2-1.90-3.144.346.51-7.06
InterFormer-Tiny [14]ViT-L-1.36-2.533.255.51-5.21
OIS [46]ViT-B-------3.80
Unsupervised: Trained on Pseudo Labels
TokenCut* [51]ViT-B3.045.746.309.9710.8213.1610.5615.01
FreeMask* [53]ViT-B4.066.105.559.028.6112.018.2613.05
DSM* [31]ViT-B3.644.645.497.758.5911.577.0810.11
MIS [21]ViT-B1.942.323.094.586.919.516.338.44
Unsupervised: Training-Free
GraphCut [38]N/A7.9810.00-14.2213.6015.9615.1317.41
Random Walk [8]N/A11.3613.77-14.0212.2215.0416.7118.31
Geodesic Matting [2]N/A13.3214.57-15.9615.3617.6018.5919.50
GSC [9]N/A7.109.12-12.5712.6915.3115.3517.52
ESC [9]N/A7.249.20-12.1112.2114.8615.4117.70
Attention-NNSD25.487.166.459.6111.6714.979.6613.12
KL-NNSD23.805.325.117.7110.7814.007.6010.89
M2N2 w/o flood fillSD23.064.504.806.519.1612.265.507.42
M2N2ViT-B1.923.403.555.687.9411.536.8510.86
M2N2SD1.11.842.202.904.938.5611.665.167.80
M2N2 (Ours)SD21.621.902.453.887.7210.944.606.72
+ +Table 3. Main comparison of M2N2 with baselines and previous work on all four datasets. $\star$ indicates pseudo label generation methods used on SBD images for training an unsupervised SimpleClick model [21]. All supervised methods were trained on SBD, except InterFormer (COCO [23] + LVIS [10]) and OIS (HQSeg44K [17]). Among the unsupervised methods, M2N2 obtains the best results in three out of four datasets, despite being training-free. + +the first unsupervised interactive point prompt based segmentation framework utilizing a pre-trained model without requiring any additional training. All other methods either are not based on any deep learning, e.g., GrabCut and related ones, or require the generation of pseudo-labels to train an interactive model, e.g., MIS. Our method surpasses the previous state-of-the-art unsupervised method MIS, which is trained on pseudo labels, on both metrics in three out of four test datasets. We observe the largest improvement on the DAVIS dataset, where we reduced the NoC85 by 1.73 and the NoC90 by 1.72 clicks. We achieve second best results in SBD. A possible explanation for this is that all deep-learning models listed in Tab. 3 are trained on the training set of SBD and therefore might have an advantage on this dataset. + +Baselines. We provide two additional baselines in Tab. 3 which use the same framework as M2N2 but without + +Markov-maps. Attention Truncated Nearest Neighbor (Attention-NN) uses attention maps as a semantic distance measure. KL-Divergence Truncated Nearest Neighbor (KL-NN) utilizes a symmetric KL-Divergence between the attention map of the prompt point and all attention maps in the attention tensor as distance function. Finally, we also provide a version of M2N2 without flood fill. We observe that the combination of Markov-maps with Flood fill achieves the best results with SD2 as our backbone compared to SD1.1 [36] and ViT-B [32]. + +SD2 Domain Bias. We notice a significant domain bias of M2N2 on medical data. Evaluating the IoU's for 10 clicks on BraTS [3] (SimpleClick: $87\%$ , M2N2: $70\%$ ) and OAIZIB [1] (SimpleClick: $76\%$ , M2N2: $66\%$ ) shows significant bias towards natural images. + +# 4.1. Implementation Details + +We use the SD2 implementation and weights provided by the Hugging Face transformers package. We don't add noise to the encoded image latent to keep the results deterministic and perform the single denoising step with empty text prompts. Due to the large memory requirements of the attention tensors, we run SD on 16-bit floating-point precision and convert it to 32-bit floating-point for the attention aggregation and further processes in our framework. We implement JBU as described in [19] with two modifications. We change the low-resolution solution sampling from sparse to dense sampling for smoother results and extend the range term to an isotropic Gaussian to better utilize RGB information in the images. We set $\sigma_{\mathrm{spatial}} = 1$ and $\sigma_{\mathrm{range}} = 0.1$ for RGB color values in the range [0, 1]. For M2N2 we choose the attention tensors of the size $128 \times 128 \times 128 \times 128$ and the SD time step of 100. We use the temperature $T = 0.65$ together with a relative probability threshold $\tau = 0.3$ to compute the Markov-maps with a maximum of 1000 iterations. By caching the attention tensor and Markov-maps of previous clicks, we observe an average of 0.6 seconds per click (SPC) for an image resolution of $854 \times 480$ on a RTX 4090, enabling a near real-time interactive process with the user. For more information on the other backbones please see Sec. 13. + +# 4.2. Ablation Study + +We perform extensive ablation studies on the hyperparameters of our segmentation algorithm to demonstrate the impact of each component of M2N2. + +Attention Aggregation. Our experiments in Fig. 4 show that higher attention tensor resolution improves NoC significantly for most of our datasets, performing best at a resolution of $128 \times 128 \times 128 \times 128$ . This is surprising since it requires an input image size of $1024 \times 1024$ which is beyond SD2's training resolution of $768 \times 768^5$ . We also evaluate the NoC for the SD time step, which is required for the single denoising step. Time steps greater than 200 increase the NoC which we assume is due to the distribution shift caused by not adding noise to the encoded latent. For the aggregation of attention tensors, we evaluate each attention block individually in Tab. 1 and observe that the attention tensors of up0 and up1 individually achieve significantly better NoC than the other layers. Aggregating up0 and up1 results in the best NoC. + +Markov-maps. Lowering the temperature $T$ of the aggregated tensor $A$ gradually improves the NoC in Fig. 4 up to $T = 0.5$ . Smaller values of $T < 0.5$ reduce the entropy and therefore require more iterations in the Markov + +![](images/4195397df701989d6850df43f745a0e74e1b2fb7ea0bbe5a54fa2338ed2f33ff.jpg) +Figure 3. Comparison of semantic maps. Each map is generated from a single prompt point. For better comparison, Markov-maps are inverted such that the lowest value is white and the highest value is black. + +chain, exceeding the maximum number of iterations and causing numerical instabilities. Different settings of the relative probability threshold $\tau$ prove to have a relatively low impact on the NoC. + +Truncated Nearest Neighbor. Experiments in Tab. 2 show the contribution of each score function $s_{i,}(\lambda)$ to the NoC of the total score function $s_i(\lambda)$ . In the second row we observe that the function $s_{i,\mathrm{prior}}$ , has the lowest impact on the NoC. Removing $s_{i,\mathrm{edge}}$ on the other hand increases NoC90 to 9.99 and is therefore the most important score function. + +# 4.3. Qualitative Results and Limitations of M2N2 + +Fig. 3 compares our proposed Markov-maps with other semantic maps obtained from a single prompt point. We observe that Markov-maps are less noisy, have clearer semantic boundaries, and have more uniform values within semantically similar regions. Additionally, we notice that Markov-maps nicely reflect a semantic hierarchy due to the segment size ambiguity of a single prompt point. For example, in the first row and right-most column, the two overlapping flowers have a hierarchy of three levels. The first level contains the right flower's ovary, the second contains both flowers together and the final level covers everything. This example also shows the strengths and weaknesses of our flood fill approach. As the ovaries are not overlapping, it enables instance segmentation of the right flower's ovary by suppressing the local minimum of the left flower's ovary. On the other hand, flood fill does not separate the right flower individually, because both flowers are semantically equal and overlapping. Please note that this limitation only applies to Markov-maps of a single point. M2N2 is still able to segment overlapping instances with the truncated nearest neighbor of multiple prompt points. (See Fig. 11) + +![](images/9bcaa5a56c5ac56eddf5bf48f9a5f9e0f7e8521eea87dd78528619881ce0f5d5.jpg) + +![](images/726916004b3d03c5bca6b11a2e43207f5af877202e71572daaee533c54087c0c.jpg) +Figure 4. Impact of the hyperparameters of SD and Markov-map, respectively, on all four datasets, each represented by a single color. Dashed lines correspond to NoC85, continues lines to NoC90. The graph of SBD is based on a randomly sampled subset of 500 images. + +![](images/8ad92083d849f5d0e751d3e218adbc107e854170ce6ebd98f5d939598ecd8ff6.jpg) + +![](images/9a5c9e231c00ca35cdeb5189355d95f2bc8dbf21ee94153c4f2fef2f569955de.jpg) + +![](images/bca9d1473a1ab51162e65d75f8c23ce7256ab2d14720e269ef0f735f333869e5.jpg) + +![](images/110789b723a8532cd796826a54110ddc3910db5ffb775b47258baf3a184d6c60.jpg) + +![](images/faa7bcf3d3efcb9501dae77662863dfbbae4ddb7d69e4447a2c12d83bff369b6.jpg) + +![](images/d9a80cc230ec5a0fd57f11e40ececd650b77ba1c2b426279e72f00fcc5ca5cac.jpg) + +![](images/48953607afe1d2480bff34b2f919d6233f7ef9cf276c2f2f7ed60b38c1366496.jpg) +NoC90 = 1 +Figure 5. Segmentation examples on DAVIS [33]. Each column shows examples slected on the NoC90 value, ranging from easy cases $\mathrm{NoC90} = 1$ on the left to difficult cases $\mathrm{NoC90} = 10$ and failure cases $\mathrm{NoC90} = 20$ on the right. Foreground points are shown in green and background points in red. The bottom right example is especially difficult for M2N2 by only having small thin isolated structures. + +![](images/32f9c85208c380d0d1fcecc577d0e4c76966d91b964f2b494efe826b2d7eda7a.jpg) + +![](images/9fea22892d7e112b086256e949b0703356a18f49adfa6a4daea8c863fc12b139.jpg) + +![](images/bdb71d46436b3d09e9049207a5720f4ca5060ca334f5e0cb8a22d6a400e88006.jpg) + +![](images/8017cbdf200d716f29962d7bac29ced73572f5febe1f172ca8b574124efc5005.jpg) +NoC90 = 2 + +![](images/6d3c2c6269bc0a28e029c0ef467823d1f6c6e7d903be4df5f263549c1166cacf.jpg) + +![](images/4e9b6e2741467ce911c768e1a730fd3d68384af22386c73f8d48cf20ebeffa06.jpg) + +![](images/de139c4874d8ce8ae7fa9bf32e3954e3ed5155af3052a24e43ff5bc73d1a95b5.jpg) + +![](images/d0c3d5e2cbacd841666b9793d30c48a032cf33db94ae4f9470e42b5e7739fee8.jpg) +NoC90 = 5 + +![](images/37420368b050b661376438d13d5e0742f634f6a47d3148bb6e2a89a527cfaf50.jpg) + +![](images/6face19d0e4b97fd85b46608e5fc8b17b5f219933c2cd4ba60cfd933ece3bdd5.jpg) + +![](images/ae74de1f68a3c75ae788f4d26b1905613f7e40651d9f5cdb1fd86b574935328b.jpg) + +![](images/d021abf34dd8b73965b8755f88b655d3fdd6e44ffa17eca37fe939f007c11abc.jpg) +NoC90 = 10 + +![](images/6a747d26adc81cd1e2ee1ac9d342a6f3687cd791ebd91b8249fc0b121412a950.jpg) + +![](images/b18bde20fd9e3d64d06032b74c8f748e332f03492deda35341d0ea53558ab3c0.jpg) + +![](images/2d81e85c446ea4ba29ad11cb1b6d98b086f5745421f2e3708e49bb601ae433f8.jpg) + +![](images/45fca1ebfbed0cf1a9e807b5379321f0c21f32100f819a7bf1fc527969387acd.jpg) +NoC90=20 + +![](images/96cdea718ea9dd77f6f8acf93ce0f4644f37049451bf93755a72f0d0b123c130.jpg) + +![](images/c67129621c7ddd8d4c574b85158100bd7b81f6b337470ef15cad67670b74a773.jpg) + +![](images/332fba86d96426fad401966892896b8134fd239c28db25919975094254a2b914.jpg) + +![](images/9f08c12b7c7c08df835064d6c98c9e48aadb74ee7df1c787a40db01e230764e2.jpg) +NoC90 = 20 + +Examples from the DAVIS dataset in Fig. 5 show a similar issue in the NoC90 = 10 column, where a single dancer is in front of a semantically similar crowd, requiring multiple corrective background points for proper separation. Another limitation of flood fill is that obstructions can split instances into multiple areas. For example, the segmentation of the obstructed rhinoceros requires two points, instead of one. Due to the limited attention resolution, M2N2 faces challenges in segmenting thin and fine structures, as shown in the 2 rightmost columns. The pixel-level truncated nearest neighbor still enables the segmentation of such structures but requires significantly more prompt points to reach the desired accuracy. In general, we observe that M2N2 generates consistent segments with sharp semantic boundaries without being trained on any segmentation labels. + +# 5. Conclusion + +We proposed M2N2, a novel method for unsupervised training-free point prompt based interactive segmentation. By interpreting an aggregated self-attention tensor of Stable Diffusion 2 as a Markov transition operator, we generated semantically rich Markov-maps. 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Recent works often attribute such deficiency in dense predictions to the self-attention layers in the final block, and have achieved commendable results by modifying the original query-key attention to self-correlation attention, (e.g., query-query and key-key attention). However, these methods overlook the cross-correlation attention (query-key) properties, which capture the rich spatial correspondence. In this paper, we reveal that the cross-correlation of self-attention in non-final layers of CLIP also exhibits localization properties. Therefore, we propose the Residual Cross-correlation Self-attention (RCS) module, which leverages the cross-correlation self-attention from intermediate layers to remold the attention in the final block. The RCS module effectively reorganizes spatial information, unleashing the localization potential within CLIP for dense vision-language inference. Furthermore, to enhance the focus on regions of the same categories and local consistency, we propose the Semantic Feedback Refinement (SFR) module, which utilizes semantic segmentation maps to further adjust the attention scores. By integrating these two strategies, our method, termed ResCLIP, can be easily incorporated into existing approaches as a plug-and-play module, significantly boosting their performance in dense vision-language inference. Extensive experiments across multiple standard benchmarks demonstrate that our method surpasses state-of-the-art training-free methods, validating the effectiveness of the proposed approach. Code is available at https://github.com/yvhangyang/ResCLIP. + +# 1. Introduction + +Recently, we have witnessed the unprecedented breakthrough of vision-language models (VLMs) [8, 13, 25, 36, + +![](images/1396e301658d3815db0fc7830c669ebb67ba312acbbd2490a1b66bb34bb2d6c0.jpg) +Figure 1. The attention visualization from different layers of CLIP [37] model. The images are sampled from PASCAL VOC [16] dataset. + +37], which are de facto foundation models across various downstream tasks such as zero-shot classification [20, 37], natural language processing [6, 14, 38] and visual question answering [2, 23, 55]. Especially, VLMs exhibit surprising open-vocabulary recognition capabilities because they are trained on large-scale image-text pairs with contrastive learning. Despite impressive performance achieved in image-level open-vocabulary tasks, they struggle with dense prediction tasks such as semantic segmentation due to the well-known limitation in localization ability [39, 45]. + +To this end, some previous works [9, 33, 40, 47, 49, 50, 57] make great efforts to address these limitations by fine-tuning CLIP with pixel-level annotations. These methods [33, 51, 61] not only consume expensive annotation costs but also are easily biased toward the training data, eliminating the generalization ability within CLIP. This has motivated a growing interest in training-free methods [18, 27, 28, 41, 45, 59] that aim to adapt pre-trained representations of CLIP for semantic segmentation without additional training and maximumly maintain the generalization ability of CLIP simultaneously. These approaches typically attribute the inferior results of CLIP on dense prediction to the self-attention layer in the last block of CLIP (last col. in Fig. 1), which presents spatial-invariant attention. For example, SCLIP proposes to replace orig + +![](images/eeecc0f557e9f46ee8cf97c4ceef1166919c6ced2a960e76cf622b2e0950e477.jpg) +(a) $C^2 SA$ + +![](images/a39f837fff0ace72cef77b87b8b09f45dfe14a2c3ba237b83b19485c20b5bb9b.jpg) +(b)SCSA + +![](images/e39106032ed7ca0501873f347737155f4c084dbb8e6a81eb10474a33663aca0f.jpg) +(c) RCS & SFR (Ours) + +![](images/ee16c1625b7bfbb9e3e7cf5172d71f3402df0e3ad4d93fc21a13e39a44cdbc25.jpg) +(d) Performance Comparison +Figure 2. (a) Cross-correlation self-attention $(\mathrm{C}^2\mathrm{SA})$ . The query and key are mapped by different project matrices. The attention is obtained by matrix multiplication between query and key. (b) Self-correlation self-attention (SCSA). The attention is calculated by the self-correlation such as key-key or query-query. (c) Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR). (d) The performance comparison between our methods and baselines. + +inal query-key self-attention with query-query and key-key self-attention. NACLIP [18] employs key-key self-attention with neighbor priors to enhance attention across adjacent patches. We summarize these attention paradigms as self-correlation self-attention (SCSA, Fig. 2 (b)), which achieves better spatial-covariant features than the original last self-attention layer (Fig. 2 (a)). However, they overlook the cross-correlation self-attention $(\mathrm{C}^2\mathrm{SA})^1$ properties that capture the diverse and spatial correspondence. Ideally, if the attention is supervised by the pixel-level data, the $C^2$ SA will learn densely class-specific representations. We, therefore, ask: Can we obtain such properties of the $C^2$ SA from CLIP even if it does not receive pixel-level supervision? + +We answer this question by examining the $\mathrm{C}^2\mathrm{SA}$ in all layers and reveal that the attention of $\mathrm{C}^2\mathrm{SA}$ in non-last layers exhibits localization properties unlike that in the last layer. We visualize the attention of CLIP across different layers in Fig. 1. We can observe that the attention in the last layer is spatial-invariant while the attentions in other layers exhibit class-specific features and localization properties. For example, the attention of the "cat" in the top image can attend to other "cat" regions in the image to some extent. This motivates us to propose a novel Residual Cross-correlation Self-attention (RCS) that borrows the cross-correlation self-attention from intermediate layers to make a residual connection with the attention in the last block. The cross-correlation could reorganize the spatial information thus unleashing the potential of CLIP for dense vision-language inference. Moreover, to explicitly enhance + +the focus on regions of the same categories and local consistency, we also propose a Semantic Feedback Refinement (SFR) module to leverage the semantic segmentation map to further tweak the attention score. It is worth noting that our method termed ResCLIP (Fig. 2 (c)) is orthogonal to existing works and can be seamlessly integrated into existing approaches as a plug-and-play module. + +We conduct extensive experiments across eight segmentation benchmarks, demonstrating substantial potential of CLIP for open-vocabulary segmentation. As a plug-and-play solution, we integrate our method with three leading models: SCLIP, ClearCLIP, and NACLIP. The experimental results demonstrate significant improvements, with consistent mIoU gains across all datasets. As shown in Fig. 2 (d), equipped with our method, the performance will be significantly boosted across all models. For example, our method makes improvements from $1.7\%$ to $13.1\%$ mIoU compared with counterparts. We also have conducted many ablation studies in both quantitative and qualitative ways to analyze the components of our method. + +Our contributions can be summarized as follows: + +- We reveal that attention from intermediate layers of CLIP exhibits class-specific features and localization properties. To the best of our knowledge, this work is the first work to discover that the cross-correlation self-attention from intermediate layers present localization properties and can heal the attention in the last layer. +- We propose a novel training-free approach, terms ResCLIP, including Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR) modules. These two modules can rectify the attention in the last layer to capture class-specific features and + +local consistency so that improve CLIP model for dense vision-language prediction tasks. + +- We have conducted extensive experiments on open-vocabulary semantic segmentation tasks including eight widely used benchmarks. The results in experiments demonstrate the effectiveness of our proposed method. + +# 2. Related Work + +Vision-language Foundation Models. In recent years, VLMs have emerged as a general paradigm in various vision tasks, demonstrating remarkable capabilities in zero-shot and few-shot learning scenarios. Unlike Segment Anything Model (SAM) [25, 53, 62] which focus on promoting semantic-agnostic segmentation, a series of contrastive learning-based approaches [1, 10, 20, 29, 34, 37, 48, 54, 56] have shown exceptional adaptability across diverse downstream tasks. CLIP, in particular, achieves robust vision-text alignment through training on image-text pairs [17, 46, 52]. This has spawned numerous extensions to expand tasks such as visual question answering [23, 24], image captioning [30] and downstream inference capabilities [10, 44]. + +Open-vocabulary Semantic Segmentation (OVSS). The OVSS extends traditional segmentation by enabling pixel-level dense prediction for arbitrary categories specified through text descriptions. Recent advances in vision-language models, particularly CLIP, have catalyzed significant progress [10, 37, 48] in this field. For their supervision requirements: fully-supervised methods [19, 21, 32] that fine-tune CLIP using pixel-level annotations, weakly-supervised approaches [9, 33, 40, 47, 47, 49, 50, 57] that leverage image-text pairs for training, and training-free methods [5, 18, 22, 27, 31, 37, 42, 45, 59] that modify architecture of CLIP with minimal changes. While fully-supervised methods achieve strong performance but require extensive labeled data, and weakly-supervised methods like GroupViT [49] introduce specialized architectures with group tokens, training-free approaches such as MaskCLIP [59] focus on adapting self-attention mechanisms to enable dense prediction capabilities. However, these existing methods often struggle to fully utilize semantic understanding of CLIP due to limited fine-tuning datasets [43] and their local understanding capability. + +Different Self-attention for Dense Visual Features. Recent training-free approaches show great interest in modifying attention mechanisms to enhance dense visual representation capabilities of CLIP. While vanilla CLIP employs query-key multiplication to obtain holistic visual representations that are invariant to spatial positions [60], subsequent works have explored various attention modifications. SCLIP [45] introduces self-correlation attention by combining query-query and key-key products as final layer attention weights to capture spatial-covariant features. This was followed by approaches such as GEM [5] + +presents a way to calculate the attention matrix as the combination of query-query, query-key and value-value attention, NACLIP [18] emphasizes key-key products with Gaussian kernels, ClearCLIP [27] utilizes query-query interactions, CLIPtrase [41] tries to use weighted average of self-correlation attention to cluster the "global" patch for segmentation and ProxyCLIP [28] exploring attention combination with vision foundation models such as SAM. Different from these works, we discover that the cross-correlation self-attention from intermediate layers present localization properties and can heal the attention in the last layer. Therefore, we propose a novel training-free approach, terms ResCLIP, including Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR) modules. These two modules can rectify the attention in the last layer to capture class-specific features and local consistency so that improve CLIP model for dense vision-language prediction tasks. + +# 3. Methodology + +In this section, we begin with an introduction to CLIP and its application to open-vocabulary semantic segmentation in a training-free paradigm in Sec. 3.1. Then, we describe the design of the proposed method including Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR) modules in Sec. 3.2. + +# 3.1. Preliminary + +Vision Encoder Architecture of CLIP. CLIP utilizes a Vision Transformer (ViT) [37] to encode images into a representation aligning with textual descriptions. In conventional ViT [15], an input image $H \times W \times 3$ is partitioned into a grid of non-overlapping patches of size $P \times P$ . This results in $h = H / P$ rows, and $w = W / P$ columns of patches. Each patch is then being projected into a $d$ dimensional space, which can be presented by vectorized feature $x_{i} \in \mathbb{R}^{d}$ with preserved spatial relationships through explicit positional embeddings. Therefore, the input at each layer can be formulated as a sequence of visual tokens $X = \{x_{\mathrm{cls}}, x_{1}, \dots, x_{h \times w}\} \in \mathbb{R}^{(1 + hw) \times d}$ , where $x_{\mathrm{cls}}$ denotes the class token to capture global information. These visual tokens will feed into several multi-head self-attention layers to obtain the final token representations. + +Self-attention Module. The core of the transformer encoder is the self-attention mechanism (see Fig. 2 (a)), which enables the model to capture relationships between different patches. Note that we only consider the single-head self-attention for simplicity. The self-attention is given by: + +$$ +q, k, v = \operatorname {P r o j} _ {q, k, v} (\mathrm {L N} (X)), \tag {1} +$$ + +$$ +S _ {q k} = q k ^ {T} / \sqrt {d _ {k}}, \tag {2} +$$ + +$$ +\operatorname {A t t n} \left(S _ {q k}\right) = \operatorname {s o f t m a x} \left(S _ {q k}\right) = \operatorname {s o f t m a x} \left(q k ^ {T} / \sqrt {d _ {k}}\right), \tag {3} +$$ + +![](images/0ae619ecc682f079927f51c9a863c223faac35ab1b92251b76651825a36721e1.jpg) +Figure 3. Comparison of attention maps across different versions of CLIP and ours. + +where $q, k, v$ indicates the query, key and value, respectively. The LN is layer normalization, Proj denotes a projection layer, and $d_{k}$ is the dimension of key $k$ . The attention scores $S_{qk} \in \mathbb{R}^{(1 + hw) \times (1 + hw)}$ imply the intrinsic global structural dependencies between patches, from which the attention map $\mathrm{Attn}(S_{qk})$ is obtained through the softmax normalization. + +Dense Vision-language Inference. CLIP was originally trained on large-scale image-text pairs using contrastive loss, demonstrating promising results in open-vocabulary image recognition tasks. The text representations $X_{\mathrm{text}} = \{t_1, t_2, \ldots, t_c\}$ are obtained through a text encoder and are used to align with $cls$ token $x_{\mathrm{cls}}$ of visual features for each image-text pair. A natural idea is to extend the CLIP model to dense vision-language inference tasks such as open-vocabulary semantic segmentation by calculating the similarity between the dense visual tokens $X_{\mathrm{dense}} = \{x_1, \ldots, x_{h \times w}\} \in \mathbb{R}^{hw \times d}$ and text tokens $X_{\mathrm{text}}$ . In particular, we can obtain the segmentation map as follows, + +$$ +\mathcal {M} = \arg \max \cos \left(X _ {\text {d e n s e}}, X _ {\text {t e x t}}\right). \tag {4} +$$ + +However, the obtained semantic segmentation maps are full of noise due to the deficiency in localization ability in the CLIP model. The purpose of this work is to improve the performance of dense vision-language inference in a training-free manner so that maximally reserves the generalization ability of CLIP by adjusting the attention in the last layers. + +# 3.2. ResCLIP + +As demonstrated in the previous works [59], CLIP exhibits inherent limitations in pixel-level semantic segmentation. To address these challenges, recent studies [18, 27, 45, 59] have proposed several approaches in a training-free manner and involve minimal modifications to the original model. These methods reveal that the attention in the last layer of CLIP exhibits spatial-invariant features, i.e., local features tend to be invariant to their spatial position in the image. + +Therefore, these methods [18, 27, 45] focus on reformulating the self-attention module in the final layer of CLIP by introducing a self-correlation self-attention (SCSA) to obtain the spatial-covariant features. These SCSA-based methods encourage each local token to attend to itself and the positions sharing similar features with it so that eliminates the spatial-invariant issues in the original CLIP, leading to improved dense prediction performance. + +However, the SCSA enforces the self-similar features response and lacks the capacity to capture the cross-feature dynamics that cross-correlation self-attention (C $^2$ SA) provides. The cross-correlation self-attention typically captures the diverse and spatial correspondence, which is beneficial for localization. But the C $^2$ SA in the last layer has shown spatial-invariant properties in CLIP. Through careful experiments, we reveal that the self-attention in non-last layers of CLIP exhibits class-specific features and localization properties (See Fig. 1). For example, the attention of the "cat" in the top image can attend to other "cat" regions in the image to some extent. + +Therefore, we propose a novel training-free approach that aggregates the $\mathrm{C}^2\mathrm{SA}$ from intermediate layers of CLIP to remold the attention in the last block. The cross-correlation could reorganize the spatial information thus unleashing the potential of CLIP for dense vision-language inference. In particular, we propose a novel Residual Cross-correlation Self-attention (RCS) that aggregates the $\mathrm{C}^2\mathrm{SA}$ from intermediate layers to make a residual connection with the attention in the last block. The RCS could reorganize the spatial information thus unleashing the potential of CLIP for dense vision-language inference. Moreover, to explicitly enhance the focus on regions of the same categories and local consistency, we also propose a Semantic Feedback Refinement (SFR) module to leverage the semantic segmentation map to further tweak the attention score. As shown in Fig. 3, our method could improve the attention of the baseline methods to attend more semantic-related regions. The overview of our method is present in Fig. 4. + +# 3.2.1. Residual Cross-correlation Self-attention + +The Residual Cross-correlation Self-attention (RCS) module borrows the attention from the intermediate layers to remold the attention module in the last layer. Specifically, we first extract the $\mathrm{C^2SA}$ from intermediate layers and aggregate information from them through the average operation. Formally, we denote the $\mathrm{C^2SA}$ attention $\mathrm{Attn}^i (S_{qk})$ as $\mathcal{A}_{qk}^i$ in $i$ -th layer, the aggregated attention $\mathcal{A}_c$ can be calculated as follows, + +$$ +\mathcal {A} _ {c} = \frac {1}{N} \sum_ {i = s} ^ {e} \mathcal {A} _ {q k} ^ {i}, \tag {5} +$$ + +where $N = e - s + 1$ indicates the number of layers from the start layer $s$ to the end layer $e$ . Based on this aggregated + +![](images/8459feaeda9e8d44c49d84780ef711272f2d02a86ab1723aec7156fae80e6354.jpg) + +![](images/2facaedb940e85054bf4675627b5b02c59b315397728923a1f4aa43c14ba1cc6.jpg) + +![](images/841d6bc711b5c677a00e18ab56172a41f9dbefd8f96da98fa1c0fade696a003c.jpg) +Figure 4. Overview of our ResCLIP consisting of Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR). The RCS module enhances attention mechanism of CLIP by fusing $\mathrm{C}^2\mathrm{SA}$ from non-last layers $\mathcal{A}_c$ with SCSA $\mathcal{A}_s$ to capture richer spatial information. The SFR module leverages an initial segmentation mask (black arrows) to refine attention scores. These refined attention scores $\hat{S}$ are combined with RCS to adjust the attention in the last layer of CLIP and produce the final prediction (blue arrows). + +![](images/5a4d42a105d8d55e3ed372865b7f3f3d27edc4d81abda21990ab7720f7db37f4.jpg) + +attention, the RCS attention can be formulated as follows, + +$$ +\mathcal {A} _ {r c s} = \left(1 - \lambda_ {r c s}\right) \cdot \mathcal {A} _ {s} + \lambda_ {r c s} \cdot \mathcal {A} _ {c}, \tag {6} +$$ + +where $\mathcal{A}_s$ is the SCSA attention used in previous works [27, 45] and $\lambda_{rcs}$ is the trade-off parameter. Our RCS absorbs information from both the $\mathcal{A}_s$ and $\mathcal{A}_c$ , which capture the local patch structure and cross-feature correspondence. This attention could better reorganize the information in the last layer and improve the final classification. + +# 3.2.2. Semantic Feedback Refinement + +Although our RCS module not only provides spatial-invariant attention but also cross-feature dynamics, the attention is still not real attention under the pixel level supervision. Some works such as NACLIP [18] add prior regularization to the attention by paying attention to the neighbor patches with discretized Gaussian kernels into attention maps. However, these kernels are isotropic and thus may introduce extra context due to the shapes of the objects being versatile. Besides, ideal attention should attend to the objects that share the same categories [36]. To this end, we propose a Semantic Feedback Refinement (SFR) module that improves the attention with the same semantics and maintains the locality simultaneously by using the semantic segmentation map from the CLIP model as feedback. + +In particular, we begin with a semantic segmentation map, which is obtained by our RCS module, and then use this semantic segmentation map to further tweak the attention in the last layer. This loop would obtain better attention, resulting in improved performance. Formally, suppose + +that we have an attention score $S \in \mathbb{R}^{hw \times hw}$ , each element $S_{ij}$ in $S$ indicates the attention from $i$ -th patch to $j$ -th patch. Now, we consider there is a semantic segmentation map $\mathcal{M} \in \mathbb{R}^{hw}$ . For brevity, we only consider the attention score $S^i \in \mathbb{R}^{hw}$ for one patch as an example, it can be obtained as follows, + +$$ +S _ {m, n} ^ {i} = \mathbb {I} \left(\mathcal {M} _ {i ^ {\prime}, j ^ {\prime}} = = \mathcal {M} _ {m, n}\right), \tag {7} +$$ + +where $m \in \{1,2,\dots,h\}$ , $n \in \{1,2,\dots,w\}$ , $i' = \lfloor i / w \rfloor$ and $j' = (i \mod w)$ indicates the grid index in mask $\mathcal{M}$ for the $i$ -row attention $S^i$ . And the $\mathbb{I}(\cdot)$ is the indicator function where 1 when $\cdot$ is true, otherwise 0. + +To further maintain the locality, we emphasize the attention to the adjacent patches of the same class. We first identify connected and disjoint regions, then reduce the attention to the disjoint ones. To be specific, we first define a decay function as follows, + +$$ +h (V, D) = V + (1 - V) \cdot D, \tag {8} +$$ + +where $V$ is the mask where $V_{mn} = 1$ if there a valid path from $(m,n)$ to $(i',j')$ , otherwise 0. $D$ is a distance-based decay function, which is defined as: + +$$ +D (p, q) = \exp \left(- \frac {d (p , q)}{\operatorname* {m a x} (d (\cdot , \cdot))}\right), \tag {9} +$$ + +where $p$ and $q$ denote the grid coordinates for the patches. We use the Chebyshev Distance for simplicity which measures the most significant difference with different patches as follows, + +$$ +d (p, q) = \max \left(\left| p _ {x} - q _ {x} \right|, \left| p _ {y} - q _ {y} \right|\right). \tag {10} +$$ + +Table 1. Open-vocabulary semantic segmentation quantitative comparison on datasets without a background class. Our results are marked in gray . The best results on each dataset for different encoders are bolded. + +
MethodsTraining-free?EncoderVOC20Context59StuffCityscapeADE20kAvg.
GroupViT [49]×ViT-S/1679.723.415.311.19.227.7
CoCu (? ]×ViT-S/16--13.615.011.1-
TCL [9]×ViT-B/1677.530.319.623.114.933.1
CLIP [37]✓ViT-B/1641.89.24.45.52.112.6
MaskCLIP [59]✓ViT-B/1674.926.416.412.69.828.0
ReCo [42]✓ViT-B/1657.722.314.821.111.225.4
CLIPSurgery [31]✓ViT-B/16--21.931.4--
SCLIP [45]✓ViT-B/1680.434.222.432.216.137.1
+ResCLIP(ours)✓ViT-B/1684.635.823.934.417.639.3 (+2.2)
ClearCLIP [27]✓ViT-B/1680.935.923.930.016.737.5
+ResCLIP(ours)✓ViT-B/1687.136.424.334.517.840.0 (+2.5)
NACLIP [18]✓ViT-B/1679.735.223.335.517.438.2
+ResCLIP(ours)✓ViT-B/1686.036.824.735.918.040.3 (+2.1)
CLIP [37]✓ViT-L/1415.84.52.42.91.25.4
MaskCLIP [59]✓ViT-L/1430.112.68.910.16.913.7
SCLIP [45]✓ViT-L/1460.320.513.117.07.123.6
+ResCLIP(ours)✓ViT-L/1483.930.621.232.215.836.7 (+13.1)
ClearCLIP [27]✓ViT-L/1480.029.619.927.915.034.5
+ResCLIP(ours)✓ViT-L/1484.233.422.334.117.938.4 (+3.9)
NACLIP [18]✓ViT-L/1478.732.121.431.417.336.2
+ResCLIP(ours)✓ViT-L/1485.534.523.433.718.239.1 (+2.9)
+ +Therefore, we can apply the decay function to attention score $S^i$ as follows, + +$$ +\hat {S} ^ {i} = \phi \left(S ^ {i} \odot h (V, D)\right), \tag {11} +$$ + +where $\phi$ is a conventional 1-dimensional Gaussian kernel to smooth the final attention score. This smoothing operation enhances the generalization of attention scores while preserving the row-independence property of the original attention mechanism. By employing the above operation to each row, we can obtain the entire attention score map $\hat{S}$ . Finally, we combine the original attention scores with our semantic feedback refinement score, which can be formulated as follows, + +$$ +S _ {r} = \left(1 - \lambda_ {s f r}\right) \cdot S _ {s} + \lambda_ {s f r} \cdot \hat {S}, \tag {12} +$$ + +where $S_{s}$ is the attention score of SCSA and $\lambda_{sfr}$ is the trade-off parameter. Now, we lead to the final version of ResCLIP, the final attention can be given by: + +$$ +\mathcal {A} _ {\text {R e s C L I P}} = \left(1 - \lambda_ {r c s}\right) \cdot \mathcal {A} _ {s f r} + \lambda_ {r c s} \cdot \mathcal {A} _ {c}, \tag {13} +$$ + +where $\mathcal{A}_{sfr} = \text{softmax}(S_r)$ . To this end, residual attention $\mathcal{A}_{ResCLIP}$ benefit from 1) SCSA attention that provides spatial-covariant features as mentioned in previous works [18, 45]; 2) $\mathrm{C}^2\mathrm{SA}$ attention from intermediate layers that capture the rich spatial correspondence; 3) SFR attention that explicitly enhances the focus on regions of the same categories and local consistency. + +# 4. Experiments + +# 4.1. Experimental Setups + +Datasets. We conduct comprehensive evaluations on eight widely-adopted benchmark datasets for open-vocabulary semantic segmentation. Following prior works [18, 27, 45], these datasets can be categorized into two groups based on the presence of a background category, whose names are abbreviated in parentheses for brevity. Firstly, datasets with background category: PASCAL VOC 2012 [16] (VOC21), PASCAL Context [35] (Context60) and COCO Object [7] (Object). Secondly, datasets with background category: COCO-Stuff [7] (Stuff), Cityscapes [12] and ADE20K-150 [58]. Additionally, we follow the construction of removing the background class in PASCAL VOC20 [16] (VOC20) and PASCAL Context59 [35] (Context59). Specifically, input images are resized to have a shorter side of 336 pixels, except for Cityscapes, where we use 560 pixels due to its inherently high-resolution images. We perform slide inference using a $224 \times 224$ window with a stride of 112 following [4, 9, 18, 27, 31, 45, 49]. + +Baselines. We compare our work with a comprehensive range of OVSS methods, including direct baseline CLIP [37], previous state-of-the-art training-free approaches: MaskCLIP [59], ReCo [42], CLIPSurgery [31], GEM [5], SCLIP [45], NACLIP [18] and ClearCLIP [27]. We also include a few influential weakly supervised methods, such as GroupViT [49], CoCu [47], TCL [9], SegCLIP [33], OVSegmentor [50], PGSeg [57], and + +Table 2. Open-vocabulary semantic segmentation quantitative comparison on datasets with a background class. Our results are marked in gray . The best results on each dataset for different encoders are bolded. + +
MethodsTraining-free?EncoderVOC21Context60ObjectAvg.
GroupViT [49]×ViT-S/1650.418.727.532.2
SegCLIP [33]×ViT-S/1652.624.726.534.6
OVSegmentor [50]×ViT-B/1653.820.425.133.1
PGSeg [57]×ViT-S/1653.223.828.735.2
ViewCo [40]×ViT-S/1652.423.023.533.0
CoCu [?]×ViT-S/1640.921.220.327.5
TCL [9]×ViT-B/1651.224.330.435.3
CLIP [37]✓ViT-B/1616.27.75.59.8
MaskCLIP [59]✓ViT-B/1638.823.620.627.7
ReCo [42]✓ViT-B/1625.119.915.720.2
CLIPSurgery [31]✓ViT-B/16-29.3--
GEM [5]✓ViT-B/1646.232.6--
SCLIP [45]✓ViT-B/1659.130.430.540.0
+ResCLIP(ours)✓ViT-B/1660.732.934.342.7 (+2.7)
ClearCLIP [27]✓ViT-B/1651.832.633.039.1
+ResCLIP(ours)✓ViT-B/1659.032.934.042.0 (+2.9)
NACLIP [18]✓ViT-B/1658.932.233.241.4
+ResCLIP(ours)✓ViT-B/1661.133.535.043.2 (+1.8)
SCLIP [45]✓ViT-L/1444.422.324.930.5
+ResCLIP(ours)✓ViT-L/1452.828.730.937.4 (+6.9)
ClearCLIP [27]✓ViT-L/1448.728.329.735.5
+ResCLIP(ours)✓ViT-L/1450.729.831.137.2 (+1.7)
NACLIP [18]✓ViT-L/1452.228.729.936.9
+ResCLIP(ours)✓ViT-L/1454.130.932.539.2 (+2.3)
+ +ViewCo [40]. Unless explicitly mentioned, all reported results are from the respective papers. Besides, we select recent state-of-the-art methods SCLIP [45], NACLIP [18], ClearCLIP [27] with specialized attention designs as baselines and evaluate performance of our method when integrated with these approaches. We also present results based on the ViT-L/14 backbone for a comprehensive evaluation. + +Implementation details. In our experiments, we utilize the implementations provided by MMSegmentation [11]. Following TCL [9], we abstain from computationally intensive post-processing techniques that could lead to unfair comparisons, such as PAMR [3] (used in TCL [9], NACLIP [18]) and DenseCRF [26] (used in ReCo [42]). We employ only standard ImageNet prompts [37] without additional textual prompting strategies. By default, our comparative experiments are conducted using the ViT-B/16 [15] backbone, with ablation studies and sensitivity analyses performed on top of NACLIP. Our approach operates in a fully training-free manner, requiring neither retraining nor finetuning. We evaluate all semantic segmentation tasks using the mean Intersection over Union (mIoU) metric. + +# 4.2. Main Results + +Quantitative results. Table 1 summarizes the performance of various open-vocabulary semantic segmentation models on datasets without a background class. Our ResCLIP demonstrates significant improvements when integrated with state-of-the-art approaches including SCLIP [45], + +ClearCLIP [27], and NACLIP [18]. Notably, when combined with NACLIP [18], our method achieves state-of-the-art performance, surpassing mainstream weakly supervised approaches. As a plug-and-play solution, consistent improvements are observed across all five datasets compared to the baseline methods, showing the great potential of ResCLIP. We also evaluate performance on ViT-L/14 and observe that when adapting to different backbones, existing methods typically decrease by over $2\%$ mIoU, e.g., SCLIP [45] has a particularly severe drop of $13.5\%$ mIoU. However, with the integration of our method, this performance degradation is significantly mitigated, demonstrating the effectiveness of the proposed method. Additionally, we conduct experiments on datasets with a background class in Table 2. We can observe that ResCLIP shows consistent improvements across all datasets with a background class over all the counterparts. Specifically, our method surpasses supervised approaches such as GroupViT [49], achieving state-of-the-art performance of $43.2\%$ mIoU when integrated with NACLIP [18] on ViT-B/16 backbone. Regarding results of the VIT-L/14, our method still provides substantial improvements compared with other baselines. These results validate that the method effectively reduces noise of original attention in the last layer. + +Qualitative results. In Fig. 5, we present qualitative comparison results with training-free methods such as SCLIP [45], NACLIP [18], and ClearCLIP [27]. From + +![](images/f3de07dd64bf84b6cf109e09cca1b7147f85ebc22eddc58d1a550b29a3bb071d.jpg) +Figure 5. Qualitative comparison between different CLIP-based training-free segmentation methods. + +Table 3. Ablation studies for the proposed method. + +
MethodsModule RCS SFRmIoU Δ
Baseline (NACLIP [18])--79.7-
ResCLIP(Ours)✓85.5+5.8
✓81.5+1.8
✓✓86.0+6.3
+ +Fig. 5, our ResCLIP predicts higher quality and more accurate segmentation maps with reduced noise. ResCLIP demonstrates superior attention to the internal regions of an object, avoiding hollow dense predictions in central areas (e.g., the 1st col. in VOC and the 1st col. in COCO Object). Compared to NACLIP, which employs key-key attention in the last layer, ResCLIP achieves both effective noise reduction and clearer segmentation maps (e.g., on ADE20k), demonstrating that ResCLIP effectively captures rich spatial correspondences between objects of the same category, while SFR successfully enhances local consistency. More qualitative results can be referred to our Supplementary. + +# 4.3. Experimental Analysis + +Ablation studies. We conduct ablation studies using NA-CLIP with ViT-B/16 backbone, as shown in Table 3. The RCS module alone improves mIoU from $79.7\%$ to $85.5\%$ on VOC20, demonstrating effectiveness of incorporating non-last layers $\mathcal{A}_{qk}$ information into the final attention map. The SFR module independently achieves a $1.8\%$ mIoU improvement, validating its effectiveness in enhancing attention between semantically similar regions while preserving local spatial consistency. When combined, these modules achieve a substantial $6.3\%$ mIoU improvement, reaching a mIoU of $86.0\%$ , demonstrating their complementary utility. Sensitivity analysis of hyper-parameters. In Fig. 6, we analyze sensitivity of two key trade-off hyper-parameters $\lambda_{rcs}$ and $\lambda_{sfr}$ . For $\lambda_{rcs}$ , optimal performance is achieved when $\lambda_{rcs} = 0.5$ . The parameter $\lambda_{sfr}$ demonstrates best re + +![](images/53d58e66e51dab8c2e573018455052f518183d895029dc1e9c95d0bc102c5764.jpg) +Figure 6. Analysis of hyper-parameters $\lambda_{rcs}$ and $\lambda_{sfr}$ . + +![](images/556237e99c92da432d5e33053a4511581c311da69dcb22af8f48734777d4ead9.jpg) + +Table 4. Analysis of layer fusion strategies in our method. + +
Fusion WaysVOC20Object
MethodsLayers
Cumulative Layers1 → 181.134.0
1 → 382.634.8
1 → 584.134.8
Aggregation1 → 784.834.9
1 → 985.535.0
Sliding Window2 → 584.234.8
4 → 785.034.7
6 → 986.035.0
Aggregation8 → 1185.834.8
+ +sults at 0.7, with stable performance in the range from 0.6 to 0.8. Both parameters exhibit similar trends: moderate values enhance performance while extreme values (e.g., 1.0) lead to degradation. This consistent behavior across different datasets suggests robustness of ResCLIP, requiring only coarse hyper-parameter tuning for effective deployment. + +Analysis of layer fusion strategies in RCS. As Eq. (5) shows, our RCS method averages attention from some layers. We explore two strategies for the aggregation $(\mathcal{A}_{qk})$ from non-last layers to capture the rich spatial correspondence. In Table 4, we compare aggregation methods: Cumulative Layers Aggregation (CLA) and Sliding Window Aggregation (SWA). CLA starts from the first layer to the $n$ -th while SWA applies a sliding window to aggregate attention where the window size is set to 4. From Table 4, we can observe that 1) for the CLA, the model increases the performance with more layers involved. 2) when leveraging the sliding window, the $6 \rightarrow 9$ achieves the best results. + +# 5. Conclusion + +In this paper, we introduce ResCLIP, a novel framework that enhances ability of CLIP for dense vision-language inference in a training-free manner. We discovered that attention from intermediate layers of CLIP exhibits class-specific features and localization properties. We propose two modules: Residual Cross-correlation Self-attention (RCS) and Semantic Feedback Refinement (SFR). These two modules not only provide rich spatial correspondence but also enhance the focus on the regions with the same semantics and local consistency to remold the attention in the last layer of CLIP. Extensive experiments show that ResCLIP improves performance across various benchmarks, demonstrating the effectiveness of the proposed method. + +# Acknowledgments + +This work is supported by National Natural Science Foundation of China (No. 62176047), Sichuan Science and Technology Program (No. 2022YFS0600), National Natural Science Foundation of China (No. 62476051) and Sichuan Natural Science Foundation (No. 2024NSFTD0041). + +# References + +[1] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelović, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. Self-supervised multimodal versatile networks. NeurIPS, 33:25-37, 2020. 3 +[2] Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. Vqa: Visual question answering. In ICCV, pages 2425-2433, 2015. 1 +[3] Nikita Araslanov and Stefan Roth. Single-stage semantic segmentation from image labels. 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Although sensor fusion architectures enhance performance in challenging environments, they still suffer significant performance drops under severe sensor failures, such as LiDAR beam reduction, LiDAR drop, limited field of view, camera drop, and occlusion. This limitation stems from inter-modality dependencies in current sensor fusion frameworks. In this study, we introduce an efficient and robust LiDAR-camera 3D object detector, referred to as MoME, which can achieve robust performance through a mixture of experts approach. Our MoME fully decouples modality dependencies using three parallel expert decoders, which use camera features, LiDAR features, or a combination of both to decode object queries, respectively. We propose Multi-Expert Decoding (MED) framework, where each query is decoded selectively using one of three expert decoders. MoME utilizes an Adaptive Query Router (AQR) to select the most appropriate expert decoder for each query based on the quality of camera and LiDAR features. This ensures that each query is processed by the best-suited expert, resulting in robust performance across diverse sensor failure scenarios. We evaluated the performance of MoME on the nuScenes-R benchmark. Our MoME achieved state-of-the-art performance in extreme weather and sensor failure conditions, significantly outperforming the existing models across various sensor failure scenarios. + +# 1. Introduction + +Accurate 3D perception is crucial for the safe and reliable operation of autonomous vehicles [1, 12, 30]. Multimodal perception systems enable more reliable understanding of environments by leveraging the complementary char + +![](images/648ff58f383a6f244db65f5acee81519bf4154fac7f3085219211e71adb37887.jpg) +Figure 1. Comparisons of several LiDAR-camera fusion methods. (a) Single decoder, (b) Separate decoder, and (c) Proposed MoME. MoME utilizes three parallel decoders, each processing camera features, LiDAR features, or a combination of both, to decouple dependencies between the modalities. It adaptively routes each query to the most suitable decoder based on the quality of the camera and LiDAR features. + +acteristics of different sensors [21, 22, 29, 33]. Each sensor modality brings distinct benefits: cameras capture rich semantic information, LiDAR provides precise 3D geometric details, and radar ensures reliable long-range detection even under adverse weather conditions. Consequently, sensor fusion plays a pivotal role in enhancing perception robustness. + +Recent advances in multi-modal perception have mainly focused on intermediate-level fusion strategies, which com + +![](images/1d46e372ab5f06c6d1355c9335e753c8a3cad5753c1653350324b00a9bdad105.jpg) +aee + +![](images/0a7bf078ca4e854c1a369bdc58c3b3efc67d4041783d045fac2dd277840cc613.jpg) + +![](images/59b3e8d1d727fcdf180187d21e262ae9b071096f5eace386df28a973e958201c.jpg) + +![](images/c92603366e154dd4cbbdb3632897abe6e04632a10a1a9427d3acc50c96d8696b.jpg) +seee eae + +![](images/9afd3a0d038c8c28d1489fd559858ff79b716b33f8b75866e0eee6ba0ec78366.jpg) + +![](images/b154fd4704111c5c5038af716a95ccf1c8784bcc786e1e3a519f7ba6364e0bf0.jpg) + +![](images/edfb962d19ce5f3bf01715bc06d46191df1af5bc63a8c9b9ca13ccafc4e972b4.jpg) +(e) MoME (Ours) + +![](images/88e0cd8ab96caa08222ffd66217ffee4fdc20c42701621cb1cd0a9ea35438d1e.jpg) +Figure 2. Comparison of predictions and performance of different fusion methods. Left: Examples of detection results for a single object. For visualization, red boxes indicate predictions from the LiDAR-camera decoder, blue boxes from the LiDAR decoder, and orange boxes from the camera decoder, with ground truth (GT) shown in black. Right: NDS performance across various scenarios—Clean, LiDAR drop, Limited FOV, and Camera drop. (a) Under sensor failure, predictions are prone to error due to the corrupted modality. (b) Due to uncalibrated confidence score scales, lower-quality predictions may have higher confidence scores. (c) The proposed method selects the optimal decoder for decoding each object query. + +![](images/b83f381ceecc177295d11f8d485640ca39b09048c3256310e84ca058603a0ee0.jpg) + +bine intermediate features extracted from multiple modalities [16, 21, 29, 31, 33, 36]. This fusion strategy can improve the quality of intermediate features, contributing to robust performance across various scenarios. However, their performance can degrade significantly when one sensor is affected by severe noise, occlusion, or failure. This limitation arises from inter-modal dependencies, where contamination in one sensor can impair the overall quality of multi-modal perception. Such dependencies are challenging to avoid in current fusion models, as utilization of high-level interactions between sensors is essential for effective information fusion. + +As autonomous vehicle safety becomes increasingly critical, ensuring robustness under sensor failure conditions has emerged as a key challenge in the field. Sensor failures encompass a range of real-world issues, including complete sensor malfunctions, partial impairments (such as a reduced field of view or decreased resolution), and adverse conditions (such as occlusion or contamination). These challenges can significantly degrade perception performance, even when sensor fusion methods are employed. + +Recent studies [9, 24, 25, 29] aimed to facilitate robustness to such sensor failures for 3D perception. MetaBEV + +[9] proposed a robust sensor fusion technique that applies successive cross-modal attention using multi-modal features. RobBEV [24] mitigated inter-modality interference by employing mutual deformable attention, where each modality queries features from the other and vice versa. UniBEV [25] aligned camera and LiDAR features adaptively through channel-normalized weights. CMT [29] employed position-encoded cross-attention for feature fusion, combined with masked-modal training. While these methods have effectively mitigated the impact of sensor failures, we argue that they have not fully resolved the issue, as the features from the two modalities remain coupled, leading to inevitable performance drops (see Fig. 2 (a)). Consequently, the performance of sensor fusion may often fall short of what could be achieved with a single, fully functioning sensor. + +This paper addresses the aforementioned challenges in LiDAR-camera fusion, a commonly used sensor suite in autonomous driving and robotics. Inspired by the Mixture of Experts (MoE) framework [19], which has been widely adopted in natural language processing to enhance model performance and efficiency, we introduce the Multi-Expert Decoding (MED) framework. In MoME, three parallel Transformer decoders, called expert decoders independently utilize camera features, LiDAR features, and their combination to decode shared object queries (see Fig. 1 (b) and (c)). This approach decouples modality dependencies, protecting the detector from the impacts of sensor failures. + +A straightforward way to utilize these expert decoders is to have them process the queries in parallel [4] and select the output based on a confidence score, as shown in Fig. 1 (b). However, this approach poses two major challenges. First, as illustrated in Fig. 2, the decoders operate independently, leading to uncalibrated confidence scores, which complicates fair comparison and results in suboptimal performance. Second, the decoding complexity is tripled, imposing a computational burden on 3D perception. Our study addresses these issues to present an efficient, robust sensor fusion architecture. + +In this paper, we propose a novel LiDAR-camera fusion model for 3D object detection, named Multi-mOdal Mixture of Expert (MoME), designed to be resilient under adverse sensor failure conditions. MoME builds upon DETR [3], utilizing a Transformer to progressively decode a fixed set of object queries into detection results across multiple layers. To enhance robustness, MoME incorporates the MED framework into DETR, where three parallel decoders are used as expert modules, as illustrated in Fig. 1 (c). + +To enable an efficient decoding process, MoME selectively assigns each object query to one of three expert decoders. This selection is managed by the Adaptive Query Router (AQR), which dynamically determines the most suitable expert based on the quality of LiDAR and camera + +features. AQR extracts positional information from each query and aggregates multi-modal features within a local region identified by the Local Attention Mask. It then applies cross-attention with these local features to compute modal selection probabilities, ensuring that each query is processed by the most appropriate expert decoder. By training with synthetic sensor drop augmentation, our MED framework learns to select the expert decoder that optimizes performance. Additionally, by assigning each query to only one of the three decoders, our approach maintains a decoding complexity comparable to that of a single decoder, as shown in Fig. 1 (a). + +We evaluated the performance of MoME on widely used nuScenes dataset [2]. We followed nuScenes-R benchmark [34], which includes six critical sensor failure scenarios. MoME achieved state-of-the-art (SOTA) performance across most sensor failure scenarios. Notably, compared to the latest SOTA method, CMT [29], MoME demonstrates significant performance gains, with $+4.2\%$ mAP in LiDAR-drop scenarios, $+1.9\%$ mAP in camera-drop scenarios, and $+6.7\%$ mAP in limited FOV scenarios. Additionally, MoME's superior performance under extreme weather conditions underscores its potential to enhance robustness in adverse real-world environments. + +The key contributions of our study are summarized as follows: + +1. We propose a new LiDAR-camera fusion architecture resilient to sensor failures. Our MoME method employs three parallel expert decoders that separately utilize camera features, LiDAR features, and a combination of both. This approach effectively decouples inter-modality dependence. +2. We propose a MED framework in which one of three decoders is selected to decode each query. To this goal, we devise an AQR model that produces the probability of selecting the expert decoder based on the quality of modality-specific features. +3. The multi-expert decoder structure in MoME is straightforward to implement and can be readily integrated into any Transformer-based feature fusion architecture. Furthermore, as each query is assigned to only one expert decoder, the computational overhead of MoME remains minimal. +4. MoME achieved SOTA performance among existing camera-LiDAR fusion methods under various sensor failure conditions and extreme weather scenarios. +5. The code will be publicly available. + +# 2. Related Works + +# 2.1. Sensor Failure + +Recent benchmarks [6, 11, 34] have introduced comprehensive evaluation protocols for sensor failures and degra + +dation, addressing the limitations of existing autonomous driving datasets that primarily focus on ideal driving conditions. Several approaches have been proposed to maintain robust perception under sensor failures. MetaBEV [9] employs modality-arbitrary BEV-evolving decoder with cross-modal attention, while UniBEV [25] proposes channel-wise normalization for BEV feature alignment. CMT [29] and MetaBEV [9] leverage sensor dropout as data augmentation to improve robustness against sensor failures. However, the joint multi-modal learning scheme in existing methods creates inter-modal dependencies, leading to cascading performance degradation under sensor failures. In this work, we propose MED framework that processes each modality independently, enabling selective handling of sensor corruption while preserving cross-modal complementarity. + +# 2.2. Mixture of Experts + +MoE [19] enables linear scaling of model capacity with minimal computational complexity by dynamically selecting top-K experts from a pool of independent networks. Each expert specializes in distinct patterns, facilitating efficient decomposition of complex tasks into specialized subnetworks. However, this multi-expert routing mechanism often leads to training instability and convergence issues. Switch Transformer [8] addressed these limitations by implementing single-expert routing, significantly improving training efficiency and scalability. The MoE approach has recently received attention in computer vision applications. V-MoE [17] extended the concept to Vision Transformers [7]. MetaBEV [9] leveraged MoE architecture to mitigate gradient conflicts in multi-task learning scenarios. + +In this work, we extends the MoE paradigm to multimodal perception tasks, by leveraging its capability to handle heterogeneous inputs through specialized expert networks. This approach naturally aligns with sensor fusion scenarios where input reliability varies dynamically. + +# 3. Proposed Method + +# 3.1. Overview + +The overall architecture of MoME is depicted in Fig. 3. We employ VoxelNet [35] as a backbone to encode LiDAR points $P_{l}\in \mathbb{R}^{M\times 3}$ . The network first discretizes $P_{l}$ into 3D voxels, then hierarchically extracts voxel features through a series of 3D sparse convolutions. The voxel features are then projected onto a BEV and processed through a series of 2D convolutional layers to generate BEV features $F_{l}\in \mathbb{R}^{H_{l}\times W_{l}\times D}$ , where $(H_{l},W_{l})$ is the size of BEV features and $D$ is the channel dimension. We utilize VoVNet [13] to encode multi-view camera images separately. It generates 2D multi-view camera features $F_{c}\in \mathbb{R}^{V\times H_{c}\times W_{c}\times D}$ , where $V$ is the number of camera views, $(H_{c},W_{c})$ is the size of 2D camera features, and $D$ is the channel dimension. These + +![](images/6df7ae0cb5fad9065c988a5c484b8ab1607e963b81fae3cd542f9686d603606c.jpg) +Figure 3. Overall structure of MoME. MoME utilizes three expert decoders, each specialized for processing LiDAR, camera, or LiDAR-camera features. The AQR dynamically assigns each object query to the most suitable expert decoder in an adaptive manner. The operation of AQR relies on local features filtered through the Local Attention Mask. + +![](images/4292c3ef3354f3d5b4341bbab139e67d1252047ec66cff2dca30802b511e9321.jpg) + +complementary features $F_{l}$ and $F_{c}$ are flattened into $F_{l}^{\prime}\in$ $\mathbb{R}^{(H_lW_l)\times D}$ and $F_{c}^{\prime}\in \mathbb{R}^{(VH_{c}W_{c})\times D}$ , respectively. These two flattened features are then concatenated to obtain the fused LiDAR-camera features $F_{lc}^{\prime}\in \mathbb{R}^{(H_lW_l + VH_cW_c)\times D}$ + +To produce detection results, MoME decodes object queries $Q \in \mathbb{R}^{N \times D}$ using $F_{l}^{\prime}, F_{c}^{\prime}$ , and $F_{lc}^{\prime}$ as keys and values. For robust decoding, we employ three expert decoders: the LiDAR decoder, the camera decoder, and the LiDAR-camera decoder. Specifically, the LiDAR decoder performs cross-attention using $F_{l}^{\prime}$ , the camera decoder uses $F_{c}^{\prime}$ , and the LiDAR-camera decoder uses $F_{lc}^{\prime}$ . The MED framework assigns each of the $N$ queries to one of the three expert decoders which is selected by the AQR module. AQR selects the appropriate decoder for each query based on local features pooled from $F_{lc}^{\prime}$ centered at the position indicated by each query. As a result, the MED framework partitions the queries into three groups, which are then processed by the LiDAR decoder, camera decoder, and LiDAR-camera decoder, respectively. Finally, the decoded queries are used to generate 3D bounding boxes and class scores. + +# 3.2. Multi-Expert Decoding + +The structure of the MED framework is illustrated in Fig. 3. The MED framework consists of two main components: (1) MED that employs three expert decoders capable + +of independently processing queries using LiDAR features, camera features, or a combination of both, and (2) AQR that dynamically assigns each query to the most suitable expert decoder in an adaptive manner. Each expert decoder adopts the decoder structure from DETR. + +Let $q_{i} \in \mathbb{R}^{1 \times D}$ represent the $i$ -th object query within the set $Q$ of object queries. The AQR processes both $q_{i}$ and the multi-modal features $F_{lc}'$ to produce the modal selection probabilities $\mathbf{p}_{i} = [p_{i,l}, p_{i,c}, p_{i,lc}]$ . The expert decoder responsible for decoding the $i$ -th query is determined based on the probability with the highest value. Consequently, the object queries are grouped into $Q_{c}$ , $Q_{l}$ , and $Q_{lc}$ , where + +$$ +Q _ {m o d} = \left[ q _ {i} \in Q \mid \arg \max (\mathbf {p} _ {i}) = m o d \right], \tag {1} +$$ + +and mod $\in \{l, c, lc\}$ . These query groups are decoded in parallel using the corresponding expert decoders, resulting in the updated queries $Q_c'$ , $Q_l'$ , and $Q_{lc}'$ . Finally, a Feed-Forward Network (FFN) is applied to these updated queries to predict the final detection results. + +# 3.3. Adaptive Query Router (AQR) + +AQR employs locality-aware adaptive routing to determine the most appropriate expert decoder for each query. This process begins by calculating a Local Attention Mask + +that identifies the local features in the LiDAR BEV and camera domains associated with the $i$ -th query. + +The construction of the Local Attention Mask is depicted in Fig. 3. The mask has the same dimensions as $F_{lc}^{\prime}$ and the elements have binary values. Let the $i$ -th object query $q_i$ be associated with a reference point $p_{i,ref} = (x,y,z)^T$ in 3D coordinates. This reference point is projected onto the LiDAR BEV domain resulting in $p_{i,ref}^{(l)} = (x_l,y_l)^T$ . Similarly, it is also projected onto one of the multi-view camera domains producing $p_{i,ref}^{(c)} = (x_c,y_c)^T$ . All elements of the Local Attention Mask are set to zero while those within an $l_l\times l_l$ window centered at $p_{i,ref}^{(l)}$ in the LiDAR BEV domain and within an $l_c\times l_c$ window centered at $p_{i,ref}^{(c)}$ in the camera view are set to one. + +Finally, AQR applies masked cross-attention, where the binary Local Attention Mask serves as the mask, the multimodal features $F_{lc}^{\prime}$ are used as the key and value, and the set of queries $Q$ is used as the query. A softmax function is applied to the output of each decoded query to compute modal selection probabilities, which are then used to assign the query to the appropriate expert decoder. + +# 3.4. Training Details + +To train MoME, it is crucial to guide the model to utilize the expert decoder unaffected by sensor failures. To achieve this, we randomly drop either the camera or LiDAR input during training, with each sensor having a $1/3$ probability of being dropped, and no sensor dropped for the remaining $1/3$ [29]. Although we simulate complete sensor failure during training, our approach is also effective in partial sensor failure scenarios, as the routing operation of AQR relies on local features identified by the Local Attention Mask. Consequently, the appropriate expert decoder is selected based on the local features pointed by each query. Furthermore, our experiments in the next section demonstrate that our method, trained solely under these synthetic drop conditions, generalizes well to other types of sensor failures. Notably, our method is data-scalable, as it does not require generating various types of sensor failures for training data. + +The training process consists of three stages. In the first stage, all object queries in $Q$ are processed in parallel by each expert decoder without applying sensor drop data augmentation. The decoded queries from each expert decoder are matched with GT through bipartite matching, and all expert decoders are simultaneously trained using the loss function + +$$ +\mathcal {L} _ {1 s t} = \mathcal {L} _ {l} + \mathcal {L} _ {c} + \mathcal {L} _ {l c}, \tag {2} +$$ + +where $\mathcal{L}_l$ , $\mathcal{L}_c$ , and $\mathcal{L}_{lc}$ represent the detection losses associated with LiDAR, camera, and LiDAR-camera decoders, respectively. We employ the focal loss [18] for classification and the L1 loss for box regression. + +In the second stage, we freeze the pre-trained expert decoders and focus on training the AQR module. During this stage, we simulate sensor failure scenarios by randomly dropping LiDAR or camera sensors. Supervisory labels are generated as $\mathbf{y}_i = [0,1,0]$ when LiDAR is dropped, $\mathbf{y}_i = [1,0,0]$ when the camera is dropped, and $\mathbf{y}_i = [0,0,1]$ when neither sensor is dropped. We train AQR using + +$$ +\mathcal {L} _ {2 n d} = \sum_ {i = 1} ^ {N} \operatorname {C E} \left(\mathbf {y} _ {i}, \mathbf {p} _ {i}\right), \tag {3} +$$ + +where CE denotes the cross entropy loss between the modal selection probabilities $\mathbf{p}_i$ and the experts label $\mathbf{y}_i$ . + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and metrics. We evaluate the performance of MoME using the nuScenes dataset [2] and its variants, nuScenes-R [34] and nuScenes-C [6]. nuScenes [2] is a driving dataset collected using a 32-beam LiDAR scanner operating at $20\mathrm{Hz}$ and six cameras providing $360^{\circ}$ coverage. In total, it consists of 1.4 million camera images, 390 thousand LiDAR sweeps, and 1.4 million annotated 3D bounding boxes across 40 thousand keyframes, with annotations at $2\mathrm{Hz}$ . The dataset includes 700 training scenes, 150 validation scenes, and 150 test scenes. + +nuScenes-R [34] is a variant of the nuScenes dataset, created by simulating sensor failures for LiDAR and camera inputs. In our experiments, we consider five types of sensor failure scenarios: + +- LiDAR Drop: All LiDAR point clouds are removed. +- Limited FOV: The scanning angle is restricted to a range of $-60^{\circ}$ to $60^{\circ}$ . +- Object Failure: LiDAR points within each bounding box are removed with a $50\%$ probability. +- Camera View Drop: All multi-view camera images are set to zero. +- Occlusion: Predefined mud masks are applied to the images. + +These scenarios enable us to evaluate models under different sensor failure conditions. + +nuScenes-C [6] systematically generates 27 types of common corruptions in 3D object detection for both Li-DAR and camera sensors. The corruptions are grouped into weather, sensor, motion, object, and alignment levels, covering the majority of real-world corruption cases. Our experiments consider extreme weather conditions including dense fog, snow, and sunlight glare. + +Our model was trained on the nuScenes [2] training set with simulated camera and LiDAR drop scenarios as described in Section 3.4. It was then evaluated on the nuScenes validation set, as well as on nuScenes-R [34] and nuScenes-C [6]. + +
MethodCleanPerf. Ratio (R)LiDAR failuresCamera failures
Beam Reduction 4 beamsLiDAR Drop allLimited FOV [-60, 60]Object Failure rate = 0.5View Drop 6 dropsOcclusion w obstacle
mAPNDSmAPNDSmAPNDSmAPNDSmAPNDSmAPNDSmAPNDSmAPNDS
DETR3D [28]34.943.420.533.4--------0.00.014.329.0
CenterPoint†[32]56.264.728.951.920.942.90.00.015.743.028.448.5----
UniBEV†[25]64.268.575.883.745.156.135.042.235.950.157.164.058.265.360.566.4
TransFusion [1]66.970.954.466.8--0.00.020.345.834.653.661.667.465.570.0
BEVFusion†[21]67.971.055.267.843.055.40.00.021.145.639.254.656.263.565.369.6
MetaBEV [9]68.071.575.482.5-57.739.042.6-47.0-67.663.669.2-70.0
BEVFusion†[16]68.571.462.172.546.457.30.24.022.045.863.268.058.866.164.869.4
DeepInteraction†[31]69.972.658.964.946.554.90.00.021.242.760.863.753.955.164.566.2
CMT†[29]70.372.978.484.454.962.238.344.743.954.066.770.461.768.165.069.8
UniTR†[23]70.573.354.868.547.759.60.11.522.448.138.355.660.467.462.768.9
SparseFusion†[36]71.073.162.471.349.859.60.00.024.045.665.269.559.767.267.271.0
MoME (ours)71.273.680.586.255.063.042.548.250.658.367.071.063.669.565.670.5
+ +We adopted two widely used performance metrics for nuScenes: mean Average Precision (mAP) and the nuScenes Detection Score (NDS). mAP was computed from a bird's-eye view over 10 object classes, with distance thresholds of $\{0.5m, 1m, 2m, 4m\}$ . NDS was obtained by combining mAP with mean errors in translation, scale, orientation, velocity, and attributes. Additionally, we evaluated the robustness using a relative performance ratio $R = mP_{R} / P_{C}$ , where $P_{C}$ denotes the clean performance and $mP_{R}$ represents the average performance across adverse conditions. The $mP_{R}$ is given by + +$$ +m P _ {R} = \frac {1}{N} \sum_ {i = 1} ^ {N} P _ {R} ^ {i}. \tag {4} +$$ + +where $N$ represents the total number of adverse cases considered and $P_{R}^{i}$ denotes the performance evaluated under the $i$ -th adverse condition among the $N$ cases. + +Implementation details. We adopt VoVNet [13] and VoxelNet [35] as the image and LiDAR backbones, respectively. In our architecture, the expert decoders utilize a 6-layer Transformer decoder with shared weights, while the AQR module consists of a single cross-attention layer. The attention mask sizes $l_{l}$ and $l_{c}$ were empirically set to 5 and 15, respectively. Our training procedure consists of two stages: We first trained the modality backbones and expert decoders for 20 epochs. Subsequently, we froze these networks and trained the AQR module for additional two epochs. While training the model, we employed Class-balanced Grouping and Sampling (CBGS) [37] and data augmentation, as suggested in [29]. The CBGS strategy was applied during the first stage only. For data augmentation, we considered random flipping along X and Y axes, rotation, scaling, translation, and ground-truth sampling. + +Table 1. Comparison under various sensor failure scenarios on nuScenes-R dataset. Italic denotes the degree of sensor failure. Note that DETR3D uses only cameras, while CenterPoint uses only LiDAR. †† indicates reproduced results using their open-source code. MoME achieves state-of-the-art performance across most tasks, significantly surpassing prior methods in the relative performance ratio R. + +
MethodModalityRainyNight
mAPNDSmAPNDS
BEVDet [10]C30.143.212.021.7
BEVFormer [14]C44.0-21.2-
PETR [15]C41.950.617.224.2
CenterPoint [32]L59.2-35.4-
Transfusion-L [1]L64.069.937.543.5
Transfusion [1]LC67.571.939.844.7
Deepinteraction [31]LC69.470.642.343.8
BEVFusion [16]LC69.9-42.8-
GraphBEV [20]LC70.2-45.1-
CMT [29]LC70.573.742.846.3
\( UniTR^†[23] \)LC71.174.436.643.3
\( SparseFusion^†[36] \)LC70.273.343.846.4
MoME (ours)LC72.274.843.046.6
+ +Table 2. Comparison under adverse weather conditions on nuScenes validation set. 'L' and 'C' represent camera, LiDAR, respectively. + +# 4.2. Performance Comparison + +Table 1 presents the performance of MoME on both the nuScenes validation set and the nuScenes-R dataset. Under sensor failure conditions, MoME significantly outperforms the latest robust sensor fusion methods designed to handle such failures, including MetaBEV [9], CMT [29], and UniTR [23]. MoME achieves substantial improvements in the relative performance ratio $R$ with gains of $+2.1\%$ and $+1.8\%$ over the previous SOTA method, CMT [29]. Notably, MoME demonstrates exceptional performance in limited FOV scenarios, surpassing CMT by $6.7\%$ in mAP and $4.3\%$ in NDS. These results highlight MoME's effectiveness in handling partial sensor failures, leveraging the local attention mask in AQR. + +Table 2 presents the performance of MoME under rainy + +
MethodModalityFogSnowSunlight
PGD [27]C12.82.322.8
FCOS3D [26]C13.52.017.2
DETR3D [28]C27.95.141.6
BEVFormer [14]C32.85.741.7
PointPillars [12]L24.527.623.7
SSN [38]L41.646.440.3
CenterPoint [32]L43.855.954.2
FUTR3D [5]LC53.252.757.7
Transfusion [1]LC53.763.355.1
BEVFusion [16]LC54.162.864.4
DeepInteraction [31]LC54.862.464.9
CMT [29]LC66.362.663.6
MoME (ours)LC67.963.565.2
+ +Table 3. Comparison under extreme weather conditions on nuScenes-C. + +
MethodCleanPerf. Ratio (R)Latency
MEAQRLAMmAPNDSmAPNDSms
70.372.978.484.4270
✓33.451.811399.5310
✓✓71.073.674.183.2274
✓✓✓71.273.680.586.2274
+ +and nighttime conditions on the nuScenes validation set. We used the same model as in Table 1 without retraining. Despite not being explicitly trained for these scenarios, MoME demonstrated superior performance. + +Under rainy conditions, where both LiDAR and camera sensors are significantly affected, MoME outperforms existing methods, achieving $72.2\%$ mAP and $74.8\%$ NDS. In nighttime conditions, MoME maintains competitive performance despite the challenges posed by low visibility. These results highlight MoME's adaptability to diverse weather conditions, with particularly strong robustness in rainy environments. + +Table 3 presents MoME's performance under extreme weather conditions on the nuScenes-C dataset. MoME consistently outperforms other methods, achieving mAP gains of $+1.6\%$ , $+0.9\%$ , and $+1.6\%$ over CMT under fog, snow, and sunlight conditions, respectively. + +# 4.3. Ablation Studies + +Contribution of Main Components. In this section, we analyze the contribution of each component to overall performance. Table 4 presents an ablation study conducted on the nuScenes validation set for the clean case and the nuScenes-R set for failure cases. + +We use the single decoder as our baseline, adopting the architecture of CMT [29]. When incorporating Multiple + +Table 4. Ablation studies on MoME components. ME denotes Multiple Expert decoders, AQR denotes Adaptive Query Router, and LAM indicates Local Attention Mask. + +
Allocated queriesLiDAR-Cam ExpertLiDAR ExpertCamera Expert
Clean94%0%6%
LiDAR Drop8%0%92%
Camera Drop0%100%0%
Limited FOV38%0%62%
Occlusion81%15%4%
Object Failure90%0%10%
Fog99%0%1%
Snow95%0%5%
Sunlight94%0%6%
Rainy99%0%1%
Night99%0%1%
+ +Table 5. Query allocation results across different failure scenarios. The table presents the percentage of query selections across different scenarios. + +Experts (ME), we utilize separate decoders without a routing procedure. Among the outputs from these decoders, we select one based on its confidence score. However, this approach leads to a significant performance drop due to uncalibrated confidence scores from independently optimized decoders. Although the relative performance ratio $R$ appears to improve, this is primarily due to a considerable decline in performance for the clean case, rather than an actual increase in robustness. + +Next, we introduce the AQR module, applying global attention while omitting the local attention mechanism of LAM. AQR effectively resolves the score calibration issue and restores performance by leveraging adaptive query routing. However, without LAM, the performance ratio $R$ does not surpass that of the baseline, suggesting that decoder selection is still suboptimal. + +Finally, enabling both AQR and LAM leads to a substantial improvement in the performance ratio $R$ , resulting in an increase of 6.4 in mAP and 3.0 in NDS. Consequently, our complete MoME model achieves an overall improvement of 2.1 in mAP and 1.8 in NDS compared to the baseline method. + +Notably, our proposed method increases latency by only $4\mathrm{ms}$ over the baseline, which is lower than $40~\mathrm{ms}$ of the parallel decoder with ME. This efficiency is attributed to the distributed query processing mechanism of MoME. + +Query Allocation Behavior of AQR. Table 5 presents the statistical distribution of decoder selection across various sensor failure scenarios. For each case, we count the number of queries assigned to each decoder by the AQR module. Under clean conditions, our AQR module predominantly routes $94\%$ of queries to the LiDAR-Camera expert, maximizing the benefits of sensor fusion. Notably, even in clean scenarios, $6\%$ of queries are allocated to the Camera expert, likely due to sparse LiDAR points for small or distant objects. + +In LiDAR Drop scenarios, the AQR module redirects $92\%$ of queries to the Camera expert, effectively avoiding + +![](images/516c6c247dfa3c6a7e42912e9cfcef0193e7574cab46e180d0afab295480a057.jpg) +Figure 4. Qualitative results under various sensor failure scenarios. Comparison of detection results under four challenging scenarios: LiDAR drop, Camera drop, Limited FOV, and Occlusion. MoME exhibits higher robustness and consistent results compared to CMT [29] + +![](images/2dfbda188f44ad875f426870acefc4607c8e1703f1c78218f6ebf7e3bbdac38b.jpg) + +![](images/ecb6257a8402d8a74065a6ca427488711bc1d9f8416adcaced68c9909e4e9457.jpg) + +![](images/43e28a1830ba47fda75997457675925059a5a1a467c74a0fa1662006db432b2c.jpg) + +the degraded modality. In Camera Drop scenarios, AQR allocates $100\%$ of queries to the LiDAR expert. For partial sensor degradation, such as Limited FOV, AQR assigns $38\%$ of queries to the LiDAR-Camera decoder and $62\%$ to the Camera decoder. In Occlusion scenarios, the model maintains robust performance by allocating $81\%$ of queries to the LiDAR-Camera decoder and $15\%$ to the LiDAR decoder. Environmental challenges such as fog, snow, and sunlight result in allocation patterns similar to those in clean conditions. However, instances where the Camera decoder is selected may play a critical role in ensuring robust performance. + +Qualitative Results. Fig. 4 presents qualitative results comparing our proposed MoME architecture with the SOTA method, CMT [29] across various sensor failure scenarios. While CMT is significantly impacted by sensor failures, leading to inaccurate detection results, MoME achieves more robust detection by leveraging multiple expert decoders, demonstrating the advantages of architectural independence. + +# 5. Conclusions + +In this paper, we introduced MoME, an efficient multimodal fusion framework designed to enhance robustness under sensor failure scenarios. Our approach adopts the Mixture of Experts concept to exploit redundancy in decoding camera and LiDAR features. Specifically, we employed three decoders—Camera, LiDAR, and Camera-LiDAR—that process camera features, LiDAR features, and both modalities, respectively. Our MoME framework selects the appropriate decoder for each query using AQR, which performs locality-aware routing based on local features identified by a local attention mask. + +To ensure robust performance, we trained the MoME model with random sensor dropouts, allowing it to adapt to missing camera or LiDAR inputs. Our evaluation on the nuScenes benchmark demonstrated that MoME achieves strong robustness across various sensor failure scenarios and adverse environmental conditions in the nuScenes-R and nuScenes-C benchmarks. Notably, our method established a new state-of-the-art performance. + +For future work, we aim to develop more effective training strategies to simulate diverse failure patterns, further enhancing robustness against rarely occurring sensor failures. + +# 6. Acknowledgements + +This work was partly supported by 1) 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)] and 2) the National Research Foundation (NRF) funded by the Korean government (MSIT) (No. RS-2024-00421129). + +# References + +[1] Xuyang Bai, Zeyu Hu, Xinge Zhu, Qingqiu Huang, Yilun Chen, Hongbo Fu, and Chiew-Lan Tai. Transfusion: Robust lidar-camera fusion for 3d object detection with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1090-1099, 2022. 1, 6, 7 +[2] 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. 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-0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:87df1b4603a72631007e7678da5d5fbce3bf9a6d89c8bf3ccebae4c4b971e0b2 +size 9658658 diff --git a/restorgsdepthawaregaussiansplattingforefficient3dscenerestoration/full.md b/restorgsdepthawaregaussiansplattingforefficient3dscenerestoration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..27f52871541dd114ba35522acb7d255c617dc690 --- /dev/null +++ b/restorgsdepthawaregaussiansplattingforefficient3dscenerestoration/full.md @@ -0,0 +1,443 @@ +# RestorGS: Depth-aware Gaussian Splatting for Efficient 3D Scene Restoration + +Yuanjian Qiao + +Mingwen Shao* + +Lingzhuang Meng + +Kai Xu + +Shandong Key Laboratory of Intelligent Oil & Gas Industrial Software, Qingdao Institute of Software, College of Computer Science and Technology, China University of Petroleum (East China) + +yjqiao@s.upc.edu.cn, smw278@126.com, lzhmeng1688@163.com, s23070014@s.upc.edu.cn + +![](images/43600f329a4ebbc16f8ca42ef078bc4c5e69f4f5b8a85de1159a7ce89d65f4b0.jpg) + +![](images/1e8b6c6dcc32126e06d614289359a597155c59e3fd581bc56cd57a2e3003b99a.jpg) + +![](images/c09d34c32b6b3d53da1ae7905bdc704f9400fbc4510d65a4072058c3aaf871c5.jpg) +Input + +![](images/3c2c7689251fc55634df02395c74fc1524746e46a79895be6775376509c6c547.jpg) + +![](images/dcead44cd65588ab95d52f021125de15cdb3c55c712858e52ddbd4742219a284.jpg) + +![](images/1e97f8a5435f7cb2f45f4b2993d9a7bcea7797efdcea8d9ae284e0e8733957ab.jpg) +Gaussian-DK +(a) Visual Results + +![](images/41d5340a2a56ee5d4fbdef8305a83e04f29f8c128af34ec025d5042cf8eff999.jpg) + +![](images/053a1a0a71fbb3c61b0a18cb9def7bad684eb82167edc1b8912598d979944414.jpg) + +![](images/525b056cb8f05ed187948c5e5e2fe1932c5ddf77adf5f76b0e919945e0d19e19.jpg) +WaterSpatting + +![](images/a22eabe24adeedee3c5164705f4179c66c8f96e0cc24f0b2a831ec7c5fdbe0be.jpg) + +![](images/bb2c450bb8f7d2a7f634d5077f3089ac8983ad2419661baaec60113ee2012447.jpg) + +![](images/28ede5a2ada355fbe09a41232777f29482ee3d697e5785f6b3576a1e9d758af0.jpg) +Ours + +![](images/5040e478336315e56aa07fa4d2e88a5caec84bb883a90fbfee43fe686b5c61a6.jpg) +(b) Quantitative Scores +Figure 1. We present RestorGS, a unified framework for 3D scene restoration that can handle multiple degraded scenes, including underwater, nighttime, and hazy situations. (a) and (b) show the visual results and quantitative scores of different methods, respectively. For a 3D degraded scene, RestorGS can produce high-quality restoration results. + +# Abstract + +3D Gaussian Splatting (3DGS) has recently achieved remarkable progress in novel view synthesis. However, existing methods rely heavily on high-quality data for rendering and struggle to handle degraded scenes with multiview inconsistency, leading to inferior rendering quality. To address this challenge, we propose a novel Depth-aware Gaussian Splatting for efficient 3D scene Restoration, called RestorGS, which flexibly restores multiple degraded scenes using a unified framework. Specifically, RestorGS consists of two core designs: Appearance Decoupling and Depth-Guided Modeling. The former exploits appearance learning over spherical harmonics to decouple clear and degraded Gaussian, thus separating the clear views from the degraded ones. Collaboratively, the latter leverages the depth information to guide the degradation modeling, thereby facilitating the decoupling process. Benefiting from the above optimization strategy, our method achieves high-quality restoration while enabling real-time rendering speed. Extensive experiments show that our RestorGS outperforms existing methods significantly in underwater, nighttime, and hazy scenes. + +# 1. Introduction + +Novel view synthesis has been a crucial task in the field of 3D vision, holding significant potential in various practical applications, such as virtual reality and robotic exploration [13, 42]. Over the past few years, Neural Radiance Field (NeRF) [30] has emerged as a promising technique for novel view synthesis through implicit scene representation. Despite the impressive results, original NeRF requires evaluating massive samples from a per-pixel field, which poses challenges to rendering speed and memory usage. To mitigate this issue, some NeRF variants attempt to speed up the rendering process by reducing sampling points or per-point computation cost [6, 17, 23, 33]. However, these solutions usually sacrifice rendering fidelity inevitably, particularly in handling large-scale scenes. + +Recently, 3D Gaussian Splatting (3DGS) [16] has attracted considerable attention by offering higher training efficiency while delivering pleasing rendering quality. Compared to the tedious volume rendering in NeRF, 3DGS explicitly projects 3D Gaussians onto 2D planes using efficient differentiable splatting for real-time rendering [7, 22, 29, 46]. Nevertheless, existing methods are heavily dependent on high-quality images and struggle to effectively process degraded scenes with inconsistent views, leading to un + +desirable rendering quality. To ameliorate this dilemma, several methods attempt to suppress degradation effects during rendering for underwater [21] and nighttime scenes [39]. However, such methods are usually tailored to a specific scene, greatly limiting their generalizability. Therefore, we pose a question: can we restore various 3D degraded scenes with a unified framework? + +To address this challenge, we delve into the shared physical properties of different degraded scenes. On the one hand, the degradation of an image primarily affects visual appearance such as color and illumination [27, 43]. This property can be extended to 3D scenes and intuitively motivates us to decouple the Gaussian into clear and degraded versions using the color-dependent spherical harmonics. On the other hand, the degradation density varies with the scene depth in underwater, nighttime and hazy situations. In particular, the farther the object is from the camera or light source, the more pronounced the light attenuation, i.e., the higher the degradation density. Inspired by this nature, we aim to optimize the Gaussian representation using depth-guided degradation modeling. + +Based on the above observations, in this paper, we propose a novel Depth-aware Gaussian Splatting for efficient 3D scene Restoration, named RestorGS, which flexibly restores diverse 3D degraded scenes using a unified framework. Specifically, RestorGS comprises two core designs: Appearance Decoupling and Depth-guided Modeling. The former embeds position and spherical harmonic information into the MLP to learn the color mapping of clean Gaussian, and introduces learnable degradation factors to optimize the degraded Gaussian. Such a paradigm is capable of facilitating Gaussian representation learning, thereby decoupling the clear background from the degradation effect adaptively. Collaboratively, the latter utilizes rasterized clear images and degraded features to estimate the attenuation and illumination maps guided by the depth information. Leveraging these physical priors, the original degraded view can be synthesized via physical modeling, thus optimizing the corresponding Gaussian attributes. Benefiting from this optimization mechanism, the proposed method achieves high-fidelity restoration while ensuring real-time rendering. Extensive experiments demonstrate that our RestorGS significantly outperforms state-of-the-art methods in various degraded scenarios, as shown in Fig. 1. + +The main contributions are summarized as follows: + +- We propose RestorGS, a novel Depth-aware Gaussian Splatting for efficient 3D scene restoration. To the best of our knowledge, this is the first unified framework for restoring multiple 3D degraded scenes. +- We design two collaborative optimization strategies: Appearance Decoupling and Depth-Guided Modeling. The former decouples clear and degraded Gaussians with color-dependent spherical harmonics, while the latter op + +timizes Gaussian representations leveraging depth-guided degradation modeling. + +- Extensive experiments suggest that our method significantly outperforms state-of-the-art methods both quantitatively and qualitatively in underwater, nighttime, and hazy scenes. + +# 2. Related Work + +# 2.1. 3D Scene Reconstruction + +NeRF-based methods. NeRF [30] has demonstrated outstanding capabilities in synthesizing novel views of various scenes by effectively encoding radiance and volumetric information into neural networks [12, 19, 25, 30, 36]. However, multi-view inconsistent scenes pose new challenges for NeRF, as they require modeling non-uniform variations in appearance. To address this issue, SeaThru-NeRF [20] integrates an underwater image formation model into the NeRF to learn the medium components. For varied exposure conditions, HDR-NeRF [11] models the physical imaging process to recover a high dynamic radiance field from low dynamic range views captured at different exposures. To render hazy scenes, ScatterNeRF [32] designs a separate representation for scattering volumes and scene objects. Despite significant progress, NeRF-based methods still face challenges regarding rendering speed and storage efficiency, hindering the practical applications. + +Gaussian-based methods. Recently, 3DGS [16] is gaining considerable attention in the field of 3D vision due to its impressive rendering quality and efficiency [24, 26, 38, 41, 45, 46]. Similar to NeRF, original 3DGS is primarily suited for high-quality scene, performing poorly under adverse conditions. To address this limitation, several methods have been proposed to reconstruct degraded scenes with inconsistent views [8, 14, 18, 35, 37]. For example, WaterSplatting [14] employs 3DGS to implement explicit geometric representation that captures the scattering media through independent volumetric fields. To cope with dark environments, Gaussian-DK [39] exploits camera response and light features to recover visually pleasing scenes from multi-viewpoint inconsistent images. Lately, LE3D [14] adopts a miniature MLP to represent the RAW linear color space to promote rendering quality. However, these methods are usually tailored to specific degraded scenes, leading to inferior scene generalizability. In contrast, we propose a depth-aware Gaussian splatting to restore multiple 3D degraded scenes in a unified framework. + +# 2.2. Physical-based Image Restoration + +Image restoration has been an essential task in the field of computer vision. To handle the degraded images captured in real-world scenes, various physical-based image restoration methods have been developed [5, 9, 15]. For instance, + +![](images/1eab51c0ed293b45c747b44ca47b69ec2a04abbb8c771ecfef27b3552aeb7afc.jpg) +Figure 2. Overview of the proposed RestorGS. Left: Appearance Decoupling. Each Gaussian is embedded into the color MLP to learn color mappings and a set of learnable degradation factors is exploited to decouple clear and degraded Gaussians. Right: Depth-Guided Modeling. The rasterized clear image and degraded features are then employed to estimate the physical components, thereby optimizing the Gaussian representation using depth-guided degradation modeling. + +GUPDM [31] introduces physical knowledge into a generalized dynamic network for underwater image restoration. To alleviate the ill-posed nature of image dehazing, C2PNet [44] proposes physical modeling in feature space based on atmospheric scattering models and customizes a curriculum learning strategy to optimize the model. Based on Retinex modeling theory, Retinexformer [4] develops a one-stage paradigm for low-light image enhancement. Different from these works that focus mainly on 2D images, we are dedicated to optimizing 3D Gaussians using physical modeling, thus enabling high-quality 3D scene restoration. + +# 3. Method + +The overview of the proposed RestorGS is displayed in Fig. 2, which contains two core designs: Appearance Decoupling and Depth-Guidance Modeling. The former decouples clear and degraded Gaussians utilizing color mapping and learnable degradation factors, while the latter optimizes Gaussian attributes by modeling degradation with depth information. Through the collaboration of these two strategies, our approach achieves high-quality 3D scene restoration and reconstruction. The following sections provide a detailed description of each component. + +# 3.1. Preliminary + +3DGS [16] is a cutting-edge technique for 3D scene reconstruction, offering substantial improvements in both rendering quality and efficiency. Unlike previous implicit neural representations that encode 3D scenes using position and view-dependent information [30], 3DGS explicitly represents the scene using a set of Gaussian ellipsoids for real-time rendering. + +The foundation of 3DGS is the 3D Gaussian function $G(x)$ , which represents the distribution of density and color across 3D space. The function is defined by the mean value + +$\mu \in \mathbb{R}^3$ and the covariance matrix $\Sigma \in \mathbb{R}^{3\times 3}$ , determining the shape and direction of the Gaussian: + +$$ +G (x) = e ^ {- \frac {1}{2} (x - \mu) ^ {T} \Sigma^ {- 1} (x - \mu)}. \tag {1} +$$ + +For efficient differentiable optimization, a scaling matrix $S \in \mathbb{R}^{3 \times 3}$ and a rotation matrix $R \in \mathrm{SO}(3)$ can be derived from the covariance matrix $\Sigma$ , which can be represented as: + +$$ +\Sigma = R S S ^ {T} R ^ {T}. \tag {2} +$$ + +As outlined in [47], the covariance matrix $\Sigma^{\prime}$ in the camera coordinates can be computed to render the image from a specified viewpoint by giving the viewing transformation matrix $W$ and the Jacobian matrix $J$ of the projective transformation. This process can be formulated as: + +$$ +\Sigma^ {\prime} = J W \Sigma W ^ {T} J ^ {T}. \tag {3} +$$ + +In general, the attributes of each Gaussian are represented by: position $x \in \mathbb{R}^3$ , color defined by the spherical harmonic coefficients $c \in \mathbb{R}^k$ , scale $s \in \mathbb{R}^3$ , rotation $r \in \mathbb{R}^4$ , and opacity $\alpha \in \mathbb{R}$ . Thus, the final color for each pixel is obtained by blending $N$ overlapping Gaussians: + +$$ +C = \sum_ {i = 0} ^ {N} c _ {i} \alpha_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {i}), \tag {4} +$$ + +where $\alpha_{i}$ and $c_{i}$ denote the opacity and color of the $i$ -th Gaussian. Ultimately, high-fidelity views can be rendered with real-time speed by iteratively optimizing the above Gaussian parameters. + +3DGS combines the advantages of efficient representation and high-quality rendering, allowing for the explicit reconstruction of 3D scenes. However, the original 3DGS relied heavily on high-quality data, making them difficult to + +efficiently model degraded scenes with multi-view inconsistencies. In our work, we intend to establish a unified framework that decouples scene representation by introducing physical modeling into 3DGS, thus enabling efficient 3D scene restoration. + +# 3.2. Appearance Decoupling + +Images taken in degraded scenes often suffer from significant appearance inconsistencies, and directly using 3DGS tends to produce levitation artifacts to compensate for these variations across views. Therefore, a flexible appearance learning strategy is crucial for restoring various degraded scenes. In response to this challenge, we propose to decouple scene appearance into clean background and degradation effects, as shown in Fig. 2. + +Specifically, given a Gaussian initialized with degraded views $G_{I} = \{\mu_{j},\Sigma_{j},\alpha_{j},SH_{j}\}$ , we embed center position $\mu_{j}$ and spherical harmonics $SH_{j}$ of the $j$ -th Gaussian into a color MLP to learn the appearance mapping from the original Gaussians to the clear ones: + +$$ +\eta , \delta = M L P (\gamma (\mu_ {j}), \gamma (S H _ {j})), \tag {5} +$$ + +where $\gamma (\cdot)$ denotes the positional coding introduced in NeRF [30]. $\eta$ and $\delta$ are the parameters of the affine transformation. Thus, the mapped clear color is denoted as: + +$$ +S H _ {j} ^ {c} = \eta \cdot S H _ {j} + \delta . \tag {6} +$$ + +To represent the degradation effect, we employ a set of learnable degradation factors as the spherical harmonics to initialize the degraded Gaussian. It is worth noting that except for the spherical harmonic, the other attributes of the degraded Gaussian share parameters with the clear Gaussian. The learnable degradation factors are expressed as: + +$$ +S H _ {j} ^ {d} = \left[ \theta_ {0}, \theta_ {1}, \dots , \theta_ {n} \right], \tag {7} +$$ + +where $\theta_{n}$ denotes the learnable parameter in the $n$ -th dimension. Hence, the original Gaussian decouples into two parts: the clear Gaussian $G_{C} = \{\mu_{j}, \Sigma_{j}, \alpha_{j}, SH_{j}^{c}\}$ and the degraded Gaussian $G_{D} = \{\mu_{j}, \Sigma_{j}, \alpha_{j}, SH_{j}^{d}\}$ . Finally, $G_{C}$ and $G_{D}$ are rasterized into a clean image and degraded features respectively for the following degradation modeling. + +# 3.3. Depth-Guided Modeling + +To facilitate Gaussian appearance decoupling, it is intuitive to utilize the corresponding clear views as supervised signals for optimizing the Gaussian representation [40]. However, such clear 3D views are generally inaccessible in real-world scenarios, making traditional supervised learning strategies unfeasible. In addition, the degradation effects often exhibit a non-uniform distribution with scene depth, increasing the complexity of the restoration process. + +To address this issue, we propose a depth-guided degradation modeling strategy to optimize the decoupled Gaussian in a self-supervised manner, as shown in Fig. 2. + +Specifically, inspired by the physical scattering theory [1, 10], we first uniformly model the scattering and illumination effects of different degraded scenes as: + +$$ +I (x) = \underbrace {J (x)} _ {\text {c o l o r}} \cdot \underbrace {A (x)} _ {\text {a t t e n u a t i o n}} + \underbrace {L} _ {\text {c o l o r}} \cdot \underbrace {(1 - A (x))} _ {\text {a t t e n u a t i o n}}, \tag {8} +$$ + +where $I(x)$ and $J(x)$ denote the degraded view and the clear view to be recovered, respectively. $L$ represents the scene illumination and $A(x)$ denotes the attenuation map, which is expressed as: + +$$ +A (x) = e ^ {- \beta d (x)}, \tag {9} +$$ + +where $d(x)$ denotes the scene depth and $\beta$ denotes the scattering coefficient. + +Subsequently, we employ rasterized 2D representation to estimate the physical components. In particular, the restored view $J(x)$ and the corresponding depth map $d(x)$ can be obtained by rasterizing the clear Gaussian. To stabilize the training, we normalize the depth map as: + +$$ +d _ {\text {n o r m}} (x) = \frac {d (x) - d _ {\text {m i n}} (x)}{d _ {\text {m a x}} (x) - d _ {\text {m i n}} (x)}, \tag {10} +$$ + +where $d_{max}(x)$ and $d_{min}(x)$ denote the maximum and minimum values of the depth map, respectively. With the normalized depth map, the attenuation map $A(x)$ can be derived using Eq. (9). Meanwhile, the degraded features can be attained by rasterizing the degraded Gaussian. Through a lightweight CNN, the degraded features $F_{d}$ are mapped into a illumination map guided by the attenuation map, which can be expressed as: + +$$ +L = f _ {C N N} \left[ F _ {d}, A (x) \right], \tag {11} +$$ + +where $[\cdot ]$ denotes the concatenation operation. By utilizing the estimated physical components, the original degraded view can be modeled using Eq. (8). + +With the collaboration of appearance decoupling and depth-guided degradation modeling, RestorGS can efficiently model 3D degraded scenes with multi-view inconsistencies. Unlike existing methods that primarily rely on high-quality data for rendering, our solution focuses on restoring multiple degraded scenes within a unified framework. This design enables our method to exhibit promising scene generalizability, thereby facilitating high-quality 3D scene restoration. + +# 3.4. Optimization + +During training, we jointly optimize the Gaussian parameters, color MLP, and CNN in an end-to-end manner. Following the original 3DGS [16], we apply $\mathcal{L}_1$ and $\mathcal{L}_{D - SSIM}$ + +Table 1. Quantitative comparison on the SeaThru-NeRF dataset [20]. The best and second-best score are marked as red and yellow, respectively. ↓: lower is better, ↑: higher is better. + +
MethodCuracaoIUI3 Red SeaPanamaJ.G. Red Sea
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
SeaThru-NeRF [20]30.190.8730.21025.900.7850.30427.840.8340.22421.840.7670.249
SeaThru-NeRF-NS [20]30.950.9150.13326.750.8260.16831.270.9370.07123.280.8760.111
ZipNeRF [3]19.950.4420.42116.930.4740.41219.010.3490.48219.020.3490.483
3DGS [16]28.310.8730.22122.980.8430.24529.200.8930.15221.490.8540.216
Gaussian-DK [39]30.760.9350.06028.190.9500.03224.670.8310.09123.210.8750.074
WaterSplatting [21]29.360.9150.14729.890.8920.21132.510.9410.08423.220.8690.149
Ours31.950.9440.05529.970.9520.02830.790.9320.04624.050.8820.071
+ +![](images/0a596b796604a77924f9df07af8c05c6e64abb4c2765379d142c44c30d5778a2.jpg) +Figure 3. Qualitative comparison of different methods on the SeaThru-NeRF [20] dataset. + +![](images/58b78f5d7cd3e67508cdc5a0f4cc474844039cd55a395d076387ba1659183d15.jpg) + +![](images/bcd0290931e7ef29ba2b9cfa0ffbfc266052202836d19acff48b539170de0613.jpg) + +![](images/aadd510477034efe4972405b824457d601a664668ca18f8a7abf5c7036914b0a.jpg) + +![](images/cbc9afa4ece614da51dd9d9bdabd58c70f6127f447099357f068ece9211ebd56.jpg) + +loss to measure the error between the rendered view and the input view, which can be represented as: + +$$ +\mathcal {L} _ {\text {r e c}} = (1 - \lambda) \mathcal {L} _ {1} + \lambda \mathcal {L} _ {D - S S I M}. \tag {12} +$$ + +To ensure that the generated image maintains a reasonable brightness distribution under different lighting conditions, we introduce an exposure loss to control the exposure level. More specifically, the exposure loss constrains the average brightness of the illumination map to be closer to the desired exposure value $E$ , thereby preventing underexposure or overexposure. This loss term can be expressed as: + +$$ +\mathcal {L} _ {e x p} = \frac {1}{N} \sum_ {k = 1} ^ {N} | L _ {k} - E |, \tag {13} +$$ + +where $N$ denotes the number of non-overlapping local regions and $L$ denotes the average exposure intensity of local regions in the estimated illumination map. Besides, the scene depth is estimated by an additional depth rasterization branch that projects Gaussians from the 3D scene to camera view and exploits the density properties of Gaussian distribution to generate per-pixel depth map. We employ an total variation loss to regularize the estimated depth information, + +making the depth map smoother: + +$$ +\mathcal {L} _ {\text {d e p t h}} = \sum_ {x, c} \left(| \nabla_ {h} d _ {c} (x) | ^ {2} + | \nabla_ {v} d _ {c} (x) | ^ {2}\right), \tag {14} +$$ + +where $d_{c}(x)$ denotes the learned scene depth. $x$ and $c$ denote the image pixels and color channels, respectively. $\nabla_{h}$ and $\nabla_{v}$ represent the horizontal and vertical gradient operations, respectively. Ultimately, the total loss is expressed as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e c}} + \lambda_ {1} \mathcal {L} _ {\text {e x p}} + \lambda_ {2} \mathcal {L} _ {\text {d e p t h}}, \tag {15} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are set to 10 and 0.001, respectively. + +# 4. Experiments + +Implementation Details: Our approach builds upon the original 3DGS [16] implementation utilizing the Pytorch platform. We use COLMAP [34] to estimate the camera positions of the images and then initialize the Gaussians. For color mapping, we employ 2-layer MLP with 128 features and add two additional heads to predict $\eta$ and $\delta$ . For the illumination map estimator, we adopt a 3-layer CNN to reduce computational complexity. We then optimize the Gaussian + +Table 2. Quantitative comparison on the Gaussian-DK dataset [39]. The best and second-best score are marked as red and yellow, respectively. ↓: lower is better, ↑: higher is better. + +
MethodAlleyFenceLivingroomStaircase
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF-W [28]21.590.6460.33123.970.7240.21422.430.7490.24323.960.8090.115
HDR-NeRF [11]17.870.5580.48819.660.5780.37220.770.6510.38518.070.5660.343
3DGS [16]16.440.6020.23218.990.5880.22619.970.7280.16718.300.5830.198
WaterSplatting [21]19.160.6960.25620.450.6240.28821.250.7670.20918.170.6430.232
Gaussian-DK [39]21.910.7730.14024.940.8010.13124.410.8260.12526.100.8850.068
Ours22.180.7810.13825.050.8030.12824.730.8300.08827.020.8820.067
MethodBicycleFlowerPianoTree
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF-W [28]23.560.7170.23821.660.6620.22325.440.8030.15721.660.6490.260
HDR-NeRF [11]19.950.6080.26718.540.5170.35921.520.6820.24018.580.5040.397
3DGS [16]19.270.6240.22016.170.5410.22618.780.5270.24819.870.5970.195
WaterSplatting [21]22.670.7260.38718.400.6320.22720.170.6830.27418.880.5460.288
Gaussian-DK [39]24.800.8090.13121.500.7280.13527.310.8330.10623.300.7650.134
Ours24.930.8110.12721.970.7420.12727.370.8370.10323.890.7930.123
MethodDormitoryKitchenStreetAverage
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF-W [28]24.510.8200.14924.840.8120.20522.850.6380.29323.320.7300.221
HDR-NeRF [11]21.230.6840.27922.270.7570.33821.200.5770.42419.970.6070.354
3DGS [16]20.530.6860.16118.680.6990.19617.040.5420.27118.550.6110.213
WaterSplatting [21]20.230.7240.21220.730.7700.24118.660.5860.30719.890.6720.265
Gaussian-DK [39]25.640.8570.08725.540.8440.11726.230.7890.14224.700.8100.120
Ours25.950.8590.08825.860.8540.09926.440.7930.14125.040.8170.112
+ +![](images/bd7dd5d5b88ffacd7e6666d7f0d83901815cf6fa2f363fe464ff8b00fcc23ff1.jpg) + +![](images/d84f8f7a2601bae57e0bc6778b7762f3c1365d14f82bad40624a0b4b49a5f281.jpg) + +![](images/9a99f7b30c211750c972d4d38f93f72dc9273b3975c1b28b7624d744fb5a53f5.jpg) + +![](images/665642860600bcc086e08fc84d45a756cd7fca452875f8d5ba07c54051d9b909.jpg) +(a) Input + +![](images/01077d5da65393623e4cd402b96f712838d4b76d8a032128f6a91fef12012c10.jpg) + +![](images/308bb6010333cd5ae4096fc747a22979ca84aee2deff9e9380866a5e18dbc67a.jpg) + +![](images/d516c1e5bff03310b416d309d9a8adffc276c56e3378885031e21cbdbc4c7090.jpg) + +![](images/b031fc441b4bedd354f6ebf031828118bcff0ac3016a654193b64639fc227b5b.jpg) +(b) 3DGS + +![](images/26a4fc9a7e6097e4bc53d5f170325e715d26adea1fd05584d13ff800fb20a613.jpg) + +![](images/c38c895a8f3d137d95ea4fee9f5782b02772987181d91bf8ef70d5f75850348d.jpg) + +![](images/7fd7e2d9b0c919add0c506993ad82922c4e6cf5d54ae23bbb9f603ec8b6c7b0d.jpg) + +![](images/d913324c455a3e3759e9e43d7c07c1cf92dbbc02bb7a8b4db65918de140cf64c.jpg) +(c) WaterSpatting + +![](images/055c4084402975e407b5ae187f969d977ef8ed690d45ca95c8f005afdd43d722.jpg) + +![](images/d2ef7e4467c1af9a11a0b856a4a14e53d59adc5ced70b718c73702ccca29780b.jpg) + +![](images/42bf2d0f6b7a3c57cf06fa7cffee666553aca24f006fce8cb7a835274e7f70c7.jpg) + +![](images/ebbad0a66a9f8c669d358411ba0fc5fba2d60c099161c31e70cb23129e4cd486.jpg) +(d) Gaussian-DK +Figure 4. Qualitative comparison of different methods on the Gaussian-DK dataset [39]. + +![](images/3223a8755f7b2ebc7facf88da5df33f1c04d61468d0a924b4a389d25af85d5bc.jpg) + +![](images/121b990b84dab0b6e18b6283970dd00e8d4d4054adb27876786aa2b8fa6e58c0.jpg) + +![](images/061cbc5496d85568bffb35d9db492da103334fd35f3c65a774c72e3d415ee356.jpg) + +![](images/4f050b2088258aee92e85ccfc614d661c36d5efeff1f26c68535299b20c8d651.jpg) +(e) Ours + +attributes using the same settings as the 3DGS. The Gaussian is densified and pruned every 100 iterations according to adaptive density control. We take independent Adam optimizers to update the color MLP and CNN with a learning rate of 0.001 and 0.0005, respectively. For each scene, we jointly optimize each part of RestorGS for 15000 iterations on a single NVIDIA RTX 2080Ti GPU. + +Datasets: We employ the SeaThru-NeRF [20], Gaussian- + +DK [39], and Mip-NeRF360 [2] datasets for evaluating underwater, nighttime, and hazy scenes, respectively. To be specific, (1) the SeaThru-NeRF dataset comprises real-world data collected from four different ocean scenes: the Curacao, IUI3 Red Sea, J.G. Red Sea, and Panama. These scenes contain 20, 29, 20, and 18 images respectively, of which 17, 25, 17, and 15 are used for training and the remaining 3, 4, 3, and 3 are utilized for validation. (2) + +![](images/339e9dbc820d3332aa30ece4cf339cb82e5a8ff855735ee681f7150a25eab04c.jpg) +(a) Input + +![](images/e938f6881d1953a54b0df6751d1531c605b61596c19f3eca045ba78318031e75.jpg) +(b) 3DGS + +![](images/7baa934cb17eab8d591d0d7d52ef8dd44ce4888e4a0278ca88e9a3ea572a74a4.jpg) +(c) Gaussian-DK + +![](images/e1c9032bbc9cf7e8c415b84b336291218097e7232e1c05064dc03552cbfa0bc9.jpg) +(d) WaterSplatting + +![](images/1e6e1b9bd59edf48937632c81bcba17cd49bc343bb2aaeea818dc8b1cf79df75.jpg) +(e) Ours +Figure 5. Qualitative comparison of different methods on the Mip-NeRF360 dataset [2]. + +Table 3. Quantitative comparison on Mip-NeRF360 dataset [2]. The best and second-best score are marked as red and yellow, respectively. $\downarrow$ : lower is better, $\uparrow$ : higher is better. + +
MethodGardenBicycle
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
3DGS [16]25.820.8910.08422.350.7120.215
Gaussian-DK [39]27.740.8860.07124.390.8070.172
WaterSplatting [21]27.820.8850.12822.670.7260.386
Ours28.320.8970.05624.860.8090.162
+ +The Gaussian-DK dataset includes a total of 12 nighttime scenes, with 5 indoor and 7 outdoor settings. Each scene comprises roughly 80 to 130 sRGB images captured from various viewpoints. (3) The Mip-NeRF 360 dataset contains 7 scenarios, of which 2 outdoor scenes Garden and Bicycle are utilized to evaluate performance in hazy scenes. We employ modified 3DGS to estimate the depth map for each view and combine $\beta \in [0.1, 0.8]$ and $L \in [0.45, 0.6]$ to synthesize inconsistent hazy views. + +Baselines and Metrics: We compare our RestorGS with the most relevant methods, including SeaThruNeRF [20], ZipNeRF [3], HDR-NeRF [11], NeRF-W [28], 3DGS [16], Gaussian-DK [39] and Waterspaltting [21]. Due to the lack of corresponding clear versions of each degraded views in the real-world scene, we employ the reconstruction results of degraded views for quantitative comparison and adopt the restoration results for qualitative analysis. All methods are performed in the same settings for fair comparisons. + +# 4.1. Comparison with SOTAs + +Underwater Scenes. The quantitative scores of different methods on the SeaThru-NeRF dataset [20] are presented in Table 1. It can be seen that our RestorGS outperforms other methods across multiple evaluation metrics. Compared to WaterSpalting [21], which focuses on underwater + +scenes, our method achieves significant gains of 2.59 dB and 0.83 dB in PSNR for the Curacao and J.G. Red Sea scenes, respectively. Although there is a slight inferiority in the Panama scene, RestorGS achieves an average PSNR improvement of 0.45 dB across the four tested scenes. The restored visual results are shown in Fig. 3. Existing methods often struggle to maintain consistent brightness and accurate color, particularly in deep water areas where images frequently exhibit uneven brightness and darkening. Such limitation mainly due to insufficient modeling of light scattering effects. In contrast, our RestorGS exhibits a better balance between brightness and texture details. This is mainly attributed to the proposed optimization mechanism, which adaptively adjusts brightness and color to produce more natural renderings. + +Nighttime Scenes. Table 2 reports the comparison of different methods on the Gaussian-DK dataset [39]. It can be noticed that our scheme shows significant superiority in both PSNR, SSIM, and LPIPS metrics for different scenes. Despite being tailored for nighttime scenes, Gaussian-DK [39] shows a $0.34\mathrm{dB}$ performance drop in the average PSNR across all scenes. The possible reason is that it neglects the depth information where the brightness generally becomes darker as the distance from the light source increases. The visual comparison in Fig. 4 further confirms the advantage embodied in the numerical results. As can be observed, the rendered results of 3DGS present prominent floating artifacts and fails to enhance the scene effectively. While Gaussian-DK [39] globally enhances the brightness and alleviates the effects of view inconsistency, it suffers from local detail loss and color shifts. In contrast, our method not only adapts to uneven lighting variations but also excels at capturing texture details in nighttime scenes. + +Hazy Scenes. Table 3 compares the quantitative results + +![](images/6bc4dc987e1043cf4b2a3d38a87e7dbf6a3de69537c8cd411951e61f645104c3.jpg) + +![](images/3ca9b86107ae30a8b9c70a845c4351c9b4dd9a1c9e7e8c04dee27b04cee3d2f4.jpg) + +![](images/3a31cb0c72b565a75f3fbd5dbee8b865ba183cd2106b15d4700d71ecf33b5340.jpg) + +![](images/1292d5d36caa5ee036993754115a83551ab51c7fb3f3392a408a1aff0261f9c1.jpg) +(a) Input +(d) w/o Physical Modeling +Figure 6. Visual results of each ablation study. The full model exhibits better color correction and detail recovery. + +![](images/c5c93b04a954a084f225fd54a76a5e383f58ada61694b80bf0de3361ece2fddb.jpg) +(b) w/o Appear. Decoupling +(e) w/o Depth Guidance + +![](images/7c4f1ee45b0dc8de0adfbe81b7a19150e59cc3777ebbbfe9dad8a5d860e5ad5c.jpg) +(c) w/o Color Mapping +(f) Ours + +Table 4. Ablation results of each module. The best and second-best score are marked as red and yellow, respectively. $\downarrow$ : lower is better, $\uparrow$ : higher is better. + +
AblationPSNR↑SSIM↑LPIPS↓
w/o Appear. Decoupling28.460.9180.071
w/o Color MLP28.830.9220.067
w/o Physical Modeling28.620.9190.064
w/o Depth Guidance29.050.9260.055
Full model (Ours)29.190.9280.050
+ +of various methods on the Mip-NeRF360 dataset [2]. We conduct our analysis on the Garden and Bicycle scene as the outdoor scenarios are more consistent with real-world degradation patterns. It can be observed that our RestorGS achieves the optimal performance across all metrics, indicating the notable superiority of our scheme in hazy scenes. + +Fig. 5 displays a visual comparison of our RestorGS with competing methods. It can be noticed that the images recovered by the existing methods suffer from obvious haze residues or artifacts, while our outcome better preserves the texture and structural information of the images. + +# 4.2. Ablation Studies + +Effectiveness of Appearance Decoupling. We validate the contribution of the appearance decoupling module in Table 4 and Fig. 6. Specifically, $w / o$ appears. Decoupling denotes that the appearance decoupling strategy is not applied, i.e., the degraded Gaussian is removed and the appearance mapping is learned directly. It can be seen that this variant exhibits performance drop in the reconstruction results due to the lack of adaptability to multi-view inconsistencies and cannot effectively repair the degraded scene due to the lack of suitable appearance constraints. Meanwhile, $w / o$ Color MLP represents that the color MLP is not employed to learn the affine transformation and only the original parameters related to the spherical harmonics are updated. Despite the feasible results achieved, this variant weakens the appearance modeling capability for complex scenes, leading to some floating artifacts in the restored views. These results reveal the essential role of appearance decoupling strategies in our RestorGS. + +![](images/e646a8ea890ac2f9ad702cbb46ceda5a2037ce668b0deca67fad86ca3ec1f3b2.jpg) + +![](images/8879efffaa5cabf241a344fead932e767ed220d6f2403c6fdcdf97e12a0a565c.jpg) + +![](images/cbcd955dc4695146869ef55405328959492072753da7a3f3146061b3abe9293b.jpg) + +![](images/ac2e957caa8dd15176b9e497222f88b4f333fab2debf6e7076225876e069ae02.jpg) +(a) Input +(d) Illumination Map +Figure 7. Visualization results of the learned physical components. + +![](images/0f68d7c8b55d865cec00870b9294a2db6d5d535405c280599989f98293c406d9.jpg) +(b) Depth Map +(e) Restored + +![](images/1fc14fb8cc4cca78c10d0fa0e9273f7ca317731f1ef8a1d535ac15f1a87741e6.jpg) +(c) Attenuation Map +(f) Rendered + +Effectiveness of Depth-Guided Modeling. We conduct ablation studies in Table 4 and Fig. 6 to verify the effectiveness of depth-guided modeling. Specifically, $w / o$ Physical Modeling indicates that we employ a simple summation operation instead of physical modeling. It can be observed that this variant shows severe pixel distortion in the restored results. In addition, the $w / o$ Depth Guidance indicates that we remove the depth-based attenuation map in the process of predicting the illumination map. Although only a slight quality degradation in the rendered degraded view is exhibited, the corresponding restoration occurs with noticeable color artifacts. The reason is that the lack of depth information leads to inaccurate illumination estimation, which in turn affects the color and detail recovery. Overall, these ablations emphasize the important role of physical modeling and depth guidance for scene restoration. + +Visualization of Physical Components. We visualize the learned depth map $d(x)$ , attenuation map $A(x)$ , and illumination map $L$ in Fig. 7. It can be observed that each physical component can accurately reflect the changes of degradation with scene depth. In addition, our method is also effective in restoring and reconstructing the degraded viewpoints. By leveraging these physical components, our approach can recover fine details in heavily degraded regions. These results demonstrate the effectiveness of the proposed physical modeling paradigm. + +# 5. Conclusion + +In this paper, we propose a novel Depth-aware Gaussian Splatting, called RestorGS, for efficient 3D scene restoration. In contrast to existing methods that are tailored to specific scenes, we develop a unified framework to handle multiple degraded scenes flexibly. The proposed RestorGS contains two core designs: Appearance Decoupling and Depth-guided Modeling. The former decouples clear and degraded Gaussian by leveraging appearance learning over spherical harmonics, while the latter optimizes the Gaussian representation through depth-guided degradation modeling. Extensive experimental results show that our method significantly outperforms existing methods both qualitatively and quantitatively across various degraded scenes. + +Acknowledgement. This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFA1000102), the National Natural Science Foundation of China (Grant Nos. 62376285 and 61673396), and Natural Science Foundation of Shandong Province, China (Grant No. ZR2022MF260). + +# References + +[1] Derya Akkaynak and Tali Treibitz. A revised underwater image formation model. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6723-6732, 2018. 4 +[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. 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However, the inherent 77-token input limitation and reliance on predominantly short-text training data restrict its ability to handle long-text tasks effectively. To overcome these constraints, we propose LongD-CLIP, a dual-teacher distillation framework designed to enhance long-text representation while mitigating knowledge forgetting. In our approach, a teacher model, fine-tuned on long-text data, distills rich representation knowledge into a student model, while the original CLIP serves as a secondary teacher to help the student retain its foundational knowledge. Extensive experiments reveal that LongD-CLIP significantly outperforms existing models across long-text retrieval, short-text retrieval, and zero-shot image classification tasks. For instance, in the image-to-text retrieval task on the ShareGPT4V test set, LongD-CLIP exceeds Long-CLIP's performance by $2.5\%$ , achieving an accuracy of $98.3\%$ . Similarly, on the Urban1k dataset, it records a $9.2\%$ improvement, reaching $91.9\%$ , thereby underscoring its robust generalization capabilities. Additionally, the text encoder of LongD-CLIP exhibits reduced latent space drift and improved compatibility with existing generative models, effectively overcoming the 77-token input constraint. + +# 1. Introduction + +Recent advancements in vision-language models have significantly propelled multimodal learning, enabling more precise alignment between images and textual descriptions. Among these models, CLIP (Contrastive Language-Image Pretraining) [20] has emerged as a powerful approach due to its unique ability to perform zero-shot learning [7, 23, 24], + +![](images/82516d388ed747fbc5479f520fc409bde1f918388fac38a2dcc650e5f70c6cf4.jpg) + +![](images/4deb6f346d425c236363477435bc767d881dec5905c11b1b66490a2c6ef375fe.jpg) +Figure 1. Performance curves for long-text retrieval and zero-shot classification during CLIP fine-tuning on the long-text image dataset ShareGPT4V. Values represent the average across our test datasets. + +effectively transferring knowledge across a wide range of tasks. This versatility spans applications from image classification [1] to more complex tasks like image-text retrieval [17], where the model demonstrates strong adaptability to varied content. CLIP's approach centers on a contrastive learning objective, which facilitates the learning of joint representations of images and concise text descriptions, such as captions or short phrases. Through this mechanism, CLIP has achieved robust performance in associating images with short text prompts. However, despite its strength with brief descriptions, CLIP's effectiveness diminishes when dealing with longer detailed text inputs. + +Long-text inputs challenge models like CLIP, which are mainly trained on short descriptions. The DCI dataset [25] allows evaluation of vision-language models on detailed, + +mask-aligned visual descriptions, serving as a fine-grained benchmark to reveal the strengths and weaknesses of CLIP-style models on densely annotated data. Another critical challenge is CLIP's text encoder, which uses a learnable absolute positional embedding capped at 77 tokens, limiting input length. This fixed-length tokenization can lose important semantic details in longer texts, reducing the model's ability to grasp extended narratives. Recent work, Long-CLIP [32], shows that only the first 20 positional embeddings in CLIP's text encoder are effectively trained. To overcome this, Long-CLIP linearly interpolates the remaining embeddings, expanding the input capacity to 248 tokens for more comprehensive long-text processing. + +However, while fine-tuning enhances CLIP's capability in representing long text, an unintended phenomenon—knowledge forgetting—emerges. Specifically, as the model's long-text retrieval performance improves, its zero-shot classification accuracy deteriorates. This tradeoff indicates that augmenting one ability may inadvertently lead to the erosion of critical, previously acquired knowledge. As illustrated in Figure 1, the performance curves of long-text retrieval and zero-shot classification exhibit a clear inverse relationship during fine-tuning. In our experiments, we extended CLIP's input limit and trained it for 10 epochs on the ShareGPT4V dataset [3], evaluating both long-text retrieval and zero-shot image classification after each epoch. The results reveal that while long-text retrieval benefits, the image classification accuracy declines by approximately $2\%$ . These findings are based on averages across multiple test datasets: long-text performance was measured on ShareGPT4V [3] and Urban-1k [32], and zero-shot image classification was evaluated on ImageNet-1K [5], ImageNet-V2 [21], ImageNet-O [9], CIFAR-10 [11], and CIFAR-100 [11]. + +To tackle these challenges, we propose a dual-teacher network distillation approach that enhances CLIP's long-text representation while mitigating knowledge forgetting. First, we extensively fine-tune a CLIP model on a long-text image dataset, thereby creating a teacher network with a strong ability to capture detailed long-text and image information. Although this teacher may suffer from some degree of knowledge forgetting, it excels in representing long-text semantics. Next, we employ knowledge distillation to train a student network using both the long-text-enhanced teacher and the original CLIP model as instructors. This dual-teacher framework allows the student to inherit the long-text proficiency from the fine-tuned teacher while preserving the broad, foundational knowledge of the original model, effectively achieving a balanced performance. + +# The contributions of this paper are threefold: + +(1) Enhanced long-text representation: We significantly improve CLIP's ability to handle long-text inputs, achieving superior performance in retrieval tasks requiring + +detailed comprehension. + +(2) Reduced knowledge forgetting: Our approach minimizes knowledge forgetting, preserving zero-shot classification accuracy while enhancing long-text processing capabilities. +(3) Improved latent space alignment: We mitigate latent space drift in text embeddings, ensuring better compatibility with image generation models. + +# 2. Related Work + +# 2.1. VLMs Knowledge Distillation + +Most VLM knowledge distillation methods focus on adapting image-level representations to region- or pixel-level tasks, such as object detection [4, 6, 8, 28] and semantic segmentation [15, 29, 35]. For example, ViLD [8] distills VLM knowledge into a two-stage detector by aligning its embedding space with that of the CLIP image encoder, while CLIPSeg [16] uses a lightweight transformer decoder to extend CLIP for segmentation tasks. LSeg [12] enhances segmentation by correlating CLIP text embeddings with pixelwise embeddings from segmentation models. ZegCLIP [35] leverages CLIP to produce semantic masks, incorporating a relationship descriptor aimed at mitigating overfitting on base classes. MaskCLIP+ [34] and SSIW [31] use pixel-level pseudo labels predicted by vision-language models (VLMs) as a basis for knowledge distillation. FreeSeg [19] initially generates mask proposals, then performs zero-shot classification on each mask individually. + +These methods rely on both image and text embeddings to effectively transfer CLIP's pre-trained knowledge to downstream tasks. We introduce a dual-teacher distillation strategy to overcome CLIP's long-text representation limitations, maintaining zero-shot generalization while enhancing long-text processing for diverse downstream tasks. + +# 2.2. Contrastive Vision-Language Models with Long Captions. + +Contrastive vision-language models like CLIP [20], ALIGN [10], and BLIP [13] have significantly advanced visual-text alignment by leveraging large-scale contrastive learning, achieving strong performance in tasks like image-text retrieval and zero-shot classification [26, 27]. However, these models are typically limited to short, global text descriptions due to restricted context windows, such as CLIP's 77-token limit. + +Building on this insight, DCI [25] proposes that "A Picture is Worth More Than 77 Text Tokens" and introduces the Densely Captioned Images (DCI) dataset, comprising 7805 natural images with human-annotated, mask-aligned descriptions that average over 1000 words each. Additionally, it evaluates CLIP-style models on these dense captions. DreamLIP [33] uses a pre-trained Multi-modality + +![](images/c6738c955245464b6d084e6ff49fb8f4df2a94d1947a4c0a43cc64f55e67dedc.jpg) +Figure 2. Overall framework of our two-stage dual-teacher distillation method. First, a highly performant CLIP model is fine-tuned on long-text and image data to serve as the teacher model. Then, the text and image encoders are distilled separately. The student text encoder is trained to handle both long-text and short-text tasks, while the student image encoder learns the teacher model's ability to capture fine details, with measures in place to prevent knowledge forgetting. + +Large Language Model (MLLM) to generate detailed captions for 30M images and investigates these captions within a contrastive learning framework. It dynamically selects sub-captions from text labels to create multiple positive pairs, aligning each sub-caption's embedding with its related local image patches in a self-supervised manner. With training on 30M image-text pairs, DreamLIP matches or even outperforms CLIP, which was trained on 400M pairs. However, DreamLIP's latent space is distinct from CLIP's, which restricts its compatibility with pre-trained modular CLIP components in downstream tasks. Long-CLIP [32] modifies CLIP by extending the absolute position encodings to 248 through interpolation and fine-tuning on long captions. However, Long-CLIP's primary component matching approach limits the model's ability to learn effectively from long text data and leads to slight knowledge forgetting. + +Our approach tackles the issue of long-text representation in CLIP by employing a dual-teacher distillation strategy, which maintains CLIP's zero-shot generalization capabilities while enhancing its ability to process long-text inputs effectively. + +# 3. Method + +First, we extensively train the CLIP model on a long text-image dataset, designating it as the teacher network in our distillation process. While this teacher model may experience some degree of knowledge forgetting, it demonstrates strong capabilities in representing long text and capturing intricate image details. We then perform knowledge distillation, enabling the student network to learn from both the long-text-enhanced teacher model and the original CLIP model, thereby enhancing the student model's overall performance. + +# 3.1. Long Text Teacher Network Training + +In the first step of our method, we train a long-text version of the CLIP model, which will serve as the teacher network in subsequent steps. This process begins by initializing the model with weights from the original CLIP. The training phase relies solely on contrastive learning to fully adapt the model. Notably, the original CLIP supports only 77-token text inputs. To extend the input length, we apply the same initialization approach as Long-CLIP, retaining the first 20 + +positional embeddings and using linear interpolation of the positional embeddings to extend the text encoder's maximum input length to 248 tokens. + +# image Encoder - Vision Transformer +# text Encoder - Text Transformer +# [n, h, w, c] - minibatch of aligned images +# T[n, l] - minibatch of aligned texts +# extract image and text features +I_f = image Encoder(I) # [n, d_i] +T_f = text Encoder(T) # [n, d_t] +# normalize image and text embeddings +I_e = I_f / I_f(norm(dim=1, keepdim=True) +T_e = T_f / T_f(norm(dim=1, keepdim=True) +# get batchsize +batch_size = I_e.shape[0] +# compute cosine similarities +logits_per_i = torch/matmul(I_e, T_e.T) +logits_per_i = logits_per_i * (logit_scale.exp()) +logits_per_t = logits_per_i.T +# compute loss +labels = torch.arange(batch_size) +loss_i2t = F.cross_entropy(logits_per_i, labels) +loss_t2i = F.Cross_entropy(logits_per_t, labels) +loss = (loss_i2t + loss_t2i) / 2 + +Figure 3. Torch-like pseudocode for contrastive learning implementation of long-text teacher model. + +In Figure 3, we present the pseudocode related to contrastive learning. Through contrastive learning with long-text inputs, the model learns to capture fine-grained information within both long texts and images. The contrastive training process is identical to that of CLIP [9]. + +# 3.2. Dual-teacher Distillation Learning + +At this stage, we have two models: one with enhanced long-text representation capabilities and the original model, which retains extensive pre-trained knowledge. We use both models as teacher networks in our knowledge distillation process. By leveraging the unique characteristics of the text encoder (Transformer) and image encoder (ViT), we apply tailored distillation strategies for each. + +# 3.2.1. Text Encoder Multi-task Distillation + +To produce robust embeddings for both long-text and short-text tasks, we train the student network's text encoder via knowledge distillation using two teacher networks: the long-text CLIP encoder, which strengthens the student's long-text representation, and the original CLIP text encoder, which preserves the base model's knowledge. + +As shown in Figure 2, the long-text embedding $\mathbf{u}^L$ is from the long text encoder, while the short-text embedding $\mathbf{u}^O$ is from the CLIP text encoder. The student text encoder receives short and long texts, outputting embeddings $\mathbf{u}^{SS}$ and $\mathbf{u}^{SL}$ , which are trained to align with $\mathbf{u}^O$ and $\mathbf{u}^L$ , respectively. + +To construct the distillation process for the text encoder, we use cosine similarity loss, defined as $1 - \langle \cdot ,\cdot \rangle$ , where $\langle \cdot ,\cdot \rangle$ denotes the cosine similarity between two vectors. Let $\mathcal{L}_{TS}$ and $\mathcal{L}_{TL}$ represent the distillation losses for the shorttext and long-text tasks, respectively. + +$$ +\mathcal {L} _ {T S} = 1 - \langle \mathbf {u} ^ {O}, \mathbf {u} ^ {S S} \rangle , \tag {1} +$$ + +$$ +\mathcal {L} _ {T L} = 1 - \langle \mathbf {u} ^ {L}, \mathbf {u} ^ {S L} \rangle . \tag {2} +$$ + +To minimize latent space drift in the text encoder, we impose a feature constraint on the first 20 word-token embeddings from the original and student text encoders, denoted as $\mathbf{w}^O$ and $\mathbf{w}^S$ . This follows Long-CLIP's observation that CLIP's effective representation length is about 20 tokens. Let $\mathcal{L}_W$ denote the distillation loss for word tokens: + +$$ +\mathcal {L} _ {W} = \left\| \mathbf {w} ^ {O} - \mathbf {w} ^ {S} \right\| ^ {2}. \tag {3} +$$ + +The distillation loss applied to the student text encoder is represented as follows: + +$$ +\mathcal {L} _ {T} = \mathcal {L} _ {T S} + \mathcal {L} _ {T L} + \mathcal {L} _ {W} \tag {4} +$$ + +The student model's text encoder is initialized with the original CLIP weights, while the position embeddings are extended through interpolation. In our experiments, multitask distillation allows the student encoder to converge well on both short-text and long-text tasks. + +# 3.2.2. Image Embedding Extending + +While the refined image encoder in the long-text teacher network captures fine details well, it experiences knowledge forgetting. Directly distilling from it risks passing this issue to the student network, so we adopt a dual-teacher distillation strategy. Unlike text encoder distillation, both image encoder teachers receive the same input. Our goal is for the student network to retain the knowledge from the original CLIP image encoder while gaining the detailed representation abilities of the long-text version's image encoder. + +The output of the student image encoder is $\mathbf{v}^S$ . We aim to learn the key information from the original CLIP image embedding $\mathbf{v}^O$ and the detailed information from the long-text version CLIP image embedding $\mathbf{v}^R$ . For a given image embedding, the importance of each dimension can be measured by its contribution to cross-modal similarity: + +$$ +\cos \langle \mathbf {u}, \mathbf {v} \rangle = \frac {\mathbf {u} \cdot \mathbf {v}}{\| \mathbf {u} \| \| \mathbf {v} \|}. \tag {5} +$$ + +We define an importance function, denoted by $g$ , which takes the image embedding $\mathbf{v}$ and the text embedding $\mathbf{u}$ as inputs. Here, $i$ refers to the $i$ th dimension of the embedding: + +$$ +g \left(\mathbf {u} _ {i}, \mathbf {v} _ {i}\right) = \exp \left(t \cdot \frac {\mathbf {u} _ {i}}{\| \mathbf {u} \|} \cdot \frac {\mathbf {v} _ {i}}{\| \mathbf {v} \|}\right). \tag {6} +$$ + +# Text + +In the foreground, a metal pole supports several signs, including a "ONE WAY" sign pointing to the left and a "NO STOP" sign with red letters on a white background. The pole is also covered in a collage of colorful stickers and flyers. Beyond the signs is a crosswalk, leading to a white, multi-story vintage building with "MOORE" in large, yellow letters above a rounded, marquee-style entrance. To the right of the building, a fire escape clings to the brick facade. In the background, modern glass buildings are under construction, with a large tower crane visible against a blue sky. Several cars are dispersed through the scene. + +The image captures a vibrant scene of a protest taking place in an urban setting. A large group of people, dressed in a variety of colorful clothing, are standing in a line on a street. They are holding up signs and banners, their messages obscured by the distance. The buildings in the background suggest an urban environment, possibly a city street. The perspective of the image is from a low angle, looking up at the protesters, giving a sense of scale and grandeur to the scene. The colors in the image are bright and varied, adding to the overall vibrancy of the scene. + +# Ours + +![](images/76d5a216e6f5618b6fc9666df3ffd48980e6999b7f1f425faea4fd86c17b7456.jpg) + +# Long-CLIP + +![](images/b49294383d532402cea5cf7c9d7179fef6c0dc43c4a0fa42ccf2e84f7698ade4.jpg) + +![](images/bc732fd0dd54245731e83b9bd2400120418299d6ca0661f5b24649e84ded1ee2.jpg) + +![](images/9777030ad4cd836df66ecd7d5d1161721794ce2bb4364c152d3786bfeda4c995.jpg) + +![](images/6045319d5a23e44e932ba6e696994d0ada99368ee826fb86307e4db46c21a5a1.jpg) +Figure 4. Long-Text to Image Retrieval Results. Our model retrieves images with more accurately matched details. The two examples shown are from the Urban-1k dataset and the ShareGPT4V validation set, respectively. + +![](images/f10ce7ce86ebe3d2772df9c021c74264b34a251c70ecdd67e4a4398c944bc632.jpg) + +Here, $t$ represents the temperature coefficient. With the dimension-wise re-weighting coefficient $g_{i}$ (where $i \in [1, N]$ ) applied to each element in the $N$ -dimensional embedding space, the distillation loss functions for the original model's image encoder $\mathcal{L}_{\mathrm{ov}}$ and the refined image encoder $\mathcal{L}_{\mathrm{rv}}$ can be formally defined as follows: + +$$ +\mathcal {L} _ {o v} = \frac {1}{N} \sum_ {i} \left(\left(\mathbf {v} _ {i} ^ {O} - \mathbf {v} _ {i} ^ {S}\right) ^ {2} \cdot g _ {i} \left(\mathbf {u} _ {i} ^ {O}, \mathbf {v} _ {i} ^ {O}\right)\right), \tag {7} +$$ + +$$ +\mathcal {L} _ {r v} = \frac {1}{N} \sum_ {i} \left(\left(\mathbf {v} _ {i} ^ {R} - \mathbf {v} _ {i} ^ {S}\right) ^ {2} \cdot g _ {i} \left(\mathbf {u} _ {i} ^ {L}, \mathbf {v} _ {i} ^ {R}\right)\right). \tag {8} +$$ + +To ensure stable training, cosine similarity loss is added. Let $\mathcal{L}_{IO}$ and $\mathcal{L}_{IR}$ represent the distillation losses for the original CLIP image encoder and the refined image encoder, respectively. + +$$ +\mathcal {L} _ {I O} = 1 - \langle \mathbf {v} ^ {O}, \mathbf {v} ^ {S} \rangle , \tag {9} +$$ + +$$ +\mathcal {L} _ {I R} = 1 - \langle \mathbf {v} ^ {R}, \mathbf {v} ^ {S} \rangle . \tag {10} +$$ + +The total loss function for training the student image encoder can be expressed as follows, where $\lambda_1, \lambda_2, \lambda_3$ and $\lambda_4$ represent the respective weighting coefficients: + +$$ +\mathcal {L} _ {I} = \lambda_ {1} \mathcal {L} _ {o v} + \lambda_ {2} \mathcal {L} _ {r v} + \lambda_ {3} \mathcal {L} _ {I O} + \lambda_ {4} \mathcal {L} _ {I R}. \tag {11} +$$ + +Through our distillation strategy, the student image encoder gains the ability to capture fine image details while retaining original knowledge. Additionally, our designed re-weighting strategy supervises both long-text and short-text matching effectively. + +# 4. Experiments + +# 4.1. Experiment Setting + +In our experiments, we assess model performance on three tasks: long-text and short-text retrieval to evaluate retrieval capabilities, and zero-shot image classification to detect knowledge forgetting in unfamiliar categories. The datasets used are as follows: + +Long-Caption Image-Text Retrieval. For long-caption image-text retrieval, we adopt the approach of Long-CLIP [32], using a random sample of 1k image and long-text pairs from ShareGPT4V [3] and Urban1K [32]. The Urban1K dataset includes 1k images depicting urban scenes, for which long captions were generated using GPT-4V [2]. short-caption image-text retrieval. For traditional short-caption image-text retrieval, we follow the approach of Long-CLIP [32], utilizing COCO2017 [14] and Flickr30k [30]. The 5k validation set is used for COCO2017, while for Flickr30k, we employ the full 30k dataset instead of the typical 1k test set. + +zero-shot image classification. The primary dataset used is ImageNet-1K [5]. Additionally, ImageNet-V2 [21], ImageNet-O [9], CIFAR-10 [11], and CIFAR-100 [11] are included to further analyze classification capability. + +# 4.2. Implement Detail + +Our model training includes two architectures: ViT-B/16 and ViT-L/14. Training is conducted solely on the ShareGPT4V dataset, with evaluation performed on other datasets. For fine-tuning the long-text teacher model, we use a batch size of 1024 and train for 10 epochs. During + +Table 1. The R@1 of long-caption text-image retrieval on 1k ShareGPT4V validation set and Urban-1k dataset. Best result is in bold. + +
ShareGPT4VUrban-1k
Image-to-TextText-to-ImageImage-to-TextText-to-Image
B/16CLIP78.279.668.153.6
Long-CLIP94.693.378.979.5
Ours99.098.487.287.3
L/14CLIP81.884.068.752.8
Long-CLIP95.895.682.786.1
Ours98.398.691.990.8
+ +Table 2. Short-citation text-image retrieval on the 5k COCO2017 validation set and the whole 30k Flickr30K dataset. Best result is in bold. + +
COCOFlickr30k
Image-to-TextText-to-ImageImage-to-TextText-to-Image
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
B/16CLIP51.876.884.332.757.768.244.168.277.024.745.154.6
Long-CLIP57.681.187.840.465.875.246.871.479.834.156.365.7
ours59.482.789.541.167.277.152.976.083.734.557.667.0
L/14CLIP56.179.586.835.460.170.248.572.680.828.049.358.7
Long-CLIP62.885.191.246.370.879.853.477.585.341.264.172.6
Ours64.485.291.547.072.080.860.282.088.442.265.574.1
+ +Table 3. Results of zero-shot image classification in the above five validation sets. Best result is in bold. + +
ImageNetImageNet-OImageNet-V2Cifar10Cifar100Average
B/16CLIP68.442.261.990.867.366.12
Long-CLIP66.842.761.290.769.366.14
ours68.141.461.792.069.966.62
L/14CLIP75.531.969.995.576.869.92
Long-CLIP73.533.767.995.378.569.78
Ours75.233.368.896.179.470.56
+ +distillation, we train for 5 epochs with a smaller batch size of 64, as this configuration enhances distillation effectiveness and improves generalization across different data distributions. The same gradient update settings are used for both training phases. A learning rate of $1 \times 10^{-6}$ is applied, with a warm-up phase during the first 200 iterations to stabilize the learning process. A weight decay of $1 \times 10^{-2}$ is employed to regularize the model. The AdamW optimizer is configured with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , and $\epsilon = 1 \times 10^{-8}$ , ensuring stable and efficient convergence. The temperature coefficient $t$ is set to 25, and the regularization weights are $\lambda_{1} = 0.5$ , $\lambda_{2} = 0.5$ , $\lambda_{3} = 1$ , and $\lambda_{4} = 2$ . + +# 4.3. Results and Analysis + +Our experimental results show that the dual-teacher distillation strategy enhances CLIP's long-text representation while also improving short-caption retrieval. The model's performance in zero-shot classification demonstrates its ability to retain CLIP's original knowledge, allowing adaptability to diverse downstream tasks. + +# Long-Caption Text-Image Retrieval + +As quantitatively demonstrated in Table 1, our model exhibits significant improvements in long-caption text-image retrieval tasks on both ShareGPT4V and Urban-1k datasets. Notably, under the ViT-B/16 configuration, our model reaches state-of-the-art R@1 scores of 99.0 and 98.4 for Image-to-Text and Text-to-Image tasks, respectively, surpassing both Long-CLIP (94.6 and 93.3) and the original CLIP (78.2 and 79.6). For the ViT-L/14 architecture, our model also achieves R@1 scores of 98.3 and 98.6 on the ShareGPT4V dataset, further improving upon the performance of the long-text version of CLIP. On the Urban-1k dataset, the Image-to-Text task with ViT-L/14 shows a $9.2\%$ improvement, demonstrating our model's strong generalization for long-text descriptions in complex urban scenarios. These results indicate that our approach effectively enhances CLIP's long-text representation capability while maintaining sensitivity to image details, which is essential for open-world retrieval applications, particularly in domain-specific scenarios with rich contextual descriptions. + +# Prompt + +An elderly man with a weathered face, deeply lined from years of life experience. He has a warm smile and kind eyes that suggest wisdom. Wearing a traditional outfit, he stands against a simple backdrop of warm, earthy tones. The light subtly highlights his silver hair, and he holds an old book close to his chest, as if it carries stories dear to him. His expression is calm and content. + +A wide-open prairie at sunset, with golden grasses stretching toward the horizon. A lone windmill stands silhouetted against the sky, its blades slowly turning in the evening breeze. A dirt road winds through the field, leading toward a distant farmhouse. The sky is painted with hues of orange, pink, and purple as the sun sets, casting a warm glow over the landscape. A few clouds drift lazily across the sky. + +A close-up portrait of a majestic lion resting on a rock in the savanna. His golden mane flows around his face as he gazes into the distance. Tall grass surrounds the rock, and a few acacia trees stand against the horizon, typical of the African landscape. In the background, a herd of antelope grazes peacefully. The setting sun casts a warm glow, enhancing the lion's regal appearance and the beauty of the savanna. + +Ours + +Long-CLIP + +![](images/c194ded1af6c8dab4a37d1c8c6a89190731547783eeb525ef13e5b109849d228.jpg) + +![](images/f34413aa23d006321b0b5e546e45f1e1bf338e29f2920b2adf1807c268f25e7d.jpg) + +![](images/271ae2122084586e1119ef8eb12e1ae0c3fb2c4cf65e4c1e7ac978a4e6e41460.jpg) + +![](images/343ecb818ac7ae10f86dc9415882d34978e9ac77581056f339e822b09789d8c3.jpg) + +![](images/1b0629af49da4afd21688dc52b0371246f159cec46bf87fb614f0a6bd4e68d0f.jpg) +Figure 5. Plug-and-Play in Image Generation Model (SDXL). Our text encoder demonstrates better compatibility with SDXL, ensuring the preservation of detailed information in generated images. + +![](images/82c2ca0336ff48c331f56947130b91b43de385118f40a57f2e3f625ff06b0b2b.jpg) + +![](images/3da2f51c97a3c4c8afb88f92ad7888adb8d51672f6cffb67772cf9cbd12ead2b.jpg) +(a) + +![](images/1beff37b5f161cbe1bb0f55ccdae17ff8f2e6fb19355715207540d0e1e39831d.jpg) +(b) + +![](images/4c12f4fcd9dc475a5c15a9b7b442c5396f494a7f79b5c3f31d3b5045186aae72.jpg) +(c) +Figure 6. SDXL Text Encoder Replacement Experiment. Comparison of CLIP Scores between our SDXL and Long-CLIP's SDXL on two sets of prompts. The bar values indicate the proportion of cases where each model achieved a higher CLIP Score, with "Identical" representing cases with equal scores. + +![](images/53bba6d730a3354b69d152fcf4126fb9a8121ae33a8b8c04944b495ebeb4c203.jpg) +(d) + +# Short-Caption Text-Image Retrieval + +In the short-caption text-image retrieval task, our model also performs well on the COCO2017 and Flickr30k datasets (see Table 2). For the ViT-B/16 architecture on the COCO dataset, our model achieves R@1 scores of 59.4 and 41.1 for + +Image-to-Text and Text-to-Image tasks, respectively, outperforming both Long-CLIP and the original CLIP. The results on the Flickr30k dataset are similar, with our approach reaching R@1 scores of 52.9 and 34.5 for Image-to-Text and Text-to-Image tasks, respectively, again surpassing other baseline models. For the ViT-L/14 architecture, our model achieves R@1 scores of 64.4 (Image-to-Text) and 47.0 (Text-to-Image) on the COCO dataset, showing a substantial improvement over Long-CLIP. On the Flickr30k dataset, our method also achieves the best results for both R@1 and R@10 metrics. This demonstrates that our dual-teacher distillation strategy significantly improves retrieval performance, even in short-caption tasks. + +# Zero-Shot Image Classification + +In the zero-shot image classification task, our model exhibits strong generalization and knowledge retention capabilities (see Table 3). On the ImageNet, ImageNet-V2, CIFAR-10, and CIFAR-100 datasets, our model performs well across most benchmarks, particularly achieving an average score of 70.56 with the ViT-L/14 architecture, significantly surpassing the original CLIP and Long-CLIP. This result verifies that our approach effectively mitigates knowledge forgetting, enabling robust adaptability across diverse data distributions. + +# 4.4. Plug-and-Play in Image Generation + +In text-to-image generation, models like Stable Diffusion [22] use a pre-trained text encoder, but the original CLIP text encoder is limited to 77 tokens. Long-CLIP overcomes this limitation with a plug-and-play capability. Our model can be integrated into text-to-image generation models like + +Table 4. Ablation Study. Comparison of our method with other training and fine-tuning approaches. I2T and T2I refer to Image-to-Text Retrieval and Text-to-Image Retrieval, respectively, and CL represents contrastive learning. + +
Cross-modal Retrieval TaskShareGPT4VUrban-1kCOCOFlickr30k
I2TT2II2TT2II2TT2II2TT2I
L/14CLIP81.884.068.752.856.135.448.528.0
O-teacher + CL97.397.181.583.257.937.249.729.9
L-teacher99.299.192.792.164.747.355.042.5
Ours98.398.691.990.864.447.060.242.2
+ +
Image Classification TaskImageNetImageNet-OImageNet-V2Cifar10Cifar100Average
L/14CLIP75.531.969.995.576.869.92
O-teacher + CL75.531.369.795.777.569.94
L-teacher70.832.464.994.976.367.86
Ours75.233.368.896.179.470.56
+ +Long-CLIP, offering better compatibility due to reduced latent space drift in text embeddings. + +In Figure 5, we show three sets of images generated by SDXL [18] using long-text prompts. Compared to LongCLIP, our text encoder adapted for SDXL can capture more detailed information, such as the book in an old man's hand, the road in a field, and the tree behind a lion. + +Additionally, we performed quantitative comparisons by randomly sampling 500 texts from ShareGPT4V (blue bars in Figure 6) and 200 long-text prompts from GPT-4 (pink bars) for the image generation experiment. With the same input and random seed, we used our model and Long-CLIP as the text encoder for SDXL to generate images and then calculated the CLIP Score for each generated image. The CLIP Score is defined as the cosine similarity between image and text embeddings. + +By comparing CLIP Scores, we determine which text encoder is better suited to SDXL. For fairness, the CLIP Score was calculated using both our model and Long-CLIP, and the comparison results were converted to ratios in Figure 6. The results indicate that our method outperforms Long-CLIP regardless of whether our model or Long-CLIP is used as the judge. Further analysis reveals that using our model as the judge leads to fewer "Identical" cases, indicating greater sensitivity to image details. + +# 4.5. Ablation Study + +In Table 4, we compare two training strategies. The first approach (O-teacher + CL) uses contrastive learning with an embedding constraint based on the original CLIP output. While this method mitigates knowledge forgetting in zero-shot tasks, it significantly restricts the model's ability to learn effective long-text representations. The second approach, L-teacher, is our long-text teacher model, which is thoroughly trained on the ShareGPT4V dataset and exhibits strong long-text retrieval capabilities. However, it suffers from knowledge forgetting, with an average drop of approx + +imately $2\%$ in zero-shot image classification accuracy, indicating a degradation in generalization. + +In contrast, our two-stage distillation strategy demonstrates clear improvements across both tasks. Notably, on the Flickr30k dataset, our method surpasses the long-text teacher model by $5.2\%$ and the original CLIP by approximately $11.7\%$ in Image-to-Text retrieval. This result suggests that our approach successfully unlocks the model's latent potential and enhances its representation capabilities. + +Table 5. Ablation study on the distillation loss of the student image encoder. I2T and T2I refer to Image-to-Text Retrieval and Text-to-Image Retrieval. Only the average values are shown for Zero-shot Image Classification. + +
ViT-L/14ShareGPT4VUrban-1kZero-Shot Image Classification
I2TT2II2TT2I
MSE96.095.983.484.169.90
Cosine97.296.588.386.770.35
Ours98.398.691.990.870.56
+ +In our experiments, the text encoder converges well in both long-text and short-text distillation. In Table 5 compared to using only MSE loss or cosine similarity loss, our distillation strategy for the student image encoder achieves better results. + +# 5. Conclusion + +We present a dual-teacher distillation framework that systematically enhances CLIP's capabilities in cross-scale text retrieval (long/short), zero-shot recognition, and cross-modal generation compatibility. These consistent gains demonstrate the model's improved long-text capabilities and its retention of valuable knowledge, laying a foundation for future multimodal learning advancements. + +# 6. Acknowledgement + +This project is sponsored by Natural Science Foundation of Shanghai under Grant No. 24ZR1407200 and Shanghai Oriental Talents Project under Grant No. QNKJ2024060. + +# References + +[1] Rabab Abdelfattah, Qing Guo, Xiaoguang Li, Xiaofeng Wang, and Song Wang. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11175-11185, 2023. 2 \ No newline at end of file diff --git a/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/images.zip b/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..35c077ba8bb5d3535167cc67e5502a3d3c1368bb --- /dev/null +++ b/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2e26c37fe46684ddc109ba9f0db6091f1028b6cb4f5fdde0eef67a57543c3d00 +size 625597 diff --git a/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/layout.json b/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..731f81681481b22b89e47fc5776f89ac03a5a602 --- /dev/null +++ b/retainingknowledgeandenhancinglongtextrepresentationsinclipthroughdualteacherdistillation/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9e464aedd77017dae384a2407ba18d6f95693bdfa381728460794bab664d6a41 +size 355580 diff --git a/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_content_list.json b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..44ad1493f7157b0cf2960d26c3352438a596ce18 --- /dev/null +++ b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9ab29fef54297402eb8526f5ff701bb399d8c98ec9ed7b0a2466d94669989960 +size 87170 diff --git a/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_model.json b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a8719cbf70273d92fbfa2cecad24efc006ed4a49 --- /dev/null +++ b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed5ac27503111d123f14f911c4d8e457e9c2fadaea56b4c4a10ba9060178fbc1 +size 101792 diff --git a/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_origin.pdf b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4fc7487ac1a1583d7c4fad30f524bda3b18cc586 --- /dev/null +++ b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/ad43205b-b19f-4ffd-bbc9-db6043026644_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:386cc7de8121e6a229a5be86a750b12ca62cdcf9f6866b518cbb8be0a460748e +size 2413359 diff --git a/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/full.md b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3eff90b1222947a9f70793e2f124556d0e9b04e3 --- /dev/null +++ b/rethinkingcorrespondencebasedcategorylevelobjectposeestimation/full.md @@ -0,0 +1,329 @@ +# Rethinking Correspondence-based Category-Level Object Pose Estimation + +Huan Ren $^{1,2}$ Wenfei Yang $^{1,2,3}$ Shifeng Zhang $^{4}$ Tianzhu Zhang $^{1,2*}$ + +1University of Science and Technology of China + +$^{2}$ National Key Laboratory of Deep Space Exploration, Deep Space Exploration Laboratory + +${}^{3}$ State Key Laboratory of General Artificial Intelligence ${}^{4}$ Sangfor Technologies + +rh hr 666@mail.ustc.edu.cn zhangshifeng@sangfor.com.cn {yangwf,tzzhang}@ustc.edu.cn + +# Abstract + +Category-level object pose estimation aims to determine the pose and size of arbitrary objects within given categories. Existing two-stage correspondence-based methods first establish correspondences between camera and object coordinates, and then acquire the object pose using a pose fitting algorithm. In this paper, we conduct a comprehensive analysis of this paradigm and introduce two crucial essentials: 1) shape-sensitive and pose-invariant feature extraction for accurate correspondence prediction, and 2) outlier correspondence removal for robust pose fitting. Based on these insights, we propose a simple yet effective correspondence-based method called SpotPose, which includes two stages. During the correspondence prediction stage, pose-invariant geometric structure of objects is thoroughly exploited to facilitate shape-sensitive holistic interaction among keypoint-wise features. During the pose fitting stage, outlier scores of correspondences are explicitly predicted to facilitate efficient identification and removal of outliers. Experimental results on CAMERA25, REAL275 and HouseCat6D benchmarks demonstrate that the proposed SpotPose outperforms state-of-the-art approaches by a large margin. + +# 1. Introduction + +Category-level object pose estimation is one of the fundamental tasks in robotic vision, which aims to predict the 6D pose and 3D size of arbitrary objects in the given categories. This task has received increasing attention from the research community due to its broad applications in augmented reality [18, 26], robotic manipulation [17, 35], and hand-object interaction [15, 25]. Compared to traditional instance-level approaches [20, 30, 31], category-level approaches do not require a CAD model for each object instance, providing stronger generalization in real-world scenarios. + +![](images/12d65ce4dab10d5349ad3f52461797a818ae23bcdab97f3212f65eb0b863c5e8.jpg) +Figure 1. Reconsideration of the two-stage correspondence-based paradigm. (a) Essential of shape-sensitive and pose-invariant features during the correspondence prediction stage. (b) Essential of outlier correspondence removal during the pose fitting stage. + +Most existing category-level methods [1, 12, 14, 24, 27] adopt a two-stage correspondence-based paradigm, which first establishes correspondences between the camera coordinate space and the Normalized Object Coordinate Space (NOCS) [32], and subsequently determines the object pose through a pose fitting algorithm. We conduct an in-depth analysis of this paradigm and introduce two crucial insights. + +(1) During the correspondence prediction stage, shape-sensitive and pose-invariant features are fundamental. Since there are significant shape variations among diverse objects within the same category, shape-sensitive features should be exploited to learn object-specific transformation. As shown in Figure 1(a), points on camera lenses of varying lengths ought to be mapped to different NOCS coordinates. Besides, since the specific object might be observed from arbitrary poses, pose-invariant features should be extracted to learn pose-irrelevant transformation. As illustrated in Figure 1(a), a static point on the camera lens under varying poses ought to be mapped to the same NOCS coordinates. (2) During the pose fitting stage, the removal of outlier correspondences is essential. Noise in the object segmentation mask and depth camera sensor can yield outlier points within the observed object point cloud. These outlier points, combined with inaccurate correspondence predictions, lead to outlier correspondences that have a detrimental impact on the pose fitting process. Therefore, a robust pose fitting + +algorithm is desired to eliminate the interference of outliers. As illustrated in Figure 1(b), the rotation fitting error is reduced from $8.4^{\circ}$ to $2.2^{\circ}$ after an outlier removal process. + +Despite the considerable progress achieved by previous methods, they either overlook these two crucial essentials or instead resort to complicated and inefficient designs. (1) During the correspondence prediction stage, point-wise features of observed objects are extracted and then mapped to the NOCS coordinates. However, existing approaches typically employ general-purpose point cloud backbones without pose-invariance, e.g., the widely deployed PointNet++ [22] incorporates absolute coordinates and yields inherently pose-sensitive features. Furthermore, point-wise features lack sufficient interaction with each other from a holistic perspective, thereby limiting their shape-sensitivity. Consequently, these methods struggle with transformation learning and instead depend on complicated and inefficient designs, e.g., category-level shape priors [1, 12, 27], shape augmentation [34], and auxiliary feature enhancers [16]. (2) During the pose fitting stage, early approaches [27, 32] employ the Umayama algorithm [28] to solve the object pose with the Random Sample Consensus (RANSAC) algorithm [6] for outlier removal. However, RANSAC requires numerous iterations to find an accurate pose while excluding outliers, leading to slow convergence. Instead, recent methods [12, 14, 16] utilize an MLP-based deep estimator to directly regress the object pose from correspondences, which can benefit from end-to-end supervised training on the final objectives. Nevertheless, they exhibit limited robustness to outlier correspondences, as all correspondences are taken for regression without any filtering. + +Motivated by the above discussions, we propose a simple yet effective two-stage correspondence-based approach for category-level object pose estimation, named as SpotPose, where Shape-sensitive and Pose-invariant features are first inherently extracted to facilitate correspondence prediction, followed by efficient identification and removal of OuTlier correspondences to enable robust and accurate pose fitting. (1) During the correspondence prediction stage, point-wise features are densely extracted from RGB-D observations, where PointNet++ [22] is adapted to extract pose-invariant point cloud features by incorporating a T-Net [21] to align the input point cloud while eliminating the injection of absolute coordinates. Afterwards, we represent object shapes with a set of sparse keypoints, and further leverage the pose-invariant geometric descriptor [23] to facilitate shape-sensitive holistic interaction among keypoint-wise features. Benefiting from the extraction of shape-sensitive and pose-invariant features, transformation between the camera and object coordinate spaces becomes more readily learned. (2) During the pose fitting stage, due to noise in the observations or predictions, there exist outliers in the derived correspondences that are harmful to the pose fitting process. + +To this end, we just utilize a lightweight outlier predictor to distinguish between inliers and outliers, and then solve the object pose based solely on inlier correspondences with the Umayama algorithm [28]. Through this intuitive outlier removal process, we achieve comparable pose fitting performance without the need for the RANSAC algorithm [6], while maintaining a fast inference speed. + +The main contributions of this work can be summarized as follows: (1) We conduct a comprehensive analysis of the existing two-stage correspondence-based paradigm for category-level object pose estimation and introduce two crucial essentials. (2) We propose a simple yet effective approach which extracts shape-sensitive and pose-invariant features during the correspondence prediction stage to facilitate transformation learning, and efficiently removes outlier correspondences during the pose fitting stage to ensure robust pose estimation. (3) Extensive experimental results on existing benchmarks demonstrate the superior performance of our method over state-of-the-art approaches. + +# 2. Related Work + +In this section, we briefly overview direct regression-based and correspondence-based category-level object pose estimation methods. + +Direct Regression-based Methods. This group of methods adopts a single-stage paradigm, which directly regresses the object pose in an end-to-end manner after feature extraction from object observations. FS-Net [2] employs a 3D graph convolution (3DGC) autoencoder for orientation feature extraction and decouples the rotation into two orthogonal vectors to handle symmetric objects. GPV-Pose [4] and HS-Pose [37] enhance pose-sensitive feature extraction by focusing on geometric consistency and local-global geometric structure perception, respectively. VI-Net [13] proposes an innovative rotation estimation network that simplifies the task on the sphere by decoupling the rotation into viewpoint and in-plane components, while SecondPose [3] further improves it by leveraging SE(3)-consistent semantics and geometric feature extraction. Although conceptually simple, these methods struggle with pose-sensitive feature learning due to the non-linearity of the full SE(3) space. + +Correspondence-based Methods. This group of methods adopts a two-stage paradigm, which first establishes correspondences between camera and object coordinates, and then derives the object pose through a pose fitting algorithm. During the correspondence prediction stage, the Normalized Object Coordinate Space (NOCS) is introduced in [32] as a shared canonical representation to align diverse object instances in a given category. SPD [27] and its subsequent works [1, 12, 33] reconstruct 3D object models by deforming a pre-learned categorical shape prior, and then predict correspondences between the observed and reconstructed object point clouds. However, acquiring the priors requires + +collecting numerous CAD models, which is labor-intensive. Query6DoF [34] and IST-Net [16] eliminate the need for explicit shape priors through implicit queries and implicit space transformation, respectively, but still rely on complicated shape augmentation or auxiliary feature enhancers. These methods disregard shape-sensitive and pose-invariant feature extraction, struggling with transformation learning. During the pose fitting stage, early approaches [1, 27, 32] adopt the Umeyama algorithm [28] to solve the object pose, combined with the RANSAC algorithm [6] to mitigate the interference of outlier correspondences. Nevertheless, the RANSAC algorithm requires massive iterations to produce a fitting pose with enough inliers while excluding outliers, which suffers from slow convergence. DPDN [12] presents a pose and size estimator to directly regress the object pose and size from correspondences, which is composed of MLPs and average pooling operations. It can benefit from end-to-end supervised training on the final pose and size objectives, rather than solely on the surrogate correspondences. However, since all correspondences are employed for regression without any filtering, the deep estimator exhibits limited robustness to outlier correspondences. + +# 3. Method + +Task Definition. Given an RGB-D image, we first utilize an offline Mask R-CNN [7] to acquire instance segmentation masks, yielding the cropped RGB image $\pmb{I}^{\mathrm{obj}} \in \mathbb{R}^{H \times W \times 3}$ and segmented depth image for each instance. The partially observed object point cloud $\pmb{P}^{\mathrm{obj}} \in \mathbb{R}^{N^{\mathrm{obj}} \times 3}$ is then derived from the segmented depth image by back-projecting and downsampling, where $N^{\mathrm{obj}}$ is the number of points. Taking $\pmb{I}^{\mathrm{obj}}$ and $\pmb{P}^{\mathrm{obj}}$ as inputs, our method aims to predict the rotation $\pmb{R} \in \mathrm{SO}(3)$ , translation $t \in \mathbb{R}^3$ , and size $s \in \mathbb{R}^3$ of the observed instance in the given categories. + +Overview. As illustrated in Figure 2, the proposed method consists of three components, which include dense feature extraction (Section 3.1), sparse feature interaction (Section 3.2) and robust pose and size estimation (Section 3.3). In Section 3.4, we further discuss the distinctions between our SpotPose and the most relevant method, AG-Pose [14]. + +# 3.1. Dense Feature Extraction + +We start with dense point-wise feature extraction with pose-invariance, which integrates the two modalities in a dense fusion manner [30]. For the point cloud $P^{\mathrm{obj}}$ , we extract pose-invariant geometric features via PoseInv-PointNet++, which is an adapted variant of PointNet++ [22]. In detail, a T-Net [21] is incorporated to predict an affine transformation matrix $T \in \mathbb{R}^{3 \times 3}$ from $P^{\mathrm{obj}}$ , which aligns the input point cloud before feeding it into PointNet++. Moreover, the injection of absolute coordinates is also excluded from the original PointNet++ to ensure pose-invariant feature extraction. As for the image $I^{\mathrm{obj}}$ , we follow SecondPose [3] + +to employ DINOv2 [19] to extract pose-consistent semantic features, followed by point-wise selection with $P^{\mathrm{obj}}$ . The final dense point-wise features $F^{\mathrm{obj}} \in \mathbb{R}^{N^{\mathrm{obj}} \times D}$ are then derived by point-wise concatenation of the image and point cloud features, with feature dimension reduction to $D$ . + +# 3.2. Sparse Feature Interaction + +After extracting the point-wise features, we further enhance their shape-sensitivity through holistic feature interaction. However, due to the large number of points, the interaction among dense point-wise features incurs significant computational overhead. Therefore, inspired by AG-Pose [14], we represent object shapes with a set of sparse keypoints, enabling more computationally friendly feature interaction. Concretely, Farthest Point Sampling (FPS) is applied on $P^{\mathrm{obj}}$ to retrieve a set of sparse keypoints $P \in \mathbb{R}^{N \times 3}$ , and the corresponding keypoint-wise features $F^{\mathrm{kpt}} \in \mathbb{R}^{N \times D}$ are indexed from $F^{\mathrm{obj}}$ , where $N$ denotes the number of keypoints. The pose-invariant distance- and angle-based geometric descriptor [23] is then leveraged to perform shape-sensitive comprehensive interaction among $F^{\mathrm{kpt}}$ and $F^{\mathrm{obj}}$ . This process involves $L$ geometric interaction blocks, each consisting of a local geometric cross-attention layer and a global geometric self-attention layer, as detailed below. + +Distance- and Angle-based Geometric Descriptor. Given a keypoint $P_{n}$ and its attended points $P^{\mathrm{att}} \in \mathbb{R}^{N^{\mathrm{att}} \times 3}$ , the geometric structure embedding between $P_{n}$ and $P_{m}^{\mathrm{att}}$ consists of a pair-wise distance embedding and a $K$ -wise angle embedding, where $N^{\mathrm{att}}$ is the number of the attended points. The distance embedding $E_{n,m}^{\mathrm{dis}}$ is computed by applying a sinusoidal function [29] on $\| P_{m}^{\mathrm{att}} - P_{n}\|_{2} / \sigma^{\mathrm{dis}}$ , where $\sigma^{\mathrm{dis}}$ is a distance hyper-parameter. As for the angle embedding, the $K$ nearest neighbors $P^{\mathrm{knn}} \in \mathbb{R}^{K \times 3}$ of $P_{n}$ is first selected from $P^{\mathrm{att}}$ . The $K$ -wise angle embedding $E_{n,m,k}^{\mathrm{ang}}$ is then computed with a sinusoidal function on $\angle (P_{k}^{\mathrm{knn}} - P_{n}, P_{m}^{\mathrm{att}} - P_{n}) / \sigma^{\mathrm{ang}}$ , where $\sigma^{\mathrm{ang}}$ is a angle hyper-parameter. Finally, the geometric structure embedding $E_{n,m} \in \mathbb{R}^{D}$ is formulated as: + +$$ +\boldsymbol {E} _ {n, m} = \boldsymbol {E} _ {n, m} ^ {\mathrm {d i s}} \boldsymbol {W} ^ {\mathrm {d i s}} + \max _ {k} \left\{\boldsymbol {E} _ {n, m, k} ^ {\mathrm {a n g}} \boldsymbol {W} ^ {\mathrm {a n g}} \right\}, \tag {1} +$$ + +where $W^{\mathrm{dis}}, W^{\mathrm{ang}} \in \mathbb{R}^{D \times D}$ are the projection matrices. Due to the pose-invariance of the pair-wise distance and $K$ -wise angle, the geometric structure embedding $E_{n,m}$ is thus pose-invariant. For more details, please refer to [23]. + +Local Geometric Cross-Attention. Since the sparse keypoints $P$ are an abstract subset of the dense points $P^{\mathrm{obj}}$ and lack local geometric details, we first aggregate local context information into keypoint features with a local geometric cross-attention layer in each geometric interaction block. Specifically, for the $n$ -th keypoint $P_{n}$ , its $K^{\mathrm{local}}$ nearest neighbors $P_{\mathrm{knn}(n)}^{\mathrm{obj}} \in \mathbb{R}^{K^{\mathrm{local}} \times 3}$ are first selected within $P^{\mathrm{obj}}$ , and the corresponding features $F_{\mathrm{knn}(n)}^{\mathrm{obj}} \in \mathbb{R}^{K^{\mathrm{local}} \times D}$ . + +![](images/686828c359e592c04d669249e8aa7e5dc738ab02503634d0fdf5ea89adf03475.jpg) +(a) Framework Overview + +![](images/bf6366b83f2b2cede3e276fad03c76f7bc7c9ffc847f7f17615cdaec7cb1eb01.jpg) +Figure 2. (a) Overview of the proposed SpotPose. Given the observation $I^{\mathrm{obj}}$ and $P^{\mathrm{obj}}$ , dense point-wise features $F^{\mathrm{obj}}$ are first extracted with pose-invariance. Subsequently, the object shape is represented by a set of sparse keypoints $P$ , whose features $F$ are enhanced with shape-sensitivity through $L$ geometric interaction blocks. The final pose $\{R, t\}$ is derived from keypoint-wise correspondences after outlier removal, while the size $s$ is directly regressed. (b) The PoseInv-PointNet++ is adapted from PointNet++ to extract pose-invariant point cloud features. (c) The local geometric cross-attention layer aims to enrich sparse keypoint-wise features with local context information from dense points. (d) The global geometric self-attention layer aims to holistically enhance keypoint-wise features with shape-sensitivity. + +are retrieved from $F^{\mathrm{obj}}$ . Then, the local geometric descriptor $E_{n}^{\mathrm{local}} \in \mathbb{R}^{K^{\mathrm{local}} \times D}$ is computed using Equation (1), with the attended points $P_{\mathrm{knn}(n)}^{\mathrm{obj}}$ and $K^{\mathrm{local}}$ -wise angle. In the $l$ -th block, the $n$ -th locally enhanced keypoint feature $F_{l,n}^{\mathrm{local}} \in \mathbb{R}^{D}$ is derived with the attention mechanism [29] that incorporates geometric information, formulated as: + +$$ +\boldsymbol {F} _ {l, n} ^ {\text {l o c a l}} = \operatorname {G C A} \left(\boldsymbol {F} _ {l - 1, n} ^ {\text {g l o b a l}}, \boldsymbol {F} _ {\operatorname {k n n} (n)} ^ {\text {o b j}}, \boldsymbol {E} _ {n} ^ {\text {l o c a l}}\right) + \boldsymbol {F} _ {l - 1, n} ^ {\text {g l o b a l}}, \tag {2} +$$ + +$$ +l \in \{1, \ldots , L \}, \quad n \in \{1, \ldots , N \}, +$$ + +where the initial input keypoint feature $F_{0,n}^{\mathrm{global}} = F_n^{\mathrm{kpt}}$ and GCA is the geometric cross-attention operation, defined as: + +$$ +\operatorname {G C A} (\boldsymbol {q}, \boldsymbol {C}, \boldsymbol {E}) = \text {A t t e n t i o n} (\boldsymbol {q}, \boldsymbol {C} + \boldsymbol {E}, \boldsymbol {C} + \boldsymbol {E}), \tag {3} +$$ + +$$ +\operatorname {A t t e n t i o n} (\boldsymbol {Q}, \boldsymbol {K}, \boldsymbol {V}) = \boldsymbol {A} \times \left(\boldsymbol {V} \boldsymbol {W} ^ {V}\right), \tag {4} +$$ + +$$ +\boldsymbol {A} = \operatorname {S o f t m a x} \left(\frac {\left(\boldsymbol {Q} \boldsymbol {W} ^ {Q}\right) \left(\boldsymbol {K} \boldsymbol {W} ^ {K}\right) ^ {\top}}{\sqrt {D}}\right), \tag {5} +$$ + +where $\pmb{W}^{Q},\pmb{W}^{K},\pmb{W}^{V}\in \mathbb{R}^{D\times D}$ are the projection matrices for query, key and value, respectively. Through the local geometric interaction, the keypoint features $\pmb{F}_l^{\mathrm{local}}\in$ $\mathbb{R}^{N\times D}$ are enhanced with the ability to represent local parts. + +Global Geometric Self-Attention. After the local context integration, we apply a global geometric self-attention layer to facilitate shape-sensitive holistic interaction among the keypoint features. Concretely, the $n$ -th keypoint $\pmb{P}_n$ attends to all keypoints $\{\pmb{P}_m \mid m = 1, \dots, N\}$ and the corresponding global geometric structure embedding $\pmb{E}_{n,m}^{\mathrm{global}} \in \mathbb{R}^D$ is computed using Equation (1) with the $K^{\mathrm{global}}$ -wise angle. To yield the geometric descriptor $\pmb{E}_n^{\mathrm{global}} \in \mathbb{R}^D$ for the $n$ -th keypoint, we average $\pmb{E}_{n,m}^{\mathrm{global}}$ over $m$ . Within the $l$ -th block, the globally enhanced keypoint features $\pmb{F}_l^{\mathrm{global}} \in \mathbb{R}^{N \times D}$ are then derived with the geometric self-attention (GSA) operation, and this process is formulated as follows: + +$$ +\boldsymbol {F} _ {l} ^ {\text {g l o b a l}} = \operatorname {G S A} \left(\boldsymbol {F} _ {l} ^ {\text {l o c a l}}, \boldsymbol {E} ^ {\text {g l o b a l}}\right) + \boldsymbol {F} _ {l} ^ {\text {l o c a l}}, \tag {6} +$$ + +$$ +l \in \{1, \dots , L \}, +$$ + +$$ +\operatorname {G S A} (\boldsymbol {C}, \boldsymbol {E}) = \text {A t t e n t i o n} (\boldsymbol {C} + \boldsymbol {E}, \boldsymbol {C} + \boldsymbol {E}, \boldsymbol {C} + \boldsymbol {E}), \tag {7} +$$ + +where the Attention operation is defined in Equation (4). After $L$ geometric interaction blocks, the final keypoint features $\pmb{F} = \pmb{F}_{L}^{\mathrm{global}}\in \mathbb{R}^{N\times D}$ are acquired. Through the local and global geometric interaction, keypoint features are enhanced with shape-sensitivity, while retaining pose + +invariance owing to the pose-invariant geometric descriptor, which facilitates subsequent transformation learning. + +# 3.3. Robust Pose and Size Estimation + +Outlier-aware Correspondence Prediction. Once shape-sensitive and pose-invariant keypoint features are extracted, we follow previous work [16] to predict the corresponding NOCS coordinates $S \in \mathbb{R}^{N \times 3}$ from $F$ with an MLP-based NOCS predictor. The ground truth NOCS coordinates $S^{\mathrm{gt}}$ are derived by applying the ground truth $R^{\mathrm{gt}}, t^{\mathrm{gt}}, s^{\mathrm{gt}}$ to the keypoint coordinates $P$ , which is formulated as below: + +$$ +\boldsymbol {S} _ {n} ^ {\mathrm {g t}} = \frac {1}{\| \boldsymbol {s} ^ {\mathrm {g t}} \| _ {2}} (\boldsymbol {R} ^ {\mathrm {g t}}) ^ {\top} (\boldsymbol {P} _ {n} - \boldsymbol {t} ^ {\mathrm {g t}}), \quad n \in \{1, \dots , N \}, (8) +$$ + +where $\top$ denotes the transpose operation. The NOCS loss function is then defined as the keypoint-wise $L^2$ distance: + +$$ +\mathcal {L} _ {n} ^ {\mathrm {n o c s}} = \left\| \boldsymbol {S} _ {n} - \boldsymbol {S} _ {n} ^ {\mathrm {g t}} \right\| _ {2}, \quad n \in \{1, \dots , N \}. \tag {9} +$$ + +However, due to noise in the object segmentation mask and depth camera sensor, the observed point cloud may contain outlier points that deviate from the object surface. Moreover, inaccurate NOCS predictions can result in outlier correspondences that are detrimental to the pose fitting process. To this end, we further predict the outlier scores $\pmb{O} \in \mathbb{R}^{N}$ from $\pmb{F}$ and $\pmb{P}$ with an intuitive outlier predictor as follows: + +$$ +\boldsymbol {O} = \operatorname {S i g m o i d} (\operatorname {M L P} ([ \boldsymbol {F}, \operatorname {M L P} (\boldsymbol {P}) ])), \tag {10} +$$ + +where $[(:,:)]$ indicates the feature concatenation operation. To identify outlier points, we follow AG-Pose [14] to produce keypoint-wise $O_{n}^{\mathrm{gt}}$ based on the instance CAD model $P^{\mathrm{cad}}\in \mathbb{R}^{N^{\mathrm{cad}}\times 3}$ , which contains $N^{\mathrm{cad}}$ points. In formula, + +$$ +O _ {n} ^ {\mathrm {g t}} = \left\{ \begin{array}{l l} 0, & \text {i f} \quad \min _ {m \in \{1, \dots , N ^ {\mathrm {c a d}} \}} \| S _ {n} ^ {\mathrm {g t}} - P _ {m} ^ {\mathrm {c a d}} \| _ {2} < \eta \\ 1, & \text {o t h e r w i s e} \end{array} , \right. \tag {11} +$$ + +where $\eta$ is the outlier threshold. The final outlier-aware correspondence loss function $\mathcal{L}^{\mathrm{corr}}$ is then formed by modulating the keypoint-wise NOCS loss $\mathcal{L}_n^{\mathrm{nocs}}$ , defined as: + +$$ +\mathcal {L} _ {n} ^ {\text {c o r r}} = \left\{ \begin{array}{l l} \boldsymbol {I} _ {n} \mathcal {L} _ {n} ^ {\text {n o c s}} - \lambda^ {\text {r e g}} \log \boldsymbol {I} _ {n}, & \boldsymbol {O} _ {n} ^ {\mathrm {g t}} = 0 \\ \boldsymbol {I} _ {n}, & \boldsymbol {O} _ {n} ^ {\mathrm {g t}} = 1 \end{array} , \right. \tag {12} +$$ + +$$ +\mathcal {L} ^ {\text {c o r r}} = \frac {1}{N} \sum_ {n = 1} ^ {N} \mathcal {L} _ {n} ^ {\text {c o r r}}, \tag {13} +$$ + +where $I_{n} = 1 - O_{n}$ denotes the keypoint-wise inlier score, and $\lambda^{\mathrm{reg}}$ is a hyper-parameter to balance the regularization. Note that when $O_{n}^{\mathrm{gt}} = 1$ , $O_{n}$ is directly constrained to be 1 to identify outlier keypoints. And when $O_{n}^{\mathrm{gt}} = 0$ , the first term suppresses the inlier score $I_{n}$ if $\mathcal{L}_n^{\mathrm{nocs}}$ is large, which in turn reduces the weight of $\mathcal{L}_n^{\mathrm{nocs}}$ . The second term acts as + +a regularizer to prevent the NOCS predictor from being lazy and not learning at all. This loss function encourages the network to prioritize correspondences that are easier to predict, while deferring constraints on more challenging correspondences, which are then identified as outliers. + +Pose and Size Estimation. Given the keypoint-wise camera coordinates $P$ , NOCS coordinates $S$ , and outlier scores $O$ , we first apply a threshold 0.5 on $O$ to filter out outliers. The remaining inlier correspondences between $P$ and $S$ are then utilized to solve the rotation $R$ and translation $t$ via the Umeyama algorithm [28]. Through this intuitive outlier removal process, robust pose fitting can be achieved without relying on the time-consuming RANSAC algorithm [6]. As for the estimation of object size $s$ , we simply employ an MLP-based size predictor for regression from the globally averaged keypoint features AvgPool( $F$ ) and utilize L2 loss for supervision, which is written as: + +$$ +\mathcal {L} ^ {\text {s i z e}} = \left\| s - s ^ {\mathrm {g t}} \right\| _ {2}. \tag {14} +$$ + +In summary, the overall loss function is as follows: + +$$ +\mathcal {L} ^ {\text {a l l}} = \mathcal {L} ^ {\text {c o r r}} + \lambda^ {\text {s i z e}} \mathcal {L} ^ {\text {s i z e}}, \tag {15} +$$ + +where $\lambda^{\mathrm{size}}$ is a balancing hyper-parameter. + +# 3.4. Discussion + +In this section, we elaborate on the distinctions between our SpotPose and AG-Pose [14], which both utilize a set of sparse keypoints to represent object shapes and incorporate geometric information to establish keypoint-wise correspondences. The primary differences lie in four aspects. (1) In terms of keypoint selection, AG-Pose adaptively detects sparse keypoints for different instances, but it fails to provide a suitable shape representation at the early stage of training. In contrast, we simply adopt the training-free farthest point sampling, reducing the risk of network collapse. (2) With regard to holistic feature interaction, keypoint-wise features in AG-Pose are simply concatenated with globally averaged keypoint features, leaving limited feature interaction with each other. By contrast, we leverage the attention mechanism to enable thorough interaction among sparse keypoint-wise features, enhancing their shape-sensitivity. (3) As for geometric feature integration, AG-Pose employs the relative position embedding as its geometric descriptor, which is inherently pose-sensitive. We instead resort to the pose-invariant distance- and angle-based geometric descriptor, ensuring the pose-invariance of the aggregated features. (4) With respect to outlier removal, AG-Pose constrains the detected keypoints to lie on inlier object surfaces, and then uses a deep estimator to regress the pose from all keypoints-wise correspondences, which still suffers from outliers due to noise in the predictions. In contrast, we explicitly predict keypoint-wise outlier scores to directly identify and remove outliers, leading to a more robust object pose estimation. + +Table 1. Performance comparison with state-of-the-art methods on the REAL275 and CAMERA25 datasets. + +
MethodREAL275CAMERA25
IoU50IoU755°2cm5°5cm10°2cm10°5cmIoU50IoU755°2cm5°5cm10°2cm10°5cm
Direct RegressionDualPoseNet [11]79.862.229.335.950.066.892.486.464.770.777.284.7
GPV-Pose [4]-64.432.042.9-73.393.488.372.179.1-89.0
HS-Pose [37]82.174.746.555.268.682.793.389.473.380.580.489.4
GenPose [36]--52.160.972.484.0--79.984.484.689.6
VI-Net [13]--50.057.670.882.1--74.181.479.387.3
SecondPose [3]--56.263.674.786.0------
CorrespondenceNOCS [32]78.030.17.210.013.825.283.969.532.340.948.264.4
SPD [27]77.353.219.321.443.254.193.283.154.359.073.381.5
SGPA [1]80.161.935.939.661.370.793.288.170.774.582.788.4
SAR-Net [10]79.362.431.642.350.368.386.879.066.770.975.380.3
DPDN [12]83.476.046.050.770.478.4------
IST-Net [16]82.576.647.553.472.180.593.790.871.379.979.489.9
Query6DoF [34]82.576.149.058.968.783.091.988.178.083.183.990.0
AG-Pose [14]83.779.554.761.774.783.193.891.377.882.885.591.6
SpotPose84.181.259.764.881.588.294.392.580.483.887.792.2
+ +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. We conduct experiments on three benchmarks including CAMERA25, REAL275 [32] and HouseCat6D [8]. CAMERA25 is a synthetic dataset that comprises 275K training and 25K testing images across 6 object categories. These images are generated using a mixed-reality approach, where foreground objects are rendered against real-world backgrounds. REAL275 is a real-world dataset consisting of 4.3K training images from 7 scenes and 2.75K testing images from 6 scenes, which shares the same object categories with CAMERA25. HouseCat6D is an emerging real-world dataset containing 20K training frames from 34 scenes, 3K testing frames from 5 scenes, and 1.4K validation frames from 2 scenes, spanning 10 household object categories. This collection encompasses photometrically challenging objects with comprehensive viewpoint and occlusion coverage, posing substantial challenges for pose estimation. + +Evaluation Metrics. Following previous works [14, 32], we report the mean Average Precision (mAP) of $n^{\circ}m$ cm for 6D pose evaluation, which indicates the percentage of prediction with rotation error less than $n^{\circ}$ and translation error less than $m$ cm. We also report the mAP of 3D Intersection over Union $(\mathrm{IoU}_x)$ at a threshold of $x\%$ for joint 6D pose and 3D size evaluation. + +Implementation Details. For a fair comparison, we employ the same instance masks as previous works [14, 27] from Mask R-CNN [7]. For data preprocessing, images are first cropped and then resized to $224 \times 224$ , and the number of sampled points is $N^{\mathrm{obj}} = 1024$ . For dense image feature extraction, images are fed into the frozen DINOv2 [19], followed by a bilinear interpolation upsampling to the original resolution for point-wise selection. For dense point cloud feature extraction, T-Net [21] is composed of a + +shared MLP(64,128,256) on each point, a MaxPool across points and a final MLP(128,64,9) to predict $T$ , while PointNet++ [22] is kept consistent with previous works [12, 14] except for the incorporation of absolute coordinates. The number of keypoints is $N = 96$ and the feature dimension is $D = 256$ . For geometric feature interaction, we adopt $L = 6$ blocks by default, with geometric hyper-parameters $\sigma^{\mathrm{dis}} = 0.2$ , $\sigma^{\mathrm{ang}} = 15.0$ and $K^{\mathrm{local}} = 16$ , $K^{\mathrm{global}} = 3$ . For outlier identification, the threshold $\eta$ is set to 0.1. In the loss function, balancing hyper-parameters are $\lambda^{\mathrm{reg}} = 0.1$ and $\lambda^{\mathrm{size}} = 0.5$ . We train our network using the Adam [9] optimizer with a initial learning rate of 0.001 and a cosine annealing schedule. All experiments are conducted on a single RTX3090Ti GPU with a batch size of 24. + +# 4.2. Comparison with State-of-the-art Methods + +Results on REAL275 and CAMERA25 datasets. Table 1 shows the comparison of our method with existing direct regression-based and correspondence-based methods on the REAL275 and CAMERA25 datasets. From the results we can see that on the REAL275 dataset, our SpotPose significantly outperforms all previous methods by a large margin in all evaluation metrics. In particular, when compared with the direct regression-based approaches, SpotPose surpasses SecondPose [3] by $3.5\%$ in $5^{\circ}2\mathrm{cm}$ and $6.8\%$ in $10^{\circ}2\mathrm{cm}$ , which also employs DINOv2 [19] as the image backbone. When compared with other correspondence-based methods, SpotPose outperforms the previous leading AG-Pose [14] by $5.0\%$ in $5^{\circ}2\mathrm{cm}$ , $6.8\%$ in $10^{\circ}2\mathrm{cm}$ and $1.7\%$ in $\mathrm{IoU}_{75}$ . In line with the discussions in Section 3.4, the results demonstrate that our approach achieves a more accurate pose estimation by extracting shape-sensitive and pose-invariant features, while explicitly removing outlier correspondences. Similar results can be found on the CAMERA25 dataset. Although SpotPose falls $0.6\%$ below GenPose [36] in the + +Table 2. Performance comparison with state-of-the-art methods on the HouseCat6D dataset. + +
MethodIoU25IoU505°2cm5°5cm10°2cm10°5cm
FS-Net [2]74.948.03.34.217.121.6
GPV-Pose [4]74.950.73.54.617.822.7
VI-Net [13]80.756.48.410.320.529.1
SecondPose [3]83.766.111.013.425.335.7
NOCS [32]50.021.2----
AG-Pose [14]81.862.511.512.032.735.8
SpotPose89.177.023.824.552.354.8
+ +![](images/0c8592794dfbaa5f6e66a32b694f368e5a088f35266190a93b3c6b0fd65222b6.jpg) +DPDN + +![](images/4a6422e14afc758bd28ac05cd3007ce7c61a0cee691a93de18017913b20e21da.jpg) +VI-Net + +![](images/11f33722448630ab5c7594c9c401ebef13d29bacd5615c5e61ab6be3fe3d18ba.jpg) +AG-Pose + +![](images/30827d542dae75faa769a7d7fb09d621b86ee2618cdc48638a5a437b1ea74ec9.jpg) +SpotPose + +![](images/f3a797b5b7309f595a33eb9b8701a142ac2c593187cb6b2b013e2ddce15d1d98.jpg) + +![](images/2efd57e1d70f37a0b00bcf1dc91261141f582cb46e7b8aae579e64eab41e92aa.jpg) + +![](images/bb97b87e020cbf2ed74a9fe880498abbb982f39c3e00ef426941f94f645959f3.jpg) + +![](images/3e9ded9b550f953385aa205b31ecd7719c13e855bc691c051ac39bfdc879a056.jpg) + +![](images/5bc6ce02d237ccb2d1f788b3e2e3b141d5b40467d36c638fa2aba417b5873a3b.jpg) +Figure 3. Qualitative comparison of DPDN [12], VI-Net [13], AG-Pose [14] and our SpotPose on the REAL275 dataset. Red/Green indicates the predicted/GT results. + +![](images/643ffb4dc5062137f9c6beda29a4f74f7ce8d6320ebe105d0a0efc6525ce2c18.jpg) + +![](images/61ba9fbf50cd97b55d29c356ad2f5721d36ccccb8bd7bb5433aeaa6734b0d4a1.jpg) + +![](images/f55e33f86aca9c3dc2e62a55203ddd6adb8f282f37ddc4261ab7ebedbe97a4c2.jpg) + +$5^{\circ}5\mathrm{cm}$ metric, it outperforms GenPose in all other metrics, e.g., $3.1\%$ higher in $10^{\circ}2\mathrm{cm}$ . Additionally, we are free from the costly sampling and filtering process of pose candidates. + +Results on HouseCat6D dataset. Table 2 provides the performance comparison on the more challenging HouseCat6D dataset. Once again, our SpotPose achieves the best performance over state-of-the-art approaches by a large margin. Concretely, SpotPose exceeds SecondPose [3] by $12.8\%$ in $5^{\circ}2\mathrm{cm}$ and $10.9\%$ in $\mathrm{IoU}_{50}$ , and surpasses AG-Pose [14] by $12.3\%$ in $5^{\circ}2\mathrm{cm}$ and $14.5\%$ in $\mathrm{IoU}_{50}$ . As for the $10^{\circ}5\mathrm{cm}$ metric, SpotPose outperforms them by almost $20\%$ (19.1% and $19.0\%$ , respectively). The superior performance on this more comprehensive and challenging real-world dataset further demonstrates the effectiveness of our approach. + +Qualitative Comparison. Figure 3 shows the qualitative comparison of SpotPose with the direct regression-based method, VI-Net [13] and correspondence-based methods, DPDN [12] and AG-Pose [14] on the REAL275 dataset. As highlighted in the blue boxes, our SpotPose yields a more accurate pose estimation across diverse shapes and poses. + +Table 3. Ablation studies on the dense point cloud backbone. + +
Dense Point Cloud Backbone5°2cm5°5cm10°2cm10°5cm
PointNet++ [22]51.456.278.986.6
PoseInv-PointNet++59.764.881.588.2
+ +Table 4. Ablation studies on the geometric descriptor. Dis-Ang denotes the distance- and angle-based geometric descriptor. + +
Geometric Descriptor5°2cm5°5cm10°2cm10°5cm
LocalGlobal
NoneNone55.862.077.085.0
Dis-AngDis-Ang59.764.881.588.2
NoneDis-Ang58.564.079.085.9
PPF [5]Dis-Ang58.062.680.987.4
Relative [14]Dis-Ang56.461.780.286.7
Dis-AngNone59.265.079.686.9
Dis-AngHP-PPF [3]59.364.680.587.4
Dis-AngRelative [14]58.063.878.185.4
+ +# 4.3. Ablation Studies + +In this section, we conduct comprehensive ablation studies to shed more light on the superiority of our method on the REAL275 dataset. + +Efficacy of Pose-invariant Feature Extraction. In order to validate the necessity of pose-invariant feature extraction, we first conduct ablation studies on the dense point cloud feature extractor in Table 3. The results reveal a significant performance drop of $8.3\%$ in $5^{\circ}2\mathrm{cm}$ when replacing the proposed pose-invariant PoseInv-PointNet++ with the original pose-sensitive PointNet++ [22], highlighting the effectiveness of extracting inherently pose-invariant features. We further conduct comprehensive ablation studies on local and global geometric descriptors in Table 4. As seen from the table, when the local geometric descriptor is replaced from our pose-invariant Dis-Ang to the pose-sensitive relative position embedding adopted by AG-Pose [14], performance drops by $3.3\%$ in $5^{\circ}2\mathrm{cm}$ . And when using other pose-invariant descriptors, such as PPF [5], or even omitting geometric descriptors to ensure pose-invariance, performance in $5^{\circ}2\mathrm{cm}$ is still higher than the relative position embedding. A similar trend can be observed in the ablation studies of the global geometric descriptor, where the pose-sensitive relative position embedding consistently performs worse than the pose-invariant HP-PPF [3] and Dis-Ang in all metrics. These results strongly demonstrate the essentiality of pose-invariant features, which can facilitate correspondence prediction and lead to a more precise object pose estimation performance. + +Efficacy of Shape-sensitive Feature Interaction. Table 5 provides the performance comparison of different local and global feature interaction strategies. It can be observed that without feature interaction, performance drops by $12.0\%$ in $5^{\circ}2\mathrm{cm}$ , indicating the importance of feature interaction + +Table 5. Ablation studies on the strategies of feature interaction. + +
Feature Interaction5°2cm5°5cm10°2cm10°5cm
LocalGlobal
NoneNone47.755.170.680.5
AttentionAttention59.764.881.588.2
NoneAttention56.362.077.685.2
AvgPoolAttention57.762.679.085.8
AttentionNone51.458.772.682.6
AvgPool [14]54.459.777.584.6
+ +Table 6. Impact of the number of geometric interaction blocks. + +
Block Number L5°2cm5°5cm10°2cm10°5cm
047.755.170.680.5
254.760.974.782.8
456.062.279.988.1
659.764.881.588.2
857.963.979.987.9
+ +from a holistic perspective. For local feature interaction, we experiment with the average pooling (AvgPool) operation, which performs better than no interaction but still lags behind the attention mechanism, which we attribute to the fact that simple AvgPool cannot adequately capture the detailed structure of local parts. For global feature interaction, when keypoint-wise features are simply concatenated with the globally averaged features yielded via an AvgPool, as in AG-Pose [14], performance drops by $5.3\%$ in $5^{\circ}2\mathrm{cm}$ . The results indicate that this approach fails to capture the holistic structure information as thoroughly as the attention mechanism, limiting the shape-sensitivity of features. Additionally, as shown in Table 4, geometric structure embedding can facilitate the shape-sensitive interaction among features, leading to a $3.9\%$ performance improvement in $5^{\circ}2\mathrm{cm}$ . We further evaluate the impact of varying number $L$ of geometric interaction blocks in Table 6. As the number of blocks increases, the performance of pose estimation improves, reaching a saturation at six layers. Further increasing the block number does not yield additional performance gains, but instead increases the computational overhead. Therefore, we choose $L = 6$ by default. + +Efficacy of Outlier Identification and Removal. We first conduct ablation studies on outlier-aware correspondence prediction in Table 7. When outlier scores are not predicted, all correspondences are indiscriminately learned, which can cause the network to be distracted by outlier points and challenging correspondences. As shown in the table, without outlier-awareness, performance drops by $9.2\%$ in $5^{\circ}2\mathrm{cm}$ . Even with the RANSAC [6] algorithm for outlier removal, the pose estimation precision remains suboptimal. These results highlight the necessity of explicit identification and removal of outliers. Table 8 further present the performance and time consumption comparison of different pose fitting algorithms. When the Umezama [28] algorithm + +Table 7. Ablation studies on outlier-aware correspondence prediction. Without outlier-awareness, all correspondences are supervised by $\mathcal{L}_n^{\mathrm{nocs}}$ and used for pose fitting. * denotes results with the RANSAC algorithm. + +
Correspondence Prediction5°2cm5°5cm10°2cm10°5cm
w/o Outlier-Aware50.556.576.485.0
w/o Outlier-Aware*53.159.477.285.8
w/ Outlier-Aware59.764.881.588.2
+ +Table 8. Ablation studies on the pose fitting algorithm. OR indicates outlier removal by applying a threshold on the outlier scores. We also report the average pose fitting time per image. + +
Pose Fitting5°2cm5°5cm10°2cm10°5cmTime (ms)
Umeyama46.451.468.078.61.55
w/ RANSAC [6]58.062.481.388.06.50
Umeyama + OR59.764.881.588.21.97
w/ RANSAC [6]59.764.881.588.24.94
Deep Estimator [12]57.164.078.587.66.41
+ +is applied on all correspondences, performance is severely affected by outliers, with only $46.4\%$ in $5^{\circ}2\mathrm{cm}$ . RANSAC improves performance to $58.0\%$ in $5^{\circ}2\mathrm{cm}$ , but the pose fitting time increases from $1.55\mathrm{ms}$ to $6.50\mathrm{ms}$ due to the need for numerous iterations. In contrast, we identify and remove outliers with a lightweight outlier predictor, achieving $59.7\%$ in $5^{\circ}2\mathrm{cm}$ with a faster pose fitting speed of $1.97\mathrm{ms}$ per image. Adding RANSAC does not lead to further performance improvements, but rather slows down the pose fitting process, indicating the effectiveness and efficiency of the proposed outlier predictor. We also experiment with a deep estimator [12] for pose fitting, which leads to a $2.6\%$ drop in $5^{\circ}2\mathrm{cm}$ , exhibiting a weaker robustness to outliers. + +# 5. Conclusion + +In this work, we perform a comprehensive analysis of the existing two-stage correspondence-based category-level pose estimation paradigm and introduce two core essentials: shape-sensitive and pose-invariant feature extraction to facilitate transformation learning during the correspondence prediction stage, and outlier correspondence removal to facilitate robust pose estimation during the pose fitting stage. Based on these insights, we propose a simple yet effective approach called SpotPose, which achieves superior performance with no bells and whistles. Extensive experimental results on three challenging benchmarks demonstrate the effectiveness of the proposed method. + +# 6. Acknowledgement + +This work was supported by the Open Fund of National Key Laboratory of Deep Space Exploration (Grant NKLDSE2023A009). + +# References + +[1] Kai Chen and Qi Dou. Sgpa: Structure-guided prior adaptation for category-level 6d object pose estimation. 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Despite advances, Transformer and CNN based methods often struggle with variations in staining and morphology, limiting feature extraction. In medical image segmentation, where datasets often have limited sample availability, recent state-of-the-art (SOTA) methods achieve higher accuracy by leveraging pre-trained encoders, whereas end-to-end methods tend to underperform. This is due to challenges in effectively transferring rich multiscale features from encoders to decoders, as well as limitations in decoder efficiency. To address these issues, we propose an architecture that captures multi-scale local and global contextual information and a novel decoder design, which effectively integrates features from the encoder, emphasizes important channels and regions, and reconstructs spatial dimensions to enhance segmentation accuracy. Our method, compatible with various encoders, outperforms SOTA methods, as demonstrated by experiments on four datasets and ablation studies. Specifically, our method achieves absolute performance gains of $2.76\%$ on MoNuSeg, $3.12\%$ on DSB, $2.87\%$ on Electron Microscopy, and $4.03\%$ on TNBC datasets compared to existing SOTA methods. Code: https://github.com/saadwazir/MCADS-Decoder + +# 1. Introduction + +Segmenting biomarkers in medical images is crucial for biomedical applications involving the evaluation of biomarkers like glands and nuclei for accurate diagnoses. Despite its importance, medical image segmentation faces challenges due to limited samples and the variability in biomarker appearances and sizes. In medical image segmentation, where datasets often have limited sample availability, recent SOTA methods achieve higher accuracy by leveraging pre-trained encoders, whereas end-to-end models tend to underperform. This underperformance is due + +to challenges in effectively transferring rich multiscale features from encoders to decoders, as well as limitations in decoder efficiency. + +Convolutional Neural Networks (CNN) based models like UNet [44] and its advanced variants (nested [38], recurrent [3], dual [16, 23] encoder-decoder structures) have improved segmentation accuracy. However, these models often struggle to capture long-range dependencies, a limitation mitigated by techniques like dilated convolutions [49] and attention mechanisms [14, 15, 37, 54]. While CNNs are crucial for vision tasks, their reliance on localized receptive fields limits their ability to capture long-range dependencies in images, leading to only modest improvements and highlighting the need for further accuracy enhancements. + +Recent transformer based models, such as Vision Transformers, excel at capturing long-range interactions but lack precision when modeling local contexts. Hybrid models like SegFormer [53] and Uformer [50] address this by integrating convolutional layers with transformers to handle local and global features. Although vision transformers address CNN's limitations in capturing long-range pixel dependencies, they require large datasets, and self-attention limits their ability to learn local pixel relations [11, 21]. + +Decoders are crucial in segmentation, transforming low-resolution features into detailed pixel-level predictions. The U-Net, with its skip connections, improves spatial information retention, but early decoders relying on simple upsampling [9, 28] often generated coarse segmentation maps. Attention based decoders [2, 37, 58] further enhanced multiscale feature fusion, but they struggled with precise boundary delineation. + +Although these advancements have brought improvements, there remains a significant need for methods that can better capture pixel dependencies across all dimensions and produce accurate segmentation. For motivation, encoders have limitations, and beyond a point, further improvements do not enhance accuracy. Experiments in this study show that even high-end pre-trained encoders may not achieve SOTA accuracy. Thus, we prioritized optimizing the decoder, testing it with both pre-trained and non-pretrained + +encoders. In this study, we focus on segmenting biomarkers such as nuclei and mitochondria in medical images, which pose significant challenges due to their size variation, unclear boundaries, and complex appearances. Our primary contribution is a significant increase in segmentation accuracy, achieved through a novel decoder design that accurately segments diverse biomarkers while overcoming the limitations of existing approaches. Our main contributions are as follows: + +- We have developed a novel Multiscale Convolution Attention with Depth-to-Space (MCADS) decoder for medical image segmentation. The MCADS decoder leverages the multi-stage feature representation of vision encoders while learning multiresolution spatial representations. It incorporates novel attention modules to suppress unnecessary information. Additionally, it utilizes a Depth-to-Space Upsampling Block (DSUB) in the distal decoder layers to prevent information loss during upsampling. +- We proposed new attention mechanisms, including the Residual Linear Attention Block (RLAB), which effectively integrates and refines features between the skip connections of the encoder and the feature maps of the decoder to prioritize the most relevant information. Additionally, the Channel and Spatial Attention Block (CASAB) was introduced to emphasize important channels and focus on relevant spatial regions. +- We proposed modifications for the U2-Net encoder, effectively capturing rich multi-scale local and global contextual information to complement our decoder for the semantic segmentation task. The encoder outperforms SOTA encoders, but it is especially strong when combined with MCADS, obtaining $2 - 3\%$ higher accuracy than SOTA. +- We conducted extensive experiments, and our evaluation demonstrates that these advancements collectively improve the performance of our proposed method compared to SOTA models. + +# 2. Related Work + +CNN's have been crucial as encoders for managing spatial relationships in images. In segmentation, U-shaped networks are favored for their efficient encoder-decoder structure, with U-Net pioneering the use of skip connections to integrate multi-level information in decoding. Hover-Net [17] further enhances this by using the distance of nuclear pixels from their centers of mass to capture detailed information. Studies [28, 44, 51, 59] have demonstrated that incorporating features from multiple deep layers can improve results. Variants of UNet like U2-Net [38] incorporate multi-scale feature fusion to capture local and global context; UNet++ [61], UNet $3+$ [19] utilize dense and full-scale skip connections enhancing feature map integration, and in + +corporate deep supervision to further improve decoder performance. Despite improvements, these models still struggle to capture long-range dependencies, sparking interest in attention based models. Examples include MA-Unet [4], which leverages multi-scale features and attention. Additional attention techniques like spatial and residual attention have been incorporated into other UNet models, such as SCAU-Net [60] and RAUNet [36]. The nnU-Net [20] model addresses adaptability by enabling self-tuned preprocessing for optimal predictions. SegResNet [32] utilizes a variational autoencoder for training along with a segmentation decoder. Although CNNs are fundamental to many vision applications, their inherent reliance on localized receptive fields constrains their capacity to effectively capture long-range dependencies within images. + +Transformers based architectures represent a recent breakthrough in computer vision. For image segmentation, TransUNet [8] uses a transformer as an encoder for robust feature representation and a U-Net-like decoder to effectively upsample the features. The Swin-UNet [6] model uses a hierarchical Swin Transformer encoder with shifted windows for context extraction and a symmetric decoder with a patch-expanding layer to efficiently restore spatial resolution during upsampling. SegFormer [53] simplifies the decoder with an MLP based approach. Additionally, UCTrasNet [48] introduces channel-wise cross-fusion and attention mechanisms for skip connections using a transformer backbone. However, these methods rely on large datasets to effectively learn long-range dependencies, and the improvements in segmentation accuracy have been limited. While vision transformers overcome the limitations of CNNs in capturing long-range pixel dependencies, the self-attention used in transformers limits their ability to learn local (contextual) relations among pixels [11, 21]. + +Improvement in Decoder design has been explored through various strategies, including multi-scale context aggregation [56], the integration of dense [61] or full-scale skip connections [19], deep supervision [7, 57], efficient spatial reconstruction modules [41, 42], dual decoder designs [47], and the incorporation of transformer blocks in the decoder [6]. For instance, PolypPVT [13] and Yang et al. [55] integrate CBAM [52] within their decoding stages. More recently, Transformer CASCADE [40], MIST [39], and EMCAD [41] have proposed decoder designs. Following [6], they integrate features across multiple stages from a transformer encoder by leveraging various attention mechanisms, which are modified and enhanced versions of [18, 37, 52] to achieve notable performance in medical image segmentation. However, several constraints are associated with these approaches, including a focus on maximizing the utility of pre-trained backbones, attention mechanisms that are suboptimal for capturing both short- and long-range dependencies, and upsampling methods that of + +ten fall short in fully restoring information. As a result, improvements in segmentation accuracy remain incremental, highlighting the need for more effective solutions. + +The Segment Anything Model (SAM) [24] has proven effective in tackling diverse image segmentation challenges. Utilizing sparse and dense prompts, SAM enables robust feature extraction and zero-shot generalization. Recent studies [10, 12, 30, 34, 46] have explored fine-tuning strategies to adapt its capabilities for biomarker segmentation. However, despite their advanced feature extraction capabilities, refined fine-tuning techniques, and expert prompting strategies, SAM-based approaches demonstrate minimal improvement or fall short of the accuracy achieved by fully trained networks that operate independently of prompting, as evidenced by our evaluation results and insights from recent studies [10, 33, 34]. Although SAM-based methods are not the central focus of this study, they are included to provide deeper insight and a more comprehensive perspective. + +# 3. Method + +In this section, we will introduce the MCADS decoder that we have proposed. After that, we will delve into detailed explanations of our proposed encoder, the overall architecture, and the loss function. + +# 3.1. Multiscale Convolution Attention with Depth-to-Space (MCADS) decoder + +The overall decoder architecture is shown in Figure 1 (b), and the different modules of our decoder are described below. + +# 3.1.1. Convolution Block + +In our Convolution Block (CB), shown in Figure 1 (c), we utilize a depthwise $3 \times 3$ convolution $DWC_{3x3}$ to extract spatial features, maintaining a lower parameter count than standard convolutions. A subsequent $1 \times 1$ convolution $\text{Conv}_{1 \times 1}$ adjusts the number of filters. Both convolution layers are followed by Batch Normalization $(BN)$ and LeakyReLU activation $(LR)$ . $LR$ introduces a small slope for negative inputs, preserving a non-zero gradient during inactivity, which helps prevent the dying ReLU problem during training [31]. The Convolution Block is formulated as: + +$$ +C B = L R \left(B N \left(\operatorname {C o n v} _ {1 x 1} \left(L R \left(B N \left(D W C _ {3 x 3} (x)\right)\right)\right)\right) \quad (1) \right. +$$ + +where $x$ represents the input feature map. + +# 3.1.2. Depth-to-Space Upsampling Block (DSUB) + +Applying Depth-to-Space $D2S$ early in the decoder preserves detailed information learned by the encoder, which compacts rich features into a smaller spatial space. Whereas + +EMCAD uses nearest-neighbor upsampling in all stages, which is more prone to information loss. The $D2S$ operation rearranges features into a higher resolution without altering their content, ensuring the decoder can immediately process detailed spatial information. We further validate this design choice through ablation studies, as discussed in Section 5.2. + +In our proposed Depth-to-Space Upsampling Block, shown in Figure 1 (d), the process begins by determining the number of filters required for upsampling. This is calculated as the product of the output channels and the square of the downsampling factor: $F = C_{\mathrm{prev}} \times 2^d$ , where $F$ is the number of filters, $C_{\mathrm{prev}}$ is the number of channels from the previous layer, and $d = 2$ is the downsampling factor. This calculation ensures that the feature map is prepared for the subsequent Depth-to-Space ( $D2S$ ) [45] transformation. The $D2S$ operation then rearranges the channels into higher spatial dimensions. A final refinement step is applied. This block is described in Equation 2: + +$$ +D S U B = C B \left(\operatorname {R e L U} \left(\operatorname {C o n v} _ {3 \times 3} \left(D 2 S \left(\operatorname {R e L U} \left(\operatorname {C o n v} _ {3 \times 3} (x)\right)\right)\right)\right)\right) \tag {2} +$$ + +# 3.1.3. Effective Upsampling Block (EUB) + +The Effective Upsampling Block (EUB), shown in Figure 1 (e), begins with a convolutional block applied before upsampling. This step reduces noise and irrelevant features learned in earlier stages. Next, the upsampling operation uses bilinear interpolation $(BI)$ . After upsampling, a second convolutional block is applied to refine the feature map further. This ensures the effective integration of high-level semantic information with the newly increased spatial resolution. Ablation studies in Table 6 confirm the computational efficiency and performance of EUB compared to transpose convolutions. The EUB is formulated as: + +$$ +E U B = C B (B I (C B (x))) \tag {3} +$$ + +# 3.1.4. Channel Attention and Spatial Attention Block (CASAB) + +We propose the Channel and Spatial Attention Block (CASAB), shown in Figure 1 (f), designed to selectively emphasize the most important channels and the most informative features in spatial dimensions. This fusion of channel and spatial attention allows CASAB to capture local spatial information and global channel dependencies, enabling the model to efficiently learn both global and local features. In contrast EMCAD utilize the enhance CBAM [15] for spatial and channel attention. The process of CASAB begins with feature refinement, followed by a Channel Attention Module (CAM). In CAM, global average pooling (GAP) and global max pooling (GMP) capture overall feature context and critical activations, respectively. The combination of GAP and GMP provides a + +![](images/48d84c89cd7565ce5658975c91f15382701b296f8a545e2bcce5c2ded5dbf6e5.jpg) +Figure 1. Overview of the proposed architecture: (a) Encoder feature levels at different scales, (b) Multiscale Convolution Attention with Depth-to-Space (MCADS) decoder, (c) Convolution Block, (d) Depth-to-Space Upsampling Block (DSUB), (e) Effective Upsampling Block (EUB), (f) Channel and Spatial Attention Block (CASAB) with Global Max Pooling (GMP), Global Average Pooling (GAP), Max Pooling (MP), Mean Pooling (MP $\alpha$ ), Min Pooling (MP $\beta$ ), and Sum Pooling (SP), (g) Residual Linear Attention Block (RLAB) with Residual Block (RB). + +more balanced information set, helping the network decide which channels to emphasize or suppress. These pooled features are combined and passed through two $FC$ layers using the Swish activation [43] for non-linearity and smooth gradients. The final dense layer with Sigmoid activation generates attention weights that scale the original feature map, emphasizing the most relevant channels. CAM is formulated as: + +$$ +C A M (x) = x \cdot \sigma \left(F C \left(S w i s h \left(F C \left(G A P (x) + G M P (x)\right)\right)\right)\right) \tag {4} +$$ + +where $\sigma$ denotes the Sigmoid activation. + +Simultaneously, in the Spatial Attention Module (SAM), the input feature map undergoes multiple pooling operations, including mean pooling $(MP)$ , max pooling $(MP_{\alpha})$ , min pooling $(MP_{\beta})$ , and sum pooling $(SM)$ . This captures the presence, prominence, weakest responses, and overall intensity of spatial features, respectively. This is formulated as: + +$$ +x _ {p o o l} = \operatorname {C o n c a t} (M P (x), M P _ {\alpha} (x), M P _ {\beta} (x), S M (x)) \tag {5} +$$ + +These concatenated features are refined using a $7 \times 7$ depthwise convolution, capturing broader contextual information. This is followed by Swish and Sigmoid activation, generating a spatial attention map to scale the input feature + +map and highlight critical spatial regions. The spatial attention module $SAM$ is formulated as: + +$$ +S A M \left(x, x _ {p o o l}\right) = x \cdot \sigma \left(\operatorname {C o n v} _ {1 \times 1} \left(S w i s h \left(\operatorname {C o n v} _ {7 \times 7} \left(x _ {p o o l}\right)\right)\right)\right) \tag {6} +$$ + +The outputs of the channel and spatial attention modules are combined using element-wise addition, as represented in: + +$$ +C A S A B = C A M (x) + S A M \left(x, x _ {p o o l}\right) \tag {7} +$$ + +# 3.1.5. Residual Linear Attention Block (RLAB) + +Our proposed Residual Linear Attention Block (RLAB), as shown in Figure 1 (g), is designed to effectively integrate and refine features between the skip connections of the encoder and the feature maps of the decoder. Furthermore, we validated this design choice through our ablation study, as mentioned in Section 5.4. The RLAB begins by refining the skip connection of the encoder through a specialized Residual Block (RB) as mentioned in Equation 8. The RB is iterated multiple times, with each iteration involving a residual connection, which ensures that essential information from the encoder is preserved while allowing the network to learn new features. Using residual connections prevents the degradation of feature quality as the input passes through multiple layers. The output of the RB at the $i$ -th iteration, $i \in (1, \dots, N)$ , where $N$ is the depth of the stage. + +We configured the number of iterations in the RLAB as [5, 4, 3, 2, 1] for stages 4 through 0, respectively, based on the intuition that the skip connections of deeper layers require more refinement [27]. It is formulated as follows: + +$$ +x _ {R B _ {i}} = B N \left(L R \left(x _ {R B _ {i - 1}} + \operatorname {C o n v} _ {1 \times 1} \left(\operatorname {C o n v} _ {3 \times 3} \left(x _ {R B _ {i - 1}}\right)\right)\right)\right) \tag {8} +$$ + +After refining the skip connection, the output from the RB is concatenated with the feature map of the decoder. This concatenation merges the high-resolution features of the encoder with the contextually rich, low-resolution features of the decoder, facilitating a comprehensive feature representation that leverages information from both the encoder and decoder pathways, as shown in the following equation: + +$$ +\bar {x} = \operatorname {C o n c a t} \left(x _ {R B}, D S U B \text {o r} E U B\right) \tag {9} +$$ + +Following the concatenation, the combined feature map is refined, after which the feature map is projected into keys, queries, and values using dense layers. The keys and queries compute attention weights through a dot product, then normalized via a softmax function as seen in Equation 10. These weights determine how much focus should be placed on different parts of the feature map, allowing the network to prioritize the most relevant information. The resulting weighted values are then added to the original feature map through a residual connection, ensuring that the features of the decoder are retained while being enhanced by the attention mechanism. In contrast, EMCAD employs a modified version of the Attention Gate [37], which filters encoder features by combining them with a gating signal from the decoder to generate attention coefficients. The RLAB block is formulated in Equation 11: + +$$ +A t t n = \text {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V \tag {10} +$$ + +$$ +R L A B = \bar {x} + A t t n (C B (\bar {x})) \tag {11} +$$ + +where $Attn$ is the attention mechanism, and $Q, K,$ and $V$ are the projection matrices of the query, key, and value, respectively. + +This series of operations within RLAB serves as an attention mechanism, which is particularly beneficial for performing precise feature alignment and integration across different levels of the network. + +# 3.2. Proposed Encoder + +Following [38], we propose modifications to the residual U-block of U2-Net with our proposed attention mechanisms. We integrated attention mechanisms between the skip connections and the upsampling layers within the residual U-block, enhancing the network's ability to focus on long-range, multi-scale features. This is illustrated in Figure 2 + +![](images/835b7b4608f8acd4839dd6e7f7ca1c3443c44abaffc5748a81292c4687fa3cbd.jpg) +(a) RSU Block / Bridge + +![](images/37cb24dbb40594e4e44b4e155c6a713e7facbc76d9c8aedd63b526813079933d.jpg) +(b) Proposed Encoder +Figure 2. Overall representation of our proposed encoder. + +(a), where $\mathbf{N}$ represents the number of layers in the encoder, equivalent to $L$ in U2-Net. Additionally, after each residual U-block, we implemented CASAB as shown in Figure 2 (b), where M repents the encoder stage, which effectively prioritizes the most significant channels and spatial regions, enabling the network to capture fine-grained details while integrating broader contextual information. We validate the effectiveness of our encoder through ablation studies as explained in Section 5.1. + +# 3.3. Overall Architecture + +To demonstrate the generalization, effectiveness, and capability of handling multi-scale features in medical image segmentation, we integrate the decoder with the proposed encoder. However, the decoder is highly adaptable and seamlessly compatible with other hierarchical backbone networks, as validated by the ablation studies in Section 5.1. The decoder processes the features extracted from multiple encoder stages at different scales (S1, S2, S3, S4, S5, and Bridge). It then generates six segmentation maps by applying sigmoid activation to outputs from six stages (B1, D5, D4, D3, D2, and D1), with each map corresponding to a specific encoder stage. Among the prediction maps, D1 is treated as the final output. We utilize binary cross-entropy loss for training. In the MCADS decoder, the segmentation heads generate six prediction maps, each contributing to a corresponding loss calculation. This approach facilitates deep supervision across all predictions, acting as a form of regularization, strengthening the gradient signal across the network, and guiding each intermediate layer to produce a reasonable segmentation map. This ensures that features useful for segmentation are learned at different levels of abstraction. As a result, the model is better at capturing both local and global context, leading to more accurate segmentation. + +The individual losses are summed to form a cumulative loss, which is the primary focus for minimization during the training process. The loss function is represented as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {B _ {1}} + \mathcal {L} _ {D _ {5}} + \mathcal {L} _ {D _ {4}} + \mathcal {L} _ {D _ {3}} + \mathcal {L} _ {D _ {2}} + \mathcal {L} _ {D _ {1}} \tag {12} +$$ + +where $\mathcal{L}$ is the binary cross-entropy loss [22]. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +We utilized four publicly available datasets that have also been benchmarked in recent SOTA studies, such as EM-CAD (CVPR 2024) [41], InstaSAM (MICCAI 2024) [34], FusionU-Net (ACML 2023) [26], and UCTransNet (AAAI 2022) [48]. The datasets include Multi-organ Nucleus Segmentation (MoNuSeg) [25], the 2018 Data Science Bowl (DSB) [5], Electron Microscopy (EM) [29], and Triple-negative Breast Cancer (TNBC) [35]. These datasets include images captured under different illumination conditions and magnifications, featuring various cell types and modalities. To assess performance, we utilized a range of metrics. For pixel based evaluation, we used Intersection over Union (IoU), Dice coefficient, Precision, Recall, and the False omission rate (FOR). For surface distance based metrics, the 95th percentile of the Hausdorff distance (HD95) and the Average Surface Distance (ASD) were used to provide a comprehensive evaluation. + +# 4.2. Experimental Setup & Implementation Details + +To train the model, we utilized the Adam optimizer with a learning rate of $1\mathrm{e}^{-4}$ and a batch size of 8, employing the HeUniform kernel initializer for the convolution operations. The encoder used standard filter sizes commonly employed in encoder-decoder frameworks [1], specifically [64, 128, 256, 512, 512, 512] for stages 0 to 4 and the bridge. We employed end-to-end training without pre-trained networks, using the provided training sets of the MoNuSeg, DSB, and EM datasets. The model was trained entirely from scratch, with over 200 epochs, and best weights were chosen based on performance on the validation set. Both offline and online augmentation were incorporated, generating $256\times 256$ overlapping patches with a stride of 128 for all datasets in the training set. For methods utilizing pre-trained backbones, patches of $224\times 224$ were generated with a stride of 128. To ensure a fair comparison, we reproduced all results for all datasets using their publicly available code and averaged them over five runs. For testing, we created similar overlapping patches, performed predictions, reassembled them, and evaluated the results. The provided test sets of the MoNuSeg and EM datasets were used for evaluation, while for DSB, we followed the evaluation strategy outlined in [41]. Additionally, we provide zero-shot results using the TNBC dataset to offer a comprehensive analysis. + +# 4.3. Results + +We compared our method with SOTA CNN, Transformer and SAM based segmentation approaches focused on biomarker segmentation tasks. Despite not using pre + +Table 1. Performance comparison on the MoNuSeg Dataset. Bold indicates the best performance, and underline indicates the second best. We reproduced all results and averaged them over five runs. For optimal performance, we performed fine-tuning on the SOTA methods. Results marked with * were copied from the original papers. '-' indicates unavailable results. + +
ModelIoU ↑Dice ↑Prec. ↑Rec. ↑FOR ↓HD95 ↓ASD ↓
U-Net [44]59.6273.4274.8773.040.07663.66090.8109
Hover-Net [17]62.9077.2677.6777.540.06893.86870.8114
UNet++ [61]69.3481.8375.3190.290.04222.79010.6458
U2-Net [38]68.8981.3377.2086.880.044413.4453.0647
nnU-Net [20]67.6080.4281.6380.880.05553.33570.6852
FusionU-Net [26]66.5779.3273.2987.260.04173.94010.8236
SegResNet [32]69.0281.0082.5080.970.058713.0292.8829
UCTransNet [48]65.5679.2075.8382.880.056118.3664.2000
TransUNet [8]67.8980.2281.5879.170.06103.56020.7379
Swin-Unet [6]65.3879.0172.3887.880.04033.78710.7893
PVT-CASCADE [40]70.7482.7978.3688.240.03623.01100.6163
EMCAD [41]71.2882.8982.0983.860.04883.18180.6285
InstaSAM [34]*59.6078.60-----
All-in-SAM [12]*69.7682.44-----
UN-SAM [10]*70.8282.86-----
SAC 0-expert [33]*72.6184.03-----
Ours74.0485.0483.7886.430.03081.85500.4810
+ +Table 2. Performance comparison on the DSB Dataset. We reproduced all results and averaged them over five runs. For optimal performance, we performed fine-tuning on the SOTA methods. + +
ModelIoU ↑Dice ↑Prec. ↑Rec. ↑FOR ↓HD95 ↓ASD ↓
U-Net [44]83.8390.1789.0993.780.01287.67971.9192
Hover-Net [17]81.2989.0488.7391.010.02467.62892.1298
UNet++ [61]83.9591.1088.4994.260.011510.0452.4359
U2-Net [38]82.9690.0390.2891.080.016310.8692.3375
nnU-Net [20]77.2486.0990.1884.330.03379.90942.7911
FusionU-Net [26]80.4788.3493.7685.120.03327.61481.8682
SegResNet [32]82.9190.0191.5489.750.02627.55802.0236
UCTransNet [48]85.2891.2593.8790.020.015811.5142.5552
TransUNet [8]84.7290.9093.3789.860.016211.2132.7168
Swin-Unet [6]84.4991.0390.7792.720.01328.04151.9232
PVT-CASCADE [40]85.0591.0790.5593.020.01307.54271.7861
EMCAD [41]86.3692.1890.5394.890.05446.45161.4400
UN-SAM [10]*86.9392.84-----
SAC 0-expert [33]*87.3293.04-----
Ours89.4894.4294.9493.940.00362.66550.8559
+ +Table 3. Performance comparison on the Electron Microscopy Dataset. We reproduced all results and averaged them over five runs. For optimal performance, we performed fine-tuning on the SOTA methods. + +
ModelIoU ↑Dice ↑Prec. ↑Rec. ↑FOR ↓HD95 ↓ASD ↓
U-Net [44]77.4585.3788.8284.950.010046.80310.658
Hover-Net [17]79.1888.3191.4385.550.008412.6242.1152
UNet++ [61]87.0192.4992.5393.380.00424.76331.1553
U2-Net [38]86.3192.0191.9292.880.004120.8174.3750
nnU-Net [20]85.0291.8694.7589.230.00645.27351.2231
FusionU-Net [26]85.9292.3793.9990.870.00534.13601.1485
SegResNet [32]84.5190.8792.7990.130.006129.4826.5738
UCTransNet [48]85.9992.3291.5593.240.00466.76781.5115
TransUNet [8]84.8691.7794.3389.420.00626.17461.4101
Swin-Unet [6]83.7291.0892.1890.100.00599.77071.8287
PVT-CASCADE [40]86.2892.0591.6493.280.004426.8405.6181
EMCAD [41]86.0292.4393.9791.020.005519.8574.1666
Ours88.8994.0994.8193.430.00402.69340.8552
+ +trained weights like Hover-Net, PVT-CASCADE, and EM-CAD, our method outperforms these SOTA models. Our evaluation shows that the proposed method leads in both segmentation accuracy and boundary precision across all + +Table 4. Zero shot performance comparison on the TNBC Dataset. We reproduced all results. + +
ModelIoU ↑Dice ↑Prec. ↑Rec. ↑FOR ↓HD95 ↓ASD ↓
U-Net [44]53.4167.5588.7958.440.054821.1015.0472
Hover-Net [17]54.8969.2088.6859.570.053923.0175.0716
UNet++ [61]60.9474.5377.8975.200.037017.1063.9056
U2-Net [38]61.8675.6372.0282.430.034914.6593.4034
nnU-Net [20]59.3573.0684.5767.630.051116.7683.3843
FusionU-Net [26]56.8071.4487.8462.210.055718.7053.6262
SegResNet [32]61.6375.1579.5975.420.036215.3143.1723
UCTransNet [48]56.6271.2986.8362.900.054918.3403.5854
TransUNet [8]59.7173.3185.6966.900.051815.2733.2620
Swin-Unet [6]55.8770.2086.7862.130.051519.4214.3773
PVT-CASCADE [40]62.4676.1182.4974.410.037913.5062.7764
EMCAD [41]65.1378.6082.5975.880.050115.9533.3419
UN-SAM [10]*72.2783.89-----
Ours69.1681.4879.6384.510.027612.5901.9611
+ +datasets, as detailed in Table 1, 2, 3, 4 and in the qualitative results shown in Figure 4. We additionally reported the performance of SAM-based methods. Despite their heavy reliance on accurate prompt strategies and fine-tuning, their performance remains moderate and often falls short. Across multiple datasets, methods such as EMCAD and PVT-CASCADE tend to perform moderately but exhibit challenges in boundary precision. UNet++, FusionU-Net and TransUNet offer varying degrees of accuracy, while models like Swin-UNet, UCTransNet, and SegResNet consistently struggle with boundary refinement and overall performance. In zero-shot evaluation, our method exhibits strong robustness. While EMCAD and PVT-CASCADE perform competitively, they lack precision. Models like Swin-UNet, UCTransNet, and SegResNet fall behind, especially in boundary refinement. UN-SAM achieves higher scores due to its fine-tuning on the TNBC dataset, which is not utilized by any other method, including ours. However, the data distribution in the UN-SAM study is unclear. Despite this, we include UN-SAM results to provide an additional evaluation of SAM-based methods. It is worth noting that training on the TNBC dataset could improve our model's accuracy as well. + +In terms of Computational Cost, the performance of our method is comparable to other approaches, as shown in Figure 3, while delivering a high IoU. This makes our approach ideal for accuracy-critical scenarios. Compared to EMCAD, which has an inference time of 0.1219 seconds, our method takes 0.1398 seconds per sample. The difference of only 0.0179 seconds is negligible, especially since both methods require a GPU for execution, ensuring comparable efficiency in practical scenarios. + +# 5. Ablation Studies + +This section discusses the ablation studies we conducted to explore the various aspects of our architecture and experimental framework. For all the ablation studies, we utilize the MoNuSeg dataset train set for training and the test set for evaluation. + +![](images/de066833643e4b49194afa01d605b1462942f2ece249b26402b072ae526bad52.jpg) +Figure 3. Computational Complexity Comparison: IoU vs. GFlops and Parameters. + +![](images/279cfd0c60979f2cf5dcf0ec139c1525602eaa47f6337d5bcaebe65a74c26952.jpg) +Figure 4. Qualitative Results Comparison: Black pixels represent the background, while white pixels represent the biomarker. The red box highlights regions with false predictions (no prediction or over-segmentation). + +# 5.1. Effect of proposed modifications on baseline encoder + +The ablation study in Table 5 evaluates the impact of modifications to the baseline U2-Net encoder, including all other proposed modules. Inner Attention enhances accuracy by focusing on relevant features, while CASAB refines the feature maps by prioritizing important input details. These modifications significantly boost the effectiveness of the encoder, confirming their contribution to the overall performance of the model. + +# 5.2. Effect of DSUB and EUB in MCADS decoder + +The ablation study in Table 6 evaluates the impact of incorporating DSUB and EUB components into the decoder of + +Table 5. Effect of proposed modifications on baseline encoder + +
Inner AttentionCASABParamsGFlopsIoU
XX50.3161.0372.03
✓X50.7461.2572.81
✓✓50.961.8974.04
+ +Table 6. Effect of DSUB and EUB in MCADS decoder + +
BridgeStage 4Stage 3Stage 2Stage 1ParamFlopsIoU
ConvTpConvTpConvTpConvTpConvTp32.3654.5970.52
EUBEUBEUBEUBEUB27.4552.5172.23
DSUBEUBEUBEUBEUB39.2554.9272.96
DSUBDSUBEUBEUBEUB50.961.8974.04
DSUBDSUBDSUBEUBEUB62.99104.474.10
DSUBDSUBDSUBDSUBEUB65.96142.674.79
DSUBDSUBDSUBDSUBDSUB66.73184.974.88
+ +the MCADS model. Even when using only Transpose Convolutions with all other modules intact, our method achieves performance comparable to the SOTA methods. However, as EUB and DSUB are gradually introduced, performance steadily improves, particularly after adding DSUB to the first two stages. Beyond this point, the performance gains become minimal while the computational complexity increases significantly. Therefore, we opted to use DSUB only in the first two stages to balance performance with efficiency, allowing further experiments to be conducted within the constraints of our available hardware resources. + +# 5.3. Ablation Study on Encoder-Decoder Configurations + +We compared our proposed decoder MCADS with the baseline decoder EMCAD using two CNN based encoders, namely ResNet-50 and the Modified U2-Net encoder (Ours), as well as two Transformer based encoders, the Multi-axis Vision Transformer (MaxViT-B) and the Pyramid Vision Transformer (PVT v2-B2). These transformer based encoders were selected because they are commonly used in SOTA methods. The ablation study presented in Table 7 provides a detailed comparison of various encoder-decoder combinations, highlighting their impact on key performance metrics. The results demonstrate that when paired with our decoder, the custom encoder consistently outperforms others, achieving the highest IoU and the lowest HD95 values, indicating superior segmentation accuracy and boundary precision. Notably, even when using different encoder architectures, such as the CNN based ResNet-50 and Transformer based MaxViT-B, our decoder performs better than the EMCAD decoder. This suggests that the architecture of our decoder is robust and effective across various encoder types, further validating the strength of the proposed design. + +Table 7. Comparison of Encoder and Decoder Combinations + +
EncoderDecoderIoUHD95
ResNet-50EMCAD63.3619.916
ResNet-50Ours65.5913.072
OursEMCAD71.932.2910
OursOurs74.041.8550
MaxViT-BEMCAD70.852.9933
MaxViT-BOurs72.342.4346
PVT v2-B2EMCAD71.283.1818
PVT v2-B2Ours72.972.1755
+ +Table 8. Effect of different components of MCADS decoder. + +
DSUB / EUBRLABCASABParamsGFlopsIoU
XXX25.4526.5969.03
✓XX43.7336.5970.71
✓✓X50.7161.7972.17
✓✓✓50.961.8974.04
+ +# 5.4. Ablation Study on MCADS Decoder Components + +We conducted an ablation study to assess the impact of different components in the MCADS decoder, as detailed in Table 8. The study evaluates the effects of incorporating these components individually and in combination. Initially, without any of these components, the decoder achieves moderate performance. Adding DSUB/EUB significantly improves the IoU, indicating enhanced feature refinement. Introducing RLAB further boosts performance by refining the feature representations through iterative processing. Finally, incorporating CASAB alongside DSUB/EUB and RLAB results in the highest IoU, demonstrating the effectiveness of combining channel and spatial attention mechanisms for optimal segmentation accuracy. This progressive improvement confirms that each component of the MCADS decoder contributes to enhancing the overall performance of the model. + +# 6. Conclusion + +We introduces MCADS, a novel decoder designed to reconstruct spatial dimensions and produce accurate segmentation by incorporating RLAB, which integrates multiscale features, and CASAB, which emphasizes important channels and spatial regions. Extensive experiments demonstrate that it consistently outperforms recent SOTA methods across all evaluation metrics. We believe the innovative design will significantly contribute to improving a wide range of medical image segmentation tasks. + +# Acknowledgments + +This work was supported by the IITP(Institute of Information & Coummunications Technology Planning & Evaluation)-ITRC(Information Technology Research Center) grant funded by the Korea government(Ministry of Science and ICT)(IITP-2025-RS-2023-00259703) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(RS-2025-00573160). + +# References + +[1] Nikolas Adaloglou. 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However, VQ-based methods have inherent limitations. Representing continuous motion data as limited discrete tokens leads to inevitable information loss, reduces the diversity of generated motions, and restricts their ability to function effectively as motion priors or generation guidance. In contrast, the continuous space generation nature of diffusion-based methods makes them well-suited to address these limitations and with even potential for model scalability. In this work, we systematically investigate why current VQ-based methods perform well and explore the limitations of existing diffusion-based methods from the perspective of motion data representation and distribution. Drawing on these insights, we preserve the inherent strengths of a diffusion-based human motion generation model and gradually optimize it with inspiration from VQ-based approaches. Our approach introduces a human motion diffusion model enabled to perform masked autoregression, optimized with a reformed data representation and distribution. Additionally, we propose a more robust evaluation method to assess different approaches. Extensive experiments on various datasets demonstrate our method outperforms previous methods and achieves state-of-the-art performances. + +# 1. Introduction + +In this paper, we study the problem of human motion generation from the textual prompt (e.g., a person walks). Due to the remarkable performance in the image generation domain [32, 80, 82], diffusion models are largely adopted for human motion generation starting with the pioneer methods [44, 88, 113]. Compared with RNN [81]-based generation methods [1, 3, 24, 57], diffusion-based models offer a simpler training objective and improved stability. + +![](images/3d59919707059e5ceb863cae34e31e0fe1260941982de161657e8e54a53b2a47.jpg) +Figure 1. The FID results on HumanML3D dataset. The bubble size is proportional to the model size. We achieve superior performance and demonstrate model scalability. + +In 2023, the exploration of Vector Quantization (VQ) techniques for human motion representation becomes increasingly dominant, marked a noticeable shift in attention away from diffusion models for the human motion generation task [25, 26, 111]. These methods transform continuous motion representations (e.g. processed joint positions) into discrete tokens, which enables the use of already proven generative architectures [6, 16, 93] and their training and sampling techniques from the field of natural language processing with minimal modifications. + +Despite the performance improvement, VQ-based methods still exhibit notable limitations. Representing continuous motion data as limited groups of discrete tokens inherently causes a loss of motion information, reduces generation diversity, and limits their ability to serve as motion priors or generation guidance (e.g., in the generation of dual-human motion and human-object interactions). Moreover, unlike language models, these discrete tokens often lack contextual richness, which can hinder model scalability. + +In contrast, the continuous space nature of diffusion-based generation methods effectively overcomes these limitations and offers potential for model scalability, as evidenced by numerous image diffusion models [51, 66]. In light of these, researchers have started to revisit diffusion-based approaches [114, 117]. However, these attempts struggle to achieve performance comparable to that of VQ- + +based methods. More importantly, the reasons for the performance gap between VQ and diffusion-based human motion generation methods remain unclear. + +In this work, we first systematically investigate why VQ-based motion generation approaches perform well and explore the limitations of diffusion-based methods from the perspective of motion data representation and distribution. Specifically, (1) We examine how VQ-based discrete formulations benefit from training with current motion data representation, which consists of redundant dimensions, while this data composition and its distribution hinder existing diffusion models. (2) We explore how VQ-based methods inherently align with current evaluation metrics, which incorporate the entire data representation including redundant dimensions, whereas diffusion-based methods are often penalized under these evaluation criteria. + +Based on our diagnostic findings and inspirations from current VQ-based approaches, we aim to close the performance gap by gradually enhancing a diffusion-based model tailored for human motion generation. We first restructure the motion data representation by removing redundant information, resulting in a distribution better suited for diffusion models. We then process them with a 1D ResNet [29]-based AutoEncoder for better per-frame smoothness. Additionally, we build a diffusion-based motion generation model with masked autoregressive strategies to simplify training objective. Finally, we propose more robust evaluators for unbiased assessments of different approaches. + +We summarize our contributions as follows: + +- We systematically investigate the reasons why VQ-based methods outperform diffusion-based methods from motion data representation and distribution perspective, providing analysis with theoretical and experimental support. +- Inspired by our diagnostic findings, we propose a scalable masked autoregressive diffusion-based generation framework and a more robust evaluation method. +- Our method achieves state-of-the-art performance on text-to-motion generation task with significant improvements on KIT-ML [77] and HumanML3D [24] datasets. + +# 2. Diagnosis: Motion Data Representation and Distribution + +In this section, we study how motion representation and distribution impact training, sampling (Sec. 2.2), and evaluation robustness (Sec. 2.3), revealing how these factors favor VQ-based methods but limit diffusion-based approaches. + +# 2.1. Preliminary + +VQ-based Human Motion Generation Methods primarily adopt either a standard Vector Quantized Variational AutoEncoders (VQ-VAEs) [92, 111] or a residual (R) VQ-VAE [26] to map motion data into discrete tokens. + +Given a motion sequence $\mathbf{x}^{1:N}\in \mathbb{R}^{N\times D}$ of length $N$ and human pose dimension $D$ , the transformation begins by encoding $\mathbf{x}^{1:N}$ into a latent sequence $\mathbf{h}^{1:n}\in \mathbb{R}^{n\times d}$ with a 1D convolutional encoder $\mathbf{E}$ . For vanilla VQ-VAE, each vector is quantized via a base VQ codebook to the nearest token. In RVQ-VAE, additional residual quantization layers are used to quantify the difference between the original latent vector and the quantized representation from the preceding layers. The indices $\mathbf{k}$ from the base layer (VQ-VAE) or all layers (RVQ-VAE) form discrete inputs for training generative models with sequence generation. + +The generated discrete sequence $\mathbf{g} = \mathbf{g}_{0:n}$ (or $\mathbf{g}_{0:n}^{0:V + 1}$ in residual case) is embedded via the codebook, then projected back (or summed then project in residual case) with an up-sample convolutional decoder $\mathbf{D}$ to obtain the final motion. + +Diffusion-based Human Motion Generation Methods. The diffusion-based methods use an interpolation function, $\mathbf{x}_t = \alpha \mathbf{x}_0 + \sigma \boldsymbol{\epsilon}$ , to combine ground truth (GT) motion data with Gaussian noise $\boldsymbol{\epsilon}$ for a noisy motion $\mathbf{x}_t$ . In motion generation, typically following DDPM [32], this function is defined as: + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon} \tag {1} +$$ + +$\bar{\alpha}_t$ controls the pace of the diffusion process where $0 = \bar{\alpha}_T < \dots < \bar{\alpha}_0 = 1$ with assumption that $\mathbf{x}_T \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ . + +During training, the model learns to predict a continuous vector from $\mathbf{x}_t$ given $t$ , usually the noise $\epsilon$ or original motion $\mathbf{x}_0$ , and is optimized with a mean squared error (MSE) loss between the predicted value and its ground truth. + +During sampling, starting from random noise $\mathbf{x}_T\sim$ $\mathcal{N}(\mathbf{0},\mathbf{I})$ , for each $t$ , the model with $\mathbf{x}_t$ as input, predicts the original motion $\mathbf{x}_0$ or the noise $\epsilon$ (then to $\mathbf{x}_0$ with Eq. (1)), and deduces intermediate samples $\mathbf{x}_{t - 1}$ (for $t\in 1$ to $T$ .. + +$$ +\frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{1 - \bar {\alpha} _ {t}} \mathbf {x} _ {t} + \frac {\sqrt {\bar {\alpha} _ {t - 1}} (1 - \alpha_ {t})}{1 - \bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon} _ {t} \tag {2} +$$ + +where $\epsilon_t\sim \mathcal{N}(0,\mathbf{I})$ , until it reaches the clean motion $\mathbf{x}_0$ + +Motion Data Representation. The majority of recent methods utilize the canonical pose representation introduced by [24] on widely-used datasets, including KIT-ML [77] and HumanML3D [24]. This representation at a given time step $i$ is defined as $\mathbf{x}^i = [\dot{r}^a,\dot{r}^{xz},\dot{r}^h,j^p,j^v,j^r,c^f]$ , comprising seven feature components: root angular velocity $\dot{r}^a$ , root linear velocities $\dot{r}^{xz}$ in the XZ-plane, root height $\dot{r}^h$ , local joint positions $j^p\in \mathbb{R}^{3(N_j - 1)}$ , local velocities $j^v\in \mathbb{R}^{3(N_j - 1)}$ , joint rotations $j^r\in \mathbb{R}^{6(N_j - 1)}$ in local space, and binary foot-ground contact features $c^f\in \mathbb{R}^4$ , where $N_{j}$ denotes the joint number. However, only the first 4 feature groups from this overparameterized representation are used to produce final human motion, making the remaining 3 components redundant. We categorize the first 4 feature groups as essential features while classifying the remaining as redundant. + +Table 1. Impact of redundant features on VQ-based models. VQ-based methods, T2M-GPT and MoMask, trained with redundant features exhibit better reconstruction performance and lead to better generation quality on the HumanML3D dataset. + +
MethodTrained WithFID ↓R-Precision ↑
RedundancyReconGenTop 1Top 2Top 3
T2M-GPT [111]✓0.0810.3350.4700.6590.758
T2M-GPT [111]✗0.0950.4180.4660.6530.753
MoMask [26]✓0.0290.1160.4900.6870.786
MoMask [26]✗0.0300.2000.4850.6810.782
+ +![](images/7cefee758aac12197c5069c1cb6bc6f02658fdb4af3f6ab95d6d062605b7564b.jpg) + +![](images/313fedf7c4fd2f9bcd76b9db933f87c117bd98af42f8a179ac34f74a11b900e5.jpg) + +![](images/29592ab4086292ef9d7a3fa20237f1e60a03a926a38061b0f32c86bc8ab8e6e4.jpg) +Figure 2. Code Usage of VQ-VAEs trained with redundancy are more balanced than VQ-VAEs trained with only essential features. + +![](images/8e42e6480473a954f7e068e4b2dac7f578259719e15c1573a15703af7fd9d611.jpg) + +# 2.2. Impacts on Training and Sampling + +In this section, we present how this motion representation and distribution impact VQ and diffusion-based methods. + +Benefiting VQ-Based Methods. The redundancy in data representation benefits VQ-VAE training which then enhances discrete generative modeling. To validate this viewpoint, we conduct ablative experiments by training VQ-VAE from T2M-GPT [111] and RVQ-VAE from MoMask [26] on HumanML3D, comparing their reconstruction performance with and without redundant data representations. Then we train T2M-GPT and MoMask following their original methods, both with and without redundant data representations, and evaluate their performance using human motion generation metrics. As shown in Tab. 1, training with redundant dimensions results in VQ-VAEs with significantly better reconstruction performance, which subsequently enhances the performance of discrete generative models. To understand the reason, we further analyze the role of data representation in VQ-VAE training. + +Let $\mathbf{x}_{\mathrm{r}}^{\mathrm{GT}}$ and $\mathbf{x}_{\mathrm{e}}^{\mathrm{GT}}$ denote the ground truth data with and without redundancy and $\mathbf{x}_{\mathrm{r}}^{\mathrm{pred}}$ and $\mathbf{x}_{\mathrm{e}}^{\mathrm{pred}}$ represent the prediction. The reconstruction loss $\mathcal{L}_r^{\mathrm{rec}}$ with redundancy can be decomposed as: + +$$ +\begin{array}{l} L _ {r} ^ {\text {r e c}} = \mathcal {L} \left(\mathbf {x} _ {\mathrm {e}} ^ {\mathrm {G T}} - \mathbf {x} _ {\mathrm {e}} ^ {\text {p r e d}} + \mathbf {x} _ {\mathrm {r} - \mathrm {e}} ^ {\mathrm {G T}} - \mathbf {x} _ {\mathrm {r} - \mathrm {e}} ^ {\text {p r e d}}\right) \tag {3} \\ = L _ {e} ^ {\text {r e c}} + \mathcal {L} \left(\mathbf {x} _ {\mathrm {r - e}} ^ {\mathrm {G T}} - \mathbf {x} _ {\mathrm {r - e}} ^ {\text {p r e d}}\right). \\ \end{array} +$$ + +where $\mathcal{L}_e^{\mathrm{rec}}$ is the reconstruction loss without redundancy + +Table 2. The results of MDM on humanML3D dataset. We report the results of MDM with original $\mathbf{x}_0$ prediction vs. with $\epsilon$ prediction. Training to predict $\mathbf{x}_0$ leads to better results. + +
MethodPredictionFID ↓R-Precision ↑
GenTop 1Top 2Top 3
MDM-50Step [88]x00.5180.4400.6360.742
MDM-50Step [88]-Cosineε31.2650.0540.1030.147
MDM-50Step [88]-Linearε1.5740.2790.3360.415
+ +representation, and $\mathcal{L}$ is typically measured with variation of $L1$ or $L2$ loss. This decomposition shows the redundancy acts as a data-level regularization + +This built-in regularization reduces model variance, making representations less sensitive to training data fluctuations. This improvement enhances generalization, ultimately leading to more effective and consistent codebook usage, as shown in Fig. 2. Specifically, on the HumanML3D test set, both VQ-VAE and RVQ-VAE, which were trained on the data with redundant dimensions, exhibit more uniform code utilization. In contrast, models trained on the data without redundancy show distinct spikes in certain codes. Numerically, for VQ-VAE, the KL divergence against uniform distribution is 0.205 vs. 0.337, and for RVQ-VAE, it is 0.243 vs. 0.351, using original vs. essential dimensions. These results demonstrate the benefit of incorporating redundancy for VQ-based methods. + +Limiting Diffusion-Based Methods. The current data representation and distribution impose constraints on the modeling approaches for diffusion-based methods. + +Most diffusion-based methods follow the DDPM [32] but predict original motion $\mathbf{x}_0$ . However, this deterministic $\mathbf{x}_0$ -only prediction in each timestep can limit training simplicity and sampling diversity. Attempts to train these methods to predict noise often result in inaccurate motion, human shape e.g. MDM [88] with cosine beta schedule, or persistent shaking e.g. MDM with linear beta schedule in Tab. 2. Below, we explain the two major factors in detail: dimensional distribution mismatch and error amplification. + +First, the current motion data do not follow a standard normal distribution with standard z-normalization due to its mixed structure consisting of features from 3D continuous (e.g. joint position), 6D rotatory (e.g. joint rotation), and categorical (e.g. foot contacts) distribution. This leads to a dimensional distribution mismatch and challenges the interpolation function (Eq. (1) for DDPM). In the forward diffusion process, due to the varying initial distributions across different feature groups of $\mathbf{x}_0$ , feature groups of $\mathbf{x}_T$ may converge to their own distinct distribution by time step $T$ , rather than all converging to a same standard distribution. Consequently, in reverse diffusion process, starting from a standard distribution leads to errors in motion generation. + +Second, when normalizing the human motion data, the standard deviation (SD) is averaged in each of 7 feature groups as $\sigma^{\prime\mathbf{x}} = \frac{\sum_{i=0}^{D-1} \sigma_i^\mathbf{x}}{D}$ , where D is the number of di + +Table 3. The result with existing evaluator on HumanML3D dataset. We alter data by adding noise or replacing it with noise in essential and redundant dimensions. The result shows the evaluator heavily emphasizes redundant dimensions during evaluation. + +
DimensionMethodFID ↓R-Precision ↑
GenTop 1Top 2Top 3
EssentialAdd Noise2.0210.4420.6340.740
RedundantAdd Noise21.0320.3100.4710.575
EssentialReplace W/ Noise15.1640.2640.4250.538
RedundantReplace W/ Noise38.1670.1540.2570.336
+ +mensions in each group. We define the ratio $\phi^{\prime\mathbf{x}} = \frac{\sigma^{\mathbf{x}^{\prime}}}{\sigma^{\mathbf{x}}}$ , where $\sigma^{\mathbf{x}}$ is the original SD. Then this ratio is further adjusted by a feature bias term $\gamma: \phi^{\prime\mathbf{x}} = \gamma \times \frac{\sigma^{\mathbf{x}^{\prime}}}{\sigma^{\mathbf{x}}}$ when the data is fed in the network. This SD ratio will cause error amplification when predicting noise. + +Suppose $\epsilon_{\theta}(\mathbf{x}_t,t)$ denote the predicted noise $\epsilon$ at time $t$ and define the squared error $\delta_{\mathbf{x}_0}$ between ground truth and predicted $\mathbf{x}_0$ , and error $\delta_{\epsilon}$ for noise prediction. Then we have $\delta_{\epsilon} = \left\| \epsilon_{\theta}(\mathbf{x}_t,t) - \epsilon \right\| _2^2$ and $\delta_{\mathbf{x}_0} = \left\| \frac{1}{\sqrt{\bar{\alpha}_t}}\left(\mathbf{x}_t - \sqrt{1 - \bar{\alpha}_t}\epsilon_\theta (\mathbf{x}_t,t)\right) - \mathbf{x}_0\right\| _2^2$ . Substitute $\mathbf{x}_0$ from Eq. (1) (detailed deduction in App. A.1), we get: + +$$ +\delta_ {\mathbf {x} _ {0}} = \left\| \frac {\sqrt {1 - \bar {\alpha} _ {t}}}{\sqrt {\bar {\alpha} _ {t}}} \right\| _ {2} ^ {2} \delta_ {\epsilon}, \tag {4} +$$ + +an standard error relation $\delta_{\epsilon} \to \delta_{\mathbf{x}_0}$ . If $\mathbf{x}_0$ is processed correctly, the relation between $\delta_{\mathbf{x}_0}$ and $\delta_{\epsilon}$ only responds to time coefficient $\bar{\alpha}$ . Since the SD ratio $\phi^{\prime \mathbf{x}}$ applies to both predicted and ground truth $\mathbf{x}_0$ , then Eq. (4) updates to: + +$$ +\delta_ {\mathbf {x} _ {0}} \times \phi_ {i} ^ {\prime} = \left\| \frac {\sqrt {1 - \bar {\alpha} _ {t}}}{\sqrt {\bar {\alpha} _ {t}}} \right\| _ {2} ^ {2} \delta_ {\epsilon}, \tag {5} +$$ + +where $\bar{\alpha}$ remains unchanged and $\epsilon$ guaranteed from normal distribution. This means unlike direct $\mathbf{x}_0$ prediction, errors from predicting $\epsilon$ are actually amplified because of the modified SD and are worsened by feature bias. + +Both dimensional distribution mismatch and noise prediction error amplification can seriously impact generation. Therefore, reformating motion representation and distribution is crucial to improve motion diffusion modeling. + +# 2.3. Impact on Method Evaluation Robustness + +The widely adopted evaluators [24] utilize all features including redundancy which is imprecise and unfair. + +To assess this, we conducted an experiment by selectively altering redundant and non-redundant dimensions of ground truth HumanML3D data to examine their impact on the evaluator. As shown in Tab. 3, the evaluator disproportionately emphasizes redundant dimensions, potentially misclassifying accurate human motion as poor if minor imperfections exist in redundancy. + +Benefiting VQ-Based Methods. The VQ codebooks enforce a discrete one-to-one token-to-embedding mapping, + +Table 4. The evaluation results using evaluators trained on all vs. essential dimensions on HumanML3D. VQ-based models significantly outperform diffusion-based models under all-dimension evaluation, but gap closes under essential evaluation. + +
MethodEvaluator With RedundancyFID ↓R-Precision ↑
GenTop 1Top 2Top 3
T2M-GPT [111]✓0.1150.4970.6850.779
Momask [26]✓0.0930.5080.7010.796
MDM-50Step [88]✓0.4810.4590.6510.753
T2M-GPT [111]X0.3350.4700.6590.758
Momask [26]X0.1160.4900.6870.786
MDM-50Step [88]X0.5180.4400.6360.741
+ +ensuring error consistency across both essential and redundant dimensions, ultimately advantage VQ-based methods under evaluators that account for all dimensions. + +Unlike traditional VAEs [45], where the continuous latent space can lead to projected output dimensional inconsistencies, VQ-VAEs establish a one-to-one correspondence between each code and its embedding. While this approach may limit data diversity, the deterministic mapping constrains outputs to a defined set of embeddings, producing stable features across all dimensions. Mathematically, each VQ codebook embedding $e_k$ represents a Voronoi cell: + +$$ +V _ {k} = \left\{z \in \mathbb {R} ^ {d} \mid \| z - e _ {k} \| _ {2} \leq \| z - e _ {j} \| _ {2} \right\}, \forall j \neq k. \tag {6} +$$ + +Generation error then corresponds to errors of cell centroids, yielding a more uniform error rate across dimensions and aligning well with evaluators that assess all dimensions. + +Limiting Diffusion-Based Methods. The continuous predictions nature of diffusion-based methods causes error inconsistency in each dimension, hindered in evaluation. + +In each timestep, diffusion-based models predict a continuous vector to recover $\mathbf{x}_0$ without dimension alignment, introducing variability across individual dimensions. As iteration continues, these dimensional fluctuations accumulate. We can express the total error with diffusion model $f$ : + +$$ +\text {T o t a l E r r o r} = \sum_ {t = 0} ^ {T} \sum_ {d = 1} ^ {D} \left\| f \left(\mathbf {x} _ {t} ^ {(d)}, \epsilon_ {t} ^ {(d)}\right) - \mathbf {x} _ {\text {t r u e}} ^ {(d)} \right\| _ {2} ^ {2} \tag {7} +$$ + +we see each dimension contributes differently to the overall error depending on its error rate and variability across dimensions results in inconsistent error rates. Since the evaluator considers all dimensions, diffusion-based models are penalized because of error rate inconsistency, especially in the redundant dimensions, leading to unfair evaluations. + +In Tab. 4, we compare model performance when evaluated on all versus essential motion dimensions. VQ-based methods (e.g., T2M-GPT) tend to outperform diffusion-based ones (e.g., MDM) under all-dimension evaluation, benefiting from more consistent error across dimensions. However, when focusing only on animation-relevant essential dimensions, MDM performs comparably to T2M-GPT, aligning better with visual perception. This suggests that diffusion-based methods, despite excelling in essential di + +mensions, may be penalized by fluctuations in redundancy and underscores a more robust evaluator is crucial. + +# 3. Revisiting Motion Diffusion + +Guided by the insights from Sec. 2 and inspirations from VQ-based methods, we revisit diffusion-based human motion generation in this section and present a new method. It does not only overcome the limitations we found in Sec. 2 but also leverages the strengths of autoregressive generation, leading to a new state-of-the-art model. + +# 3.1. Reforming Motion Representations + +To systematically address the limitations of motion representations in Sec. 2.2, we only use the essential feature groups (i.e., the first #joints $\times 3 + 1$ dimensions). After excluding the redundant dimensions, we avoid mixing representations from various distributions, such as 6D rotational and categorical. The retained features are all 3D continuous representations, ensuring a uniform distribution that aligns better with the diffusion-based generation framework. + +To further optimize the motion representations, we then project those essential features into a compact and fine-grained latent space using a motion AutoEncoder (AE). Compared with the motion Variational AutoEncoder (VAE) [12], the deterministic AE projection avoids the variation in the motion latents (i.e. $\epsilon$ incorporation), providing more stable representations that are better suited for diffusion modeling and motion reconstruction. (In Appendix, we show training baseline methods using only essential dimensions can already lead to significant improvements, and processing into latent space may further enhance the results.) + +The AE architecture is shown in the left-most part of Fig. 3, where the motion sequence with essential representations $\mathbf{X}^{0:N}$ is projected into a latent space using a 1D ResNet [29]-based encoder $E$ . This latent embedding $\mathbf{x}^{0:n}$ then passes through a 1D ResNet decoder $D$ , which uses nearest-neighbor upsampling to reconstruct the motion feature $\mathbf{X}^{\prime 0:N}$ . Formally, the training loss of AE is defined as: + +$$ +\mathcal {L} _ {\mathrm {a e}} = \left\| \mathbf {X} ^ {0: N} - \mathbf {X} ^ {' 0: N} \right\| _ {1}. \tag {8} +$$ + +Following previous works [12, 26, 111], the encoder $E$ downsamples $\mathbf{X}$ from $N$ length to $\mathbf{x}$ of $n$ length. The decoder $D$ upsamples it back to $N$ length. With this integration, our method can also use motion latent $\mathbf{x}$ in the diffusion process, which offers acceleration for both training and sampling. In addition, since the downsampling introduces temporal awareness [24], it can improve the temporal coherence of autoregressive diffusion in Sec. 3.2. + +More importantly, since our reformed motion representations can effectively address the issues highlighted in Sec. 2.2, it free diffusion models from the constraint of predicting only $\mathbf{x}_0$ to $\epsilon$ and more advanced diffusion predictions are now feasible, e.g. score and velocity. Following + +SiT [62], we define a linear interpolation function as: + +$$ +\mathbf {x} _ {t} = \alpha_ {t} \mathbf {x} _ {0} + \sigma_ {t} \boldsymbol {\epsilon} = (1 - t) \mathbf {x} _ {0} + t \boldsymbol {\epsilon}, \tag {9} +$$ + +where $t$ is continuous timestep and define velocity as: + +$$ +\mathbf {v} (\mathbf {x}, t) = \dot {\alpha} _ {t} \operatorname {E} [ \mathbf {x} _ {0} \mid \mathbf {x} _ {t} = \mathbf {x} ] + \dot {\sigma} _ {t} \operatorname {E} [ \epsilon \mid \mathbf {x} _ {t} = \mathbf {x} ]. \tag {10} +$$ + +The score is another form of velocity: + +$$ +\mathbf {s} (\mathbf {x}, t) = \sigma_ {t} ^ {- 1} \frac {\alpha_ {t} \mathbf {v} (\mathbf {x} , t) - \dot {\alpha} _ {t} \mathbf {x}}{\dot {\alpha} _ {t} \sigma_ {t} - \alpha_ {t} \dot {\sigma} _ {t}}, \tag {11} +$$ + +where $\alpha_{t}$ , $\sigma_{t}$ are continuous time coefficients, $\dot{\alpha}_{t} = \frac{\mathrm{d}\alpha_{t}}{\mathrm{d}t}$ , $\dot{\sigma}_{t} = \frac{\mathrm{d}\sigma_{t}}{\mathrm{d}t}$ . We can also deduce score $\mathbf{s}(\mathbf{x}, t)$ from $\mathbf{v}(\mathbf{x}, t)$ . + +# 3.2. Diffusion: An Autoregressive Approach + +Autoregressive methods [26, 75, 76, 111] demonstrate significant advantages in motion generation. Instead of generating the entire sequence $\mathbf{x}^{1:n}$ with a condition $c$ by modeling $p(\mathbf{x}^{1:n}|c)$ , autoregressive generation can simplify training and generation into a chain probability: + +$$ +p \left(\mathbf {x} ^ {1: n} \mid c\right) = p \left(\mathbf {x} ^ {1} \mid c\right) \prod_ {i = 1} ^ {n} p \left(\mathbf {x} ^ {i} \mid \mathbf {x} ^ {< i}\right), \tag {12} +$$ + +where each conditional probability $p(\mathbf{x}^i | \mathbf{x}^{MethodsFrameworkR-Precision↑FID↓Matching↓MModality↑CLIP-score↑Top 1Top 2Top 3HumanML3DT2M-GPT [111]VQ0.470±.0030.659±.0020.758±.0020.335±.0033.505±.0172.018±.0530.607±.005MMM [76]0.487±.0030.683±.0020.782±.0010.132±.0043.359±.0091.241±.0730.635±.003MoMask [26]0.490±.0040.687±.0030.786±.0030.116±.0063.353±.0101.263±.0790.637±.003MDM-50Step [88]Diffusion0.440±.0070.636±.0060.742±.0040.518±.0323.640±.0283.604±.0310.578±.003MotionDiffuse [113]0.450±.0060.641±.0050.753±.0050.778±.0053.490±.0233.179±.0460.606±.004MLD [12]0.461±.0040.651±.0040.750±.0030.431±.0143.445±.0193.506±.0310.610±.003ReMoDiffuse [114]0.468±.0030.653±.0030.754±.0050.883±.0213.414±.0202.703±.1540.621±.003Ours-DDPMAutoregressive0.492±.0060.690±.0050.790±.0050.116±.0043.349±.0102.470±.0530.637±.005Ours-SiTDiffusion0.500±.0040.695±.0030.795±.0030.114±.0073.270±.0092.231±.0710.642±.002KITT2M-GPT [111]VQ0.359±.0070.553±.0070.690±.0130.593±.0533.765±.0461.798±.1570.651±.005MMM [76]0.363±.0050.569±.0060.724±.0060.478±.0343.629±.0281.455±.1060.660±.003MoMask [26]0.369±.0050.588±.0050.731±.0050.411±.0263.577±.0211.309±.0580.669±.002MDM [88]Diffusion0.333±.0120.561±.0090.689±.0090.585±.0434.002±.0331.681±.1070.605±.007MotionDiffuse [113]0.344±.0090.536±.0070.658±.0073.845±.0874.167±.0541.774±.2170.626±.006MLD [12]0.351±.0070.536±.0070.658±.0070.492±.0473.746±.0441.803±.1640.646±.006ReMoDiffuse [114]0.356±.0040.572±.0070.706±.0091.725±.0533.735±.0361.928±.1270.665±.005Ours-DDPMAutoregressive0.375±.0060.597±.0080.739±.0060.340±.0203.489±.0181.479±.0780.681±.003Ours-SiTDiffusion0.387±.0060.610±.0060.749±.0060.242±.0143.374±.0191.312±.0530.692±.002 + +Table 5. Quantitative evaluation on HumanML3D and KIT-ML datasets. We repeat the evaluation 20 times and report the average with $95\%$ confidence interval. For our methods, we report both method results trained to predict noise (DDPM[32]) and velocity (SiT[62]). We use Bold face to indicate the best result and underscore to present the second best. + +end-of-sentence token from the text embeddings and the CLS token from the motion embeddings are extracted to represent each modality. The model learns to align these representations by maximizing the per-batch cosine similarity between the normalized features of two modalities scaled by a learnable logit scale. This CLIP-based evaluator is also trained using only essential dimensions. + +By training exclusively on essential dimensions, we ensure the evaluators capture only meaningful features from the final generated motion. The adoption of dual evaluators also provides a more robust and comprehensive framework to accurately compare different-based generation methods. More importantly, all baselines can generate outputs containing essential dimensions with no additional operations. + +# 4. Experiment + +# 4.1. Datasets and Evaluation Protocols. + +Datasets. To accurately and fairly evaluate our method in comparison with baselines, we adopts two representative motion-language benchmarks: HumanML3D [24] and KIT-ML [77]. The KIT-ML dataset comprises 3,911 motions sourced from the KIT and CMU [65] motion data, each accompanied with one to four textual annotations (6,278 total annotations). The KIT-ML motion sequences are standardized to 12.5 FPS. The HumanML3D dataset contains 14,616 motions sourced from the AMASS [64] and HumanAct12 [23] datasets, each described by three textual scripts (44,970 total annotations). The HumanML3D motion sequences are adjusted to 20 FPS with a maximum duration of 10 seconds. We augment data by mirroring and splitting both datasets into train, test, and validation sets with a ratio of 0.8:0.15:0.05. We follow the pose representation from T2M [23], however, we incorporate only essential dimen + +sions for methods' evaluation and training in our method. + +Evaluation Metrics. Following Section 3.3, we employ two evaluators trained with only essential dimensions: one architecturally identical to the one proposed in T2M [24] and a CLIP-based evaluator. Using the T2M evaluator, we adopt evaluation metrics from T2M, including (1) R-Precision (Top-1, Top-2, and Top-3 accuracies) and Matching, which measures the semantic alignment between generated motion embeddings and their corresponding captions' glove embedding; (2) Fréchet Inception Distance (FID), which assesses the statistical similarity between ground truth and generated motion distributions; and (3) Multi-Modality, which measures the diversity of generated motion embeddings per same text prompt. Using the CLIP-based evaluator, we include the CLIP-score [30], which measures the compatibility of motion-caption pairs by calculating the cosine similarity between generated motion and its caption. + +# 4.2. Results and Analysis + +Following previous works [24, 88], we conduct each experiment 20 times on both datasets and report the mean result along with a $95\%$ confidence interval. To ensure a fair comparison on the new evaluators, we train all baseline models from scratch following their original methods on the same obtained dataset (full dimension). We present the quantitative results of our method alongside baseline state-of-the-art human motion generation methods in Tab. 5, and the qualitative comparison results in Fig. 4. In addition we also present model scalability results in App. D + +As observed, our method achieves superior performance across multiple metrics, including FID, R-Precision, Matching score, and CLIP-score, consistently outperforming baseline methods with non-marginal improvements on both KIT-ML and HumanML3D datasets. Compared to + +Text Prompt: A person who is running, stops, bends over and looks down while taking small steps, then resumes running. + +![](images/1f816532b7c2b1433dfa5fbfa72aed527242e138f5276f06c92e11bd4c0126ad.jpg) +T2M-GPT + +![](images/40796a51849dba2a87c62345fe78f5109634e18bc0fe4eb89c7b7629f7af2c64.jpg) +ReMoDiffuse + +![](images/b4f37320a7a58b60c7233c7cb6bdae128514195438d61f7b94071440edb27706.jpg) +Momask + +![](images/c13e2ced373fc7d4af34e527b447f20c8d412827a40d69a845ace438b8c81e86.jpg) +Ours +Figure 4. Visualization Comparison between our method and baseline state-of-the-art methods. Our method generates motion that is more realistic and more accurately follows the fine details of the textual condition. + +Table 6. Ablation study results comparing our method to variations without reform data representation and distribution and without autoregression. The study is conducted on the HumanML3D dataset. + +
MethodFID ↓R-Precision ↑
Top 1Top 2Top 3
Full Components0.1160.4920.6900.790
W/o Motion Representation Reformation2.1960.3870.5950.703
W/o Autoregression0.5510.4350.6210.732
+ +diffusion-based baseline methods, our approach showcases a significantly stronger ability to generate stable motion that follows closely to text instructions and aligns with ground truth. Notably, while the SOTA diffusion-based baseline method ReMoDiffuse [114] relies on additional data retrieval from a large database to achieve high-quality motion generation, our method surpasses ReMoDiffuse's performance results without requiring auxiliary formulations. In comparison to VQ-based baseline methods, our approach maintains better motion quality and also delivers greater diversity, a quality where VQ methods underperform. + +# 4.3. Ablation Study + +In the ablation study, we further study the impact of reforming data representation and distribution, and autoregressive modeling in our method. We present ablation results in Tab. 6 and an optimization routine in Appendix. The results show that both proposed components contribute greatly. + +Data Representation and Distribution Without reform motion data representation and distribution, FID increased by 2.080, and R-precisions dropped by 8.7 percent for Top 3. Therefore, reforming data and representation is crucial. + +Autoregressive Modeling Without autoregressive modeling, FID increased by 0.435, and R-precisions dropped by 5.8 percent for Top 3. Therefore autoregressive modeling also contributes greatly to our proposed method. + +# 5. Related Work + +In this section, we provide a brief overview of related works due to space constraints. We also provide a more detailed version of related works in the Appendix. + +VQ-Based Human Motion Generation TM2T [25] first introduces Vector Quantization (VQ) to text-to-human motion generation, enabling discrete motion token modeling. + +T2M-GPT [111] extended this by leveraging a GPT[6] to motion autoregressive generation. Subsequent methods have sought to integrate a larger model[37, 115] (e.g. large language models), or manipulate attention mechanisms [119]. Most recently, MMM [76] and MoMask [26] revisit generation methodology by employing bidirectional masked generation techniques inspired by MaskGIT [8]. In this paper, we examine the strengths of these methods and improve a diffusion model with these insights. + +Diffusion-Based Human Motion Generation. Inspired by the success of denoising diffusion models in image generation domain [32, 86], several pioneering works [44, 88, 113] have adapted denoising diffusion processes to human motion generation. Building on these works, MLD [12] further optimized the denoising process in latent space to improve training and sampling efficiency. Recent methods have diversified their focus, exploring retrieval-augmentation [114], controllable generation [15], as well as investigating advanced architectures [117] such as Mamba [21]. In this paper, we thoroughly investigate the limitations of diffusion-based methods and propose to address them. + +Autoregressive Generation with Continuous Data. GIVT first introduced the idea of leveraging outputs from an autoregressive model as parameters for a Gaussian Mixture Model, enabling probabilistic autoregressive modeling and generation. MAR then utilized logits from a masked autoregressive model as input to a small diffusion branch, producing more fine-grained generation. Inspired by these approaches, in this paper, we propose a novel framework that integrates diffusion-based motion generation with autoregression to achieve enhanced generative performance. + +# 6. Conclusion + +In conclusion, we introduce a novel diffusion-based generative framework for text-driven 3D human motion generation. Our method reforms motion data representation and distribution to better fit the diffusion model, incorporates masked autoregressive training and sampling techniques and is evaluated by more robust evaluators. Extensive experiments demonstrate our method's superior generation performance in KIT-ML and HumanML3D datasets. + +Acknowledgement. Yiming Xie was supported by the Apple Scholars in AI/ML PhD fellowship. + +# References + +[1] Gunjan Aggarwal and Devi Parikh. Dance2music: Automatic dance-driven music generation. arXiv preprint arXiv:2107.06252, 2021. 1 +[2] Chaitanya Ahuja and Louis-Philippe Morency. Language2pose: Natural language grounded pose forecasting. In 3DV, 2019. 14 +[3] Chaitanya Ahuja and Louis-Philippe Morency. Language2pose: Natural language grounded pose forecasting. In 2019 International Conference on 3D Vision (3DV), pages 719–728. 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Existing works rely on direct matching for end-to-end lifting, yielding inferior results, or employ a two-stage solution constrained by complex pre- or post-processing. In this work, we design Unified-Lift, a new end-to-end object-aware lifting approach that aims for high-quality 3D segmentation based on our object-aware 3D Gaussian representation. To start, we augment each Gaussian point with a Gaussian-level feature learned using a contrastive loss to encode instance information. Importantly, we introduce a learnable object-level codebook to account for individual objects in the scene for an explicit object-level understanding and associate the encoded object-level features with the Gaussian-level point features for segmentation predictions. While promising, achieving effective codebook learning is nontrivial and a naive solution leads to degraded performance. Hence, we formulate the association learning module and the noisy label filtering module for effective and robust codebook learning. We conduct experiments on three benchmarks LERF-Masked, Replica, and Messy Rooms. Both qualitative and quantitative results manifest that our Unified-Lift clearly outperforms existing methods in terms of segmentation quality and time efficiency. + +# 1. Introduction + +Accurate 3D scene segmentation enhances scene understanding and facilitates scene editing, benefiting many downstream applications in virtual reality, augmented reality, and robotics. However, accurate 3D scene segmentation is challenging to obtain, due to limited 3D dataset size and labor-intensive manual labeling in 3D. To bypass these challenges, recent studies [1, 33, 44] suggest lifting 2D segmentations predicted by foundation models [3, 15] to the 3D scene modeled by a radiance field for instance-level understanding. Yet, 2D instance segmentations predicted by models like SAM [15] lack consistency across + +different views, e.g., the same object may have different IDs when viewed from different angles, leading to conflicting supervision. Besides, inferior segmentations, e.g., under- or over-segmentation, make the lifting process challenging. + +Various strategies have been proposed to address the above issues. An early work Panoptic Lifting [33] trains a NeRF to render instance predictions in an end-to-end manner and matches the model's 3D predictions with the initial 2D segmentation masks to provide supervision. However, this approach tends to produce multi-view inconsistent segmentation as it is highly sensitive to the variances of matching results. Subsequently, [23, 39] propose object association techniques as a preprocessing to prepare view-consistent 2D segmentation maps with improved multiview consistency (see Fig. 1 (b)). However, the preprocessing stage often struggles to produce accurate results and the accumulated error can further degrade the performance. The recent state-of-the-art methods [1, 40] encode instance information in the feature field using contrastive learning and apply a clustering as a postprocessing to produce the final segmentations (see Fig. 1 (c)). Though significant improvements are achieved, their performance is always constrained by the naive clustering postprocess, which is hyperparameter-sensitive and also induces error accumulation. Given the above concerns, we come up with this question: "Can we have an end-to-end lifting framework for accurate 3D scene segmentation, without the need of pre- or post-processing?" + +In this work, we propose Unified-Lift, a new end-to-end object-aware lifting method for accurate 3D scene segmentation, facilitating the generation of coherent and view-consistent instance segmentation across different views. We exploit recent advancement of the radiance field, i.e., 3D Gaussian splatting (3D-GS) [12], as the 3D scene representation due to its superior efficiency and rendering quality. Specifically, we augment each Gaussian point in 3D-GS with a Gaussian-level feature and learn these features using contrastive learning defined in individual views. In particular, we introduce a novel global object-level codebook to represent each object in the 3D scene. This code + +![](images/d4c8d6e13e74e6777a547e20a2943b22391d731100350bb2cdeb8ffbd4145494.jpg) +Figure 1. Comparing the pipeline of our method against previous lifting solutions. + +![](images/a2f9571413bc95394ae014f03b2edb84f4bdf299a3b2cf96e5500d91b6a1c86c.jpg) + +book is further associated with the rendered Gaussian-level features to predict segmentation results, enhancing object-level awareness during training. However, effective codebook learning is nontrivial. Naive training solutions can lead to suboptimal performance. Hence, we present effective learning strategies to optimize the object-level codebook. First, we introduce a novel association learning module, in which we design an area-aware ID mapping algorithm to generate pseudo-labels of association with enhanced multi-view consistency. Additionally, we present two complementary loss functions, i.e., sparsity and concentration parts, to achieve more reliable object-level understanding. Second, we design a novel noisy label filtering module to enhance the robustness of our method by estimating an uncertainty map for the segmentation masks, leveraging the learned Gaussian-level features in a self-supervised manner. During inference, we obtain novel-view instance segmentation results without any pre- or post-processing, effectively avoiding error accumulation. + +To evaluate the effectiveness of Unified-Lift, we conduct experiments on the widely-used LERF-Masked [39] dataset and the indoor scene dataset Replica [35]. Both quantitative and qualitative results demonstrate that Unified-Lift outperforms all the existing lifting methods by a notable margin. Further, we conduct additional experiments on the challenging Messy Rooms dataset [1], where each scene contains up to 500 objects, demonstrating the scalability of Unified-Lift in handling large numbers of objects. + +Our main contributions are summarized as follows: + +- We propose a new end-to-end object-aware lifting method (named Unified-Lift) for accurate 3D scene segmentation by jointly learning the Gaussian-level features and a global object-level codebook. +- We present a novel association learning module and a noisy label filtering module to facilitate effective learning of the object-level codebook. +- Unified-Lift sets a new state-of-the-art performance on + +multiple datasets and demonstrate strong scalability in handling scenes with a large number of objects, without requiring pre- or post-processing. + +# 2. Related Work + +Radiance field: from implicit to explicit. Radiance field emerges as a promising representation for reconstructing 3D scenes with various properties, e.g., geometries, colors, and semantics, from only 2D inputs such as RGB images and segmentation masks. Neural Radiance Field (NeRF) [25] models the radiance field using a neural network composed of layers of multilayer perceptrons. Since then, various works attempt to improve the efficiency of NeRF, e.g., by explicitly formulating the field using 3D structures such as voxels [2, 22] and hash grids [27]. Later on, 3D Gaussian Splatting (3D-GS) [5, 11, 12, 21, 38, 41, 43] is introduced to model the radiance field as a set of explicit Gaussian points. This approach allows for a splattering-style rendering [16], which is highly efficient and demonstrates great potential of real-time rendering. Given the advantages, we employ 3D-GS as the backbone representation in our framework for creating consistent 3D segmentations. + +Segmentation: from 2D to 3D. Segmentation is a longstanding task in computer vision research. Recent progress witnesses advancements in 2D, thanks to the availability of large-scale datasets. Notably, various foundation models, such as SAM [15] and its subsequent works [18, 37], show great performance in numerous 2D segmentation tasks and demonstrate robust zero-shot segmentation capabilities. + +Beyond segmenting pixels in image level, 3D segmentation aims to partition 3D structures, such as point clouds and voxels [10, 26, 34, 45], or to perform segmentation and 3D reconstruction simultaneously from input 2D images [7, 28, 32]. However, due to tedious work needed in collecting annotated 3D data, the scale of 3D datasets (e.g., 1,503 scenes in ScanNet [8]) is usually at least one order + +of magnitude smaller than that of 2D datasets (e.g., 11M diverse images and 1.1B high-quality segmentation masks in SA-1B [15]). Hence, the trained models are applicable mostly to limited 3D object categories within the available dataset. To effectively construct 3D segmentation, we propose lifting the segmentation results from 2D foundation models by explicitly incorporating an object-level understanding of the 3D scene. + +Lifting 2D segmentation to 3D scene understanding in radiance field. Various works [1, 30, 44] propose leveraging radiance fields to lift independently-inferred 2D information into the 3D space for 3D scene segmentation and understanding. Some works focus on semantic segmentation, aiming to infer semantic information in the 3D scene, such as object properties and categories, where 2D segmentation predictions are obtained via differentiable rendering. To accomplish this, most existing works tend to optimize a 3D radiance field, which is supervised by semantic or feature maps derived from 2D foundation models. For example, Semantic-NeRF [44] optimizes an additional semantic field from 2D semantic maps for novel-view semantic rendering. Besides, some studies [13, 19, 30, 42] distill CLIP [31] or DINO [29] features into a feature radiance field to facilitate open-vocabulary semantic segmentation. + +Unlike semantic segmentation, instance segmentation predicted by 2D foundation models, such as SAM [15] and MaskFormer [3], lack consistency across multiple views. An early work, Panoptic Lifting [33], formulates the radiance field as a distribution of instance IDs and employs the Hungarian algorithm for each 2D segmentation to obtain pseudo labels as the supervision signal. To improve the performance, later works [9, 23, 39] attempt to pre-process the 2D instance segmentations (e.g., using video tracker [4] or heuristic Gaussian matching [23]) to simplify the task and obtain view-consistent labels for supervision. Recent state-of-the-art methods [1, 6, 9, 14, 40, 46] construct 3D consistent feature fields and supervise them using contrastive loss within each 2D segmentation. This avoids the need to establish correspondences between different views. However, since radiance fields contain only features, inferring the final segmentation requires an additional clustering step, such as HDBSCAN [24], which can be rather sensitive to the choice of the hyperparameters. In this work, we propose a new end-to-end object-aware lifting pipeline for accurate 3D scene segmentation, avoiding the need of pre- or post-processing. By formulating an object-level codebook representation and designing dedicated modules for effective codebook learning, we obtain an object-level understanding of the scene to greatly enhance the segmentation quality. + +# 3. Method + +Given a set of posed images with 2D instance segmentation masks $\{\mathcal{K}\}$ , our goal is to lift 2D segmentations to 3D and + +produce an accurate and consistent 3D segmentation of the scene, represented by the 3D Gaussian Splating (3D-GS) model. In this work, we obtain the initial 2D masks using a zero-shot 2D segmentation model, specifically the Segment Anything Model (SAM [15]). Fig. 2 illustrates the overview of our Unified-Lift, which consists of three major components. (i) We augment each Gaussian point in the 3D-GS representation with an additional Gaussian-level feature and employ contrastive loss to optimize the rendered Gaussian-level features (Fig. 2 top; detailed in Sec. 3.1). (ii) We impose an object-level understanding on the 3D scene to enhance segmentation quality by formulating an object-level codebook and associating the codebook with the Gaussian-level features through an object-Gaussians association for segmentation predictions (Fig. 2 bottom-left; detailed in Sec. 3.2). (iii) We introduce two novel modules for effective codebook learning based on the object-Gaussians association: the association learning module and the noisy label filtering module (Fig. 2 bottom-right: detailed in Sec. 3.3). + +# 3.1. Learning Gaussian-level features + +3D-GS backbone. The 3D Gaussian Splitting (3D-GS) model [12] encapsulates a 3D scene using explicit 3D Gaussians and utilizes differentiable rasterization for efficient rendering. Mathematically, 3D-GS aims to learn a set of $N$ 3D Gaussian points $G = \{g_i\}_{i=1}^N$ , where $g_i = \{\mathbf{p}_i, \mathbf{s}_i, \mathbf{q}_i, o_i, \mathbf{c}_i\}$ represents the trainable parameters for the $i$ -th Gaussian point. The 3D Gaussian function $G_i(x)$ is defined by the center point $\mathbf{p}_i$ , the scaling factor $\mathbf{s}_i$ , and the quaternion $\mathbf{q}_i$ . Moreover, $o_i$ is the opacity value and $\mathbf{c}_i$ is the color values modeled by spherical harmonics coefficients. Following an efficient tile-based rasterization introduced in [12], the 3D Gaussian function $G_i$ is first transformed to the 2D Gaussian function $G_i'$ on the image plane. Then, a rasterizer is designed to sort the 2D Gaussians and employ the $\alpha$ -blending to compute the color $\mathbf{C}_u$ for the query pixel $u$ : $\mathbf{C}_u = \sum_{i \in \mathcal{N}} \mathbf{c}_i \alpha_i \prod_{t=1}^{i-1} (1 - \alpha_t)$ , $\alpha_i = o_i G_i'(u)$ , where $\mathcal{N}$ is the number of sorted 2D Gaussians associated with pixel $u$ . Subsequently, all parameters in $\{g_i\}_{i=1}^N$ are optimized using the photometric loss between the rendered colors and the observed image colors. + +Contrastive learning for Gaussian-level features. To encode the instance segmentation information of the 3D scene, each 3D Gaussian point $g_{i}$ is augmented with a Gaussian-level learnable feature $\mathbf{f}_i \in \mathbb{R}^d$ , where $d$ is the feature dimension. Similar to the color information, we can apply differentiable rasterization to efficiently render the feature $\mathbf{F}_u$ for pixel $u$ : $\mathbf{F}_u = \sum_{i \in \mathcal{N}} \mathbf{f}_i \alpha_i \prod_{t=1}^{i-1} (1 - \alpha_t)$ , $\alpha_i = o_i G_i'(u)$ . Following existing state-of-the-art methods [1, 40], we employ the contrastive learning technique to optimize the Gaussian-level features $\mathbf{f}_i$ from individual views. Specifically, we apply the following InfoNCE loss [20] to supervise the rendered features: + +![](images/c93152720c043c0d35ceecca0ad847ce49e6c59e1a61319f873b2549573b8b2a.jpg) +Figure 2. Overview of our Unified-Lift, which is built on the 3D Gaussian Splitting (3D-GS) representation (top-left). In our pipeline, we first augment each Gaussian point in 3D-GS with a Gaussian-level feature and utilize the contrastive loss to optimize the rendered features (see top; detailed in Sec. 3.1). To impose an object-level understanding of the 3D scene, we introduce an additional object-level codebook and establish associations between the object-level features and the Gaussian-level features (see bottom-left; detailed in Sec. 3.2). Further, we propose two novel modules, the association learning module and the noisy label filtering module, to robustly and accurately learn the codebook (see bottom-right; detailed in Sec. 3.3). + +$$ +\mathcal {L} _ {\text {c o n t r a}} = - \frac {1}{| \Omega |} \sum_ {\Omega_ {j} \in \Omega} \sum_ {u \in \Omega_ {j}} \log \frac {\exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \overline {{\mathbf {F}}} _ {j}\right)\right)}{\sum_ {\Omega_ {l} \in \Omega} \exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \overline {{\mathbf {F}}} _ {l}\right)\right)}, \tag {1} +$$ + +where similarity kernel function sim uses the dot product operation here and $\Omega$ is the set of pixel samples. In specific, $\Omega_{j}$ denotes the pixel samples with the same instance ID $j$ according to the 2D segmentation $\mathcal{K}$ , $\overline{\mathbf{F}}_j$ and $\overline{\mathbf{F}}_l$ represent the mean features (centroids) for $\Omega_{j}$ and $\Omega_{l}$ , respectively. + +# 3.2. Object-level codebook representation + +While Gaussian-level features implicitly encode instance information within the scene, they lack explicit object-level understanding and require an additional clustering postprocess to extract this information for segmentation prediction [1, 40]. Consequently, these instance predictions not only suffer from tedious hyperparameter tuning but also encounter issues such as under- or over-segmentation due to the accumulated errors (see, e.g., Fig. 3). Hence, we aim to obtain an explicit object-level understanding of the 3D scene by jointly learning it with the Gaussian-level features, getting rid of the constraints of post-processing. + +Object-level codebook. As shown in Fig. 2 bottom-left, based on the Gaussian-level features, we introduce a learnable and global object-level codebook representation to impose an object-level understanding of the 3D scene. Practically, we represent the object-level codebook as a compact matrix $\mathbf{F}_{obj} := [\mathbf{F}_{obj}^{1}, \mathbf{F}_{obj}^{2}, \dots, \mathbf{F}_{obj}^{L}]^{T}$ , where $\mathbf{F}_{obj} \in \mathbb{R}^{L \times d}$ , $L$ is the maximum object number, and $d$ denotes the same feature dimension used in the Gaussian-level features. + +![](images/000f74cc1a88af76c54784e6edf3ec7eb1884699c16b8aeb31c75eb67e742256.jpg) +Figure 3. Visual comparisons. Segmentation results produced by our method and the Gaussian-level feature-based method [40] with post-processing [24]. Their result tends to overlook small objects and produces artifacts. In contrast, our method generates more accurate segmentations. + +Notably, each row in the matrix $\mathbf{F}_{obj}$ corresponds to an underlying object in the 3D scene. + +We further establish the object-Gaussians association formulation to connect the object-level codebook with the Gaussian-level features. Given a pose, we render the feature map $\mathbf{F}$ from the optimized Gaussian-level features, with $\mathbf{F}_u\in \mathbb{R}^d$ denoting the feature for pixel $u$ . Particularly, we propose the following association equation to calculate the probability distribution $\mathbf{P}_u\in \mathbb{R}^L$ for pixel $u$ : + +$$ +\begin{array}{l} \mathbf {P} _ {u} = \left[ \frac {\exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {1}\right)\right)}{\sum_ {o = 1} ^ {L} \exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {o}\right)\right)}, \frac {\exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {2}\right)\right)}{\sum_ {o = 1} ^ {L} \exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {o}\right)\right)} \right. \\ , \dots , \frac {\exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {L}\right)\right)}{\sum_ {o = 1} ^ {L} \exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \mathbf {F} _ {o b j} ^ {o}\right)\right)} ], \tag {2} \\ \end{array} +$$ + +where we use the same similarity kernel function sim as in Eq. 1, maintaining consistency with the learning of Gaussian-level features. + +![](images/6fd2cfd63fe6157e57c78d64809bbbeba20b8ab7a728782b6204e5b40c9cd1dd.jpg) + +![](images/ee7337aa05922e79f4f588ec7ce506f020a83cd9ca8c8b7adc4681a8da126968.jpg) +Figure 4. The comparison between the generated pseudo label results by Panoptic Lifting [33] and our method. With the designed area-aware ID mapping, we can obtain more view-consistent segmentation as the pseudo labels to facilitate the codebook learning. + +![](images/090ae51435aefeeaecab74a136cd7666cb26c0ebb42ae545448aa3e2e90f6ffe.jpg) + +![](images/e187d27bb4ebb4292525168d074786c097e5d00b514c9a330003c0d69dc83fc2.jpg) + +To automatically learn the object-level codebook during training, a straightforward solution is to directly optimize the object-Gaussians association predictions. To obtain the pseudo-labels for this optimization, we can match the 2D segmentation results with the current object-Gaussians association results via the linear assignment algorithm [17]. In practice, we first need to recover the mapping $\Pi$ from the original instance IDs in the 2D segmentation to the global IDs $\{0,1,2,\dots ,L - 1\}$ in the 3D scene. Following [33], the expected mapping $\Pi^{\star}$ is defined by: + +$$ +\Pi^ {\star} := \underset {\Pi} {\operatorname {a r g m a x}} \sum_ {\Omega_ {j} \in \Omega} \sum_ {u \in \Omega_ {j}} \frac {\mathbf {P} _ {u} (\Pi (j))}{| \Omega_ {j} |}, \tag {3} +$$ + +where $\mathbf{P}_u(\Pi (j))$ is the $\Pi (j)$ -th value in the probability prediction $\mathbf{P}_u$ . Then, we apply the cross-entropy loss as a sparsity term to regress the probability distribution based on calculated pseudo-labels: + +$$ +\mathcal {L} _ {\text {c l a s s}} := - \frac {1}{| \Omega |} \sum_ {u \in \Omega} \log \mathbf {P} _ {u} \left(\Pi^ {\star} \left(\mathcal {K} _ {u}\right)\right), \tag {4} +$$ + +where the $\kappa_{u}$ is the instance ID for pixel $u$ , given the 2D instance segmentation masks $\kappa$ . + +Inference with the object-level codebook. Benefiting from the learned explicit object-level codebook representation, our method achieves an end-to-end segmentation inference without the need for a complicated post-processing. In general, to render a segmentation in novel views, we first (i) render the Gaussian-level features; then (ii) calculate the probability using the object-Gaussians association equation; and (iii) determine the segmentation ID by selecting the index of the codebook that exhibits the highest similarity. Furthermore, the same association equation can be directly applied to determine the instance ID for each 3D Gaussian. + +# 3.3. Learning strategy for object-level codebook + +Although our baseline strategy for learning the codebook is technically feasible, it faces limitations in terms of performance and robustness. To address these challenges and improve codebook learning, we introduce two novel modules: the association learning module and the noisy label filtering module. + +![](images/6ed7d474ff0a4506b591f46dad8f7ad7659eaa71810f22473eea3e8e27e50005.jpg) +Figure 5. Visual comparison of the generated uncertainty maps and 2D instance segmentation masks from different views of the "Office3" scene in the Replica dataset [35]. + +![](images/6a4537725fe67f70d99a72da8824f133f5b3e38acba7bcb52b4e289b4d157be2.jpg) + +![](images/f60e0226b3745576e3cb051701978c7060fc7ba1883eb5ab15602c14c9da97c8.jpg) + +![](images/9da6bd66d739d6e31aefdef8d30acfda597fb4cfa20dcce6ba14f927d049b0e2.jpg) + +# 3.3.1. Association learning module + +Our association learning module aims to improve the multiview consistency of pseudo-labels and provide more robust association constraints. To achieve this, we introduce an area-aware ID mapping method and a concentration part to ensure more comprehensive association constraints. + +Area-aware ID mapping. We observe that the ID mapping described in Eq. 2 is sensitive to the small segments in specific views, thereby further causing the multi-view inconsistency issue, as shown in Fig. 4. To mitigate this issue and improve the multi-view consistency of the generated pseudo-labels, we propose an area-aware ID mapping function, formulated as: + +$$ +\Pi^ {\star} := \underset {\Pi} {\operatorname {a r g m a x}} \sum_ {\Omega_ {j} \in \Omega} \sum_ {u \in \Omega_ {j}} \mathbf {P} _ {u} (\Pi (j)). \tag {5} +$$ + +Compared to the previous formulation in Eq. 3, the key distinction lies in the removal of the normalization term. This design prioritizes the influence of large segments in the mapping process, resulting in more consistent mapping across views, as qualitatively shown in Fig. 4. More analysis is provided in Sec. 4.4 and the supplementary material. + +Concentration constraint. We assume that the object-level features assigned in the codebook should align with the clustered Gaussian-level features. Moreover, the clustered Gaussian-level features, optimized using a contrastive loss with dot product similarity, tend to exhibit similar directions. Building on this insight, we propose an additional concentration constraint to minimize the directional differences between the codebook and all corresponding normalized Gaussian-level features: + +$$ +\mathcal {L} _ {\text {c o n c e n}} := \frac {1}{| \Omega |} \sum_ {u \in \Omega} \| \mathbf {F} _ {o b j} ^ {\Pi^ {*} (\mathcal {K} _ {u})} - \mathbf {F} _ {u} / \| \mathbf {F} _ {u} \| \| _ {1}. \tag {6} +$$ + +Thus, we formulate the total association constraint loss as a linear combination of the sparsity component in Eq. 4 and the concentration component in Eq. 6, providing a comprehensive association constraint for the object-level codebook. + +# 3.3.2. Noisy label filtering module + +To enhance the robustness against noise in the 2D instance segmentation masks, we propose a filtering module that removes less accurate 2D predictions by leveraging multiview consistently rendered Gaussian-level features. Specifically, we calculate the uncertainty value $\mathbf{W}_u$ for pixel $u$ as + +$$ +\mathbf {W} _ {u} = 1 - \frac {\exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \overline {{\mathbf {F}}} _ {\left(\mathcal {K} _ {u}\right)}\right)\right)}{\sum_ {\Omega_ {l} \in \Omega} \exp \left(\operatorname {s i m} \left(\mathbf {F} _ {u} , \overline {{\mathbf {F}}} _ {l}\right)\right)}, \tag {7} +$$ + +where $\overline{\mathbf{F}}_{(\mathcal{K}_u)}$ is the mean feature (centroid) for $\Omega_{(\mathcal{K}_u)}$ . In practice, we model the uncertainty by assessing whether the features corresponding to the current 2D instance segmentation are sufficiently discriminative. Accordingly, we can effectively filter out labels with high uncertainty values (i.e., noisy labels) and integrate this filtering into our association constraints. The overall loss for our proposed learning strategy of the object-level codebook is + +$$ +\mathcal {L} = - \frac {1}{| \Omega |} \sum_ {u \in \Omega} \mathbf {1} _ {\left(\mathbf {W} _ {u} \leq \tau\right)} \underbrace {\left(w _ {\text {c l a s s}} \log \mathbf {P} _ {u} \left(\Pi^ {\star} \left(\mathcal {K} _ {u}\right)\right) \right.} _ {\text {S p a r s i t y p a r t i n E q . 4}} + \underbrace {w _ {\text {c o n c e n}} \left\| \mathbf {F} _ {o b j} ^ {\Pi^ {\star} \left(\mathcal {K} _ {u}\right)} - \mathbf {F} _ {u} / \| \mathbf {F} _ {u} \| \| _ {1}\right)} _ {\text {C o n c e n t r a t i o n p a r t i n E q . 6}}, \tag {8} +$$ + +where $w_{\mathrm{class}}$ , $w_{\mathrm{concen}}$ are weight hyper-parameters, and $\tau = 0.8$ is a pre-defined threshold for filtering noisy labels. As verified in Fig. 5, regions with high values in the calculated uncertainty map largely align with areas of noisy segmentation. More analysis can be found in Sec. 4.4. + +# 4. Experiments + +# 4.1. Experiments setting + +Implementation details. Our implementation is based on the official codebase of 3D-GS [12]. We utilize the same photometric loss term in [12] to optimize the associated 3D Gaussian parameters. For the Gaussian-level features, we set the feature dimension to 16, following the baseline works such as OmniSeg3D-GS [40] and Gaussian Grouping [39]. To optimize the Gaussian-level features, we apply the same contrastive loss used in [40]. For the object-level codebook, we set the maximum object number $L$ to 256 and use the proposed loss defined in Eq. 8 to optimize the object-level codebook from a random initialization. Empirically, we set $w_{\mathrm{class}} = 1 \times 10^{-3}$ and $w_{\mathrm{concen}} = 1 \times 10^{-1}$ by default. All parameters are jointly optimized, with the number of training iterations set to 30,000 for all datasets. More details are provided in the supplementary material. + +Datasets. We conduct experiments on the widely-used LERF-Mask dataset [39] and the Replica dataset [35] to present both quantitative and qualitative comparisons. The LERF-Mask dataset includes three scenes, "figures", "ramen", and "teatime", each with six to ten object segmentation annotations. For the Replica dataset, we prepare our customized data and re-evaluate all comparative methods using this dataset since the data used in Gaussian Grouping [39] is not publicly available until March 2025. Following the processing in [36], we select eight scenes for experiments. Besides, we use the official Segment Anything Model (SAM) [15] to make predictions and obtain the initial + +
MethodVenueTypemIoU (%)mBIoU (%)
LERF [13]ICCV'23CLIP feature37.229.3
LangSplat [30]CVPR'24CLIP feature57.653.6
Gaussian Grouping [39]ECCV'24Pre-processing72.867.6
Gaga [23]Arxiv'24Pre-processing74.772.2
OmniSeg3D-GS [40](†)CVPR'24Post-processing74.771.8
Panoptic-Lifting-GS [33](*)CVPR'23End-to-end70.765.8
Unified-Lift (ours)-End-to-end80.977.1
+ +Table 1. Results on the LERF-Mask dataset [39]. We report the mIoU and mBIoU metrics following Gaussian Grouping [39]. * indicates self-implementation, and † indicates that the results are reported under the best-found hyper-parameter (i.e., minimal cluster size in HDBSCAN [24]). + +
MethodTypemIoU (%)F-score (%)
Gaussian Grouping [39]Pre-processing23.630.4
OmniSeg3D-GS [40](†)Post-processing39.135.9
Panoptic-Lifting-GS [33](*)End-to-end25.332.9
Unified-Lift (ours)End-to-end41.643.9
+ +Table 2. Results on the Replica dataset [35]. We report the mIoU, and F-score metrics. * indicates self-implementation, and † indicates that the results are reported under the best-found hyperparameter (i.e., minimal cluster size for HDBSCAN [24]). + +2D segmentation, empirically choosing the largest granularity that provides the object-level segmentation context. + +Metrics. For the LERF-Mask dataset, we adopt the evaluation protocol from [39] following the existing works [23, 39], using the mean Intersection over Union (mIoU) and the boundary IoU (mBiIoU) metrics. For the Replica dataset, we first use the linear assignment algorithm to calculate the best matching of IoU between the segmentation predictions and ground-truth data; we then report both the mIoU metric and F-score, using an IoU threshold of 0.5 as the criterion. + +Comparisons. We compare our proposed method with three types of lifting approaches based on 3D-GS: (i) lifting methods with a preprocessing, such as Gaussian Grouping [39] and Gaga [23]; (ii) the lifting method with a post-processing, i.e., OmniSeg3D-GS [40]; and (iii) a direct lifting baseline (i.e., "Panoptic-Lifting-GS" denoted in Tab. 1, Tab. 2, and Tab. 3) that is derived from Panoptic-Lifting [33]. To ensure fair comparisons, we evaluate the OmniSeg3D-GS baseline using the HDBSCAN [24] algorithm to automatically generate segmentation results. Further, we report metrics under the best-found hyperparameters, following the common practice used in [1]. Moreover, we benchmark our method against the recent open-vocabulary 3D segmentation techniques, including LERF [13] and LangSplat [30]. + +# 4.2. Main experiments + +LERF-Mask dataset. To evaluate performance on real-world data, we conduct the experiments using the LERF-Mask dataset [39]. Quantitative comparisons provided in + +![](images/0ea449b083e4c397b4d1e8d864bb9ec78d4d0db9944a902233f7a309127b487e.jpg) +Figurines + +![](images/b71ace74718577e2d1f9fe8ff66b4787f1ebe04207c52e39eeb5e54690779678.jpg) + +![](images/2e5fab9a0ff47d5a968f26048bedca5c7cd3f5cd510c619e5048637af7b3a1e6.jpg) +(a) Segmentation results on LERF-Mask dataset + +![](images/99170bc003c3b1ff53e6f77c699508bff988293e304bb38b91361f919204b517.jpg) + +![](images/995563277651c5fbd22ae162674d6f9b91607a98548647d33f4cca3e1903b88c.jpg) + +![](images/092b1f0a9d9fbfa30e5e8c1d81817715de9f32deab151d79132d9448cf531210.jpg) + +![](images/3480473a2d184291ddacc33b6a07f2e276527905bf757f057591eca5101cf431.jpg) +Room0 + +![](images/6c6c2b39fc6d5efe72177c54992781b17d6fba64ddd4e976cb02bbba293cd262.jpg) + +![](images/9506cce1d4112060ed8e3c68e01eda39295ea16f9d67f5a22b7a46bf974f37bd.jpg) +(b) Segmentation results on Replica dataset + +![](images/59951761aad5a4f94d4f558b96a848248d6a57421c69059ed73cefb19b0f859e.jpg) + +![](images/7ef17b0d6cd04e32248766a16b6ba706dcb458c16efed9480a9841aab4a9d17d.jpg) + +![](images/f4ea99ee4befe8782340030222cc8eba3d560d158f382fe3dd5ab4a95293855c.jpg) + +![](images/9e2198d71efaf677b061065f2158781f14e72622255cb837a9d9f3bc0a23e19d.jpg) +Office3 +RGB + +![](images/c2c848fdd953a4a2cf907ab4ce8e1d14dfe84f4c7c76de80ddbfa7f3d964f0ee.jpg) + +![](images/b2f1048187e2108ef05ed2641430909d38a40e0960b775301b56f351bcd95c19.jpg) +Panoptic-Lifting-GS + +![](images/374143a0ccc33e26112628a801d8020d4f6bceacf86ebd4dae8f35c307c8f5c5.jpg) + +![](images/4f8d497e0250801aea4f58f0b4dcd608d4f129e4c7b8e265404685a551bff910.jpg) +Gaussian Grouping + +![](images/49c6dbdb5d1f61f6a26ea4cc90d159b30bb0d264b30c6a2c58d69986ff912854.jpg) + +![](images/b6040620be5161c8610e4f91b0e8051cd008ee76f664a7400d3a9481e9aa74e1.jpg) +OmniSeg3D + +![](images/a0c71182cf5762778619d2d3d092a736715eb3af646c6e98d23a735b2a9dcf23.jpg) + +![](images/9a01576f4640c9a3c26ca59867bf1681fe5871a1b6bf938bb69914a4e27d12a5.jpg) +Unified-Lift (ours) + +![](images/932d704a7b3fe8169bee3e46329bbdd939717d6c4cc0a1fa0ef32f1463c140a5.jpg) + +![](images/7772ec06fad1aa6f6406880b96c290a7af3cc7e523d0ae93c8a99cf5bf275bb6.jpg) +GT + +![](images/d5d7601ff91f0375670736ecbad3846c5aa4e5564e4f5f694d588564da0e3973.jpg) +Scene editing (copy & paste) + +![](images/7e749307740a09cdc0fa35b5012bdcb0cfa6b0293ea2dff8fec000cdabd06498.jpg) +Figure 6. Qualitative comparison of our Unified-Lift with previous methods. We provide visual comparisons on the LERF-Masked dataset [39] in (a); and on the Replica dataset [35] in (b). Moreover, we present the application results in (c). As shown in the left part of (c), we select the potted plants in view 1 and apply the copy & paste operations to the associated Gaussian points. The consistent editing results in view 2 and view 3 further demonstrate the advantages of our method. In contrast, using segmentations derived from Gaussian Grouping [39] leads to severe artifacts and can even adversely affect unrelated object such as the vase observed in view 3. In addition, we illustrate the multi-scale object selection application in the right part of (c). By clicking on the red point in view 1, we consistently select the sofa instance at three different granularities across multiple views. + +![](images/86db69c98aa66cbe46ef7d8caedc836e8cf924966872df9c3c4265cce8aa5fc1.jpg) +(c) Application + +![](images/d43ca512010bb704e3eaf1bf1f4b71740831b8b64e57c084af8bf51ad5a69e42.jpg) + +![](images/d5681af7ee74acb725a3dcd1966c94609a462f7b01eee9e7e23d6f7cece20e05.jpg) +Multi-scale object selection + +![](images/c6955eb33c054d5d5fc12b3adb5e90ca33d52adc8360ff8e0cbc56436fb309d5.jpg) + +
BackboneTypeMethod/ NumberOld Room Environment (%)Large Corridor Environment (%)Mean (%)Training (h)
25501005002550100500
NeRFEnd-to-endPanoptic Lifting [33]73.269.964.351.065.571.061.849.063.2≥ 20
Post-processingContrastive Lift [1]78.975.869.155.076.575.568.752.569.0≥ 20
GSPost-processingOmniSeg3D-GS [40](†)80.172.461.446.874.979.663.948.566.0≈ 1
End-to-endPanoptic-Lifting-GS [33](*)67.565.159.446.162.265.357.545.558.6≈ 1
End-to-endUnified-Lift (ours)79.172.265.953.977.078.970.754.169.0≈ 1
+ +Table 3. Results on the Messy Rooms dataset [1]. Following [1], PQ $^{\text{scene}}$ metric is reported on both the "old room" and "large corridor" environments with an increasing number of objects in the scene (25, 50, 100, 500). * indicates self-implementation, and † indicates that the results are reported under the best-found hyper-parameter (i.e., minimal cluster size for HDBSCAN [24]). Note that, we test the training time for all methods using a single NVIDIA 3090 RTX GPU. + +
MethodmIoU (%)F-score (%)
Previous end-to-end baseline [33]25.332.9
Our baseline solution (with codebook)29.539.2
+ concentration constraint36.341.3
+ area-aware ID mapping39.241.0
+ noisy label filtering (full method)41.643.9
+ +Table 4. Ablation study on the Replica dataset [35]. + +Tab. 1 demonstrate that our Unified-Lift outperforms all existing lifting methods, as well as open-vocabulary approaches like LERF [13] and LangSplat [30]. Moreover, visual comparisons between our Unified-Lift and other methods are presented in Fig. 6 (a), demonstrating the effectiveness of our approach in achieving consistent and accurate 3D segmentation. Following the process in the baseline work [39], we set the segmentation result to empty if the calculated IoU between predictions and ground truth falls below a predefined threshold. + +Replica dataset. To further validate the effectiveness of our Unified-Lift, we conduct experiments on the Replica dataset [35], which comprises eight distinct scenes. Quantitative comparisons with state-of-the-art methods, presented in Tab. 2, demonstrate that our Unified-Lift achieves the best performances across all metrics. Visual results, illustrated in Fig. 6 (b), further verify that our method not only produces more accurate segmentations for small objects (e.g., vase and button) but also generates significantly fewer artifacts compared to the existing methods. Notably, even when using the optimal hyper-parameters in HDBSCAN [24] for OmniSeg3D-GS [40], its post-processing clustering algorithm struggles to balance accuracy for small objects and smooth segmentation for larger objects. + +# 4.3. Scalability on varying object numbers + +To demonstrate the scalability of our Unified-Lift across varying object quantities, we conduct additional experiments on the widely-used Messy Rooms dataset [1], which covers scenes containing up to 500 distinct objects. For fair comparisons, we follow the same evaluation protocol used in the previous work [1] to calculate the metric that assesses the consistency of instance IDs across multiple views [33], denoting as $\mathbf{PQ}^{\mathrm{scene}}$ in Tab. 3. Specifically, we choose the segment with largest area in the generated instance segmentation across different views as the background, to generate the binary semantic segmentations for $\mathbf{PQ}^{\mathrm{scene}}$ metric calculations. This approach avoids the need to optimize an additional semantic feature in our method, as well as in all 3D-GS-based baselines. We compare our method with the 3D-GS-based baselines (i.e., OmniSeg3D-GS and Panoptic-Lifting-GS) and the NeRF-based baselines (i.e., Panoptic Lifting [33] and Contrastive Lift [1]) for a comprehensive evaluation. As shown in Tab. 3, the quantita + +tive results demonstrate that our method achieves improved performance compared to 3D-GS-based baselines, particularly in scenes with a large number of objects. Moreover, our method achieves results comparable to the current state-of-the-art NeRF-based method [1], while requiring significantly less training time. + +# 4.4. Ablation study + +We conduct a detailed ablation study to validate the effectiveness of each component in our proposed method. Quantitative results presented in Tab. 4 show that our new end-to-end lifting method, combined with a baseline codebook learning solution, achieves improved performance compared to the previous end-to-end baseline (i.e., Panoptic-Lifting-GS [33]). Moreover, each proposed learning strategy further enhances our method's performance. + +# 4.5. Applications + +Our method effectively offers an object-level understanding of the 3D scene, which can further facilitate downstream applications. For example, it enables the direct selection of objects in the 3D domain for fundamental copy-and-paste operations. Benefiting from our accurate segmentation results, the edited outputs appear more natural and exhibit fewer artifacts, as illustrated in Fig. 6 (c) left. Furthermore, our method can be easily extended to provide multi-granularity understanding, by simply employing segmentation at various granularities (e.g., three-level granularity for SAM). This capability enables end-to-end multi-scale object selections, as showcased in Fig. 6 (c) right. + +# 5. Conclusion + +We presented Unified-Lift, a new end-to-end object-aware lifting approach based on 3D-GS for constructing accurate and efficient 3D scene segmentations. Specifically, we introduce a novel object-level codebook to incorporate an explicit object-level understanding of the 3D scene by learning a representation for each object. Method-wise, we first augment each Gaussian point with a Gaussian-level point feature and adopt the contrastive loss to optimize these features. Then, we formulate the object-level codebook representation and associate it with the Gaussian-level features for object-aware segmentation prediction. To ensure effective and robust learning for the object-level codebook, we further propose the association learning module and the noisy label filtering module. Extensive experimental results manifest the effectiveness of our method over the state of the arts, without the need of pre- or post-processing. Further analysis on the Messy Rooms dataset also shows its scalability in handling large numbers of objects. + +# Acknowledgment + +This work is supported by the InnoHK Clusters of the Hong Kong SAR Government via the Hong Kong Centre for Logistics Robotics; and the Research Grants Council of the Hong Kong Special Administrative Region, China, under Project CUHK 14200824. + +# References + +[1] Yash Bhalgat, Iro Laina, João F Henriques, Andrew Zisserman, and Andrea Vedaldi. Contrastive Lift: 3D object instance segmentation by slow-fast contrastive fusion. arXiv preprint arXiv:2306.04633, 2023. 1, 2, 3, 4, 6, 7, 8 +[2] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. 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Springer, 2024. 3 \ No newline at end of file diff --git a/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/images.zip b/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..83c052d64e4776a5096c5c7f40b8f9ee2c570079 --- /dev/null +++ b/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f1254b83516e1d55747193f5b02a8619eb4aca0323c3395dfab608ff337a1e5b +size 705029 diff --git a/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/layout.json b/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..92297e418cacb325c577bf920c42502a846d4deb --- /dev/null +++ b/rethinkingendtoend2dto3dscenesegmentationingaussiansplatting/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c121bc0935173b60e160e4bec46ec6be459359e4824b9bec31587a0a44aa16e2 +size 409631 diff --git a/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_content_list.json b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3c3ae8e1de54e49d337567ef6ec04331ddcbe4d9 --- /dev/null +++ b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ab5c3d289b3efdc05388a9fe669a53dd0ddfd865e84deeecd085d62feaa9226f +size 69424 diff --git a/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_model.json b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_model.json new file mode 100644 index 0000000000000000000000000000000000000000..56c364d6d80a9239a0f0c06276bc66b166ba927a --- /dev/null +++ b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:85a99dd5f816830c342021b50e9e164e6a676ccb13baa7172461c09c0055a198 +size 87963 diff --git a/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_origin.pdf b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ed4b733a631e2332b2e8d161795bc32859456bdd --- /dev/null +++ b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/10abeb08-de67-449d-8076-ebf6c3a92a89_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9b4f7974a34c8db4edfcc2dd83e58856a146eaa21c691f97aa0bb9ea8b2de937 +size 1929314 diff --git a/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/full.md b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ce2c4b0c3091400ee4bffa91e89419ac977659b6 --- /dev/null +++ b/rethinkingepistemicandaleatoricuncertaintyforactiveopensetannotationanenergybasedapproach/full.md @@ -0,0 +1,298 @@ +# Rethinking Epistemic and Aleatoric Uncertainty for Active Open-Set Annotation: An Energy-Based Approach + +Chen-Chen Zong, Sheng-Jun Huang* +Nanjing University of Aeronautics and Astronautics +Nanjing, 211106, China +{chencz, huangsj}@nuaa.edu.cn + +# Abstract + +Active learning (AL), which iteratively queries the most informative examples from a large pool of unlabeled candidates for model training, faces significant challenges in the presence of open-set classes. Existing methods either prioritize query examples likely to belong to known classes, indicating low epistemic uncertainty (EU), or focus on querying those with highly uncertain predictions, reflecting high aleatoric uncertainty (AU). However, they both yield suboptimal performance, as low EU corresponds to limited useful information, and closed-set AU metrics for unknown class examples are less meaningful. In this paper, we propose an Energy-based Active Open-set Annotation (EAOA) framework, which effectively integrates EU and AU to achieve superior performance. EAOA features a $(C + 1)$ -class detector and a target classifier, incorporating an energy-based EU measure and a margin-based energy loss designed for the detector, alongside an energy-based AU measure for the target classifier. Another crucial component is the target-driven adaptive sampling strategy. It first forms a smaller candidate set with low EU scores to ensure closed-set properties, making AU metrics meaningful. Subsequently, examples with high AU scores are queried to form the final query set, with the candidate set size adjusted adaptively. Extensive experiments show that EAOA achieves state-of-the-art performance while maintaining high query precision and low training overhead. The code is available at this link. + +# 1. Introduction + +The success of deep neural networks (DNNs) is largely fueled by large-scale, accurately labeled datasets [16, 49]. However, acquiring such data is often expensive and time-consuming primarily due to the labor-intensive nature of manual labeling [30, 50]. To save labeling costs, recent research has focused on developing effective model training + +![](images/2f9c0c0917d39611108b8b0a911d7d9d4b8e308b7d16d1cb23a90c79886b1a7b.jpg) +Figure 1. Dataset: CIFAR-10; mismatch ratio: $40\%$ . Our motivation: in open-set scenarios, querying examples with low epistemic uncertainty yields high query precision, but the overall information content is low, resulting in poor model performance. Focusing on examples with high aleatoric uncertainty also leads to poor performance, as the model's assessment of this uncertainty becomes meaningless for open-set examples. Nevertheless, an effective combination of the two can lead to a superior outcome. + +techniques that leverage limited and insufficiently labeled data [30, 37, 46]. Among them, active learning (AL) has emerged as a popular framework, which iteratively selects the most informative examples from the unlabeled data pool and queries their labels from the Oracle [12, 30, 34]. + +Existing AL methods can be categorized into three types based on their sampling strategies: uncertainty-based [2, 10, 42, 50], diversity-based [25, 33, 40], and hybrid strategies [1, 11, 31]. Most of these methods operate under the closed set assumption, which posits that the classes in the unlabeled data match those in the labeled data. However, in real-world scenarios, it is challenging and often costly to ensure that no open-set classes are present in the unlabeled data. Meanwhile, several studies [6, 26, 28, 31] have shown that these methods perform poorly when open-set classes are involved, as such examples tend to receive uncertain model predictions and exhibit distinct features. Therefore, developing effective AL methods for open-world scenarios, where open-set classes exist, is of significant importance. + +Recently, this emerging research problem has garnered + +considerable attention [6, 26, 28, 31, 50]. For instance, in LfOSA [26], the authors formulate this problem as open-set annotation (OSA) and utilize queried unknown class examples to train a $(C + 1)$ -class detector for rejecting open-set examples and focusing more on selecting known class ones. Two recent methods, EOAL [31] and BUAL [50], adopt a structure similar to LfOSA, with EOAL aimed at improving the recognition of known class examples, while BUAL focuses more on sampling highly uncertain examples. Despite demonstrating high query precision, our findings reveal that these methods can not achieve satisfactory test accuracy and struggle to identify the most informative examples. + +To analyze the reasons behind their failure, we review the concept of uncertainty quantification1. Epistemic uncertainty refers to a measure that remains high for instances not previously encountered and decreases when these instances are included in the training [14, 35]. In contrast, aleatoric uncertainty is characterized by elevated values in ambiguous examples [14, 35]. In closed-set settings, examples with high epistemic uncertainty tend to reside in low-density regions of the representation space, while those with high aleatoric uncertainty may appear around the decision boundary due to ambiguous features. Both types are potential targets for our queries. However, in open-set scenarios, examples with high epistemic uncertainty are likely to be open-set instances, and aleatoric uncertainty is meaningful only in closed-set contexts, as it reflects the ambiguity between different observable classes2 [14, 22]. Therefore, selecting examples with low epistemic uncertainty (to ensure a closed set) and high aleatoric uncertainty is a more reasonable choice. However, LfOSA and EOAL focus on querying examples with low epistemic uncertainty, while BUAL prioritizes querying those with high aleatoric uncertainty. This may be the potential reason for their failure. + +To validate this, we present the results in Figure 1. As shown, focusing solely on either epistemic or aleatoric uncertainty in an open-world scenario results in suboptimal performance. However, effectively combining both leads to a significant improvement. Inspired by this, we propose Energy-based Active Open-set Annotation (EAOA), an approach that effectively queries the most informative examples by considering both types of uncertainty. EAOA maintains two networks: a $(C + 1)$ -class detector and a $C$ -class target classifier, with the following contributions: + +- An energy-based epistemic uncertainty measure is designed for the detector, expressed as the free energy score on known classes minus that on the unknown class. This measure integrates both learning-based and data-driven perspectives, enabling reliable uncertainty assessment in data-limited scenarios. + +- An energy-based aleatoric uncertainty measure is proposed for the target classifier, defined as the free energy score on all classes minus that on secondary classes. +- A coarse-to-fine querying strategy is proposed. It first selects examples with low epistemic uncertainty to form a smaller candidate set, ensuring closed-set properties, which makes aleatoric uncertainty meaningful. Then, it queries examples with high aleatoric uncertainty within this set, with the candidate set size adaptively adjusted through a novel target-driven strategy. +- A margin-based energy loss is introduced for the detector training, aimed at maximizing the free energy score on known classes while minimizing that on the unknown class, thereby enhancing the unknown class detection. +- Extensive experiments show that EAOA outperforms current state-of-the-art methods in test accuracy, query precision, and training efficiency. + +# 2. Related Work + +Active learning (AL) has garnered great research interest as a primary framework for reducing labeling costs by querying the most informative examples for model training. AL's query methods can be categorized based on their data sources into three types: query-synthesizing [19, 20, 47], stream-based [7, 23], and pool-based approaches [2, 6, 10, 12, 50]. Among these, pool-based methods are currently the mainstream, operating under the assumption of a large pool of available unlabeled data, from which a subset of examples is selected for annotation in each AL round. These query methods can be further divided into three categories: 1) uncertainty-based strategies [2, 10, 17, 42], which select instances for which labeling is least certain; 2) diversity-based strategies [25, 33, 40], which query instances that are most representative or exhibit the greatest feature diversity; and 3) hybrid strategies [1, 11, 31], which combine both to achieve better performance. + +Open-set recognition (OSR) refers to a system's ability to differentiate between data types it has encountered during training (in-distribution (ID) data) and those it has not previously seen (out-of-distribution (OOD) data). Earlier studies employed traditional machine learning techniques such as support vector machines [13, 32], extreme value theory (EVT) [43], nearest class mean classifier [3], and nearest neighbor [21]. Recently, there has been growing interest in using generative models to learn representation spaces focused exclusively on known examples [27, 29, 36, 44]. Other techniques often aim to simulate unknown examples, providing a more intuitive approach to OSR [4, 5, 8, 24, 45]. However, simply applying these methods in AL scenarios under the open-world assumption often leads to failure for two main reasons. First, the recognition performance of these methods heavily relies on the classifier's effectiveness; when the classifier underperforms—a common occur + +rence in AL scenarios—the overall performance can decline significantly [38]. Second, some genuine unknown class examples are inevitably labeled during the labeling process, and OSR methods may not effectively utilize them. + +Active open-set annotation (AOSA) refers to AL tasks under open-world scenarios, which aligns more closely with practical application scenarios and has become a research hotspot in recent years [6, 26, 28, 31, 50]. CCAL [6] and MQNet [28] employ contrastive learning and established metrics respectively to assess sample purity and informativeness, utilizing heuristic and meta-learning approaches, respectively, to achieve a balance. However, by not fully leveraging labeled unknown class examples, they provide inadequate assessments, leading to poorer model performance. LfOSA [26] incorporates labeled unknown class examples to train an additional $(C + 1)$ -class classifier (a.k.a., detector), using the maximum activation values (MAVs) to identify known class examples. EOAL [31] enhances the detector by adding an additional binary classifier head and uses entropy values, calculated separately for known and unknown classes, to identify known class examples. BUAL [50] defines positive uncertainty and negative uncertainty respectively, and utilizes the detector's OOD probabilities to balance, aiming to identify highly uncertain examples. However, as previously noted, these methods fail to select examples with both low epistemic uncertainty and high aleatoric uncertainty, resulting in suboptimal performance. + +# 3. Methodology + +# 3.1. Preliminaries + +Notations. Consider the problem of ordinary $C$ -class classification. In active open-set annotation (AOSA) tasks, we start with a limited labeled dataset $\mathcal{D}_L^{kno} = \{(x_i^L,y_i^L)\}_{i = 1}^{\mathcal{N}_L}$ containing $\mathcal{N}_L$ examples from known classes for training, alongside a sufficiently large unlabeled data pool $\mathcal{D}_U = \{x_i^U\}_{i = 1}^{\mathcal{N}_U}$ consisting of $\mathcal{N}_U$ examples from both known and unknown classes for querying. The label $y_{i}^{L}$ of an instance $x_{i}^{L}$ belongs to $\{1,\dots ,C\}$ , whereas the label $y_{i}^{U}$ of an instance $x_{i}^{U}$ is not provided prior to Oracle labeling and falls within $\{1,\dots ,C + 1\}$ , with $C + 1$ representing all unknown classes. At each active learning (AL) cycle, a batch of $b$ examples, denoted as $X^{query} = X_{kn0}^{query}\cup X_{unk}^{query}$ , is selected according to a specified query strategy and sent to Oracle for labeling. Then, $\mathcal{D}_L^{kno}$ and $\mathcal{D}_U$ are updated accordingly, and $X_{unk}^{query}$ forms the unknown class dataset $\mathcal{D}_L^{unk}$ with $\mathcal{D}_L = \mathcal{D}_L^{kn0}\cup \mathcal{D}_L^{unk}$ . + +Overview. As outlined in the Introduction, addressing the AOSA problem requires first ensuring that the queried examples exhibit low epistemic uncertainty to approximate a closed set, enabling meaningful aleatoric uncertainty assessment, and then querying examples with high aleatoric uncertainty. To achieve this goal, we propose an Energy- + +based Active Open-set Annotation (EAOA) framework, as illustrated in Figure 2, which primarily consists of three key components: active sampling, detector training, and classifier training. Specifically, we begin by training a detector network to evaluate the epistemic uncertainty of examples from both learning-based and data-driven perspectives, leveraging the labeled data from both known and unknown classes. Next, we assess the aleatoric uncertainty of examples by utilizing the free energy discrepancy in predictions made by the target classifier. Finally, we query a smaller candidate set of examples with low epistemic uncertainty first, with the set dynamically adjusting by rounds, and then acquire the query set with high aleatoric uncertainty. + +# 3.2. Energy-based Epistemic and Aleatoric Uncertainty for Active Sampling + +Energy-based epistemic uncertainty. Energy-based models (EBMs) [18, 39] build a function $E(x): \mathbb{R}^D \to \mathbb{R}$ to map a $D$ -dim data point to a scalar and defines the probability distribution in multi-class settings through logits as: + +$$ +p (y | x) = \frac {e ^ {- E (x , y)}}{\int_ {y} e ^ {- E (x , y)}} = \frac {e ^ {f _ {y} (x)}}{\sum_ {c = 1} ^ {C} e ^ {f _ {c} (x)}} = \frac {e ^ {- E (x , y)}}{e ^ {- E (x)}}, \tag {1} +$$ + +where $f_{y}(x)$ denotes the predicted logit of model $f$ for instance $x$ regarding label $y$ , $E(x,y) = -f_{y}(x)$ , and $E(x) = -\log \sum_{c=1}^{C} e^{-E(x,c)}$ is called free energy. The probability density of $x$ in an EBM can be written as: + +$$ +p (x) = \frac {e ^ {- E (x)}}{\int_ {x} e ^ {- E (x)}} = \frac {\int_ {y} e ^ {- E (x , y)}}{\int_ {x} \int_ {y} e ^ {- E (x , y)}} = \frac {e ^ {- E (x)}}{\mathcal {Z}}. \tag {2} +$$ + +This implies that for two data points, $x_{1}$ and $x_{2}$ , if $E(x_{1}) > E(x_{2})$ , then $x_{1}$ lies in a sparser region compared to $x_{2}$ w.r.t. the marginal distribution. This aligns with epistemic uncertainty: high-uncertainty examples are distributed in low-density regions due to their lower occurrence frequency. + +Nevertheless, free energy is not ideal for directly measuring epistemic uncertainty in the AOSA task, as the underlying EBM does not fully utilize the information contained in the labeled unknown class examples. To counter this, we group all unknown classes into the $C + 1$ category, train a multi-class classifier (i.e., the detector), and extend the free energy theory by making the following Remark 1. + +Remark 1 For AOSA tasks, the epistemic uncertainty (EU) of $x$ can be expressed through the free energy score on known classes minus that on the unknown class3, + +$$ +\begin{array}{l} E U (x) = E _ {k n o} (x) - E _ {u n k} (x) \\ = - \log \sum_ {c = 1} ^ {C} e ^ {- E (x, c)} + \log \left(1 + e ^ {- E (x, C + 1)}\right). \tag {3} \\ \end{array} +$$ + +![](images/39d2bd029804b11f335bc43b456460e751dfe76c41f57c3cf4aeddff41adaacc.jpg) +Update the corresponding data pool +Figure 2. The framework of EAOA. It consists of three general steps: model training, example selection, and Oracle labeling. In the model training phase, a detector is trained to assess epistemic uncertainty (EU) from both learning-based and data-driven perspectives, along with a target classifier to evaluate aleatoric uncertainty (AU) based on class confusion. In the example selection phase, $kb$ examples with the lowest EU scores are chosen first, followed by querying $b$ examples with the highest AU scores, where $k$ is adaptively adjusted based on the target precision. In the Oracle labeling phase, the queried examples are assigned labels, and all relevant data pools are updated accordingly. + +As such, for two given data points $x_{1}$ and $x_{2}$ , the inequality $EU(x_{1}) > EU(x_{2})$ implies that $x_{1}$ is occurring from a denser region w.r.t. the unknown class compared to $x_{2}$ . + +Since labeled data in AL is often quite limited, relying solely on the detector's predictions to assess the epistemic uncertainty of examples may not be sufficiently reliable. To obtain a more reliable measurement, we evaluate the epistemic uncertainty of examples in two ways: 1) a learning-based perspective that directly uses the detector's predictions, and 2) a data-driven perspective that relies on the similarity to labeled examples from different classes. To this end, we utilize the detector to extract features and emit $K$ arrows from each instance in the labeled data pool $\mathcal{D}_L$ to its $K$ nearest neighbors in the unlabeled data pool $\mathcal{D}_U$ based on cosine distance. For a data point $x_i^U$ , its probability given class $y$ can be approximated as: + +$$ +p \left(x _ {i} ^ {U} | y\right) = \frac {\# \text {o f A r r o w s} _ {\left(x _ {j} ^ {L} , y\right)}}{| X ^ {y} |} \tag {4} +$$ + +where $\#$ of $\mathrm{Arrows}_{(x_j^L,y)}$ denotes the total number of arrows directed at $x_{i}^{U}$ from examples with label $y$ , and $|X^y|$ represents the total number of examples with label $y$ in $\mathcal{D}_L$ . If $x_{i}^{U}$ is in a region where examples with label $y$ densely exist, it is likely to receive more arrows, and vice versa. + +Then, by virtue of Bayes' theorem, we define the data + +centric class probability distribution of $x_{i}^{U}$ as + +$$ +p \left(y \mid x _ {i} ^ {U}\right) = \frac {p \left(x _ {i} ^ {U} \mid y\right) p (y)}{\sum_ {c = 1} ^ {C + 1} p \left(x _ {i} ^ {U} \mid c\right) p (c)}. \tag {5} +$$ + +Here, the prior $p(y)$ is the probability of observing class $y$ , and can be approximately determined by the sample count for each class in $\mathcal{D}_L$ : + +$$ +p (y) = \frac {\left| X ^ {y} \right|}{\sum_ {c = 1} ^ {C + 1} \left| X ^ {c} \right|}. \tag {6} +$$ + +Based on Eqs. (1), (4), (5), and (6), we can obtain: + +$$ +p \left(y \mid x _ {i} ^ {U}\right) = \frac {\# \operatorname {o f A r r o w s} _ {\left(x _ {j} ^ {L} , y\right)}}{\sum_ {c = 1} ^ {C + 1} \# \operatorname {o f A r r o w s} _ {\left(x _ {j} ^ {L} , c\right)}} = \frac {e ^ {- E \left(x _ {i} ^ {U} , y\right)}}{e ^ {- E \left(x _ {i} ^ {U}\right)}}. \tag {7} +$$ + +As such, we can define the specific form of the energy function from a data-driven perspective to calculate the epistemic uncertainty of examples, as stated in Remark 1. + +Here, for a given data point $x_{i}^{U}$ , the uncertainty scores calculated in two different ways are denoted as $EU_{L}(x_{i}^{U})$ and $EU_{D}(x_{i}^{U})$ . We first gather the uncertainty scores for all examples in $\mathcal{D}_U$ to form sets $\{EU_L(x_1^U),\dots ,EU_L(x_{\mathcal{N}_U}^U)\}$ and $\{EU_D(x_1^U),\ldots ,EU_D(x_{\mathcal{N}_U}^U)\}$ , and then fit two two-component Gaussian Mixture Models (GMMs) respectively to convert these scores into a probabilistic format. Suppose a tilde is added to denote the probabilistic format, we apply + +an element-wise product rule to obtain the final epistemic uncertainty score of $x_{i}^{U}$ : + +$$ +\tilde {E U} (x _ {i} ^ {U}) = \tilde {E U} _ {L} (x _ {i} ^ {U}) \odot \tilde {E U} _ {D} (x _ {i} ^ {U}). \tag {8} +$$ + +Energy-based aleatoric uncertainty. Aleatoric uncertainty arises through inherent noise in the data, that is, for the same instance $x$ , different labels might be observed if multiple annotators label it independently. This means that aleatoric uncertainty can be defined based on the confusion between classes. As such, we further extend the free energy theory by making the following Remark 2. + +Remark 2 For AL tasks, the aleatoric uncertainty (AU) of $x$ can be expressed through the free energy scores on all classes minus that on secondary classes, + +$$ +\begin{array}{l} A U (x) = E (x) - E _ {\text {s e c o n d a r y c l a s s e s}} (x) \\ = - \log \sum_ {c = 1} ^ {C} e ^ {- E (x, c)} + \log \left[ \sum_ {c = 1} ^ {C} e ^ {- E (x, c)} - e ^ {- E (x, y _ {\max })} \right], \tag {9} \\ \end{array} +$$ + +where $y_{max}$ is the most probable label for $x$ . This implies that for two data points $x_{1}$ and $x_{2}$ , if inequality $AU(x_{1}) > AU(x_{2})$ holds, then $x_{1}$ occurs in a region closer to the decision boundary compared to $x_{2}$ . + +Similarly, we gather the uncertainty scores for all examples in $\mathcal{D}_U$ to form set $\left\{AU(x_1^U),\ldots ,AU(x_{\mathcal{N}_U}^U)\right\}$ and then fit a two-component GMM to convert these scores into a probabilistic format, i.e., $\left\{\tilde{A} U(x_1^U),\dots ,\tilde{A} U(x_{\mathcal{N}_U}^U)\right\}$ . + +Target-driven adaptive active sampling. After having epistemic uncertainty scores and aleatoric uncertainty scores, we form the query set based on the strategy outlined in Figure 2. Specifically, in each active sampling round, we perform the querying in two rounds. In the first round, $kb$ examples with the lowest epistemic uncertainty scores are selected. Then, according to aleatoric uncertainty, we choose the top $b$ examples with the highest scores from the candidates obtained in the first round to query their labels. + +Obviously, the choice of the $k$ value is critical. If $k$ is too small, such as $k = 1$ , it maximizes the likelihood that the queried examples belong to the closed-set classes. However, since the candidate set size matches the query set size, aleatoric uncertainty cannot effectively contribute. On the contrary, if the $k$ value is too large, the closed-set condition of the candidate set cannot be ensured, rendering aleatoric uncertainty meaningless. Meanwhile, the optimal $k$ value often varies for different datasets. To enhance the strategy's generalizability, we introduce the expected target precision for known class queries to drive the adaptive adjustment of the $k$ value. The relation between the two is as follows: + +$$ +k _ {t + 1} = \left\{ \begin{array}{l l} k _ {t} + a & \text {i f} r P - t P > z, \\ k _ {t} - a & \text {i f} t P - r P > z, \\ k _ {t} & \text {i f} | t P - r P | \leq z, \end{array} \right. \tag {10} +$$ + +where $k_{t}$ is the value of $k$ in the $t$ -th AL round, $tP$ is the expected target precision, $rP$ is the real query precision calculated as $rP = \frac{|X_{kno}^{query}|}{|X_{query}|}$ after Oracle labeling, $a$ is the variation amplitude and $z$ is the triggering threshold. Notably, although the number of hyper-parameters increases, setting them becomes significantly easier, and they are less sensitive to dataset variations. + +# 3.3. Detector and Target Classifier Training + +Detector training. All labeled examples from the known classes and unknown classes are jointly used to train a detector with $C + 1$ classes. For a given data point $x_{i}$ with label $y_{i}$ , let $p_i$ denote its one-hot label, i.e., $p_{ic}$ is set to 1 and the others to 0, and $q_{i}$ denote its probability vector predicted by the detector. On the one hand, we use the following cross-entropy loss to train the detector: + +$$ +\mathcal {L} _ {c e} ^ {x _ {i}} = - p _ {i} \log q _ {i} = - \sum_ {c = 1} ^ {C + 1} p _ {i c} \log q _ {i c}. \tag {11} +$$ + +On the other hand, we propose a margin-based energy loss to ensure that, for examples from known classes, the free energy scores for the first $C$ classes are high, while for examples from unknown classes, the free energy score for the $(C + 1)$ -th class remains low, referring to Remark 1. The energy loss is calculated by: + +$$ +\mathcal {L} _ {\text {e n e r g y}} ^ {x _ {i}} = \left\{ \begin{array}{l} \left(\max \left(0, E _ {\text {k n o}} \left(x _ {i}\right) - m _ {\text {k n o}}\right)\right) ^ {2} \text {i f} x _ {i} \in \mathcal {D} _ {L} ^ {\text {k n o}}, \\ \left(\max \left(0, m _ {\text {u n k}} - E _ {\text {k n o}} \left(x _ {i}\right)\right)\right) ^ {2} \text {i f} x _ {i} \in \mathcal {D} _ {L} ^ {\text {u n k}}, \end{array} \right. \tag {12} +$$ + +where $m_{kno}$ and $m_{unk}$ are the margins for known classes and unknown classes, respectively. + +Thus, the total loss for training the detector is: + +$$ +\mathcal {L} _ {\text {d e t e c t o r}} ^ {x _ {i}} = \mathcal {L} _ {c e} ^ {x _ {i}} + \lambda_ {e} \mathcal {L} _ {\text {e n e r g y}} ^ {x _ {i}}, \tag {13} +$$ + +where $\lambda_{e}$ is a hyper-parameter that balances the two losses. + +Target classifier training. All labeled examples from the known classes are used to train the target classifier by minimizing the standard cross-entropy loss: + +$$ +\mathcal {L} _ {\text {c l a s s i f i e r}} ^ {x _ {i}} = - p _ {i} \log q _ {i} = - \sum_ {c = 1} ^ {C} p _ {i c} \log q _ {i c}. \tag {14} +$$ + +The pseudocode of EAOA is shown in Appendix C. + +# 4. Experiments + +# 4.1. Implementation Details + +Datasets. We validate the effectiveness of our method on three benchmark datasets: CIFAR-10 [15], CIFAR-100 + +![](images/93aadc4a48c88ba583ffd541dbf9aecc1c93a905331ed7f548f1e6763af458c2.jpg) +Figure 3. Test accuracy comparison on CIFAR-10, CIFAR-100, and Tiny-ImageNet. + +[15], and Tiny-/ImageNet [41], with category counts of 10, 100, and 200, respectively. To perform active open-set annotation (AOSA), we create their open-set versions by randomly selecting a subset of classes as known according to the specified mismatch ratio, while the remaining classes are treated as unknown. The mismatch ratio is defined as the proportion of known classes in the total number of classes. For CIFAR-10 and CIFAR-100, we set the mismatch ratios to $20\%$ , $30\%$ , and $40\%$ . For Tiny-/ImageNet, we set the ratios to $10\%$ , $15\%$ , and $20\%$ , making it more challenging. + +Training details. Initially, we randomly select $1\%$ , $8\%$ , and $8\%$ of known class examples from CIFAR-10, CIFAR-100, and Tiny/ImageNet, respectively, to construct the labeled dataset. The active learning (AL) process consists of 10 rounds, with 1,500 examples queried in each round. For all experiments, we choose ResNet-18 [9] as the base model and train it by SGD [48] optimizer with momentum 0.9, weight decay 5e-4, and batch size 128 for 200 epochs. The initial learning rate is set to 0.01 and is reduced by a fac + +tor of 10 every 60 epochs. We repeat all experiments three times on GeForce RTX 3090 GPUs and record the average results for three random seeds (seed = 1, 2, 3). We generally set the values of $K$ , $tP$ , $k_1$ , $a$ , $z$ , $m_{kno}$ , $m_{unk}$ , and $\lambda_e$ to 250, 0.6, 5, 1, 0.05, -25, -7, and 0.01, respectively, and these values generalize well across datasets. + +Baselines. We consider the following methods as baselines: Random, Uncertainty, Certainty, Coreset, BADGE, CCAL, MQNet, EOAL, and BUAL. Among them, EOAL and BUAL are currently state-of-the-art (SOTA). A detailed overview of these methods is provided in Appendix D. + +# 4.2. Performance Comparison + +Figure 3 displays the test accuracy of various methods on CIFAR-10, CIFAR-100, and Tiny-/ImageNet, varying with the number of AL rounds. Figure 4 presents scatter plots of the average query precision across all rounds and the final round test accuracy for each method on CIFAR-10, CIFAR-100, and Tiny-/ImageNet. Here, the query precision refers to + +![](images/05b1b5be41981771dcaf478f5aa9c41fd3002d0740276d9cb37e6b9ae31b6f5d.jpg) +Figure 4. Query precision comparison on CIFAR-10, CIFAR-100, and Tiny-ImageNet. + +the proportion of queried known class examples to the total number of queried examples in each round. + +As shown in Figure 3, our method achieves optimal test accuracy across all datasets and mismatch ratios, and in most AL rounds, the curve of our method entirely surpasses those of other methods, demonstrating its superiority. In Figure 4, our method achieves optimal final round test accuracy and mean query precision in most scenarios, particularly on the challenging Tiny-ImageNet dataset, demonstrating its strong recognition capabilities. Compared to the existing SOTA methods, BUAL and EOAL, our method ensures that queried examples exhibit low epistemic uncertainty while maintaining high aleatoric uncertainty. The significant test performance improvement over them validates the effectiveness of our proposed framework, suggesting that the examples selected by our method are more informative. All methods that employ a $(C + 1)$ -class detector to leverage labeled unknown class examples—BUAL, EOAL, + +LfOSA, and our method—exhibit significant performance advantages over the remaining methods, both in test performance and recognition capability. Although CCAL and MQNet consider both sample purity and informativeness, they fail to achieve an effective balance and adopt inadequate measurement metrics. Certainty shows similar recognition performance to Random, supporting that entropy, i.e., a measure of aleatoric uncertainty, is only meaningful in closed-set scenarios. Traditional AL methods, Uncertainty, Coreset, and BADGE, are significantly hindered by open-set examples, as these examples are prone to receive low-confidence predictions and exhibit diverse features, thus leading to poorer performance. + +# 4.3. Ablation Studies + +Effect of each component. Figure 5 (left) shows the ablation results to validate the effectiveness of each component in our method. Our proposed energy-based epistemic + +![](images/baeb581d2fd2694282378382326661d24247814d27a7acecddda4ea6efdaabd8.jpg) +Figure 5. Ablation results on CIFAR-100 with a mismatch ratio of $40\%$ . 1) The left validates the effectiveness of each method component. "Part 1" represents energy-based epistemic uncertainty and "Part 2" indicates energy-based aleatoric uncertainty. "mQP" denotes mean query precision across all AL rounds. 2) The middle assesses the sensitivity of the energy loss weight $\lambda_{e}$ . "mDA" denotes mean detector test accuracy across all AL rounds. 3) The right shows the runtime comparison. The numbers on the bar chart correspond to mQP scores. + +![](images/d647ae86a02cc2673e3f928c9faff918b2643323a5bf52dc8d67c2c1853ed19b.jpg) + +![](images/799cb491100421a7ad322c8827f3be55bc50167526c0e429a230c64c73f60a11.jpg) + +![](images/7b9cefea22c0de0ebd0ce49b12a8363771c9757c79a04c435a69bfa7787b2d5d.jpg) +Figure 6. Ablation results for target precision $tP$ on CIFAR-10 (Left) and CIFAR-100 (Right). "MR" denotes mismatch ratio. "Best" indicates the top-performing method in the comparisons. + +uncertainty ("Part 1") utilizes information from labeled unknown class examples, leading to significant improvements in both recognition and test performance compared to free energy alone. The proposed energy-based aleatoric uncertainty ("Part 2") performs poorly on its own, as aleatoric uncertainty is only meaningful in closed-set scenarios. However, when combined with "Part 1", it shows significant improvement, validating the superiority of the entire framework. Additionally, removing the data-driven epistemic uncertainty score or the margin-based energy loss leads to a decline in performance, confirming their necessity. + +Hyper-parameter sensitivity. Figure 6 presents the ablation results for the hyperparameter target query precision $tP$ on CIFAR-10 and CIFAR-100, with values set to [0.4, 0.5, 0.6, 0.7, 0.8]. Overall, the fluctuations in test performance are minimal, and as $tP$ increases, the method's recognition performance improves. Figure 5 (middle) displays the ablation results for the energy loss weight $\lambda_{e}$ on CIFAR-100 with a $40\%$ mismatch ratio, using values of [0.001, 0.005, 0.01, 0.05, 0.1]. A higher loss weight can impede model training, leading to reduced detector accuracy and reliability. Conversely, a lower loss weight fails to effectively separate the energy distributions of known and + +unknown class examples, adversely affecting the detector's recognition performance. + +The ablation results for additional hyper-parameters are provided in Appendix E, which can demonstrate their ability to generalize effectively across different datasets. + +Runtime comparison. Figure 5 (right) presents the running times and mean query precision of various methods on CIFAR-100 with a mismatch ratio of $40\%$ . A higher mean query precision indicates that a larger number of examples are involved in training, often resulting in longer training times. Traditional AL methods, characterized by lower mean query precision and the training of a single model, generally have shorter training times. Notably, our method has the shortest runtime among all AOSA methods, achieving the highest test accuracy and maintaining a very high recognition rate. + +# 5. Conclusion + +In this paper, we demonstrate that focusing solely on either epistemic uncertainty (EU) or aleatoric uncertainty (AU) in open-world active learning scenarios does not yield satisfactory performance. We argue that the most informative examples should primarily belong to closed-set classes, exhibiting low EU scores, ensuring that the derived AU metric is meaningful, and secondarily, should show high AU scores. To achieve this, we propose EAOA, a novel framework for addressing the challenging active open-set annotation problem. In EAOA, both types of uncertainty are defined in the form of free energy: EU is evaluated by the detector from both learning-based and data-driven perspectives, while AU is measured by the target classifier through class confusion. Additionally, we introduce a margin-based energy loss to enhance the detector's ability to distinguish known from unknown classes and a target-driven strategy to adaptively adjust the size of the candidate set obtained in the first query stage. 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When only a handful of samples are available per category, as in Few-Shot Adaptation (FSA), data are insufficient to fit a large number of parameters, rendering the above impractical. This is especially true with large pre-trained Vision-Language Models (VLMs), which motivated successful research at the intersection of Parameter-Efficient Finetuning (PEFT) and FSA. In this work, we start by analyzing the learning dynamics of PEFT techniques when trained on few-shot data from only a subset of categories, referred to as the "base" classes. We show that such dynamics naturally splits into two distinct phases: (i) task-level feature extraction and (ii) specialization to the available concepts. To accommodate this dynamic, we then depart from prompt- or adapter-based methods and tackle FSA differently. Specifically, given a fixed computational budget, we split it to (i) learn a task-specific feature extractor via PEFT and (ii) train a linear classifier on top. We call this scheme TwoStage Few-Shot Adaptation (2SFS). Differently from established methods, our scheme enables a novel form of selective inference at a category level, i.e., at test time, only novel categories are embedded by the adapted text encoder, while embeddings of base categories are available within the classifier. Results with fixed hyperparameters across two settings, three backbones, and eleven datasets, show that 2SFS matches or surpasses the state-of-the-art, while established methods degrade significantly across settings. + +# 1. Introduction + +Effective visual classification requires two key components: a good feature extractor and a strong classifier operating on features. This is established knowledge in computer vision, and multiple influential works [35, 44] have demonstrated that a simple linear classifier, optimized atop a frozen feature extractor pre-trained at a larger scale (e.g., on ImageNet + +![](images/6d21bd6da7612b2548eef37e11ad4b666fb110de404aff6c7b0820aea19a6901.jpg) +Figure 1. We present 2SFS, a technically simple revision of classifier tuning. 2SFS exhibits favorable performance both in all-to-all FSA, where train/test categories coincide, as well as in the more challenging base-to-novel setup, where only a subset of base annotated categories are available, and the test suite further spans a set of unseen (novel) classes. Conversely, setting-specific SOTA approaches [42, 47] degrade between settings. + +[34]), achieves state-of-the-art or competitive results on a variety of downstream tasks [49]. Throughout adaptation, the feature extractor can also be fine-tuned together with the classifier, commonly with a lower learning rate to avoid disrupting the knowledge instilled from pretraining. Notably, the success of this latter paradigm is linked to the curse of dimensionality and the risk of overfitting when there are too few annotated samples relative to the parameters. + +In this work, we deal with the Few-Shot Adaptation (FSA) of Vision-Language Models (VLMs), where the data-to-parameter ratio is at a critical level: there are typically hundreds of millions of parameters, but only a handful of data points are available on a per-category basis (i.e., the "shots"). Such a dilemma is emphasized when shots are available for a restricted subset of categories, often referred to as the "base" categories, and the downstream task is assumed to span a broader range, comprising both base and "novel" semantic concepts. This non-trivial chal + +lenge fueled modern research on Parameter-Efficient FineTuning (PEFT) [6, 12, 23], with successful examples in the FSA of VLMs that are mostly categorized into two (nonconflicting) paradigms: (i) prompt tuning, which optimizes a set of context vectors in either the text [52, 53] or the vision encoder [43] and (ii) adapter-based methods, where parametric functions are wrapped as external entities around (or on top of) the frozen VLM [10, 42, 47]. + +All of the methods above consistently outperform full fine-tuning and linear probing. However, this is mostly an a-posteriori observation, and despite the abundance of literature in the field, very little is known about the learning dynamics in FSA, i.e., about what happens throughout training with only a handful of examples. We start this work by filling this gap, analyzing the behavior of CLIP [33] when adapting it to downstream tasks with different PEFT strategies. Surprisingly, we find that the learning dynamics exhibit consistent patterns across datasets when evaluated on held-out data: (i) an initial stage of joint performance increase on both seen and unseen concepts; (ii) a breakpoint, after which PEFT strategies still largely improve on base categories at the expense of degradation on unseen semantic concepts. In other words, the initial stages of PEFT make for good task-level feature extraction, while the second stage specializes in the available data. + +Exploiting this finding, we introduce Two Stage Few-Shot Adaptation (2SFS), a technically simple revision of the old-school classifier tuning paradigm. Specifically, we split a fixed compute budget into two stages: first, we fine-tune only LayerNorm [21] instances of both modality-encoders to obtain a generalizable task-level feature extractor; second, we optimize a classifier on top, i.e., the text embeddings of base categories, to improve the discrimination ability of the model. In contrast to existing methods, 2SFS enables a novel form of selective inference at a category level, i.e., at test-time, only novel categories are embedded by the adapted text encoder, while base categories are available in $\mathcal{O}(1)$ , being rows of the classifier matrix. + +We thoroughly validate 2SFS with fixed hyperparameters across a suite of 11 publicly available datasets, 2 different settings (i.e., base-to-novel and all-to-all), and 3 backbones, showing that our simple approach matches or surpasses setting-specific state-of-the-art methods, while they conversely degrade across settings (see Fig. 1). + +# 2. Related work + +Parameter-efficient fine-tuning (PEFT) [24] adapts a large pretrained model by optimizing a small subset of parameters, while keeping the rest of the model frozen. One can identify three main categories among PEFT techniques: prompt tuning, selective approaches and adapter-based methods. Prompt tuning [15, 22] adds trainable tokens either to the input or within intermediate layers. Ini + +tially designed for language prompts [23], recent works have incorporated visual tokens into the recipe [15]. Selective methods optimize only a carefully chosen subset of existing model parameters. With vision architectures, popular choices are batch- or layer-normalization modules [14, 21]. Within the same categorization, BitFit (BIas-Term FinTuning) [46], originally evaluated on NLP tasks, focuses on bias terms. In contrast, adapter-based methods introduce external functions to adapt the model. Examples are scaling and shifting hidden features [25], adding non linear parametric functions on top of the frozen model outputs [10], or side adapters, slightly refining features across layers [30]. Recently, reparametrization-based adapters have gained significant attention [6, 12, 19, 26], since their design allows to merge the newly introduced parameters with the frozen model, incurring no additional inference cost. LoRA [12] is arguably the most popular example, optimizing a low-rank decomposition of the network's parameters. + +Few-shot adaptation of VLMs. The impressive performance of modern VLMs has motivated researchers to develop adaptation techniques to expand their capabilities to specific tasks [41]. While some of these techniques are purely test-time methods requiring no supervision [8, 36, 48], a common setup is to assume a handful of labeled examples are given. In such a context, PEFT strategies have been designed to account for the multimodal nature of VLMs. Following the previous categorization, the earliest approaches belong to the prompt tuning family [51-53]. CoOp (Context Optimization) [52] learns a set of soft context vectors to circumvent effortful manual prompting. CoCoOp (Conditional Context Optimization) [51] improves CoOp, by generating an image-conditioned context. ProGrad (Prompt-aligned Gradient) [53] strives to preserve pretraining knowledge by only updating prompts when the gradient aligns with a specific direction. Similarly, KgCoOp (Knowledge-guided CoOp) [43] mitigates forgetting by guiding prompt learning with a hand-crafted prompt. PLOT (Prompt Learning with Optimal Transport) [2] and MaPLe (Multi-modal Prompt Learning) [16] make a step further, connecting the visual and textual branches. In PLOT [2], class specific prompts are transported to visual features via optimal transport; MaPLe [16] conditions deep visual prompts with their textual counterparts, with successful results. A second category of FSA techniques relies on adapters [10, 38, 45, 50]. For example, CLIP-Adapter [10] mixes pretrained features with their non-linearly-transformed versions. TaskRes [45] tunes a set of residual parameters instead of introducing a non-linear bottleneck. Other methods [38, 50] avoid fine-tuning and use the few-shot data as a cache to refine predictions. + +In this work, we introduce a new perspective: the benefit of a two-stage design that adapts to the downstream task while improving generalization to unavailable categories. + +![](images/f3c19389b4f4e7da4b73fd81ea63cd1bbb3373f19d6e1ac37729510e130cebc2.jpg) + +![](images/6995e2ef2aaf7cb9bf7cf4f2bc067cd36d425383d844e9987ac1944e8735b8ac.jpg) +(a) FGVC Aircraft + +![](images/934fcc6b89daefc7bc44b09b1369c25316f315d66227dde286fce7632d1ea7e8.jpg) + +![](images/5ffb69aa2ce154d91e2a5dfeebe4c9910fae825e0c785b63b8539b9c9614ed8f.jpg) + +![](images/c8bc125883a060c41186da9f0bd28efe550d1e25d720e558d43e57678f1aa54a.jpg) +Figure 2. The natural emergence of a breakpoint during few-shot adaptation with different PEFT strategies. Before the breakpoint (to the left of the line), PEFT learns good task-level features, showed by joint performance increase on both base and novel categories. After the breakpoint (to the right of the line), PEFT specializes in the available data, incurring unrecoverable performance degradation on novel categories accompanied by consistent improvement in base concepts. Results refer to CLIP [33] with the ViT-B/16 visual backbone [7]. + +![](images/3e58039f1f33ad024fe1ecea5f45a5effb13f84c219faa8667cc6db17936707a.jpg) +(b) DTD + +![](images/bbfe65b353a79d10bfffdc4737331ec48c8ba35338a10ee2f5e33ca96aae03b1.jpg) + +![](images/bed5d36ac00d7d9328a735929bbf8fee99a9bbbb19e9852c86649fd9427b6a44.jpg) + +![](images/da06b812f07a724b2bd8bb04cf278ea9d293eff2d7c397118a8b2ff64ae82d47.jpg) + +# 3. Preliminaries + +In this section, we first formalize the FSA setup (Sec. 3.1). We then conduct a preliminary investigation on the impact of PEFT on the learning dynamics of FSA, with a particular emphasis on the relationship between generalization performance on base and novel categories (Sec. 3.2). + +# 3.1. Problem formulation + +FSA aims at adapting a model $f$ to a specific downstream task given a few annotated examples per category. Formally, the available data in FSA are a collection of (image, category) pairs $D = \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}$ , with $x_{i}\in \mathcal{X}$ and $y_{i}\in \mathcal{B}$ being the available images and the set of base categories, respectively. A small number $k\in \mathbb{N}$ of available samples, referred to as shots, is constant across categories, entailing that the available dataset has cardinality $n = k\times |\mathcal{B}|$ . In general, the downstream task spans a set $\mathcal{C}$ of semantic categories, which is a superset of the available annotated categories, i.e., $\mathcal{B}\subseteq \mathcal{C}$ , and no reliable assumptions can be made on the annotated data. Hence, $\mathcal{B}$ can coincide with $\mathcal{C}$ , but also a set of novel categories $\mathcal{N}\subseteq \mathcal{C}$ may exist such that $\mathcal{B}\cap \mathcal{N} = \emptyset$ and $\mathcal{B}\cup \mathcal{N} = \mathcal{C}$ . One talks about all-to-all FSA when $\mathcal{N} = \emptyset$ (or, equivalently, $\mathcal{B} = \mathcal{C}$ ). Conversely, we talk about base-to-novel generalization. + +The function $f$ is typically a contrastive VLM [33], thus it contains a visual encoder $f^v: \mathcal{I} \to \mathbb{R}^d$ and a text encoder $f^t: \mathcal{T} \to \mathbb{R}^d$ mapping images and texts in a shared $d$ - + +dimensional Euclidean space. The domains $\mathcal{I}$ and $\mathcal{T}$ can be thought of as the image and text spaces. When classes are specified in natural language, i.e., each $c\in \mathcal{C}$ is mapped to a string in $\mathcal{T}$ , zero-shot classification with $f$ takes the form: + +$$ +f (x, \mathcal {C}) = \underset {c \in \mathcal {C}} {\arg \max } \left\{< f ^ {v} (x), f ^ {t} (c) >, \forall c \in \mathcal {C} \right\} \tag {1} +$$ + +where $< \cdot, \cdot >$ denotes cosine similarity. Typically, the VLM $f$ is parametrized by $\theta \in \mathbb{R}^N$ , which largely exceeds the number of available examples (i.e., $N >> n$ ), rendering the optimization of $\theta$ subject to a high risk of overfitting. Thus, a common strategy is to optimize a smaller set of task-specific parameters $\omega$ , according to a PEFT technique. Since $\omega$ may influence both vision and text encoders, without loss of generality, we write it as $\omega = \omega_v \cup \omega_t$ . In most cases, $\omega$ are optimized through the standard softmax cross-entropy objective computed across base categories (we omit the temperature for ease of notation): + +$$ +\mathcal {L} \left(x _ {i}, y _ {i}\right) = - \log \frac {\exp \left(< f _ {\omega_ {v}} ^ {v} \left(x _ {i}\right) , f _ {\omega_ {t}} ^ {t} \left(y _ {i}\right) >\right)}{\sum_ {b \in \mathcal {B}} \exp \left(< f _ {\omega_ {v}} ^ {v} \left(x _ {i}\right) , f _ {\omega_ {t}} ^ {t} (b) >\right)}, \tag {2} +$$ + +where $f_{\omega_v}^v$ and $f_{\omega_t}^t$ are the visual and textual encoders modified by $\omega_v$ and $\omega_t$ , respectively. The objective in Eq. (2) is minimized for a predefined number of iterations $m$ . When optimization ends, the updated parameters $\omega^* = \omega_v^* \cup \omega_t^*$ are used to parametrize $f$ , and Eq. (1) reads: + +$$ +f (x, \mathcal {C}) = \underset {c \in \mathcal {C}} {\arg \max } \left\{\langle f _ {\omega_ {v} ^ {*}} ^ {v} (x), f _ {\omega_ {t} ^ {*}} ^ {t} (c) >, \forall c \in \mathcal {C} \right\}. \tag {3} +$$ + +# 3.2. What happens during Few-Shot Adaptation? + +A desideratum of FSA methods is that, by minimizing Eq. (2), the optimized set of parameters $\omega^{*}$ improves on base classes and generalizes to novel ones. Mechanisms such as weight sharing across encoders [42] or cross-modal prompting [16, 51] have been explicitly developed to promote such behavior, suggesting that ad-hoc designs are required to instill general task knowledge into $f$ . In this section, we challenge this assumption by studying the learning dynamics of PEFT in FSA, when no explicit mechanism promoting generalization is involved in the learning recipe. + +Preliminary PEFT Setup. To conduct our study, we focus on three PEFT methods: LayerNorm tuning [18], LoRA [12], and BitFit [46]. In LayerNorm tuning, typically used for visual adaptation [5], $\omega$ are the scale and bias parameters of the LayerNorm instances of the model. LoRA (low-rank adapters), recently shown effective for VLMs [47], adds trainable low-rank matrices into each linear projection of the model, following a low-rank decomposition of the form $\mathbf{W}\mathbf{x} + \gamma \mathbf{B}\mathbf{A}\mathbf{x}$ . In this case, $\omega$ is the set of all low-rank matrices B, A. We adopt the design of CLIP-LoRA [47], which has extensively studied rank and placement of LoRA modules within CLIP, thereby plugging low-rank modules in all query, key, and value matrices of both encoders, with a rank $r = 2$ . BitFit, originally developed for language encoders [46], adapts the bias terms of all layers. In this latter case, $\omega$ contains the shift vectors of all affine transformations in the network. We apply such PEFT techniques on CLIP ViT-B/16, training with $k = 16$ shots from both Describable Textures [3] and FGVC Aircraft [29]. We follow the established base/novel classes split introduced in CoCoOp [51] and set a budget of $m = 8000$ iterations (i.e., gradient steps) for all PEFT techniques, which allows us to study the exact learning dynamics of the recent CLIP-LoRA [47]. See Appendix E for the same analysis on other datasets. + +Experimental Outcome. Fig. 2 displays the learning dynamics when the adapted model is evaluated on held-out samples. From the outcome, it emerges that the dynamics of PEFT methods exhibit a breakpoint, naturally separating adaptation into two distinct phases: + +1. First Stage: consistent and joint improvement on both base and novel categories. In other words, this means that PEFT is learning good task-level features from both encoders. If this were not the case, then only the performance on available categories would increase; +2. Second Stage: good task-level features are disrupted in favor of exploitation of the available categories. Note that, while this phenomenon looks akin to overfitting, it is not, since models are evaluated on held-out data for both $\mathcal{B}$ and $\mathcal{N}$ . In contrast, it has a different flavor: after the first stage, PEFT specializes in the available categories, overriding knowledge that would have been helpful for the downstream task as a whole. + +We find that the pattern is consistent across datasets and PEFT techniques. Between the two stages, the First Stage is the most counter-intuitive: PEFT learns good vision-language features, although no ad-hoc designs were injected to promote such behavior. We also observe traits characterizing PEFT methods. For example, LoRA tends to better discriminate among base categories, while LayerNorm appears less capable in this respect. However, it is much more robust in the second stage and reaches the breakpoint far later than LoRA and BitFit. We now leverage these observations to design a simple yet effective FSA strategy. + +# 4. Two-Stage Few-Shot Adaptation + +This section introduces Two-Stage Few-Shot Adaptation (2SFS), and describes how we leverage the natural emergence of two stages during FSA. 2SFS revises the old-school paradigm of classifier tuning [39], which has been set aside in favor of prompt- or adapter-based methods. Given a fixed computational budget expressed as a maximum number of iterations $m$ , 2SFS acts in two short stages: + +1. First Stage: initially, 2SFS allocates $\alpha \times m$ iterations to update the feature extractor via PEFT to improve base and novel class performance, with $\alpha \in [0,1]$ . Motivated by the results of Fig. 2, highlighting the enhanced robustness of Layer Normalization, we describe the rest of this section assuming that $\omega$ are LayerNorm scale and shifts. We additionally report 2SFS with LoRA in Appendix A.1. +2. Second Stage: for the remaining $(1 - \alpha) \times m$ steps, 2SFS switches parameters to avoid disrupting helpful task-level features and learns a base classifier. + +At inference time 2SFS enables a novel form of adaptive inference on a per-category basis, i.e., we skip the computation of the text encoder when embedding categories in $\mathcal{B}$ , as they are readily available as rows of the classifier. We now dive into the details of these components. + +# 4.1. First stage: learning task-level features + +In the first stage, we want to learn a good feature extractor for base categories that also generalizes to novel concepts. To achieve this, we exploit the first learning phase in PEFT, where the performances on both sets increase. In this phase, we tune all LayerNorm instances of both visual and textual encoders. Formally, given a $d$ -dimensional vector $\mathbf{a} \in \mathbb{R}^d$ of activations, LayerNorm [21] operates by scaling and shifting the standardized features in $\mathbf{a}$ , i.e. + +$$ +\operatorname {L a y e r N o r m} (\mathbf {a}) = \gamma \odot \left(\frac {\mathbf {a} - \mu (\mathbf {a})}{\sigma (\mathbf {a})}\right) + \beta , \tag {4} +$$ + +where $\mu (\mathbf{a})\in \mathbb{R}$ is the mean of the vector, $\sigma (\mathbf{a})\in \mathbb{R}$ is its standard deviation, while $\gamma$ and $\beta$ are known as the "scale" and "shift" parameters. Both $\gamma$ and $\beta$ are learnable $d$ -dimensional vectors and are subject to fine-tuning. + +![](images/b3fcd26946c85c58ebe8c8f4c764ffdd7ff385de62bccf1e4c9add28adc2d88a.jpg) +Figure 3. 2SFS. Given a computational budget of $m$ iterations, 2SFS operates in two separate stages. In the First Stage, 2SFS learns task-level features by tuning LayerNorm instances. In the Second Stage, a simple classifier initialized with the text embeddings of base categories learns to separate task-level features. At inference time, 2SFS allows to selectively embed categories. Specifically, only novel categories are embedded by the adapted text encoder, while embeddings of base categories are available as rows within $\Phi_{\mathcal{B}}$ . + +![](images/cb422a8dc7a4d1695260cda97fbe602d857cf6462bda81dfb7039782c91c54d3.jpg) + +![](images/c7262eb33c70677d384c43a44cc6bf3824629bd07090fe3b52e53ff692490ab7.jpg) + +Borrowing from the notation of Sec. 3, we denote as task-specific parameters the scale and shift vectors of each LayerNorm instance of the network. Assuming a total of $L$ instances, we have $\omega_{\mathrm{LN}} = \{(\gamma_1,\beta_1),\dots ,(\gamma_L,\beta_L)\}$ , which are the union of modality-specific parameters $\omega_{\mathrm{LN}}^v$ and $\omega_{\mathrm{LN}}^t$ The objective function in Eq. (2) now reads: + +$$ +\mathcal {L} _ {\omega_ {\mathrm {L N}}} \left(x _ {i}, y _ {i}\right) = - \log \frac {\exp \left(< f _ {\omega_ {\mathrm {L N}} ^ {v}} \left(x _ {i}\right) , f _ {\omega_ {\mathrm {L N}} ^ {t}} \left(y _ {i}\right) >\right)}{\sum_ {b \in \mathcal {B}} \exp \left(< f _ {\omega_ {\mathrm {L N}} ^ {v}} \left(x _ {i}\right) , f _ {\omega_ {\mathrm {L N}} ^ {t}} \left(b\right) >\right)}, \tag {5} +$$ + +which we optimize for a $\alpha \times m$ iterations, where $\alpha \in [0,1]$ . Thus, this stage only takes a fraction of the available compute budget and ensures that no further optimization is carried out w.r.t. $\omega_{\mathrm{LN}}$ after the natural breakpoint is reached (i.e., ideally, $\alpha \times m$ should match the pink line of Fig. 2). + +# 4.2. Second stage: simple classifier tuning + +After the first stage, we obtain optimized parameters $\omega_{\mathrm{LN}}^{*} = \omega_{\mathrm{LN}}^{*v} \cup \omega_{\mathrm{LN}}^{*t}$ that incorporate general task knowledge. From Sec. 3.2, we know that further tuning $\omega_{\mathrm{LN}}^{*}$ disrupts helpful features for novel categories, hence we circumvent this issue by carrying out optimization w.r.t. a different set of parameters. We employ arguably the simplest form to do so: we freeze $\omega_{\mathrm{LN}}^{*}$ and train a linear classifier on top. Let $\phi_b = f_{\omega_{\mathrm{LN}}^{*t}}^t(b)$ denote the embedding of the category $b$ , obtained with the first-stage text encoder. We initialize the classifier weights $\Phi_{\mathcal{B}} = \{\phi_b\}_{b \in \mathcal{B}}$ by stacking all embeddings of base categories, and optimize $\Phi_{\mathcal{B}}$ for the remaining $(1 - \alpha) \times m$ steps. At this stage, Eq. (2) becomes: + +$$ +\mathcal {L} _ {\Phi_ {\mathcal {B}}} \left(x _ {i}, y _ {i}\right) = - \log \frac {\exp \left(< f _ {\omega_ {\mathrm {L N}} ^ {* v}} ^ {v} \left(x _ {i}\right) , \phi_ {y _ {i}} >\right)}{\sum_ {b \in \mathcal {B}} \exp \left(< f _ {\omega_ {\mathrm {L N}} ^ {* v}} ^ {v} \left(x _ {i}\right) , \phi_ {b} >\right)}, \tag {6} +$$ + +where $\Phi_{\mathcal{B}}$ learns to separate features obtained with the frozen first-stage visual parameters $\omega_{\mathrm{LN}}^{*^v}$ . Along with its sim + +plicity, this design fully exploits helpful task-level representations: $\Phi_{\mathcal{B}}$ is initialized with first-stage text embeddings and learns to separate first-stage visual embeddings. The optimized classifier weights are denoted as $\Phi_{\mathcal{B}}^{*} = \{\phi_{b}^{*}\}_{b\in \mathcal{B}}$ . + +# 4.3. Category-level Selective Inference + +The proposed two-stage design provides unique advantages, allowing for selective inference within the text encoder. Specifically, given an image $x$ and a set of downstream categories $\mathcal{C}$ to discriminate, our prediction function follows: + +$$ +f _ {\omega_ {L N} ^ {*}, \Phi_ {\mathcal {B}} ^ {*}} (x) = \underset {c \in \mathcal {C}} {\arg \max } < f _ {\omega_ {L N} ^ {* v}} ^ {v} (x), \phi_ {c} ^ {*} > \tag {7} +$$ + +with each $\phi_c^*$ being: + +$$ +\phi_ {c} ^ {*} = \left\{ \begin{array}{l l} \phi_ {b} ^ {*} & \text {i f} \exists b \in \mathcal {B} \mid b = c \\ f _ {\omega_ {\mathrm {L N}} ^ {* t}} ^ {t} (c) & \text {o t h e r w i s e .} \end{array} \right. \tag {8} +$$ + +In essence, at inference time, the two-stage design allows to skip computations within the text encoder, instead of embedding the categories that were available in the annotated data (which are always known in FSA), and to pick the corresponding row of the classifier in $\mathcal{O}(1)$ directly. In contrast, images and unseen categories are always processed with the parameters obtained after the first stage. + +In summary, 2SFS provides a unified recipe for FSA: splitting into stages and optimizing a different parameter subset allows to $①$ preserve helpful knowledge for unseen categories and $②$ exploit available annotations. The overall pipeline of 2SFS is schematized by Fig. 3. + +# 5. Experiments + +This section highlights the experimental results of 2SFS, evaluating: (i) all-to-all FSA, in which train/test categories + +Table 1. Experiments in base-to-novel generalization with the ViT-B/16 visual backbone. All methods use $k = 16$ shots per base class. "CLIP" refers to zero-shot performance with dataset-specific templates, e.g., "a photo of a \{\}, a type of flower" for Oxford Flowers. +Average across datasets. + +
MethodBaseNovelHM
CLIP [33]69.3474.2271.70
CoOp [52]82.6963.2271.66
CoCoOp [51]80.4771.6975.83
MaPLe [16]82.2875.1478.55
ProGrad [53]82.4870.7576.16
KgCoOp [43]80.7373.6077.00
CLIP-LoRA [47]85.3270.6377.28
MMA [42]83.2076.8079.87
2SFS85.5575.4880.20
+ +Oxford Flowers + +
MethodBaseNovelHM
CLIP [33]72.0877.8074.83
CoOp [52]97.6059.6774.06
CoCoOp [51]94.8771.7581.71
MaPLe [16]95.9272.4682.56
ProGrad [53]95.5471.8782.03
KgCoOp [43]95.0074.7383.65
CLIP-LoRA [47]97.9168.6180.68
MMA [42]97.7775.9385.48
2SFS98.2976.1785.83
+ +Food 101 + +
MethodBaseNovelHM
CLIP [33]90.1091.2290.66
CoOp [52]88.3382.2685.19
CoCoOp [51]90.7091.2990.99
MaPLe [16]90.7192.0591.38
ProGrad [53]90.3789.5989.98
KgCoOp [43]90.5091.7091.09
CLIP-LoRA [47]86.8486.6786.76
MMA [42]90.1391.3090.71
2SFS89.1191.3490.21
+ +DTD + +
MethodBaseNovelHM
CLIP [33]53.2459.9056.37
CoOp [52]79.4441.1854.24
CoCoOp [51]77.0156.0064.85
MaPLe [16]80.3659.1868.16
ProGrad [53]77.3552.3562.45
KgCoOp [43]77.5554.9964.35
CLIP-LoRA [47]83.9562.8471.39
MMA [42]83.2065.6373.38
2SFS84.6065.0173.52
+ +ImageNet + +
MethodBaseNovelHM
CLIP [33]72.4368.1470.22
CoOp [52]76.4767.8871.92
CoCoOp [51]75.9870.4373.10
MaPLe [16]76.6670.5473.47
ProGrad [53]77.0266.6671.46
KgCoOp [43]75.8369.9672.78
CLIP-LoRA [47]77.5868.7672.91
MMA [42]77.3171.0074.02
2SFS77.7170.9974.20
+ +Oxford Pets + +
MethodBaseNovelHM
CLIP [33]91.1797.2694.12
CoOp [52]93.6795.2994.47
CoCoOp [51]95.2097.6996.43
MaPLe [16]95.4397.7696.58
ProGrad [53]95.0797.6396.33
KgCoOp [43]94.6597.7696.18
CLIP-LoRA [47]94.3695.7195.03
MMA [42]95.4098.0796.72
2SFS95.3297.8296.55
+ +FGVC Aircraft + +
MethodBaseNovelHM
CLIP [33]27.1936.2931.09
CoOp [52]40.4422.3028.75
CoCoOp [51]33.4123.7127.74
MaPLe [16]37.4435.6136.50
ProGrad [53]40.5427.5732.82
KgCoOp [43]36.2133.5534.83
CLIP-LoRA [47]50.1026.0334.26
MMA [42]40.5736.3338.33
2SFS47.4835.5140.63
+ +EuroSAT + +
MethodBaseNovelHM
CLIP [33]56.4864.0560.03
CoOp [52]92.1954.7468.69
CoCoOp [51]87.4960.0471.21
MaPLe [16]94.0773.2382.35
ProGrad [53]90.1160.8972.67
KgCoOp [43]85.6464.3473.48
CLIP-LoRA [47]97.0462.5076.03
MMA [42]85.4682.3483.87
2SFS96.9167.0979.29
+ +Caltech101 + +
MethodBaseNovelHM
CLIP [33]96.8494.0095.40
CoOp [52]98.0089.8193.73
CoCoOp [51]97.9693.8195.84
MaPLe [16]97.7494.3696.02
ProGrad [53]98.0293.8995.91
KgCoOp [43]97.7294.3996.03
CLIP-LoRA [47]98.1993.0595.55
MMA [42]98.4094.0096.15
2SFS98.7194.4396.52
+ +Stanford Cars + +
MethodBaseNovelHM
CLIP [33]63.3774.8968.65
CoOp [52]78.1260.4068.13
CoCoOp [51]70.4973.5972.01
MaPLe [16]72.9474.0073.47
ProGrad [53]77.6868.6372.88
KgCoOp [43]71.7675.0473.36
CLIP-LoRA [47]83.9365.5473.60
MMA [42]78.5073.1075.70
2SFS82.5074.8078.46
+ +SUN 397 + +
MethodBaseNovelHM
CLIP [33]69.3675.3572.23
CoOp [52]80.6065.8972.51
CoCoOp [51]79.7476.8678.27
MaPLe [16]80.8278.7079.75
ProGrad [53]81.2674.1777.55
KgCoOp [43]80.2976.5378.36
CLIP-LoRA [47]81.1174.5377.68
MMA [42]82.2778.5780.38
2SFS82.5978.9180.70
+ +UCF101 + +
MethodBaseNovelHM
CLIP [33]70.5377.5073.85
CoOp [52]84.6956.0567.46
CoCoOp [51]82.3373.4577.64
MaPLe [16]83.0078.6680.77
ProGrad [53]84.3374.9479.35
KgCoOp [43]82.8976.6779.65
CLIP-LoRA [47]87.5272.7479.45
MMA [42]86.2380.0382.20
2SFS87.8578.1982.74
+ +coincide (i.e., $\mathcal{B} = \mathcal{C}$ ) and (ii) base-to-novel generalization, where each task further spans a set $\mathcal{N}$ of unseen categories. + +Datasets. For both settings, we consider a suite of 11 benchmarks. Specifically, these include ImageNet [34], Caltech101 (CAL) [9], SUN397 [40], Describable Textures (DTD) [3], FGVC Aircraft (AIR) [29], Oxford Pets (PETS) [32], Oxford Flowers 102 (FLWR) [31], Stanford Cars (CARS) [20], Food-101 (FOOD) [1], EuroSAT (ESAT) [11] and UCF-101 (UCF) [37]. We use the splits of [51]. + +Baselines. In base-to-novel generalization, we consider a total of 8 comparative methods: CoOp [52] and CoCoOp [51] as established baselines of the field; ProGrad [53], KgCoOp [43] and MaPLe [16] as modern advancements; Multi-Modal Adapter (MMA) [42] and CLIP-LoRA [47] as the strongest and most recent strategies. Zero-shot performance using hand-crafted templates is also reported as a reference. In the all-to-all setup, we expand the suite to a total of 12 methods, with 5 additional strategies that are in + +Table 2. All-to-all experiments, where train/test categories coincide, with the ViT-B/16 (top), ViT-B/32 (middle), and ViT-L/14 (bottom) backbones. All methods use $k = 16$ shots per class. In each group, the best performer is marked by bold text; the second best is underlined. + +
BACKBONEMETHODIMAGENETSUNAIRESATCARSFOODPETSFLWRCALDTDUCFMEAN
ViT-B/16Zero-Shot66.762.624.747.565.386.189.171.492.943.666.765.1
CoOp [52] (ctx=16)71.974.943.285.082.984.292.096.895.869.783.180.0
CoCoOp [51]71.172.633.373.672.387.493.489.195.163.777.275.4
TIP-Adapter-F [50]73.476.044.685.982.386.892.696.295.770.883.980.7
CLIP-Adapter [10]69.874.234.271.474.087.192.392.994.959.480.275.5
PLOT++ [2]72.676.046.792.084.687.193.697.696.071.485.382.1
KgCoOp [43]70.473.336.576.274.887.293.293.495.268.781.777.3
TaskRes [45]73.076.144.982.783.586.992.497.595.871.584.080.8
MaPLe [16]71.974.536.887.574.387.493.294.295.468.481.478.6
ProGrad [53]72.175.143.083.682.985.892.896.695.968.882.779.9
LP++ [13]73.076.042.185.580.887.292.696.395.871.983.980.5
CLIP-LoRA [47]73.676.154.792.186.384.292.498.096.472.086.783.0
MMA [42]73.276.644.785.080.287.093.996.895.872.785.081.0
2SFS73.777.050.092.485.486.193.797.796.473.286.682.9
ViT-B/32Zero-Shot61.962.019.345.160.480.587.567.091.142.662.261.8
CoOp [52] (ctx=16)66.872.232.983.376.078.688.795.494.965.378.675.7
CoCoOp [51]66.069.822.670.464.681.991.082.594.359.775.370.7
TIP-Adapter-F [50]68.474.134.883.477.081.790.494.395.168.080.577.1
CLIP-Adapter [10]64.971.826.764.768.981.990.188.794.858.176.571.6
PLOT++ [2]67.473.436.391.177.479.789.196.394.967.081.577.6
KgCoOp [43]65.471.023.770.167.381.790.886.194.465.177.572.1
TaskRes [45]68.273.637.077.778.081.489.495.595.768.380.676.9
MaPLe [16]66.772.028.083.366.982.191.789.095.163.477.374.1
ProGrad [53]66.973.233.381.076.180.189.395.195.065.879.675.9
LP++ [13]68.174.034.382.875.281.890.593.995.067.880.176.7
CLIP-LoRA [47]68.474.044.991.879.778.288.896.295.268.282.878.9
MMA [42]68.074.034.080.173.581.491.594.395.668.981.776.7
2SFS68.474.840.292.180.280.890.396.395.870.482.379.2
ViT-L/14Zero-Shot72.967.632.658.076.891.093.679.494.953.674.272.2
CoOp [52] (ctx=16)78.277.555.288.389.089.894.699.197.274.487.384.6
CoCoOp [51]77.876.745.279.882.791.995.495.397.471.485.281.7
TIP-Adapter-F [50]79.379.655.886.188.191.694.698.397.574.087.484.8
CLIP-Adapter [10]76.478.046.475.883.891.694.397.397.371.386.181.7
PLOT++ [2]78.679.144.192.287.290.293.698.897.575.087.183.9
KgCoOp [43]76.876.747.583.683.291.795.396.497.473.686.482.6
TaskRes [45]78.176.955.084.387.691.594.797.897.374.486.684.0
MaPLe [16]78.478.846.385.483.692.095.497.497.272.786.583.1
ProGrad [53]78.478.355.689.388.890.894.998.797.573.787.784.9
LP++ [13]79.379.754.689.387.791.794.998.597.476.188.185.2
CLIP-LoRA [47]79.679.466.293.190.989.994.399.097.376.589.986.9
MMA [42]79.980.256.476.388.092.095.598.497.675.888.084.4
2SFS79.480.364.192.990.391.195.599.197.578.089.587.1
+ +applicable to unseen categories: TIP-Adapter-F [50], CLIP-Adapter [10], PLOT++ [2], TaskRes [45] and LP++ [13]. + +Implementation Details. Following CLIP-LoRA [47], we express the number of iterations as $m = M \times k$ , where $k$ is the number of shots and $M \in \mathbb{N}$ is a hyperparameter. We also inherit the optimizer setup, using AdamW [27] with a learning rate of $2 \times 10^{-4}$ , a weight decay factor of 0.01 and a mini-batch size of 32. We do not use dataset-specific templates, but we format all categories via the generic template "a photo of a {}". For all settings and competitors, we report numbers from the original works or from [47]. + +When unavailable, we reproduce the results using the official code. Results are averaged over 3 different runs. + +Shots configurations. Due to space constraints, here we only report results with $k = 16$ available shots. Complementary experiments with $k \in \{4,8\}$ are in Appendix C. + +Fixed hyperparameters. For a realistic evaluation, we fix $M$ and $\alpha$ by tuning on ImageNet [34] with the ViT-B/16 backbone and $k = 16$ shots only. Search intervals are defined as $M \in \{100, 300, 500\}$ and $\alpha \in [0.2, 0.8]$ (using a coarse step size of 0.1). We obtain values of $M = 300$ and $\alpha = 0.6$ , which are always fixed unless stated otherwise. + +# 5.1. Base-to-novel generalization + +For this setting, we follow recent works [16, 42] and experiment with the ViT-B/16 backbone and $k = 16$ shots. The evaluation metrics are threefold: (i) top-1 accuracy on base categories, (ii) top-1 accuracy on novel categories, and (iii) the harmonic mean between them. + +Results for all datasets are reported in Tab. 1, where (i), (ii), and (iii) are denoted as Base, Novel and HM, respectively. 2SFS provides a greater harmonic mean than all competitors in 8 out of 11 benchmarks, and outperforms all competitors on average across datasets. Notable success cases are Stanford Cars [20] and FGVC Aircraft [29], with margins in the harmonic mean of $+2.76\%$ and $+2.30\%$ , while the worst case is EuroSAT. We attribute this to the tiny size of the dataset, as there are only 5 base categories, which leads 2SFS to exit the first stage when $\omega_{\mathrm{LN}}^*$ are disrupted already. We verify this hypothesis by simply decreasing the batch size, hence collecting gradients for fewer examples in the first stage, observing notable performance improvements (i.e., HM of $84.32\%$ with a batch size of 1). + +# 5.2. All-to-all Few-Shot Adaptation + +We further validate 2SFS in the all-to-all setup, where train/test categories coincide, i.e., $\mathcal{B} = \mathcal{C}$ . Intuitively, strong performance in this setting should support the hypothesis that the first stage learns good task-level features since a linear classifier is trained to separate them. Here, note that we have $\phi_c^*$ for all categories, hence selective inference always skips the computations within the text encoder. + +Setup details. We follow recent work [47], and evaluate 2SFS across a variety of 3 different backbones: ViT-B/16, ViT-B/32 and ViT-L/14. We keep hyperparameters fixed. + +Results are given in Tab. 2, confirming the hypothesis that a simple linear classifier, trained on top of frozen task-level features obtained with $\omega_{\mathrm{LN}}^*$ , is sufficient to match or surpass state-of-the-art methods. The best competitor in this setting is definitely CLIP-LoRA [47], which, nevertheless, is outperformed by 2SFS on average across backbones. We emphasize that 2SFS exhibits stable performance across settings, a missing trait in both CLIP-LoRA and MMA [42]. 2SFS outperforms the former by $+2.9\%$ in base-to-novel settings, and surpasses the latter by $+1.9\%$ , $+2.5\%$ and $+2.7\%$ in the all-to-all setup for the three backbones. + +# 5.3. Analysis + +We conclude the experimental section by (i) reporting the sweep conducted on $\alpha$ and (ii) highlighting the benefits of switching parameters in the second stage. + +Selection of $\alpha$ . Fig. 4 reports the outcome of the hyperparameter sweep on the fraction of iterations $\alpha$ . We conduct this search for the base-to-novel setting using the validation set of ImageNet [34] and report the Harmonic Mean corresponding to each $\alpha$ value in $[0.2, 0.8]$ , with a step size of + +![](images/6a5bede1e97512a58e998baf96c92a60cf5f48c71731c0175ad00ece9940ae0d.jpg) + +![](images/298aa6b8efbfed74f2617272fcc65ac364022f7882570b1ae53af34e4d47d037.jpg) +Figure 4. Hyperparameter sweep on $\alpha \in [0.2, 0.8]$ with a step size of 0.1, conducted on ImageNet [34]. The optimal value $\alpha = 0.6$ is transferred to every other experiment of this work. +Figure 5. Visualization of the absolute accuracy improvement across the 11 benchmarks in the all-to-all setting, relative to exiting after the first stage, i.e., relative to using $\omega_{\mathrm{LN}}^*$ only. + +0.1. We use the CLIP ViT-B/16 model and $k = 16$ shots. In line with the evidence of Sec. 3.2, an optimal value $\alpha = 0.6$ emerges, preceded and followed by decreased performance. The benefit of having two stages. Fig. 5 compares 2SFS relative to only optimizing LayerNorm instances, showing that large margins are obtained on average (e.g., more than $+10\%$ improvement on Stanford Cars and FGVC Aircraft, and $+4\%$ margin for SUN397, UCF-101, DTD, and Oxford Flowers further). We spot failure cases in Food-101 and Oxford Pets, which we examine in detail in Appendix E. + +# 6. Conclusions + +In this work, we investigated the dynamics of PEFT techniques in the FSA of VLMs. We empirically showed that PEFT learns good task-level features, even without ad-hoc mechanisms promoting cross-modal generalization, and that PEFT techniques exhibit different degrees of robustness to unseen categories. Through experiments on 11 benchmarks with fixed hyperparameters, we showed that training a linear classifier on top of frozen PEFT features, a scheme we call 2SFS, matches or outperforms the established state-of-the-art in different settings, thereby serving as a simple unified recipe. We hope our work will be useful for future research on VLM transfer. + +Acknowledgements. The authors acknowledge the CINECA award under the ISCRA initiative for the availability of high-performance computing resources and support. M.F. is supported by the PRIN B-FAIR (Prot. 2022EX F3HX) project and the PAT project "AI@TN". This work was supported by the projects EU Horizon ELIAS (No. 101120237), AI4TRUST (No.101070190), FAIR - Future AI Research (PE00000013), funded by NextGeneration EU, and carried out in the Vision and Learning joint laboratory of Fondazione Bruno Kessler and the University of Trento, Italy. + +# References + +[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In ECCV, 2014. 6, 11, 16, 17, 20 +[2] Guangyi Chen, Weiran Yao, Xiangchen Song, Xinyue Li, Yongming Rao, and Kun Zhang. PLOT: Prompt Learning with Optimal Transport for Vision-Language Models. In ICLR, 2023. 2, 7, 11, 13, 16, 17, 18 +[3] Mircea Cimpoi, Subhransu Maji, Iasonas Kokkinos, Sammy Mohamed, and Andrea Vedaldi. Describing textures in the wild. In CVPR, 2014. 4, 6, 16 +[4] Victor G Turrisi da Costa, Nicola Dall'Asen, Yiming Wang, Nicu Sebe, and Elisa Ricci. 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Although sparse-point methods lower computational load and maintain high accuracy in complex lane geometries, current methods fail to fully leverage the geometric structure of lanes in both lane geometry representations and model design. In lane geometry representations, we present a theoretical analysis alongside experimental validation to verify that current sparse lane representation methods contain inherent flaws, resulting in potential errors of up to $20\mathrm{m}$ , which raise significant safety concerns for driving. To address this issue, we propose a novel patching strategy to completely represent the full lane structure. To enable existing models to match this strategy, we introduce the EndPoint head (EP-head), which adds a patching distance to endpoints. The EP-head enables the model to predict more complete lane representations even with fewer preset points, effectively addressing existing limitations and paving the way for models that are faster and require fewer parameters in the future. In model design, to enhance the model's perception of lane structures, we propose the PointLane attention (PL-attention), which incorporates prior geometric knowledge into the attention mechanism. Extensive experiments demonstrate the effectiveness of the proposed methods on various state-of-the-art models. For instance, in terms of the overall F1-score, our methods improve Persformer by 4.4 points, Anchor3DLane by 3.2 points, and LATR by 2.8 points. The code will be available soon. + +# 1. Introduction + +In recent years, advances in autonomous driving have significantly improved vehicle perception and control. However, + +accurately detecting 3D lanes remains a challenging task due to complex road geometries, occlusions, and the lack of sufficient 3D annotations [30]. This task is crucial for applications like trajectory planning [49] and high-definition map construction [6, 20, 26, 34]. However, detecting the geometric structure and spatial location of 3D lanes solely from monocular images is highly challenging due to the lack of depth information. + +To advance this task, various methods have been proposed, including pixel-wise [52], grid-based [8, 48], curve-based [1, 2, 33], anchor-based [4, 16], and query-based approaches [29]. Among these, anchor-based and query-based methods model lanes as sparse points, categorizing them as sparse-point methods. Sparse-point methods not only significantly lower computational load but also maintain high accuracy in complex lane geometries. However, existing sparse-point methods do not fully consider the geometric structure of lanes. In lane geometry representations, we find that existing training ground truth generation methods fail to represent the complete extent of the original ground truth. Specifically, during the generation of training ground truth, the original ground truth is truncated at the endpoints, as shown in Fig. 1 (b). The truncated distance cannot be predicted by the model, which makes the model's results inherently inaccurate. In model design, these methods do not fully leverage prior geometric knowledge of lane structures. For example, Anchor3DLane [16] imposes parallel constraints on lanes, but these constraints are insufficient for handling real-world complex scenarios. Although LATR [29] introduces 3D ground positional embedding priors and enhances cross-attention, it lacks more detailed modeling of lane structures and modifications to self-attention. + +To this end, we propose two modules to enhance existing methods. In lane geometry representations, we first introduce a novel endpoint patching strategy. This strategy increases the F1-score of training ground truth on the + +(a) ours: patched training GT +![](images/6700085af52b16b851246bd30e96ffa8b93720c422468fd7134bcf5d57a81421.jpg) +location of preset point original GT + +![](images/d8a2e729bc81c8f8c25728bfa71e6f4d6c567a2a97662cb1d7d4517f05d56c03.jpg) +(b) short mode: truncated training GT +Figure 1. (a) Our method patches both endpoints and uses the EP-head to predict the patching distance, bringing the training ground truth closer to the original ground truth. (b) The short mode truncates both ends of the original ground truth, while (c) the long mode extends them. However, both methods produce inaccurate training ground truth and fail to fully capture the original ground truth. + +![](images/d8c76b10d46d0a99ce4f26f4e655ce216715e591836972eab6a9b49fc050b300.jpg) +(c) long mode: expanded training GT + +OpenLane dataset from $78.9\%$ to $98.5\%$ . To align existing models with this patching strategy, we propose the EP-head, which predicts the distances from each preset point to the endpoints of the original ground truth. After minimal processing, the EP-head yields more complete lane predictions. Its straightforward design allows for seamless integration into existing models, enhancing performance without substantial modifications. Additionally, the EP-head enables models to achieve more complete lane predictions even with fewer preset points, paving the way for future models that are faster and more parameter-efficient. + +Additionally, in model design, we propose PL-attention to better utilize the prior geometric knowledge of lanes. Lane detection tasks inherently possess prior geometric knowledge, which we summarize into three key aspects: a) On a single lane, adjacent points exhibit close relationships. Attributes (e.g., visibility) of neighboring points are highly likely to be similar, and the lane generally maintains overall smoothness. b) In a single image, relationships between lanes are closely linked. For instance, yellow-solid lines typically appear in the middle of the lane, while white-solid lines are usually located on the sides. c) Lanes at the same y-position share close relationships. Lanes on one road often have similar lengths and curvatures. PL-attention guides the model to learn features from three perspectives: within points on each lane, between different lanes, and among points at the same y-coordinate. + +The designed methods can be easily instantiated on existing methods for better performance. Moreover, extensive ablation studies have been conducted to elaborate on its superiority in effectiveness of each component, achieving consistent performance improvements with little computational overhead. For example, our approach improves the overall F1-score by 4.4 points for Persformer, 3.2 points for + +Anchor3DLane, and 2.8 points for LATR, thereby setting a new state-of-the-art performance. + +Our primary contributions can be summarized as follows: + +1) We reveal, through theoretical analysis and experimental results, the flaws in current sparse lane representation methods, which have not been explored in previous research. Then, we propose a patching strategy using EP-head to patch endpoints, enabling the model to predict more complete lanes even with fewer preset points. +2) We propose PL-attention which incorporates prior geometric knowledge related to points on each lane, interactions between different lanes, and connections among points at the same y-coordinate. This allows the model to utilize attention mechanisms to better perceive and adapt to diverse environments. +3) Thorough experiments demonstrate the effectiveness of our methods. Our methods achieve an F1-score improvement of 4.4 points for Persformer, 3.2 points for Anchor3DLane, and 2.8 points for LATR, setting a new state-of-the-art performance. + +# 2. Related Work + +# 2.1. Different Lane Geometry Representations + +How to model the lane geometry, specifically how to construct the training ground truth, is a crucial step in deep learning-based lane detection, which can be categorized into the following types: (1) Pixel-wise methods [15, 31, 35, 54], in 3D such as SALAD [52], frame lane detection as a segmentation task by combining lane segmentation with depth prediction. These approaches, however, demand high computational resources due to the extensive number of parameters required. (2) Grid-based methods partition the space into cells, representing lanes with localized segments Hu + +val et al. [17] or key points [18, 37, 47]. For instance, 3D-LaneNet+[8] utilizes local line segments, while BEV-LaneDet[48] defines key points on a BEV (Birds Eye View) grid plane. Both methods rely heavily on grid resolution and involve costly post-processing to reconstruct continuous lanes. Together, pixel-wise and grid-based representations can be considered dense training ground truth representations since they require numerous parameters to describe the training ground truth. In contrast, the following methods represent sparse training ground truth representations: (3) Curve-based methods use predefined functions to model smooth lane curves, decoupling the position and shape of the lane [1, 9, 24, 25, 32, 33, 43, 45]. The lanes position is determined by its start and end points (typically along the y-axis), while x-y and z-y functions capture its shape. However, relying solely on endpoints for positioning introduces a risk of misalignment: if the endpoint prediction is inaccurate, even a correctly predicted shape may lead to significant lane position errors. Notably, even though these approaches predict the lane endpoints, they still employ preprocessing steps in their code, as shown in Fig. 1 (b), which truncates the original training ground truth. This highlights a gap in previous research, which has not prioritized maintaining the completeness of the training ground truth relative to the original training ground truth. (4) Sparse-point methods sample preset points within the detection range, a common approach in both anchor-based [10, 11, 16, 23, 36, 55] and query-based models [12, 29]. Nearly all existing models employ preprocessing (as shown in the top part of Fig. 1) to generate their training ground truth. As a result, they cannot capture the full extent of the original lane, and fewer preset points generally lead to increased error. Our approach (patching strategy with EP-head) address this gap, allowing current models to predict a complete lane even with fewer preset points. + +# 2.2. Geometry Priors + +Several methods have been proposed to incorporate prior knowledge into learning-based techniques, such as embedding invariance into the model architecture or utilizing task-specific transformations. In the lane detection task, for instance, LaneATT [42] aggregates global features to infer location, while LATR [29] predicts a 3D plane for positional embedding. SGNet [28] enforces constant lane width by penalizing lateral distance deviations in the IPM-transformed top-view, and LaneCPP [33] learns parallelism and other geometric priors through analytical formulations of tangents and normals. Anchor3DLane [16] applies an equal-width constraint to adjust the x-coordinates of lane predictions. Simply considering lane parallelism and overall relationships cannot fully address the challenges posed by complex lane scenarios. We propose PL-attention, which optimizes the model structure by leveraging three types of relationships + +between lane points and lines, allowing the model to more effectively learn lane structures across a range of conditions. + +# 3. Preliminary Analysis + +In this section, we first describe the issues we identify, then introduce the current mainstream evaluation methods. Next, we analyze in which scenarios the flaws in the lane representation method we identify are reflected in the performance metrics. Finally, we provide two commonly used datasets to validate our findings. + +# 3.1. Problem Description + +Lane datasets provide dense original ground truth, consisting of varying numbers of points (e.g., possibly fewer than 100 or more than 200). Such data cannot be directly used to train a model; instead, trainable ground truth (training GT) must be generated. To keep the model complexity low, we aim to reduce the number of points as much as possible. Generally, a rule is set to sample 10 or 20 preset points within the detection range. If a lane exists at a preset point, that point is marked as valid (visibility=1), and the x/z values at that point are retained. However, during the generation of training ground truth, the original ground truth is truncated twice at the endpoints, as shown in Fig. 1 (b). The truncated distance can never be predicted by the model, making the model's results inherently inaccurate. The fewer the preset points representing the training ground truth, the greater the distance loss. If there are 20 preset points, up to $10\mathrm{m}$ may be lost. If there are 10 preset points, up to $20\mathrm{m}$ may be lost. Notably, this issue has not been explored before. + +# 3.2. Evaluation Method + +During evaluation, we need to ensure that the ground truth and the predicted lanes have the same number of points. The more points we have, the more accurate our evaluation will be, with 100 preset points typically used. The original ground truth is first sampled at 100 preset points (3, 4, 5, 6, ..., 102, $103\mathrm{m}$ ) to obtain the evaluating ground truth. Then, the predicted lane (training prediction) is sampled at the same 100 preset points to obtain the evaluating prediction. Finally, utilize bipartite matching to evaluate the evaluating ground truth and the evaluating prediction. If the evaluating ground truth's preset point (e.g. the preset point at $5\mathrm{m}$ ) and the evaluating prediction's corresponding point (at $5\mathrm{m}$ ) are within $1.5\mathrm{m}$ , that point is considered matched. If $75\%$ of the preset points of a lane are matched, the matched lane is considered true positive. We refer to this $75\%$ threshold as Lane-IoU. Recall is determined by the percentage of matched ground-truth lanes, while precision is calculated based on the percentage of matched predicted lanes. By averaging both the recall and precision metrics, the F1-score is computed. [4] + +![](images/2906ada8a598ba29b6429a98f2de33f5bef7092170d13b26b3793c3bc1dcc3a5.jpg) +Figure 2. Lane length distribution comparisons between ApolloSim and OpenLane. + +# 3.3. Theoretical Analysis + +Assume the training ground truth has 20 preset points, with an approximate distance of $5\mathrm{m}$ between each preset point. If one endpoint is truncated, the loss will be between 0 and $5\mathrm{m}$ ; if both endpoints are truncated, the loss will be between 0 and $10\mathrm{m}$ . For simplicity of analysis, we assume the loss to be $10\mathrm{m}$ . If the lane length is less than $40\mathrm{m}$ , its training ground truth will be less than $30\mathrm{m}$ , and its training prediction will most likely be less than $30\mathrm{m}$ . When the Lane-IoU is $75\%$ , its evaluating prediction will be matched, but the evaluating ground truth will not, which means recall declines. We obtain the result from Eq. (1), + +$$ +\frac {x - 1 0}{x} < 0. 7 5, x < 4 0, \tag {1} +$$ + +where $\mathbf{x}$ denotes the length of lane. + +We refer to this method of truncating both endpoints as the short mode. In contrast, extending each endpoint to the next one is called the long mode. Fig. 1 (b) and (c) present the difference between the two modes. The effect of the long mode is the opposite of the short mode—it causes the lanes training ground truth to become longer, the training prediction to be longer, the evaluating ground truth to be matched, but the evaluating prediction not, which results in a decline in precision. + +# 3.4. Experimental Validation + +To validate our theoretical analysis, we evaluate the training ground truth on different datasets (ApolloSim1[11] and OpenLane[4]). As shown in Fig. 2, OpenLane contains a higher proportion of shorter lanes compared to ApolloSim. In OpenLane, lanes shorter than $20\mathrm{m}$ account for approximately $40\%$ , and those shorter than $40\mathrm{m}$ make up around $70\%$ . In contrast, in ApolloSim, lanes shorter than $40\mathrm{m}$ account for only $20\%$ . This significant difference will highlight the flaws in the current lane representation methods. + +According to the evaluation setup in Sec. 3.2, we evaluate the training ground truth generated by both the short mode + +Table 1. Results of training ground truth evaluated with different preset points (M). + +
MmodeOpenLane [4]ApolloSim [11]
Rec ↑Pre ↑F1 ↑Rec ↑Pre ↑F1 ↑
5long82.325.138.595.682.888.7
5short10.796.319.345.896.462.1
10long94.248.764.298.391.094.5
10short35.498.852.184.497.390.4
20long98.171.682.898.496.697.5
20short65.499.578.994.297.795.9
40long99.386.692.5---
40short82.299.790.1---
100long99.895.797.7---
100short94.799.897.2---
+ +and long mode methods. From Tab. 1, three phenomena can be observed: (1) fewer preset points result in a lower F1-score; (2) the long mode shows lower precision, while the short mode shows lower recall; and (3) comparing OpenLane to ApolloSim, the higher the proportion of short lanes, the lower the F1-score. These phenomena all demonstrate that the training ground truth is inaccurate, and the current lane representation methods have significant flaws. + +# 4. Methods + +In this section, we first describe our 3D lane representation method, which uses a patching strategy. And we then introduce EP-head, enabling the model to implement the patching strategy and address the issues outlined in Sec. 3. At last, we present the detailed process of incorporating prior geometric knowledge with PL-attention. + +# 4.1. Lane Representation + +Given an input image $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ , the goal of Monocular 3D Lane Detection is to predict the position and category of lanes. A 3D lane is described by $M$ preset 3D points uniformly sampled along the y-coordinate, implying that there are $m - 1$ equal intervals between the two endpoints. For each preset point in a single lane, there exists an attribute denoting its visibility status. Also, an attribute is assigned to describe the category of lanes. Mathematically, each 3D lane is defined as + +$$ +\boldsymbol {l} _ {\boldsymbol {i}} = \left\{\boldsymbol {p} _ {\boldsymbol {i}}, c _ {\boldsymbol {i}} \right\}, \tag {2} +$$ + +and + +$$ +\boldsymbol {p} _ {i} = \left\{\left(x _ {i} ^ {j}, y _ {i} ^ {j}, z _ {i} ^ {j}, \operatorname {v i s} _ {i} ^ {j},\right) \right\} _ {j = 1} ^ {M}, \tag {3} +$$ + +where the first three elements represent the spatial coordinates of the point $p_i^j$ in 3D space, $\mathrm{vis}_i^j$ represents the visibil + +ity of point $p_i^j$ , and $c_{i}$ represents the category of lane $l_{i}$ . If $\mathrm{vis}_i^j = 1$ , the preset point is considered valid. + +With the patching strategy, each preset point during training requires a patching distance to both the start point and end point of the original ground truth. + +$$ +\pmb {p} _ {i} = \{(x _ {i} ^ {j}, y _ {i} ^ {j}, z _ {i} ^ {j}, \mathrm {v i s} _ {i} ^ {j}, \pmb {s} _ {i} ^ {j}, \pmb {e} _ {i} ^ {j}) \} _ {j = 1} ^ {M}, \qquad (4) +$$ + +$$ +\boldsymbol {s} _ {i} ^ {j} = \left(s _ {x i} ^ {j}, s _ {y i} ^ {j}, s _ {z i} ^ {j}\right), \tag {5} +$$ + +$$ +\boldsymbol {e} _ {i} ^ {j} = (e _ {x i} ^ {j}, e _ {y i} ^ {j}, e _ {z i} ^ {j}). \qquad (6) +$$ + +During inference, we only need to add the patching distance to the first and last valid preset points. + +# 4.2. EP-head + +To mitigate the issue in Sec. 3, we patch endpoints of training ground truth. Patching distances of each preset point have to be predicted because each preset point is possibly to become endpoint including start point and end point. We propose EndPoint head (EP-head) to predict them. EP-head works in the same position as regression head and visibility head, which predict $\{\pmb{x}_i,\pmb{z}_i\}$ and $\pmb{vis}_i$ of $i$ -th lane respectively. We assume that point-aware features of $i$ -th lane are denoted as $\mathbf{P}_i\in \mathbb{R}^{M\times C_p}$ , where $M$ is the number of preset points on each training ground truth and $C_p$ is the channel number of point-aware features. Like other heads, EP-head can be implemented using MLP. EP-head inputs $\mathbf{P}_i$ and outputs the distances of each preset point from two endpoints, which can be succinctly described using Eq. (7). + +$$ +\hat {\mathbf {s}} _ {i}, \hat {\mathbf {e}} _ {i} = \operatorname {M L P} \left(\mathbf {P} _ {i}\right), \tag {7} +$$ + +where $\hat{\mathbf{s}}_i$ and $\hat{\mathbf{e}}_i$ denote predicted distances from each preset point to start point and end point of original ground truth. + +Loss. Its training loss is described in Eq. (8). $\mathbf{s_i}$ and $\mathbf{e_i}$ are easily obtained when we process the data. Note we just describe the loss of $i$ -th lane. + +$$ +\operatorname {L o s s} _ {e p} = \frac {1}{M} \sum \left(\left| \left| \hat {\mathbf {s}} _ {\mathbf {i}} - \mathbf {s} _ {\mathbf {i}} \right| \right| _ {1} + \left| \left| \hat {\mathbf {e}} _ {\mathbf {i}} - \mathbf {e} _ {\mathbf {i}} \right| \right| _ {1}\right), \tag {8} +$$ + +# Algorithm 1 Inference of EP-head + +Input: $\mathbf{P}_i$ represents point-aware features of i-th lane, $\mathbf{y}_i$ represents y-axis preset points of i-th training ground truth, $\mathbf{x}_i$ and $\mathbf{z}_i$ represents predicted x and z distances, $\hat{\mathbf{vis}}_i$ represents predicted visibility of i-th prediction. +Output: $\mathbf{y}_i^*$ +1: $\hat{\mathbf{s}}_i, \hat{\mathbf{e}}_i \gets \mathrm{MLP}(\mathbf{P}_i)$ +2: $\mathbf{idx}_i\gets$ find the indices of the first and last valid points from $\hat{\mathbf{vis}}_i$ +3: $\mathbf{x}_i^*,\mathbf{y}_i^*,\mathbf{z}_i^*\gets$ modify the $\mathbf{x}_i,\mathbf{y}_i,\mathbf{z}_i$ based on $\mathrm{id}\mathbf{x}_i,\hat{\mathbf{s}}_i$ and $\hat{\mathbf{e}}_i$ + +Inference. If the $j$ -th preset point of the $i$ -th lane is valid, namely $\mathrm{vis}_i^j = 1$ , and it is the first valid point, we add $(\hat{s}_{xi}^j, \hat{s}_{yi}^j, \hat{s}_{zi}^j)$ to $(x_i^j, y_i^j, z_i^j)$ . If the $k$ -th preset point of the $i$ -th lane is valid, namely $\mathrm{vis}_i^k = 1$ , and it is the last valid point, We add $(\hat{e}_{xi}^k, \hat{e}_{yi}^k, \hat{e}_{zi}^k)$ to $(x_i^k, y_i^k, z_i^k)$ . For clarity, we describe it using code in Alg. 1. For simplicity, we do not consider the case where only one valid preset point exists. We only consider two or more valid preset points. + +# 4.3. PL-Attention + +To help the model learn features more effectively, we introduce prior knowledge derived from our understanding of lane design. Lane detection differs from object detection [3, 14, 19, 38, 57] in that it aims to represent the shape of lanes with a small number of points, rather than enclosing objects with bounding boxes. Lane detection tasks inherently possess some prior knowledge, which we summarize into three key aspects: within points on each lane, between different lanes, and among points at the same y-coordinate. + +We propose PointLane attention (PL-attention) to introduce prior knowledge of lanes. PL-attention consists of three components, including point-point attention(PPA), lane-lane attention(LLA), and point-y attention(PYA). Specifically, we implement them using three simple multi-head self-attentions, but combining them in a way that conforms to the structure of lanes. Before PL-attention, we first reshape point-aware features $\mathbf{P}$ into $N\times M\times C$ , where $N$ is the number of lanes, $M$ is the number of preset points and $C$ is channel number. Features of points on the $i$ -th lane are denoted as $[\mathbf{p}_{i,1},\mathbf{p}_{i,2},\dots,\mathbf{p}_{i,M}]$ . After the end of each lane, we insert a [CLS] token (denoted as $\mathbf{p}^s$ ), which is widely used in NLP [5, 50, 53] and CV [7, 51] tasks. There, we use it to convey the contextual information within this lane. + +Point-point attention. Position embeddings are added to features $\mathbf{P}$ . features need to output X and Z positions, hence, position embeddings can not be preset. We use MLP to learn position embeddings described in Eq. (9). + +$$ +\mathbf {P} ^ {\prime} = \mathbf {P} + \operatorname {M L P} (\mathbf {P}), \tag {9} +$$ + +Point-point attention (PPA) takes $\mathbf{P}_i^{\prime}$ as input to fully model the interactions between points on $i$ -th lane (Eq. (10)). Output are denoted as $\mathbf{P}_i^* = [\mathbf{p}_{i,1}^*,\mathbf{p}_{i,2}^*,\dots,\mathbf{p}_{i,M}^*,\mathbf{p}_i^{s*}]$ . + +$$ +\mathbf {P} _ {i} ^ {*} = \operatorname {P P A} \left(\mathbf {P} _ {i} ^ {\prime}\right), \tag {10} +$$ + +Lane-lane attention. Next, we extract lane-aware features as $\mathbf{P}^{s*}$ , which entail the information of lanes, and we apply lane-lane attention (LLA) to them to capture the global information. The process is described in (Eq. (11)) and output is denoted as $\mathbf{H}^s = [\mathbf{h}_1^s,\mathbf{h}_2^s,\dots,\mathbf{h}_N^s]$ . + +$$ +\mathbf {H} ^ {s} = \operatorname {L L A} \left(\mathbf {P} ^ {s *}\right), \tag {11} +$$ + +![](images/5d50897c78c86c6e9a8b32ebdfa479eb8231e72b1b01914495256a3078b3f937.jpg) +Figure 3. Overview flow of PL-attention with Point-point attention (Point-Attn), lane-lane attention (Lane-Attn) and point-y attention (PointY-Attn). + +where $\mathbf{P}^{s*} \in \mathbb{R}^{N \times C}$ , $\mathbf{H}^s \in \mathbb{R}^{N \times C}$ . $\mathbf{P}^*$ without $\mathbf{P}^{s*}$ is denoted as $\mathbf{P}^\dagger$ . + +Point-y attention. To further provide prior knowledge to the model, we use Point-y attention (PYA) to flexibly constrain, rather than enforcing strict control as in [16]. We reshape $\mathbf{P}^{\dagger}$ into $M\times N\times C$ , so that points at the same y position are in the same group. Point-y attention takes $\mathbf{P}_i^\dagger$ as input and output $\mathbf{H}_i^\dagger$ . This process is summarized in Eq. (12). + +$$ +\mathbf {H} _ {i} ^ {\dagger} = \operatorname {P Y A} \left(\mathbf {P} _ {i} ^ {\dagger}\right), \tag {12} +$$ + +After PL-attention, lane-aware features $\mathbf{H}^s$ can be used to predict classification of lanes, instead of using max pooling in point-aware features as in [29]. + +Complexity. We implement PL-attention with three multi-head self-attention [46]. Its complexity is $O(NM^2 + N^2 + MN^2)$ . In theory, its complexity is lower than sending all points into multi-head self-attention, whose complexity is $O(N^2 M^2)$ . + +How to apply it to existing methods. Applying PL-attention to query-based methods is straightforward. For instance, simply replace the self-attention in LATR [29] with PL-attention. For other methods, we put the PL-attention between abstracting lane feature and predicting lane attribute. The details will be discussed in the supplementary material. + +# 5. Experiments + +In this section, we first conduct the same experiment as in Sec. 3.4 to verify that our patching strategy produces a complete and accurate training ground truth. Next, we introduce the dataset and metrics, followed by implementation details. We then demonstrate the effectiveness of our method through comparisons with leading approaches. Finally, we present an analysis of each component. + +Table 2. Results of patched training ground truth evaluated with different preset points(M). + +
MRec ↑Pre ↑F1 ↑X error (m) ↓Z error (m) ↓
nearfarnearfar
572.380.976.40.3520.2810.4640.352
1091.996.093.90.1430.1110.1490.122
2097.799.198.50.0530.0430.0510.051
+ +# 5.1. Effectiveness of Patching Strategy + +We evaluate the training ground truth after applying the patching strategy on OpenLane, and the results are shown in Tab. 2. There is no abnormal decrease in recall and precision. Even with fewer preset points, a high F1-score is maintained. However, the F1-score still drops significantly when there are only 5 preset points. This occurs because, with 5 preset points, most training ground truth has only one valid preset point, and for simplicity, we currently consider only cases with two or more valid preset points, though it is straightforward to extend to a single preset point. These results indicate that the patching strategy can generate complete and accurate training ground truth. + +# 5.2. Datasets and Metrics + +OpenLane [4] is a comprehensive benchmark for 3D lane detection, based on the Waymo Open dataset [41]. It comprises 1000 segments with 200K frames, capturing diverse conditions at $1280 \times 1920$ resolution. It includes complex lane structures, 5 weather types, and 14 categories. It is currently the most challenging lane detection dataset. Therefore, we select it to showcase our methods and perform ablation studies. + +In assessing 3D lane detection, we follow OpenLane [4] metrics, framing it as a matching problem based on predictions and ground truth. In addition to the F1-score presented in Sec. 3.2, local accuracy is evaluated using point-wise distance errors along the x-axis and z-axis, with lane points divided into near points and far points. + +# 5.3. Implementation Detail + +To verify the effectiveness of our proposed method, we conduct experiments on the LATR [29] framework unless otherwise specified. The LATR provides a simple architecture that can be used to reveal the properties of our method. In the default configuration of LATR, it adopts max-pooling along the point dimension followed by MLP for lane category. For the lane category, We directly employ MLP on lane-aware features produced by PL-attention. For all our experiments, we utilize the AdamW [27] optimizer with a weight decay of 0.01. We set the learning rate to $2 \times 10^{-4}$ and employ a cosine annealing scheduler. We utilize a total batch size of + +Table 3. Comparisons with other 3D lane detection methods on the OpenLane validation dataset. Note that the results are officially published. + +
MethodsBackboneF1 ↑Acc. ↑X error (m) ↓Z error (m) ↓
nearfarnearfar
3DLaneNet [10]VGG-16 [40]44.1-0.5930.4940.1400.195
GenLaneNet [11]ERFNet [39]32.3-0.5910.6840.4110.521
CurveFormer [1]EffNet-B7 [44]50.5-0.3400.7720.2070.651
BEV-LaneDet [48]ResNet-34 [13]58.4-0.3090.6590.2440.631
GroupLane [21]ResNet-50 [13]60.291.60.3710.4760.2200.357
PVALane [56]ResNet-50 [13]62.793.40.2320.2590.0920.118
Persformer [4]EffNet-B7 [44]50.592.30.4850.5530.3640.431
Persformer+oursEffNet-B7 [44]54.988.50.3110.3290.1860.229
Anchor3DLane [16]ResNet-18 [13]53.190.00.3000.3110.1030.139
Anchor3DLane+oursResNet-18 [13]56.391.20.2570.2630.0790.110
LATR [29]ResNet-50 [13]61.992.00.2190.2590.0750.104
LATR+oursResNet-50 [13]64.792.80.2050.2550.0740.105
+ +Table 4. Comparisons with leading methods on OpenLane benchmark in different scenarios. The evaluation metric is F1-score. + +
MethodsAllUp & DownCurveExtreme WeatherNightIntersectionMerge & Split
Persformer [4]50.542.455.648.646.640.050.7
Persformer+ours54.9 ↑ 4.448.1 ↑ 5.758.0 ↑ 3.655.6 ↑ 7.051.2 ↑ 4.644.4 ↑ 4.455.0 ↑ 4.3
Anchor3DLane [16]53.145.556.251.947.244.250.5
Anchor3DLane+ours56.3 ↑ 3.248.9 ↑ 3.459.2 ↑ 3.054.7 ↑ 2.850.7 ↑ 3.547.9 ↑ 3.754.4 ↑ 3.9
LATR [29]61.955.268.257.155.452.361.5
LATR+ours64.7 ↑ 2.855.3 ↑ 0.171.5 ↑ 3.358.5 ↑ 1.458.5 ↑ 3.155.5 ↑ 3.265.5 ↑ 4.0
+ +64, distributed across 8 NVIDIA GeForce RTX 3090 GPUs. Training spans 24 epochs on OpenLane [4]. + +# 5.4. Application on State-of-the-art Method + +To demonstrate the superiority of our proposed method, we apply EP-head and PL-attention on several state-of-the-art methods. All the methods are trained with their original configuration. The weight of $loss_{ep}$ is set to 1.0. For lane category, MLP is used on lane-aware features produced by PL-attention. The experiment results are presented in Tab. 3. Our method consistently outperforms the baseline across all metrics by a significant margin. For instance, when applying our method, LATR [29] achieves a $2.8\%$ absolute gain in F over the baseline and a $0.8\%$ increase in accuracy, setting a new state-of-the-art. Additionally, we evaluate the performance in different scenarios. As shown in Tab. 4, our method achieves a better performance. Especially, our methods show particularly significant improvements in challenging scenarios, including curves (e.g. LATR $+3.3\%$ ), night $(+3.1\%)$ , intersections $(+3.2\%)$ , and merge-split scenarios $(+4.0\%)$ . These improvements demonstrate that our methods substantially enhance the model's ability to identify lane structures in complex scenarios. + +# 5.5. Ablation Study + +# 5.5.1. Module Ablations + +To demonstrate the impact of EP-head and PL-attention on the model's detection performance, we conduct ablation experiments on both two components. In Tab. 5, both EP-head $(+1.2\%)$ and PL-attention $(+0.6\%)$ , even when used separately, can improve the model's performance. Particularly, when they are used together $(+2.8\%)$ , the results are even better, surpassing the individual improvements of both components. + +Furthermore, we conduct additional experiments with the preset point count set to 10. These experiments demonstrate the impact of preset point count on model performance and the effectiveness of components when preset points are sparse. Results are shown in Tab. 5, with the effect being more pronounced when the preset point count is low (40.6% vs. 54.8%). + +Table 6 presents the evaluation results for short lanes (0-40m). It is evident that the EP-head improves recall by 3.2 percentage points (55.4% vs. 58.6%), indicating that the EP-head enables the model to predict more complete short lanes. + +As the Lane-IoU threshold increases, the impact of an incomplete training ground truth progressively extends to lanes + +Table 5. Ablation study on EP-head and PLA. (10) indicates LATR with 10 preset points. The evaluation metric is F1-score. + +
EP-headLATRLATR(10)LATR+PLALATR(10)+PLA
X61.940.662.544.7
✓63.149.964.754.8
+ +Table 6. Evaluated results of short lanes(0-40m) on OpenLane. + +
Lane-IoU=0.75F1RecPre
LATR43.255.435.4
Latr+EP-head44.258.635.5
Latr+EP-head+PLA45.458.936.8
+ +Table 7. Evaluated results of lanes on OpenLane with different Lane-IoU. + +
F1Lane-IoU=0.75Lane-IoU=0.90
LATR61.943.6
Latr+EP-head63.147.1
Latr+EP-head+PLA64.748.1
+ +of varying lengths, with the effect on longer lanes becoming increasingly evident in the metric. At a Lane-IoU threshold of 0.75, the metric primarily reflects the incompleteness in short lane predictions, while at a threshold of 0.90, it further highlights the incompleteness in longer lane predictions. With the use of the EP-head, we observe an improvement of 3.5 F1 points at Lane-IoU=0.9 and an improvement of 1.2 F1 points at Lane-IoU=0.75, as shown in Tab. 7. This indicates that the EP-head has a positive effect on lanes of varying lengths. More experiments on EP-head and PLA are included in the appendix. + +# 5.5.2. Effectiveness of PL-attention + +Different prior information brings varying degrees of information to the model, demonstrated in Tab. 8. When only points within the same lane are allowed to interact (PPA), the performance is poor, with only $55.3\%$ F1-score. However, with only lane-lane attention (LLA) or point-y attention (PYA), the performance is higher than with only PPA, demonstrating the superiority of lane-level prior interaction. Performance improves with more priors involved in guidance. When all three priors are simultaneously introduced, the F1-score reaches its highest $(64.7\%)$ . + +# 5.6. Visual Comparison + +Apart from quantitative results, we present qualitative examples in Fig. 4. In various scenarios, our method consistently predicts lanes with more complete endpoints and closer alignment to the original lanes position and shape. (a) illustrates multi-lane turns, where LATR fails to capture the turn, while + +Table 8. Results of different components for PLA. + +
PPALLAPYAF1
✓✓✓64.7
✓✓63.9
✓✓63.5
✓✓61.9
✓55.3
✓57.2
✓61.5
+ +![](images/323bca71264415a1c496d08b055dcb3518519745d6f03d64753f5a9491209304.jpg) +Figure 4. Qualitative evaluation on OpenLane val set. It presents the original ground truth (green) and the model's training prediction (red) in 2D space. + +our method accurately predicts it. (b) depicts a multi-lane, long-distance straight scenario, demonstrating our method's superior performance even with multiple lanes. + +# 6. Conclusion + +In this work, we identify flaws in current sparse lane representation methods, provide theoretical analysis, and support our findings through carefully designed experiments. To mitigate these issues, we propose a new sparse lane representation incorporating patching strategy and introduce the EP-head, which effectively integrates with existing models. Additionally, we apply PL-attention to embed lane prior geometric knowledge into the attention mechanism. Our experimental results confirm that these methods enhance the model's adaptability to complex scenarios. 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While numerous VTR methods have achieved success, most of them assume accurate visual-text correspondences during training, which is difficult to ensure in practice due to ubiquitous noise, known as noisy correspondences (NC). In this paper, we rethink how to mitigate the NC from the perspective of representative reference features (termed agents), and propose a novel relation-aware purified consistency (RPC) network to amend direct pairwise correlation, including representative agents construction and relation-aware ranking distribution alignment. The proposed RPC enjoys several merits. First, to learn the agents well without any correspondence supervision, we customize the agents construction according to the three characteristics of reliability, representativeness, and resilience. Second, the ranking distribution-based alignment process leverages the structural information inherent in inter-pair relationships, making it more robust compared to individual comparisons. Extensive experiments on five datasets under different settings demonstrate the efficacy and robustness of our method. + +# 1. Introduction + +Video-text retrieval [5, 20, 24, 27] aims to identify videos that most accurately correspond to a textual query, and vice versa, where textual descriptions are retrieved based on video content. With the exponential growth of online videos and the increasing use of video platforms, video-text retrieval has become a critical task and benefits broad applications across various domains [2, 11, 42]. This task is fundamental to cross-modal understanding and presents significant challenges due to the substantial disparities in representation between video and text modalities. + +![](images/fabd6229456836d2457993bda321a0e897793d673506a887c3d969097d8d5c33.jpg) +Figure 1. The motivation of our proposed method. (a) The illustration of noisy correspondence. (b) A set of representative reference pairs (termed agents). (c) False matches tend to occur under conditions where noise correspondence leads to inaccurate supervision signals. (d) The proposed ranking distribution consistency suppresses false matches and provides a more reliable supervision. + +In prior literature, the dominant paradigm for video-text retrieval is to establish correspondences between the video and text modalities by global-level and local-level alignments. Specifically, global-level methods [8, 24, 25, 27] achieve semantic alignment by leveraging contrastive learning on holistic representations of videos and texts. For local-level methods [5, 15, 44, 45], cross-modal correspondences are established through more fine-grained alignments, such as frame-to-word [44] or action-entity-level alignments [5, 15]. Although these methods have shown promising results, they are based on the core assumption of accurate visual-language correspondences during training, making their performance heavily reliant on the availability of high-quality annotated data. + +However, collecting such high-quality annotated data is resource-intensive and time-consuming. In fact, due to factors such as non-expert annotators and web crawling noise, it is often difficult or unrealistic to maintain the assumption that every video-text pair in a dataset is accurately + +matched (see Fig. 1(a)). Therefore, the dataset collection process inevitably introduces some semantically irrelevant video-text pairs, which are erroneously treated as matched pairs, referred to as noisy correspondences (NC). Aligning these mismatched pairs during training can mislead the model and substantially degrade its matching performance. + +To mitigate the negative impact of noisy data pairs, a series of noise-rectify approaches [10, 13, 49, 52] have been developed. These works typically divide the original training data into clean and noisy subsets based on the memory effect of DNNs [3] and achieve robust matching through label correction. Despite achieving some success, these methods are highly sensitive to clean sample selection, which relies heavily on the model's similarity prediction. Confident yet erroneous predictions tend to be self-perpetuating, where noisy correspondences can be strengthened and memorized in subsequent training, resulting in a feedback loop of error accumulation, especially with high noise ratios. Furthermore, erroneous supervision from noisy data can impair the model's representation ability, increasing the likelihood of mismatches between video and text. This situation further deteriorates the establishment of connections between the video and text modalities. + +In this paper, we investigate the limitations of noise-rectify methods, and provide a novel viewpoint on representative reference features (termed agents) to establish more reliable supervision for robust video-text retrieval under noisy correspondences (NC). Intuitively, most methods ignore that video-text retrieval involves rich inter-pair correlation in addition to simple single-pair similarity. This highlights the potential of closer cooperation between the inter-pair correlation and single-pair similarity to reliably mitigate the effects of NC. The core point is that, for each video/text, we can acquire the agent-level correlation (i.e., a likelihood vector) via a group of representative reference agents (see Fig.1(b)) to capture the inter-pair relation. Essentially, the agent-level correlation captures the consistency across a wider scope. Therefore, it encapsulates a higher-order correlation regularization to rectify erroneously matched video-text pairs caused by NC. Building on the preceding analysis, it follows logically to enforce the regularization based on the agent-level correlation. However, this simple regularization considers each agent in isolation and is overly dependent on independent and identically distributed (i.i.d.) assumption, resulting in limited model optimization. Indeed, specific structural relations exist among the agents. For instance, as depicted in Fig. 1(b), agent $\alpha$ and agent $\gamma$ are both 'a man', while agent $\beta$ is 'a woman'. Accordingly, agent $\alpha$ should be more closely related to agent $\gamma$ than agent $\beta$ . To utilize the inter-agent structural relations, rather than treating each agent in isolation, we meticulously develop a relation-aware alignment based on ranking distribution. The main principle is + +to treat the agent ranking as a stochastic event instead of a fixed permutation. Given a video/text, the varying similarity among different agents can be viewed as ranking probabilities. The ranking permutation indicates the relation of the corresponding agents to video/text. By associating every ranking permutation of the agents, we build the relation-aware ranking distribution of video and text. As shown in Fig. 1(d), the consistency of the relation-aware ranking distribution between video and text provides more reliable guidance for the model optimization under NC. + +However, it is non-trivial to learn the agents well without any correspondence supervision. For agent mining, we meticulously design this customized for the following three characteristics. (1) Reliability. Since similarity calculation plays a crucial role in video-text retrieval particularly under NC, confident yet erroneous calculations can adversely affect all subsequent processes. Therefore, we design a semantic purification mechanism instead of a simple dot product. Based on this, we perform a bi-directional evaluation strategy to select agents with relatively high reliability. (2) Representativeness. Intuitively, the agents should represent a broad array of semantics from both video and text modality. Therefore, we adopt a cross-aggregation mechanism that allows the agents to recognize the semantics of current pair and extend to the semantics of various videotext pairs. (3) Resilience. Given the substantial gap between video and text, it is essential for agents to narrow this gap and increase their referability. Specifically, we attach a self-aggregation mechanism to refine agents by harmonizing the inherent resilience between video and text. + +In this work, our contributions can be concluded as follows: (1) We analyze the bottlenecks exist in noise-rectify methods for amending video-text pair consistency regularization. To the best of our knowledge, this is the first work to mitigate the NC in VTR methods, from the perspective of representative reference features. (2) We develop a coherent RPC network, including construction of reliable and representative agents and a ranking distribution-based alignment to capture structure information inherent in inter-agent relationships. They can cooperate well to enable more robust matching. (3) Extensive experimental results on five challenging benchmarks show that our method achieves notable performance improvements, with particularly pronounced gains under high noise ratios. + +# 2. Related Work + +In this section, we briefly overview several lines of research in video-text retrieval and noisy correspondence learning. + +# 2.1. Video-Text Retrieval + +Building on advances in deep neural networks [22, 28, 31, 33, 39, 41, 46, 47], many video-text retrieval methods have been proposed and achieved remarkable results. + +These methods broadly fall into two categories based on the alignment: global-matching [6, 8, 24, 25, 27] and local-matching methods [5, 15, 44, 45]. Global-matching methods aim to learn and align holistic video/text features within a joint embedding space. Local-matching methods establish fine-grained alignments, such as frame-word, action, and event levels, enabling more precise matching. Recently, visual-language pre-training (VLP) [14, 21, 37], particularly CLIP [37], has gained increasing attention. Benefiting from VLP, several works [9, 16, 19, 25, 27, 30, 53] have been proposed to exploit the powerful knowledge of CLIP for VTR. Despite achieving promising results, these methods typically rely on the implicit assumption that all training pairs are accurately matched. However, this assumption is often unrealistic, as real-world data is frequently affected by pervasive noise. In this paper, we tackle the unavoidable and intractable issue of noisy correspondences. + +# 2.2. Learning with Noisy Correspondence + +Noisy correspondence (NC) was first proposed in NCR [13] and is a novel paradigm in the field of noise learning. Unlike conventional noisy label which denotes incorrect category labels [23, 40], NC denotes alignment errors in paired data, i.e., semantically irrelevant videos and texts are incorrectly treated as matched. To mitigate this problem, various approaches have emerged, which are mainly classified into two categories: noise-rectify paradigm [10, 13, 29, 36, 49, 52] and robust loss functions [7, 12, 34, 35]. Noise-rectify methods typically partition the training set into clean and noisy subsets and alleviate the effects of noise through the label correction. Robust loss function methods concentrate on designing noise-tolerant loss functions to enhance the robustness of the model against NC during training. Although these methods have shown promising results in numerous tasks, the area of VTR still lacks sufficient exploration. In this paper, we offer a fresh perspective on representative reference features to construct more safe and effective supervision signals for robust video-text retrieval under NC. + +# 3. Method + +# 3.1. Problem Definition + +Given a dataset $D = \{(v_{i},t_{i})\}_{i = 1}^{N}$ , where $(v_{i},t_{i})$ is the $i$ -th video-text pair and $N$ is the dataset size, video-text retrieval seeks to learn a similarity function $s(\cdot)$ that assigns a high similarity score to semantically related video-text pair and a low similarity score to irrelevant pair. Formally, given a pair of text $t_i$ with $N_{t}$ words and a video $v_{i}$ with $N_{v}$ frames, we feed $t_i$ and $v_{i}$ into a text encoder and a video encoder, respectively, to obtain their corresponding embeddings $\mathbf{t}_i = [\mathbf{w}_i^0,\mathbf{w}_i^1,\dots ,\mathbf{w}_i^{N_t}]$ and $\mathbf{v}_i = [\mathbf{f}_i^1,\mathbf{f}_i^2,\dots ,\mathbf{f}_i^{N_v}]$ . Here, $\mathbf{w}_i^0$ denotes the [CLS] token and $\mathbf{f}_i^n$ denotes the $n$ -th frame feature. The similarity between video and text is calculated + +based on the features $\mathbf{t}_i$ and $\mathbf{v}_i$ , for instance, by computing the inner product of the [CLS] token $\mathbf{w}_i^0$ and the average frame features $\overline{\mathbf{v}}_i = Avg([f_i^1, f_i^2, \dots, f_i^{N_v}])$ : + +$$ +s (v _ {i}, t _ {i}) = \left\langle \mathbf {w} _ {i} ^ {0}, \overline {{\mathbf {v}}} _ {i} \right\rangle . \tag {1} +$$ + +Given a batch of $B$ video-text pairs $\{(v_i, t_i)\}_{i=1}^B$ , the InfoNCE loss [32] is employed to maximize the similarity between annotated video-text pairs $(v_i, t_i)$ and minimize the similarity for irrelevant pairs $(v_i, t_j, i \neq j)$ : + +$$ +\mathcal {L} _ {t 2 v} = - \frac {1}{B} \sum_ {i} ^ {B} \left(\log \frac {e ^ {s \left(t _ {i} , v _ {i}\right) / \tau}}{\sum_ {j} ^ {B} e ^ {s \left(t _ {i} , v _ {j}\right) / \tau}}\right), \tag {2} +$$ + +$$ +\mathcal {L} _ {v 2 t} = - \frac {1}{B} \sum_ {i} ^ {B} \left(\log \frac {e ^ {s \left(v _ {i} , t _ {i}\right) / \tau}}{\sum_ {j} ^ {B} e ^ {s \left(v _ {i} , t _ {j}\right) / \tau}}\right), \tag {3} +$$ + +$$ +\mathcal {L} _ {i n f o} = \frac {1}{2} \left(\mathcal {L} _ {t 2 v} + \mathcal {L} _ {v 2 t}\right), \tag {4} +$$ + +where $\tau$ is the temperature parameter. In reality, due to unavoidable annotation errors during the dataset collection process, some mismatched pairs are erroneously labeled as matched, resulting in noisy correspondences (NC) and consequently causing a decline in performance. Our objective is to alleviate the detrimental effects of NC for robust VTR. + +# 3.2. Overview of Framework + +As illustrated in Fig. 2, the proposed RPC mainly includes two procedures, i.e., 1) representative agents construction, and 2) relation-aware ranking distribution alignment. In procedure 1), we develop the semantic purification mechanism, cross-aggregation, and self-aggregation to ensure the reliability, representativeness, and resilience of the agents, respectively. In procedure 2), we conduct agent-ranking probability distributions for each video/text features on corresponding agents. The details are as follows. + +# 3.3. Agents Construction + +It is non-trivial to construct agents well-tailored for each video-text pair without any correspondence supervision. The agent construction process comprises three components, namely semantic purification, cross-aggregation, and self-aggregation, which equip the agents with reliability, representativeness, and resilience, respectively. + +Semantic Purification Mechanism. Similarity calculation is crucial for video-text alignment, with further increased demands for similarity reliability in the NC. However, few noisy correspondence learning methods have explored this area. In the mainstream noise-rectify paradigm, confident yet incorrect similarity calculations can lead to errors in subsequent noisy subset partitioning and label correction, which tend to be self-perpetuating. Thus, to improve the reliability of similarity calculation, we use + +![](images/445b7fa3c5f06cbd9f55f1ac1f8175bc918afde43f1daf531d110f18e9249d3d.jpg) + +![](images/d3eb817b1afe452c3cd58afc44fd4d968e55653c854b8a110322219c365fb403.jpg) +Figure 2. Framework of proposed Relation-aware Purified Consistency (RPC) Network. There are two main procedures: 1) representative agents construction and 2) relation-aware alignment based on ranking distribution, with noisy pairs in red border and clean pairs in green. + +![](images/ba986521661c8e0b944f2cb9d22aa517069d922e197772ae33fe9b4ecb707985.jpg) + +a purified maximum-correspondence interaction to consolidate the alignment. In specific, we begin by computing the token-wise similarity between frame embeddings $\mathbf{v}_p = [\mathbf{f}_p^1,\mathbf{f}_p^2,\dots ,\mathbf{f}_p^{N_v}]$ and word embeddings $\mathbf{t}_q = [\mathbf{w}_q^0,\mathbf{w}_q^1,\dots ,\mathbf{w}_q^{N_t}]$ to generate the frame-word similarity matrix $S\in \mathbb{R}^{N_v\times N_t}$ , where $(S)_{ij} = \frac{(\mathbf{f}^i)^{\top}\mathbf{w}^j}{\|\mathbf{f}^i\|_{\|}\|\mathbf{w}^j\|}$ denotes the similarity between $i$ -th frame and $j$ -th word. For simplicity, we omit the subscript indicating the $p$ -th video and $q$ -th text. + +Next, we select the most closely aligned word (frame) for each frame (word), i.e., the highest scores in each row and column of $S$ . We then calculate the weighted average of these highest scores to obtain the overall similarity score between the video $v_{p}$ and text $t_{q}$ , denoted as $s(v_{p},t_{q})$ : + +$$ +s \left(v _ {p}, t _ {q}\right) = \sum_ {i = 1} ^ {N _ {v}} \omega_ {v} ^ {i} \max _ {j} (\boldsymbol {S}) _ {i j} + \sum_ {j = 1} ^ {N _ {t}} \omega_ {t} ^ {j} \max _ {i} (\boldsymbol {S}) _ {i j}, \tag {5} +$$ + +$$ +\omega_ {v} ^ {i} = \frac {d \left(\mathbf {w} ^ {0} , \mathbf {f} ^ {i}\right)}{\sqrt {L}}, \quad \omega_ {t} ^ {j} = \frac {d \left(\overline {{\mathbf {v}}} , \mathbf {w} ^ {j}\right)}{\sqrt {L}}, \tag {6} +$$ + +where $\mathbf{w}^0$ denotes [CLS] of text, $\overline{\mathbf{v}}$ is obtained by average pooling over all frame features, $d(\cdot ,\cdot)$ denotes the dot product similarity in [43] and $\sqrt{L}$ is a scaling factor. Moreover, due to the presence of semantic inconsistency and noise, some frames may be semantically irrelevant to any of the words, and vice versa. Hence, it is unreasonable to include all the so-called 'most aligned' frame-word pairs in the similarity computation. To reduce the negative impact and purify similarity calculation, we measure the holistic relevance + +of the video and text as a threshold in a data-driven manner: + +$$ +\omega_ {\star} ^ {i} = \left\{ \begin{array}{l l} \omega_ {\star} ^ {i} & \omega_ {\star} ^ {i} > \delta \\ 0 & \omega_ {\star} ^ {i} \leq \delta \end{array} , \delta = \frac {d \left(\mathbf {w} ^ {0} , \overline {{\mathbf {v}}}\right)}{\alpha \sqrt {L}}, \star \in \{v, t \}. \right. \tag {7} +$$ + +Finally, we use the purified similarity from Eqs. 5-7 to determine the relative reliability of video-text pairs based on bidirectional cross-modal correspondences. + +$$ +y _ {i} = \frac {1}{2} \left(\frac {e ^ {s \left(t _ {i} , v _ {i}\right) / \tau}}{\sum_ {j} ^ {B} e ^ {s \left(t _ {i} , v _ {j}\right) / \tau}} + \frac {e ^ {s \left(v _ {i} , t _ {i}\right) / \tau}}{\sum_ {j} ^ {B} e ^ {s \left(v _ {i} , t _ {j}\right) / \tau}}\right), \tag {8} +$$ + +where $s(t_i, v_j)$ is the similarity between $i$ -th text and $j$ -th video in Eq. 5 and $\tau$ is the temperature parameter. For clean pairs, $t_i$ and $v_i$ should exhibit dominant similarity in both retrieval directions, yielding a metric value close to 1. In contrast, for noisy pairs, the similarity dominance in both directions cannot be simultaneously achieved, leading to a smaller metric value. Thus, $y_i$ can be used to indicate cleanliness of $i$ -th pair. The top- $K$ clean pairs are selected as reference agents, denoted as $A = \{(v_k^a, t_k^a)\}_{k=1}^K$ . The corresponding video and text features are represented as $F_v^A = [\mathbf{v}_1^a, \mathbf{v}_2^a, \dots, \mathbf{v}_K^a]$ and $F_t^A = [\mathbf{t}_1^a, \mathbf{t}_2^a, \dots, \mathbf{t}_K^a]$ . + +Cross-aggregation Mechanism. The agents should resonate favorably with the rich semantics of different videos and texts. To enrich the semantics of the initial agents above, we employ the cross-aggregation mechanism to condense the various semantics into the corresponding agents. In specific, we derive the queries $\mathbf{Q}_{\star}$ from the agent features $F_{\star}^{A}$ , the keys $\mathbf{K}_{\star}$ for obtaining aggregation weights + +from the video or text features $F_{\star}$ , and the values $\mathbf{V}_{\star}$ for feature aggregation from $F_{\star}$ . Here, we use $\star$ to indicate the subscript, with $\star \in \{V,T\}$ for brevity. + +$$ +\mathbf {Q} _ {\star} = F _ {\star} ^ {A} \mathbf {W} _ {\star} ^ {\mathcal {Q}}, \mathbf {K} _ {\star} = F _ {\star} \mathbf {W} _ {\star} ^ {\mathcal {K}}, \mathbf {V} _ {\star} = F _ {\star} \mathbf {W} _ {\star} ^ {\mathcal {V}}, \tag {9} +$$ + +$$ +\hat {\boldsymbol {F}} _ {\star} ^ {A} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {\star} \mathbf {K} _ {\star} ^ {\top}}{\sqrt {L}}\right) \mathbf {V} _ {\star}, \tag {10} +$$ + +where $\mathbf{W}_{\star}^{\mathcal{Q}}, \mathbf{W}_{\star}^{\mathcal{K}}, \mathbf{W}_{\star}^{\nu} \in \mathbb{R}^{L \times L}$ are linear projections, and $\sqrt{L}$ is scaling factor. Subsequently, a feed-forward network is employed to derive the $\hat{\pmb{F}}_v^A = [\hat{\mathbf{v}}_1^a, \hat{\mathbf{v}}_2^a, \dots, \hat{\mathbf{v}}_K^a]$ and $\hat{\pmb{F}}_t^A = [\hat{\mathbf{t}}_1^a, \hat{\mathbf{t}}_2^a, \dots, \hat{\mathbf{t}}_K^a]$ , which include abundant semantics. + +Self-aggregation Mechanism. The formulated $\hat{\pmb{F}}_v^A$ and $\hat{\pmb{F}}_t^A$ are respectively derived from the video and text features that exhibit substantial disparities due to significant modality gap. To narrow this gap, we introduce the self-aggregation mechanism to integrate complementary information. Specifically, we first concatenate the $\hat{\pmb{F}}_v^A$ and $\hat{\pmb{F}}_t^A$ : + +$$ +\hat {\boldsymbol {F}} ^ {A} = \operatorname {c o n c a t} \left(\hat {\boldsymbol {F}} _ {v} ^ {A}, \hat {\boldsymbol {F}} _ {t} ^ {A}\right). \tag {11} +$$ + +Next, we employ multi-head self-attention on the $\hat{\pmb{F}}^A$ : + +$$ +\mathbf {Q} = \hat {\boldsymbol {F}} ^ {A} \mathbf {W} ^ {\mathcal {Q}}, \mathbf {K} = \hat {\boldsymbol {F}} ^ {A} \mathbf {W} ^ {\mathcal {K}}, \mathbf {V} = \hat {\boldsymbol {F}} ^ {A} \mathbf {W} ^ {\mathcal {V}}, \tag {12} +$$ + +$$ +\tilde {\boldsymbol {F}} _ {\star} ^ {A} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {\star} \mathbf {K} _ {\star} ^ {\top}}{\sqrt {L}}\right) \mathbf {V} _ {\star}, \tag {13} +$$ + +where $\mathbf{W}^{\mathcal{Q}},\mathbf{W}^{\mathcal{K}},\mathbf{W}^{\mathcal{V}}\in \mathbb{R}^{L\times L}$ are the linear projections. After these three processes, we establish highly reliable agents $\tilde{\pmb{F}}_v^A,\tilde{\pmb{F}}_t^A\in \mathbb{R}^{K\times L}$ that capture rich semantic information and exhibit cross-modal resilience. + +# 3.4. Relation-aware Alignment + +With the obtained agents as references, a straightforward approach is to enforce consistency constraint on the agent-level alignment $(\mathbf{r}_v$ and $\mathbf{r}_t)$ between the $i$ -th video-text pair. + +$$ +\mathbf {r} _ {\star} ^ {i} = \operatorname {s o f t m a x} \left(\boldsymbol {F} _ {\star} ^ {i} \left(\tilde {\boldsymbol {F}} _ {\star} ^ {A}\right) ^ {\top}\right), \star \in \{v, t \}, \tag {14} +$$ + +where $\mathbf{r}_{\star} \in \mathbb{R}^{1 \times K}$ . However, considering each agent separately increases the likelihood of misalignment, especially under noise correspondence. By further incorporating the structural information inherent in inter-agent relations, we meticulously develop the relation-aware alignment based on ranking distribution for more reliable supervision. The primary concept is to treat agent ranking as a random event instead of a fixed permutation. In other words, each permutation of the agents occurs with a certain probability, instead of a fixed order from largest to smallest. Given $\mathbf{r}$ , the probability associated with a permutation $\pi \in \mathcal{P}$ ( $|\mathcal{P}| = N!$ ) is computed as: + +$$ +P (\pi | \mathbf {r}) = \prod_ {k = 1} ^ {K} \frac {\mathbf {r} _ {\pi (k)}}{\sum_ {k ^ {\prime} = k} ^ {K} \mathbf {r} _ {\pi \left(k ^ {\prime}\right)}}. \tag {15} +$$ + +Here, $\pi (k)$ refers to $k$ -th agent index in this permutation. For example, assume that for a given video-text pair, the constructed agents are $\alpha, \beta$ and $\gamma$ . One possible permutation of these three agents is $\pi = (\alpha, \beta, \gamma)$ . The probability of $\pi$ can be obtained from the agent correlation $\mathbf{r}$ : + +$$ +P (\pi | \mathbf {r}) = \frac {\mathbf {r} (\alpha)}{\mathbf {r} (\alpha) + \mathbf {r} (\beta) + \mathbf {r} (\gamma)} \cdot \frac {\mathbf {r} (\beta)}{\mathbf {r} (\beta) + \mathbf {r} (\gamma)} \cdot \frac {\mathbf {r} (\gamma)}{\mathbf {r} (\gamma)}. \tag {16} +$$ + +Based on the probabilities of all $|\mathcal{P}|$ permutations, we convert simple dot product alignment $\mathbf{r}$ into relation-aware ranking distribution $P(\mathcal{P}|\mathbf{r})\in \mathbb{R}^{1\times |\mathcal{P}|}$ . Under this view, ranking distribution captures the inter-agent relationship. Generally, calculating all permutations of the K agents would incur prohibitively high costs. In this regard, we observed that the top-4 agents account for nearly all the weight in Eq. 14. Therefore, we consider only the permutations of the top-4 agents for each video/text for efficiency. Note that for simplicity, we omitted the subscript denoting modality of $\mathbf{r}$ in the above process, as the principles are consistent across both modalities. Based on the agent-ranking distribution of video $P(\mathcal{P}|\mathbf{r_v})$ and text $P(\mathcal{P}|\mathbf{r_t})$ , we can obtain the consistency between them as supervision: + +$$ +S _ {r a n k} ^ {i j} = \cos \left(P \left(\mathcal {P} \mid \mathbf {r} _ {v} ^ {i}\right), P \left(\mathcal {P} \mid \mathbf {r} _ {t} ^ {j}\right)\right). \tag {17} +$$ + +As a result, the relation-aware ranking distribution alignment regularization can be derived as: + +$$ +\mathcal {L} _ {\text {r a n k}} = \frac {1}{B} \sum_ {i} ^ {B} K L \left(S _ {\text {r a n k}} ^ {i,:}, s ^ {i,:}\right), \tag {18} +$$ + +where $B$ is the batch size, $KL$ denotes KL divergence and $s^{ij} = s(v_i,t_j)$ is defined in Eq. 5. Finally, the overall loss function is formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {i n f o}} + \lambda \mathcal {L} _ {\text {r a n k}}, \tag {19} +$$ + +where $\lambda$ is weight coefficient. + +# 4. Experiments + +# 4.1. Experiment Setup + +Datasets. MSR-VTT [48] includes 10,000 videos, each accompanied by 20 captions. Following [52], we use two data splits: full and 1k-A [50]. LSMDC [38] contains 118,081 videos with equal captions from 202 movies. The 1,000 test videos are from movies disjoint with the training set. MSVD [4] contains 1,970 videos with 80,000 captions. We use 1,200, 100, and 670 videos to train, validate, and test, respectively. ActivityNet [18] contains 20,000 YouTube videos. Following [27, 51], we concatenate all descriptions of a video to form a paragraph and evaluate with videoparagraph retrieval on the 'val1' split. DiDeMo [1] contains + +Table 1. Retrieval performance under $0\%$ , $20\%$ and $50\%$ noise rates on MSR-VTT full and 1k-A. The best results are highlighted in bold. + +
NoiseMethodMSR-VTT FullMSR-VTT 1kA
Text to VideoVideo to TextText to VideoVideo to Text
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
0%CE [24]10.029.041.215.640.955.220.948.862.420.650.364.0
MMT [8]------24.654.067.124.456.067.8
TT-CE+ [6]15.038.551.725.355.668.6------
T2VLAD [45]12.734.847.120.748.962.129.559.070.131.860.071.1
CLIP4Clip [27]23.646.457.139.667.577.544.571.481.642.770.980.6
RVTR [52]24.347.259.040.969.479.345.873.083.543.972.682.0
Ours29.855.866.551.681.290.647.673.283.646.373.983.4
20%CE [24]7.422.332.810.230.642.314.840.352.515.239.240.4
MMT [8]------20.450.165.719.850.364.4
TT-CE+ [6]7.522.633.610.932.144.7------
T2VLAD [45]------21.344.756.322.445.459.0
CLIP4Clip [27]9.323.131.915.835.346.327.652.063.722.647.660.0
RVTR [52]20.843.154.734.662.775.042.369.781.041.070.879.3
Ours28.353.764.450.080.088.146.172.382.445.572.982.6
50%CE [24]4.414.321.63.513.120.19.123.631.06.419.827.3
MMT [8]------14.828.039.713.626.436.1
TT-CE+ [6]5.317.627.37.323.134.7------
T2VLAD [45]------2.97.810.73.012.821.7
CLIP4Clip [27]11.728.037.78.621.931.324.448.759.623.447.158.5
RVTR [52]18.438.949.930.660.971.036.261.673.736.061.773.0
Ours27.152.162.748.178.287.844.671.181.244.371.982.4
+ +10,000 videos with 40,000 captions. Following [20, 24], we also evaluate with video-paragraph retrieval. + +Evaluation Metrics. We evaluate the retrieval performance by standard video-text retrieval metrics Recall at K (R@K, higher is better). R@K is defined as the percentage of correct videos/texts within the top K retrieved videos/texts. Following [27, 52], K was set to 1, 5, and 50 for ActivityNet, and 1, 5, and 10 for the other four datasets. + +Implementation Details. Following [27, 52], visual and text encoders are initialized from CLIP with ViT-B/32 [37]. For MSR-VTT, LSMDC, and MSVD, the frame length $N_{v}$ and text length $N_{t}$ are set as 12 and 32. For ActivityNet and DiDeMo, $N_{v}$ and $N_{t}$ are 64. Feature dimension $L$ is set as 512 for all benchmarks, and $\alpha$ is set as 5. All frames are resized into $224 \times 224$ . Our model is optimized with Adam [17] and the cosine learning rate schedule [26] is employed. The initial learning rate is set as 1e-7 for CLIP encoders and 1e-4 for others. The batch size is set as 128. The number of agent $K$ is 10 and weight coefficient $\lambda$ is 0.2. + +# 4.2. Comparison with State-of-the-arts + +We compared our method with previous state-of-the-art methods on five popular benchmarks. To comprehensively evaluate the robustness of our method, we simulate two levels of noisy correspondences, namely $20\%$ , and $50\%$ by randomly shuffling the captions like [52]. + +Results on MSR-VTT. As shown in Tab. 1, our method consistently outperforms previous advanced methods across various scenarios, clearly demonstrating its effectiveness. + +Specifically, we analyze the results from the following perspectives. (1) In the synthetic NC settings, our method significantly exceeds all methods under all noise ratios. Notably, at $50\%$ noise, our method achieves R@1 gains of 8.7, and 8.4 over the best baseline RVTR [52] across full and 1k-A splits. (2) As the noise rate rises, other methods experience significant performance degradation, while ours decreases only slightly. For example, on 1k-A split, as the noise rate rises from $20\%$ to $50\%$ , the R@1 of the RVTR decreases by 6.1, whereas our method only decreases by 1.5. (3) In the NC-free setting, our method also outperforms state-of-the-art approaches, further demonstrating the effectiveness and advantage of our method. + +Results on Other Four Datasets. Tabs. 2 and 3 demonstrate the performance comparison on MSVD, LSMDC, ActivityNet, and Didemo. It can be found that our method constantly surpasses other methods across all metrics by a significant margin. These results underscore the powerful reliable semantic alignment capability under the noisy correspondence setting of our method. + +Stability Comparison. To further highlight the stability of our method, we plot the text-to-video R@1 curves for each method in MSR-VTT 1k-A at increasing noise ratios in Fig. 3. It can be observed that our method exceeds all other methods across all noise ratios. Meanwhile, as the noise ratio increases, the performance degradation of our method is much smaller compared to other methods. The results show that our method is highly noise-resistant. + +Table 2. Retrieval performance under ${50}\%$ noise rates on MSVD and LSMDC. The best results are highlighted in bold. + +
MethodMSVDLSMDC
Text to VideoVideo to TextText to VideoVideo to Text
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CE [24]9.927.840.611.827.938.74.613.922.25.214.821.7
MMT [8]------5.113.920.15.113.719.9
TT-CE+ [6]10.532.547.412.131.943.76.220.527.38.818.024.7
CLIP4Clip [27]8.422.333.46.217.429.814.332.341.713.929.840.4
RVTR [52]28.757.070.330.064.980.019.238.047.019.938.146.5
Ours38.569.980.948.171.881.322.842.352.422.039.850.9
+ +Table 3. Retrieval performance under ${50}\%$ noise rates on DiDeMo and ActivityNet. The best results are highlighted in bold. + +
MethodDiDeMoActivityNet
Text to VideoVideo to TextText to VideoVideo to Text
R@1R@5R@10R@1R@5R@10R@1R@5R@50R@1R@5R@50
CE [24]5.718.128.06.519.327.65.115.855.44.215.461.0
MMT [8]------19.148.087.019.848.186.6
TT-CE+ [6]12.531.542.511.831.142.27.324.169.14.915.351.1
CLIP4Clip [27]14.536.248.315.637.750.78.425.838.34.216.326.8
RVTR [52]26.949.559.927.050.159.531.261.395.934.262.894.9
Ours34.763.474.433.461.873.233.063.296.135.965.996.4
+ +Table 4. Ablation on different agent initialization strategies. + +
Text-to-VideoVideo-to-Text
MethodR@1R@5R@10R@1R@5R@10
All43.170.280.542.970.881.1
Learnable42.969.880.643.371.180.2
Random42.870.079.743.170.680.5
Ours44.671.181.244.371.982.4
+ +Table 5. Ablation on agents construction. + +
Agents ConstructionText-to-VideoVideo-to-Text
SPMCrossSelfR@1R@5R@10R@1R@5R@10
40.466.177.440.167.676.8
✓42.969.879.542.670.880.5
✓✓43.770.381.143.371.681.7
✓✓43.370.480.443.571.781.4
✓✓✓44.671.181.244.371.982.4
+ +Table 6. Ablation on relation-aware correlation consistency. + +
Text-to-VideoVideo-to-Text
MethodR@1R@5R@10R@1R@5R@10
Pair-wise39.365.576.140.166.775.3
Agent-level42.670.678.742.970.080.4
Ours44.671.181.244.371.982.4
+ +# 4.3. Ablation Study + +To examine the effectiveness of our method, we conduct extensive ablation studies on MSR-VTT 1k-A at $50\%$ noise. + +Effectiveness of Agent Construction. As shown in Tab. 5, we conduct diagnostic experiments progressively to verify the effectiveness of each components in the agents construction process. Note that the first line indicates the result of applying relation-aware alignment in the absence of proposed agent construction process. We can observe that this result has already surpassed the previous state-of-the-art methods, which fully demonstrates the effectiveness of relation-aware alignment. The 2-nd row shows the introduction of semantic purification mechanism (SPM) yields a substantial performance lift, i.e., 2.5 on R@1. The gains can primarily be attributed to our more reliable similarity calculation method, which effectively suppresses false matches. By further integrating the cross-aggregation, performance improved by $0.8\mathrm{R}@\mathrm{l}$ . This can be mainly ascribed to various semantic cues absorbed during cross-attention. Finally, when the self-aggregation is adopted, the performance increases by $0.9\mathrm{R}@\mathrm{l}$ . This proves that refined agents after self-aggregation bridge the modality gap. + +Ablation on Agent Initialization. To explore the effectiveness of different agent selection strategies, we compare the performance of several intuitive initialization ways in Tab. 4. In these methods, 'All' indicates that all video-text pairs are used as agents. 'Random' refers to randomly selecting $k$ video-text pairs as agents. 'Learnable' means that agents are randomly initialized trainable parameters. It can be found that our bidirectional selection consistently exceeds other methods. This can be attributed to the fact that + +![](images/843ed5ff3ec4fb0ccd7550a52071c7a4eeb2dc51ff00a0f7d279811069028ab1.jpg) +Figure 3. R@1 comparison for each method at various noise ratios. + +![](images/1ebbf955fffd15c66531581a8d30d09cd36132d8cb7a41fd2527287e9386c991.jpg) +Figure 4. Hyperparameter experiments on the number of agents and weight for the regularization in Eq. 19. + +![](images/2657ccd5023d5b0e64466f50c9e6efe07643bb58fcb36717406fff6c16d72da1.jpg) + +![](images/7efb1aebb04fe697170ff099659e93fa3f616235ec4fa4eebb534de638925b42.jpg) +Figure 5. The similarity distribution of clean pairs and noisy pairs before and after training on MSR-VTT with a $50\%$ noise rate. + +![](images/305e0f82f07c187b04ba2702037828005c759587c04320aded2003d7976302d1.jpg) + +![](images/c55b3ada9ddbfbd4a9fa51ee9f9f84bcf23d5a4c97480bf4ded8ea566b895c3d.jpg) + +![](images/ee7bc5f922955c70f5b524d8f48c95ebe6800038f31b845d6b9542885f624bd5.jpg) + +a man stirs the liquid in a pot with a spoon + +Similarity: 0.31 Rank Consistency: 0.04 + +GT: people are parodying a beauty pageant in a comedy show + +![](images/b63fe77c4c3c9581ed6d952d6124a305b6c27b3021624164b9f19eae098d284d.jpg) +Figure 6. Instances of NC in MSR-VTT training set with $50\%$ noise, where noisy texts are highlighted in red, and for clarity, the corresponding ground truth is displayed below in green. The proposed ranking consistency more accurately reflects the true degree of correspondence compared to pair-wise similarity. + +![](images/4081d1ab7ce53e958504df8a720205db8317650ab7081e94af82d5f23660262a.jpg) + +a young blonde girl is lying down on a bed + +Similarity: 0.28 Rank Consistency: 0.05 + +GT: someone explaining how to surf the website view47 + +our method selects more reliable agents as references, while effectively alleviating the interference from noisy pairs. + +Effectiveness of Relation-aware Alignment. As shown in Tab. 6, we compare the performance of different correlation schemes. 'Pair-wise' denotes directly calculating one-to-one similarity between video and text. 'Agent-level' refers to measuring the similarity of agent-level correlation in Eq. 14 via the dot product or L2 distance. The former may lead to considerable false matches, while the latter overlooks the inherent relationships between agents. The proposed relation-aware alignment yields optimal results, underscoring that modeling inter-agents relationships provides more effective and reliable supervision. + +Hyperparameter Evaluations. Quantitative experiments are conducted to explore the appropriate number of agents and weight for the ranking regularization. As illustrated in Fig. 4(a), the performance continues to grow until the number reaches 10, beyond which it starts to decline. It is reasonable as too few agents cannot represent diverse semantic information while too many agents increase the risk of interference from noisy samples. Similarly, in Fig. 4(b), both too small or too large for $\lambda$ will lead to suboptimal results, and we select 0.2 in our experiments. Overall, our method exhibits robustness to variations in hyperparameters. + +# 4.4. Qualitative Results + +To further analyze and understand the proposed RPC, we show several qualitative examples in MSR-VTT under $50\%$ noise. In Fig. 5, it can be observed that after training, the mean of the clean sample distribution becomes distinctly separated from that of the noisy sample distribution. In Fig. 6, it can be noticed that noisy samples incorrectly learn relatively high similarity due to erroneous supervision, whereas our ranking consistency accurately and reliably reflects the true semantic relevance. Note that 0.3 is already a relatively high similarity (see Fig. 5). For more results, please refer to Supplementary Material. + +# 5. Conclusion + +In this paper, we present a novel and coherent RPC network, including reliable, representative, and resilient agents construction and relation-aware ranking distribution alignment, to tackle the challenging video-text retrieval under NC. We not only achieve consistent performance gains over state-of-the-art methods on five datasets under different settings, but also opens up new avenues from the perspective of representative reference features. 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With the surging demand for customization, PAA enables applications to generate personalized outcomes by aligning with individual aesthetic preferences. The prevailing PAA paradigm involves two stages: pre-training and fine-tuning, but it faces three inherent challenges: 1) The model is pretrained using datasets of the Generic Aesthetics Assessment (GAA), but the collective preferences of GAA lead to conflicts in individualized aesthetic predictions. 2) The scope and stage of personalized surveys are related to both the user and the assessed object; however, the prevailing personalized surveys fail to adequately address assessed objects' characteristics. 3) During application usage, the cumulative multimodal feedback from an individual holds great value that should be considered for improving the PAA model but unfortunately attracts insufficient attention. To address the aforementioned challenges, we introduce a new PAA paradigm called $\text{PAA+}$ , which is structured into three distinct stages: pre-training, fine-tuning, and continual learning. Furthermore, to better reflect individual differences, we employ a familiar and intuitive application, physique aesthetics assessment (PhysiqueAA), to validate the $\text{PAA+}$ paradigm. We propose a dataset called PhysiqueAA50K, consisting of over 50,000 annotated physique images. Furthermore, we develop a PhysiqueAA framework (PhysiqueFrame) and conduct a large-scale benchmark, achieving state-of-the-art (SOTA) performance. Our research is expected to provide an innovative roadmap and application for the PAA community. The code and dataset are available in here. + +# 1. Introduction + +The saying "beauty is in the eye of the beholder" implies that each individual possesses a distinct perception of aesthetics. + +While the Generic Aesthetics Assessment (GAA) partially captures subjectivity, it primarily reflects collective aesthetic judgments. The Personalized Aesthetics Assessment (PAA) aims to accurately predict an individual's unique perception of aesthetics, thereby catering to the increasing demand for customization. PAA enables applications such as recommendations or enhancements to generate personalized outcomes that align with individual aesthetic preferences. + +The prevailing PAA paradigm [1] typically consists of two stages, namely pre-training and fine-tuning (Fig. 2 (a)). In the pre-training stage, GAA datasets are used for supervised training to build a foundational backbone that imparts prior knowledge to the PAA model. In the fine-tuning stage, the user's PAA dataset is employed to fine-tune the PAA model by incorporating individual aesthetic experiences. However, the practical application of the prevailing paradigm gradually reveals three inherent questions: + +Q1: Is a GAA Model a Superior Choice for PAA Pretraining? The GAA model possesses an inherent characteristic: the collective preferences of GAA cannot satisfy the transitivity conditions as rational individual preferences do. This limitation can be proved by the voting paradox [2], which highlights issues of non-transitivity or obstacles in translating individual choices to collective decisions based on the "majority rule." + +# Individual Preferences + +# Collective Preferences + +
Annotator ①: A > B > CA vs. B: (①,③) A > B (②)
Annotator ②: B > C > AB vs. C: (①,②) B > C (③) ⇌ A > B > C > A?
Annotator ③: C > A > BA vs. C: (②,③) C > A (①)
+ +Figure 1. Simple example of the voting paradox in GAA, where three annotators do aesthetic assessments for images $A$ , $B$ , and $C$ . If $A > B$ , it implies A's aesthetic score is higher than B's. + +In GAA, as shown in Fig. 1, collective preferences create a preference order of $A > B > C > A$ , resulting in an inevitable cyclical majority when the number of assessed images reaches a certain large quantity (where the likelihood of a cyclical majority occurring is $100\%$ [3, 4]), regardless of the number of annotators. This example demonstrates that, in GAA datasets, collective preferences fail to satisfy the transitivity conditions as rational individual preferences + +![](images/ff7b7b474d4888c6c83ae14d6fc3931f8a9cce9235df5d4acf85781343b95aed.jpg) +(a) Prevailing PAA paradigm +Figure 2. Paradigm comparison between the Prevailing PAA and our $\mathrm{PAA + }$ + +![](images/e04a975c4cb49e636b502cff8e3546db021d63e411224083a8701241d5e051d8.jpg) +(b) Our PAA+ paradigm + +do. Thus, the incorporation of prior knowledge pre-trained on GAA datasets into the PAA model may result in conflicts, potentially leading to personalized issues. + +Q2: Are the Scope and Stage of Personalized Surveys Sufficiently Comprehensive? Prevailing personalized surveys consider both the user and the assessed object, which plays a critical role in PAA. However, prevailing surveys come with notable limitations. 1) Preferences should be Static or Changeable? To our knowledge, prevailing personalized surveys are conducted only at the fine-tuning stage and do not account for the timeliness of individual preferences. Given that individual preferences can evolve over time, employing static surveys may lead to a misalignment with users' current tastes. 2) Capturing Comprehensive Aesthetic Experiences? Prevailing surveys typically summarize users' private data into users' attributes, such as age, gender, and big-five personality traits [5, 6]. However, these attributes are less correlated with the objects' characteristics (e.g., preferences for specific color combinations) + +Q3: Does Insufficient Accumulation of User Feedback During Usage Influence Model Performance? The prevailing PAA paradigm typically incorporates user feedback during the fine-tuning stage; however, this type of feedback lacks temporal sensitivity and fails to reflect changes or support modification in user preferences over time. Additionally, the form of feedback is usually restricted to aesthetic scores or rankings, thereby constraining the PAA model's ability to capture a broader understanding of user preferences. Actually, user feedback during usage offers crucial personalized insights that can significantly enhance the PAA model. Regrettably, the prevailing PAA paradigm fails to adequately leverage this data. + +This study aims to establish a more comprehensive and advanced PAA paradigm, called $\mathrm{PAA+}$ , which addresses the aforementioned issues while employing physique aesthetics assessment (PhysiqueAA) as an exemplification. Our contributions can be summarized as follows: + +- This study identifies and analyzes three challenges in PAA, discussing their implications for PAA and emphasizes the necessity for innovative solutions. Notably, we present a novel finding suggesting that GAA can adversely impact the transitivity of personalized aesthetic preferences. +- This study establishes our PAA+ paradigm (Fig. 2 (b)) that addresses the aforementioned crucial challenges. The proposed paradigm, structured into three distinct stages: pre-training, fine-tuning, and continual learning, offers an innovative roadmap for the PAA community. +- To validate the proposed PAA+ paradigm, we employ a personalized PhysiqueAA task. Guided by our paradigm, we establish a dataset called PhysiqueAA50K (Fig. 4), consisting of over 50,000 fully annotated physique images. Additionally, a Human-AI collaborative annotation method is adopted to enhance the efficiency of the annotation process. Furthermore, we develop a PhysiqueAA framework (PhysiqueFrame), and conduct a large-scale benchmark, achieving state-of-the-art (SOTA) performance. Our exemplification of the new paradigm offers an innovative application for the PAA community. + +# 2. Related Work + +# 2.1. Personalized Aesthetics Assessment + +The concept of PAA was initially introduced by Ren et al. [7], with a primary focus on image aesthetics assessment. + +They proposed training a GAA model to establish fundamental prior knowledge, which was further refined through the incorporation of aesthetic attributes and content features using residual learning techniques, thereby enabling personalized aesthetic "offset" learning. Additionally, they employed the FLICKR-AES [7], REAL-CUR [7], and AADB [8] datasets for PAA. + +Subsequently, many outstanding studies have built upon this work, further advancing the field of PAA. Prevailing PAA methods utilize user-annotated labels (scores, ranks, or aesthetic reviews) and personalized surveys (age, gender, personality traits, etc.) to develop PAA models. Wang et al. [9] first designed a convolutional neural network (CNN) with user-image relation embedding to train a GAA model. They then employed a collaborative matrix to analyze aesthetic correlations among users and fine-tune the GAA model into a PAA model for a specific user. Other studies have utilized users' interactive behaviors to enhance PAA. For example, Lv et al. [10, 11] collected feedback by having users re-rank the aesthetic order of images to explore their preferences. With ongoing developments in PAA research, more studies recognize the importance of personalized surveys for PAA. Li et al. [6] proposed a method for modeling aesthetic differences between GAA and PAA scores by utilizing personality traits obtained through personalized surveys. Yang et al. [5] introduced a new PAA dataset, PARA, including users' attributes from personalized surveys, such as age, gender, education, photographic experience, and Big-Five personality traits. Their study aims to demonstrate, for the first time, how image aesthetics and individual user attributes interact to shape intricate personalized tastes. + +Prevailing PAA methods have several common aspects: 1) they generally utilize GAA models for pre-training; 2) prevailing personalized surveys do not adequately address preferences directly related to the characteristics of the assessed objects; 3) there is insufficient attention given to feedback data during usage, which is primarily focused on the fine-tuning stage; and 4) the assessed objects are images. However, as analyzed in the introduction, the prevailing PAA paradigm encounters three challenges. To address these challenges, we propose a novel $\mathrm{PAA + }$ paradigm structured into three stages: pre-training, fine-tuning, and continual learning. Furthermore, prevailing PAA methods primarily assess the overall aesthetics of images, but we argue that lots of images fail to adequately reflect personalized differences. In contrast, physique aesthetics is closely intertwined to human health and well-being, as individuals possess an inherent desire to evaluate their own physiques, which highlights aesthetic differences among users. Additionally, the new $\mathrm{PAA + }$ paradigm necessitates substantial personal data for effective pre-training while also requiring continuous feedback during the continual learning stage. Regrettably, the prevailing PAA datasets do not satisfy these requirements. + +# 2.2. Physique Aesthetics Assessment + +"Physique aesthetics" predominantly focuses on the study of aesthetics in relation to the physical appearance, form, and build of the body [12, 13]. Physique aesthetics is closely tied to individuals, reflecting strong subjective preferences and individual aesthetic differences, rendering PhysiqueAA particularly suitable for validating our new PAA paradigm. The classical literature of aesthetics [14], authored by Shusterman, argues that the aesthetics of the body should not solely focus on the body's appearance but should also encompass considerations of health and behavioral performance. Therefore, we summarize the evaluative dimensions of physique aesthetics as appearance, health, and posture: appearance represents the expressive nature of the physique; health emphasizes its overall well-being; and posture reflects structural control and balance, serving as a crucial factor in harmonizing appearance with health (cf. Appendix A.2). + +Building on Shusterman's perspective, PhysiqueAA primarily focuses on individuals' perceptions and preferences toward diverse body shapes and postures. It holds significant application value in various fields, such as healthcare and medical aesthetics [15] as well as recommendation systems [16]. However, PhysiqueAA encounters substantial challenges: 1) the assessed objects exist in a 3D space, complicating evaluations beyond traditional 2D image aesthetics assessment (IAA); 2) it entails a highly subjective task without explicitly designed datasets for PhysiqueAA due to difficulties in deconstructing physique aesthetics. + +Potential Approaches for Investigating PhysiqueAA. To our knowledge, there is currently no publicly available learning-based PhysiqueAA model. However, potential approaches for investigating PhysiqueAA can be found in three tasks: PAA, IAA, and human-centric visual tasks. Prevailing PAA [17-19] and IAA [19-26] approaches primarily focus on assessing the overall visual aesthetics of images. Although these approaches are not specifically designed for PhysiqueAA, the underlying principles of aesthetic assessment can also contribute to differentiating the aesthetic qualities of physique. On the other hand, human-centric visual task [27] approaches possess strong perception capabilities that effectively capture crucial physique-related information; hence they hold promise as valuable methods for exploring PhysiqueAA. Building on these foundational insights, we have established a benchmark for PhysiqueAA by selecting approaches based on the following criteria: 1) classical architectures with available code; 2) excellence in aesthetic assessment or human-centric perception. + +In this paper, we propose the PhysiqueAA50K dataset, which is collected across different personality types based on the 16 MBTI personality types [28], and introduce the PhysiqueFrame framework, tailored specifically for PhysiqueAA to validate our novel paradigm. + +![](images/d4d6eb1bbe32b84be9a2e10717ba7bb690293dd4b72363b631bcd9fb502539a6.jpg) +(a) + +![](images/a81a055d603cd9206df465eb5ea2b04327a6c04d6b68d6b8b663c224e6ba4daf.jpg) +(b) +Figure 3. (a) Validation for our PAA+ paradigm. (b) PhysiqueFrame architecture (comprising two networks: PANet, which utilizes a dual-branch module to extract 3D physique-related features such as shape, posture, and facial expression; and PENet, designed to effectively capture user preferences from multimodal preference data). + +# 3. Validation for our PAA+ Paradigm + +As illustrated in Fig. 3, the proposed PAA+ paradigm is structured into three stages. + +# 3.1. Stage 1: Pre-training + +In this stage, we construct datasets corresponding to each of the 16 MBTI personality types [28], and develop personalized models for all 16 types to replace the traditional GAA model as the pre-training model. + +Data Organization. Firstly, we compile a dataset comprising 40,000 images. Subsequently, to facilitate PhysiqueAA annotations, we employ a Large Language Model (LLM), LLaVA++ [29], augmented with Reinforcement Learning from Human Feedback (RLHF) to generate pseudo-labels, thereby alleviating the burden on annotation experts. The RLHF workflow is iterative and involves three primary steps for each cycle: + +1) A subset of 1,000 images is selected. The LLaVA++ utilizes expert-defined prompts to generate PhysiqueAA scores (pseudo-labels) for each personality type, accompanied by corresponding explanations. +2) Each annotation expert, representing one of the 16 MBTI personality types, independently reviews and verifies the pseudo-labels corresponding to their respective type. Experts rectify any identified errors by adjusting the PhysiqueAA scores accordingly. +3) The revised scores are subsequently utilized to fine-tune the LLaVA++ using the Low-Rank Adaptation (LoRA) method [30], thereby augmenting the model's predictive accuracy for subsequent annotation iterations. + +This iterative process is repeated for each new batch of 1,000 images until the complete 40,000-image dataset is annotated. Through this process, we have generated a compre + +hensive PAA-16-personality dataset comprising annotated data for 40,000 images across 16 personality types. This dataset covers 3 assessment dimensions: appearance score, health score, and posture score. Additionally, to enhance the comprehensiveness of personalized surveys, we collected additional information on the annotation experts, including their characteristics (e.g., age, gender) as well as their preferences regarding physique (e.g., preference for a slender or curvy physique). For more details on data organization and the 16 MBTI personality types, cf. Appendix A.1, A.2, B. + +Training Strategy. Utilizing PhysiqueFrame (cf. Sec. 3.4), we employ pre-training to develop a set of 16 personalized models $(F_{1}, F_{2}, \ldots, F_{16})$ , with each model tailored specifically to one of the 16 distinct personality types based on the PAA-16-personality dataset. + +To optimize the prediction of PhysiqueAA scores across the three assessment dimensions, an automated weight adjustment strategy is applied. The objective function for the $i$ -th model $(i = 1,2,\dots,16)$ is formulated as follows: + +$$ +\mathcal {L} _ {i} = \sum_ {j} ^ {3} \left(\frac {1}{\sigma_ {j} ^ {2}} \cdot \left(S _ {i, j} - F _ {i, j} \left(X, P _ {i}\right)\right) ^ {2} + \log \sigma_ {j} ^ {2}\right), \tag {1} +$$ + +where $X$ is the input image, $S_{i,j}$ indicates the target score for the $j$ -th dimension, and $P_i$ refers to the survey annotation data relevant to the $i$ -th personality type. Here, $\sigma_j$ is a learnable parameter that dynamically adjusts the weighting of the loss for each PhysiqueAA score, and $\log \sigma_j^2$ acts as a regularization term to prevent overfitting. + +# 3.2. Stage 2: Fine-tuning + +In this stage, an individual user $U_{i}$ has two options: $U_{i}$ can either directly select the pre-trained model most compatible with $U_{i}$ 's personality as the personalized model, or alternatively, fine-tune the selected model using $U_{i}$ 's personalized + +![](images/af2e761f35ce87625fa3f45c47be7da165cd53a7a94ecbc88e92f81d598d4294.jpg) +Figure 4. Overview of the PhysiqueAA50K dataset: (a) distribution; (b) visualization; (c) examples with the annotations. + +![](images/682f7ba72d924327ccf6779ccd02daa16ebfb820de7db170d82a8cbe90278ee6.jpg) + +![](images/374f5f2cc6022a4d098c0d49d38db009fec8b3df2cc8be486fd6e6906991cf1d.jpg) + +data to achieve a closer alignment with $U_{i}$ 's specific preferences. Here, we focus on the latter approach. The main steps are as follows: + +1) Collect a sufficient amount of personalized image data from $U_{i}$ , including annotated scores and surveys. +2) Use the 16 pre-trained personalized models to predict scores for $U_{i}$ 's images, then select the model that aligns best with $U_{i}$ annotated scores as the base model $F_{i}$ . Note: the user also has the option to choose any model they prefer directly. +3) Fine-tune the selected base model $F_{i}$ with the user-specific data, obtaining the user-specific model $F_{i}^{*}$ . + +Specifically, we collected 10,000 images for validation, each paired with personalized data from three users, User-ISFJ, User-ESFJ and User-ISTJ, representing the most common MBTI personality types: ISFJ, ESFJ, and ISTJ. This dataset, referred to as the PAA-3-User dataset, was used to fine-tune the models with the same loss function as specified in Equation (1). For more details, cf. Appendix A.1 and A.2. + +# 3.3. Stage 3: Continual Learning + +Due to potential limitations in the sampling of training data or changes in user preferences over time, prediction errors are inevitable during the model's usage. In this stage, we continuously refine the user-specific model $F_{i}^{*}$ by collecting user feedback and personalized surveys throughout usage, allowing the model to adapt to the user's evolving aesthetic preferences. + +For the user $U_{i}$ and the user-specific model $F_{i}^{*}$ , this stage involves the following three main steps in each update epoch: + +1) Use the model $F_{i}^{*}$ to assess images and provide scores to $U_{i}$ ; +2) Allow $U_{i}$ to provide various forms of feedback (e.g., thinking the scores are higher, lower, or about the same, revised scores, texts, images, videos) on the provided scores; +3) Collect a batch of feedback and integrate it with $U_{i}$ 's personalized surveys, then update $F_{i}^{*}$ . + +For validation, we collected feedback data from User-ISFJ, User-ESFJ, and User-ISTJ on a set of 400 images, covering 4 update epochs. Each epoch contained 100 feedback entries. We applied the same loss function as defined in Equation (1) to optimize the model. + +# 3.4. Architecture of PhysiqueFrame + +Overview. The primary objective of the PhysiqueAA task is to perform a regression analysis that assesses physique aesthetics. Our model is designed to 1) extract physique-related features and 2) capture user preferences and adapt them for personalized assessments. + +Fig. 3 (b) illustrates the pipeline of the proposed framework. Given the input image, the Physique Analysis Network (PANet) extracts 3D physique-related features such as shape, posture, and facial expression through a dual-branch module. Meanwhile, the Preference Extraction Network (PENet) captures user preferences such as physique style, body proportions, and muscle definition from personalized surveys and feedback. + +# 3.4.1. Physique Analysis Network (PANet) + +How can we effectively represent the human physique? Previous studies have shown that it can be deconstructed into two components: the shape, defined by the external features of flesh, and the posture, determined by the internal skeleton [31-33]. However, current IAA and PAA methods lack 3D analysis capabilities, limiting their ability to capture the spatial and volumetric characteristics of the human physique. + +In this paper, the proposed PANet includes two modules. The Mesh Perceiving Module (MPM) leverages 3D human mesh data to analyze body shape, while simultaneously capturing facial features and expressions. The Posture Analyzing Module (PAM), on the other hand, utilizes skeleton keypoints and their connections to assess posture. + +Mesh Perceiving Module (MPM). Human mesh data is extracted by an encoder [34], which is pre-trained on datasets such as MSCOCO [35], MPI [35], Human3.6M [36], and + +Ubody [37]. Processing the mesh data is challenging due to its inherent irregularity and sparsity [38-40]. A key challenge is to standardize this data to create a coherent representation of a 3D human mesh. To tackle this issue, we propose an affine geometry-based method that normalizes local points while preserving their intrinsic geometric properties. Affine geometry facilitates geometric transformations, including scaling, translation, and rotation, which maintain essential spatial relationships within the data structure. + +Specifically, for an initial point $v_{i} \in \mathbb{R}^{m}$ , we define $v_{i}$ 's local neighborhood as $\{v_{i,j}\}_{j=1,\dots,k} \in \mathbb{R}^{m \times k}$ , containing $k$ neighboring points. Each neighbor point $v_{i,j}$ has dimension $m$ . The transformation of these local points is represented by the following formula: + +$$ +\left\{v _ {i, j} ^ {*} \right\} = \frac {\left\{v _ {i , j} \right\} - v _ {i}}{\mu + \varepsilon} \odot \xi + \delta , \tag {2} +$$ + +$$ +\mu = \sqrt {\frac {\sum_ {i = 1} ^ {n} \sum_ {j = 1} ^ {k} \left(v _ {i , j} - v _ {i}\right) ^ {2}}{n \times m \times k}}, \tag {3} +$$ + +where $\{v_{i,j}^{*}\}$ represents the transformed points, $\odot$ indicates Hadamard product, and $\xi \in \mathbb{R}^m$ and $\delta \in \mathbb{R}^m$ are learnable parameters. The scalar $\mu$ quantifies the feature deviation across all local groups and channels, where $\varepsilon$ is a small constant added for numerical stability. Finally, the normalized mesh data is processed by an MLP-based mesh decoder for further analysis to extract the feature $f_{mpm}$ (cf. Appendix C.1 for details). + +Posture Analyzing Module (PAM). Posture is a critical aspect of body language and nonverbal communication, reflecting the fluidity and grace of movement while conveying emotions and attitudes of the PhysiqueAA. Structurally, posture can be modeled as a skeleton, where joints are represented as nodes and bones as edges. This structural representation makes graphs a suitable tool for capturing posture features [41-43]. To exploit this representation, we developed the PAM integrated with a Graph Convolutional Network (GCN) to extract relevant posture features. Here, keypoints are the computational representation of human joints [41-43]. + +![](images/91c7e45075261755fffabfb6456a21959c1e403d05db2109c4ef72a0a1b8acbd.jpg) +Figure 5. Structure of the keypoints decoder. + +Human keypoints are extracted using a pre-trained encoder, which is pre-trained on datasets [35, 35-37], and then processed with the input image through a keypoints decoder to generate features. This decoder first utilizes the Swin Transformer V2 [44] and ROI Pooling [45] to obtain both image and keypoints features. Subsequently, these features are fed into a GCN built upon an adjacency matrix that reflects the human skeletal framework. A residual structure is incorporated to preserve critical low-level details, allowing + +these details to be retained through successive transformation layers (Fig. 5). Finally, the output undergoes further processing through activation and linear layers, producing the feature $f_{pam}$ . + +# 3.4.2. Preference Extraction Network (PENet) + +Our framework integrates data from user surveys and feedback, encompassing a range of intricate modalities, including images, text, scores, and videos. This multimodal data captures comprehensive user preferences to support the final prediction of the PhysiqueAA scores. However, multimodal data is inherently diverse and complex, lacking a unified representation. Understanding the relationship between these multimodal data and users' preferences for physique images is challenging. + +To solve the above issue, we implement the PENet based on an LLM, $\mathrm{LLaVA}++$ [29], and utilize a Chain of Thought (CoT) methodology [46] to consolidate diverse modalities into a standardized, quantitative format. The key steps in this process are as follows: + +1) Task Decomposition and Factor Scoring. The primary task is to understand user preferences as reflected by multimodal data. We decompose the task into a series of subtasks, with each structured as a question-answer prompt directed to ChatGPT. These prompts assess sentiment polarity regarding five specific factors: physique expressiveness, physique style, physique shape, physique posture, and personality traits (cf. Appendix C.2 for details). Each factor is assigned a probability score, where scores close to 1 indicate a positive user preference, while scores near 0 suggest a negative preference. Moreover, we prompt ChatGPT to provide a final conclusion, asking: "Does the user like this image?" This is represented by a binary output, scored as 1 for "yes" and 0 for "no." +2) Applying CoT to Train PENet. After reorganizing the data, we apply the CoT approach to train PENet. The training is supported by a Q&A mechanism based on the question: “Q: Does the following data suggest that the user likes this image?” An example of a ground-truth response could be: “The physique expressiveness score is 0.6, and the physique style score is 0.8... therefore, the answer is 1.” +3) Score Aggregation. In the final stage, the scores are aggregated into the feature $f_{preference}$ with $f_{mpm}, f_{pam}$ , and the original image, to predict the PhysiqueAA scores. + +# 4. Experiments + +# 4.1. Experimental Settings + +Benchmark Dataset. We conducted experiments on the proposed PhysiqueAA50K dataset (Fig. 4), which encompasses data across the three stages: PAA-16-Personality, PAA-3-User, and 400 images for stage 3 validation (see Sec. 3.1-3.3 for details). The PhysiqueAA50K dataset includes PhysiqueAA scores, personalized user surveys, and user + +
User-ISFJUser-ESFJUser-ISTJ
MetricGAAOursGAAOursGAAOurs
AppearanceS↑.650.699.628.649.603.617
L↑.676.724.650.678.631.650
A↑.739.759.721.744.701.716
HealthS↑.601.625.516.540.509.546
L↑.626.657.539.567.552.570
A↑.747.761.725.740.704.726
PostureS↑.652.664.632.657.568.597
L↑.689.703.684.695.616.641
A↑.744.764.740.761.691.701
Satisfaction Sat↑75.3%84.5%70.6%81.0%68.9%80.9%
+ +Table 1. Performance comparison of the GAA model and personality-matched personalized models by comparing them as pre-training models, with each being fine-tuned on the three datasets (User-ISFJ, User-ESFJ, User-ISTJ) for stages 2 and 3 to evaluate performance. + +
MethodAppearanceHealthPostureSatisfaction
S↑L↑S↑L↑S↑L↑Sat↑
w/o preferences.683.704.614.639.651.68679.4%
w/ preferences.699.724.625.657.664.70384.5%
+ +feedback, with scores across three dimensions: appearance, health, and posture (cf. Appendix A.2 and A.3 for details). + +Benchmark Models and Training Protocols. In the proposed paradigm, the PANet for physique feature extraction can be replaced with other models to establish a comprehensive PhysiqueAA benchmark. As described in Sec. 2.2, we selected 8 representative baseline models [17-23, 27]. Each model was trained with its recommended parameter settings (e.g., optimizer and batch size) and evaluated under the same training and testing conditions. Equation (1) was used as the loss function across all models, with the training strategy for each stage outlined in Sec. 3.1-3.3. + +Evaluation Metrics. We employ three popular evaluation metrics to assess the model's capabilities in stages 1 and 2: Spearman's rank correlation coefficient (SRCC, $\mathcal{S}$ ), the linear correlation coefficient (LCC, $\mathcal{L}$ ), and binary classification accuracy (ACC, $\mathcal{A}$ ). SRCC and LCC provide fine-grained assessments of the model's performance in score regression, while ACC, based on a 5-point threshold, evaluates the model's coarse-grained ability to classify PhysiqueAA scores as aesthetically positive or negative. + +In stage 3, however, user feedback is immediate and dynamic with each update epoch, making it impossible to establish a fixed testing dataset. As a result, the above metrics are not applicable. Instead, we assess performance based on user satisfaction, measuring the proportion of positive feedback. The average user satisfaction rate $(\overline{Sat})$ reflects the overall performance across this stage. + +Table 2. Performance comparison in stages 2 and 3, when user preferences are included or excluded from the personalized survey. + +
StageAppearanceHealthPostureSatisfaction
123S↑L↑S↑L↑S↑L↑Sat↑
✓✓.686.710.617.642.653.69078.5%
✓✓.682.705.613.637.651.68576.7%
✓✓.691.719.618.651.658.69682.3%
✓✓✓.699.724.625.657.664.70384.5%
+ +Table 3. Impact of incorporating personalized surveys in different stages on model performance. + +![](images/04f968d3575e2a6af1111155085521d1e552930a79a5ae3ff240a93f452e9b1c.jpg) +Figure 6. Impact of personalized surveys on PhysiqueAA predictions, with icons $\mathbb{I}$ , $\mathbb{I}$ and $\mathbb{I}$ representing scores of appearance, health, and posture, respectively. + +# 4.2. Ablation Study of our PAA+ Paradigm + +Validation for Q1: Is a GAA Model a Superior Choice for PAA Pre-training? To answer this question, for three users with different personalities (ISFJ, ESFJ, ISTJ), we pretrained both a GAA model and three personality-matched personalized models, as pre-training models in stage 1. For the GAA model, pre-training was conducted using the average scores across all personalities from our PAA-16-personality dataset, while each personalized model was pretrained on personality-specific data (without personalized surveys). We then evaluated the final PAA performance on the PAA-3-User dataset. As shown in Table 1, the GAA model, when used as a pre-training model, performed worse than the personality-matched personalized models. This suggests that integrating prior knowledge from the GAA dataset into the PAA model may introduce conflicting influences. + +Validation for Q2: Are the Scope and Stage of Personalized Surveys Sufficiently Comprehensive? The personalized surveys used in prevailing methods primarily assess user attributes without exploring their preferences. As shown in Table 2 (on the User-ISFJ dataset), excluding user preferences from the personalized survey leads to a performance decline, revealing a limitation in the scope of these methods' personalized surveys. Moreover, Table 3 demonstrates that incorporating personalized surveys across all three stages enhances the model's prediction accuracy, compared to applying personalized surveys in only a single stage. Fig. 6 provides qualitative examples illustrating the impact of personalized surveys on model predictions. + +Validation for Q3: Does Insufficient Accumulation of User Feedback During Usage Influence Model Performance? In stage 3, the sufficiency of user feedback in + +![](images/3dfefae472a9ce2658885971b10f53ca567db24b1e9f3ccb952c8bb9d77ae25e.jpg) +Figure 7. Relationship between the number of feedback update epochs (100 images each) from three users and their satisfaction rate during the continual learning stage. + +![](images/60438041c9fb969c3bfc4968d5159617c0d649c8404f6aa89ad4d17fd6849ec7.jpg) +Figure 8. Feedback process and its impact on PhysiqueAA. + +
MetricCNN-based modelsTransformer-based modelsOurs
NIMABIAAHGCNTANetMaxViTTCFormerEATQ-Align
AppearanceS↑.598.567.419.601.574.452.628.619.699
L↑.612.583.435.625.599.477.650.634.724
A↑.732.694.667.712.705.673.732.731.759
HealthS↑.559.485.362.528.513.383.573.555.625
L↑.582.513.391.569.547.417.599.575.657
A↑.731.665.601.705.691.612.732.726.761
PostureS↑.581.536.486.572.563.508.592.609.664
L↑.616.574.502.617.596.523.629.644.703
A↑.736.682.618.706.695.633.729.735.764
+ +creases with the number of update epochs in the continual learning process, which in turn enhances model performance. As shown in Fig. 7, user satisfaction improves as feedback epochs accumulate. Fig. 8 presents qualitative examples illustrating how specific user feedback impacts the outcomes of PhysiqueAA. + +# 4.3. Ablation Study of proposed PhysiqueFrame + +Performance Comparison with PANet Alternatives. As shown in Table 4, our model achieves the best performance across all metrics when compared with alternative models on the User-ISFJ dataset. Appendix D.1 provides experiments on the User-ESFJ and User-ISTJ datasets. This indicates that our model more effectively captures features related to physique aesthetics. + +The GradCAM method [47] is applied to visualize the saliency maps in Fig. 9. Our model, with its comprehensive + +Table 4. Comparison of the night models conducted on the UserISFJ dataset for stage 2. We retrained the models to maximize performance, using the recommended parameters and settings. + +
PAMMPMPENetAppearanceHealthPosture
S↑L↑S↑L↑S↑L↑
✓.663.688.594.615.648.685
✓.676.696.608.627.641.678
✓✓.680.702.611.634.647.682
✓✓✓.699.724.625.657.664.703
+ +Table 5. Ablation studies of PANet modules (PAM, MPM) and PENet, conducted on the User-ISFJ dataset for stage 2. + +![](images/76d935a2d2cdc0cfe6e6a6e04435b8dfa92e7eebff51cbe75216b0bfb2bdf230.jpg) +Figure 9. Saliency maps of the 9 models. The attention of our model is focused more on the human physique. + +integration of physique aesthetics knowledge, enables a more human-centric assessment by directing the model's attention specifically toward the human body. + +Ablation Study on Modules of PANet. As shown in lines 1-3 of Table 5, we examined the effectiveness of the PAM and MPM modules. The results suggest that incorporating PAM and MPM enables PhysiqueFrame to extract more physique-related features, thereby enhancing performance. + +Ablation Study of PENet. A comparison between line 3 and line 4 in Table 5 shows that incorporating PENet improves the model's performance. These results show that PENet enhances the model's alignment with user preferences. + +# 5. Conclusions + +In this paper, we present the innovative $\mathrm{PAA + }$ paradigm that addresses three challenges of prevailing approaches and incorporates multi-modal dynamic surveys across all stages to enhance model adaptability. We conduct a preliminary validation of the proposed $\mathrm{PAA + }$ paradigm using a typical PAA task, PhysiqueAA. Following the $\mathrm{PAA + }$ paradigm, we develop PhysiqueFrame, construct a physique-specific dataset, and establish the largest-scale benchmarks to date. Compared with potential models for investigating PhysiqueAA, PhysiqueFrame achieves SOTA performance and produces visually consistent results. We aim to make a valuable contribution to the PAA community through our work. However, we acknowledge that scoring alone is an insufficient means of assessment; therefore, we will optimize the $\mathrm{PAA + }$ paradigm to enhance its effectiveness and applicability. + +# 6. Acknowledgement + +This work is supported by the National Natural Science Foundation of China under Grant U24B20176. + +# References + +[1] Hancheng Zhu, Yong Zhou, Leida Li, Jiaqi Zhao, and Wenliang Du. The review of personalized image aesthetics assessment. Journal of Image and Graphics, 27(10):2937-2951, 2022. 1 +[2] Kenneth J. Arrow. Social Choice and Individual Values. Yale University Press, 2012. 1 +[3] William H Riker. Liberalism against populism. 1988. 1 +[4] William V. Gehrlein. Condorcet's paradox and the condorcet efficiency of voting rules. Mathematica Japonicae, 45(1):173-199, 1997. 1 +[5] Yuzhe Yang, Liwu Xu, Leida Li, Nan Qie, Yaqian Li, Peng Zhang, and Yandong Guo. Personalized image aesthetics assessment with rich attributes. In CVPR, pages 19861-19869, 2022. 2, 3, 12 +[6] Leida Li, Hancheng Zhu, Sicheng Zhao, Guiguang Ding, and Weisi Lin. Personality-assisted multi-task learning for generic and personalized image aesthetics assessment. 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To leverage the built-in objectness of query-based transformers, which mitigates catastrophic forgetting of mask proposals, current methods often decouple mask generation from the continual learning process. This study, however, identifies two key issues with decoupled frameworks: loss of plasticity and heavy reliance on input data order. To address these, we conduct an in-depth investigation of the built-in objectness and find that highly aggregated image features provide a shortcut for queries to generate masks through simple feature alignment. Based on this, we propose SimCIS, a simple yet powerful baseline for CIS. Its core idea is to directly select image features for query assignment, ensuring "perfect alignment" to preserve objectness, while simultaneously allowing queries to select new classes to promote plasticity. To further combat catastrophic forgetting of categories, we introduce cross-stage consistency in selection and an innovative "visual query"-based replay mechanism. Experiments demonstrate that SimCIS consistently outperforms state-of-the-art methods across various segmentation tasks, settings, splits, and input data orders. All models and codes will be made publicly available at https://github.com/SooLab/SimCIS. + +# 1. Introduction + +Continual learning empowers models to progressively acquire, learn, and assimilate new knowledge from an ever-evolving environment. It serves as a fundamental task in image classification [4, 8, 18, 20, 25, 31, 40, 42, 48, 49, 57, 58, 60, 64, 71, 72, 75] where models are required to recognize new classes (plasticity) and preserve old class knowledge (avoid catastrophic forgetting). Extending be + +![](images/e27093835b227af9268a06880566695714a1c27d1ece31de1f2161f0d92a1339.jpg) +Figure 1. Boxplots of PQ metric for our SimCIS and previous SOTA [38] on ADE20K. We train each model on randomly shuffled continual data input orders and report average PQ for base and novel classes. We observe that recent query-based transformers suffer from a loss of plasticity (low average PQ) and heavy reliance on the input data order (high variance). + +yond classification, continual image segmentation adapts this to the image segmentation, unlocking a myriad of practical applications [50, 53]. However, it also confronts more challenges: 1) Additional catastrophic forgetting of mask prediction, beyond that of class prediction; 2) Background semantic shift occurs when the current foreground becomes background in subsequent stages, driven by the need for image segmentation to predict the background class and the constraint of only having class annotations from current stage. Recently, query-based transformers [10, 17, 34, 35, 55, 56, 59, 63, 79] are introduced into continual image segmentation, as their built-in objectness has been shown to mitigate catastrophic forgetting in mask generation. Leveraging this built-in objectness, many studies [7, 26, 38, 74] decouple mask segmentation from the continual learning process by freezing the parameters associated with mask proposal generation. However, we observe two notable yet suboptimal behaviors in the aforementioned methods. + +![](images/e1b57e9119ebea780037143e2662b930d4c1e1fa5b921b1432585deaecad9d26.jpg) +Figure 2. Clustering results from feature map. Pixel feature provides sufficient semantic priors (Person) even after finetuning. + +![](images/d07ea719cdadb5ed3ea1cce66d4bfa7761f39231baaf843fa67ca36af31f6692.jpg) + +![](images/8f0dd45b115c6601b53eea533b4e21e38d4b2c2684c5b8eeb1049af5d0513c59.jpg) + +- The advantage of objectness diminishes and even has a detrimental effect on plasticity as the task sequence shortens. In the shortest two-task setting, they typically achieve performance comparable to or even slightly lower than the baseline. +- The built-in objectness is fragile and lacks robustness, showing heavy dependence on the split and order of input data. As shown in Fig 1, in ten random trials, the worst trial shows a significant performance drop on new classes compared to the default setting. + +Therefore, in this work, we aim to understand the built-in objectness and achieve consistent improvements (especially on plasticity) across different task lengths and varying data input orders. This is crucial, as it is impractical to assume fixed task lengths and data sequences in real-world scenarios. The conclusion from a series of investigations is: + +- The built-in objectness emerges from the alignment between the query and the semantic priors within the image feature, mediated by the decoder. As shown in Fig 2, the clustering results indicate that image features contain sufficient semantic priors where pixels belonging to the same semantic are grouped together) even after finetune. Meanwhile, the query continuously aligns with specific regions of the feature map at each layer of the decoder as shown in Fig 3 (right). In summary, the highly aggregated image feature provides a shortcut for queries to generate masks by simply aligning themselves to semantic priors in the image feature through the decoder. +- ② The built-in objectness diminishes over training stages due to the query's failure to align with the semantic priors of the feature map. As shown in Fig 3 (left), since semantic priors vary at different stages due to background semantic shift, causing the updated learnable query to gradually misalign with the pixel feature from old classes in previous stages, even after the decoder's post-alignment (observed in ①). + +Inspired by 1 and 2, to ensure objectness is preserved throughout the continual learning stages, we propose a lazy Query Pre-Alignment (QPA) method, where query features are selected from specific locations in the image feature map, rather than being learned from scratch, to "perfectly" pre-align query feature with semantic priors. Specif + +![](images/696ca13b9bd9967ea0cbaf25569e90c5e4ee4d6a33cc855b15b8952bda5282b3.jpg) +Figure 3. Similarity between queries and feature map changes across decoder layers and training stages (right). The query gradually misaligns with the pixel feature (left). + +![](images/7971154e225df108b28f364a029086e4909612f06756909c82cef27a4a3974a7.jpg) + +ically, based on the current stage's semantic classes, we select the most semantically significant locations in the image feature, preserving objectness at each stage. However, objectness is still lost across stages due to varying semantic classes in different stages. + +To overcome cross-stage selection issues, a naive solution involves distillation on the feature map or query features between stages. However, in turn, while it preserves old priors from previous stages, it re-introduces incorrect priors for current stages (where old priors label current semantics as background), leading to a loss of plasticity. Fortunately, thanks to our query pre-alignment method, we can easily maintain old classes by keeping queries corresponding to old class positions, while enabling the selection of remaining queries for new classes in the current stage. Thus, we propose a Consistent Selection Loss (CSL) to ensure that, for the same image, the most semantically significant locations selected in the previous stage are revisited in the current stage. + +With QPA and CSL, objectness in the query-based transformer is fully utilized to generate mask proposals. However, for class prediction, catastrophic forgetting may still occur. Previous methods typically rely on image replay to mitigate catastrophic forgetting. In contrast, thanks to our query pre-alignment, our query inherently contains category semantics. By storing the query feature, we can simulate specific semantics without requiring the actual image to contain the corresponding category. Therefore, we propose a novel Virtual Query (VQ) strategy to replay the virtual queries corresponding to previous classes in the decoder layer to avoid catastrophic forgetting. Compared to conventional image replay methods, our approach reduces storage requirements by $10\mathrm{x}$ , is independent of input data order, and preserves dataset privacy. + +In summary, our contributions are multi-fold: + +- We provide a thorough analysis of the built-in objectness, revealing the reasons behind its emergence and demise. +- By addressing the root cause, we can successfully leverage built-in objectness to mitigate catastrophic forgetting + +and background semantic shift through the introduction of three simple yet novel modules—QPA, CSL, and VQ. + +- Our model, SimCIS, consistently and significantly outperforms state-of-the-art results on ADE20K in both continual panoptic and semantic segmentation. +- We introduce new dataset splits to evaluate the model's robustness to input order in continual learning. SimCIS shows superior robustness over state-of-the-art methods, thanks to the effective utilization of built-in objectness. + +# 2. Related Work + +Continual Learning is a longstanding field which possesses significant importance in addressing dynamic environments, enhancing model adaptability, and improving resource efficiency. The objective of continuous learning is to enable the model to efficiently acquire and adapt to new tasks and data, while retaining previously learned knowledge as it encounters additional information. The greatest challenge of continual learning is catastrophic forgetting [24, 49, 65]. The early research are categorized into three primary types: those that rely on regularization constraints [8, 9, 19, 20, 39, 41], those employing replay techniques [46, 49, 60], and those based on dynamic structures [22, 42, 43, 61, 71, 75]. Regularization-based methods aim to reduce the interference of new tasks on old knowledge by constraining the learning process of the model, ensuring that the model parameters remain closely aligned with previously learned representations when updated due to task changes. Replay-based methods employ strategies to store, replay [4, 33, 48, 67], or generate [46, 60, 66] samples from old tasks to mitigate catastrophic forgetting. Those methods based on dynamic structure [42, 43, 52] allocate distinct subsets of parameters to various subtasks by facilitating the expansion of their network architecture. + +Universal Image Segmentation. Before MaskFormer proposed, traditional segmentation methods developed specialized architectures and models for each task to achieve top performance [2, 12-15, 28, 30, 36, 62, 69, 73, 78]. MaskFormer [16] is the first unified segmentation architecture to achieve state-of-the-art performance across three image segmentation tasks. Mask2Former [17] improves MaskFormer by adapting multi-scale features and introducing mask attention mechanism and achieve better performance. Follow its success in segmentation, we use Mask2Former as our baseline aims to extend its capability into the field of continual learning. + +Continual Segmentation is the application of continual learning within the field of image segmentation. The challenge of continual segmentation tasks lies in the ability to identify new categories while generating high-quality masks for each category. This dual requirement underscores the complexity of maintaining accurate segmentation performance while adapting to an evolving set of class labels. + +Methods for continual segmentation are also categorized into three types as previously mentioned: regularization-based [5, 6, 21, 44, 45, 47, 54, 68, 74, 77], replay-based [7, 11, 23, 76, 81], and dynamic structure-based [1, 26, 27, 38, 70]. Among these methods, those query-based architectures demonstrate notable performance. CoMFormer [6] is the first query-based method in the field of continuous panoptic segmentation, employing distillation and pseudo label to combat catastrophic forgetting. CoMasTRe [26] is inspired by the methods of CoMFormer and, while maintaining the use of distillation loss, decouples mask and class predictions in continuous segmentation tasks. ECLIPSE [38] adapts the strategy of VPT [37], freezing the majority of model parameters and providing a set of trainable queries for fine-tuning across different tasks. BalConpas [11] attempts to combat catastrophic forgetting by employing a method that combines feature-based distillation and a replay sample set, aiming to learn new classes without negatively impacting previously acquired knowledge. + +# 3. Preliminary + +# 3.1. Problem Setting + +Following the same continual learning setting in [6], we train our model over $T$ steps. At each step $t$ , the model $\mathcal{M}^t$ has access only to a subset $\mathcal{D}^t = \{\pmb{x}^t, \pmb{y}^t\}$ of the entire dataset $\mathcal{D}^{1:T}$ , where $\pmb{x}^t \in \mathbb{R}^{C \times H \times W}$ denotes the image at the current step and $\pmb{y}^t$ represents the corresponding annotations (where it can only contain annotations for classes $\mathcal{C}^t$ ). This setup, where each stage involves learning different classes, makes the model highly susceptible to catastrophic forgetting as it tends to lose previously acquired knowledge at each training step. Meanwhile, as the same image may appear across different learning steps with entirely different annotations, we also face the issue of so-called background shift [5]. Given these challenges, our objective is to design a model $\mathcal{M}$ such that, at any stage $t$ , the model $\mathcal{M}^t$ not only effectively learns from $\mathcal{D}^t$ but also preserve the previous class knowledge from $\mathcal{D}^{1:t-1}$ . + +# 3.2. Mask2Former + +We leverage Mask2former [17] as our meta-architecture for image segmentation. Mask2Former is a transformer-based model, which predicts a set of binary masks instead of per-pixel classification, for universal segmentation tasks. It primarily consists of three components: 1) An image encoder as backbone $f_{\mathrm{backbone}}$ to extract image embeddings. 2) A pixel decoder $f_{\mathrm{pixel}}$ to embed image embeddings to multiscale pixel features, which we denote as $F$ : + +$$ +F = \left\{\mathcal {F} _ {(l, h, w)} \mid \forall (l, h, w) \in \Omega \right\}, \mathcal {F} \in \mathbb {R} ^ {D \times H _ {l} \times W _ {l}}, \tag {1} +$$ + +where $l$ denotes the multi-scale layer, $D$ represents the hidden dimension, $\mathcal{F}_{(l,h,w)}$ refers to the feature point at po + +![](images/9ea38782e28b3fd09678c9c6249205022506b97357ecdc344e89ca5c2efab5fd.jpg) +Figure 4. The Overall Architecture of our SimCIS: a lazy Query Pre-Alignment (Sec 4.1) with a Consistent Selection loss (Sec 4.2) to ensure built-in objectness inner and across stages, and Virtual Query (Sec 4.3) to avoid catastrophic forgetting in class prediction. + +sition $(h,w)$ on the $l$ -th layer and $\Omega$ represents the spatial set of multi-scale features. 3) A transformer decoder $f_{\mathrm{decoder}}$ takes $N$ learnable queries $Q_{N} = \{q_{1},q_{2},\ldots ,q_{N}\} \in \mathbb{R}^{N\times D}$ with positional encodings $e_{pos}\in \mathbb{R}^{N\times D}$ to first conduct cross-attention and then self-attention with $\mathcal{F}$ as follows: + +$$ +Q _ {N} ^ {\prime} = \operatorname {F F N} (\operatorname {S A} (\operatorname {C A} (Q _ {N} + e _ {p o s}, F))), \tag {2} +$$ + +where $\mathrm{CA}(\cdot)$ denotes the cross-attention, $\mathrm{SA}(\cdot)$ represents self-attention, and $Q_N'$ denotes the updated query feature. The final prediction for each query is $Z_N = \{(c_i, m_i)\}_{i=1}^N$ , where $c_i \in \mathbb{R}^C$ and $m_i \in \mathbb{R}^{H \times W}$ represent the predicted class and mask for $q_i$ , respectively. + +# 4. Method + +In this section, we introduce the overall architecture of our proposed SimCIS model for continual image segmentation. As shown in Fig 4, SimCIS contains three modules: 1) Lazy Query Pre-alignment (Sec 4.1), 2) Consistent Selection Loss (Sec 4.2) and Virtual Query (Sec 4.3). + +# 4.1. Lazy Query Pre-alignment + +To preserve the objectness across continual learning stages, we propose to pre-align the object query $Q_{N}$ with semantic priors in the pixel feature $\mathcal{F}_{(l,h,w)}$ by directly initializing query feature with the most semantically significant pixel feature. To determine the semantic score of each pixel feature, we learn a prototype for each category and select pixel features as initial features by calculating the similarity between the pixel feature and each prototype. + +Specifically, for each training step $t$ , we maintain a set of trainable prototypes $\{p^i \mid i \in C^t\}$ , $p^i \in \mathbb{R}^D$ for each + +class in $C^t$ . By concatenating the prototypes of the past step, $\mathcal{P}^{t - 1}$ , with those of the current classes, we obtain the current prototype set $\mathcal{P}^t$ as follows, + +$$ +\mathcal {P} ^ {t} = \operatorname {c o n c a t} \left(\mathcal {P} ^ {t - 1}, \left\{p ^ {i} \mid i \in C ^ {t} \right\}\right). \tag {3} +$$ + +Then for each feature point on $F$ , we compute its similarity with $\mathcal{P}^t$ to select the best feature points. The selection process is as follows: + +$$ +\mathcal {I} ^ {t} = \operatorname {t o p K} \left(\left\{\max S \left(\mathcal {F} _ {(l, h, w)} ^ {t}, \mathcal {P} ^ {t}\right) \mid \forall (l, h, w) \in \Omega \right\}, N\right), \tag {4} +$$ + +$$ +Q _ {N} = \mathcal {E} _ {m = t} ^ {n = t} = \left\{\mathcal {F} _ {i} ^ {m = t} \mid i \in \mathcal {I} ^ {n = t} \right\}, \tag {5} +$$ + +where $\mathcal{I} = \{(l_i, h_i, w_i)\}_{i=0}^N \in \Omega$ represents the spatial positions of the selected feature points, $\mathcal{E}_m^n$ represents the feature points from $\mathcal{F}^m$ selected by $\mathcal{I}^n$ and $S(\cdot)$ denotes the similarity calculation by dot product. The topK $(X,Y)$ function returns the indices of the $Y$ largest values in $X$ and $N$ is the number of object query $Q_N$ . We select $N$ feature points with the highest similarity with the prototype to initialize $Q_N$ . To supervise our selection process, we use a classification loss during training and update $\mathcal{P}^t$ through backpropagation [51]. Additionally, we apply stop gradient on $Q_N$ to ensure that the information in $F$ is not disrupted during training, keeping the objectness information stable across different stages. + +# 4.2. Consistent Selection Loss + +To ensure selection $\mathcal{I}$ is stable for the same image across stages, we propose a consistent selection loss. Specifically, when training our model $\mathcal{M}^t$ at current stage, we can easily obtain feature points $\mathcal{E}_t^{t-1} = \{\mathcal{F}_i^t \mid i \in \mathcal{I}^{t-1}\}$ . Then, + +to maintain consistency in object selection across different steps, we calculate the similarity between selected feature points with $\mathcal{P}^{t - 1}$ , after that, we use the Kullback-Leibler (KL) divergence loss [32] to compute the loss: + +$$ +L _ {c s l} = \frac {1}{\left| \mathcal {I} ^ {t - 1} \right|} \sum_ {i = 1} ^ {\left| \mathcal {I} ^ {t - 1} \right|} S \left(\mathcal {E} _ {t - 1} ^ {t - 1}, \mathcal {P} ^ {t - 1}\right) \log \frac {S \left(\mathcal {E} _ {t - 1} ^ {t - 1} , \mathcal {P} ^ {t - 1}\right)}{S \left(\mathcal {E} _ {t} ^ {t - 1} , \mathcal {P} ^ {t - 1}\right)}. \tag {6} +$$ + +In this way, we successfully maintain the most semantically significant locations from the previous stage, ensuring that the selection of $Q_{N}$ remains stable across stages. + +# 4.3. Virtual Query + +To overcome catastrophic forgetting in class prediction, we propose the virtual query to bypass the limitations of previous methods that rely on data order. Virtual Query replays the previous query feature in the decoder layer to simulate semantics. Specifically, our innovative virtual query strategy can be divided into three steps: Firstly, we use the results of bipartite matching to select object queries and build our VQ bank. Then we analyze the pseudo-distribution to focus on rare categories in the current stage. Finally, we sample VQs in the new stage according to the pseudodistribution and concatenate them into the object query $Q_{N}$ for input into the decoder. + +(1) Query Storage. During training, we maintain a queue of length $h$ for each class, forming our virtual query bank + +$$ +\mathcal {B} _ {\mathrm {v q}} = \left\{b _ {1} ^ {h}, b _ {2} ^ {h}, \dots , b _ {| c ^ {1: T} |} ^ {h} \right\}, \tag {7} +$$ + +where $b_{i}^{h}$ represents a queue of length $h$ for class $i$ where $b_{i}^{h}$ is the queue for class $i$ . Queries matched through bipartite matching [3] from the decoder's final layer output, $Z_{N}$ (defined in Sec 3.2), are stored in the appropriate class queues based on their bipartite matching results with ground truth $y$ . + +$$ +\left\{ \begin{array}{l} \mathcal {I} _ {b} = \operatorname {B i p a r t i t e} \left(Z _ {N}, \boldsymbol {y}\right), \\ \mathcal {B} _ {\mathrm {v q}} \leftarrow \underset {\forall i = \left(i _ {q}, i _ {y}\right) \in \mathcal {I} _ {b}} {\text {E n q u e u e}} \left(Q _ {N} \left(i _ {q}\right), b _ {\hat {g} ^ {(i _ {y})}}\right), \end{array} \right. \tag {8} +$$ + +where $N$ denotes the number of queries. The set $\mathcal{I}_b$ consists of tuples, where each tuple $i = (i_q,i_y)$ represents the correspondence between query and ground truth. Here, $i_q$ denotes the query index, and $i_y$ denotes the ground truth index. $\hat{y}^i$ represents the class label of the $i^{th}$ ground truth. + +(2) Pseudo-Distribution Statistics. In each continual learning step, the category distribution of images changes at each stage. To ensure the decoder retains the category information for all old classes, we use the pre-trained last-stage model $\mathcal{M}^{t - 1}$ 's outputs on current stage's dataset $D^t$ to simulate the distribution of real classes which helps mitigate the forgetting of rare classes in the current stage. We use this pseudo-distribution statistics by calculating + +$$ +\omega = \left\{ \right.\left(\sum_ {i = 1} ^ {m} \sigma_ {i}\right) / \sigma_ {j}\left. \right) _ {j = 1} ^ {\frac {1}{2}} \left. \right\} _ {j = 1} ^ {m}, \tag {9} +$$ + +where $\sigma_{i}$ is the pseudo number of class $i$ in the current stage and $m = |c^{1:t - 1}|$ represents the number of categories from the previous stages. + +(3) VQ Utilization. Based on the pseudo-distribution statistics, in each iteration, we sample $j$ virtual queries $Q_{j} = \{vq_{1},\dots ,vq_{j}\}$ for each batch based on $\omega$ . These queries are then concatenated with $Q_{N}$ as + +$$ +Q _ {N + j} = \left\{q _ {1}, \dots , q _ {N}, v q _ {1}, \dots , v q _ {j} \right\}, \tag {10} +$$ + +and fed into the decoder. As shown in Fig 4, within the decoder, we design a skip attention strategy for the VQs. Specifically, since the objects represented by the VQs do not appear in the image, to prevent the VQs from influencing $Q_{N}$ during the self-attention and cross-attention processes, we allow the VQs to bypass the attention layers and directly affect the FFN layers as follows: + +$$ +Q _ {N + j} ^ {\prime} = \operatorname {F F N} (\operatorname {c o n c a t} [ \mathrm {C A} (S A (Q _ {N} + e _ {p o s}, F)), Q _ {j} ]). \tag {11} +$$ + +Finally, the virtual query only computes $L_{\mathrm{class}}$ to address the model's category forgetting. + +# 5. Experiments + +# 5.1. Experimental Setup + +Dataset and Evaluation Metric. Following previous works [6, 11, 38], we compare our SimCIS with other approaches using the ADE20K dataset [80] to evaluate its effectiveness. The images in the dataset include annotations for 150 classes, which are ranked by their total pixel ratios in the whole dataset. Among these 150 classes, 50 amorphous background classes are labeled as "stuff" classes, while 100 discrete object classes are labeled as "thing" classes. Following[6], we use Panoptic Quality (PQ) as the performance metric for continual panoptic segmentation and mean Inter-over-Union (mIoU) for continual semantic segmentation. After incremental learning steps, we report results for base classes $(\mathcal{C}^1)$ , new classes $(\mathcal{C}^{2:T})$ , all classes $(\mathcal{C}^{1:T})$ , and an average of all visible classes at each step (avg), respectively. + +Continual Learning Protocol. Following existing continual segmentation methods [5-7, 11, 21, 26, 38], we evaluate our method on different continual learning settings. In particular, our incremental learning tasks are represented in the form of $A-B$ , where $A$ denotes the number of base classes partitioned from the dataset, and $B$ denotes the number of new classes. For both continual panoptic (CPS) and semantic segmentation (CSS), we conduct tasks of 100 - 5, 100 - + +
Method100-5 (11 tasks)100-10 (6 tasks)100-50 (2 tasks)
1-100101-150allavg1-100101-150allavg1-100101-150allavg
FT0.02.20.74.70.04.81.68.90.032.410.826.8
MiB [5]2.30.01.513.46.80.24.619.123.314.920.531.7
PLOP [21]31.111.924.731.337.723.332.937.842.423.736.239.5
SSUL [7]30.27.922.827.931.611.925.030.335.918.130.033.8
CoMFormer [6]34.415.928.234.036.017.129.735.341.127.736.738.8
BalConpas [11]36.120.330.835.840.722.834.738.842.825.737.140.0
ECLIPSE [38]41.116.632.9-41.418.833.9-41.723.535.6-
Our SimCIS42.121.935.438.742.230.138.140.544.730.840.042.7
joint43.634.240.4-43.634.240.4-43.634.240.4-
+ +Table 1. Continual Panoptic Segmentation results on ADE20K dataset in PQ. All methods use the same network of Mask2Former [17] with ResNet-50 [29] backbone. joint means an oracle setting training all classes offline at once. + +
Method50-10 (11 tasks)50-20 (6 tasks)50-50 (3 tasks)
1-5051-150all1-5051-150all1-5051-150all
FT0.01.71.10.04.42.90.012.08.1
MiB [5]34.97.716.838.810.920.242.415.524.4
PLOP [21]39.915.023.343.916.225.445.818.727.7
CoMFormer [6]38.515.623.242.717.225.745.019.327.9
ECLIPSE [38]45.917.326.846.419.628.646.020.729.2
BalConpas [11]44.624.831.449.228.235.251.226.534.7
Our SimCIS48.830.036.351.631.938.552.130.737.9
joint51.135.140.451.135.140.451.135.140.4
+ +Table 2. Continual Panoptic Segmentation results on ADE20K dataset in PQ. All methods use Mask2Former [17] with ResNet-50 [29]. + +10, and 100 - 50. Additionally, we conduct tasks of 50 - 10, 50 - 20, and 50 - 50 for panoptic segmentation. + +Implementation Details. We adapt an pre-trained ResNet-50 [29] backbone for CPS and an pre-trained ResNet-101 for CSS. Following previous work [11], the input image resolution for the CPS tasks is set to $640 \times 640$ , while for the CSS tasks, it is set to $512 \times 512$ . For the number of virtual queries $N$ , it be set up to 80. For more details, please refer to the Appendix. + +# 5.2. Quantitative Results + +Tab 1, Tab 2 and Tab 3 present the performance of SimCIS and other approaches on the continual panoptic segmentation and semantic segmentation benchmark. In these tables, "FT" refers to fine-tuning the base model without employing continual learning methods, while "joint" indicates training the base model using all available data. They represent the lower and upper-performance bounds for continual learning methods, respectively. + +Continual Panoptic Segmentation. Tab 1 and Tab 2 present the performance of SimCIS and other approaches under different continual panoptic segmentation settings. (1) Compared to regularization-based methods MiB [5], PLOP [21], and CoMFormer [6], SimCIS achieves superior + +results on both new and base classes. Notably, compared to CoMFormer, the best-performing among them, SimCIS improves PQ by $+6.0\%$ on new classes and $+7.7\%$ on base classes in the 100 - 5 task, maintaining a consistent lead in the 100 - 10 and 100 - 50 tasks. Especially in the 100 - 10 task, it surpasses CoMFormer by $+6.2\%$ PQ on base and $+13.0\%$ PQ on new classes. When using 50 base classes, SimCIS significantly outperforms these methods, demonstrating its superiority. (2) Compared with the method also using built-in objectness, SimCIS achieves better performance on new classes without freezing the model parameters. In the 100 - 5, 100 - 10, and 100 - 50 tasks, SimCIS outperforms ECLIPSE [38] by $+5.3\%$ PQ, $+11.3\%$ PQ, and $+7.6\%$ PQ, respectively. In the tasks with 50 classes as base classes, SimCIS outperforms ECLIPSE [38] by over $+10\%$ PQ on new classes, demonstrating the stability of our approach. (3) BalConpas [11] is a continual learning method based on the Mask2Former [17] architecture. In the 100 - 10 and 100 - 50 tasks, SimCIS outperforms BalConpas [11] by more than $+5.0\%$ PQ on new classes. In the longer step sequence of the 100 - 5 task, SimCIS surpasses BalConpas [11] by $+6.0\%$ PQ on base classes. In the 50 - 20 and 50 - 50 tasks, SimCIS maintains strong performance, averaging $+4\%$ PQ higher than BalConpas [11] on new + +
Model100-5 (11 tasks)100-10 (6 tasks)100-50 (2 tasks)
1-100101-150allavg1-100101-150allavg1-100101-150allavg
FT0.00.30.15.60.00.10.09.10.03.21.126.3
MiB [5]36.05.726.0-31.814.125.9-37.927.934.6-
PLOP [21]39.17.828.835.340.514.131.636.641.914.932.937.4
SSUL [7]42.917.834.6-42.917.734.5-42.817.534.4-
EWF [68]41.413.432.1-41.516.333.2-41.221.334.6-
CoMFormer [6]39.513.630.936.540.615.632.337.439.526.238.441.2
ECLIPSE [38]43.316.334.2-43.417.434.6-45.021.737.1-
BalConpas [11]42.117.233.841.347.324.238.643.649.930.143.347.4
CoMasTRe [26]40.815.832.638.642.318.434.438.445.726.039.241.6
Our SimCIS46.722.838.747.449.727.442.349.254.936.048.652.0
Joint57.139.151.2-57.139.151.2-57.139.151.2-
+ +Table 3. Continual Semantic Segmentation results on the ADE20K dataset, measured by mIoU. + +
PsdQPACSLVQPanoptic 100-5 (11 tasks)Semantic 100-5 (11 tasks)
1-100101-150all1-100101-150all
✓31.621.328.215.68.513.2
✓✓30.722.327.937.416.730.5
✓✓✓35.724.031.843.217.034.5
✓✓✓35.123.331.242.519.534.8
✓✓✓✓42.121.935.446.722.838.7
+ +Table 4. Ablation Study on Proposed Components. Psd: pseudo label, QPA: lazy query pre-alignment, CSL: consistent selection loss, and VQ: virtual query. + +classes. In the longer step sequence of the 50 - 10 task, SimCIS exceeds BalConpas [11] by $+4.2\%$ PQ on base classes. It is noteworthy that in the 100 - 50 task, SimCIS almost matches the performance of the "joint", with base classes performance even exceeding that of the "joint". + +Continual Semantic Segmentation. As shown in Tab 3, we further compare SimCIS with state-of-the-art works in continual semantic segmentation. (1) Across three tasks, SimCIS surpasses prior approaches by at least $+4\%$ mIoU on base classes. For new classes, it outperforms SSUL [7] by $+5.0\%$ and $+9.7\%$ mIoU in the 100 - 5 and 100 - 10 tasks, respectively. In the 100 - 50 task, SimCIS surpasses MiB [5], which achieves $27.9\%$ mIoU, by $+8.1\%$ mIoU. (2) Among Mask2Former [17]-based methods, SimCIS also achieves the best results. In the 100 - 5 task, it outperforms ECLIPSE [38] on base classes by $+3.4\%$ mIoU and BalConpas [11] on new classes by $+5.6\%$ mIoU. In the 100 - 10 task, SimCIS achieves the performance of new classes exceeding all other architectures by at least $+3.0\%$ mIoU while maintaining high performance on base classes. + +# 5.3. Qualitative Comparison. + +Comparison with Previous SOTAs. We compare SimCIS with BalConpas [11] in the 100 - 5 continual panoptic segmentation task of the ADE20K dataset, and the visual results are illustrated in Fig 5. In the first, second, and fifth examples, BalConpas [11] encounters forgetting on base + +classes such as path, bus, and building. Additionally, in the third example, BalConpas incorrectly classifies the microwave and bag as cabinet and box, respectively. Benefiting from the VQ, our SimCIS has a significant advantage in preserving class information, allowing it to perform well in these examples. Furthermore, BalConpas [11] fails to provide segmentation masks for the bus and refrigerator instances in the second and third examples. In contrast, our proposed the keep built-in objectness strategy effectively preserves object information within the encoder, enabling SimCIS to accurately segment object instances. + +Comparison in Different Steps. To further illustrate the effectiveness of our method, we select certain visual examples from the continual learning steps of the 100 - 5 task. In the two examples shown in Fig 6, our method is able to correct errors during the continual learning steps, such as the microwave and bag in the first image, as well as the sink, vase, and stair in the second image. SimCIS refines itself during the continual learning process, ultimately achieving accurate classification and segmentation of object instances based on our proposed flexible VQ. + +# 5.4. Ablation Study + +In this section, we report the results of the ablation experiments to validate the effectiveness of each component and configuration in our SimCIS. We select the 100 - 5 task in CPS and CSS to report the performance of SimCIS. + +Main Components. As shown in Tab 4, each component contributes to the overall performance. We take Mask2Former [17] with pseudo label as our baseline performance. The second row of the table shows the performance of QPA with an increase of $+18.2\%$ mIoU on base classes and an increase of $+8.2\%$ mIoU on new classes. With the help of CSL (the third row), the CSL strategy achieves increases of $+8.2\%$ PQ and $+5.8\%$ mIoU for base classes, respectively. + +Effectiveness of VQ. As shown in Tab 5, compared to the + +![](images/60a55267bd0bfc1ceb453b86fd48fd25b61128381b80416752b231076a508d32.jpg) +Figure 5. Qualitative comparisons between SimCIS and BalConpas [11] on the ADE20K 100-5 continual panoptic segmentation scenario. Our SimCIS demonstrates significant results, highlighting the effectiveness of our strategies. + +![](images/4c6a776b5e4d0f9d614f59d84c26d55ab8ec58fbaafdb4f4fe4e300a90188a0c.jpg) +Figure 6. Qualitative examples in continual learning. + +
Reply TypeNum SamplesDisk Memory100-5 (11 tasks)
baseall
Image0 (*20)0.0MB35.731.8
75 (*20)3.4MB38.933.4
150 (*20)6.1MB38.934.0
300 (*20)11.8MB38.533.7
600 (*20)21.9MB39.234.3
Virtual Query0 (*150)0.0MB35.731.8
20 (*150)1.5MB40.634.6
40 (*150)3.0MB40.434.1
80 (*150)5.9MB42.135.4
160 (*150)12.0MB40.934.2
+ +conventional image replay method, our VQ strategy demonstrates significant improvements in both storage efficiency and performance. Firstly, when using 300 samples for the image replay and 80 samples for VQ, we achieve a $+1.4\%$ increase in PQ across all classes while using almost the same disk memory. When comparing the optimal cases for both storage methods, our VQ strategy outperforms the conventional image replay method by $+1.1\%$ PQ, while utiliz + +Table 5. Effect of Replay Type and Storage Requirements. + +
Method100-10 (6 tasks)
1-100101-150all
BalConpas [11]38.9(39.4)27.8(26.8)35.2
ECLIPSE [38]32.7(32.1)22.3(23.8)29.3
Ours40.3(40.2)25.4(25.7)35.3
Joint(43.6)(34.2)(40.4)
+ +Table 6. Continual Panoptic Segmentation with random order. We also report the performance evaluated in the original class order in $(\cdot)$ . For detailed experiments, please refer to the Appendix. + +ing only $27\%$ of the storage space. + +Robust to Input Data Order. As shown in Tab 6, our model has great robustness in random data order. We have a $+0.1\%$ PQ increase compared to BalConpas and a $+6.0\%$ PQ increase against ECLIPSE across all classes. + +# 6. Conclusion + +In this work, we present a novel class-incremental image segmentation (CIS) method called SimCIS, which addresses the challenges of catastrophic forgetting and background shift. We first explore the emergence and diminishing of built-in objectness in query-based transformers and then propose two novel modules: lazy query pre-alignment and consistent selection loss, to ensure both intra-stage and cross-stage built-in objectness. 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(a) Quantitative comparison on reconstruction and denoising tasks, highlighting the superior performance of the proposed method across various metrics. (b) Visual comparison with state-of-the-art methods, demonstrating the enhanced clarity and color fidelity of our approach. (c) Flexibility demonstration of the proposed method through seamless integration into other individual reconstruction methods. + +![](images/ff31fa0c8b42c0271ed5116620e66e61baf89468fa27e7ad8043d3ec3261aa1c.jpg) + +![](images/a8f863b7473774abfb24a8975862fe34e804e35867b378e29742f87131d5f41b.jpg) +(c) Flexibility + +# Abstract + +Recently, enhancing image quality in the original RAW domain has garnered significant attention, with denoising and reconstruction emerging as fundamental tasks. Although some works attempt to couple these tasks, they primarily focus on cascade learning while neglecting task associativity within a broader parameter space, leading to suboptimal performance. This work introduces a novel approach by rethinking denoising and reconstruction from a "backbone-head" perspective, leveraging the stronger shared parameter space offered by the backbone, compared to the encoder used in existing works. We derive task-specific heads with fewer parameters to mitigate learning pressure. By incorporating chromaticity-and-noise perception module into the backbone and introducing task-specific supervision during training, we enable simultaneous high-quality results for reconstruction and denoising. Additionally, we design a dual-head interaction module to capture the latent correspondence between the two tasks, significantly enhancing multi-task accuracy. Extensive experiments validate the superiority of the proposed method. Code is available at: https://github.com/csmty/CANS. + +# 1. Introduction + +RAW imaging under extremely dark conditions seeks to reveal hidden details within dark areas [6], thereby enhancing image quality and playing a crucial role in image enhancement [9, 22], semantic understanding [18, 27, 39], cross-modality image analysis [21, 31, 32], and related applications [24, 33]. Compared to image restoration in the RGB domain, RAW-based methods deliver superior results by preserving uncompressed sensor data [12, 16]. In contrast, RGB-based methods inherently suffer from irreversible distortions induced by the Image Signal Processing (ISP) pipeline [2], such as noise amplification and compression artifacts, which introduce additional challenges in learning and optimization [19, 20]. + +# 1.1. Related Works + +Recently, the establishment of the SID benchmark [3] significantly advanced the field by revealing challenges in extremely poor color representation and substantial noise [26]. Since then, various innovations have emerged, including the integration of residual structures [28, 30], the use of multiscale features [7, 29], supervision with perceptual loss [48] and data argumentation [1, 37, 45]. As shown in the top right of Fig. 2, these methods typically rely on a single-task process to produce specific outputs. Unfortunately, single- + +![](images/e84a6bcccd47d596251efc4ad256b8f4d2b08136958f1399164e581338e53c53.jpg) +Figure 2. Illustration of RAW imaging approaches. Left: Standard ISP pipeline. Right, top: Single-task method specialized for specific outputs. Right, middle: Multi-task architecture integrating denoising into reconstruction. Right, bottom: Proposed method formulated in a "backbone-head" perspective to achieve effective denoising and reconstruction simultaneously. + +task methods cannot achieve denoising and reconstruction simultaneously, and they often neglecting the interplay between these tasks, resulting in inherent problems such as residual noise and incorrect color. + +To further advance the effect of denoising and reconstruction, some approaches have adopted a multi-task strategy [17, 41], where denoising is addressed first [44], followed by detail enhancement [40]. As shown in the middle right of Fig. 2, denoising in this pipeline is primarily employed to facilitate reconstruction. For example, methods such as EEM [49], REENet [10], and LDC [38] follow this pipeline to sequentially address the complexities of low-light image processing. More recently, MCR [5] introduced an innovative technique that leverages simulated monochrome RAW data to learn structural textures. Consistent with previous studies [23, 36, 42], the reconstruction of original low-light images is beneficial by leveraging learned texture. DNF [11] similarly connects reconstruction and denoising by integrating denoising features to support the reconstruction process. Such approaches [4, 34] provide deeper insights into individual ISP tasks. However, these methods are computationally intensive and do not achieve an optimal trade-off between the two tasks, as they neglect task relevance within a broader parameter space. + +# 1.2. Our Contributions + +Unlike previous works that address denoising and reconstruction through a divide-and-conquer paradigm, we introduce a novel paradigm for parameter effect learning, termed + +Chromaticity-Aware and Noise-Sensitive (CANS) design. Our contributions are as follows: + +- New Perspective. We propose a novel architecture splitting paradigm, rethinking denoising and reconstruction tasks from a "backbone-head" perspective. By leveraging a shared parameter backbone rather than traditional multi-task learning, we expand the effective parameter space to better accommodate multi-task learning. +- General Architecture. Our framework integrates task-specific heads with a minimal number of parameters, enabling efficient specialization without heavy training overhead. Furthermore, integrating chromaticity-and-noise perception module into the backbone design effectively counteracts RAW-specific degradations. +- Mutual-Promotion Mechanism. To enhance task associativity, we introduce a mutual-promotion mechanism that captures latent correspondence between denoising and reconstruction, termed CANS++. Central to this is a dual-head interaction module, which fosters mutual learning and markedly enhances performance across both tasks. +- Comprehensive Evaluations. We conduct extensive evaluations across diverse datasets, including standard benchmarks and scenarios captured by smartphones. Downstream perceptual tasks such as depth estimation and segmentation further demonstrate the adaptability and effectiveness of our approach in real-world applications. + +# 2. Backbone-Head Perspective + +In this section, we examine the relationship between the de-noising and reconstruction tasks and introduce a backbonehead perspective to elucidate both. Subsequently, we propose a general architecture and learning strategy for these tasks within this framework. The schematic diagram of the proposed CANS is presented in the bottom right of Fig. 2. + +# 2.1. Rethinking Denoising and Reconstruction + +Traditional RAW image processing follows a "divide-and-conque" paradigm, treating denoising and reconstruction as separate sequential stages. Typically, sensor noise is first removed by a denoising network, followed by reconstruction to generate the final RGB image. This design assumes a unidirectional dependency, denoising serves reconstruction, thus overlooking their intrinsic equivalence and complementarity in both physical signal recovery and visual perception. For instance, denoising provides cleaner intermediate features for reconstruction, while reconstruction's understanding of color space and semantics can guide denoising to avoid over-smoothing and detail loss. Furthermore, this pipeline overlooks potential correlations in the feature space. Denoising involves modeling the boundary between noise and signal distributions, whereas reconstruction requires learning cross-channel local correlations and global color mapping. As a result, independently trained + +models often extract similar low-level features (e.g., noise patterns, and cross-channel correlations) from RAW data, leading to computational redundancy and hindering effective cross-task knowledge sharing. + +Given that denoising and reconstruction play equally critical and complementary roles in both physical signal recovery and visual perception mapping, their joint optimization for end-to-end synergy may yield superior performance. Notably, this equivalence and complementarity reflect the backbone-head architecture commonly employed in high-level visual tasks. For example, in object detection, the backbone network typically extracts shared features for both the classification head and the localization head. Then, a straightforward idea is to extract shared backbone features that enhance both tasks within a broader learning space. And task-specific heads can then jointly process features, thereby avoiding redundant computations and feature partitioning. In this context, a unified backbone network with dual task heads not only circumvents the error accumulation inherent in traditional serial pipelines but also enables the network to learn a generalized representation that integrates both chromaticity-aware and noise-sensitive features through joint training and gradient back-propagation. + +# 2.2. Architecture Design + +Building on this foundation, we design a U-shaped backbone integrated with the Chromaticity-and-Noise Perception Module to refine visual representations via two core components: the Global Chromatic Perceptor (GCP) and the Refined Detail Extractor (RDE). As illustrated in Fig. 3, the GCP captures overall color patterns to provide a comprehensive view of global chromatic information. We introduce the global chromatic perception attention, which employs pooling to downsample spatial dimensions, thereby enabling extensive color perception while reducing computational complexity. Meanwhile, the RDE uses spatial gating to preserve fine-grained local details. Together, these components achieve a balanced approach that captures both global color distribution and intricate details, resulting in improved feature representation for complex visual tasks. + +Given the distinct characteristics of the denoising and reconstruction tasks, the head network adopts a lightweight, task-sensitive modular design. Based on the common features extracted by the shared backbone network, task adaptation is achieved through dedicated operations with minimal computational overhead. Both heads employ convolution operations; however, for the reconstruction head, image resolution is enhanced through the use of Pixel Shuffle. + +# 2.3. Learning Strategy + +By jointly optimizing within a unified feature space, the model reformulates the previously distinct tasks of physical restoration and visual mapping into mutually constrained, + +![](images/a84daab122720e7045cd07d56d8a4d775ba77bb8213a2b494c3fd9c6038ea364.jpg) +Figure 3. Architecture of the proposed chromaticity-and-noise perception module. + +co-evolving processes. Based on these considerations, this strategy achieves a better balance among noise suppression, detail preservation, and color reconstruction. Denoising and reconstruction processes are integrated into a unified architecture in this framework. Specifically, parameters $\theta_{\mathrm{n}}$ and $\theta_{\mathrm{m}}$ are introduced to adaptively focus on the denoising head and the reconstruction head, respectively, under the guidance of backbone parameters $\theta_{\mathrm{b}}$ . The learning objective is: + +$$ +\min _ {\boldsymbol {\theta} _ {\mathrm {b}}, \boldsymbol {\theta} _ {\mathrm {m}}, \boldsymbol {\theta} _ {\mathrm {n}}} \mathcal {L} _ {\text {d e n}} (\mathbf {x}; \boldsymbol {\theta} _ {\mathrm {b}}, \boldsymbol {\theta} _ {\mathrm {n}} (\boldsymbol {\theta} _ {\mathrm {b}})) + \mathcal {L} _ {\text {r e c}} (\mathbf {x}; \boldsymbol {\theta} _ {\mathrm {b}}, \boldsymbol {\theta} _ {\mathrm {m}} (\boldsymbol {\theta} _ {\mathrm {b}})). \tag {1} +$$ + +This learning constraint enables the model to dynamically allocate resources according to the task-specific requirements of the output, thereby effectively managing both denoising and reconstruction within a single optimization framework. In this architecture, $\theta_{\mathrm{n}}$ or $\theta_{\mathrm{m}}$ can be completely discarded during testing, without incurring any additional computational burden compared with single-task methods. + +# 3. Mutual-Promotion Mechanism + +# 3.1. Motivation + +The proposed CANS network decomposes denoising and reconstruction into distinct functional modules, enabling targeted optimization for low-light RAW imaging process. While multi-task methods offer refined restoration at high computational costs and single-task methods prioritize efficiency but struggle with task balancing, CANS bridges this gap, achieving single-task efficiency with performance comparable to multi-task approaches by focusing on color and detail processing through dedicated modules. + +The learning phase optimizes image quality while maintaining efficiency. The loss function integrates denoising and reconstruction losses, aligning with noise reduction + +and image restoration objectives. Parameter decomposition $\{\theta_{\mathrm{b}},\theta_{\mathrm{n}},\theta_{\mathrm{m}}\}$ embodies multi-objective learning, allowing task-specific parameter groups to be jointly optimized for adaptive performance across tasks. Challenges remain due to the competing nature of denoising and color restoration. Excessive focus on one task can compromise the other, and the additional parameters in the multi-objective framework increase model complexity, complicating hyperparameter tuning and raising training costs. + +# 3.2. Dual-Head Interaction via Cross Attention + +In the multi-objective learning process, balancing denoising and reconstruction presents a significant challenge due to inherent conflicts in optimization directions. Traditional multi-objective loss weighting strategies often struggle with such tasks, leading to instability or increased computational demands. To overcome these limitations, we propose a dual-head interaction module to facilitate dynamic information exchange and adaptive adjustment between the denoising and reconstruction tasks. This mechanism introduces additional interaction parameters $\theta_{\mathrm{c}}$ , enabling parameter sharing and task-specific adaptation. By leveraging cross-attention, the model dynamically aligns task priorities, balancing weights between denoising and reconstruction to mitigate conflicts and improve stability. This enhanced design, denoted as CANS++, outperforms traditional approaches by promoting collaborative optimization while preserving task-specific goals. + +The dual-head interaction mechanism operates by integrating shared base features $\theta_{\mathrm{b}}$ with task-specific parameters $\{\theta_{\mathrm{c}},\theta_{\mathrm{m}},\theta_{\mathrm{n}}\}$ to generate distinct representations for key, value, and query features. Specifically, the shared key $\mathbf{K}$ and value $\mathbf{V}$ features are generated using the interaction parameter $\theta_{\mathrm{c}}$ , while task-specific queries $(\mathbf{Q}_{\mathrm{r}}$ for reconstruction head and $\mathbf{Q}_{\mathrm{d}}$ for denoising head) are computed using $\theta_{\mathrm{m}}$ and $\theta_{\mathrm{n}}$ , respectively. This dual-head interaction design ensures that shared features are effectively utilized while maintaining the independence of task-specific feature spaces, enabling robust cross-domain information fusion. + +Table 1 and Fig. 4 summarize the results for different strategies. In the single-task approach, the absence of RAW denoising supervision leads to suboptimal reconstructions by exacerbating domain ambiguity [11]. By contrast, multitask strategies mitigate these issues and enable information propagation across stages. Under the "backbone-head" perspective, the expanded shared parameter space provides superior results and reduces the learning burden for specific tasks. Furthermore, integrating cross-attention into different heads improves stability and performance, effectively handling joint optimization challenges and advancing multi-objective visual task processing. + +![](images/5ced37fcfbbfd9d984a81c7578cc66c447ba3903ffe67baa2722701dceaa932e.jpg) + +![](images/9c49ae5fc79888116bff828866e6d7fcfd9ce5b4cf8817cf8ab647f8807fbd50.jpg) + +![](images/ef9e7c2b9b947b7d26459ea60ac1ad58873d91321d923ab145032506567d45f4.jpg) + +![](images/f72ccb06f3082c06a457666dc2153697a1ce5e72c5dd6832b0e79a811f9e589d.jpg) +Figure 4. Visual comparison of different strategy. + +![](images/8afa291c0a398f886013285c403399f07f4d0db76a0fb80d8d0f4d31d69adb8c.jpg) + +![](images/ddd8c48d5b63537fbfc81c6b1176cd9f3fa06ec43dd39450de6f720aba0d5a38.jpg) + +
StrategyPSNR↑SSIM↑LPIPS↓
Single30.4600.7970.167
Multi30.6070.7960.165
CANS30.6580.7980.164
CANS++30.8560.7990.163
+ +Table 1. Comparison of different strategy. Every strategy are conducted based on our backbone to make sure the fairness. + +# 4. Experiments + +# 4.1. Implementation Details + +We evaluated our approach on three benchmark datasets: SID [3] (including Sony subset and Fuji subset), MCR [5], and LRD [47], created by adjusting camera settings to capture paired low-exposure and normal-exposure images. For reconstruction, we compared our proposed method with several state-of-the-art approaches, including SID [3], DID [28], SGN [8], LLP [15], RRT [14], EEM [49], MCR [5], BGL [25], and DNF [11]. For denoising, we selected SID [3], ELD [35], LRD [47], and DNF [11] as comparison methods. The proposed method was implemented with the PyTorch framework on a single NVIDIA GTX 4090 GPU. Both $\mathcal{L}_{\mathrm{den}}$ and $\mathcal{L}_{\mathrm{rec}}$ , defined using the $\ell_1$ loss function, have been assigned loss coefficients of 1. + +# 4.2. Reconstruction Comparisons + +Quantitative Evaluation. As shown in Table 2 and Table 3, our proposed CANS and $\mathrm{CANS}++$ achieve notable improvement on all of these metrics. On all the datasets, our approach achieved the best PSNR, SSIM, LPIPS and DISTS scores, significantly improving the performance compared with the previous state-of-the-art methods and especially surpassing them by a large margin of $0.972\mathrm{dB}$ in terms of PSNR metric on MCR dataset. Additionally, Table 4 presents the Floating Point Operations (FLOPs) of various methods, with CANS and $\mathrm{CANS}++$ exhibiting lower FLOPs to ensure computational efficiency. + +Qualitative Evaluation. Fig. 5 shows the visual comparison on Sony dataset, and Fig. 6 further indicates the visual comparison effects on Fuji and LRD dataset. Across all images, CANS and $\mathrm{CANS + + }$ consistently deliver sharper and more detailed reconstructions than other methods. The + +![](images/6ae96b454a3bfcdf89cb7065143328349912653b413f1d16578d8334f72dc63c.jpg) + +![](images/2ce28a7c1d40efb9d6bbd560f056fc27317a165afafbdd4ae8e7d0bdc012024b.jpg) +Figure 5. Visual comparison of state-of-the-art methods for reconstruction and denoising on the Sony dataset, with PSNR/SSIM scores shown below each result. "Input" denotes the low-light RAW image, and "GT" is the ground truth. + +(a) Reconstruction + +
MethodPSNR↑SSIM↑LPIPS↓DISTS↓FSIM↑
SID28.9330.7850.1720.1480.956
DID28.4460.7830.1790.1650.952
SGN29.0070.7870.1730.1470.956
LLP28.2110.7770.1940.1680.952
RRT28.6850.7760.1810.1700.952
EEM29.5530.7950.1710.1390.961
MCR29.7440.7890.1720.1480.957
BGL29.5280.7890.1710.1400.960
DNF30.6160.7970.1690.1360.964
CANS30.6580.7980.1640.1340.965
CANS++30.8560.7990.1630.1290.965
+ +(b) Denoising + +
RatioMetricSIDLRDELDDNFCANSCANS++
×100PSNR↑40.53542.50441.25942.12742.13742.373
SSIM↑0.9510.9580.9570.9570.9590.960
LPIPS↓0.1720.1760.1690.1790.1700.176
×250PSNR↑39.16039.69739.25639.49640.23140.503
SSIM↑0.9410.9410.9410.9430.9450.947
LPIPS↓0.1920.2000.1980.1960.1880.192
×300PSNR↑36.51636.37736.21736.97137.44237.548
SSIM↑0.9240.9190.9250.9290.9310.933
LPIPS↓0.2190.2320.2220.2180.2100.211
AveragePSNR↑38.73739.52638.91139.53139.93740.141
SSIM↑0.9390.9390.9410.9430.9450.947
LPIPS↓0.1940.2030.1960.1980.1890.193
+ +Table 2. Quantitative comparison on the Sony dataset for both reconstruction and denoising tasks. (a) Reconstruction: Performance comparison of various methods based on PSNR, SSIM, LPIPS, DISTS, and FSIM metrics. (b) Denoising: Evaluation across different exposure ratios ( $\times 100$ , $\times 250$ , $\times 300$ ) using PSNR, SSIM, and LPIPS metrics. The best and second performance for each metric is highlighted in red and blue, respectively. + +PSNR and SSIM metrics at the bottom of each comparison section reflect the quantitative superiority of CANS and $\mathrm{CANS + + }$ . In both the darker and well-lit images, $\mathrm{CANS + + }$ shows the highest PSNR/SSIM scores, indicating better reconstruction quality and structural similarity to the ground truth. In Fig. 7, CANS and $\mathrm{CANS + + }$ outperform MCR and DNF in terms of structural clarity, especially in complex areas like the windows and reflections on the floor. The histograms for each color channel further indicate the better color distribution of the proposed method. + +# 4.3. Denoising Comparisons + +Quantitative Evaluation. As shown in Table 2, our proposed method demonstrates superior performance across all noise levels. In particular, $\mathrm{CANS}++$ consistently achieves the highest PSNR and SSIM values, highlighting its effectiveness in preserving detail and overall image quality. + +At lower noise levels ( $\times 100$ ), although all methods perform well, CANS++ stands out by achieving the best metrics. As the noise increases ( $\times 250$ and $\times 300$ ), both CANS and CANS++ maintain their high performance, while other methods (e.g., SID and LRD) exhibit a more significant drop in SSIM and PSNR. These results underscore the robustness of CANS++ across a range of noise intensities. + +Qualitative Evaluation. As shown in Fig. 5, CANS and $\mathrm{CANS}++$ achieve superior denoising, particularly in the highlighted text area. $\mathrm{CANS}++$ offers a sharper result than CANS, while other methods introduce artifacts or blur, reducing text clarity. CANS and $\mathrm{CANS}++$ also maintain better color accuracy, notably in orange and white regions, whereas methods like ELD and DNF display slight color distortions, lowering perceptual quality. $\mathrm{CANS}++$ ’s colors closely match the ground truth, indicating effective color preservation. In Fig. 8, $\mathrm{CANS}++$ provides the cleanest out- + +
DatasetMetricSIDDIDSGNLLPRRTMCRDNFCANSCANS++
FujiPSNR ↑26.67326.55726.50826.23226.41327.20628.69828.72728.887
SSIM ↑0.7100.7120.7050.7060.7080.7110.7270.7260.728
LPIPS ↓0.2160.2250.2180.2410.2280.2240.2070.2050.204
DISTS ↓0.1670.2010.1870.1920.1860.1820.1520.1500.149
FSIM ↑0.9400.9370.9240.9360.9360.9270.9520.9520.953
MCRPSNR ↑29.00126.03426.65026.47327.49632.11832.00732.62333.090
SSIM ↑0.9010.8810.8900.8480.8560.9130.9140.9130.916
LPIPS ↓0.04900.05620.05050.08960.07650.04860.04690.04620.0457
DISTS ↓0.06410.07740.07260.09160.08990.05270.05270.05430.0526
FSIM ↑0.9600.9510.9500.9490.9470.9750.9730.9730.974
LRDPSNR ↑29.85429.63929.73828.72129.52530.21030.85330.92031.106
SSIM ↑0.8510.8490.8490.8130.8330.8490.8530.8540.855
LPIPS ↓0.1210.1310.1280.1590.1470.1260.1220.1220.120
DISTS ↓0.07570.08410.08580.10210.09030.07340.07000.07280.0682
FSIM ↑0.9840.9840.9840.9810.9830.9860.9870.9870.988
+ +Table 3. Quantitative comparison on the Fuji, MCR and LRD datasets. + +
17.3667/0.1313SID +Packag +r MaterDID +Packag +r MaterSGN +Packag +r MaterSID +RRTDID +SGN
33.4152/0.905433.4678/0.905034.1020/0.905831.6423/0.878432.1619/0.875131.8504/0.8761
LLP +Packag +r MaterRRT +Packag +r MaterMCR +Packag +r MaterLLPRRTMCR
32.4308/0.895432.9474/0.897933.3521/0.897129.9663/0.837432.0685/0.860433.4889/0.8776
DNF +Packag +r MaterCANS +Packag +r MaterCANS++ +Packag +r MaterDNFCANSCANS++
PSNR/SSIM35.6678/0.915035.9117/0.916435.9637/0.916333.6186/0.880134.0890/0.882034.3066/0.8808PSNR/SSIM
+ +![](images/bc45fa75fc11ed97befa24e7bc1c4f349528b6903b306a0b7144d90ad84575ad.jpg) +Figure 7. Visual comparison of state-of-the-art reconstruction methods on the MCR dataset. RGB histograms below each image depict color distribution, and the bottom row displays zoomed-in views of highlighted regions to demonstrate detail restoration. + +Figure 6. Visual comparison on the Fuji (left) and LRD (right) datasets among state-of-the-art reconstruction approaches. + +
MetricEEMSGNBGLSIDDNFCANSCANS++
FLOPs (G)715.668.6964.4648.3959.9639.3440.66
Param. (M)40.75.657.777.762.834.924.93
+ +put, with error distribution graphs showing minimal noise and detail loss, closely aligning with the ground truth. + +Table 4. The FLOPs and model parameters of different reconstruction methods and two versions of our proposed methods. + +
EncoderDecoderMetrics
RDEGCPRDEGCPPSNR↑SSIM↑LPIPS↓
✓✓29.0090.7780.177
✓✓29.8790.7950.177
✓✓30.4010.7940.167
✓✓✓✓30.5280.7960.166
△△✓30.6030.7960.163
✓✓○30.7140.7970.163
✓✓✓30.8560.7990.163
+ +Table 5. Ablation study on the backbone structure of the proposed method. $\checkmark$ signifies that the corresponding module is adopted in the backbone. $\triangle$ indicates replacement of the corresponding module by CID [11]. $\bigcirc$ denotes replacement of the corresponding module by Restormer Attn [46]. + +# 4.4. Ablation Studies + +Structural Ablation. We evaluate our structure by systematically removing or substituting specific modules with alternatives from our method or other approaches with similar parameters. As shown in Table 5, removing the GCP mod + +![](images/443f4d2a27a2be2d69b46a0db44f6561c4e48f1adaf36e50b9d300cefdf9d6b9.jpg) +Figure 8. Visual comparison of denoising methods on a noisy input image. The top row shows denoised images with a red line indicating the pixel profile location. The bottom row displays pixel intensity profiles, with the ground truth in red and denoised results in blue. + +![](images/05dd0cb2dbac0c58d090f87d172c8d19c1319d44844df09833fd6f0344e4d39f.jpg) + +![](images/eabe8217cf56968cb09f378355a8c73395c4ecde4aa81d45adc5c7ca4f6db5a7.jpg) + +![](images/eca1c94e6f28ced0ded40e07873eddba474b242ec16fc7980f6c455374da55d4.jpg) + +![](images/6d4f4e66c4aff71c5f82c43643eae64472713c6fcc618f890b5d01999c6e8f4e.jpg) + +![](images/54b2016daa7eb37dcf027ad264c007beb5e59a485ba734315a5aa4ab7d85f1aa.jpg) + +
MethodAdaptive SizePSNR↑SSIM↑LPIPS↓
CANS++130.68510.79860.1678
230.85590.79940.1671
430.61640.79740.1679
830.57660.79640.1688
1630.56170.79840.1679
Original29.85820.79350.1726
+ +Table 6. Ablation study on the pooling size in the global chromatic perception attention. + +ule reduces PSNR by 0.977 dB, while removing the RDE module causes a 1.847 dB drop, highlighting the importance of both color correction and denoising in low-light RAW reconstruction. Including the GCP module in the encoder decreases performance, confirming the encoder's focus on denoising and the decoder's role in color correction. Similarly, removing the GCP module from the decoder impairs detail reconstruction. Compared to state-of-the-art methods, our module outperforms alternatives like the CID Block [11] (denoising, -0.253 dB PSNR) and the Restormer Attention [46] (color correction, -0.142 dB PSNR). + +Chromatic Attention Ablation. We explain the rationale for selecting an adaptive size that matches the RAW format's block size. Experiments based on our CANS++ model were conducted to assess performance across a range of adaptive sizes. Table 6 illustrates the performance impact of varying the adaptive size in average pooling. Notably, aside from when the adaptive size is 2, increasing the adaptive size generally leads to a decline in performance. In contrast, setting the adaptive size equal to the RAW block size yields optimal results (e.g., 2 for the Sony subset and 3 for the Fuji subset), likely due to enhanced aggregation of color information critical for accurate color restoration. + +# 5. Analyses + +# 5.1. Mechanism Flexibility + +In this part, we extend our approach to other individual reconstruction methods. As shown in Fig. 9, both CANS and + +![](images/a57dd9e6c27c71f53012ff65dd152c08a2f4ba796819900f9cac7b2100d0555b.jpg) +Figure 9. Flexibility of the proposed method demonstrated on SGN and SID models. + +![](images/8005e0b9038abe96188170520b9644d7a9bb78b685c75cac653047eef9d0aeff.jpg) + +![](images/0007b4e45158cf3e68d952b20b9ef621497b6115fd69bb6633ed06c85a48f1a1.jpg) + +CANS++ improve the performance of two representative works. Specifically, CANS achieves notable gains without incurring additional computational burden, while CANS++ delivers significant improvements of 0.921 dB in SID and 0.849 dB in SGN, surpassing most existing methods with under a $3\%$ increase in computational complexity. + +# 5.2. Downstream Applications + +To comprehensively evaluate enhancement performance, we assess the impact of different methods on high-level tasks such as depth estimation and segmentation, shown in Fig. 10. Depth estimation is performed using Depth Anything [43], and segmentation utilizes Segment Anything [13], with pseudo ground truth labels derived from low-light RAW enhancement ground truth. The noisy RAW input poses significant challenges, blurring object outlines and introducing ambiguity for downstream tasks. However, our approach effectively preserves high-frequency details, delivering superior results in both depth estimation and segmentation compared to alternative methods. + +# 5.3. Scenario Generalization + +Fig. 11 displays a selection of low-light RAW images captured from real-world scenarios, intended to evaluate the generalization capabilities of different models. To ensure + +![](images/91efcd5b26d6633df72186e32eecc698079a911f612ded254d7304c02c39c337.jpg) +Figure 10. Visual comparison of depth estimation and segmentation tasks. + +![](images/bb0cdad4e7690ed46c2f1c42c5f7520c9f61244b182f53bc33def04eb06adf34.jpg) +Figure 11. Additional evaluation on low-light scenarios captured by four different smartphones. + +fairness, we employed the model pretrained on the SID-Sony dataset and converted the RAW images into RGBG format. To comprehensively evaluate various methods, we selected four different smartphones equipped with diverse sensors. Notably, our proposed method outperforms competing approaches for low-light RAW reconstruction across all tested devices, delivering superior noise reduction, detail preservation, and color fidelity. + +# 6. Conclusion + +In this work, we revisit the tasks of reconstruction and denoising in the RAW domain from a "backbone-head" perspective, addressing the limitations of prior multi-task methods that fail to fully exploit inter-task correlations. By integrating chromaticity-and-noise perception module into the backbone and introducing task-specific supervision, our + +method effectively suppresses noise while preserving crucial image details. Furthermore, the proposed dual-head interaction module fully leverages the synergy between denoising and reconstruction, resulting in improved performance and efficiency. Extensive experiments demonstrated the superiority of our proposed method. + +Acknowledgments. This work is partially supported by the National Natural Science Foundation of China (Nos. 62450072, U22B2052), Central Guidance for Local Science and Technology Development Fund (Youth Science Fund Project, Category A, No. 2025JH6/101100001), the Distinguished Young Scholars Funds of Dalian (No. 2024RJ002), China Postdoctoral Science Foundation (No. 2023M740491), Postdoctoral Fellowship Program of CPSF (No. GZB20240098), Dalian Science and Technology Innovation Fund-Young Tech Star (No. 2023RQ017), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Tim Brooks, Ben Mildenhall, Tianfan Xue, Jiawen Chen, Dillon Sharlet, and Jonathan T Barron. Unprocessing images for learned raw denoising. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11036-11045, 2019. 1 +[2] Mark Buckler, Suren Jayasuriya, and Adrian Sampson. 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However, a notable performance gap remains between existing spiking Transformers and their artificial neural network counterparts. Here, we first analyze the cause of this gap and attribute it to the dot product's ineffectiveness in measuring similarity between spiking queries and keys, due to numerous non-spiking events. To address this, we propose a novel $\alpha$ -XNOR similarity measure tailored for spike trains. It redefines the correlation between non-spike pairs as a specific value $\alpha$ , effectively overcoming the limitations of dot-product similarity. Furthermore, considering the sparse nature of spike trains where spikes carry more information than non-spikes, the $\alpha$ -XNOR similarity correspondingly highlights the distinct importance of spikes over non-spikes. Extensive experiments demonstrate that $\alpha$ -XNOR similarity significantly improves performance across different spiking Transformer architectures on various static and neuromorphic datasets, further revealing the potential of spiking Transformers. + +# 1. Introduction + +Transformer in Artificial Neural Networks (ANNs) [10, 11, 31, 38] offers an effective method for processing long sequences in parallel, significantly improving performance in various tasks [6, 10, 16, 23, 37]. However, its reliance on large-scale parameters [31] and the complexity of its self-attention mechanism [52] result in high energy consumption and hardware costs [18, 41]. Consequently, developing energy-efficient and high-performance Transformer [3, 24] remains a prominent research focus. + +Spiking Neural Networks (SNNs) [17, 26, 32, 33], as the third generation of neural networks, gain significant attention due to their superior energy efficiency [33, 42]. + +![](images/13dc4ae2b9accdb0a478bc0eee4beb0730c3ef99958c2526ef21de498e89e7cc.jpg) +Figure 1. (a) Illustration of the Spiking Self-Attention (SSA) mechanism. (b) Similarity calculation in SSA, highlighting dot-product limitations with three spike train pairs: (1) $\pmb{q}_1$ and $\pmb{k}_1$ have 3 matching values and a consistent score of 3; (2) $\pmb{q}_2$ and $\pmb{k}_2$ have 6 matching values but only score 2; and (3) identical all-zero train $\pmb{q}_3$ and $\pmb{k}_3$ yield a clearly unreasonable score of 0. + +![](images/5eca52e7df5d5e138aeb04aff1ef85a80b4723bd54a5b89c0c9f7f482a03c2a1.jpg) + +Spiking neurons fire only when activated and remain silent in others. This event-driven mechanism [5] greatly enhances energy efficiency by promoting sparse synaptic operations and avoiding multiply-accumulate (MAC) computations [7, 34, 49]. Recently, numerous researchers focus on developing spiking Transformer models, such as Spikformer [54], Spike-driven Transformers [44, 46], and SpikingResformer [36]. These approaches enhance SNNs' performance limits in various aspects. However, a substantial performance gap remains compared to their ANNs' counterparts [40]. Through theoretical analysis, we attribute this gap to the unsuitability of dot-product similarity for the binary nature of spike trains in existing spiking Transformers. + +In ANNs, self-attention calculates token similarities by taking the dot product of Queries (Q) and Keys (K), assigning similarity scores to Values (V) to model human selective attention [12]. However, the sparse, event-driven nature of SNNs results in numerous non-spikes (represented as 0) and a limited number of spikes (represented as 1) in spiking Q + +and K. Due to the unique behavior of 0 in multiplication, both $0 \times 0$ and $0 \times 1$ result in 0, making effective distinction challenging in dot product. As illustrated in Fig.1, the relationship between dot-product similarity and true matching for spike trains is examined. Even when Q and K vectors are entirely identical (e.g., $q_{3}$ and $k_{3}$ in Fig.1), the presence of zero multiplications causes the dot-product similarity to diverge significantly from the true matches. Thus, designing a specialized similarity calculation method for spike trains could improve spiking Transformers' performance. + +In this paper, we propose the $\alpha$ -XNOR similarity calculation specifically designed for SNNs. The $\alpha$ -XNOR similarity redefines the correlation of non-spike pairs as a specific value $\alpha$ to address the ineffectiveness in similarity assessments. Furthermore, given the sparse nature of spike trains, spikes convey more critical information than non-spikes. Therefore, the $\alpha$ -XNOR similarity method also emphasizes distinguishing the relative roles of spikes and non-spikes. Based on $\alpha$ -XNOR similarity, we integrate it into the spiking self-attention mechanism and and develop an $\alpha$ -XNOR Spiking Self-Attention ( $\alpha$ -SSA) module. Extensive experiments demonstrate that $\alpha$ -SSA significantly improves the performance of spiking Transformers across various architectures. The main contributions of this paper are summarized as follows: + +- We thoroughly analyze the reasons why the dot product is unsuitable for calculate spiking similarity. Our findings reveal that the unique multiplicative properties of non-spike hinder the dot-product's ability to accurately capture the similarity between sparse spiking Q and K. +- To address this issue, we propose the $\alpha$ -XNOR similarity, which redefines the correlation of non-spike pairs as a specific value $\alpha$ . This adjustment not only overcomes the ineffectiveness of dot-product similarity but also emphasizes the distinct importance of spikes over non-spikes, enabling richer information representation. +- Based on the $\alpha$ -XNOR similarity, we propose the $\alpha$ -XNOR Spiking Self-Attention ( $\alpha$ -SSA) module. Extensive experiments show that $\alpha$ -SSA achieves significant performance improvements across various Transformer architectures on both static and neuromorphic datasets. + +# 2. Related Work + +Spiking Neural Networks: The event-driven mechanism of SNNs greatly enhances energy efficiency, providing a critical advantage for compute-constrained edge devices. The advent of ANN-to-SNN conversion [4, 22] and direct training methods [20, 42] significantly reduce the challenges of training high-performance SNNs. Leveraging these advanced learning algorithms, some studies [25, 51] propose deep residual SNNs, while others [43, 48] develop multi-dimensional spiking attention mechanisms, achieving competitive results on ImageNet [8, 35] and various neuro- + +morphic datasets [1, 28, 30]. Further research explores parallel training strategies [15] and shortcuts residual connections [13, 25] for SNNs in the ResNet framework, extending SNNs' applicability to diverse tasks. However, despite these advances, a notable performance gap remains between the deep SNN architectures and the latest Transformers. + +Spiking Transformers: Recently, growing attention has been paid to high-performance, energy-efficient spiking Transformers. Some models [39, 53, 54] adopt a single-stage Vision Transformer (ViT) architecture [11], while recent approaches [36, 44, 46] favor a multi-stage architecture [31] to enable hierarchical feature extraction. For instance, Spikformer [54] first proposes spike-based self-attention computation, establishing the first spiking Transformer. Building on this, Spikingformer [53] introduces a hardware-friendly residual learning architecture that avoids non-spike computations in SNNs. Additionally, the Spikes-driven Transformer [44] incorporates the Hadamard product into the self-attention module, achieving a fully spikeredriven mechanism. Furthermore, SpikingResformer [36] integrates a Dual Spike self-attention module, enhancing both performance and energy efficiency. Nonetheless, these models primarily utilize self-attention as a token mixer [47], without paying attention to exploring effective similarity calculations suited to spike trains [2, 50]. Therefore, designing spiking self-attention mechanisms tailored to the binary nature of SNNs is essential for further advancement. + +# 3. Preliminaries + +# 3.1. Leaky Integrate-and-Fire model + +The Leaky Integrate-and-Fire (LIF) model [32] is one of the most widely used spiking neuron models in SNNs due to its efficiency in mimicking biological neurons. In a LIF neuron, the membrane potential $\mathbf{H}[t]$ accumulates synaptic input and decays over time. When $\mathbf{H}[t]$ exceeds the threshold $V_{\mathrm{th}}$ , the neuron emits a spike. After firing, $\mathbf{H}[t]$ is reset to $V_{\mathrm{reset}}$ , and the postsynaptic potential $\mathbf{U}[t]$ continues to evolve, decaying back to the resting potential if no further input arrives. These dynamics are governed by: + +$$ +\mathbf {H} [ t ] = \tau \mathbf {U} [ t - 1 ] + \mathbf {W S} [ t ], \tag {1} +$$ + +$$ +\mathbf {S} [ t ] = \Theta (\mathbf {H} [ t ] - V _ {\mathrm {t h}}), \tag {2} +$$ + +$$ +\mathbf {U} [ t ] = \mathbf {H} [ t ] (1 - \mathbf {S} [ t ]) + V _ {\text {r e s e t}} \mathbf {S} [ t ], \tag {3} +$$ + +where $\tau$ is the decay constant, $\mathbf{W}$ the synaptic weight matrix, $\mathbf{S}[t]$ the input spike at time $t$ , and $\Theta(\cdot)$ the Heaviside function. $\Theta(\cdot)$ outputs 1 when a spike is fired, and 0 for the absence of a spike (i.e., a non-spike). For brevity, we denote the spiking neuron layer as $\mathcal{SN}(\cdot)$ in subsequent sections. + +# 3.2. Vanilla Self-attention + +The self-attention mechanism, a key component of the Transformer model, efficiently processes large-scale data by + +capturing global dependencies and flexibly allocating attention across tokens in the input sequence [38]. Let the input matrix be $\mathbf{X} \in \mathbb{R}^{n \times d}$ , where $n$ is the sequence length and $d$ is the embedding dimension. The vanilla self-attention (VSA) first projects $\mathbf{X}$ into query $\mathbf{Q}$ , key $\mathbf{K}$ , and value $\mathbf{V}$ matrices using three distinct weight matrices $\mathbf{W}_Q$ , $\mathbf{W}_K$ , and $\mathbf{W}_V$ as follows: + +$$ +\mathbf {Q} = \mathbf {X} \mathbf {W} _ {Q}, \quad \mathbf {K} = \mathbf {X} \mathbf {W} _ {K}, \quad \mathbf {V} = \mathbf {X} \mathbf {W} _ {V}. \tag {4} +$$ + +Next, the similarity between the elements is computed to determine the level of attention each token should receive. This is achieved by calculating the dot-product similarity between the corresponding tokens in $\mathbf{Q}$ and $\mathbf{K}$ and generates the attention scores: + +$$ +\mathbf {S c o r e} = \operatorname {S i m} _ {\mathrm {D P}} (\mathbf {Q}, \mathbf {K}) = \mathbf {Q K} ^ {\top}, \tag {5} +$$ + +where $\mathrm{Sim}_{\mathrm{DP}}(\cdot)$ denote the similarity function by dot product. Then, a scaling factor $\sqrt{d}$ is applied to prevent the dot-product values from becoming large, and $\mathrm{Softmax}(\cdot)$ is utilized to obtain the attention scores. The final output $\mathbf{Z}$ is then computed as the weighted sum of the value matrix $\mathbf{V}$ : + +$$ +\mathbf {Z} = \operatorname {S o f t m a x} \left(\frac {\text {S c o r e}}{\sqrt {d}}\right) \mathbf {V}. \tag {6} +$$ + +Based on the dot-product similarity, the model is able to flexibly distribute attention across the sequence, allowing long-range dependencies capture. + +# 3.3. Spiking Self-Attention + +Building on VSA, Spikformer [54] introduced a spiking variant called Spiking Self-Attention (SSA). For the input $\mathbf{X} \in \mathbb{R}^{n \times d}$ , the queries, keys, and values are first computed using learnable weight matrices $\mathbf{W}_Q, \mathbf{W}_K, \mathbf{W}_V$ and then transformed into spike trains as follows: + +$$ +\mathbf {Q} = \mathcal {S N} (\mathrm {B N} (\mathbf {X W} _ {Q})), \tag {7} +$$ + +$$ +\mathbf {K} = \mathcal {S N} \left(\mathrm {B N} \left(\mathbf {X W} _ {K}\right)\right), \tag {8} +$$ + +$$ +\mathbf {V} = \mathcal {S N} (\mathrm {B N} (\mathbf {X W} _ {V})), \tag {9} +$$ + +where $\mathbf{Q},\mathbf{K},\mathbf{V}\in \mathbb{R}^{T\times n\times d}$ , $\mathrm{BN}(\cdot)$ denotes batch normalization, and $\mathcal{SN}(\cdot)$ refers to the spiking neuron layer, ensuring the attention mechanism operates entirely in spike form. Similar to VSA, SSA computes the similarity between spiking $\mathbf{Q}$ and $\mathbf{K}$ using a dot-product operation: + +$$ +\mathbf {S c o r e} = \operatorname {S i m} _ {\mathrm {D P}} (\mathbf {Q}, \mathbf {K}) = \mathbf {Q} \mathbf {K} ^ {\top}. \tag {10} +$$ + +Unlike VSA, SSA omits the softmax operation while retaining scaling to control the magnitude of the attention output. The attention output Attn is computed as a weighted sum of $\mathbf{V}$ , scaled by factor $s$ , and then converted to spiking form: + +$$ +\mathbf {A t t n} ^ {\prime} = s \cdot \mathbf {S c o r e V}, \quad \mathbf {A t t n} = \mathcal {S N} (\mathbf {A t t n} ^ {\prime}). \tag {11} +$$ + +![](images/d3ee4d3000cde8a45266c0756ac56a219fee83617d9e07b8299ceb52e13227ce.jpg) +(a) Dot-product operation in ANNs. + +![](images/a9580d7cdfb9aa2009f0133549df7048e0869a501f839e7f75414e5d794ff26f.jpg) +(b) Dot-product operation in SNNs. +Figure 2. Dot-product operation in ANNs and SNNs. (a): Dot-product operation in ANNs, with data sampled from VSA. (b): Dot-product operation in SNNs, with data sampled from SSA. + +Finally, the attention result passes through a linear layer and batch normalization, followed by the spiking neuron layer, to produce the final SSA output $\mathbf{Z}$ : + +$$ +\mathbf {Z} = \mathcal {S N} (\mathrm {B N} (\text {L i n e a r} (\mathbf {A t t n}))), \tag {12} +$$ + +where $\operatorname{Linear}(\cdot)$ is the fully connected layer. Thus, SSA provides a spiking version of self-attention, enabling the spiking Transformer to capture global dependencies efficiently while maintaining scalability. + +# 4. Methods + +# 4.1. Spiking Dot-Product Similarity Ineffectiveness + +In ANNs, the attention mechanism effectively captures relevant information by using dot products to calculate querykey similarity, where higher similarity increases the weight of the corresponding value. However, in SNNs, the spikedriven nature poses two major challenges, making the spiking dot products ineffective for calculating similarity between spike trains. + +Firstly, the unique mathematical properties of 0 prevent dot product from effectively capturing correlations involving non-spike events (represented as 0) in SNNs. As shown in Fig.1, in the first spike train pair $q_{1}$ and $k_{1}$ , the 3 matching values yield a dot-product similarity score of 3, which is consistent. However, this consistency relies on the absence of 0-0 pairs. In the second pair $q_{2}$ and $k_{2}$ , despite 6 matching values, the dot-product score is only 2, as 0-0 pairs do not contribute in multiplication. A more extreme case is the third pair $q_{3}$ and $k_{3}$ , where both spike trains are entirely identical, yet the dot-product similarity score is 0, which + +is significantly unreasonable. Notably, due to the sparsity of spike trains, pairs like the second are the most common. Thus, the dot-product similarity is ineffective in SSA due to the multiplication properties of 0. + +Secondly, dot-product operations in ANNs effectively capture a wide range of attentional preferences, with sign bits indicating the direction of correlation between corresponding elements. In contrast, due to the binary nature of spike trains in SNNs, dot product results are limited to two states. Additionally, they lack sign bits to denote the direction of correlation. Consequently, these limitations lead to a significant deficiency in information capacity during dot-product similarity calculations. As depicted in Fig.2, compared to the rich dot product outcomes in ANNs, the results become increasingly sparse following dot-product calculations in SNNs and fail to represent the correlation direction. + +# 4.2. $\alpha$ -XNOR Similarity + +To address the issue wherein matching non-spike pairs do not contribute to the dot-product similarity score, we intuitively expect that identical pairs, whether they are spikes or non-spikes, contribute equally to the similarity score. Thus, we replace the multiplication operation in dot product with an operation where matching values contribute a score of 1 while differing values contribute a score of 0. This adjustment aligns with the XNOR operation in binary logic: + +$$ +\operatorname {X N O R} (x, y) = \left\{ \begin{array}{l l} 1, & \text {i f} x = y, \\ 0, & \text {i f} x \neq y. \end{array} \right. \tag {13} +$$ + +The XNOR operation therefore measures the similarity by evaluating the exact matches between two spike trains. + +However, most current SNNs operate at a low firing rate, spikes typically represent rare but significant events, making each spike occurrence carry a higher informational value (details provided in Suppl. B). Consequently, spikes can be considered more important than non-spikes within the spiking data. Building on this insight, we further adapt the XNOR operation to distinguish between matching spikes and matching non-spikes. Specifically, we assign a lower weight to matching non-spikes, making them less significant than matching spikes yet more significant than non-matching pairs. This weight, denoted as $\alpha$ , is set between 0 and 1. The modified operation is formulated as: + +$$ +\alpha \text {- X N O R} (x, y) = \left\{ \begin{array}{l l} 1, & \text {i f} x = y = 1, \\ \alpha , & \text {i f} x = y = 0, \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {14} +$$ + +Here, $\alpha$ -XNOR(\cdot) denotes the modified XNOR operation. + +Since $\alpha$ -XNOR( $\cdot$ ) is non-differentiable, we define custom gradients to ensure smooth gradient flow during backpropagation: + +$$ +\frac {\partial \alpha - \mathrm {X N O R} (x , y)}{\partial x} = - 2 \alpha x + (1 + \alpha) y, \tag {15} +$$ + +![](images/5cb710f4bd7a2e4bc4ab27e6c05a607b0bfa5c2e535a64f104188ef23bd5a7ea.jpg) +Figure 3. Illustration of $\alpha$ -XNOR similarity with $\alpha$ values of 0.3, 0.6, 1, and 0. Cases where $\alpha = 1$ and $\alpha = 0$ correspond to XNOR similarity and dot-product similarity, respectively. + +$$ +\frac {\partial \alpha - \mathrm {X N O R} (x , y)}{\partial y} = - 2 \alpha y + (1 + \alpha) x. \tag {16} +$$ + +These gradients are derived from a differentiable function that is numerically equivalent to $\alpha$ -XNOR( $\cdot$ ): + +$$ +\alpha \text {- X N O R} _ {\text {g r a d}} (x, y) = (1 - \alpha) x y - \alpha (x - y) ^ {2} + \alpha . \tag {17} +$$ + +By adopting the gradients in Eq. 17, the $\alpha$ -XNOR operation achieves both computational efficiency and a smooth gradient flow, facilitating effective parameter updates during training. + +Building on $\alpha$ -XNOR( $\cdot$ ), we define the $\alpha$ -XNOR similarity between two spike trains $\mathbf{x}, \mathbf{y} \in \mathbb{R}^d$ as: + +$$ +\operatorname {S i m} _ {\alpha - \mathrm {X N O R}} (\boldsymbol {x}, \boldsymbol {y}) = \sum_ {i = 1} ^ {d} \alpha - \mathrm {X N O R} \left(x _ {i}, y _ {i}\right). \tag {18} +$$ + +For notational simplicity, we overload $\operatorname{Sim}_{\alpha \text{-XNOR}}(\cdot)$ to also support batched similarity calculation between spike matrices. Given $\mathbf{X}, \mathbf{Y} \in \mathbb{R}^{n \times d}$ , we define $\operatorname{Sim}_{\alpha \text{-XNOR}}(\mathbf{X}, \mathbf{Y}) \in \mathbb{R}^{n \times n}$ as the pairwise $\alpha$ -XNOR similarity matrix between all tokens in $\mathbf{X}$ and $\mathbf{Y}$ : + +$$ +[ \operatorname {S i m} _ {\alpha - X N O R} (\mathbf {X}, \mathbf {Y}) ] _ {i j} = \operatorname {S i m} _ {\alpha - X N O R} \left(\mathbf {X} _ {i}, \mathbf {Y} _ {j}\right), \tag {19} +$$ + +where $i,j$ index the tokens and range from 1 to $n$ . + +Additionally, there are two special cases for the $\alpha$ -XNOR similarity: when $\alpha = 0$ , $\alpha$ -XNOR( $\cdot$ ) reduces to the traditional dot-product similarity ( $\mathrm{Sim}_{\mathrm{DP}}$ ), where only matching spikes contribute; and when $\alpha = 1$ , it becomes the original XNOR operation, referred to as XNOR similarity ( $\mathrm{Sim}_{\mathrm{XNOR}}(\cdot)$ ), where all matching values contribute equally, regardless of being spikes or non-spikes. + +As illustrated in Fig. 3, $\alpha$ -XNOR similarity effectively addresses the issue of non-spike pairs making no contribution in dot-product similarity. Compared to XNOR similarity, $\alpha$ -Similarity further differentiates the contributions of spikes and non-spikes by assigning less weight to non-spike matches, resulting in a more balanced and accurate similarity score for spiking data. + +![](images/53d4e78852a329476a1540e0cd7e328a1a053d7d90cc753ec6ac8c8d68a14f66.jpg) +(a) $\alpha$ -XNOR Spiking Self-Attention + +![](images/12880003e7885b1d21f42c101b8c72e79cd9b07f4b08599307a9b97c45a72de9.jpg) +(b) Distributions of Some Selected Data in $\alpha$ -SSA + +![](images/a3e63d77fa8c52f2e6333bf9bb28f756fd05c670f4afbe89a5834486ed5cec0b.jpg) + +![](images/622bd336bfe3fbf491917099e60c06cdb61a880e31426bbaa56eb6c9f882d3ff.jpg) + +![](images/62f2413c79dffd9b00dcd68e91227bf5132244dc2fdf41c2c39956fb98f69099.jpg) + +![](images/1c220e9b2f5af20307f7914177601a37675279b36efb91b5ff162ac34813a007.jpg) + +![](images/7840bec2af2e5af91759a028e0fc1b99ce8816995dfe01fb50e85c9bd9a8a11f.jpg) + +![](images/27712516c3afa38f10422b68d707a5d80d6a180adc7ca9bdfc20cc74c2157793.jpg) +Figure 4. $\alpha$ -XNOR Spiking Self-Attention ( $\alpha$ -SSA) mechanism. (a) Overall architecture of $\alpha$ -SSA. (b) Distributions of similarity scores calculated using $\alpha$ -XNOR similarity with $\alpha = 0.4$ and $\alpha = 1$ (XNOR similarity) before and after linear transformation, alongside the membrane potential distribution prior to firing in the LIF neuron that generates the self-attention outputs Attn. For a clear comparison, corresponding distributions from the original SSA are also shown. + +![](images/6cbac1d56cb7d59a250af036c0ac5ceaff33804f1ba8d8aa791506180d5c2271.jpg) + +![](images/057b1446c558607a85b587d6f2fbd2d0df3058cf393962cd8f671afdcc028ada.jpg) + +Moreover, $\alpha$ -XNOR similarity also significantly increases the information representation within the spiking self-attention module. In the following, we present a theoretical analysis for this. We begin with the information entropy as our criterion, which is defined as: + +$$ +H (X) = - \sum_ {i = 1} ^ {n} p _ {i} \log_ {2} p _ {i}, \tag {20} +$$ + +where $X$ is a random variable with outcome probabilities $p$ . Higher entropy values signify greater variability and informational content in the similarity scores. The entropy can be calculated based on the distribution of the scores. + +Theorem 1. Let $\mathbf{q}, \mathbf{k} \in \{0,1\}^d$ be independent spike trains with firing rates $f_{\mathbf{q}}$ and $f_{\mathbf{k}}$ , respectively. The similarity scores for dot-product and XNOR similarity both follow a binomial distribution: + +$$ +\operatorname {S i m} _ {\mathrm {D P}} (\boldsymbol {q}, \boldsymbol {k}) \sim \operatorname {B i n} (d, p _ {1}), \tag {21} +$$ + +$$ +\operatorname {S i m} _ {\mathrm {X N O R}} (\boldsymbol {q}, \boldsymbol {k}) \sim \operatorname {B i n} (d, p _ {1} + p _ {2}), \tag {22} +$$ + +where $p_1 = f_qf_k$ , and $p_2 = (1 - f_q)(1 - f_k)$ , represent the probability of matching spikes and non-spikes, respectively. + +Theorem 1 (proof in Suppl. A.1) shows that scores generated by the two special cases of $\alpha$ -XNOR similarity, dot-product similarity and XNOR similarity, both approximately follow a binomial distribution, with different probability parameters. However, the score distribution of $\alpha$ -XNOR similarity in the general case is much more complex. + +Theorem 2. Let $q, k \in \{0,1\}^d$ be independent spike trains with firing rates $f_{q}$ and $f_{k}$ , respectively. The score calculated by $\alpha$ -XNOR similarity is distributed as: + +$$ +P (s = k + l \alpha) = \frac {d !}{k ! l ! (d - k - l) !} \cdot p _ {1} ^ {k} p _ {2} ^ {l} p _ {3} ^ {d - k - l}, \tag {23} +$$ + +for $0 \leq k \leq d$ and $0 \leq l \leq d - k$ , where $p_1 = f_q f_k$ , $p_2 = (1 - f_q)(1 - f_k)$ , and $p_3 = 1 - p_1 - p_2$ . + +Theorem 2 (proof in Suppl. A.2) demonstrates that the similarity score calculated by $\alpha$ -XNOR similarity approximately follows a weighted multinomial distribution, where matching spikes and non-spikes contribute to the score with weights 1 and $\alpha$ , respectively. The introduction of $\alpha$ increases the complexity of the score distribution. By distinguishing between spikes and non-spikes, $\alpha$ -XNOR similarity captures a broader range of variability in similarity scores, resulting in higher information entropy. The following Theorem 3 further reveals the relationships among scores produced by these similarity calculations. + +Theorem 3. Let $\mathbf{q}, \mathbf{k} \in \{0,1\}^d$ be independent spike trains with firing rates $f_{\mathbf{q}}, f_{\mathbf{k}} \in (0,1)$ and $\alpha \in (0,1)$ . Then the entropies satisfy: $H(\text{Sim}_{\alpha - XNOR}(\mathbf{q}, \mathbf{k})) > H(\text{Sim}_{DP}(\mathbf{q}, \mathbf{k}))$ and $H(\text{Sim}_{\alpha - XNOR}(\mathbf{q}, \mathbf{k})) > H(\text{Sim}_{XNOR}(\mathbf{q}, \mathbf{k}))$ . + +Theorem 3 (proof provided in Suppl. A.3) shows that the $\alpha$ -XNOR similarity achieves higher information entropy compared to dot-product and XNOR similarities, reflecting its enhanced capacity for information representation. Fig. 4 (b) compares the similarity scores calculated by these methods under the parameters $f_{q} = f_{k} = 0.2$ , $d = 32$ , and + +$\alpha = 0.4$ . Unlike dot-product and XNOR similarities, which generate highly discretized distributions with limited variability, the $\alpha$ -XNOR similarity produces smoother, more centrally distributed scores. This broader value range enables richer information representation and more nuanced similarity assessments. The information entropy of scores from $\alpha$ -XNOR similarity is 5.50, significantly exceeding the 2.07 and 3.44 from dot-product and XNOR similarities, respectively, highlighting the effectiveness of $\alpha$ -XNOR similarity for spiking data. + +# 4.3. $\alpha$ -XNOR Spiking Self-Attention + +In Sec. 4.2, we introduce $\alpha$ -XNOR similarity to address dot-product limitations, and differentiate spikes and non-spikes in similarity calculations. Leveraging this spiking similarity calculation, we develop an improved spiking self-attention module, termed as $\alpha$ -XNOR Spiking Self-Attention ( $\alpha$ -SSA). + +The overall architecture of $\alpha$ -SSA is shown in Fig. 4 (a). Initially, the spiking $\mathbf{Q}$ , $\mathbf{K}$ , and $\mathbf{V}$ matrices are generated similarly to SSA using Eq. 4. Then, we calculate the similarity scores with $\alpha$ -XNOR similarity instead of the original dot-product similarity: + +$$ +\mathbf {S c o r e} = \operatorname {S i m} _ {\alpha - \mathrm {X N O R}} (\mathbf {Q}, \mathbf {K}). \tag {24} +$$ + +Following this, the obtained attention scores undergo transformation. In the original SSA, only a scaling factor adjusts the score magnitudes, which is inadequate for scores based on $\alpha$ -XNOR similarity, as they exhibit different distribution patterns (see Fig. 4(b)). In $\alpha$ -SSA, we use a linear transformation for the score with an added bias term: + +$$ +\mathbf {A t t n} ^ {\prime} = (k \cdot \mathbf {S c o r e} + b) \mathbf {V}, \tag {25} +$$ + +where $k$ and $b$ are constants that help adjust the attention output distribution. For Score derived from $\alpha$ -XNOR, the corresponding Attn' has an expected value $\mathbb{E}[\mathbf{Attn}']$ and variance $\mathbb{V}[\mathbf{Attn}']$ , which can be given by (proof provided in Suppl. A.4): + +$$ +\mathbb {E} [ \mathbf {A t t n} ^ {\prime} ] = n f _ {\mathbf {V}} (k d \gamma_ {1} + b), \tag {26} +$$ + +$$ +\mathbb {V} [ \mathbf {A t t n} ^ {\prime} ] = n f _ {\mathbf {V}} \left(k ^ {2} d \left(\gamma_ {2} - \gamma_ {1} ^ {2}\right) + \left(1 - f _ {\mathbf {V}}\right) \left(k d \gamma_ {1} + b\right) ^ {2}\right), \tag {27} +$$ + +where $\gamma_{1}$ and $\gamma_{2}$ are determined by the firing rates of $\mathbf{Q}$ , $\mathbf{K}$ , and $\mathbf{V}$ , denoted as $f_{\mathbf{Q}}$ , $f_{\mathbf{K}}$ , and $f_{\mathbf{V}}$ , respectively: + +$$ +\gamma_ {1} = f _ {\mathbf {Q}} f _ {\mathbf {K}} + \alpha (1 - f _ {\mathbf {Q}}) (1 - f _ {\mathbf {K}}), \tag {28} +$$ + +$$ +\gamma_ {2} = f _ {\mathbf {Q}} f _ {\mathbf {K}} + \alpha^ {2} (1 - f _ {\mathbf {Q}}) (1 - f _ {\mathbf {K}}), \tag {29} +$$ + +To achieve a balanced membrane potential distribution, we set $\mathbb{E}[\mathbf{Attn}^{\prime}] = 0$ and $\mathbb{V}[\mathbf{Attn}^{\prime}] = 1$ , leading to the following values for $k$ and $b$ : + +$$ +k = \frac {1}{\sqrt {n d \left(\gamma_ {2} - \gamma_ {1} ^ {2}\right) f _ {\mathbf {V}}}}, b = - \frac {\gamma_ {1} \sqrt {d}}{\sqrt {n \left(\gamma_ {2} - \gamma_ {1} ^ {2}\right) f _ {\mathbf {V}}}}. \tag {30} +$$ + +![](images/e9b17ab2cc0bd9be7f46187fd45762db1b5b15586cd39d79c53ac4e07b25657d.jpg) +Figure 5. Attention heatmaps of $\alpha$ -SSA and SSA models on ImageNet1K, showing $\alpha$ -SSA's sparser focus on key visual features. + +Here, we select the positive solution of $k$ to ensure that the scores after the linear transformation are positively correlated with the original values. + +Finally, the attention output is converted to spiking form as $\mathbf{Attn} = \mathcal{SN}(\mathbf{Attn}')$ . Following [45], the multiplication of floating-point data in Eq. 25 can be merged into the threshold of this spiking neuron layer, preserving the spikedriven nature of SNNs. Subsequently, Attn is processed using Eq. 12 in SSA to generate the final output. + +Fig. 4 (b) shows the data distributions in $\alpha$ -SSA alongside those in SSA for comparison. In $\alpha$ -SSA, scores calculated using $\alpha$ -XNOR yield not only more reasonable similarity values but also a distribution closer to normal with significantly higher information entropy. By comparison, the dot-product similarity in SSA produces a positively skewed distribution with lower entropy. Furthermore, the simple scaling in SSA results in a discrete and skewed membrane potential distribution, which previous studies [19, 21] suggest may impact model performance. Meanwhile, the linear transformation in $\alpha$ -SSA with XNOR similarity and $\alpha$ -XNOR produces a more balanced membrane potential distribution. These improvements in similarity scores, distribution balance, and entropy in $\alpha$ -SSA highlight its advantage in capturing richer information from spiking input patterns for spiking self-attention mechanisms. + +# 5. Experiments + +# 5.1. Image Classification + +In image classification experiments, we evaluate the proposed $\alpha$ -SSA module on both static and dynamic image datasets, including ImageNet [8], CIFAR-10, CIFAR100 [27], and CIFAR10-DVS [28]. We implement $\alpha$ -SSA module within both Single-stage ViT (S-ViT) and Multi-stage ViT (M-ViT) architectures and conduct detailed com + +Table 1. Detailed comparison with other similar methods on ImageNet + +
TypeMethodArchitectureTime StepParam. (M)Acc. (%)
ResNetSEW ResNet [13]Sew ResNet-50425.667.78
Sew ResNet-101444.668.76
MS ResNet [25]MS-ResNet-50421.869.40
MS-ResNet-104477.375.30
Att-MS-ResNet [43]Att-ResNet-50122.169.20
Att-ResNet-104478.476.30
Single-stage ViTsSpikformer [54]Spikformer-8-384416.870.24
Spikformer-8-512429.773.38
Spikingformer [53]Spikingformer-8-384416.870.45
Spikingformer-8-512429.774.49
S-ViT + α-SSA (α = 0.3)α-SSA-ViT-8-384416.871.36
S-ViT + α-SSA (α = 0.3)α-SSA-ViT-8-512429.775.39
Muti-stage ViTsSpike-driven Transformer [44]Spike-driven-8-384416.872.28
Spike-driven-8-512429.774.57
SpikingResformer [36]SpikingResformer-S417.875.95
SpikingResformer-M435.577.24
Meta-SpikeFormer [45]Meta-SpikeFormer-384415.174.10
Meta-SpikeFormer-512455.479.70
M-ViT + α-SSA (α = 0.3)α-SSA-Swin-10-384431.877.89
M-ViT + α-SSA (α = 0.3)α-SSA-Swin-10-512454.680.62
+ +parisons with the latest spiking Transformers [36, 44, 45, 53, 54]. The results are as follows: + +ImageNet: For the ImageNet dataset, we set the input image dimensions to $224 \times 224$ , with a batch size of 128 and a total of 300 training epochs. In this set of experiments, the value of $\alpha$ is set to 0.3 for all $\alpha$ -SSA layers across different models. As shown in Table 1, our $\alpha$ -SSA module enhances performance across both S-ViT and M-ViT architectures. Specifically, in the S-ViT architecture, $\alpha$ -SSA increases accuracy to $75.39\%$ in the 512-dimensional setting. Similarly, in the M-ViT Transformer architecture, $\alpha$ -SSA achieves $80.62\%$ in the 512-dimensional setting. Additionally, we compared the attention maps of the original SSA and our $\alpha$ -SSA. As shown in Fig. 5, $\alpha$ -SSA demonstrates sparser attention with a sharper focus on key visual features. + +CIFAR10/100 and CIFAR10-DVS: CIFAR10 and CIFAR100 [27] are widely used benchmarks for image classification, while CIFAR10-DVS [28] is an event-based dataset specifically designed for SNN models. In both architectures, we conducted experiments with two different values of $\alpha = 0.3$ and $\alpha = 0.5$ . As demonstrated in Table 2, our proposed $\alpha$ -SSA module consistently boosts performance across various architectures and datasets while maintaining model simplicity. Notably, in M-ViT mod + +![](images/0b574cc990d53da3039acaad9ec189eb5dc2d5806cfdf75964d60f87f39a10f9.jpg) +Figure 6. Parallel coordinate plots of $\alpha$ -SSA parameters $(\alpha, k, b)$ and metrics (firing rates for $\mathbf{Q}(f_{\mathbf{Q}})$ , $\mathbf{K}(f_{\mathbf{K}})$ , $\mathbf{V}(f_{\mathbf{V}})$ , attention output $(f_{\mathbf{Attn}})$ , and accuracy), showing correlations between $\alpha$ and other variables. Results are based on CIFAR100 with $\alpha$ -SSA in the Spikformer architecture. + +els, $\alpha$ -SSA achieves exceptional outcomes, attaining accuracies of $96.15\%$ on CIFAR10, $81.08\%$ on CIFAR100, and $84.24\%$ on CIFAR10-DVS, underscoring its effectiveness in enhancing model robustness and accuracy. Notably, The performance improvements in the M-ViT architecture are less significant compared to those in the S-ViT architecture. This can be attributed to the relatively minor role of self-attention modules in the Swin Transformer's design, by findings in metaformer [47] research. + +Table 2. Detailed comparison with other similar methods across CIFAR10, CIFAR100 and CIFAR10-DVS + +
TypeMethodCIFAR10CIFAR100CIFAR10-DVS
Param. (M)Acc. (%)Param. (M)Acc. (%)Param. (M)Acc. (%)
ResNetPLIF [14]-93.50---74.8
tdBN [51]-93.2---67.8
DSpike [29]-94.25-74.24-75.4
TET [9]12.6394.4412.6374.47-77.33
Single-stage ViTsSpikformer [54]9.3295.519.3278.212.5780.9
Spikingformer [53]9.3295.819.3279.092.5781.3
S-ViT + α-SSA (α = 0.5)9.3295.929.3279.972.5781.45
S-ViT + α-SSA (α = 0.3)9.3295.979.3280.222.5781.64
Multi-stage ViTsSpike-driven Transformer [44]10.2895.6010.2878.402.5780.0
M-ViT + α-SSA (α = 0.5)6.5096.056.5080.661.5482.24
M-ViT + α-SSA (α = 0.3)6.5096.156.5081.081.5482.22
+ +# 5.2. Study of Different $\alpha$ + +In the $\alpha$ -SSA module, $\alpha$ serves as a critical parameter. We conducted experiments on the Spikformer architecture on CIFAR100 dataset to investigate the effect of varying $\alpha$ values on metrics. These metrics include the linear scaling factors $k$ and $b$ ; the spiking firing rates $f_{\mathbf{Q}}$ , $f_{\mathbf{K}}$ , $f_{\mathbf{V}}$ , and $f_{\mathrm{Attn}}$ responsible for generating $\mathbf{Q}$ , $\mathbf{K}$ , $\mathbf{V}$ , and the spiking self-attention output Attn, respectively; and the network's performance accuracy (Acc.). We set $\alpha$ to [0, 0.2, 0.4, 0.6, 0.8, 1], where $\alpha = 0$ and $\alpha = 1$ correspond to dot-product similarity and XNOR similarity, respectively, while intermediate values represent $\alpha$ -XNOR similarities. Fig. 6 illustrates the average values of these metrics, and detailed data across different $\alpha$ -SSA layers are provided in Suppl.D. The results show a clear negative correlation between $\alpha$ and the parameters $k$ and $b$ . The parameters $f_{\mathbf{Q}}$ , $f_{\mathbf{K}}$ , $f_{\mathbf{V}}$ , and $f_{\mathrm{Attn}}$ exhibit no clear correlation and present a complex interaction, with $f_{\mathbf{V}}$ showing relatively minimal variation. Moreover, model accuracy peaks when $\alpha$ ranges from 0.2 to 0.4, indicating that this range optimally reflects the differential importance of spikes and non-spikes in attention scoring. + +# 5.3. Ablation Study + +To evaluate the effectiveness of our proposed model's components, we conducted an ablation study on the CIFAR100 dataset using Spikformer as the baseline. We replaced Spikformer's SSA with our proposed $\alpha$ -SSA, testing three values of $\alpha$ : 0, 1, and 0.3. For $\alpha = 0$ , the original SSA replaces only the linear transformations of attention scores, maintaining the traditional dot-product similarity. For $\alpha = 1$ and $\alpha = 0.3$ , the model employs XNOR similarity and $\alpha$ -XNOR similarity, respectively. As shown in Table 3, adding the linear transformations for attention scores increased accuracy from $78.21\%$ to $79.04\%$ . Incorporating + +Table 3. Ablation study on CIFAR100 dataset + +
ModelParam. (M)Acc. (%)
Spikeformer (baseline)9.3278.21
+ α-SSA (α = 0)9.3279.04
+ α-SSA (α = 1)9.3279.33
+ α-SSA (α = 0.3)9.3280.22
+ +XNOR similarity resulted in a further $0.29\%$ gain. Finally, the $\alpha$ -SSA with $\alpha = 0.3$ achieved an accuracy of $80.22\%$ , marking a $2.01\%$ improvement over the baseline. These results demonstrate that both the introduction of $\alpha$ -SSA and the linear transformations of attention scores yield substantial gains with minimal increase in parameters. + +# 6. Conclusion + +This work identifies a fundamental challenge in spiking Transformers: the dot product is ineffective for calculating spiking similarity due to the binary and sparse nature of spike trains. To address this issue, we propose a novel $\alpha$ -XNOR similarity method specifically tailored to spike trains, which effectively resolves the limitations of dot-product similarity caused by numerous non-spiking events. Moreover, given the sparse nature of spike trains, where spikes carry more information than non-spikes, the $\alpha$ -XNOR similarity emphasizes the distinct importance of spikes, with enhanced representation capability in spiking self-attention. Extensive experiments demonstrate significant performance improvements across various Transformer architectures. 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Ltd. + +# Abstract + +We present GDFusion, a temporal fusion method for vision-based 3D semantic occupancy prediction (VisionOcc). GDFusion opens up the underexplored aspects of temporal fusion within the VisionOcc framework, focusing on both temporal cues and fusion strategies. It systematically examines the entire VisionOcc pipeline, identifying three fundamental yet previously overlooked temporal cues: scene-level consistency, motion calibration, and geometric complementation. These cues capture diverse facets of temporal evolution and make distinct contributions across various modules in the VisionOcc framework. To effectively fuse temporal signals across heterogeneous representations, we propose a novel fusion strategy by reinterpreting the formulation of vanilla RNNs. This reinterpretation leverages gradient descent on features to unify the integration of diverse temporal information, seamlessly embedding the proposed temporal cues into the network. Extensive experiments on nuScenes demonstrate that GDFusion significantly outperforms established baselines, achieving $2.2\% -4.7\%$ mIoU improvement and reducing memory consumption by $30\% -72\%$ . Codes are available at https://github.com/cdb342/GDFusion. + +# 1. Introduction + +Dynamic environment perception and understanding play crucial roles in applications like autonomous driving and robotics [10, 18, 22]. A key aspect of this understanding is 3D semantic occupancy prediction [21, 41, 42, 47], which + +*Corresponding author: Jianbing Shen. This work was supported in part by the Science and Technology Development Fund of Macau SAR (FDCT) under grants 0102/2023/RIA2 and 0154/2022/A3 and 001/2024/SKL, the Jiangyin Hi-tech Industrial Development Zone under the Taihu Innovation Scheme (EF2025-00003-SKL-IOTSC), the University of Macau SRG2022-00023-IOTSC grant, and the State Key Laboratory of Internet of Things for Smart City (University of Macau) (Ref. No.: SKL-IoTSC(UM)-2024-2026/ORP/GA04/2023). + +provides a detailed representation of both the spatial layout and semantic properties of the environment. + +Given the continuous nature of dynamic perception tasks, temporal information is increasingly recognized as a key enhancer of performance [15, 19, 34, 46]. By exploiting multi-frame data, these systems attain improved consistency and robustness in predictions. However, in vision-based 3D semantic occupancy prediction (VisionOcc), the potential of temporal fusion mechanisms remains largely underexplored. In this work, we conduct a systematic investigation into the temporal dynamics of VisionOcc, with a focus on analyzing comprehensive temporal cues and their unified integration within an RNN-style framework. + +In general VisionOcc frameworks (Fig. 1a), image features are first transformed into volumetric features via a 2D-to-3D lifting module and decoded into occupancy predictions using task heads. For temporal integration, existing methods [5, 25, 28, 32] primarily focus on voxel-level feature fusion. This intuitively enriches each voxel with additional temporal context to resolve ambiguities. Yet beyond this, we identify three crucial but unexplored temporal cues, as shown in Fig. 1b, each capturing distinct temporal aspects in VisionOcc: i) Scene-level temporal cue: Autonomous driving systems must adapt to various road conditions, weather patterns, and lighting situations, requiring robust domain generalization capabilities. Since scene conditions remain stable over short time spans, historical data provides valuable scene-specific cues (such as consistent environmental priors) that have been overlooked in prior research. ii) Temporal motion cue: In voxel-level temporal fusion, historical volumetric features must be aligned with the current frame's coordinate system, with dynamic objects requiring additional motion compensation. While mispredictions of motion can occur in the current frame, the potential of leveraging historical motion information to correct these errors remains untapped. iii) Temporal geometry cue: Advanced VisionOcc methods utilize geometric priors (e.g., depth) [5, 19, 25, 32] for 2D-to-3D lifting. Historical geometric information could effectively compensate + +![](images/3d64aa9bb44be470871b87b61f8d06adb78cb62cedbc85dfaa1150d0aae081ba.jpg) +(a) VisionOcc Pipeline +Figure 1. Motivation behind the proposed temporal fusion. (a): VisionOcc pipeline. (b): Proposed temporal cues, showing historical motion and geometric data enhancing current viewpoints, with scene consistency priors from historical information. + +![](images/46bea6ee3031379d101f96ea4d741261a2883783e53457c12eacfb5ae7cf114e.jpg) +(b) Proposed Temporal Cues + +for the predicted geometry of the current frame. + +These cues drive comprehensive temporal fusion in VisionOcc by fulfilling diverse roles in its pipeline. Scene-level fusion captures information distinct from voxel-level fusion, reflecting broader contextual cues. Temporal motion fusion refines the accuracy of voxel-level fusion by correcting alignment errors. Unlike other fusion strategies that target post-lifting 3D features, temporal geometry fusion improves current-frame 2D-to-3D lifting with historical geometry. Each type of temporal information has a distinct representation. As shown in Fig. 2, voxel-level information is encoded in 3D volume feature maps; scene-level information is represented as network parameters, inspired by test-time adaptation [6, 39] and large language models [40]; motion is captured via 3D flow maps; and geometry is encoded as probabilistic point clouds (detailed in Sec. 3.2). + +To integrate temporal information from heterogeneous representations, we propose a unified fusion framework, GDFusion. We seek to model comprehensive temporal fusion through efficient RNN processes, tailored to resource-constrained tasks like autonomous driving. However, vanilla RNNs struggle to embed temporal priors (scene-level information) into network parameters. They also fail to explicitly capture motion dynamics (motion information) and probabilistic geometry (geometry information) during fusion. To address this, we deconstruct the standard RNN by reinterpreting it as an optimization process. Specifically, it minimizes the MSE loss between current and historical features via gradient descent on the feature space. Based on this, we design specific loss functions to quantify discrepancies between each temporal representation and its current-frame counterpart. The gradients of these losses serve as temporal residuals, which are added to the corre + +sponding representation to produce fused features. Through this mechanism, we effectively model all temporal fusions within an RNN-style structure, enabling efficient and adaptive integration of diverse temporal information. + +GDFusion acts as a plug-and-play enhancement for VisionOcc methods. Extensive experiments across multiple baselines validate its robustness and broad applicability. Moreover, GDFusion showcases marked memory efficiency gains over traditional temporal fusion techniques like SOLOFusion [34]. The main contributions of this work are fourfold: i) We conduct an in-depth investigation of the temporal dynamics within the VisionOcc pipeline, uncovering three previously unexplored cues: scene-level, motion, and geometry. These cues respectively enable the incorporation of scene consistency priors, facilitate voxel-level temporal fusion, and enhance the 2D-to-3D feature transformation. ii) We deconstruct the vanilla RNN, reinterpreting it as gradient descent within the feature space. This allows the RNN to operate on a wide array of diverse representation forms. iii) Through this reinterpretation, we propose a unified RNN-style temporal fusion framework that efficiently integrates each type of temporal representation into the VisionOcc pipeline. iv) Our method demonstrates consistent performance gains of $2.2\%$ to $4.7\%$ in mIoU across multiple baselines. It also achieves reduced memory consumption by $30\% -72\%$ , highlighting its broad applicability. + +# 2. Related Work + +# 2.1. Vision-Based 3D Semantic Occupancy + +Vision-based 3D semantic occupancy prediction estimates voxelized semantic states of 3D environments from visual inputs [21, 41, 47, 49, 53]. MonoScene [4] pio + +neers this by lifting features and using 3D context priors for spatial consistency. SurroundOcc [49], Occ3D [41], and OpenOccupancy [47] build dense occupancy annotations for autonomous driving by stacking multiple frames of sparse LiDAR point clouds. Studies like TPVFormer [21], FlashOcc [51], COTR [32], SparseOcc [27], and OSP [38] explore efficient occupancy representations or acceleration techniques. TPVFormer introduces tri-perspective view representation, FlashOcc proposes height-to-channel compression, COTR proposes encoding on downsampled features, SparseOcc focuses on occupancy pruning, and OSP develops resolution-independent occupancy prediction. UniOcc [33], OccNeRF [52], GaussianOcc [12], etc. leverage techniques such as NeRF and 3D Gaussian Splating to perform 3D semantic occupancy prediction with 2D annotations. OCCWorld [55], OCCSora [45], ViewFormer [23], and ALOcc [5] focus on dynamic occupancy prediction tasks, varying from future frame occupancy to occupancy flow prediction. Additionally, works like OCCWorld [55] and OccLLaMA [48] model autonomous driving planning tasks based on occupancy world models. + +# 2.2. Temporal Fusion in Autonomous Driving + +Temporal fusion has attracted growing interest in autonomous driving [17, 19, 30, 34, 50]. In 3D object detection, BEVDet4D [19], BEVFormer v2 [50], PETR v2 [30], and StreamPETR [46] build upon BEVDet [20], BEVFormer [24], and PETR [29], by integrating historical data, effectively improving detection performance. SOLOFusion [34] first explores long-term temporal fusion in BEV space. StreamPETR [46] and Sparse4D v2 [26] further advance temporal fusion by propagating object-centric temporal data via sparse queries across frames. VideoBEV [15] uses recurrent fusion in BEV space for efficiency. Recent efforts extend temporal fusion to occupancy prediction. FBOcc [25], COTR [32], SparseOcc [27], OPUS [44], ALOcc [5], etc. direct adapt temporal fusion techniques from 3D object detection to fuse volume features. OccWorld [55], OccSora [45], ALOcc [5] leverage temporal information to predict future frames or occupancy flow. However, these methods only focus on voxel-level temporal fusion. In contrast, this work thoroughly explores temporal dynamics in the VisionOcc framework and proposes a unified method to integrate diverse temporal representations. + +# 2.3. Optimization-Inspired RNNs + +Optimization-inspired RNNs [2, 14, 36, 40, 54] model classic optimization processes with RNN structures. LISTA [14] converts ISTA's iterations into network layers. CRFasRNN [54] mimics CRF inference through RNN steps. RIM [36] unfolds inverse problems into timesteps, refining updates with RNNs. Recent works such as TTT [40], Titans [2] frame language model updates as a local optiza + +tion problem solved by RNNs. Similarly, this work employs RNNs to fuse diverse temporal cues in VisionOcc. Unlike them, it reinterprets RNNs as optimization processes, delivering a generalized, interpretable approach to unify the fusion of heterogeneous temporal representations. + +# 3. Multi-Level Temporal Cues in VisionOcc + +# 3.1. VisionOcc Pipeline + +VisionOcc processes a sequence of frames $\{I_i^t\}_{i = 1,t = 1}^{N,T}$ from $N$ camera views over $T$ timesteps. At each timestep $t$ the image network extracts 2D features $\{\mathbf{X}_i^t\}_{i = 1}^N$ from each camera view. These multi-view features are transformed to 3D through a 2D-to-3D lifting function [24, 35]: + +$$ +\mathbf {V} ^ {t} = \operatorname {L i f t} \left(\left\{\mathbf {X} _ {i} ^ {t} \right\} _ {i = 1} ^ {N}; \left\{\mathbf {G} _ {i} ^ {t} \right\} _ {i = 1} ^ {N}\right), \tag {1} +$$ + +where $\mathrm{Lift}(\cdot ;\cdot)$ denotes the lifting function, $\mathbf{G}^t$ represents the geometry prior (typically depth maps [5, 19, 25]), and $\mathbf{V}^t$ is the resulting 3D volume features. The task head $f_{o}$ further encodes and decodes these volume features to generate 3D semantic occupancy predictions, i.e., + +$$ +\mathbf {O} ^ {t} = f _ {o} \left(\mathbf {V} ^ {t}\right). \tag {2} +$$ + +Conventional VisionOcc approaches [5, 19, 25] typically use a fusion module to incorporate voxel-level temporal information before the task head. This module maintains a memory queue that stores volume features from the previous $N_{h}$ frames, i.e., $\mathbf{H}_v^{t - 1} = \{\mathbf{V}^{t - 1},\mathbf{V}^{t - 2},\dots,\mathbf{V}^{t - N_h}\}$ , where $\mathbf{H}_v^{t - 1}$ represents the historical memory state. When processing the current frame's volume features, it fuses memorized temporal features to enhance them, i.e., + +$$ +\mathbf {V} _ {f} ^ {t} = \operatorname {F u s e} \left(\mathbf {V} ^ {t}, \mathbf {H} _ {v} ^ {t - 1}\right). \tag {3} +$$ + +Here, $\mathbf{V}_f^t$ is the fused features, used to replace $\mathbf{V}^t$ in Eq. (2). + +# 3.2. Temporal Cue Analysis and Formulation + +Traditional voxel-level temporal fusion [5, 25, 32] stacks position-level evidence over time for reliable occupancy prediction. However, we argue that several temporal cues remain underutilized. Within the VisionOcc pipeline, we propose three distinct types of temporal information, each serving a unique role, as illustrated in Fig. 1. + +Scene-level Cue. The environment evolves continuously over short time spans, implying exploitable scene consistency priors. Accordingly, we design scene-level information to encode global properties, such as lighting, weather, and road characteristics. Drawing from domain adaptation [13, 39], this information is expected to capture abstract, domain-specific features. It complements voxel-level features, which focus on per-voxel semantics. Inspired by test-time adaptation [6, 39, 40], we introduce additional scene-adaptive network parameters $\mathbf{S}^t$ (Sec. 4.2). These parameters engage in inference across all volume features, capturing a global receptive field and serving as a proxy for scene + +![](images/18b072937d82b75081a06a76420600a59abe9282b78bbefd696a8e928ffe88b7.jpg) +Figure 2. Multi-level temporal fusion in the VisionOcc pipeline. Volume features $\mathbf{V}^t$ , geometry $\mathbf{G}^t$ , motion $\mathbf{M}^t$ , and scene-adaptive parameters $\mathbf{S}^t$ are enhanced through RNN-style temporal fusion, each capturing distinct temporal dynamics. Single-frame-sized historical states $\mathbf{H}_v^{t-1}$ , $\mathbf{H}_g^{t-1}$ , $\mathbf{H}_m^{t-1}$ , and $\mathbf{H}_s^{t-1}$ are stored in memory and updated frame-by-frame. + +information. They are dynamically updated with temporal inputs to enable continuous scene adaptation. + +Motion Cue. In voxel-level temporal fusion, historical features must align with the current frame's coordinate system for positional semantic consistency. Ideally, this should handle dynamic object motion and camera pose estimation errors. We formulate the alignment with these corrections: + +$$ +\hat {\mathbf {P}} = \mathbf {R} _ {t \rightarrow t - 1} (\mathbf {P} + \mathbf {M} ^ {t}), \operatorname {W a r p} \left(\mathbf {H} _ {v} ^ {t - 1}\right) = \operatorname {S a m p l e} \left(\mathbf {H} _ {v} ^ {t - 1}; \hat {\mathbf {P}}\right), \tag {4} +$$ + +where $\mathbf{P}$ is the standard volume grid coordinates, and $\mathbf{R}_{t\rightarrow t - 1}$ denotes the transformation matrix from the current to the last frame. The warping function $\mathrm{Warp}(\cdot)$ aligns features $\mathbf{H}_v^{t - 1}$ to the current frame's ego coordinate system. This is implemented via the Sample $(\cdot ;\cdot)$ function [35], which samples features based on the transformed coordinates $\hat{\mathbf{P}}$ .The term $\mathbf{M}^t$ represents the offset intended to account for potential motion compensation and pose estimation error correction. It is estimated by a linear layer $f_{m}$ .. + +$$ +\mathbf {M} ^ {t} = f _ {m} \left(\mathbf {V} ^ {t}\right). \tag {5} +$$ + +Notably, the estimation of $\mathbf{M}^t$ requires no additional supervision. Instead, it is adaptively learned, similar to deformable networks [9, 56]. As this learned offset facilitates positional alignment between frames, we refer to it as motion in the subsequent discussions, despite its implicit learning. Temporal coherence in consecutive frames allows historical motion patterns to refine current estimates. Details of the temporal motion fusion are provided in Sec. 4.3. + +Geometry Cue. In VisionOcc, depth maps typically act as geometric priors for 2D-to-3D lifting [5, 20, 25], encoded as discretized probability distributions over uniform bins: + +$$ +\mathbf {G} ^ {t} = \left\{P \left(d = d _ {k} \mid \mathbf {X} ^ {t}\right) \right\} _ {k = 1} ^ {K}, \quad P (d \mid \mathbf {X} ^ {t}) = f _ {g} (\mathbf {X} ^ {t}), \tag {6} +$$ + +where $d_{k}$ is the center of the $k$ -th depth bin, $K$ is the total number of bins, and the network $f_{g}$ estimates depth from image features. The view index of 2D features $\mathbf{X}^t$ is omitted for notational simplicity. We argue that scene geometry remains consistent over time (assuming motion is ignored in + +its estimation). Geometry derived from past camera viewpoints provides complementary information for the current frame. Thus, we propose temporal geometry fusion to yield a more robust geometric prior, detailed in Sec. 4.4. + +# 4. Gradient Descent-based Temporal Fusion + +The complex representations of each temporal cue inherently make their fusion non-trivial. To address this, we propose a unified RNN-style framework to streamline and standardize the integration of distinct temporal representations (i.e., V, S, M, G, as defined earlier). Fig. 2 illustrates the VisionOcc pipeline with multi-level temporal fusion, detailed in Alg. 1's pseudocode, where fused information is highlighted in red. For notational consistency, temporally enhanced features use subscript $f$ (e.g., $\mathbf{V}_f$ ), and historical states are denoted by $\mathbf{H}$ , further distinguished by subscripts. + +# 4.1. Modeling RNN Dynamics via Gradient Descent + +To unify temporal fusion, we reinterpret standard RNN updates as gradient descent steps to minimize discrepancies between current and historical information. This perspective allows us to integrate diverse temporal representation types within one theoretical framework. See Fig. 3 for an illustration of gradient-descent-based temporal fusion. + +Proposition 1. The RNN update step $h^t = Ah^{t-1} + Bx^t$ is equivalent to a gradient descent step on $h^{t-1}$ minimizing the loss function $\mathcal{L}^t = \|Ah^{t-1} - Bx^t\|^2$ . + +Proof. The gradient of $\mathcal{L}^t$ w.r.t. $h^{t - 1}$ is: + +$$ +\frac {\partial \mathcal {L} ^ {t}}{\partial h ^ {t - 1}} = 2 A ^ {\top} (A h ^ {t - 1} - B x ^ {t}). +$$ + +Applying gradient descent with learning rate $\eta$ : + +$$ +h ^ {t} = h ^ {t - 1} - \eta \cdot 2 A ^ {\top} (A h ^ {t - 1} - B x ^ {t}). +$$ + +Let $A' = I - 2\eta A^\top A$ and $B' = 2\eta A^\top B$ , then: + +$$ +h ^ {t} = A ^ {\prime} h ^ {t - 1} + B ^ {\prime} x ^ {t}. +$$ + +matching the RNN update form, proving the equivalence. + +□ + +![](images/f752cfefa0843f7af36ef8ad23d8546a05bb3ab2ed7a88219bfd7251f582eb3c.jpg) +Figure 3. Update dynamics of gradient descent-based temporal fusion pipeline. $\mathbf{f}^t$ denotes the (geometry, motion, voxel-level, scene-level) feature of the current frame. $\mathbf{H}^{t - 1}$ and $\mathbf{H}^t$ represent the prior and current historical states, respectively. + +Next, we will detail how Prop. 1 guides the fusion of distinct temporal cues, deriving loss functions and historical state update equations for each fusion type. + +# 4.2. Scene-Level Temporal Fusion + +We interpret scene-level fusion as a mini domain adaptation task over time. This perspective allows us to capture and adapt to varying environmental conditions across temporal sequences. Motivated by research in test-time adaptation [6, 39], large language models (LLM) [37, 40], and self-supervised learning [7], we propose encoding scene information into network parameters via a self-supervised task: + +$$ +\mathcal {L} _ {s} ^ {t} = \left\| f _ {s} ^ {t} \left(\operatorname {a u g} _ {1} \left(\mathbf {V} ^ {t}\right)\right) - \operatorname {a u g} _ {2} \left(\mathbf {V} ^ {t}\right) \right\| ^ {2}, \tag {7} +$$ + +where $\mathrm{aug}_1(\cdot)$ and $\mathrm{aug}_2(\cdot)$ are distinct augmentation functions. Given the high dimensionality of $\mathbf{V}^t$ , we use linear mappings as augmentations: $\mathrm{aug}_i(\mathbf{V}^t) = \mathbf{Q}_i\mathbf{V}^t$ , $i = 1,2$ , where $\mathbf{Q}_i \in \mathbb{R}^{c \times c}$ are learnable parameters. With slight abuse of notation, $\mathbf{V}^t$ henceforth denotes flattened volume features, $c$ as the channel dimension, $n$ as the flattened spatial dimensions. Inspired by sequence modeling in LLM [2, 40], we build the parameterized network $f_s$ as: + +$$ +f _ {s} ^ {t} (\mathbf {X}; \mathbf {S} ^ {t}) = \gamma^ {t} \odot \hat {\mathbf {Z}} + \beta^ {t} + \mathbf {X}, \hat {\mathbf {Z}} = \operatorname {N o r m} \left(\mathbf {W} ^ {t} \mathbf {X} + \mathbf {b} ^ {t}\right), \tag {8} +$$ + +where $\mathrm{Norm}(\cdot)$ denotes Z-score normalization, $\odot$ represents the Hadamard product, $\gamma^t\in \mathbb{R}^c$ $\beta^t\in \mathbb{R}^c$ are learnable scale and shift parameters for layer normalization, and $\mathbf{W}^t\in \mathbb{R}^{c\times c}$ and $\mathbf{b}^t\in \mathbb{R}^c$ form the linear transformation. These four parameters serve as an instantiation of scene-level temporal information, i.e., + +$$ +\mathbf {H} _ {s} ^ {t} = \mathbf {S} ^ {t} = \left\{\gamma^ {t}, \beta^ {t}, \mathbf {W} ^ {t}, \mathbf {b} ^ {t} \right\}, \tag {9} +$$ + +where $\mathbf{S}^0$ denotes the initial parameters. Building upon established meta-learning paradigms [1, 11, 40], $\mathbf{S}^0$ is optimized jointly with the network's primary objective function during training. During inference, $\mathbf{S}^t$ can be updated frame-by-frame from $\mathbf{S}^0$ , memorizing global scene information by minimizing $\mathcal{L}_s^t$ . Following Prop. 1, we compute the scene-level historical residual as: + +$$ +\nabla_ {s} ^ {t} = \nabla_ {\gamma^ {t}, \beta^ {t}, \mathbf {W} ^ {t}, \mathbf {b} ^ {t}} \mathcal {L} _ {s} ^ {t}. \tag {10} +$$ + +Algorithm 1 Multi-Level Temporal Fusion in VisionOcc Pipeline at Time $t$ + +Input: Image features of time $t$ : $\{\mathbf{X}_i^t\}_{i=1}^N$ , historical states $\mathbf{H}_v^{t-1}, \mathbf{H}_s^{t-1}, \mathbf{H}_m^{t-1}, \mathbf{H}_g^{t-1}$ , hyper-parameters $\eta_m, \eta_s$ . + +Output: Predicted 3D semantic occupancy map $\mathbf{O}^t$ , updated historical states $\mathbf{H}_v^t, \mathbf{H}_s^t, \mathbf{H}_m^t, \mathbf{H}_g^t$ . + +1: $\mathbf{G}^t = f_g(\mathbf{X})$ # Geometry prediction +https://www.temporalGeometryFusion.com +2: $\eta_{g} =$ sigmoid $\left(f_{\eta_g}\left(\operatorname {cat}(\operatorname{Warp}_c(\mathbf{H}_q^{t - 1}),\mathbf{G}^t)\right)\right)\# Eq.$ (22) +3: $\mathbf{H}_g^t = (1 - \eta_g)\hat{\mathbf{H}}_g^{t - 1} + \eta_g\mathbf{G}^t$ $\mathbf{G}_f^t = \mathbf{H}_g^t$ +4: $\mathbf{V}^t = \mathrm{Lift}(\{\mathbf{X}_i^t\}_{i=1}^N; \{\mathbf{G}_{f_i}^t\}_{i=1}^N)$ # Lift 2D to 3D +>>> Temporal Motion Fusion +>>> +5: $\mathbf{H}_m^t = \mathbf{M}^t -\eta_m\nabla_m^t$ $\mathbf{M}_f^t = \mathbf{H}_m^t\# \nabla_m^t$ is from Eq. (16) +6: $\mathbf{H}_v^t = A_v\mathrm{Sample}(\mathbf{H}_v^{t - 1};\mathbf{R}_{t\to t - 1}(\mathbf{P} + \mathbf{M}_f^t)) + B_v\mathbf{V}^t,\mathbf{V}_f^t = \mathbf{H}_v^t$ ### Scene-Level Temporal Fusion ### +7: $\mathbf{H}_s^t = \mathbf{H}_s^{t - 1} - \eta_s\nabla_s^t$ $\mathbf{S}_f^t = \mathbf{H}_s^t\# \nabla_s^t$ is from Eqs. (10, 11) +8: $\hat{\mathbf{V}}^t = f_s^t (\mathbf{Q}_o\mathbf{V}_f^t;\mathbf{S}_f^t)$ +9: $\mathbf{O}^t = f_o(\tilde{\mathbf{V}}^t)$ #Map to 3D semantic occupancy +10: return $\mathbf{O}^t, \mathbf{H}_v^t, \mathbf{H}_s^t, \mathbf{H}_m^t, \mathbf{H}_g^t$ + +This gradient is efficiently computed via matrix operations (see supplemental material): + +$$ +\nabla_ {\gamma} ^ {t} = 2 \left(\Delta_ {1} \odot \hat {\mathbf {Z}} ^ {t}\right) \mathbf {1} _ {n}, \quad \nabla_ {\beta} ^ {t} = 2 \Delta_ {1} \mathbf {1} _ {n}, +$$ + +$$ +\nabla_ {W} ^ {t} = \Delta_ {3} (\mathbf {Q} _ {1} \mathbf {V} ^ {t}) ^ {\top}, \quad \nabla_ {\mathbf {b}} ^ {t} = \Delta_ {3} \mathbf {1} _ {n}, +$$ + +$$ +\Delta_ {3} = \left(\Delta_ {2} - \frac {1}{n} \mathbf {1} _ {c} \mathbf {1} _ {c} ^ {\top} \Delta_ {2} - \frac {1}{n} \hat {\mathbf {Z}} ^ {t} \odot \left(\mathbf {1} _ {c} \mathbf {1} _ {c} ^ {\top} (\hat {\mathbf {Z}} ^ {t} \odot \Delta_ {2})\right)\right) \oslash \left(\mathbf {1} _ {c} \boldsymbol {\sigma}\right), +$$ + +$$ +\Delta_ {2} = 2 \gamma^ {t - 1} \odot \Delta_ {1}, \quad \Delta_ {1} = \gamma \odot f _ {s} ^ {t - 1} \left(\mathbf {Q} _ {1} \mathbf {V} ^ {t}\right) - \mathbf {Q} _ {2} \mathbf {V} ^ {t}, \tag {11} +$$ + +where $\varnothing$ denotes Hadamard division, $\mathbf{1}_c\in \mathbb{R}^{c\times 1}$ and $\mathbf{1}_n\in$ $\mathbb{R}^{n\times 1}$ represent vectors of ones. To simplify notation, we define $\hat{\mathbf{Z}}^t = \mathrm{Norm}(\mathbf{W}^{t - 1}\mathbf{Q}_1\mathbf{V}^t +\mathbf{b}^{t - 1})$ as the normalized features of $\mathbf{V}^t$ , computed using parameters from time step $t - 1$ . The historical scene-level state $\mathbf{H}_s^t$ is updated as: + +$$ +\mathbf {H} _ {s} ^ {t} = \mathbf {H} _ {s} ^ {t - 1} - \eta_ {s} \nabla_ {s} ^ {t}, \quad \mathbf {S} _ {f} ^ {t} = \mathbf {H} _ {s} ^ {t}, \tag {12} +$$ + +where $\eta_{s}$ controls the update magnitude, and $\mathbf{S}_f^t$ denotes the historical fused scene-level representation. Per specific scene, $\mathbf{H}_s^t$ undergoes continuous updates through the self-supervised task during both training and inference, enabling dynamic adaptation to changing scene conditions. + +As shown in Fig. 2, the scene-level fusion module is positioned after voxel-level temporal fusion. At each time step $t$ , we first update the scene-adaptive parameters via Eq. (12), then perform forward propagation: + +$$ +\hat {\mathbf {V}} ^ {t} = f _ {s} ^ {t} \left(\mathbf {Q} _ {o} \mathbf {V} _ {f} ^ {t}; \mathbf {S} _ {f} ^ {t}\right), \tag {13} +$$ + +thus injecting historical scene-level information into the volume features. Here, $\mathbf{Q}_o$ denotes additional learnable weights, distinct from the augmentation matrices $\mathbf{Q}_1$ , $\mathbf{Q}_2$ . + +# 4.3. Temporal Motion Fusion + +To mitigate frame-to-frame alignment errors in voxel-level temporal fusion, we exploit historical motion information by minimizing the discrepancy between consecutive frames. This leads to our motion-based loss function: + +$$ +\mathcal {L} _ {m} ^ {t} = \left\| \operatorname {W a r p} \left(\mathbf {H} _ {m} ^ {t - 1}\right) - \mathbf {M} ^ {t} \right\| ^ {2}, \tag {14} +$$ + +where $\mathbf{M}^t$ (Eq. (5)) denotes the predicted motion map for the current frame and $\mathbf{H}_m^{t - 1}$ is the historical motion state. Same to Eq. (4), the warping operation is formulated as: + +$$ +\operatorname {W a r p} \left(\mathbf {H} _ {m} ^ {t - 1}\right) = \operatorname {S a m p l e} \left(\mathbf {H} _ {m} ^ {t - 1}; \mathbf {R} _ {t \rightarrow t - 1} (\mathbf {P} + \mathbf {M} ^ {t})\right). \tag {13} +$$ + +The motion residual is computed as: + +$$ +\nabla_ {m} ^ {t} = \nabla_ {\mathbf {M} ^ {t}} \mathcal {L} _ {m} ^ {t} = 2 \left(\mathrm {W a r p} (\mathbf {H} _ {m} ^ {t - 1}) - \mathbf {M} ^ {t}\right)\left(\mathbf {R} _ {t \rightarrow t - 1} ^ {\top} \mathbf {J} - \mathbf {I}\right), (1 6 +$$ + +where $\mathbf{J}$ represents the Jacobian matrix of the sampling operation w.r.t. the sampling coordinates (detailed derivation in supplementary material). For notational simplicity, we omit spatial dimensions in this formulation. We use the derivative w.r.t. $\mathbf{M}^t$ as the historical residual, rather than $\mathbf{H}_m^{t - 1}$ , to avoid additional coordinate transformations. The historical motion state is updated according to: + +$$ +\mathbf {H} _ {m} ^ {t} = \mathbf {M} ^ {t} - \eta_ {m} \nabla_ {m} ^ {t}, \quad \mathbf {M} _ {f} ^ {t} = \mathbf {H} _ {m} ^ {t}. \tag {17} +$$ + +Here, $\eta_{m}$ balances current motion predictions against the warped historical motion. $\mathbf{M}_f^t$ is the fused motion, which not only gathers position-level clues from historical motion but also gets information from interpolation gradients (cf. deformable networks [9, 56]). It is used for subsequent voxel-level temporal fusion, as shown in Fig. 2. + +# 4.4. Temporal Geometry Fusion + +To further enhance the 2D-to-3D lifting process, we leverage historical geometry as prior information, introducing a geometry fusion loss function defined as follows: + +$$ +\mathcal {L} _ {g} ^ {t} = \left\| \operatorname {W a r p} _ {c} \left(\mathbf {H} _ {g} ^ {t - 1}\right) - \mathbf {G} ^ {t} \right\| ^ {2}. \tag {18} +$$ + +Here, $\mathbf{G}^t$ represents the geometry representation of the current frame, while $\mathbf{H}_g^{t - 1}$ symbolizes the historical geometry state. The function $\mathrm{Warp}_c(\cdot)$ transforms $\mathbf{H}_g^{t - 1}$ from the previous camera coordinate system to the current one. For notational simplicity, we define $\hat{\mathbf{H}}_g^{t - 1} = \mathrm{Warp}_c(\mathbf{H}_g^{t - 1})$ . The historical geometry residual is then computed as: + +$$ +\nabla_ {g} ^ {t} = \nabla_ {\hat {\mathbf {H}} _ {g} ^ {t - 1}} \mathcal {L} _ {g} ^ {t} = 2 \left(\hat {\mathbf {H}} _ {g} ^ {t - 1} - \mathbf {G} ^ {t}\right). \tag {19} +$$ + +The updated rule of the historical geometric state is: + +$$ +\mathbf {H} _ {g} ^ {t} = \hat {\mathbf {H}} _ {g} ^ {t - 1} - \eta_ {g} \nabla_ {g} ^ {t}, \tag {20} +$$ + +![](images/f81f5ad2d0f0b18e80a946c08df8a8cb04cdbb17cf520a07e81ff954e9aa95e2.jpg) +(a) Performance + +![](images/fa806bd27eeb2b35194462e5cd58446e876dd9bb1d8283c18fab7db48853bf60.jpg) +(b) Inference Memory +Figure 4. Comparison of our GDFusion and SOLOFusion w.r.t. memory consumption. SOLOFusion boosts performance with longer sequences but increases inference memory, while GDFusion achieves high performance with low memory consumption. + +where $\eta_{g}$ is a learning rate that controls the balance between the current geometry prediction and the historical geometric residual. Incorporating Eq. (19) and, for simplicity, absorbing the factor of 2 into the learning rate, we obtain: + +$$ +\mathbf {H} _ {g} ^ {t} = \left(1 - \eta_ {g}\right) \hat {\mathbf {H}} _ {g} ^ {t - 1} + \eta_ {g} \mathbf {G} ^ {t}, \quad \mathbf {G} _ {f} ^ {t} = \mathbf {H} _ {g} ^ {t}, \tag {21} +$$ + +where $\mathbf{G}_f^t$ denotes the fused geometry representation, which is used for subsequent 2D-to-3D lifting, as shown in Fig. 2. Since $\mathbf{G}^t$ is predicted as discrete probabilities along the camera's line of sight, we seek to preserve its normalized probabilistic distribution. To this end, we reinterpret its update as weighted averaging with a per-frame adaptive $\eta_g$ , resembling GRU gating [8]. Specifically, we define: + +$$ +\eta_ {g} = \operatorname {s i g m o i d} \left(f _ {\eta_ {g}} \left(\operatorname {c a t} \left(\hat {\mathbf {H}} _ {g} ^ {t - 1}, \mathbf {G} ^ {t}\right)\right)\right), \tag {22} +$$ + +where $\operatorname{cat}(\cdot)$ denotes vector concatenation, and the network $f_{\eta_g}$ maps the concatenated features to a scalar value. + +# 4.5. Memory-Efficient Voxel-Level Temporal Fusion + +Traditional voxel-level temporal fusion [5, 19, 25, 32] struggles with storing volume features from $N_{h}$ frames, causing excessive memory use as $N_{h}$ grows. To overcome this, we build on the central insight of this paper, employing a single-frame-sized RNN hidden state for temporal modeling. This is modeled directly using a vanilla RNN as: + +$$ +\mathbf {H} _ {v} ^ {t} = A _ {v} \operatorname {w a r p} \left(\mathbf {H} _ {v} ^ {t - 1}\right) + B _ {v} \mathbf {V} ^ {t}, \quad \mathbf {V} _ {f} ^ {t} = \mathbf {H} _ {v} ^ {t}. \tag {23} +$$ + +Here $\mathbf{H}_v^t$ is redefined as the single-frame-sized historical voxel-level state, $\mathbf{V}_f^t$ is the temporal-enhanced volume feature, and $A_v, B_v \in \mathbb{R}^{c \times c}$ are learnable fusion parameters. + +# 5. Experiment + +Benchmark. Our experiments are based on the nuScenes dataset [3], which provides extensive data to develop and evaluate essential 3D perception algorithms. This dataset comprises 1,000 scenes in total, with 700 designated for + +
MethodBackboneInput SizemIoUmIoUDIoUMemory
UniOCC [33]ResNet-50256 × 70439.7---
SurroundSDF [28]ResNet-50256 × 70442.436.2--
FlashOCC [51]ResNet-50256 × 70432.024.765.31205
COTR [32]ResNet-50256 × 70444.538.675.08063
ViewFormer [23]ResNet-50256 × 70441.935.070.22875
OPUS [44]ResNet-50256 × 70436.233.354.02671
BEVDetOcc-SF [19, 34]ResNet-50256 × 70441.934.475.110717
BEVDetOcc-GFResNet-50256 × 70443.6 ↑1.736.0 ↑1.677.8 ↑2.73017 ↓7700
FB-Occ [25]ResNet-50256 × 70439.834.269.94099
FB-Occ-GFResNet-50256 × 70441.7 ↑1.935.8 ↑1.673.2 ↑3.32879 ↓1224
ALOcc [5]ResNet-50256 × 70445.539.375.310793
ALOcc-GFResNet-50256 × 70446.5 ↑1.040.2 ↑0.977.4 ↑2.14347 ↓6446
+ +Table 1. Comparison of 3D semantic occupancy prediction performance on the Occ3D dataset, evaluated with mIoU, mIoU, and IoU metrics. Relative improvements are highlighted with red arrows $\uparrow$ . Our GDFusion (-GF) consistently enhances the performance of existing 3D semantic occupancy prediction methods and reduces memory consumption. + +
MethodBackbonemIoUmIoUDIoUMemory
BEVFormer [24]ResNet-10139.237.2-4667
OSP [38]ResNet-10141.237.0-2671
SurroundOcc [49]InternImage-Base40.7---
COTR [32]Swin-Base46.241.374.9-
BEVDetOcc-SFSwin-Base47.141.276.813682
BEVDetOcc-GFSwin-Base48.5↑1.442.9↑1.879.5↑2.74492↓9190
ALOccSwin-Base50.646.178.124072
ALOcc-GFSwin-Base51.8↑1.247.4↑1.379.9↑1.88312↓15760
+ +training, 150 for validation, and 150 for testing. Occ3D [41] extends the nuScenes dataset by incorporating voxel-wise annotations with a voxel resolution of $0.4m$ across all spatial dimensions. The spatial range extends from $-40m$ to $40m$ along both the X and Y axes, and from $-1m$ to $5.4m$ along the Z axis. It includes 18 semantic categories: 17 object classes plus an empty class for unoccupied regions. Following existing literature [5, 25, 32], we use mIoU across all semantic classes as the primary metric. We also report the mIoU for dynamic object categories $(\mathrm{mIoU}_{\mathrm{D}})$ and category-agnostic IoU as supplementary metrics, focusing on foreground and scene-overall performance, respectively. + +Implementation Details. We evaluate GDFusion by incorporating it into 3 baseline models, BEVDetOcc [19], FBOcc [25], and ALOcc [5], yielding the enhanced variants BEVDetOcc-GF, FB-Occ-GF, and ALOcc-GF. Following prior work [5, 23, 51], we use a ResNet-50 [16] backbone and a $256 \times 704$ image size for most experiments, scaling up to Swin Transformer Base [31] with $512 \times 1408$ images in larger-scale tests. Similar to FB-Occ and ALOcc, we adopt the video-level data shuffling strategy from SOLO-Fusion [34] during training. For BEVDet, we follow [5, 25] to implement a 16-frame temporal fusion version based on SOLOFusion as a baseline (BEVDetOcc-SF). Both the baseline and the version with GDFusion were trained for 12 + +Table 2. Scaling-up experiment of 3D semantic occupancy prediction on the Occ3D dataset. The top three rows feature an input size of $900 \times 1600$ , while the remaining use $512 \times 1408$ . + +
Exp.ConfigurationmIoUmIoUDIoU
0Baseline38.031.071.1
1+ SOLOFusion (16f)41.434.074.4
2+ History fusion from start41.233.674.6
3Baseline + RNN fusion41.333.674.8
4+ History fusion from start41.4 ↑0.133.9 ↑0.374.8 ↑0
5+ No video split41.6 ↑0.233.7 ↓0.275.3 ↑0.5
6+ Sinusoidal time embedding41.8 ↑0.234.0 ↑0.376.5 ↑1.2
+ +Table 3. Ablations on improving RNN-based voxel-level fusion. + +epochs using CBGS [34] with a learning rate of $2 \times 10^{-4}$ and a global batch size of 16. The image and BEV augmentation strategies are the same as in the original BEVDet codebase [19]. The relevant parameters for FB-Occ and ALOcc are kept the same as in their original papers. + +# 5.1. Memory Consumption + +GDFusion reduces inference memory by storing all historical information in a single-frame-sized hidden state. As shown in Tab. 1, replacing baseline temporal fusion modules with GDFusion significantly reduces memory consumption. To emphasize our approach's memory efficiency, we further compared it with SOLOFusion, using BEVDetOcc as the baseline. As illustrated in Fig. 4, the memory consumption of SOLOFusion scales linearly with the number of stored historical frames, whereas GDFusion maintains memory usage comparable to non-temporal fusion levels. Despite utilizing less memory, GDFusion harnesses information from all historical frames and outperforms the long-history fusion variant of SOLOFusion. Notably, although GDFusion stores various types of temporal information, the additional memory overhead relative to voxel features is negligible. + +# 5.2. Comparison with SOTAs + +Tab. 1 compares GDFusion with SOTA methods. We implemented three baseline models (BEVDetOcc, FB-Occ, + +
VoxelSceneMotionGeometrymIoUmIoUDIoU
B38.031.071.1
BG✓39.232.073.0
BS✓39.031.974.1
BV✓41.834.076.5
BVS✓✓42.534.877.0
BVM✓✓42.434.976.4
BVG✓✓42.735.373.8
BVMG✓✓✓43.035.577.0
BVSG✓✓✓43.035.577.5
BVSM✓✓✓42.634.877.3
Full✓✓✓✓43.335.377.8
+ +ALOcc) using official codes, citing or reevaluating other methods with their official checkpoints. GDFusion leads to consistently substantial improvements across all metrics. Specifically, it achieves 1-2 point gains in mIoU (all-class average). Notable improvements are also observed in $\mathrm{mIoU_D}$ , which focuses on dynamic object classes. Most remarkably, it delivers significant gains of 2-4 points in IoU, indicating superior scene geometry quality. These improvements highlight GDFusion's effectiveness, leveraging comprehensive temporal information to boost geometric consistency and semantic understanding. + +In Tab. 2, we scale the backbone and input size with BEVDetOcc-SF and ALOcc. GDFusion consistently maintains the improvements noted in smaller experiments and significantly cuts memory usage to about $1/3$ of the original, underscoring our method's scalability. + +# 5.3. Ablation Study + +In this subsection, we conduct an ablation study on our method. Unless stated otherwise, we use a spatially compressed BEVDet as our baseline model, which compresses height features into the channel dimension and applies 2D convolution for volume encoding [51]. + +Pre-Uplift on Voxel-Level Temporal Fusion. As shown in Tab. 3, vanilla RNN-based temporal fusion (Exp. 3) achieved comparable performance to SOLOFusion (Exp. 1), demonstrating its effectiveness. We then explored several further refinements. First, the previous method [25] delays fusion training until the second epoch to avoid noisy gradients from immature features (Exps. 1-2). Exps. 3-4 show that RNN-based fusion does not require this delay, as its single-frame hidden state is less affected by erroneous gradients than multi-frame stacking methods. Second, SOLOFusion [34] splits videos to diversify training, whereas RNN fusion excels with continuous videos (Exp. 5), avoiding discontinuities and utilizing full temporal information. Finally, adding sinusoidal time embedding [43] further boosts performance (Exp. 6). + +Effect of Individual Temporal Cues. The ablation results + +Table 4. Ablations on different temporal cues. B, G, V, S, and M represent baseline, temporal geometry fusion, voxel-level fusion, scene-level fusion, and temporal motion fusion, respectively. + +
ModuleRuntime (ms)Proportion (%)
BEVDet-SF (16)155.6-
BEVDet-GF (ours full)146.6100
Scene-AutoGrad8.8-
Scene-Custom Matmul6.74.57
Motion-AutoGrad9.9-
Motion-Custom Matmul7.75.25
Geometry4.83.27
Voxel6.54.43
+ +Table 5. Runtime analysis of key components, vs. SOLOFusion (16 frames). AutoGrad refers to PyTorch's automatic differentiation; Custom Matmul is our custom matrix multiplication. Fusion modules are abbreviated (e.g., scene, voxel) for clarity. + +in Tab. 4 highlight the role of different temporal cues in our GDFusion framework. Using only the geometry cue (BG), scene cue (BS), or voxel-level temporal fusion (BV) each brought a substantial boost in performance. Combining different temporal cues (BVS - Full) led to further improvements, with motion (BVM) adding gains atop voxel-level fusion. Integrating all cues (voxel-level, scene-level, motion, and geometry) yielded optimal performance (Full). These findings underscore the complementary nature of different temporal cues. Omitting any of them reduced accuracy, affirming the value of GDFusion's comprehensive integration for robust 3D scene understanding. + +# 5.4. Wall-Clock Time + +We conduct a runtime analysis of key components in GDFusion. As shown in Tab. 5, our method outperforms the multi-frame stacking method SOLOFusion in total time consumption. Each temporal fusion component consumes less than $6\%$ of the total inference time (146.6ms), demonstrating the efficiency of GDFusion. Moreover, our custom matrix multiplication method for backpropagation outperforms PyTorch's built-in AutoGrad, achieving $32\%$ and $22\%$ efficiency gains in scene-level and motion fusion, respectively, demonstrating enhanced deployment feasibility. + +# 6. Conclusion and Discussion + +In this work, we introduce a novel temporal fusion framework for vision-based semantic occupancy prediction. Our method examines untapped temporal signals in VisionOcc, including scene-level, motion, and geometry cues. We reinterpret vanilla RNNs from a gradient descent perspective, unifying the fusion of diverse temporal representations. The proposed GradFusion integrates these signals seamlessly, boosting performance over baselines while significantly reducing memory usage. Our contributions include exploring varied temporal cues for VisionOcc and advancing gradient descent-based fusion techniques for complex temporal data. We believe the principles outlined here extend beyond VisionOcc, potentially benefiting a wide range of tasks. + +# References + +[1] Antreas Antoniou, Harrison Edwards, and Amos Storkey. How to train your maml. In Proceedings of International Conference on Learning Representations, 2018. 5 +[2] Ali Behrouz, Peilin Zhong, and Vahab Mirrokni. Titans: Learning to memorize at test time. arXiv preprint arXiv:2501.00663, 2024. 3, 5 +[3] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscene: A multimodal dataset for autonomous driving. 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While some defense methods have been raised to strengthen the adversarial robustness of multi-exit neural networks, we identify a long-neglected flaw in the evaluation of previous studies: simply using a fixed set of exits for attack may lead to an overestimation of their defense capacity. Based on this finding, our work explores the following three key aspects in the adversarial robustness of multi-exit neural networks: (1) we discover that a mismatch of the network exits used by the attacker and defender is responsible for the overestimated robustness of previous defense methods; (2) by finding the best strategy in a two-player zero-sum game, we propose AIMER as an improved evaluation scheme to measure the intrinsic robustness of multi-exit neural networks; (3) going further, we introduce NEED defense method under the evaluation of AIMER that can optimize the defender's strategy by finding a Nash equilibrium of the game. Experiments over 3 datasets, 7 architectures, 7 attacks and 4 baselines show that AIMER evaluates the robustness $13.52\%$ lower than previous methods under AutoAttack, while the robust performance of NEED surpasses single-exit networks of the same backbones by $5.58\%$ maximally. + +# 1. Introduction + +Deep neural networks have achieved remarkable advancements in the field of computer vision, yet researchers are drawn to two pressing issues. First, the computational cost escalates as the networks grow deeper, leading to the rise of multi-exit neural networks [11, 12, 33, 37, 43]. These networks utilize an early-exit mechanism to produce results + +![](images/88dcd1363104002e9fea7e433417e732b2e6a6c3d87eb070d99d8c5498089af7.jpg) +Figure 1. The triple focuses of this paper and their relationship. (1) the A-D mismatch phenomenon we find; (2) The improved evaluation scheme AIMER we propose; (3) The NEED method to optimize the defense under the evaluation of AIMER. (2) and (3) are principled by game theory. + +from shallower branches, maintaining accuracy while reducing computational load. Second, the vulnerability of neural networks to adversarial attacks [2, 22, 32, 42] poses a significant challenge, where small, carefully crafted perturbations can be added to input data to deceive the predictions of models. In recent years, enhancing the robustness of models under adversarial attacks has thus emerged as a pivotal research topic [9, 19, 22, 27, 41, 47]. + +Inspired by the above work, increasing efforts have been devoted to the study of the adversarial robustness of multi-exit neural networks [3, 10, 13, 15, 16]. However, we identify a subtle defect long-neglected in the current robustness evaluation: simply using fixed network exits as the targets of attack results in insufficient flexibility that unfairly weakens the attacker while favoring the defender. This might lead to an overestimation in the robustness evaluation of multi-exit neural networks. In this paper, by delving into the following + +three challenging problems, we strive to expose the negative consequence of such flawed exit-fixed evaluation and resort to game theory to amend it. + +What does exit-fixed robustness evaluation lead to? Through experimental investigations of multi-exit neural networks, we observe a notable phenomenon, which we term as Attack-Defense (A-D) mismatch. In multi-exit neural networks, both the attacker and defender have the freedom of choosing which exit (or an ensemble) they use for generating adversarial examples or inference. However, when the attacker avoids the exact ensemble of exits the defender uses for inference (i.e., a mismatch), the evaluated robustness is always higher than that of the matching case (Figure 1), bringing additional robustness apart from the intrinsic robustness obtained from adversarial training. Especially when the exits for attack are fixed, it is quite easy to cause an A-D mismatch by detouring with a different inference strategy. Therefore, we argue that such exit-fixed evaluation exacerbates the additional robustness brought by A-D mismatch, leading to an overestimation of defense capacity long-neglected by previous researchers. + +Can we reduce A-D mismatch during the evaluation? Aware of the drawbacks of using exit-fixed robustness evaluation, we aim to find a better attack scheme that can reduce A-D mismatch during robustness evaluation. However, due to the uncertainty of the defender's choice of exits, this task can be quite challenging. To approach the tricky problem, we seek inspiration from game theory [35], model the adversarial attack and defense of multi-exit neural networks as a two-player zero-sum game, and identify the best strategy for the attacker as the criterion for evaluating adversarial robustness. We refer to this white-box evaluation scheme as Adaptive evaluation of Multi-Exit Robustness (AIMER). It does not involve any modifications to attack algorithms but rather optimizes the choice of victim exits. Considering the robust performance of a network remains constant under a fixed attack algorithm, AIMER can reduce the additional robustness and thus more accurately reflect the network's intrinsic robustness. + +Is it still possible to utilize A-D mismatch under AIMER? Though A-D mismatch is largely avoided under the more stringent evaluation of AIMER, it cannot be completely eliminated due to the uncertainty of the attack-defense game. To maximize the robustness of defense in the worst-case evaluation, we devise the Nash Equilibrium Enhanced Defense (NEED) method to reach the minimax point of the game. Specifically, NEED operates a stochastic strategy inferring with ensembles of exits with a certain probability, making both the defender and attacker perform their best strategies by seeking a Nash equilibrium [25]. + +The efficacy of both AIMER and NEED are verified with extensive experiments, covering different network architectures, datasets, attack algorithms and adversarial training + +![](images/df052e194f37fe85016896b3f4726e58faeece5e83d1d4f911cc9816c8fd9fee.jpg) +Figure 2. The structure of a multi-exit neural network. + +methods. An illustration of the main focuses of this paper and their relationship can be found in Figure 1, and our contributions can be summarized as follows: + +- We find the A-D mismatch phenomenon in the robustness evaluation of multi-exit neural networks, which explains the overestimated robustness of defense in previous work. +- We raise a more stringent scheme AIMER to evaluate the adversarial robustness of multi-exit neural networks, where the attacker operates his best strategy in the attack-defense game. +- We devise a NEED method for defense by finding a mixed-strategy Nash equilibrium, which maximizes the robustness brought by A-D mismatch under AIMER. +- We conduct extensive experiments covering 7 network architectures, 3 datasets, 7 attack settings and combine NEED with 4 adversarial training methods, which consistently demonstrate the efficacy of AIMER and NEED. + +# 2. Preliminaries + +A multi-exit neural network can be equivalently modeled as a set of single-exit networks partially sharing their parameters. Suppose a multi-exit neural network $\theta$ with $L$ exits is divided into $L$ sequential blocks $[\theta_i']_{i=1}^L$ and the final-exit classifier $c_L$ . Each subnetwork of $\theta$ can be expressed as $\theta_i$ , where $\theta_i = [\theta_1', \dots, \theta_i', c_i]$ with $c_i$ being the classifier in the $i$ -th exit of $\theta$ . Given an input $x$ , the output is formulated as a group of predictions from the subnetworks: $f_\theta(x) = [f_{\theta_i}(x)]_{i=1}^L$ . The detailed structure of a multi-exit neural network is depicted in Figure 2. + +This paper focuses on the adversarial attack and defense of multi-exit neural networks, which are very flexible due to the multiple prediction outcomes. The defender makes an inference by choosing from or aggregating the results in $f_{\theta}(x)$ , and some typical inference strategies are specified in Appendix D. The attacker also has ample choices of attack schemes to fool the model. Following the previous work [16], adversarial attacks for multi-exit neural networks come mainly in three forms, i.e., single attack, average attack, and max-average attack: + +$$ +x _ {\sin , i} ^ {\mathrm {a d v}} = \underset {x ^ {\prime} \in \{x ^ {\prime}: | x ^ {\prime} - x | _ {\infty} < \epsilon \}} {\arg \max } | \mathcal {L} \left(f _ {\theta_ {i}} \left(x ^ {\prime}\right), y\right) | \tag {1} +$$ + +$$ +x _ {\text {a v g}} ^ {\text {a d v}} = \underset {x ^ {\prime} \in \{x ^ {\prime}: | x ^ {\prime} - x | _ {\infty} < \epsilon \}} {\arg \max } \left| \frac {1}{L} \sum_ {i = 1} ^ {L} \mathcal {L} \left(f _ {\theta_ {i}} \left(x ^ {\prime}\right), y\right) \right| \tag {2} +$$ + +$$ +x _ {\max } ^ {\text {a d v}} = x _ {\sin , i ^ {*}} ^ {\text {a d v}} \text {w h e r e} i ^ {*} = \arg \max _ {i} \left| \frac {1}{L} \sum_ {j = 1} ^ {L} \mathcal {L} \left(f _ {\theta_ {j}} \left(x _ {\sin , i} ^ {\text {a d v}}, y\right) \right. \right. \tag {3} +$$ + +A detailed explanation of the formulations can be found in Appendix E. Generally, These three recipes of attacks are simple in form and easy to implement; however, they only consider rather limited scenarios for attack (i.e., using either a single exit or all the exits for attack), leaving the remaining overlooked (e.g., picking several particular exits for attack). Unfortunately, the evaluation in previous attempts to improve the robustness of multi-exit neural networks [3, 10, 16] was limited to these paradigms, without considering the risks above. Although they have undertaken valuable research into the robustness of multi-exit neural networks, we argue that the evaluation results using limited recipes of victim exits cannot truthfully reflect the intrinsic robustness of these defense methods. This is what motivates us to conduct a more in-depth exploration of this issue. + +# 3. Methodology + +In this section, we clarify the problem setup and then sequentially detail the main components of our work, i.e., the Attack-Defense (A-D) mismatch phenomenon we identify, the AdaptIVE evaluation of Multi-Exit Robustness (AIMER) and the Nash Equilibrium Enhanced Defense (NEED) method. + +# 3.1. Problem Setup + +To better convey the following concepts, we define a new attack form for multi-exit neural networks dubbed partial attack. Let a set of exit indices $E_{a} = \{n : n \in \{i\}_{i=1}^{L}\}$ , $E_{a} \neq \emptyset$ denotes an ensemble of exits selected by the attacker, an adversarial example generated by partial attack is formulated as: + +$$ +x _ {\operatorname {p a r}, E _ {a}} ^ {\mathrm {a d v}} = \underset {x ^ {\prime} \in \left\{x ^ {\prime}: | x ^ {\prime} - x | _ {\infty} < \epsilon \right\}} {\arg \max } \left| \frac {1}{| E _ {a} |} \sum_ {i \in E _ {a}} \mathcal {L} \left(f _ {\theta_ {i}} \left(x ^ {\prime}\right), y\right) \right| \tag {4} +$$ + +It allows the attacker $a$ to select any ensemble of network exits for attack, which unifies single attack (Equation 1) and average attack (Equation 2) and, in the meantime, considers more possibilities. Similarly, the defender $d$ also has the freedom to choose any ensemble of exits $E_{d} = \{n : n \in \{i\}_{i=1}^{L}\}$ and $E_{d} \neq \emptyset$ to infer with the mean of logits. + +Threat Model. This paper focuses on the white-box adversarial robustness of multi-exit neural networks with the following setups: + +- The gradient information from every network exit can be utilized for the generation of adversarial examples. +- We assume that $a$ and $d$ decide their strategies beforehand, are aware of the probabilistic strategies of each other, and are not allowed to alter their strategies during evaluation. + +- $a$ first generates adversarial examples following the attack strategy, and then uses the adversarial examples to challenge $d$ that independently makes the inference. +- Although $a$ and $d$ are aware of the probabilistic strategies of each other, $a$ has no access to the specific exit ensemble $E_{d}$ being selected for inference by $d$ . + +# 3.2. Attack-Defense Mismatch + +Following the above setup of attack and defense, we carry out an empirical study into the adversarial robustness of multi-exit neural networks. Specifically, we test the robust accuracy scores using different partial inferences under different partial attacks. $\mathrm{Acc}(\theta ,E_a,E_d)$ evaluates the robust accuracy of multi-exit neural network $\theta$ under partial attack with $E_{a}$ and the defender uses partial inference with $E_{d}$ . Delving into the example displayed in Figure 3, we make the following observations: + +Remark 3.1. When $E' \subset E$ , $\operatorname{Acc}(\theta, E, E) \leq \operatorname{Acc}(\theta, E', E)$ , i.e., using fewer exits for attack than for inference weakens the attack. The unattacked exits in the ensemble can partially mitigate the attack received by other exits. + +Remark 3.2. When $E' \supset E$ , $\operatorname{Acc}(\theta, E, E) \leq \operatorname{Acc}(\theta, E', E)$ , i.e., using more exits for attack than for inference also weakens the attack, for the impact is dispersed onto more inactive exits in inference. + +Remark 3.3. When $E' \cap E = \emptyset$ , $\operatorname{Acc}(\theta, E, E) \leq \operatorname{Acc}(\theta, E', E)$ . Using completely different exits for attack from those for inference weakens the attack, for the exits for inference are not directly attacked. The decrease in accuracy is simply due to the shared model parameters or transferability. + +Remark 3.4. When $E' \cap E \neq \emptyset$ , $|E' \cup E| > \max(|E'|, |E|)$ , $\operatorname{Acc}(\theta, E, E) \leq \operatorname{Acc}(\theta, E', E)$ . Using exits partially different from those for inference weakens the attack, suffering from both the unattacked exits and the dispersed impact in Remark 3.1 and 3.2. + +Attack-Defense (A-D) mismatch happens when $E_{d} \neq E_{a}$ (correspondingly, A-D match when $E_{d} = E_{a}$ ), consisting of the 4 situations in the remarks above. Thereby we summarize them into a more concise assumption about the robust performance of multi-exit neural networks: + +Assumption 3.5 (A-D Mismatch). We assume that when $E' \neq E$ , $\operatorname{Acc}(\theta, E, E) \leq \operatorname{Acc}(\theta, E', E)$ . + +It indicates that the most effective partial attack for a multi- exit neural network is to attack exactly the same ensemble of exits as the defender uses for inference, which is an A-D match case. As a result, for the defender, evading such precisely "matching" attacks and taking advantage of A-D mismatch makes a cunning yet indeed effective defensive + +![](images/e5f2e2dc45bbfdf255147ef5bcfc3f67a7a853f425b64358d7ad891a9dd705e8.jpg) +Figure 4. The principle of finding the best strategy for the attacker with AIMER. +Figure 5. The principle of finding the best strategy for the defender in the Nash equilibrium with NEED. + +![](images/0c399eaddf32b3fee3cbf6ec9b2fbdf6499b681b4b3176df6337bcb1789915f2.jpg) + +![](images/30fa36c5746eba29e18dc8b8857758750b3d79f7c5670d0b23c8573ae25d0292.jpg) +Figure 3. A demonstration of A-D mismatch. The accuracy scores of a 4-exit ResNet-18 under PGD-20 attack are plotted, enumerating all the cases in which the attacker and defender use continuous exit ensembles. + +tactic, which can provide an additional portion of robustness apart from the intrinsic robustness of the networks as depicted in Figure 1. + +Despite the seemingly enhanced robustness thanks to A-D mismatch, the crux of the issue lies in that a savvy attacker, fully aware of the defender's strategy, will strive to minimize the occurrence of mismatch. However, the practice of using three fixed attack recipes to evaluate multi-exit neural networks, as demonstrated in previous works such as [3, 10, 16], has largely overlooked the impact of A-D mismatch. We believe this is problematic for evaluation since the additional robust scores brought by A-D mismatch obscure the intrinsic robustness of the networks. + +# 3.3. Adaptive Evaluation of Multi-Exit Robustness + +Through the phenomenon above, mismatched choice of exits between the attacker and defender is responsible for an overestimation in adversarial robustness. Therefore, to more accurately reflect the intrinsic robustness of multi-exit neural networks, a desirable evaluation should maximally hit exits used by $d$ for inference. To this end, we attempt to provide a solution called AIMER that models the problem with game theory [35] and seeks the best strategy for the attacker to reduce the impact of A-D mismatch. + +Model setup. The white-box adversarial attack and defense of multi-exit neural network $\theta$ can be modeled as a two-player complete information static game $G$ , with a set of + +players $\mathcal{P} = \{a,d\}$ , where $a$ denotes the attacker and $d$ denotes the defender. Suppose $a$ performs partial attacks and $d$ uses partial inference, then the action space for these two players is $\mathcal{A} = \left\{E:E\in \{n:n\in \{i\}_{i = 1}^{L}\} ,|E| > 0\right\}$ Note that $|\mathcal{A}| = 2^L -1$ , indicating each player has $2^{L} - 1$ types of actions to take. + +Payoff functions. Since $d$ endeavors to make the network reliable enough under attacks, i.e. to maximize the accuracy score, while $a$ aims to do quite the opposite, the payoff function for $a$ and $d$ when $a$ attacks $E_{a}$ and $d$ infers with $E_{d}$ can be formulated into a zero-sum game: + +$$ +\pi^ {a} (E _ {a}, E _ {d}) = - \pi^ {d} (E _ {a}, E _ {d}) = - \operatorname {A c c} (\theta , E _ {a}, E _ {d}) \tag {5} +$$ + +The function values of $\pi^a$ and $\pi^d$ under every $E_{a}$ and $E_{d}$ constitute payoff matrices $\mathbf{M}^a, \mathbf{M}^d \in \mathbb{R}^{|\mathcal{A}| \times |\mathcal{A}|}$ , and $\mathbf{M}^a = -\mathbf{M}^d$ . In practical scenarios, due to the expensive cost to have complete tests of the network (see Appendix F.2), it is impossible to precisely understand the payoff matrix of this game. Therefore, we employ an approximation approach, selecting a subset of the dataset for an average attack to ascertain the characteristics of the network (Algorithm 3 in Appendix). Subsequent calculations are then based on this approximate matrix $\hat{\mathbf{M}}^a = -\hat{\mathbf{M}}^d \in \mathbb{R}^{|\mathcal{A}| \times |\mathcal{A}|}$ . + +The best strategy for the attacker. Aware of the payoff matrix $\hat{\mathbf{M}}^a$ , $a$ can calculate his best strategy in $G$ with the following method. We default the strategy in $G$ in a + +mixed form, i.e., performing each action in $\mathcal{A}$ with a certain probability. Let the strategies of $a$ and $d$ be $\boldsymbol{s}^a = [s_1^a,s_2^a,\dots ,s_{|\mathcal{A}|}^a ]^\top$ and $\boldsymbol{s}^{d} = [s_{1}^{d},s_{2}^{d},\dots ,s_{|\mathcal{A}|}^{d}]^{\top}$ , which satisfy $\boldsymbol{s}^a,\boldsymbol{s}^d\in \mathcal{S},\mathcal{S} = \{\boldsymbol {s}\in \mathbb{R}^{|\mathcal{A}|}:s_i\geq 0,\sum_{i = 1}^{|\mathcal{A}|}s_i = 1\}$ , representing the probability vector of $a$ and $d$ selecting the corresponding ensemble of exits. In such a case, the objective of each player is to maximize his own expected payoff $u^{a}(s^{a},s^{d}) = (s^{a})^{\top}\hat{\mathbf{M}}^{a}s^{d}$ or $u^{d}(s^{a},s^{d}) = -u^{a}(s^{a},s^{d})$ . + +As shown in Figure 4, $a$ maximizes his expected payoff via allocating all the probability to the action corresponding to the maximum value in vector $\hat{\mathbf{M}}^a s^d$ . Also, when multiple actions correspond to the same maximum value, $a$ will not favor any particular one but will randomly choose among them. Therefore, $a$ 's best strategy can be represented as a probabilistic vector $s^{a*} = [s_i^{a*}]_{i=1}^{|\mathcal{A}|}$ , where + +$$ +s _ {i} ^ {a *} = \left\{ \begin{array}{l l} 1 / | I ^ {*} |, & i \in I ^ {*} = \underset {i \leq | A |} {\arg \max } \left(\hat {\mathbf {M}} ^ {a} s ^ {d}\right) _ {i} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {6} +$$ + +and $(\cdot)_i$ denotes the $i$ -th element of a vector. This formulation obtains the corresponding best strategy $s^{a*}$ once the strategy of the defender $s^d$ is given. We categorize the calculation of $s^d$ into three cases (see Appendix D for details): + +- For static inference, $d$ simply uses a fixed exit or ensemble for inference: $\boldsymbol{s}^d = [0,\dots ,0,1,0,\dots ,0]^\top$ , with the probability of corresponding action set to 1. +- For dynamic inference, $d$ follows a certain rule to choose exits and it is difficult to model his strategy. In this case we test the frequency of using each exit under an average attack as a surrogate for $s^d$ . +- For random inference, $d$ picks his exits or ensemble with $\pmb{p}^d$ . Since in a white-box setting $\pmb{p}^d$ is common knowledge, we can easily obtain $\pmb{s}^d = \pmb{p}^d$ . + +With the best strategy of $a$ , one can generate the adversarial example $x_{\mathrm{AIMER}}^{\mathrm{adv}}$ for AIMER evaluation (Algorithm 1 in Appendix) by the following formulation, where $\text{random}(C, p)$ denotes random choice from set $C$ according to the probability distribution $p$ : + +$$ +x _ {\text {A I M E R}} ^ {\text {a d v}} = x _ {\text {p a r , r a n d o m} (\mathcal {A}, \mathbf {s} ^ {a *})} ^ {\text {a d v}} \tag {7} +$$ + +# 3.4. Nash Equilibrium Enhanced Defense + +From the attacker's perspective, A-D mismatch should be minimized to obtain a more accurate evaluation (Section 4.2); yet on the opposite side, A-D mismatch can also be utilized by the defender to confuse the attacker: avoiding the exits chosen by the attacker makes the gradients in the attacks less effective (see Appendix C.2 for detailed discussions). Specifically, under the strict evaluation of AIMER, the key to increasing the mismatch is to find the minimax point of the adversarial game. Thus, we intuitively devise the Nash Equilibrium Enhanced Defense (NEED) for multi-exit neural networks as a robust inference strategy for the + +defender. It seeks the Nash Equilibrium (NE) [25] of the adversarial game, where both players are performing their best strategies. + +As shown in Figure 5, we formulate the NE in this two-player zero-sum attack-defense game with the following description. Given that in a zero-sum game, both players seek their best strategy while assuming the opponent is also using their best strategy (which is the most disadvantageous to each other), we can view this as an optimization problem aimed at maximizing the expected payoff in the worst-case scenario. Consider the defender's payoff as the objective to optimize, $a$ is faced with a maximin problem, i.e., while $d$ strives to maximize the payoff, $a$ seeks the tight lower bound $\underline{u}^d$ in the formula. + +$$ +\begin{array}{l} \min _ {\boldsymbol {s} ^ {a} \in \mathcal {S}} \left(\boldsymbol {s} ^ {a}\right) ^ {\top} \hat {\mathbf {M}} ^ {d} \boldsymbol {s} ^ {d} = \min _ {i \leq | \mathcal {A} |} \left(\hat {\mathbf {M}} ^ {d} \boldsymbol {s} ^ {d}\right) _ {i} \tag {8} \\ = \max \left\{\underline {{u}} ^ {d} \in \mathbb {R} | \hat {\mathbf {M}} ^ {d} s ^ {d} \succeq \underline {{u}} ^ {d} \cdot \mathbf {1} \right\} \\ \end{array} +$$ + +where $\mathbf{1} = [1, \dots, 1]^{\top} \in \mathbb{R}^{|A|}$ . Conversely, the defender deals with a minimax problem seeking the tight upper bound $\overline{u}^d$ in the formula: + +$$ +\begin{array}{l} \max _ {\boldsymbol {s} ^ {d} \in \mathcal {S}} (\boldsymbol {s} ^ {a}) ^ {\top} \hat {\mathbf {M}} ^ {d} \boldsymbol {s} ^ {d} = \max _ {i \leq | \mathcal {A} |} ((\hat {\mathbf {M}} ^ {d}) ^ {\top} \boldsymbol {s} ^ {a}) _ {i} \\ = \min \left\{\bar {u} ^ {d} \in \mathbb {R} \mid \left(\hat {\mathbf {M}} ^ {d}\right) ^ {\top} \boldsymbol {s} ^ {a} \preceq \bar {u} ^ {d} \cdot \mathbf {1} \right\} \tag {9} \\ \end{array} +$$ + +By the Minimax Theorem [34], the NE can be finally achieved in the two-player zero-sum attack-defense game, where the best strategy of the defender $s^{d*}$ can be solved. Given the page limit, we encourage interested readers to consult Theorem A.3, its proof and the solution of NE provided in Appendix A, which systematically explain why $s^{d*}$ is optimal and how it can be obtained. + +# 4. Experiments + +In this section, we first provide our experiment setup (Section 4.1). Next, we show our experimental results and analysis of the performance of AIMER evaluation scheme (Section 4.2) and NEED defense method (Section 4.3). Finally, we compare the computational cost of AIMER (Section 4.4). Due to page limit, more detailed settings and additional results are deferred to Appendix B and F. + +# 4.1. Experiment Setup + +Dataset and network architectures. We consider three datasets for evaluation: SVHN [26], CIFAR-10 [20] and Tiny ImageNet [5]. For multi-exit neural networks, we directly modify common networks into multi-exit versions, including VGG-16 [31], ResNet-18 [14], WideResNet-34-10 [46], ViT-B/16 [7] and employ existing multi-exit architectures MSDNet [17], RANet [43] and L2W-DEN [12]. + +Adversarial attacks. We apply the following 7 attack settings, with all of them restricted by $l_{\infty}$ perturbation bound + +Table 1. Robust accuracy scores (%) obtained by different evaluation schemes. The lowest scores of each column are set in bold. Results on more architectures/datasets, and under LAFIT [45] attack can be found in Appendix B. + +
MethodNetworkDatasetEvaluationFGSMPGD-20PGD-100EoT-PGD-20VMI-FGSMAutoAttack
Static (3/4)ResNet-18(4 exits)CIFAR-10Single attack60.29 ± 0.0056.04 ± 0.0854.12 ± 0.1254.42 ± 0.0655.30 ± 0.0559.34 ± 0.02
Average attack56.54 ± 0.0052.09 ± 0.0450.51 ± 0.0450.72 ± 0.0451.38 ± 0.0556.49 ± 0.03
Max-average attack54.32 ± 0.2050.26 ± 0.3449.72 ± 0.0548.96 ± 0.3349.36 ± 0.2955.92 ± 0.10
AIMER (ours)52.81 ± 0.0045.85 ± 0.0543.21 ± 0.0143.60 ± 0.0345.10 ± 0.0342.40 ± 0.03
RandomVGG-16(5 exits)SVHNSingle attack66.57 ± 0.1952.77 ± 0.4645.04 ± 0.0447.60 ± 0.6648.04 ± 0.6646.63 ± 0.09
Average attack62.87 ± 0.0747.49 ± 0.1840.86 ± 0.0642.42 ± 0.1344.00 ± 0.0943.42 ± 0.04
Max-average attack62.11 ± 0.0745.90 ± 0.1839.17 ± 0.0440.40 ± 0.1142.45 ± 0.0946.31 ± 0.05
AIMER (ours)60.87 ± 0.0043.61 ± 0.0437.70 ± 0.0338.55 ± 0.0340.87 ± 0.0240.70 ± 0.10
Dynamic [16]VGG-16(5 exits)SVHNSingle attack62.90 ± 0.0044.81 ± 0.0537.08 ± 0.0439.23 ± 0.0341.17 ± 0.0339.59 ± 0.12
Average attack62.01 ± 0.0044.81 ± 0.0537.93 ± 0.0539.23 ± 0.0341.17 ± 0.0339.97 ± 0.08
Max-average attack59.82 ± 0.0043.53 ± 0.0835.98 ± 0.0637.78 ± 0.1139.70 ± 0.0239.50 ± 0.05
AIMER (ours)59.65 ± 0.0042.30 ± 0.0435.69 ± 0.0337.30 ± 0.0439.56 ± 0.0438.56 ± 0.06
Dynamic [3]MSDNet(5 exits)CIFAR-10Single attack51.32 ± 0.0042.31 ± 0.0638.79 ± 0.0539.34 ± 0.0840.31 ± 0.0535.21 ± 0.06
Average attack54.70 ± 0.0043.65 ± 0.1238.40 ± 0.0539.71 ± 0.1141.81 ± 0.0335.10 ± 0.04
Max-average attack60.17 ± 0.0048.96 ± 0.2443.72 ± 0.0344.98 ± 0.1852.90 ± 0.3234.22 ± 0.12
AIMER (ours)51.04 ± 0.0040.47 ± 0.1533.73 ± 0.0735.53 ± 0.1037.69 ± 0.0533.64 ± 0.08
Dynamic [3]ViT-B/16 [7](4 exits)CIFAR-10Single attack58.76 ± 0.0056.71 ± 0.0549.79 ± 0.0456.31 ± 0.0456.43 ± 0.0359.55 ± 0.10
Average attack55.19 ± 0.0052.09 ± 0.0350.78 ± 0.0650.91 ± 0.0851.47 ± 0.0556.58 ± 0.07
Max-average attack53.63 ± 0.0050.57 ± 0.0449.53 ± 0.0549.88 ± 0.1050.22 ± 0.0655.29 ± 0.09
AIMER (ours)53.45 ± 0.0050.47 ± 0.0849.10 ± 0.0349.67 ± 0.0450.17 ± 0.0454.98 ± 0.05
+ +$\epsilon = 8 / 255$ : FGSM [9], PGD-20 (which means PGD attack with 20 perturbation steps), PGD-100, EoT-PGD-20 [1], VMI-FGSM [36], AutoAttack [4], and LAFIT [45]. Among them, EoT-PGD addresses the stochastic behavior of the networks, while VMI-FGSM enhances the transferability of attacks among different network exits. + +Evaluation protocol. Given the unique nature of multi-exit neural networks, we employ a distinct approach for evaluation compared to traditional networks. Overall, we assume that all attacks are conducted under the white-box setup in Section 3.1. The attacker first chooses his exit ensemble to generate the adversarial examples, and the defender then chooses his exit ensemble for inference. Considering the possible randomness in evaluation, we obtain the results by repeating the same test 5 times and report the mean value and standard deviation. + +# 4.2. Evaluation with AIMER + +This section primarily validates the effectiveness of the AIMER evaluation scheme. We select single attack (against the last exit; see Appendix B for other exits), average attack and max-average attack in [16] as our baselines, and use these four schemes to evaluate different adversarial defense methods for multi-exit neural networks including [3, 16]. Additionally, we construct two ad-hoc models with static and random inference strategies. For the static inference method, we use the third exit for inference; for the random inference method, we use the 3rd and 5th exits for inference, with probability $[0.5, 0.5]$ respectively. + +An ideal scheme for robustness evaluation should maximally reduce the impact of A-D mismatch and achieve + +a lower accuracy than others. In Table 1, it can be observed that AIMER measures lower robustness compared with other evaluation schemes in all the cases. The margin is largest in evaluating static and random defense methods, reducing the robustness score under AutoAttack by $13.52\%$ compared with max-average attack. + +Noticeably, in the evaluation of [3], max-average attack does not necessarily outperform single or average attack. This reveals its limitation in averaging the adversarial loss on all exits, for it might be inconsistent with the objective of seeking the "best" single attack in some cases. Another key insight from the results is that AutoAttack is not necessarily the strongest attack against multi-exit neural networks, probably because the black-box ingredients in the algorithm fail to generalize on the unattacked inference exits. + +We are also highly interested in whether AIMER can truly reduce the occurrence of A-D mismatch. Therefore, we first define the following metrics to measure the mismatch rate of two exit ensembles $(r_{\mathrm{mis}})$ and two strategies $(R_{\mathrm{mis}})$ for attack and defense: + +$$ +r _ {\mathrm {m i s}} \left(E _ {a, i}, E _ {d, j}\right) = 1 - \frac {\left| E _ {a , i} \cap E _ {d , j} \right|}{\left| E _ {a , i} \cup E _ {d , j} \right|} \tag {10} +$$ + +$$ +R _ {\mathrm {m i s}} (\boldsymbol {s} ^ {a}, \boldsymbol {s} ^ {d}) = \sum_ {i = 1} ^ {| \mathcal {A} |} \sum_ {j = 1} ^ {| \mathcal {A} |} s _ {i} ^ {a} s _ {j} ^ {d} r _ {\mathrm {m i s}} (E _ {a, i}, E _ {d, j}) \qquad (1 1) +$$ + +Then we uniformly generate 200 random strategies for the defender, and find the corresponding strategies for the attacker using the following 4 schemes: (1) a random strategy that uniformly attacks every possible ensemble, (2) a single attack strategy only considering the main exit, (3) + +![](images/da688b2997a9489440232b15dd9dd147255379ffa45c3a40c51a1606039cf0c1.jpg) +(a) ResNet-18, SVHN + +![](images/f70ba2c21207a332187f518a7760debf7a14b2e5beba11939fa5622f386218a1.jpg) +(b) ResNet-18, CIFAR-10 + +![](images/40c13dc428ff692c578370590e80fee689408f4459f67bc7eef579e79d573cb5.jpg) +(c) VGG-16, SVHN +Figure 6. Mismatch rate $R_{\mathrm{mis}}$ and expected robust accuracy of different attack schemes on different network architectures datasets. Expected robust accuracy is calculated with the payoff matrix. + +![](images/108b3c121fa6744d99cdbf5171c8aaeee35f31fef3d117649202eff6e779fb99.jpg) +(d) VGG-16, CIFAR-10 + +Table 2. The Accuracy (\%) of different defense strategies evaluated with AIMER. $R_{\mathrm{mis}}$ indicates the mismatch rate; Robust accuracy is obtained under PGD-20 attack. The best result of each column is set in bold. + +
MethodRmisClean Acc.Robust Acc.
Network: ResNet-18 (4 exits), Dataset: CIFAR-10
Single-exit-84.37 ± 0.0049.82 ± 0.00
Multi-exit (static)0.0084.83 ± 0.0050.65 ± 0.04
Multi-exit (dynamic)0.3883.02 ± 0.0051.30 ± 0.12
Multi-exit (NEED)0.4383.60 ± 0.0052.77 ± 0.30
Network: VGG-16 (5 exits), Dataset: SVHN
Single-exit-89.66 ± 0.0043.35 ± 0.00
Multi-exit (static)0.0092.40 ± 0.0042.33 ± 0.03
Multi-exit (dynamic)0.3692.19 ± 0.0042.33 ± 0.04
Multi-exit (NEED)0.4693.70 ± 0.0045.32 ± 0.16
+ +an average strategy only considering using an ensemble of all exits, and (4) a strategy found by AIMER. Finally, we plot the mismatch rate $R_{\mathrm{mis}}$ and the expected robust accuracy of the strategy pairs in Figure 6. According to the results, AIMER greatly reduces both the robust accuracy and the mismatch rate compared with other schemes. Notably, none of the 4 schemes tested makes any change to the attack algorithms, which maintains the intrinsic robustness of the network. Therefore, we can assume that the robust accuracy reduced by AIMER is an extra portion that is closely related to the A-D mismatch phenomenon. + +# 4.3. Defense with NEED + +In this section, we primarily showcase the experimental results demonstrating the efficacy of NEED in enhancing the adversarial robustness of networks. We conducted tests on two different network architectures (ResNet-18 and VGG-16), assessing 4 scenarios for both clean accuracy and robust accuracy (where robust accuracy is obtained using AIMER evaluation based on PGD-20 attacks): (1) multi-exit neural networks using a static strategy for inference with the main exit; (2) multi-exit neural networks employ + +ing a dynamic strategy for inference; (3) multi-exit neural networks using the NEED method for inference; and (4) single-exit networks, where the AIMER evaluation reverts to standard evaluation. + +Interestingly, according to the results in Table 2, with the aid of the NEED-enhanced multi-exit structure, the robust accuracy can even surpass that of single-exit networks. This suggests that NEED is not just a strategy for multi-exit neural networks but also has the potential to be a method for enhancing general adversarial defense performance through modifications in network structure. + +To validate this viewpoint, we conduct further research, integrating it with various types of adversarial training methods including PGD-AT [22], TRADES [47], MART [38], and FAT [48]. Testing with different attack algorithms, the results in Table 3 consistently demonstrate stable improvements. Results on more network architectures and datasets can be found in Appendix B. + +# 4.4. Computational Cost + +This section compares the computational cost of AIMER and max-average attack that have similar performance in some cases. In Table 4, we list three aspects of the evaluation schemes: the per-example cost of each attack algorithm, the cost of pre-processing and the cost of a complete evaluation (including pre-processing and evaluation with every attack algorithm for 5 runs). From the results in the table, it is evident that AIMER has a significant advantage in both single-sample evaluation and overall evaluation time cost. This strongly indicates that AIMER is not only more accurate in reflecting the network's intrinsic adversarial robustness but also more cost-friendly. + +# 5. Related Work and Discussions + +Game theory for adversarial robustness. Game theory [35] has been applied in various fields of computer science [8, 21, 23], yet there is limited previous work looking into adversarial robustness from a game-theoretic perspective [28, 29]. The most recent work is [24], which models + +Table 3. Accuracy (%) under different attacks when combining NEED with AT methods on the VGG-16 model and CIFAR-10 dataset. Better results are set in bold. + +
MethodCleanFGSMPGD-20PGD-100EoT-PGD-20VMI-FGSMAutoAttack
Standard92.24 ± 0.008.37 ± 0.000.11 ± 0.010.00 ± 0.000.08 ± 0.020.03 ± 0.000.00 ± 0.00
Standard + NEED91.30 ± 0.2018.33 ± 2.291.70 ± 0.442.34 ± 0.314.12 ± 0.193.02 ± 0.280.29 ± 0.03
PGD-AT [22]77.30 ± 0.0052.50 ± 0.0047.86 ± 0.0346.13 ± 0.0546.43 ± 0.0347.17 ± 0.0343.09 ± 0.02
PGD-AT + NEED75.17 ± 0.1254.31 ± 0.1650.61 ± 0.1147.03 ± 0.0946.63 ± 0.1447.29 ± 0.2446.07 ± 0.15
TRADES [47]79.26 ± 0.0052.60 ± 0.0047.30 ± 0.0445.48 ± 0.0345.83 ± 0.0246.76 ± 0.0242.06 ± 0.02
TRADES + NEED81.77 ± 0.0453.42 ± 0.0748.26 ± 0.0745.87 ± 0.1645.92 ± 0.0547.63 ± 0.0647.77 ± 0.24
MART [38]76.15 ± 0.0051.10 ± 0.0044.88 ± 0.0342.44 ± 0.0342.86 ± 0.0644.01 ± 0.0238.58 ± 0.02
MART + NEED76.12 ± 0.1251.60 ± 0.0845.58 ± 0.0643.90 ± 0.0444.07 ± 0.0844.34 ± 0.1143.58 ± 0.07
FAT [48]83.65 ± 0.0050.42 ± 0.0044.73 ± 0.0942.73 ± 0.0342.84 ± 0.0643.35 ± 0.0438.03 ± 0.02
FAT + NEED82.65 ± 0.1954.18 ± 0.3047.76 ± 0.1243.80 ± 0.1945.62 ± 0.2846.88 ± 0.2343.61 ± 0.10
+ +Table 4. Computational cost (ms) of different methods on on ResNet-18 backbone and CIFAR-10 dataset. Experiments are conducted on a single NVIDIA RTX A6000. Lower results of each row are set in bold. + +
Evaluation ProcessMax-averageAIMER
Single sampleFGSM3.0964 ×1002.4472 ×100
PGD-201.3540 ×1013.8754 ×100
PGD-1001.1438 ×1021.4013 ×101
EoT-PGD-202.5308 ×1017.5075 ×100
VMI-FGSM7.3650 ×1011.9740 ×101
AutoAttack1.9590 ×1035.5118 ×102
Pre-processing0.0000 ×1001.0187 ×105
Complete evaluation1.0945 ×1083.0040 ×107
+ +the attack and defense of randomized classifiers into a game and identifies the mixed Nash equilibrium [25]. Despite a similar framework of game theory, this paper for the first time studies the unexplored A-D mismatch problem and has essentially different motivation, purpose, methodology, and design of experiments from previous work, identifying a more direct application of theory to realistic problems. More discussion can be found in Appendix G. + +Adversarial robustness of multi-exit neural networks. multi-exit neural networks for efficient inference [11, 12, 40, 43] and their adversarial robustness have attracted increasing research interest. [16] is the first to adversially train an input-adaptive multi-exit neural network; [3] proposes a fast adversarial training method for multi-exit neural networks with reduced time complexity; [10] employs knowledge distillation to prompt each exit to produce orthogonal results. Unlike previous works, our paper focuses on the phenomenon of A-D mismatch that reveals the possible flaws in the evaluation of these works. Compared with existing techniques like EoT [1] that address the randomness in the networks, AIMER pioneers a novel perspective and a tailored solution for multi-exit neural networks (further discussion can be found in Appendix C.1). We believe that our findings and methodology can provide a more rig- + +orious evaluation on the research of multi-exit robustness. + +Adversarial training. Adversarial Training (AT) [22] has greatly advanced in recent years and has become the most widely researched defense against adversarial attacks. Improved regularization methods like TRADES [47], MART [38] and FAT [48] seek to achieve a better balance between accuracy and robustness; Methods like [18, 30] are devoted to faster AT. As a promising defense method, AT is also combined with other types of defenses such as feature-level robustness [6, 19, 39] and input transformation methods [44]. By default, the finding and methodology in this paper are based on AT-enhanced multi-exit neural networks. + +# 6. Conclusion and Future Work + +In this paper, we identify A-D mismatch as another source of adversarial robustness apart from the intrinsic robustness of multi-exit neural networks. Taking this finding into consideration, we devise a game-theoretically principled methodology for the adversarial attack and defense of multi-exit neural networks: AIMER evaluation with an enhanced strength of attack minimizes the mismatch and more accurately reflects the true adversarial robustness, while NEED defense under AIMER evaluation can still maximally confound the attacker with the best defense strategy in the game. The experimental results over different datasets, attack algorithms, and network architectures fully demonstrate the effectiveness of the methods. + +While there exist several possible limitations in this work (Appendix H), we believe the problems identified and the methods proposed in this paper have not been thoroughly considered and empirically verified before, which provides a novel perspective for the research of adversarial robustness of multi-exit neural networks. Also, we expect that our work can serve as a constant reminder for researchers of adversarial defense methods: when one seeks to prove the strength of his shield, he must sharpen the blade of offense. + +# Acknowledgement + +This work is supported in part by the National Natural Science Foundation of China (No. 62372339, 62371350, and 62372336). We would like to sincerely thank Prof. Xiang Sun from the Economics and Management School, Wuhan University for his insightful discussions and guidance. 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This challenge is even more pronounced in pixel-level tasks, which require longer input sequences compared to image-level tasks. Although token reduction (TR) techniques can help reduce computational demands, they often lead to homogeneous attention patterns that compromise performance in pixel-level scenarios. This study underscores the importance of maintaining attention diversity for these tasks and proposes to enhance attention diversity while ensuring the completeness of token sequences. Our approach effectively reduces the number of tokens processed within transformer blocks, improving computational efficiency without sacrificing performance on several pixel-level tasks. We also demonstrate the superior generalization capability of our proposed method compared to challenging baseline models. The source code will be made available at https://github.com/AVC2-UESTC/DAR-TR-PEFT. + +# 1. Introduction + +Recent advancements in visual pre-trained foundation models [2, 15, 16, 44, 67] have gained widespread popularity due to their exceptional generalization capabilities across a broad spectrum of tasks. Building on this success, parameter-efficient fine-tuning (PEFT) techniques [22, 23, 26] have further enhanced the practicality of these models by enabling efficient adaptation to various downstream tasks and data domains, requiring updates to only a minimal number of parameters. Despite the efficiency that PEFT methods bring to training, they still encounter significant computational challenges during inference. For image-level tasks like classification, these challenges can be alleviated using token reduction (TR) techniques [1, 3, 30, 32, 34, 49, + +[65]. In image classification, a class token is used, enabling the reduction of patch tokens without negatively impacting prediction accuracy, as fewer and more abstract tokens are sufficient to capture the overall content of the image. + +At first glance, pixel-wise tasks such as segmentation [27, 38, 60] appear well-suited to benefit from token reduction (TR) due to their requirement for longer token sequences to capture fine-grained, high-resolution details. However, this very need introduces a significant trade-off between efficiency and accuracy: reducing the number of tokens can compromise the model's ability to produce precise and detailed predictions. Although prior studies on dynamic transformers [32, 33, 49, 63] have shown that TR effectively reduces inference costs for image-level tasks, extending these techniques to pixel-level tasks remains challenging. This is partly because pixel-wise tasks are highly sensitive to spatial resolution and coherence. Specifically, reduced token sequences often lack a spatially coherent representation, which is problematic for pixel decoders that require tokens with a complete spatial structure to function effectively. Additionally, segmentation tasks demand maintaining semantic and boundary details across all tokens, and any loss of fine-grained information can degrade performance. Therefore, balancing token reduction while preserving both spatial structure and high-resolution details remains an unresolved challenge. + +Moreover, the diversity of features captured by the attention mechanism is crucial for the success of pixel-level tasks. Namuk et al. [47] and Xie et al. [61] emphasize that a diverse set of attention heads allows the model to focus on various aspects of the input, facilitating the learning of rich and comprehensive representations. This diversity is essential for accurately capturing fine-grained details and complex patterns, which are critical for tasks such as segmentation and depth estimation. Without sufficient diversity, models may struggle to differentiate subtle features, ultimately leading to a decline in performance for pixel-level applications. We further examine existing TR methods from the perspective of diversity and discuss our findings below. + +In Fig. 1 (a), we present the normalized mean attenuated signal $S_{\mathrm{m}}$ for a given $\lambda$ . + +![](images/79b145f58e312b5ccaa6d010feb49af4df2b71eb3ef1d43c4e961ac4903dc2e4.jpg) +(a) Dinov2-B + +![](images/4825a32e7dd5c793db72094ba08e3cbbb996e09590437da17149187d53b762ce.jpg) +(b) Dinov2-B w/ TR + +![](images/9dda34b61bd7128419a5f270f553ea8fdcd46c0a53d04cc4a98b0f7a60c6d1e6.jpg) +(c) Ours + +![](images/fc2637b401d9d77e21fe3775f7a0bc9809294caccc0301a8dd347f96a33d7b85.jpg) +(d) NMI + +![](images/2daf750622c2efc9877bc3e64d1ef8b8001854efb4c42a17a1583144c3da4b4e.jpg) +(e) Relative log amplitude + +![](images/82c5971367c6897586afb8070ea66b704da8669c003b92e33bebf4444a0a04ce.jpg) +(f) Ours +Figure 1. Comparison of the normalized mean attention distance (MAD) for (a) DINOv2 without token reduction (TR), (b) DINOv2 with TR, and (c) DINOv2 using our proposed method. Each point within a column corresponds to a specific attention head, with the vertical axis representing the normalized MAD. Higher values indicate a larger receptive field, while greater separation between points reflects increased diversity among attention heads. In (d), a lower value of normalized mutual information (MI) suggests a weaker dependence of the attention map on query tokens, implying that the attention distribution collapses into homogeneity, thereby reducing diversity. Notably, the normalized MI of DINOv2 with TR is significantly lower than that of DINOv2 without TR, especially after the $5^{\text{th}}$ transformer block. Furthermore, the curves for different token activation rates of 0.5, 0.7, and 0.9 exhibit consistent patterns. In (e) and (f), a higher value of $\Delta$ Log amplitude indicates that the representations leverage high-frequency components. DINOv2 with TR begins to show a reduction in high-frequency components after the $5^{\text{th}}$ transformer block, whereas DINOv2 without TR only exhibits this reduction starting from the $10^{\text{th}}$ block. Details of the procedure are provided in the supplementary materials. + +tion distance (MAD) for DINOv2 [44]. The figure illustrates that nearly all transformer blocks exhibit diverse attention distributions, as reflected by the varying normalized MAD values across different attention heads in each column. However, when a fixed token reduction strategy [32, 34] is applied, this diversity significantly diminishes. As shown in Fig. 1 (b), the attention heads in the later transformer blocks tend to have nearly identical normalized MAD values, indicating a loss of variability. + +To further quantify attention diversity, we use normalized mutual information (NMI) [53] in Fig. 1 (d), comparing the diversity of attention heads across transformer blocks. The green curve reveals that the NMI of DINOv2 with TR drops rapidly and remains much lower than that + +of the model without TR. This sharp decline indicates that TR causes the attention mechanisms to collapse into homogeneous distributions. While such uniformity may not noticeably harm image classification performance, it can be detrimental to pixel-level tasks [47]. Such homogenization of attention patterns reduces the model's expressive power, particularly undermining its performance in tasks that require a nuanced understanding of complex visual details. + +Given that fixed TR leads to homogeneous attention patterns, we hypothesize that it may also cause a loss of high-frequency details. To explore this, we conduct a Fourier analysis following the methods outlined in [46, 47]. As shown in Fig. 1 (e), we present the relative log amplitude of Fourier-transformed representations, computed as the dif + +ference in amplitude between the highest and lowest frequencies. The analysis reveals that DINOv2 without TR retains more high-frequency components in the later transformer blocks compared to DINOv2 with TR. Notably, we observe that a higher token keep rate within the TR configuration is associated with a significant reduction in high-frequency components in the final transformer blocks. This counterintuitive result may be due to the increased uniformity among longer tokens at higher keep rates. Fixed TR inherently leads to the loss of high-frequency details, which are crucial for pixel-level tasks. High-frequency components capture important information about edges, textures, and subtle variations within an image. By reducing the number of tokens, the model risks discarding these features, resulting in diminished fidelity and performance. + +We contend that the loss of high-frequency information can significantly degrade the performance of pixel-level tasks, which depend heavily on these components to capture essential fine-grained details such as edges, boundaries, and small-scale textures required for accurate predictions. When high-frequency details are diminished, the model's ability to distinguish between different regions or objects is compromised, leading to blurred or imprecise outputs and ultimately reducing overall task performance. + +Motivated by this phenomenon, in this paper, we seek to deepen the understanding of how TR affects attention mechanisms and visual representations, pinpointing the barriers and challenges that complicate the use of TR in PEFT for pixel-level tasks. We propose Diverse Attention Restorer (DAR) that preserves attention diversity, retains the high-frequency components of visual representations, and maintains the completeness of the token sequence, all while reducing the number of tokens processed within transformer blocks. By striking an optimal balance between performance and inference efficiency for pixel-level tasks, our method enhances the practical applicability of PEFT techniques in this crucial area. To summarize, we make the following contributions: + +- We systematically analyze the limitations of current token reduction (TR) techniques and identify that they often lead to a loss of attention diversity and high-frequency information representation, which we believe are critical for pixel-level tasks. +- Based on these findings, we propose a decoupled design of the Token Compensator and PEFT Module. We further develop a learnable mask mechanism to address the perturbation issue caused by the FFN bias, enhancing the effectiveness of token reduction without compromising performance. +- Our method demonstrates outstanding performance across several pixel-level tasks with minimal FLOPs. Additionally, we showcase the superior generalization capability of our approach in zero-shot settings compared to + +strong baseline models, highlighting its practical efficacy and efficiency. + +# 2. Related Work + +# 2.1. Pixel-Level Tasks + +Pixel-level tasks involve classifying or detecting each pixel within an image, as seen in applications like segmentation [27]. In real-world scenarios, many critical applications rely on precise pixel-level analysis for accurate detection and interpretation. For example, in the medical domain, accurately segmenting pathological regions is essential. Tasks such as polyp segmentation [25] and skin lesion segmentation [6] are crucial for providing clinicians with reliable delineations to aid in effective diagnosis. + +Additionally, salient object segmentation and camouflaged object segmentation [13, 14] play a vital role in computer vision by enhancing visual perception, enabling the accurate separation of relevant objects from complex backgrounds. In the field of remote sensing [17, 56], high-precision detection is required for the effective analysis and interpretation of satellite imagery, demonstrating the broad and impactful applications of pixel-level tasks. + +# 2.2. Token Reduction + +Token reduction has become a widely adopted strategy in Vision Transformers (ViTs) to enhance inference efficiency. Several methods have incorporated token reduction into the full training process of ViTs, such as EViT [32], DynamicViT [49], and DiffRate [3]. In addition, recent studies have leveraged token reduction to enable parameter-efficient fine-tuning of ViT models. Prominent examples include CoDA [30], Dynamic-Tuning [65], and Sparse-Tuning [34]. Moreover, ToMe [1] introduces a training-free approach designed to improve the inference efficiency of ViTs. + +# 2.3. Parameter-Efficient Fine-Tuning (PEFT) + +PEFT techniques aim to minimize computational overhead by fine-tuning a small subset of model parameters while keeping most of the parameters unchanged. One notable method is LoRA [23], initially popularized for language tasks and has recently gained attention in vision applications. VPT [26] is a simple yet effective approach for fine-tuning visual models by adding learnable prompt tokens to the input sequence. Another approach, the adapter method, introduces small, learnable modules between transformer layers [18]. A serial adapter strategy has been used effectively for language tasks, as demonstrated by the NLP Adapter [22, 48], while AdaptFormer [4] employs a parallel strategy optimized for vision tasks. More recently, EVP [35, 59] has emerged, combining the parameter efficiency of VPT with the robustness of adapters and incorporating + +high-frequency priors to further enhance performance. + +# 3. Methodology + +# 3.1. Facilitating TR-PEFT for Pixel-level Tasks + +Let $\mathbf{X}^i$ be the input tokens to the $i^{\mathrm{th}}$ transformer block with TR. This process can be formulated as follows: + +$$ +\mathbf {X} ^ {i + 1} = \mathbf {X} ^ {i} + \mathcal {M} (\operatorname {T R} (\mathbf {X} ^ {i})), \tag {1} +$$ + +where $\mathcal{M}$ represents the entire transformer block or any of its internal modules, such as the self-attention mechanism or feed-forward networks (FFN). While the token reduction process effectively reduces the number of tokens, the residual connection [10, 19] is designed to mitigate the loss of information and structural integrity. However, the inherent limitations of the residual connection can also lead to inadequate feature aggregation, which is critical for pixel-level tasks. To overcome this limitation, there is a strong need for an additional token compensator that can preserve spatial structure and further enhance the representation of the reduced token sequence. + +Adapter as a token compensator. In CoDA [30] and Dynamic Tuning [65], the authors introduce an adapter [4, 22] in parallel with the token reduction module. Thus, Eq. (1) can be rewritten as: + +$$ +\mathbf {X} ^ {i + 1} = \mathbf {X} ^ {i} + \mathcal {M} (\operatorname {T R} \left(\mathbf {X} ^ {i}\right)) + \text {A d a p t e r} \left(\mathbf {X} ^ {i}\right), \tag {2} +$$ + +We posit that this adapter serves a dual function: it not only facilitates the learning of new information from the incoming data but also plays a crucial role in preserving the spatial structure inherent in the original, unreduced tokens. Thus, the adapter can be viewed as a composition of these two essential functions. + +$$ +\text {A d p a t e r} = \mathcal {F} \circ \mathcal {G}, \tag {3} +$$ + +where $\mathcal{F}$ represents the function that aims to learn new knowledge, potentially realized through a PEFT module, and $\mathcal{G}$ denotes the token compensator, which is designed to retain the spatial integrity of the unreduced tokens while aggregating information that may be advantageous for pixel-level tasks. + +Decoupled design of token compensator and PEFT module. Usually, visual tokens are represented as the concatenation of class tokens, register tokens [8], and patch tokens. + +$$ +\mathbf {X} ^ {i} = \operatorname {c o n c a t} \left[ \mathbf {E} ^ {i}, \mathbf {P} ^ {i} \right], \tag {4} +$$ + +where $\mathbf{E}^i\in \mathbb{R}^{l\times d}$ denotes class and register tokens with length $l$ and embedding dimension $d$ , and $\mathbf{P}^i\in \mathbb{R}^{p\times d}$ is patch tokens derived from the images with length $p$ . $\mathcal{F}$ receives the entire token sequence $\mathbf{X}^i$ to learn new knowledge, while $\mathcal{G}$ processes only the patch tokens $\mathbf{P}^i$ to preserve spatial structure. We believe that separating the design + +of the PEFT module and the token compensator provides greater flexibility and efficiency for model adaptation. This can be formulated as: + +$$ +\mathbf {X} ^ {i + 1} = \mathbf {X} ^ {i} + \mathcal {M} \left(\mathrm {T R} \left(\mathbf {X} ^ {i}\right)\right) + \mathcal {F} \left(\mathbf {X} ^ {i}\right) + \mathcal {G} \left(\mathbf {P} ^ {i}\right), (5) +$$ + +The rationale behind the decoupled design of the PEFT module and the token compensator lies in the need to address distinct requirements for model adaptation efficiently. By decoupling these components, the PEFT module can be optimized specifically for learning new knowledge from incoming data, focusing on parameter efficiency and minimizing computational overhead. Meanwhile, the token compensator can be independently designed to preserve the spatial structure and integrity of the original tokens, ensuring that crucial details necessary for tasks like segmentation or depth estimation are maintained. Additionally, this architectural separation facilitates the application of the token compensator across a diverse range of PEFT methodologies, thereby promoting generalizability beyond the confines of adapter tuning [4, 22]. + +# 3.2. Our Method + +Building on the preceding discussion, we propose the implementation of a token compensator that functions independently from adapters or other PEFT modules. This design is specifically intended to preserve the spatial structure of the tokens. Furthermore, we introduce the idea of using a learnable mask as the token reduction strategy. This adaptive mechanism enables dynamic token selection, allowing the model to adjust which tokens are activated during processing based on the input's characteristics. Together, the independent token compensator and the learnable mask are designed to restore attention diversity and enhance the high-frequency components within visual representations, ultimately improving performance on pixel-level tasks. + +Strategy for reducing tokens. A simple strategy for reducing tokens involves using a learnable mask $\mathbf{M}^i$ to index the complete token sequence $\mathbf{X}^i$ . However, in a given batch, each image token sequence $\mathbf{X}^i$ can generate a different mask $\mathbf{M}^i$ , resulting in varying numbers of active tokens. This variability leads to different lengths $p$ for $\mathbf{X}^i$ within a single batch. While this approach is acceptable during inference, it hinders the use of parallel computation during training. To address this issue, the authors in [49] directly sparsify the token sequence $\mathbf{X}^i$ by performing a Hadamard product between $\mathbf{X}^i$ and a mask $\overline{\mathbf{M}^i} \in \mathbb{R}^{(l + p) \times d}$ . The mask $\overline{\mathbf{M}^i}$ is obtained by repeating $\mathbf{M}^i$ along the last dimension, leading to the formulation: + +$$ +\overline {{\mathbf {X} ^ {i}}} = \operatorname {F F N} \left(\mathbf {X} ^ {i} \odot \overline {{\mathbf {M} ^ {i}}}\right). \tag {6} +$$ + +where $\odot$ denotes the Hadamard product. While this approach demonstrates effectiveness when the model is + +![](images/8f5a209d5e52fd2905f139969ce44e62cdc4f9be9bb2ad29c8011aced9366c1d.jpg) +(a) Training + +![](images/fedb885a664f21d3b9507921a8fa860af7843291d875333e1e9c3e3f687c6a66.jpg) +(b) Inference + +trained from scratch, our empirical observations indicate that it encounters significant convergence difficulties within the context of PEFT, as illustrated in Fig. 3. We hypothesize this is due to the perturbation of the FFN bias from the pre-trained weights. We take the first linear layer of an MLP FFN for instance. + +$$ +\mathbf {Z} = \left(\mathbf {X} ^ {i} \odot \overline {{\mathbf {M} ^ {i}}}\right) \mathbf {W} + \mathbf {b}. \tag {7} +$$ + +where $W \in \mathbb{R}^{d \times r d}$ and $b \in \mathbb{R}^{r d}$ are the weight and bias, respectively, and $r$ is FFN ratio. Here, $\mathbf{Z}$ denotes the output of the linear layer. The bias term $\mathbf{b}$ is not affected by the mask $\overline{\mathbf{M}^i}$ . To address this issue, we apply the mask $\overline{\mathbf{M}^i}$ again after the FFN to block the perturbation, resulting in the equation + +$$ +\overline {{\mathbf {X} ^ {i}}} = \overline {{\mathbf {M} ^ {i}}} \odot \operatorname {F F N} \left(\mathbf {X} ^ {i} \odot \overline {{\mathbf {M} ^ {i}}}\right). \tag {8} +$$ + +This adjustment ensures successful model convergence. However, applying $\overline{\mathbf{M}^i}$ before the FFN becomes ineffective. Since the FFN performs channel-wise transformations, masking prior to the FFN has negligible impact on spatial feature interactions. The benefits of masking are most pronounced when applied after the FFN, as depicted in Fig. 2 (a). This strategy maintains the spatial structure of the input while effectively reducing the biases introduced by the FFN. Thus, we have designed our method to leverage this strategic placement of masking as follows: + +$$ +\overline {{\mathbf {X} ^ {i}}} = \overline {{\mathbf {M} ^ {i}}} \odot \operatorname {F F N} \left(\mathbf {X} ^ {i}\right). \tag {9} +$$ + +Mask generation. We directly generate the mask from the patch token sequence $\mathbf{P}^i$ by a $3 \times 3$ convolution layer + +![](images/688102070c8fe700af5b8b72af1886d4ac035c2047700b87db55e3929c33023c.jpg) +Figure 2. Overall architecture of the proposed method. During training, the PEFT module, token compensator, and token reduction components are tuned, while FFN and other modules within the transformer block remain fixed. A masking technique is applied after the FFN to prevent perturbation of the bias weights. During inference, the mask is utilized to reduce the length of the patch tokens $\mathbf{P}^i$ , thereby lowering the computational resource requirements. +Figure 3. Training Curves of Different TR methods. DynamicViT, based on Eq. (6), faces convergence difficulties. In contrast, our approach, which utilizes Eq. (8), converges successfully. + +$\mathcal{C}_m: \mathbb{R}^{d \times h \times w} \to \mathbb{R}^{1 \times h \times w}$ , where $h = w = \sqrt{p}$ is the height and width of the reshaped patch tokens. Then, we apply a sigmoid function followed by a threshold operation to generate masks $\mathbf{M}_P^i$ for patch tokens. To ensure differentiability, we add Gumbel noise [21] prior to the sigmoid function. This process can be formulated as follows: + +$$ +\mathbf {S} ^ {i} = \sigma \left(\frac {\mathcal {C} _ {m} \left(\mathbf {P} ^ {i}\right) + \mathbf {G} _ {1} - \mathbf {G} _ {2}}{\tau}\right), \tag {10} +$$ + +$$ +\left(\mathbf {M} _ {P} ^ {i}\right) _ {m, n} = \left\{ \begin{array}{l l} 0, & \left(\mathbf {S} ^ {i}\right) _ {m, n} < T \\ 1, & \left(\mathbf {S} ^ {i}\right) _ {m, n} \geq T \end{array} \right. \tag {11} +$$ + +where $\mathbf{G}_1, \mathbf{G}_2 \sim \mathrm{Gumbel}(0, 1)$ , $\tau$ is the temperature pa + +rameter set to 5.0 by default, and $\sigma$ is the sigmoid function. The threshold value $T$ is set to 0.5. $(\mathbf{M}_P^i)_{m,n}$ and $(\mathbf{S}^i)_{m,n}$ denote the element of $\mathbf{M}_P^i$ and $\mathbf{S}^i$ respectively. Then, We choose not to apply masking to class and register tokens, thus setting $\mathbf{M}_E^i = \mathbb{1} \in \mathbb{R}^{l \times 1}$ . Finally, we concatenate the flattened $\mathbf{M}_P^i \in \mathbb{R}^{p \times 1}$ with $\mathbf{M}_E^i$ to obtain the final mask $\mathbf{M}^i$ . + +$$ +\mathbf {M} ^ {i} = \operatorname {c o n c a t} \left[ \mathbf {M} _ {E} ^ {i}, \mathbf {M} _ {P} ^ {i} \right]. \tag {12} +$$ + +Masking in training and inference. As illustrated in Fig. 2 (a), we repeat the values in $\mathbf{M}^i$ along the embedding dimension to obtain $\overline{\mathbf{M}^i}\in \mathbb{R}^{(l + p)\times d}$ , during training. During inference, we remove the Gumbel noise and apply $\mathbf{M}^i$ directly to $\mathbf{X}^i$ to determine which tokens to mask at FFN, as shown in Fig. 2. + +Token compensator. The goal of the token compensator is to preserve the spatial structure of the tokens and restore high-frequency information. To achieve this, we design a simple and lightweight token compensator by incorporating local biases and enhancing high-frequency components using convolution layers [46]. Fig. 2 illustrates the architecture of our token compensator. The formulation of the token compensator (TC) is given as: + +$$ +\operatorname {T C} (z) = \operatorname {C o n v} (\gamma (\operatorname {D W C o n v} (\operatorname {C o n v} (z)))) \tag {13} +$$ + +where $\gamma$ is the GELU function, DWConv refers to the $\times 3$ depth-wise convolution, and Conv denotes the $1\times 1$ convolution layer. To maintain the computational efficiency of the token compensator, we maintain a low-rank design strategy for two $1\times 1$ convolution layers. This approach minimizes the number of additional parameters. + +Loss function. In our approach, we incorporate a composite loss function that consists of the segmentation loss $\mathcal{L}_{seg}$ , the distillation loss $\mathcal{L}_{cos}$ , and a regularization term $\mathcal{L}_{rate}$ , which regulates the token activation rate $k$ . The segmentation is employed to regularize the generation of segmentation maps, combining binary cross-entropy (BCE) and DICE. We directly adopt the Ada loss from [65] to control the token activation rate. For the distillation process, we employ cosine similarity to align the learned representations between the fine-tuned and pre-trained models. The total loss function is thus formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s e g}} + \lambda_ {1} \mathcal {L} _ {\text {r a t e}} + \lambda_ {2} \mathcal {L} _ {\text {c o s}} \tag {14} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are hyperparameters that balance the contributions of the $\mathcal{L}_{rate}$ and $\mathcal{L}_{cos}$ and $\mathcal{L}_{seg} = \lambda_{bce}\mathcal{L}_{bce} + \lambda_{dice}\mathcal{L}_{dice}$ . The complete formulae for each loss function is provided in Supp. + +# 4. Experiments + +# 4.1. Experimental Setting + +Datasets. We conduct experiments across three different scenes, focusing on real-world tasks. The datasets include + +simple scenes, complex scenes, and medical scenes. For simple scenes, we utilize the DUTS [57] dataset for salient object segmentation (SOS) and the CUHK [50] dataset for defocus blur detection. For complex scenes, we employ the COD10K [14] and CAMO [28] datasets for camouflaged object segmentation (COS) [13, 14]. In the medical domain, we use the Kvasir [25] and ISIC 2017 [6] datasets for polyp segmentation and skin lesion segmentation, respectively. For additional results on more datasets, please refer to the Supp. + +Implementation details. Our method was implemented using the PyTorch and the experiments were conducted on a RTX4060Ti GPU. In our implementation, the backbone was a pre-trained DINOv2-B [44] model, while the remaining modules were randomly initialized. We utilized the AdamW [40] optimizer for all experiments, with an initial learning rate set at $1.5 \times 10^{-4}$ and a cosine decay scheduler. During the training phase, we followed the resolution used in DINOv2, resizing input images to $518 \times 518$ pixels and applying random horizontal flips. For additional implementation details, please refer to Supp. + +Evaluation metrics. To thoroughly evaluate the model's performance, we employed three widely-used metrics for binary segmentation: weighted F-measure $(F_{\beta}^{w})$ [42], S-measure $(S_{\alpha})$ [5], and mean E-measure $(E_{\phi})$ [11, 12]. + +Loss weights. We employed a straightforward approach for assigning loss weights. Specifically, we set $\lambda_{bce} = 1.0$ and $\lambda_{dice} = 0.5$ for mask loss $\mathcal{L}_{mask}$ . Additionally, We set $\lambda_1 = 2.0$ and $\lambda_{2} = 0.1$ . + +# 4.2. Quantitative Results + +Comparison with PEFT methods. In Tab. 1, all PEFT methods outperform the linear probing and decoder-only methods, highlighting the significance of PEFT in enhancing foundation models for challenging scene understanding in difficult data domains. Specifically, in the medical domain, our methods demonstrate superior performance compared to DyT, as well as methods that do not utilize token reduction, particularly referring to weighted f-measure $F_{\beta}^{w}$ . In simple scenes, our methods consistently outperform DyT and achieve comparable performance to PEFT methods without token reduction, such as AdaptFormer and VPT, while exceeding the performance of other PEFT methods without token reduction, including EVP and LoRA. In the complex domain, our methods continue to show an advantage over DyT, reinforcing the effectiveness of our approach across varying levels of scene complexity. + +Comparison with pixel-level TR methods. We also include additional comparison with TR methods based on full fine-tuning for pixel-level tasks in Sec. 12.2 of Supp. + +Analysis of inference efficiency. In Tab. 1, we present a comparative analysis of the number of parameters and FLOPs for PEFT methods. Notably, our method demon + +Table 1. Quantitative and efficiency comparison of three different scenes using parameter-efficient fine-tuning (PEFT), both without and with token reduction (TR). In terms of the backbone, "Total Params." denotes the total number of parameters. "Trainable Params. (M) / Ratio (\%) " indicates the number of trainable parameters and their proportion relative to the total number. "FLOPs" refers to the floating-point operations per second. Bold values indicate the best performance for configurations both without TR and with TR, respectively. Ours† denotes our method with distillation. + +
MethodsTotal Params. (M)Trainable Params. (M) / Ratio (%)FLOPs (G)FPSSimpleComplexMedical
DUTS [57]CUHK [50]COD10K [14]CAMO [28]Kvasir [25]ISIC 2017 [6]
\( F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\alpha}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w}\uparrow S_{\alpha}\uparrow E_{\phi}\uparrow F_{\beta}^{w} \)
w/o TRLinear85.510 / 0.00%117.1824.20.658.841.832.675.659.670.657.860.866.707.853.852.482.782.747.571.779.755
Decoder Only85.510 / 0.00%117.1824.20.756.879.889.723.683.743.769.888.918.796.886.904.723.870.872.772.839.839
VPT [26]86.100.59 / 0.68%122.5227.98.896.931.938.800.752.809.816.903.936.850.908.933.891.939.951.860.872.883
AdaptFormer [4]86.701.19 / 1.37%118.7027.71.906.937.946.767.712.791.826.906.941.866.911.939.935.957.967.874.855.874
LoRA [23]86.861.33 / 1.53%118.9026.45.897.932.942.764.712.803.814.897.935.852.905.934.936.956.966.880.862.882
EVP [35]86.250.74 / 0.86%117.4427.82.887.929.935.771.736.791.803.900.933.832.901.921.857.934.943.854.866.875
w/ TRDyT [65]86.711.20 / 1.38%95.5129.02.859.921.930.735.691.759.796.894.934.839.901.932.897.944.963.843.868.884
Ours87.862.57 / 2.92%90.8328.84.895.933.944.793.749.812.810.899.935.842.902.932.938.960.975.871.862.881
Ours†87.862.57 / 2.92%91.5428.11.901.935.947.755.698.776.808.899.936.848.905.933.940.959.974.875.863.882
+ +strates the smallest FLOPs among the evaluated approaches, indicating a significant advantage in inference efficiency. Our method also achieves a competitive $F_{\beta}^{w}$ of 0.901 on the DUTS dataset, closely aligning with the performance of AdaptFormer, which records a $F_{\beta}^{w}$ of 0.906. It is important to highlight that AdaptFormer does not implement TR, which suggests that our approach effectively balances complexity and performance. + +# 4.3. Recovering High-Frequency Components + +In Fig. 1 (f), we show the relative log amplitude of Fourier-transformed representations for both TR and our method. The results highlight that our model effectively restores high-frequency components, particularly in the middle blocks, between the $6^{\text{th}}$ and $10^{\text{th}}$ layers. While our approach leverages a convolution-based token compensator to enhance high-frequency recovery, we also observe that further distillation of the fine-tuned model with the pretrained model significantly boosts this process. This enhancement is likely due to the pre-trained model's prior exposure to high-frequency components during MIM pretraining. Moreover, the learnable masks integrated into the fine-tuned model may also serve as a latent regularizer, guiding the model to focus on high-frequency components and local patterns. This mechanism improves the model's ability to capture intricate details, which are essential for high-precision pixel-level tasks. + +# 4.4. Ablation Study + +In order to assess the effectiveness of each component of our methods, we conducted ablation studies on DUTS and Kvasir datasets. + +Different components. In Tab. 2, we present an ablation study evaluating four combinations of components within our proposed methods. we assess the impact of applying TR both with and without the inclusion of the token compensator (TC), as well as the effects of utilizing distillation in + +Table 2. Ablation study on various aspects. The rows highlighted in gray represent our method (default setting). Bold values denote the optimal performance. + +
MethodsDUTSKvasir
Fwβ↑Sα↑Eφ↑Fwβ↑Sα↑Eφ↑
ComponentsNo TR.906.937.946.935.957.967
DyT-TD.859.921.930.897.944.963
Our TR.886.930.942.899.942.959
Our TR + Distill..887.931.943.928.954.973
Our TR + TC.895.933.944.938.960.975
Our TR + TC + Distill..901.935.947.940.959.974
Rank of token compensator24 (0.52 M).878.927.939.910.946.960
48 (1.38 M).895.933.944.938.960.975
96 (2.90 M).896.934.945.906.943.958
Token activation rateDyT-0.3 (66.39 GFLOPs).861.909.922.856.918.936
DyT-0.5 (95.51GFLOPs).859.921.930.897.944.963
DyT-0.7 (107.38 GFLOPs).871.928.934.908.938.954
Ours-0.3 (67.91 GFLOPs).863.917.926.911.935.950
Ours-0.5 (90.83 GFLOPs).895.933.944.938.960.975
Ours-0.7 (106.14 GFLOPs).883.932.940.920.951.963
+ +these configurations. Our results indicate that the configuration incorporating both the token compensator and distillation yields the highest performance on the DUTS dataset. In the Kvasir dataset, the method without distillation demonstrates a slight performance advantage on S-measure and E-measure. This observation implies that while distillation is beneficial for certain tasks, the inherent characteristics of the Kvasir dataset may favor configurations that prioritize direct token manipulations. + +Rank of token compensator. Furthermore, Tab. 2 compares the performance of three different ranks of the token compensator. The rank of 48 achieves the best results on the Kvasir dataset, while it performs slightly lower than the rank of 96 on the DUTS dataset. Considering the trade-off between performance and the number of parameters, we have chosen a rank of 48 to achieve an optimal balance. + +Token activation rate. Tab. 2 presents the impact of varying token activation rates of 0.3, 0.5, and 0.7 on model performance. Our methods achieve optimal results on both the + +![](images/bb554b03ef8096ebac83a7398251bb7c9c54c9a348faf7b546309ae7dc601422.jpg) +Figure 4. Visualization of the effects of our token reduction on DINOv2-B. The masked regions indicate areas of lower relevance, allowing the model to focus on informative parts of the images. Notably, some objects retain only their boundaries such as the red mushroom. + +![](images/5c7c5dae5c8068d5dde9a782fb99acf300d0b245292e47a5d5e17d3bd2c11f8f.jpg) +Figure 5. Segmentation outputs from various methods. Zoom in for a clearer view. + +DUTS and Kvasir datasets when the token activation rate is set to 0.5. Furthermore, at this setting, our approach demonstrates a reduced number of FLOPs compared to DyT. + +# 4.5. Analysis of Generalization Ability + +Previous research [34, 65] have primarily focused on task-specific effectiveness, often ignoring the capacity of models to generalize to novel tasks. To address this gap, we employ a zero-shot COS setting [29] to further evaluate the generalization capabilities of our proposed methods. Specifically, we utilize our well-trained model on the DUTS dataset for SOS, to directly address the problem of COS. As demonstrated in Tab. 3, our methods outperform previous approaches, such as CaMF [29] and GenSAM [24], particularly in terms of S-measure and E-measure. These results suggest that the restored diversity of attention and the high-frequency components in representations contribute significantly to the model's effectiveness in this zero-shot COS which is biased towards high-frequency information [29]. + +# 4.6. Visualization + +Masked tokens. In Fig. 4, we illustrate the effects of our token reduction method. In most images, the informative areas are retained while less relevant regions are masked, demonstrating that our approach effectively reduces computational requirements by prioritizing the processing of useful areas. Notably, we observe that certain objects, such as those in the bottom left and middle images, have only their + +Table 3. Comparison with other supervised (S), weakly-supervised (WS), and zero-shot (ZS) COS methods. Bold values denote the best performance. + +
MethodsSup.CAMOCOD10K
Fwβ↑Sα↑Eφ↑Fwβ↑Sα↑Eφ↑
SINet [13]S.606.751.829.551.771.806
ZoomNeXt [45]S.857.889.945.827.898.956
CRNet [20]WS.641.735.815.576.733.805
GenSAM [24]ZS.659.719.775.681.775.838
CaMF [29]ZS.729.788.814.717.808.832
OursZS.730.812.838.695.812.844
+ +boundaries unmasked. This suggests that our method emphasizes the local patterns and high-frequency components of the images, resulting in a relatively higher masking rate to further conserve computational resources. + +Segmentation maps. As shown in Fig. 5, our method produces segmentation maps with smoother boundaries compared to other methods. Additional results are provided in the Supp.. + +# 5. Conclusion + +In this paper, we investigate the impact of TR on attention mechanisms and visual representations, identifying barriers that impede its application within PEFT for pixel-level tasks. We introduce a novel TR-PEFT method that effectively preserves attention diversity, high-frequency components, and the completeness of the token sequence while reducing the length of tokens. This innovative approach aims to achieve an optimal balance between performance and inference efficiency, thereby enhancing the practical applicability of PEFT methods in pixel-level tasks. + +# Acknowledgements + +This work was supported by the Key Program for International Cooperation of Ministry of Science and Technology of China (No.2024YFE0100700) and the National Natural Science Foundation of China (NSFC) under Grant 62020106011. + +# References + +[1] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. Token merging: Your ViT but faster. In International Conference on Learning Representations, 2023. 1, 3 +[2] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. 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Existing debiasing techniques rely heavily on additional training, which imposes high computational costs and risks of compromising core image generation functionality. This hinders them from being widely adopted to real-world applications. In this paper, we explore Stable Diffusion's overlooked potential to reduce bias without requiring additional training. Through our analysis, we uncover that initial noises associated with minority attributes form "minority regions" rather than scattered. We view these "minority regions" as opportunities in SD to reduce bias. To unlock the potential, we propose a novel de-biasing method called 'weak guidance,' carefully designed to guide a random noise to the minority regions without compromising semantic integrity. Through analysis and experiments on various versions of SD, we demonstrate that our proposed approach effectively reduces bias without additional training, achieving both efficiency and preservation of core image generation functionality. + +# 1. Introduction + +With their ability to generate high-quality images, diffusion-based text-to-image (T2I) models are gaining widespread use across various platforms [10, 24, 26, 27, 32]. However, concerns have emerged about biases in these models, particularly the severe underrepresentation of minority groups in terms of gender, race, or other demographics, diverging from real-world distribution. In some cases, this even has led to some service backlash [3, 5, 7]. Even the recently open-sourced model Stable Diffusion 3 (SD3) [10] produces biased outputs, e.g., generating nearly $100\%$ female CEO, + +![](images/77c3adafea239b9cefbf6562624722c8e9a9f4fd31b3acd5c063cbf7f7976b8d.jpg) +(a) Conventional observation + +![](images/2ad8bca81225a5ef96b7641916d5800148e6e6b610b4e30f2494d8944c95fff6.jpg) +(b) Mode test observation + +![](images/cbc7c365400e1e698c28292061ea8d551a3c1f59a873e3bd393bc6b21b955fe2.jpg) +(c) Identified minority region + +![](images/ea8fa53712693af9f6c38d3a916cfaa8cfc32cce7d60c375779d7b89f4f2f82c.jpg) +(d) Proposed de-biasing + +![](images/58d8e18344b91547b7f8cc1bfbfb31c47b0ea20367809d3eb7cfaf0658f45309.jpg) +Figure 1. Conceptual illustration of our contributions. + and o denotes observed minority and majority images. + denotes noises associated with a minor attribute. Mode test (Section 3.1) identifies the existence of minority regions (b, c) and the proposed method (Section 4) guides an initial noise to the minority regions (d). + +showing that these issues persist. + +Several approaches have been explored to mitigate these biases, primarily through additional training. Previous efforts have involved fine-tuning all or parts of the model parameters or using techniques like prompt tuning for more efficient learning [12, 16, 21, 31]. However, these approaches have substantial drawbacks, including high computational costs and the risk of compromising the core image generation capabilities of T2I models. For most companies deploying T2I models, maintaining high-quality image generation remains the top priority. Consequently, the widespread adoption of existing de-biasing techniques in commercial T2I services like SD3 has been hindered, as they can impair both model performance and scalability. + +Is training truly essential to de-bias T2I models? Specifically, can any aspects of the pre-trained Stable Diffusion (SD) model itself be leveraged to mitigate bias? In this study, we explore the existence of "minority regions" by using a newly introduced "mode test." We define a "minor + +ity region” as the area in the noise space whose significant portion is generated to minority images (e.g., female CEO) when conditioned with an attribute-neutral prompt (e.g., “A photo of a CEO”). Our analysis in Section 3 reveals that the noises associated with these minor attributes form regions rather than being sparse or randomly scattered, more prevalently than previously observed. This is conceptually illustrated in Figure 1. These findings suggest that, if we can effectively harness those regions, we can reduce bias without requiring additional training. + +The newly enlightened minority regions inspire the concept of navigating random initial noises toward these regions. To begin, we analyze whether weakening the original guidance can serve as an implicit guidance. Specifically, given that the typical SD employs textual guidance, we test two schemes as follows: 1) reducing the strength of the textual guidance, and 2) adding noise to the textual guidance to perturb its direction. Experimental results demonstrate that both effectively reduce bias, yet they also compromise image-text alignment, underscoring the need for a more refined guidance mechanism. The following analysis reveals that explicitly directing perturbations towards minority regions offers a promising alternative where it impacts only the attribute without compromising image-text alignment. + +Building on these analyses, we propose a novel de-biasing method that adopts more direct guidance to the minority regions. Specifically, attribute directions are randomly selected and added to the textual condition. To preserve the semantics of the original text condition, the addition is conducted in a weak manner; the attribute direction is not added to every dimension, but rather to a less meaningful part of the text condition embedding. Our experiments demonstrate that our design choices preserve the image generation capability of SD while ensuring strong de-biasing performance. + +Final experimental results demonstrate the effectiveness of our method in mitigating gender and racial bias in various professions while preserving the aesthetic quality and prompt alignment of images generated by SD with minimal impact on overall output. We test our method across multiple SD versions, including SD1.5, SD2, SDXL, and SD3 developed by different entities, distinguishing our work from previous works that were limited to only a single version of SD. This highlights the generalizability of our analysis and the proposed approach. + +Our main contributions can be summarized as follows: + +- We propose for the first time a mode test to closely examine minority regions, previously perceived as sparse and minuscule, and explore their potential for enabling training-free de-biasing by steering initial noise toward these regions through text guidance adjustment. +- Motivated by our findings, we propose a novel de-biasing method based on weak text guidance that redirects random noise to generate minority images. + +- We experimentally demonstrate that our method reduces bias while preserving the image generation capability of SD. Results across multiple versions of SD further assure the broad applicability and effectiveness of our method. + +# 2. Related Works + +Analysis on bias in text-to-image generation Recent studies have analyzed biases in T2I models. Luccioni et al. [19] and Perera and Patel [23] brought attention to how these models often produce images that reflect societal stereotypes. Bianchi et al. [4] and Seshadri et al. [30] demonstrated that T2I models can amplify stereotypes, leading to skewed representations in generated images. While these works provide valuable insights into the existence of bias, they largely focus on analyzing outputs rather than deeply investigating the potential of harnessing SD's property to reduce such biases. + +De-biasing with additional training Training-based de-biasing approaches aim to introduce fairness to SD by using additional resources. However, fully fine-tuning large T2I models is prohibitively costly. Recent approaches have adopted parameter-efficient fine-tuning techniques, such as prefix tuning [16], text embedding projection weight [8], or low-rank adaptation [31]. Other efforts have focused on modifying the cross-attention layer in the UNet of SD [12, 21]. Some studies also explore fine-tuning h-space vectors, located in the UNet's bottleneck layer, known to encapsulate rich semantic information [17, 22]. However, there has been little examination of whether additional training is essential. + +De-biasing without additional training There are very few existing de-biasing techniques that bypass additional training entirely, typically opting to modify text prompts instead. ENTIGEN [2] inserts ethics-oriented phrases to prompts. However, manipulating the prompt explicitly risks distorting the semantic integrity of images generated with generic prompts that do not induce bias. FairDiffusion [11], the work most similar to ours, modifies the diffusion direction by employing SEGA [6], a concept editing technique. However, as discussed in Section 4.3, FairDiffusion tends to compromise image-text alignment, especially when a major attribute is explicitly mentioned in the text prompt or when prompt is devoid of potential stereotypes. In contrast, our method is carefully designed to ensure the text-image alignment after de-biasing. + +# 3. Exploring the Potential for Training-free De-biasing + +In this section, we delve into the minority regions as the potential for training-free de-biasing. First, we propose a mode test in Section 3.1, which examines the existence and range of the minority regions. In Section 3.2, we explore + +![](images/0377f6b4a830e3ac89e3e2200e381e515c3224ebd8c2bf38a17f06d25360e272.jpg) +Figure 2. (a) Conceptual illustration of our mode test. The encoding and decoding steps of the latent diffusion model are omitted from the figure. Noise is added to minor attribute images, followed by reverse diffusion process with an attribute-neutral prompt. (b) Change in the minor attribute ratio with the mode test (Section 3.1). + +![](images/7f5cbe87e49c3aca26c6cdd141c9c6274c95d3ff932cfce160e60de5b35a7bb0.jpg) + +text condition as a means of guiding initial noise to the enlightened minority regions. + +The primary analysis centers on binary gender bias (male and female) across four professions (doctor, CEO, nurse, and teacher). To classify gender in the generated images, we apply the CLIP zero-shot classifier1 with prompts such as "A photo of a male/female". For racial bias testing, we follow Chuang et al. [8] and use text prompts like "A photo of a White person/Black person/Asian/Indian/Latino". The attribute that appears most frequently in generated images is identified as the major attribute, with other attributes labeled as minor. Further details are described in the Appendix. + +# 3.1. Exploring Minority Regions: Mode Test + +To motivate the mode test, we first clarify its necessity. The conventional bias assessment has been conducted by generating a finite number of images, typically a few hundred to a few thousand, and counting the number of minority images, e.g., 30 female CEO images out of 1,000 CEO images (SD1.5). This approach led to the perception that the minority regions are sparse and minuscule (Figure 1 (a)) suggesting that additional training is essential. If it is possible to generate images infinitely, all existing minority regions will be fully uncovered. However, since this is impractical, the mode test helps to explore the existence of minority regions without requiring infinite generation. + +Mode test works as follows; we purposefully generate minority images (e.g., female CEO) by using prompts that specify minor attributes ("A photo of a female CEO"). Then we add standard Gaussian noise to those images to convert the images back to the initial noise space. This can be thought of as simulating a forward diffusion process similar to SDEdit [20]. Then the noises are denoised by given attribute-neutral prompts (e.g., "A photo of a CEO"). The overall process of the mode test is illustrated in Figure 2(a). Because the added noise is sampled from a standard Gaussian distribution, the resulting noise points are + +![](images/02780a5d7ca9f803a6f69b627a6947a29928fe0a81700f4741b3b181215fab14.jpg) +Figure 3. Impact of CFG: A higher CFG scale raises both the ratio of major attributes and the CLIP score (Section 3.2.1). + +likely to be located near the regions corresponding to the original images. Therefore, if minor attributes reappear in the images generated from attribute-neutral prompts, it suggests that the noises associated with minority attributes are not randomly scattered but instead clustered closely, forming a defined region. This insight reveals the structured nature of these regions and their potential for training-free de-biasing. + +Figure 2 (b) presents a comparison of the minor attribute ratio between images generated by vanilla SD and those produced through the mode test, with 1,000 images evaluated for each profession. The results show that the ratio of minor attributes increases in mode test generation compared to the vanilla SD. These suggest the existence of minority regions, i.e., the initial noises are clustered rather than sparse and randomly dispersed, motivating us to harness those regions. + +# 3.2. Exploring Guidance to the Minority Region + +In this section, we propose that the text condition can steer initial noise toward the minority regions. To test this, we perform two experiments: (1) reducing the classifier-free guidance scale (Section 3.2.1) and (2) introducing noise into the text conditions (Section 3.2.2). + +# 3.2.1. Impact of Classifier Free Guidance + +The Classifier-Free Guidance (CFG) [14] guides an initial noise to the final image that depicts the semantics specified + +![](images/f9031800693274f2256d093427ba5ef374f080857c2b2a45db432a3a61c084cd.jpg) +(a) Bias in Gender + +![](images/8e81845614bec54e94d675cb5c35d2f89f65310ba88b2f99835f1c299bff3f3c.jpg) +(b) Bias in Race + +![](images/6592e8fa412c860f9af9860037f45978ce5ae42f6623a2c7f8a8d3032f9db5ff.jpg) +(c) CLIP Score + +![](images/137d426eabaa86e5ad209748b67f63b23c9c1130f27b603ccdbb87dff1f972ef.jpg) +(d) Generated Images + +![](images/54bac489092cb5411a4c7ab9ad9722eb699f098ea5694f49d3e47c738d14b838.jpg) +Figure 4. Impact of CADS on bias and CLIP score: Increasing noise injection in the text condition (higher $s$ and lower $\tau_{1}$ ) effectively reduces bias (a, b) but also lowers the CLIP score (c). (d) Generated samples from vanilla SD and CADS ( $\tau_{1} = 0.6$ , $\tau_{2} = 0.9$ , $s = 0.25$ ) using the prompt 'a photo of a doctor'. CADS improves diversity in gender and race representation, though occasional misalignment with the prompt is observed (Section 3.2.2). + +![](images/0f45bec7787d6c51bf7aa68c02249eeac35ebbcca44e5ee1b8b9046f53ec9f14.jpg) + +![](images/8a9b292ad85628aa6892c875723b03773b68724451fbec3b33018298dd8bbeb2.jpg) + +![](images/74aac6602a05ba1a94a3a734b435c8849d74cac9d49cd6adfa03fa4287f49f7e.jpg) + +in the text condition. Specifically, with CFG, the predicted noise $\tilde{\epsilon}_{\theta}$ can be written as $\tilde{\epsilon}_{\theta}(z,c) = (1 + \alpha)\cdot \epsilon_{\theta}(z,c) - \alpha \cdot$ $\epsilon_{\theta}(z)$ , where $z$ represents the unconditional embedding, $c$ is the conditional embedding derived from the text prompt, and $\alpha$ is the CFG scale. It is well-established that a larger value of $\alpha$ , representing stronger guidance, results in higher coherence between the generated image and the text prompt, but this comes at the expense of sample diversity [14]. + +In this study, we examine how bias changes as the CFG scale varies, generating a total of 5,000 images for each profession (five CFG scales $\times$ 1,000 generations per profession). Figure 3 presents the ratio of the major attribute (y-axis) against the CLIP score (x-axis), with color intensity indicating the magnitude of the CFG scale. As the CFG scale decreases (represented by lighter colors), the ratio of the major attribute also declines. These findings support our hypothesis that weakening the text condition can reduce bias, though it comes at the cost of decreased alignment between the generated images and the text prompts. + +# 3.2.2. Noisy Text Condition + +We explore an alternative method for weakening text conditions by injecting noise, inspired by Condition-Annealed Sampling (CADS) [28]. CADS introduces noise to text conditions to diversify the composition of generated images. CADS perturbs a given text condition $c$ to $\hat{c}$ as follows: + +$$ +\begin{array}{l} \hat {\boldsymbol {c}} = \sqrt {\gamma (t)} \boldsymbol {c} + s \sqrt {1 - \gamma (t)} \boldsymbol {n}, \\ \text {w h e r e} \gamma (t) = \left\{ \begin{array}{l l} 1 & 0 \leq t \leq \tau_ {1}, \\ \frac {\tau_ {2} - t}{\tau_ {2} - \tau_ {1}} & \tau_ {1} < t < \tau_ {2}, \\ 0 & \tau_ {2} \leq t \leq 1. \end{array} \right. \tag {1} \\ \end{array} +$$ + +Here, $s$ determines the noise scale, $\gamma(t)$ represents the annealed coefficient dependent on time step $t$ , and $n \sim \mathcal{N}(0, I)$ denotes Gaussian noise. As diffusion models generate images through a reverse process from $t = 1$ to $t = 0$ , noise perturbations are applied to a text condition in earlier steps. $\hat{c}$ is then normalized to have the same mean and standard deviation as $c$ . To study the effect of noise injection to text conditions on diversifying attributes, we conduct experiments addressing gender and racial bias. Building on CADS default settings, we extend our analysis to explore the impact of noise intensity and injection duration. + +The results in Figure 4(a,b) demonstrate the effect of CADS on reducing the ratio of major attributes (y-axis), indicating bias mitigation. Across all variations in intensity and duration, the major attribute ratio decreases compared to vanilla SD (blue) for both gender and racial bias. Strong perturbations-achieved by increasing $s$ from 0.15 (yellow) to 0.25 (red) or decreasing $\tau_{1}$ from 0.8 (green) to 0.6 (red)-further enhance bias reduction. These observations also show that weakening text conditions helps mitigate bias. Figure 4(d) compares the images generated with vanilla SD and CADS. While CADS-generated images display diverse gender and race attributes, the alignment between prompt and generated images degrades, as shown in $3^{rd}$ and $4^{th}$ columns of the generated samples. This decline in alignment is further reflected in Figure 4(c), which shows a decrease in CLIP scores with CADS. Similar trends are observed for SD2 and SDXL (please refer to Appendix). These results indicate that, although perturbing text conditions can effectively reduce bias, it is important to carefully design the guidance to preserve SD's image quality and maintain prompt alignment. + +![](images/f3e8b44a9aef09d1f26c3952d972492e6c6092ef94ee5eeb686cd3d7991debc0.jpg) +Figure 5. Ratio of the minor attribute. The x-axis represents the fraction of diffusion steps guided by minor attribute-specific prompts (Section 3.3). + +# 3.3. Attribute Guidance + +We examine whether introducing a minor attribute-specified prompt during partial diffusion steps enhances bias reduction. Here's the approach: for a neutral prompt, the text condition in the early diffusion stages is replaced with a prompt focused on a minor attribute. The neutral prompt is then provided for the remaining steps. + +Figure 5 shows how varying the proportion of minor attribute-specified prompts (x-axis) influences the minor attribute ratio (y-axis), with different lines representing various professions. When minor attribute prompts are not used at all (proportion $= 0$ ), the results are heavily biased. On the other hand, using only minor attribute prompts (proportion $= 1$ ) yields a minor attribute ratio near 1. The gradual increase in the proportion of minor prompts clearly increases the minor attribute ratio, demonstrating that guidance during early diffusion steps is an effective strategy for addressing bias. This inspires our proposed de-biasing method in the next section which controls text condition perturbation through minor attribute guidance. + +# 4. Unlocking the Potential for Fairness in SD + +Building on our previous observations, we propose a straightforward yet effective method to reduce the influence of text prompts that tend to favor major attributes by perturbing the diffusion direction. This approach balances applicability with SD's image generation capability. Specifically, it focuses on two goals: 1) Efficiency: The method should not require high costs for training or inference. 2) Versatility: It should address bias only when needed, without hindering general-purpose image generation, such as responding accurately to prompts like "A photo of a car". In the following section, we introduce our weak conditioning scheme designed to satisfy both objectives. + +# 4.1. Method Design + +T2I models, including SD, rely on text encoders such as CLIP [25], which support arithmetic operations within their embedding space. These operations allow for the addition + +![](images/a848e1ca881d904257b60260c5e039e51df3e44f278e4ac2f86cfa64542983ef.jpg) +Figure 6. Our weak text embedding creation with attribute embedding. This approach guides the diffusion direction effectively while preserving the original text's semantics (Section 4.1). + +and subtraction of conceptual directions [9]. We define the attribute embedding direction $\mathbf{a}_k$ for an attribute $k$ as $\phi(k) - \phi(\ldots)$ , where $\phi(\cdot)$ represents the text encoder's encoding function, and “” denotes an empty text. Here, $k$ is the text representing an attribute, such as “female” and “male” for gender bias. By adding $a_k$ to a given text condition embedding $c$ , we obtain a modified embedding $c + a_k$ . This guides the diffusion process toward $k$ without requiring additional training, ensuring computational efficiency. + +To ensure versatility, we redesign the perturbation to be weak, ensuring that it maintains the semantic integrity of the input. In T2I models, the text encoder processes fixed-length inputs by appending an end-of-sequence ([EOS]) token to mark the end of the meaningful text, with padding added to fill the remaining length. Instead of adding $\pmb{a}_k$ to all positions of $\pmb{c}$ , we add a portion of $\pmb{a}_k$ only to the positions starting from the [EOS] token up to the maximum length of $\pmb{c}$ . This selective addition directs the diffusion process toward the desired attribute while preserving the original semantics of the prompt up to the [EOS] token. The benefits of this approach are explored further in Section 4.2. In formal terms, our new text embedding is expressed as $\hat{\pmb{c}} = \pmb{c} + \pmb{m} \odot \pmb{a}_k$ , where $m_i = \mathbb{1}(i \geq [\mathrm{EOS}])$ with $m$ being a mask whose value is 1 for the positions starting from the [EOS] token onward, and 0 elsewhere. Figure 6 illustrates our text embedding creation process. + +Given a prompt, we sample a target attribute from a uniform distribution over a pre-defined attribute set. After obtaining the weak attribute guidance, we use $\hat{c}$ exclusively for the initial $\tau$ denoising steps to establish the target attribute's influence. Following this, $c$ and $\hat{c}$ are alternated throughout the remaining denoising steps. This phased approach helps ensure the effective incorporation of the target attribute while preserving the original text's semantics. + +While our bias mitigation method appears straightforward, it meets the key goals of being both computationally + +![](images/0d6e18384fe7521b002a5bebee64254d22923df04531279e39d674a8773ef339.jpg) +Figure 7. Change in ratio of attributes with gender-neutral (left) gender-specified (right) prompts. The y-axis represents the ratio of the targeted attribute with guidance. Higher values indicate better alignment with the intended outcome (Section 4.2). + +practical and versatile. Experimental results in Section 4.3 will further highlight the effectiveness of this approach. + +# 4.2. Investigating the Design Choices + +In this section, we explain the rationale behind our design choices and demonstrate their effectiveness in reducing bias, promoting fairness, and preserving versatility compared to alternative methods. Figure 7 illustrates the impact of different design choices on attribute ratios. The left plots show the influence of guidance with neutral prompts, while the right plots depict the effects with attribute-specific prompts. Our goal is to achieve weak guidance—a subtle adjustment that encourages the generation of specific attributes (as seen in the high ratios in the left plots) without overriding explicit instructions in the text prompt. For example, if the prompt specifies "male," the guidance toward "female" should not interfere (indicated by high ratios in the right plots). + +**Specifying in the prompt vs. adding direction** Our method adds attribute embedding direction rather than explicitly specifying the attribute in the prompt. Inserting an attribute into a text prompt directly requires parsing the sentence to determine the appropriate placement for the attribute. This process is inefficient and may result in grammatically incorrect sentences, compromising image generation. By contrast, with the adding scheme, there is no need to parse or decide where to insert the attribute, making it more efficient and reliable. Simply appending the attribute text to the prompt (green in the left plots of Figure 7) can guide the generation toward the specified attribute. However, this approach compromises versatility and the ability to prioritize the original prompt (the right plots). + +Adding the attribute direction at every position vs. upon the [EOS] token Adding the attribute direction upon the [EOS] token (yellow) reliably generates the targeted attribute. This indicates that the embedding upon [EOS] carries sufficient information to guide the generation toward + +![](images/d2fcf326a4620f7a6a78d3b71ee3f92f9be07cc170112e353b40b54c0a34973b.jpg) +Figure 8. Ratio of gender in generations when it is specified in a given text prompt. If a certain attribute is explicitly specified in the text prompt (e.g., "a photo of a male doctor"), the attribute should be present in generated images. Higher is better (Section 4.3.1). + +
ModelMethodCLIP Score (↑)CMMD (↓)
SD1.5Vanilla SD26.420.532
FairDiff26.030.586
UCE18.101.240
FTDiff25.610.783
SelfDisc24.970.900
Ours26.560.509
SD2Vanilla SD26.550.524
FairDiff25.910.602
Ours26.290.549
SDXLVanilla SD26.510.794
Ours26.580.757
SD3Vanilla SD26.540.646
Ours26.480.664
+ +Table 1. Comparison of image fidelity and image-text alignment on MS COCO 2014-30k. Images are generated as $512 \times 512$ using SD1.5 and SD2 and $1024 \times 1024$ using SDXL and SD3, respectively (Section 4.3.1). + +the target attribute. While adding an attribute embedding at every position (red) also increases the ratio of attributes, it generates mostly female images even with "male" stated in the prompt, indicating excessive guidance. In contrast, adding the direction upon [EOS] generates mostly male images, preserving the prompt's intent. This demonstrates the effectiveness of weak perturbation in maintaining the original semantics of a text prompt. + +# 4.3. Experimental Comparison with Debiasing Methods + +Baselines We compare the proposed method with four baseline methods: FairDiffusion (FairDiff) [11], Unified Concept Editing (UCE) [12], Fine-Tuning Diffusion (FT-Diff) [31], and Self-Discovering latent direction (Self-Disc) [17]. FairDiffusion serves as our primary compari + +son target since it is the only method that does not require additional training. + +For all baselines, we use the official code and checkpoints if available. Otherwise, we train from scratch following the authors' instructions. For additional context, we also report gender statistics of LAION-5B [29], which comprises the training data for SD [30]. Further details are in the Appendix. + +Evaluation We evaluate bias using CLIP zero-shot classifier, as described in Section 3. Image-text alignment is measured with the CLIP score [13] using the CLIP-ViT-L/14 model $^2$ , while image fidelity is evaluated with the CMMD score [15]. Both metrics are computed on 30,000 images from the MS-COCO-2014 [18] validation set. + +Prompt configurations for debiasing We primarily focus on professions where the bias in generated images is more pronounced than in the training data. Based on analyses of gender ratios within the training dataset [30], we select eight professions where the difference in the ratio of minor attributes between the training dataset and images generated with SD1.5 exceeds or approaches $10\%$ p. These professions span both male-dominated fields (CEO, doctor, pilot, technician) and female-dominated fields (fashion designer, librarian, teacher, nurse). Unless specified otherwise, all images are generated using the template "A photo of a/an profession" to evaluate debiasing performance. + +# 4.3.1. Image-Text Alignment and Image Fidelity + +Our method is designed to uphold the image generation quality of SD while actively pursuing fairness, ensuring that both image-text alignment and image fidelity are preserved. Otherwise, it may result in significant reliability challenges when being deployed, such as depicting racial demographics inaccurately [1]. We have established two fundamental requirements for our quality assurance efforts. The first requirement mandates that if an attribute is explicitly defined in the text prompt (e.g., "a photo of a male doctor"), it must be present in the generated images. The second requirement dictates that our de-biasing technique should not adversely affect the generation of other images. For instance, a prompt without any potential stereotypes, such as "a photo of a car", should still yield a high-quality (CMMD score) and accurate car image (CLIP score). + +Specified attribute To test our first requirement, we generate 300 images with text prompts that explicitly specify gender. Figure 8 shows the prompt templates and results for eight professions generated using our method, compared with four baselines and the vanilla SD. The detailed numerical results are provided in Appendix. The left plot illustrates + +![](images/e726fc2d43968169c2c50bf89ea548f7c5fe6e0df0cb8284a62f73c216416c93.jpg) +Vanilla SD +FairDiffusion +Ours +"A cat sits atop a night stand next to a bike." + +![](images/b1587a1a6abb75b343012396c916979e73a546a6f42e455470623da854f96669.jpg) +"A baby giraffe that is under an adult giraffe." + +![](images/ce02f87259b2081b97b35fcaf107a9fc49401cc3251a2af6800cba85d79fbbf4.jpg) +"a photo of a librarian" +Figure 9. Comparison of generations with vanilla SD, FairDiffusion, and our method. Images are generated with captions from COCO-30k (first and second) and a prompt for profession (third) using SD1.5. The third image generated from FairDiffusion (middle) present physical characteristics of both women and men simultaneously (Sections 4.3.1 and 4.3.2). + +the female ratio from female-specified prompts, while the right plot reflects the male-specified prompts. Since gender is explicitly defined in each prompt, the target ratio is 1. The vanilla SD1.5 (grey) achieves a ratio close to 1 in both scenarios. Our method (purple) also reaches a ratio near 1, indicating that the weak perturbation approach does not disrupt the generation of the specified attribute. Conversely, other methods do not exclusively generate the specified gender. Notably, when using the male-specified prompt (right), FairDiff (blue) shows an almost balanced ratio, indicating that it almost ignores the gender specified in the prompt. + +General image generation For the second requirement, we generate images using captions from the COCO-30k dataset and evaluate their quality using CLIP and CMMD scores, as presented in Table 1. Our method achieves scores comparable to the vanilla SD, demonstrating that it maintains both image-text alignment and image fidelity without compromise. In contrast, other methods show decreased CLIP scores and increased CMMD scores, suggesting a notable decline in image generation quality for general text + +
Minor attributeProfessionTraining Data [30]Vanilla SDFairDiff [11]UCE [12]†FTDiff [31]SelfDisc [17]†Ours
FemaleCEO0.1500.0300.4520.0270.1900.4450.389
Doctor0.4080.0810.5020.0490.1980.5020.334
Pilot0.3040.1500.7390.2440.2600.5680.408
Technician0.3120.0070.5530.0050.1680.3470.164
MaleFashion designer0.2400.0780.3330.0180.1670.0670.451
Librarian0.2560.1940.3000.2970.5380.1740.421
Teacher0.3700.2220.2050.1550.2310.0810.492
Nurse0.1120.0070.1620.0030.2080.0040.039
Avg. Δ (↓)-0.4030.1670.4000.2640.2440.167
+ +Table 2. Ratio of minor attributes within 1,000 images generated with SD1.5, where a value closer to 0.5 is preferred. $\dagger$ indicates results reproduced through training using the official code. Avg. $\Delta$ represents the average absolute difference from the target ratio of 0.5 across all professions (Section 4.3.2). + +
SD2SDXLSD3
Vanilla SD0.4440.3630.481
Ours0.3620.2420.349
+ +Table 3. De-biasing results of our method across various versions of SD, with average $\Delta$ (explained in Table 2) values reported (lower values indicate better performance) (Section 4.3.2). + +prompts. This issue is particularly pronounced in training-based approaches, which exhibit greater compromises in performance. Qualitative comparison in Figure 9 further highlights the superiority of our method over FairDiffusion, our closest competitor. The images generated by FairDiffusion (second column) frequently include unintended artifacts, such as a hybrid of a human face and a cat (first row) or a giraffe with human-like features (second row), even when the text prompts contain no reference to humans. In contrast, our method consistently generates coherent and artifact-free images, showcasing its ability to achieve superior alignment between text and imagery. + +# 4.3.2. De-biasing Results + +Table 2 shows the de-biasing results across eight different professions when using SD1.5. The values represent the ratio of the minor attribute, i.e., for the first four professions where males are dominant, the female ratio is shown. The bottom row (Avg. $\Delta$ ) reports the average absolute differences between the ratio and the target ratio of 0.5 across the professions. A lower Avg. value indicates a more balanced ratio between males and females. + +The two leftmost columns show that SD tends to amplify biases present in the training data distribution, leading to skewed outcomes. Compared to the results of the vanilla SD, our results, shown in the rightmost column, show the increased ratio of the minor attribute even without additional training. The superiority of our method is particularly ev + +ident in female-dominant professions (bottom four rows). While training-based de-biasing methods (UCE, FTDiff, and SelfDisc) increase the minor attribute ratios, they rarely reach the target ratio of 0.5, even with additional training. FairDiffusion (FairDiff) achieves the same average results as our method but struggles to maintain image-text alignment, as highlighted in Section 4.3.1. Our method, on the other hand, achieves both effective de-biasing and robust image generation functionality. Table 3 compares the Avg. $\Delta$ value of vanilla SD and our method, supporting the generalizability of our method across different versions of SD. + +Figure 9 (b) shows the examples generated for two professions. The images generated from FairDiffusion (middle) present physical characteristics of both women and men simultaneously, such as breasts and mustaches. In contrast, our method generates images with clearer gender cues. + +# 5. Conclusion + +In this paper, we uncover the built-in potential in SD for training-free de-biasing. Based on the identification of minority regions through the proposed mode test, our de-biasing approach efficiently and effectively reduces bias by applying weak guidance to random noise so that it is guided toward the minority regions. Experimental results demonstrate that our method consistently reduces bias across multiple versions of Stable Diffusion, underscoring its applicability and robustness. Additionally, by not requiring additional training, the core image generation functionalities of SD are not compromised. + +There are more diverse and complex types of bias, but most de-biasing research focuses on gender and race due to their significant societal impact. Although our work follows previous studies by focusing only on gender and race, we believe it can serve as a foundation for future de-biasing research on other biases. + +Acknowledgement Sincere gratitude to Robin Rombach for invaluable discussions. This work was supported by Stability.ai, 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)], the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University in 2024, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A3B1077720, 2022R1A5A708390811), and Samsung Electronics Co., Ltd (IO240124-08661-01). + +# References + +[1] Gemini. https://finance.yahoo.com/news/black-nazi-gaffe-unacceptable-says-121548209.html. Accessed: 2024-05-21. 7 +[2] Hritik Bansal, Da Yin, Masoud Monajatipoor, and Kai-Wei Chang. How well can text-to-image generative models understand ethical natural language interventions? 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Unlike prior methods that provide either binary classification results or textual explanations separately, we introduce a novel method capable of generating both simultaneously. Our method harnesses the multi-modal learning capability of the pre-trained CLIP and the unprecedented interpretability of large language models (LLMs) to enhance both the generalization and explainability of deepfake detection. Specifically, we introduce a multi-modal face forgery detector (M2F2-Det) that employs tailored face forgery prompt learning, incorporating the pre-trained CLIP to improve generalization to unseen forgeries. Also, M2F2-Det incorporates an LLM to provide detailed textual explanations of its detection decisions, enhancing interpretability by bridging the gap between natural language and subtle cues of facial forgeries. Empirically, we evaluate M2F2-Det on both detection and explanation generation tasks, where it achieves state-of-the-art performance, demonstrating its effectiveness in identifying and explaining diverse forgeries. Source code is available at link. + +# 1. Introduction + +Generative Models (GMs) [9, 18, 23, 30, 57] have demonstrated impressive capabilities in synthesizing highly realistic and visually compelling images. However, they also facilitate the proliferation of AI-generated content (AIGC), like deepfakes, raising serious concerns over the spread of deceptive or manipulated facial imagery. To counter these threats, substantial efforts have been made to develop deepfake detection techniques, including subtle artifacts indentification [6, 22, 40, 41, 61, 91], frequency analysis [19, 45, 49, 55, 72], disentangling forgery traces via specialized neural networks [15, 20, 26, 44, 47, 76, 77, 90], modeling temporal inconsistencies [24, 62, 73, 92], among others. + +![](images/96caa9acdd1ce9b28255f36c57635c6513dd9e69233c5042ea31ee0f85b9b9c7.jpg) +(a) + +![](images/f37db694c059323501a5a989152740b73419f43be9c175558c56f05b11714986.jpg) +(c) +Figure 1. (a) and (b) represent conventional deepfake detectors and DDVQA-BLIP [85], which take an image as the input and output the fake probability (e.g., score) and textual explanations, respectively. (c) In this work, we propose a multi-modal face forgery detector (M2F2-Det) that produces both fake probability and textual explanations. + +Recently, the powerful capability of vision-language models, e.g., CLIP [56], also inspired efforts in detecting deepfakes. For example, DDVQA-BLIP [85] reformulates deepfake detection as an explanation generation task using a vision-language model [37], which enhances interpretability through natural language descriptions (Fig. 1b). In addition, several binary detectors [10, 52, 60] leverage CLIP's robust recognition capabilities to achieve impressive performance. However, three key limitations remain in these works. First, DDVQA-BLIP relies on a general text-generation model without dedicated mechanisms for deepfake detection, resulting in lower detection accuracy compared to conventional binary detectors. Secondly, prior CLIP-based detectors often lack effective input text prompts to describe diverse forgeries, restricting the adaptation of CLIP's multi-modal learning ability in the detection task. Third, while CLIP's open-set recognition capability — enabling it to identify diverse visual semantics — is successfully combined with LLMs in domains like document parsing [25, 48, 79] and medical diagnosis [34, 50, 83], its integration with LLMs for deepfake detection remains largely unexplored. + +![](images/1da580bb6b3263ed19094dcfb7983519e47ea8eb86ba7f210c835ca777792887.jpg) +(a) + +![](images/1a23f6096f77e80078d0914a4a1bacec38f0869133a0d8e4d2998e48ff2e0743.jpg) +(b) +Figure 2. (a) Forgery Prompt Learning (FPL) adapts CLIP to deepfake detection by optimizing UF-prompts and layer-wise forgery tokens (LF tokens). UF-prompts consist of three segments: trainable general forgery tokens (i.e., $\mathbf{V}_1$ , $\mathbf{V}_2$ , and $\mathbf{V}_3$ ), specific forgery tokens (i.e., $\mathbf{V}_4$ , $\mathbf{V}_5$ , and $\mathbf{V}_6$ ), and a fixed textual description ``Forged Face''. LF tokens are introduced in the CLIP text encoder and detailed in Fig. 3b and Sec. 3.2.1. (b) The Bridge Adapter connects the CLIP image encoder to the deepfake detector. It integrates with an LLM and a classification head, which output textual explanations and a predicted fake score, respectively. + +To address these limitations, we propose a multi-modal face forgery detector (M2F2-Det), which contains dedicated forgery detection mechanisms for accurate detection and generating convincing textual explanations (Fig. 1c): explanations enhance detection's trustworthiness, while accurate detection, in turn, supports reliable explanation generation through effective representation learning. Moreover, the M2F2-Det introduces Forgery Prompt Learning, an efficient adaptation strategy that produces discriminative text embeddings for diverse forged face images. We also introduce a Bridge Adapter to leverage the frozen CLIP image encoder, enhancing M2F2-Det's detection performance and facilitating its integration with the LLM for textual explanation generation. + +Forgery Prompt Learning (FPL) comprises two key components: universal forgery prompts (UF-prompts) and layer-wise forgery tokens (LF-tokens) (Fig. 2a). First, UF-prompts include both general and specific forgery tokens: general forgery tokens capture common forgery patterns and invariants shared across various manipulated facial images — critical for generalizing to unseen forgeries; specific forgery tokens, by contrast, encode fine-grained, image-dependent artifacts, such as blurred eyes from attribute manipulation and blending boundaries from face swapping. Secondly, we freeze the CLIP text encoder and introduce trainable layer-wise forgery tokens as inputs to its Transformer [69] layers (Fig. 3b). These task-specific tokens improve CLIP's adaptability to deepfake while largely preserving the recognition ability of its pre-trained weights. + +We further propose a Bridge Adapter (Bri-Ada) to harness capabilities of the pre-trained CLIP image encoder for both forgery detection and explanation generation. As depicted in Fig. 2b, the Bri-Ada reuses intermediate features from the CLIP image encoder, preserving its foundational strengths in representation learning, which proves generalizable enough to identify unseen forgeries [10, 52, 60]. + +To enhance domain-specific discrimination, Bri-Ada incorporates a deepfake encoder that provides forgery-aware knowledge, enabling the construction of more robust and effective visual representations for deepfake detection. In addition, Bri-Ada is employed jointly with FPL in M2F2-Det (Fig. 3a). Such text embeddings generated by FPL are used to produce forgery attention maps, serving as prior knowledge to guide forgery identification. Furthermore, Bri-Ada's output is connected to the LLM, which leverages CLIP's open-set recognition capability to translate visual features into textual explanations. Specifically, Bri-Ada's output is transformed into a frequency-based token. This token then is concatenated with tokens from other modalities to guide the LLM in generating trustworthy explanations for deepfake detection, detailed in Sec. 3.2.3. In summary, our contributions are: + +$\diamond$ We propose a multi-modal face forgery detector, M2F2-Det, which innovatively outputs both deepfake detection scores and textual explanations, achieving remarkable detection accuracy and enhanced interpretability. +M2F2-Det introduces a Forgery Prompt Learning mechanism—automated and effective prompt learning tailored for deepfake detection—that transfers CLIP's powerful multi-modal learning ability into deepfake detection. +$\diamond$ M2F2-Det employs a Bridge Adapter that enhances the integration of LLM, facilitating the generation of trustworthy explanations for detection decisions. +$\diamond$ M2F2-Det achieves state-of-the-art (SoTA) deepfake detection performance, measured by 6 datasets, showing the effectiveness of capturing diverse forgeries. It also obtains SoTA explanation generation performance on the DD-VQA dataset [85], both quantitatively and qualitatively. + +# 2. Related Works + +Deepfake Detection. The image forensics community develops various effective deepfake detection techniques, in + +![](images/b9961d0bfac75d4aff27aa257da24d8fc290edb20fb4b57e2a2c0e59cea941ca.jpg) +Figure 3. (a) The multi-modal face forgery detector (M2F2-Det) comprises pre-trained CLIP image and text encoders (i.e., $\mathcal{E}_I$ and $\mathcal{E}_T$ ), a deepfake encoder, as well as an LLM. Given the universal forgery prompts (UF-prompts) as input, $\mathcal{E}_T$ generates a global text embedding, e.g., $\mathbf{g}^{\mathrm{T}}$ , that guides the generation of a forgery attention mask, e.g., $\mathbf{M}_b$ . The deepfake encoder utilizes the bridge adapter, i.e., $\mathcal{E}_A$ , for detecting face forgeries (Sec. 3.2.2), while the LLM generates explanations conditioned on a frequency token $\mathbf{H}_{\mathrm{F}}$ transformed from the forgery representation $(\mathbf{F}^{0})$ (Sec. 3.2.3). (b) In the CLIP text encoder, we introduce trainable layer-wise forgery tokens as inputs to each Transformer [69] encoder layer. + +![](images/e20b97e06e2cfaa04c384d46d092f1272c0790c7ec572be4fab877a123c850ca.jpg) + +cluding data augmentation [11, 40, 41, 61, 91], frequency clues [45, 49, 72], disentanglement leaning [44, 76, 77], specified networks [21, 28, 66, 71, 78], and biometric information analysis [42, 65, 97]. These works belong to the conventional deepfake detector that outputs binary prediction scores. Recently, DDVQA-BLIP [85] defines a paradigm that generates textual explanations for deepfake detection, enhancing interpretability. In contrast, the M2F2-Det outputs both a prediction score and textual explanations, using the latter to enhance detection interpretability, while the prediction score helps more convincing explanations. Moreover, unlike prior CLIP-based forgery detectors [10, 52, 60] that only rely on detection capabilities of pre-trained CLIP, our M2F2-Det further integrates the open-set visual recognition ability of the CLIP image encoder for enhanced interpretability. + +Prompt Learning. Prompt learning offers an efficient strategy adapting the pre-trained CLIP to downstream tasks [27, 32, 62, 64, 89, 93, 95]. For example, CoOp [94] and CoCoOp [93] integrate continuous prompts in the textual space, enhancing the pre-trained CLIP's generalizability. Meanwhile, MaPLE [31] and VPT [27] modify the learning procedure in visual spaces by altering the CLIP image encoder. These works learn global image information for recognition tasks while our FPL conducts the pixel-wise task to localize facial forgeries. + +Multimodal Large Language Models (MLLMs) [37, 38, 46, 80] use generative capabilities from LLMs to obtain impressive performance across a wide range of tasks [29, 68, 82, 87]. For example, early studies concentrate on generating text-based content grounded on image [84, 86], video, and audio [3, 13, 39, 46, 74, 81]. Recently, MLLMs broaden applications to more complex downstream domains, includ + +ing embodied AI [54, 88], document parsing [25, 48, 79], and medical diagnosis [34, 50, 83]. We propose a frequency token that implicitly aligns deepfake domain knowledge with MLLM, bridging the gap between language and subtle facial forgeries. + +# 3. Method + +# 3.1. Preliminaries + +We denote the input image and text prompts as $\mathbf{I}$ and $\mathbf{S}$ , respectively. The proposed M2F2-Det utilizes CLIP's image and text encoders, $\mathcal{E}_I$ and $\mathcal{E}_T$ , together with a deepfake encoder, $\mathcal{E}_D$ , for forgery detection. Also, a large language model (i.e., $\mathcal{L}$ ) is employed to generate textual explanations. + +Prompt Learning. Contrastive Language-Image Pretraining, known as CLIP [56], is a large-scale vision-language foundation model that has powerful zero-shot classification capabilities. Given a set of $K$ text prompts $\{\mathbf{S}_1,\mathbf{S}_2,\dots ,\mathbf{S}_K\}$ , CLIP can estimate the likelihood that $\mathbf{I}$ corresponds to each of these text prompts: + +$$ +p (y | \mathbf {I}) = \frac {\exp \left(\left\langle \mathcal {E} _ {I} (\mathbf {I}) , \mathcal {E} _ {T} (\mathbf {S} _ {k}) \right\rangle / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\left\langle \mathcal {E} _ {I} (\mathbf {I}) , \mathcal {E} _ {T} (\mathbf {S} _ {k}) \right\rangle / \tau\right)}, \tag {1} +$$ + +where $\langle \cdot, \cdot \rangle$ and $\tau$ denote cosine similarity and a temperature hyper-parameter, respectively. To enhance the pre-trained CLIP's performance on downstream tasks, CoOp [94] proposes the prompt learning strategy that uses trainable tokens to automatically learn effective text prompts as follows: + +$$ +\mathbf {S} _ {k} = [ \mathbf {v} _ {1} ] [ \mathbf {v} _ {2} ] \dots [ \mathbf {v} _ {n} ] [ \mathrm {c l a s s} _ {k} ], \qquad (2) +$$ + +where $[\mathbf{v}_1][\mathbf{v}_2]\ldots [\mathbf{v}_n](\mathbf{v}_n\in \mathbb{R}^d)$ are trainable tokens, and $[\mathrm{class}_k]$ represents the fixed and non-trainable class name of the $k$ -th class. + +Visual Instruction Tuning. MLLMs tackle complicated reasoning tasks by generating responses based on visual and textual inputs. In general, a MLLM consists of three main components: 1) a pre-trained image encoder, e.g., $\mathcal{E}_I$ , that transforms $\mathbf{I}$ into a set of visual features. 2) a projector, e.g., MLP layers, that converts visual features to visual tokens denoted as $\mathbf{H}_{\mathrm{V}} \in \mathbb{R}^{N \times D}$ . 3) an LLM, i.e., $\mathcal{L}$ , that generates free-form responses in an auto-regressive manner when prompted with $\mathbf{H}_{\mathrm{V}}$ and textual tokens $\mathbf{H}_{\mathrm{T}} \in \mathbb{R}^{M \times D}$ . $\mathbf{H}_{\mathrm{T}}$ is generated by the tokenizer that takes user-input questions. Let us define target answer tokens as $\mathbf{X}_{\mathrm{A}} = [\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_z] \in \mathbb{R}^{Z \times D}$ , where $Z$ represents the sequence length, then the probability of generating $\mathbf{X}_{\mathrm{A}}$ becomes + +$$ +p \left(\mathbf {X} _ {\mathrm {A}} \mid \mathbf {H} _ {\mathrm {V}}, \mathbf {H} _ {\mathrm {T}}\right) = \prod_ {z = 1} ^ {Z} p _ {\theta} \left(\mathbf {x} _ {z} \mid \mathbf {H} _ {\mathrm {V}}, \mathbf {H} _ {\mathrm {T}, < z}, \mathbf {x} _ {\mathrm {A}, < z}\right), \tag {3} +$$ + +where $\theta$ are trainable parameters; $\mathbf{H}_{\mathrm{T}, < \mathrm{z}}$ and $\mathbf{x}_{\mathrm{A}, < \mathrm{z}}$ are instruction and answer tokens in all turns before the current prediction token $\mathbf{x}_{\mathrm{z}}$ , respectively. + +# 3.2. Multi-modal Face Forgery Detector + +# 3.2.1. Forgery Prompt Learning + +Forgery Prompt Learning captures forgeries via Universal Forgery Prompts e.g., UF-prompts, that contain two types of learnable tokens, e.g., general-forgery and specific-forgery tokens, e.g., $[\mathbf{v}^{\mathrm{G}}] \in \mathbb{R}^{d}$ and $[\mathbf{v}^{\mathrm{S}}] \in \mathbb{R}^{d}$ , respectively. Formally, we use MLP layers to transform the global visual embedding $\mathbf{g}^{\mathrm{I}} \in \mathbb{R}^{d} = \mathcal{E}_{I}(\mathbf{I})$ into $[\mathbf{v}^{\mathrm{S}}]$ , which helps inject image-dependent information into $[\mathbf{v}^{\mathrm{S}}]$ . Consequently, $[\mathbf{v}^{\mathrm{G}}]$ and $[\mathbf{v}^{\mathrm{S}}]$ are optimized together to leverage the powerful multi-modal representation capability of the CLIP for capturing both general and image-specific forgery patterns. Next, without loss of generality, we use ``forged face' as the generic textual description for various input face images, which stabilizes the training empirically. Therefore, we construct UF-prompts as: + +$$ +\mathbf {S} = \left[ \mathbf {v} _ {1} ^ {\mathrm {G}} \right] \dots \left[ \mathbf {v} _ {m} ^ {\mathrm {G}} \right] \left[ \mathbf {v} _ {1} ^ {\mathrm {S}} \right] \dots \left[ \mathbf {v} _ {u} ^ {\mathrm {S}} \right] [ \text {f o r g e d} ] [ \text {f a c e} ], \tag {4} +$$ + +where $m \in \{0, 1 \dots M\}$ , $u \in \{0, 1 \dots U\}$ ; forged and face are non-trainable tokens converted by fixed words. + +To enhance the conversion of S into textual embeddings that facilitate CLIP's adaptation, similar to the prior work [27], we introduce trainable layer-wise forgery tokens as inputs to each Transformer encoder layer of $\mathcal{E}_T$ while keeping its pre-trained weights frozen, depicted in Fig. 3b. More formally, for $\mathcal{E}_T$ 's $(r + 1)$ -th layer, e.g., $\mathcal{E}_T^{r + 1}$ , we denote collections of input $O$ layer-wise forgery tokens and $P$ ordinary tokens as $\mathbf{Q}_r = [\mathbf{q}_1,\mathbf{q}_2,\dots,\mathbf{q}_o]\in \mathbb{R}^{O\times d}$ and $\mathbf{E}_r = [\mathbf{e}_1,\mathbf{e}_2,\dots,\mathbf{e}_p]\in \mathbb{R}^{P\times d}$ , respectively. Then, $\mathcal{E}_T$ 's + +![](images/705ade176996102f3c7561e27e573ffece6d3989342e1fc1a3e0a5642c868e71.jpg) +Figure 4. The illustration on the Bridge Adapter, in which $\Theta$ represents the transformation conducted by Eq. 7. [Key: T-Block: transformer encoder block; Block: convolution block.] + +forward propagation of taking S is: + +$$ +\mathbf {E} _ {0} = \operatorname {E m b e d} (\mathbf {S}), \tag {5} +$$ + +$$ +[ -, \mathbf {E} _ {r + 1} ] = \mathcal {E} _ {T} ^ {r + 1} \left(\mathbf {Q} _ {i}, \mathbf {E} _ {i}\right), \tag {6} +$$ + +where $r$ is the layer index and Embed denotes the procedure that converts $\mathbf{S}$ into the $d$ -dimensional latent space with positional embeddings. + +Specifically, taking $\mathbf{S}$ as the input, the $\mathcal{E}_T$ outputs the global textual embedding, denoted as $\mathbf{g}^{\mathrm{T}}\in \mathbb{R}^{d}$ . Meanwhile, we obtain output features from the last layer of $\mathcal{E}_I$ , denoted as $\mathbf{F_I}\in \mathbb{R}^{N\times d} = \mathbb{R}^{W\times H\times d}$ . Then, a forged attention map, i.e., $\mathbf{M}_b\in \mathbb{R}^{W\times H}$ , can be obtained by calculating the text-to-image score for its each patch, i.e., $\mathbf{M}_b^{ij} = \langle \mathbf{F}_1^{ij},\mathcal{E}_T(\mathbf{S})\rangle$ , where $\mathbf{M}_b^{ij}$ and $\langle \cdot ,\cdot \rangle$ represent text-to-image score for $(i,j)$ -th patch of $\mathbf{M}_b$ and a cosine similarity operation, respectively. Next, we use $\mathbf{M}_b$ to help detect global image-level forgeries because it provides prior knowledge of the spatial forgery location, and this technique is similar to prior works [20, 63, 90]. Please note unlike prior works [27, 32, 93, 94] that adopt the prompt learning to capture global information of images, we innovatively propose the FPL to conduct a pixel-wise task of localizing forged regions (e.g., $\mathbf{M}_b$ ). + +# 3.2.2. Bridge Adapter + +As depicted in Fig. 4, the Bridge Adapter (Bri-Ada), i.e., $\mathcal{E}_A$ , is composed of Transformer encoder blocks and takes intermediate features from both $\mathcal{E}_I$ and $\mathcal{E}_D$ as inputs. In this way, $\mathcal{E}_A$ fully leverages the detection and open-set recognition capabilities of $\mathcal{E}_I$ , further enriched by domain knowledge from $\mathcal{E}_D$ to produce more robust and effective representations for deepfake detection. + +Bri-Ada is jointly used with FPL, which generates local forged attention maps. Specifically, we concatenate feature maps output from $\mathcal{E}_D$ and $\mathcal{E}_A$ into a fused feature map $\mathbf{F}^0\in \mathbb{R}^{w\times h\times c}$ , as illustrated in Fig. 4. We then use $\mathbf{M}_b$ and $\mathbf{F}^0$ to obtain refined forgery vector, e.g., $\mathbf{f}^0\in \mathbb{R}^d$ , as the final forgery representation for deepfake detection. Specifically, + +we have + +$$ +\mathbf {f} ^ {0} = \operatorname {A V G P O O L} \left(\operatorname {C O N V} \left(\mathbf {F} ^ {0} \odot \mathbf {M} _ {b}\right)\right), \tag {7} +$$ + +where AVGPOOL and CONV represent the average pooling operation and convolution layers, respectively. + +The joint use of FPL and $\mathcal{E}_A$ for detection has two key advantages. First, FPL and $\mathcal{E}_A$ mutually benefit each other. For global detection, $\mathcal{E}_A$ reuses intermediate features from $\mathcal{E}_D$ and then employs $\mathbf{M}_b$ as prior knowledge of forgery regions. This encourages FPL to update $\mathbf{S}$ and $\mathbf{Q}_i$ , such that $\mathbf{g}^{\mathrm{T}}$ can be used to generate accurate forged attention maps. For generating forgery attention maps, FPL needs feedback from $\mathcal{E}_A$ and $\mathcal{E}_D$ , on if its generated $\mathbf{M}_b$ enhances binary detection. Secondly, M2F2-Det is only supervised by the binary ground truth label, indicating that $\mathbf{M}_b$ is learned via an efficient unsupervised manner. + +# 3.2.3. Forgery Explanation Module + +The Forgery Explanation Module helps the M2F2-Det generate texts, as depicted in Fig. 3a. These generated texts contain the judgment and explanation, which claims if the image is forged and explicitly describes the rationale behind this decision, respectively. Specifically, we obtain the representation $\mathbf{F}^0$ for the detection task. We convert it into $\mathbf{H}_{\mathrm{F}} \in \mathbb{R}^{N \times D}$ . As a result, $\mathbf{H}_{\mathrm{F}}$ informs the LLM (e.g., $\mathcal{L}$ ) if the input image is fake. Meanwhile, we transform $\mathcal{E}_I$ 's output feature into visual tokens $\mathbf{H}_{\mathrm{V}}$ , which helps $\mathcal{L}$ describe the facial pattern. Both $\mathbf{H}_{\mathrm{F}}$ and $\mathbf{H}_{\mathrm{V}}$ are fed into $\mathcal{L}$ for explanation generation. Therefore, we update the Eq. 3 into as follows: + +$$ +p \left(\mathbf {X} _ {\mathrm {A}} \mid \mathbf {H} _ {\mathrm {V}}, \mathbf {H} _ {\mathrm {F}}, \mathbf {H} _ {\mathrm {T}}\right) = \prod_ {\mathrm {z} = 1} ^ {Z} p _ {\theta} \left(\mathbf {x} _ {\mathrm {z}} \mid \mathbf {H} _ {\mathrm {V}}, \mathbf {H} _ {\mathrm {F}}, \mathbf {H} _ {\mathrm {T}, < \mathrm {z}}, \mathbf {x} _ {\mathrm {A}, < \mathrm {z}}\right). \tag {8} +$$ + +# 3.3. Train and Inference + +Training. First, we train the deepfake encoder $\mathcal{E}_D$ as well as $\mathbf{S}$ and $\mathbf{Q}$ in FPL, such that M2F2-Det can perform the binary deepfake classification. We minimize the cross entropy distance between binary classification probability $p(y|\mathbf{I})$ and a ground truth categorical $\hat{y}$ . + +Secondly, we align $\mathbf{H}_{\mathrm{V}}$ and $\mathbf{H}_{\mathrm{F}}$ with the input space of a frozen LLM, such that outputs from $\mathcal{E}_I$ and $\mathcal{E}_D$ can be interpreted by the LLM. More formally, we maximize the likelihood defined in Eq. 8 via only training MLP layers while freezing other components in this stage. + +Thirdly, to better tame the LLM for explanation generation, we again keep the entire model frozen while only updating MLP layers and LLM based on Eq. 8. Trainable parameters, e.g., $\theta$ , thus become MLP layers and a subset of LLM's parameters. Please note we use LoRA for efficient LLM fine-tuning. + +In second and third-stage training, we use the DD-VQA [85] dataset that contains high-quality image-text + +
DatasetReal SamplesFake Samples
FF++ [58]1,000 V4,000 V
CDF [43]590 V5,639 V
DFD [1]363 V3,068 V
WDF [98]3,805 I3,509 I
DFDC [17]1,131 V4,113 V
FFIW [96]10,000 V10,000 V
+ +Table 1. Six datasets used for evaluating detection performance. [Key: V: Video; I: Image]. + +pairs annotated by the Amazon mechanical Terk. The DDVQA dataset consists of 14,782 question-answer pairs using the train/test IDs from FF++ [58]. This results in 13,559 question-answer pairs for training and 1,223 pairs for testing. Note that the second and third training stages are similar to LLaVA [46], and the difference is we align one more representation, i.e., $\mathbf{H}_{\mathrm{F}}$ . + +Inference. Given the input image and user-input questions, we produce the binary result and textual explanations. User-input questions can be flexible, such as 'Determine the authenticity of the image.' and 'Is this image real or fake?''. + +# 4. Experiment + +# 4.1. Setup + +Datasets. We evaluate our method on both detection and explanation generation tasks. For detection, we compare against existing detection approaches using datasets listed in Tab. 1, including FaceForensics++ (FF++) [58], CelebDF [43], WildDeepfake (WDF) [98], DFD [17], DFDC [14], and FFIW [96]. For explanation generation, we evaluate on the publicly available DD-VQA dataset [85]. + +Metrics. First, we use Area Under the Curve (AUC) and accuracy to measure the detection performance. Second, for explanation generation performance, we evaluate judgment performance and explanation quality. For judgment performance, we extract keywords, e.g., "Fake" and "Real", from generated texts to compute accuracy and F1-Score. To assess explanation quality, we employ standard natural language generation metrics such as BLUE-4 [53], CIDEr [70], ROUGE-L [59], METEOR [12], and SPICE [2]. These metrics evaluate the similarity between generated and annotated textual answers comprehensively. Additional evaluation details are provided in the supplementary material. + +Implementation Details. We employ EfficientNet-B4 [67] as the deepfake detector, i.e., $\mathcal{E}_D$ . Additionally, we use the CLIP/ViT-L-patch14-336 model [16] for the pre-trained CLIP image encoder $(\mathcal{E}_I)$ and text encoder $(\mathcal{E}_T)$ . The LLM is Vicuna-7b [8], and more details are in the supplementary. + +
MethodsVenueFF++ (c23)FF++ (c40)Celeb-DFWDF
Metric: Acc (% ↑) / AUC (% ↑)
RFM [71]CVPR2195.6998.7987.0689.8397.9699.9477.3883.92
Freq-SCL [36]CVPR2196.6999.2889.0092.39----
Add-Net [98]ACMMM2096.7897.7487.5091.0196.9399.5576.2586.17
F3-Net [55]ECCV2097.5298.1090.4393.3095.9598.9380.6687.53
MultiAtt [90]CVPR2197.6099.2988.6990.4097.9299.9482.8690.71
RECCE [5]CVPR2297.0699.3291.0395.0298.5999.9483.2592.02
TALL [75]ICCV2398.6599.8792.8294.5797.5798.55--
DDVQA-BLIP [85]ECCV2480.69-72.73-----
M2F2-Det98.7999.3493.8396.5898.9899.9286.0593.14
+ +Table 2. Intra-dataset Detection Performance. Results of prior works are mainly cited from [5, 75]. [Key: Best, Second Best]. + +
MethodVenueTraining setTest set AUC (% ↑)
RealFakeDFDCFFIWCeleb-DFDFD
LocalRL [7]AAAI21✓✓76.53-78.2689.24
CADDM [76]CVPR23✓✓--93.8899.03
UCF [76]ICCV23✓✓80.50-82.4094.50
SBI [61]CVPR22✓86.1584.8393.1897.56
AUNet [4]CVPR23✓86.1681.4592.7799.22
Seeable [33]ICCV23✓-86.30-87.30-
LAA-Net (w/ SBI) [51]CVPR24✓86.94-95.4098.43
FreqBlender [35]NeurIPS24✓87.5686.1494.59-
M2F2-Det (w/SBI)✓87.8088.7095.1097.70
+ +Table 3. Inter-dataset Detection Performance. Results of prior works are mainly cited from [4, 35, 51, 61]. [Key: Best, Second Best]. + +# 4.2. Detection Performance + +Tab. 2 and 3 report detection performance on intra- and inter-dataset setups, respectively. + +Intra-dataset performance. Tab. 2 shows our M2F2-Det achieves the best overall detection performance in $\mathrm{FF}++$ . For example, in $\mathrm{FF}++$ (c40), M2F2-Det has $1.01\%$ higher accuracy and $2.01\%$ higher AUC than the second-best method, i.e., TALL. Please note that TALL takes multiple frames as inputs, which generally contain more forgery information than using one frame as the input. While being a detector that takes single-frame input, our method still outperforms TALL, indicating the effectiveness of the proposed Forgery Prompt Learning and Bridge Adapter. Such effectiveness can be further demonstrated in Celeb-DF, in which our method surpasses TALL by $1.41\%$ accuracy and $1.37\%$ AUC score. + +Furthermore, WDF collects diverse real-life forged faces from the web on which our method outperforms the second-best performer, e.g., RECCE, by $2.80\%$ and $1.12\%$ in accuracy and AUC score, respectively. One key difference between RECCE and our method is that we adapt the pretrained CLIP image encoder, which is also trained on web samples. Such an adaptation improves M2F2-Det's detection ability by leveraging CLIP's robust representation, which proves generalizable enough to detect unseen forgeries [10, 52]. DDVQA-BLIP [85] predicts fake images based on if keywords like "fake" in generated sentences, + +whereas its detection accuracy is $18.1\%$ and $21.1\%$ lower than us on $\mathrm{FF}++$ c23 and c40, respectively. This shows accurate deepfake detection requires a specific mechanism that learns forgeries, like using forged attention masks as local forged contexts, instead of applying the text-generation model [37]. + +Inter-dataset performance. Tab. 3 reports the performance, in which we follow prior works [51, 61] to train methods on real and pseudo-fake images from FF++. Our M2F2-Det achieves $0.24\%$ and $2.56\%$ higher AUC than FreqBlender [35] on DFDC and FFIW, respectively. We believe our method's superior generalization ability comes from the usage of a pre-trained CLIP image encoder. Specifically, the CLIP is trained on diverse real-world web samples instead of a forgery detection dataset, making its learned features more generalizable and less overfitting on specific forgery patterns [10, 52, 60]. Moreover, M2F2-Det outperforms AUNet with higher AUC scores on three datasets but performs worse on the DFD dataset. AUNet learns forgery clues from relations between different facial action units. Similarly, specific forgery information from action units could also be considered in M2F2-Det's FPL, which uses UF-prompts and layer-wise forgery tokens to adapt CLIP in discerning both general and specific facial forgeries. The learned text embedding is used to generate forged attention maps, as depicted in Fig. 7, that act as local forged contexts to help the global detection task. + +
MethodFine-tunedDetection
Acc ↑F1 ↑
DDVQA-BLIP✓87.4990.07
LLaVAX51.4137.04
LLaVA✓86.4192.10
QwenX59.4151.04
InternVLX42.3347.35
M2F2-Det w/o Hf✓85.1184.21
M2F2-Det✓95.2396.61
+ +(a) + +![](images/27d17af34ccee9dcdfe1293028d18beafc316b6f85ffe18b8754e6e2d4582bce.jpg) +Explanation Quality +(b) + +![](images/8f5e658d187241dfe703abb618de823d9a771c26ac062a65fb3ac872c9716291.jpg) + +![](images/f7b23058c62663ce1837181092a4c8005b64bdfa198d2343ab33b3bed6729278.jpg) +(c) + +![](images/32f7fa60564dbe30e91e9825ad1182b0f473546dee21c133719cef334380a96c.jpg) + +![](images/af2fcceb1ad0ea24f2672b08e3b616a48877659aa22eeb5c3ff508d0f9c03be6.jpg) +Figure 5. Explanation generation performance on DD-VQA. (a) Judgment performance. [Key: Best results, Acc: Accuracy, F1: F1 Score] (b) Explanation quality is measured by 5 metrics. (c) Visualizations of forged attentions. +Figure 6. Qualitative results of explanation generation from DDVQA-BLIP, GPT-4o, and M2F2-Det. + +# 4.3. Explanation Generation Performance + +Quantitative Result. Fig. 5a reports explanation generation performance regarding judgment performance and explanation quality. First, from the judgment perspective, our method achieves the best accuracy and F1 score, which have $7.74\%$ higher accuracy than DDVQA-BLIP and $4.51\%$ higher F1 score than fine-tuned LLaVa. This demonstrates the advantage of the proposed frequency-based token (i.e., $\mathbf{H}_{\mathrm{F}}$ ), which helps our method generate correct descriptions based on learned deepfake domain knowledge. The usage of $\mathbf{H}_{\mathrm{F}}$ is different from previous MLLMs that only judge if visual artifacts exist in the color domain, which is less effective in capturing the discrepancy between real and fake images at frequency domains. Fig. 5a shows that a removal of $\mathbf{H}_{\mathrm{F}}$ decreases M2F2-Det's judgment performance by $10.12\%$ in accuracy. Secondly, Fig. 5b shows that M2F2-Det achieves the best explanation quality. Specifically, M2F2-Det has the best CIDEr score, which measures semantic consistency between generated sentences and ground truth (GT): Fig. 6 shows other works with error + +neous judgments and explanations, different from GT's semantics, hence causing low CIDEr. Also, ROUGE_L measures if generated explanations summarize GT's information with lexical variations, and our results include more diverse phrases, e.g., naturally wrinkled skin in Fig. 6's 3rd sample. Fig. 5c shows learned forged maps used in the M2F2-Det can better identify artifacts and forgeries than the cross-attention mechanism of DDVQA-BLIP. + +Qualitative Performance. Fig. 6 reports qualitative results, where our M2F2-Det generates explanations with accurate judgments and convincing explanations for both real and fake images. First, for image (a), DDVQA-BLIP cannot offer detailed explanations, whereas our model provides convincing reasonings, i.e., blurry hairlines. For (b), M2F2-Det again provides correct judgment and sophisticated explanations, e.g., clearly identifying unnatural patterns of eye regions and unnatural skin textures. We believe that such performance superiority of M2F2-Det comes from the effective deepfake representation (i.e., $\mathbf{H}_{\mathrm{F}}$ ). Lastly, we also show generated sentences on a real image (c), showing M2F2-Det's effectiveness in discerning genuine faces. + +![](images/2eee005f508841e0b2977be8a09bd5205bec5add3df8b1a2b5483c162bc765b6.jpg) +Figure 7. Forged attention maps on samples from 6 datasets introduced in Tab. 1. [Key: LF: layer-wise forgery tokens] + +
Forgery PLBri-AdaTest set AUC (%)
UF-PLFFF++(c40)Celeb-DF
191.0365.78
2✓92.5767.37
3✓92.6666.08
4✓✓93.6568.68
5✓93.8070.71
6✓✓94.2071.08
7✓✓✓96.5874.82
+ +# 4.4. Ablative Study and Analysis + +Forged Attention Map. Tab. 4's line $\# 1$ represents the deepfake detection baseline performance, e.g., EfficientNet-B4 [67]. Line $\# 2$ and $\# 3$ show layer-wise forgery tokens (LF tokens) and UF-prompts improve performance — e.g., $1.54\%$ and $1.63\%$ higher AUC scores on $\mathrm{FF}++$ , respectively. This shows that LF tokens and UF-prompts are effective designs to learn deepfake domain knowledge. Furthermore, in line $\# 4$ , we employ both UF-prompts and LF tokens, which is the full version of FPL, further increasing the performance of line $\# 2$ by $1.08\%$ AUC on $\mathrm{FF}++$ . This is because accurate forged attention maps can assist detection. For example, in Fig. 7's first sample, when using FPL, the person's nose and eye areas are precisely identified as forged regions. Such visualizations further demonstrate the quality of forged attention maps obtained from the FPL. + +Bridge Adapter. The comparison between lines #1 and #5 demonstrates the effectiveness of the Bri-Ada — increasing baseline's performance, e.g., line 1, by $2.77\%$ AUC score on $\mathrm{FF} + +$ . In addition, it enhances the generalizable detection ability and increases performance on CelebDF by $4.93\%$ . We believe this is because Bri. Ada. employs the CLIP image encoder that helps become less overfitting on specific manipulation types of $\mathrm{FF} + +$ samples. Line #6 indicates the integration between Bri-Ada and FPL further + +Table 4. Ablation Study. Each model is trained by FF++(c40) and tested on FF++(c40) and Celeb-DF. [Keys: Forgery PL: Forgery Prompt Learning; UF-P: Universal Forgery Prompts; LF: layer-wise forgery tokens; Bri-Ada: Bridge Adapter.] + +
MethodAUCMethodAUC
Uni.Fake [52]72.40CoOp [94]71.44
DEFAKE [60]76.84CoCoOp [93]72.62
M2F2-Det96.58FPL80.75
(a)(b)
+ +Table 5. Comparisons to (a) existing CLIP-based forgery detection methods and (b) prompt learning methods. The performance is reported on FF++(c40). + +increases detection performance. Lastly, the full M2F2-Det (i.e., line #7) achieves the best overall performance. + +Comparison to CLIP-based forgery detectors. Tab. 5a shows that M2F2-Det achieves $24.18\%$ and $19.74\%$ higher AUC scores than previous CLIP-based image forensic methods, Uni-Fake [52] and DEFAKE [60], respectively. These two methods use the CLIP image encoder with simple architecture, e.g., linear layers and ResNet-18, which lack specific facial forgery mechanisms. In contrast, the M2F2-Det not only employs the CLIP but also uses specified forgery detection mechanisms like FPL. + +Comparison to Prompt learning methods. We compute cosine similarities between CLIP image and text encoders' outputs for detection after applying different prompt learning schemes, and the performance is reported in Tab. 5b. Our FPL achieves $9.31\%$ and $8.13\%$ higher AUC scores than CoOp [94] and CoCoOp [93], respectively. This is because prior works are developed to adapt the CLIP to tasks that focus on recognizing semantics, which is different from deepfake detection. + +# 5. Conclusion + +In this work, we introduce M2F2-Det for interpretable deepfake detection. Specifically, M2F2-Det uses the Forgery Prompt Learning to adapt CLIP's multi-modal learning ability for deepfake detection. Then, an efficient Bridge Adapter connects the CLIP image encoder with a dedicated deepfake detection network, yielding more robust and effective visual representations for detection and seamlessly integrating with an LLM for enhanced interpretability. + +# References + +[1] Contributing data to deepfake detection research. https://ai.googleblog.com/2019/09/contributing-data-to-deepfake-detection.html. Accessed: 2021-11-13. 5 +[2] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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Hamza Mughal1 + +Rishabh Dabral1 + +Merel C.J. Scholman3 + +Vera Demberg1,2 + +Christian Theobalt1,2 + +$^{1}$ Max Planck Institute for Informatics, SIC + +$^{2}$ Saarland University + +3Utrecht University + +![](images/168491b7565faaee61646fde489f19f8529c525dfc2259fa015eb783369e839b.jpg) +Figure 1. Our RAG-GESTURE approach produces semantically meaningful gestures by leveraging explicit knowledge to retrieve exemplar gestures from the sparse semantic data [34] and guiding the diffusion-based generation process through Retrieval Augmentation. + +# Abstract + +Non-verbal communication often comprises of semantically rich gestures that help convey the meaning of an utterance. Producing such semantic co-speech gestures has been a major challenge for the existing neural systems that can generate rhythmic beat gestures, but struggle to produce semantically meaningful gestures. Therefore, we present RAGGESTURE, a diffusion-based gesture generation approach that leverages Retrieval Augmented Generation (RAG) to produce natural-looking and semantically rich gestures. Our neuro-explicit gesture generation approach is designed to produce semantic gestures grounded in interpretable linguistic knowledge. We achieve this by using explicit domain knowledge to retrieve exemplar motions from a database of co-speech gestures. Once retrieved, we then inject these semantic exemplar gestures into our diffusion-based gesture generation pipeline using DDIM inversion and retrieval guidance at the inference time without any need of training. Further, we propose a control paradigm for guidance, that allows the users to modulate the amount of influence each retrieval insertion has over the generated sequence. Our comparative evaluations demonstrate the validity of our approach against recent gesture generation approaches. The reader is urged to explore the results on our project page. + +# 1. Introduction + +Human communication is a complex and multifaceted process that involves both verbal and non-verbal elements. Non-verbal communication comprises co-speech gestures, which are defined as body and hand movements that are temporally aligned and semantically integrated with the speech [38]. Gestures convey information in tandem with speech and language, and can carry additional meaning that enhances the semantic construct of the message. Generating meaningful full-body gestures is therefore important for the communicative efficacy of virtual humans in telepresence and content-creation domains. + +McNeill [38, 39] categorizes gestures into beat gestures, which are rhythmic movements driven by prosody, and semantics-driven gestures, which carry the communicative intent. Semantic gestures are context-driven and bear a specific meaning that complements the utterance [6, 38]. Rule-based approaches retrieve these semantic gestures and combine them for generation, while neural methods leverage the data to learn the synthesis process. However, the former tends to result in an unnatural outcome and the latter struggles to generate semantic gestures because these gestures, while being a part of the existing datasets, occur rather sporadically compared to the rhythmic beat gestures [47]. + +In this work, we address this issue by framing the problem as a Retrieval Augmented Generation (RAG) task. We + +![](images/ee4d2e9c48871f9719464275a96263d1595481b7ea6f07f8da59b567123a11eb.jpg) +Figure 2. Overview. Our approach retrieves example gestures on semantically important words in speech and inserts those examples into the generated gesture by using them to guide the generation. + +propose RAG-GESTURE - a diffusion-based gesture synthesis approach that generates natural and semantically rich gestures by retrieving context-appropriate exemplars from a database and injecting them into the gesture generation process. Motivated by the insights from Neff [44], we decompose the generation problem into two tasks: specification, which ascertains "what gesture" to produce for "which word" in the speech, and animation, which determines "how to generate" that specified gesture. + +To solve the specification problem, we explicitly retrieve the relevant exemplar motions from a gesture database using either of the two retrieval algorithms proposed in Sec. 3.4. More specifically, we show that the chain-of-thought reasoning abilities of Large Language Models [48, 67] can be exploited to extract which parts of the utterance would likely be semantically gestured, and what 'type' of semantic gesture (iconic, deictic, metaphoric, etc.) the phrase would invoke. We also demonstrate that one could, alternatively, use specific linguistic elements to base the retrieval on. In particular, we focus on discourse connectives such as because, while, and on one hand, which have been shown to affect the gestural patterns [9, 40]. + +The animation problem, in our context, requires integrating the retrieved gesture motions (corresponding to a subset of the sentence) into the overall motion generated for the full sentence/utterance (see Fig. 1). To this end, we design an inference-time approach to augment the gesture generation capability of diffusion models with retrieved gesture clips. Our approach allows us to surgically integrate the semantic gestures into the generation process of the base model, while not affecting the synthesis for the remaining parts of the utterance. + +Through comprehensive numerical and perceptual evaluations, we demonstrate the effectiveness of our proposed neuro-explicit approach compared with purely neural state-of-the-art approaches like [34, 35, 46, 63] that typically struggle to synthesize semantically meaningful gestures. To summarize, our core contributions are as follows: + +- We introduce RAG-GESTURE - a diffusion-based approach which leverages RAG to generate natural-looking and semantically rich gestures by injecting meaningful motion exemplars into the gesture generation process. +- We introduce multiple retrieval algorithms to extract semantically relevant exemplars from the sparse semantic data distribution by leveraging either the linguistic structure of utterances or LLM-based gesture type prediction. +- Further, we propose a novel inference-time RAG approach for our framework and demonstrate how gesture exemplars can be transferred onto the generated motion locally through the combination of Latent Initialization and Retrieval Guidance technique, which provides a way to control the influence of the retrieval insertion. + +# 2. Related Work + +We first provide an overview of gesture synthesis approaches, followed by a discussion of relevant approaches from RAG literature. Lastly, we discuss recurrent patterns of gestures used to express discourse structure, which motivates the design of the retrieval-based method. + +# 2.1. Co-Speech Gesture Synthesis + +Co-speech gestures consist of hand and arm movements that occur in sync with speech and help convey meaning and structure discourse. Earlier methods in co-speech gesture generation [10, 56] perform well on semantics and appropriateness of gestures [47]. These systems retrieve the most appropriate gesticulation units for given speech, resulting in high semantic alignment. However, since they insert predefined units into animation, the synthesis quality of these systems tends to be unnatural. To mitigate the lack of naturalness, recent learning-based methods [2, 16, 20, 30] employ deep networks to convert speech input to gesture output and aim to ensure smooth motions. These methods are mostly data-driven and rely on learning speech-to-gesture matching through large scale gesture datasets [15, 18, 34, 60]. Most of these recent methods [1, 30, 59, 61] suffer from reduced communicative efficacy and low semantic alignment, due to bad generalization to semantic co-speech gestures in the dataset. Furthermore, generation and reproduction of semantically appropriate gestures corresponding to speech still remains a challenge for these systems [62]. + +A few recent approaches directly addressed this problem. Kucherenko et al. [31] use speech to predict the gesture properties, which inform the model on what type of gesture to generate. Instead, our framework proposes to use RAG to follow the gesture type information instead of taking the properties as conditioning input. Mughal et al. [42] generate semantic gestures by providing word-level semantic control and use it to sample semantically meaningful gestures. Zhi et al. [68] initialize diffusion-based generation with text-aligned embeddings by adding noise to them (sim + +ilar to inpainting [36]). In contrast, our approach inverts semantic exemplars into the diffusion latent space and uses them to initiate the denoising process. SemanticGesticulator [65] is a generative framework which retrieves semantic gestures from a curated motion library and aligns them with rhythmic gestures through a training-based approach. In comparison, our framework performs inference-time RAG using a diffusion model rather than fine-tuning the gesture generator to follow the retrieval. Secondly, our approach also utilizes prosody information for every retrieval instead of only using textual transcription. Thirdly, instead of relying on a curated library, our approach introduces explicit algorithms to retrieve semantics from the existing data [34]. Lastly, our framework is flexible enough to leverage any retrieval algorithm at inference time. + +# 2.2. Retrieval Paradigms for Generative Methods + +Employing database retrieval for improved animation performance is a prevalent paradigm in motion and gesture synthesis. Classical [8, 11] and learning-based motion matching approaches [24, 25] have been applied for better character control in motion synthesis [53]. Diffusion-based text-to-motion synthesis frameworks also deal with the problem of semantic control at a global level [63] or at the local keyframe level [19, 26]. Zhang et al. [63] apply RAG to diffusion-based text-to-motion synthesis using global text similarity for retrieval. Unlike text-to-motion, gesture generation is affected by language content and prosody at varying levels of semantic granularity. That means one can neither perform global semantic matching between the retrieved and generated motion [63] nor simply copy and paste retrieved motion parts onto the keyframe locations [19] without considering the differences in context. + +Gesture synthesis approaches have also utilized database retrieval both in classical and learning based paradigms. Early approaches [5, 29, 45] utilize statistics to retrieve gestures from a database of gesticulation units. A few learning-based approaches combine rule-based retrieval and deep learning-based synthesis to improve upon the semantic quality of gesture generation. ExpressGesture [17] introduces a database-driven framework to ensure that generated gestures retain the expressive and defined gesture form. Habibie et al. [21] employ nearest neighbor search to retrieve most appropriate gestures and provide a style-control mechanism over the generative framework. In comparison, our retrieval approach is not limited to style or select keywords but is grounded in explicit rules for semantic retrieval that are driven from linguistic and gestural structure. + +# 2.3. The effect of Linguistic Dynamics on Gestures + +The goal of our retrieval approach is to extract semantic gestures from the database. Our proposed design is therefore motivated by the relation between language dynamics and + +co-speech gestures. Laparle [32] demonstrates how gesture features like hand shape or orientation are important to distinguish between topics in discourse. Gestures can also indicate the relations between different parts of the message. For example, a contrast relation can be expressed by the lexical marker on the one hand...on the other hand, framing the two contrasting arguments as items placed on separate hands [22]. The raised index finger draws the attention of the interlocutor to new and important topics, and is commonly used to express exceptions or concessions (which can be expressed linguistically using however) [7, 27, 28]. + +In sum, gestures can be used to convey the semantic structure of a message, but existing generation works fail to reproduce these context-driven patterns [62], which results in repetitive gestures. We attempt to leverage the linguistic information in our retrieval framework. This framework can, in turn, improve semantic grounding of generated gestures through RAG based insertion. + +# 3. Approach + +Our primary goal is to generate semantically meaningful co-speech gesture sequences that are consistent with the content of the corresponding speech. This goal can be partly achieved by our latent-diffusion based gesture generation model, which is trained to synthesize gestures while being conditioned on the corresponding modalities (refer to Sec. 3.1). This data-driven gesture generation approach is capable of generating natural looking and beat-aligned gesture sequences from the input speech. + +However, this basic generation framework is not sufficient to exhibit rich semantics in the generated gestures. Therefore, we propose additional steps that ensure the solution to two key problems - animation (refer to Sec. 3.2 and Sec. 3.3) and specification (refer to Sec. 3.4) of semantically rich gestures [44]. Our approach is illustrated in Fig. 3. + +# 3.1. Gesture Generation with Latent-Diffusion + +As the first step, we build a robust generation framework based on latent-diffusion modeling [50], which serves as our base model to generate plausible co-speech gesture sequences. The gesture sequence $\mathbf{x} \in \mathbb{R}^{N \times d_{\mathbf{x}}}$ consists of $N$ frames of human motion with $d_{\mathbf{x}}$ representing a combination of $J$ full body joints represented using the 6D rotation representation of [69], FLAME model parameters for face motion, root translation and foot contact labels [35]. Instead of training our diffusion framework on raw motion $\mathbf{x}$ , we encode motion using VAE encoders, which provide separate encodings for different body parts [42]. These part-wise VAE encodings are then used to train our conditional latent-diffusion model that generates co-speech gestures. + +Decoupled Gesture Encoding. Based on the observations that each body region has different relations with + +![](images/017a47a7c0b8e3ae0d1a0afc2dd96be19c4aa1a1e7e9b06861ed58b2583e03b2.jpg) +Figure 3. RAG-GESTURE Framework. Our approach leverages a diffusion model which predicts clean sample $\hat{\mathbf{z}}^{(0)}$ from noisy gesture sample $\mathbf{z}^{(t)}$ . We then utilize retrieval algorithms (Sec. 3.4) to modify the gesture sampling at inference time by inserting the retrieved motion through Latent Initialization (Sec. 3.2) and further controlling the sampling process through Retrieval Guidance (Sec. 3.3). This results in a sampled motion which follows the semantic retrieval. + +speech [35] and scale differences between them affect the generation quality [42], we decouple the gesture sequence $\mathbf{x}$ into four different body regions: $\mathbf{x_u} \in \mathbb{R}^{N \times 6J_u}$ , $\mathbf{x_h} \in \mathbb{R}^{N \times 6J_h}$ , $\mathbf{x_f} \in \mathbb{R}^{N \times 100}$ and $\mathbf{x_l} \in \mathbb{R}^{N \times (6J_l + 3 + 4)}$ for upper body, hands, face and a combined representation for lower body and translation respectively. We train separate time-aware VAEs [42] for each body region, which can encode and decode the motion for each region: $\mathbf{z}_i = \xi_i(\mathbf{x}_i)$ , $\mathbf{x}_i' = D_i(\mathbf{z}_i)$ . These VAEs are trained using a combination of standard reconstruction/geometric losses for motion and the KL-Divergence loss for the VAE latent space (see supplemental). The resulting gesture representation is a set of decoupled encodings: $\mathbf{z} = \{\mathbf{z_u}, \mathbf{z_h}, \mathbf{z_f}, \mathbf{z_l}\}$ . This set can be concatenated to form a gesture representation $\mathbf{z} \in \mathbb{R}^{M \times d_{\mathbf{z}}}$ , where $M < N$ is the length of time-compressed encoding corresponding to each $\mathbf{x}_i$ and $d_{\mathbf{z}}$ is embedding length of the representation. Refer to the supplemental for more details. + +Conditional Diffusion for Gesture Generation. Once we have obtained $\mathbf{z}$ as our gesture representation, we can frame the gesture synthesis task as that of conditional diffusion [23, 50], where the conditioning set $\mathbf{C}$ comprises of audio, text and speaker embeddings. In this framework, the forward diffusion process consists of Markovian chain of successive noising steps, where Gaussian noise $\epsilon$ is added to the encoded gesture $\mathbf{z}^{(0)}$ for $T$ timesteps until $\mathbf{z}^{(T)} \sim \mathcal{N}(0, \mathbf{I})$ . For gesture generation, the reverse process is employed which iteratively denoises $\mathbf{z}^{(T)}$ to generate the gesture representation $\hat{\mathbf{z}}^{(0)}$ . The process utilizes a + +neural network $f_{\theta}(\mathbf{z}^{(t)}, t, \mathbf{C})$ for denoising, that is trained to predict clean state $\hat{\mathbf{z}}^{(0)}$ with the following objective: + +$$ +\min _ {\boldsymbol {\theta}} \mathbb {E} _ {t \sim [ 1, T ], \mathbf {z} ^ {(0)}, \epsilon} | | \mathbf {z} ^ {(0)} - f _ {\boldsymbol {\theta}} (\mathbf {z} ^ {(t)}, t, \mathbf {C}) | | _ {2} ^ {2} \qquad (1) +$$ + +During inference, we utilize DDIM [52] sampling for efficient generation of the gesture representation i.e. we generate a sample $\hat{\mathbf{z}}^{(t - 1)}$ from $\hat{\mathbf{z}}^{(t)}$ using: + +$$ +\hat {\mathbf {z}} ^ {(t - 1)} = \sqrt {\bar {\alpha} _ {t - 1}} \hat {\mathbf {z}} ^ {(0)} + \sqrt {1 - \bar {\alpha} _ {t - 1} - \sigma_ {t} ^ {2}} \boldsymbol {\epsilon} _ {\theta} (\hat {\mathbf {z}} ^ {(t)}) + \sigma_ {t} \boldsymbol {\epsilon} ^ {(t)} \tag {2} +$$ + +Here $\bar{\alpha}_t$ controls rate of diffusion and $\sigma_t$ controls stochasticity such that $\sigma_t = 0$ results in deterministic sampling. + +Our denoising network consists of a transformer decoder network with $L$ decoder layers containing a separate cross-attention head for each modality from the conditioning set $\mathbf{C}$ . The resulting activations from each head are combined using a linear layer in each decoder layer. Diffusion timestep $t$ is passed to the decoder layers through Stylization block [64] after every self-attention, cross-attention and linear layer. We encode speech signal using wav2vec2 [4] and construct frame-aligned representation for transcription using BERT embeddings for each word [12]. Additionally, we create identity-specific speaker embeddings for input. + +# 3.2. Latent Initialization through DDIM Inversion + +So far, our base neural generation framework is purely data-driven and lies on one end of neural-to-explicit spectrum. It resembles the majority of state-of-the-art gesture generation frameworks [3, 46, 66], which rely on learned pat + +terns to sample relevant gestures for corresponding speech and struggle to sample the semantic ones. On the other hand of the spectrum, pure retrieval based approaches can naively "paste" raw exemplar motions during the generation process which hurts the naturalness of motion. For instance, one could simply add noise to the retrieval and generate the rest through diffusion-based sampling [36], which forces the generation to exactly follow the retrieval, achieving subpar results (see Sec. 4.3 for analysis). Therefore, we carefully infuse the retrieved gestures into the inference process by performing the retrieval transfer in the latent space of the trained diffusion model and provide a better sampling path for its generation through retrieval guidance (Sec. 3.3). This preserves the quality of the base model, adapts it to generate semantically rich gestures and provides further control over the influence of retrieval insertion. + +In our framework, all retrieval algorithms (discussed later in Sec. 3.4) must output an exemplar motion $\mathbf{m}$ , which can be encoded as the retrieval $\mathbf{r} \in \mathbb{R}^{M \times d}$ through our gesture encoder (Sec. 3.1). We also have access to the text and audio corresponding to the retrieved motion. Our goal is to extract the motion chunk for the retrieved semantic gesture around a word of interest (e.g. 'because' in Fig. 3) and insert it into the motion around the corresponding words in the input text. Specifically, let the retrieved motion contain the semantically relevant gesture chunk in the frame window $(s_{\mathrm{retr}}, e_{\mathrm{retr}})$ for the marked word. The gesture in this window must be transferred onto the corresponding word location $(s_{\mathrm{query}}, e_{\mathrm{query}})$ in the to-be-generated sequence, also referred to as query $\hat{\mathbf{z}}$ (see Fig. 3). + +Here, the challenge is how to insert the retrieved gesture chunk such that it is seamlessly integrated into the final inference output in terms of temporal and semantic alignment. We perform this insertion through a combination of DDIM [13, 41, 52] inversion based latent initialization and a retrieval guidance objective. DDIM inversion lets us represent the retrieval $\mathbf{r}$ into the latent space of our base diffusion model, which we then use to initialize our generation. + +By reversing Eq. (2) and keeping $\sigma_{t} = 0$ for deterministic sampling path, we can invert $\mathbf{r}^{(0)}$ as follows: + +$$ +\hat {\mathbf {r}} ^ {(t + 1)} = \sqrt {\bar {\alpha} _ {t + 1}} \hat {\mathbf {r}} ^ {(0)} + \sqrt {1 - \bar {\alpha} _ {t + 1}} \boldsymbol {\epsilon} _ {\theta} (\hat {\mathbf {r}} ^ {(t)}) \tag {3} +$$ + +This iterative process inverts the clean $\mathbf{r}^{(0)}$ to full noise $\hat{\mathbf{r}}^{(T)}$ , which represents retrieved gesture in the diffusion latent space and provides the initial starting point for DDIM sampling such that it ends up at $\hat{\mathbf{r}}^{(0)} \approx \mathbf{r}^{(0)}$ . + +To transfer the retrieved gesture onto the query gesture generation, we slice the time axis of the latent $\hat{\mathbf{r}}^{(T)}$ to extract the relevant parts using the retrieval window $[s_{\mathrm{retr}}:e_{\mathrm{retr}}]$ and then, place these parts onto the query window in $\hat{\mathbf{z}}^{(T)}$ . + +$$ +\hat {\mathbf {z}} ^ {(T)} \left[ s _ {\text {q u e r y}}: e _ {\text {q u e r y}} \right] \leftarrow \hat {\mathbf {r}} ^ {(T)} \left[ s _ {\text {r e t r}}: e _ {\text {r e t r}} \right] \tag {4} +$$ + +The retrieval augmented $\hat{\mathbf{z}}^{(T)}$ can be represented as $\hat{\mathbf{z}}_{\mathrm{retr}}^{(T)}$ . + +# 3.3. Retrieval Guidance + +As a result of latent initialization step, $\hat{\mathbf{z}}_{\mathrm{retr}}^{(T)}$ comes out to be the starting point for gesture sampling process, which can be used to generate a sequence that follows the retrieved semantic gesture around the marked word. However, there is still no control over how strongly the retrieval is followed and how the diffusion sampling process goes from $\hat{\mathbf{z}}_{\mathrm{retr}}^{(T)}$ to $\hat{\mathbf{z}}_{\mathrm{retr}}^{(0)}$ . Therefore, we present Retrieval Guidance mechanism, that provides modulation control over the retrieval-augmented diffusion generation process from $\hat{\mathbf{z}}_{\mathrm{retr}}^{(T)}$ to $\hat{\mathbf{z}}_{\mathrm{retr}}^{(0)}$ . We utilize the sequence of inverted diffusion latents $(\hat{\mathbf{r}}^{(0)}, \hat{\mathbf{r}}^{(1)}, \dots, \hat{\mathbf{r}}^{(T-1)}, \hat{\mathbf{r}}^{(T)})$ and form our guidance objective. At a given diffusion timestep $t$ , guidance objective and its corresponding latent update are as follows: + +$$ +G _ {r e t r i e v a l} = \left\| \hat {\mathbf {z}} _ {\mathrm {r e t r}} ^ {(t)} [ s _ {\mathrm {q u e r y}}: e _ {\mathrm {q u e r y}} ] - \hat {\mathbf {r}} ^ {(t)} [ s _ {\mathrm {r e t r}}: e _ {\mathrm {r e t r}} ] \right\| _ {2} ^ {2} (5) +$$ + +$$ +\tilde {\mathbf {z}} _ {\text {r e t r}} ^ {(t)} \leftarrow \hat {\mathbf {z}} _ {\text {r e t r}} ^ {(t)} - \lambda \nabla_ {\hat {\mathbf {z}} _ {\text {r e t r}} ^ {(t)}} G _ {\text {r e t r i e v a l}} \tag {6} +$$ + +The updated $\tilde{\mathbf{z}}_{\mathrm{retr}}^{(t)}$ can be used further in the diffusion sampling by acting as input to the denoising network $f_{\theta}(\tilde{\mathbf{z}}^{(t)},t,\mathbf{C})$ . This guidance paradigm ensures that latent $\hat{\mathbf{z}}_{\mathrm{retr}}^{(t)}$ follows $\hat{\mathbf{r}}^{(t)}$ at the generation timestep $t$ . + +To control the amount of guidance at each step, one can control the number of iterations for latent update at each diffusion timestep $t$ . As an example, the generation from $\hat{\mathbf{z}}_{\mathrm{retr}}^{(T)}$ without any guidance will be the weakest form of retrieval augmentation where gestures are constrained to match only at the starting timestep $t = T$ . On the other hand, if one were to make sure retrieval is followed to its strongest extent, $\tilde{\mathbf{z}}_{\mathrm{retr}}^{(t)}$ can be updated at each diffusion timestep $t$ such that $G_{\mathrm{retrieval}} \to 0$ . Similarly, one can perform more latent updates when $t$ is closer to $T$ and lesser or no updates when $t \to 0$ , in order to only perform guidance at the start of the sampling process. Refer to Sec. 4.3 for analysis. + +# 3.4. Retrieval for Semantic Gesture Extraction + +Having discussed how to insert a retrieved gesture chunk into the gesture generation process, we now discuss retrieval algorithms that utilize linguistic context to determine which words in the query utterance are likely to invoke semantic gestures and what are those gestures. These algorithms retrieve semantically relevant gestures using domain knowledge of language and gesture type information. However, our approach is not limited to these algorithms and it can be extended using any retrieval paradigm for gestures. + +At the core, each retrieval algorithm ranks examples in a database (the BEAT2 dataset [35] in our case) according to a specific focus. During ranking, some of the steps are common across algorithms and are driven by overarching themes in gesture understanding. For example, motion exemplars from the same speaker typically have less + +![](images/303aecfc4ef542e3fb6e7b0230b2d21524b1f5fa081e97485f482c0807a3488a.jpg) + +![](images/ea74cf3515047addd7349b68a7708700af0ce2263ed725316725afff00430805.jpg) +(a) LLM-driven Gesture Type Retrieval +(b) Discourse based Retrieval +Figure 4. Retrieval Algorithms. Each algorithm parses the relevant semantic information (gesture types from LLM or discourse relations) and extracts gestures from a database by filtering examples using that information. Moreover, it also considers textual and prosodic context. + +speaker-dependent variation and should be ranked higher. Another common step across algorithms is ranking based on prosodic prominence extraction [14]. Certain elements of speech typically stand out due to variations in pitch, loudness, or duration, referred to as prosodic prominence [55, 57]. Prosodic prominence and gestures are closely connected: co-speech gestures often align with prosodically stressed parts of speech [49]. Therefore, we identify utterances in the database that match the prominence values of the marked word in the input speech [54]. An overview of individual steps is provided in Fig. 4. + +LLM-based Gesture Type Retrieval. One of the commonly used classification for semantic gestures divides them into iconic, metaphoric and deictic gestures [38]. Kucherenko et al. [31] demonstrate the benefit of utilizing these gesture properties in the synthesis framework, as gesture type information can decouple the specification problem from the animation. Therefore, we leverage the reasoning abilities of an LLM [48] and prompt it to identify words which may elicit a semantically meaningful gesture. We also use it to predict the gesture type on each predicted word. This results in a word-to-gesture type mapping, which we can use to retrieve examples from the database that contains type labels. Details on prompts and LLM are given in the supplemental material. + +Given the word-to-gesture type mapping, we take an identified word and its corresponding gesture type and filter examples in the database based on gesture type. We leverage the semantic gesture type annotations in the BEAT2 dataset [35] for this task. We then perform ranking based on speaker similarity, followed by ranking according to the text + +feature similarity between the query and database examples in order to match the semantic context. Lastly, we re-rank the top semantically similar examples based on prosodic prominence values. Fig. 4a illustrates the steps involved. + +Discourse-based Retrieval. A text has a structure that organizes its information into a coherent flow. This structure is achieved through discourse relations, semantic-pragmatic links such as CAUSE-CONSEQUENCE and CONTRAST, which hold between clauses and sentences [37, 51]. These relations can be signaled by lexical cues referred to as connectives, such as on the other hand or because. For example, in an utterance from BEAT2 dataset [35]: "I'll go shopping if I'm not that tired", the word "if" marks the conditional relation between two sentence segments. Prior works have demonstrated that discourse connectives have an effect on the gestural patterns [9, 40]. + +We leverage connectives to retrieve the relevant semantic gestures that co-occur with specific discourse relations. However, connectives can be ambiguous. For example, the connective since can signal a causal relation or a temporal one. We therefore retrieve the gesture co-occurring with a connective with the same meaning, but not necessarily the same word. For example, we can retrieve a gesture co-occurring with because to inform the generation of a gesture co-occurring with a causal since. Additionally, it allows us to retrieve more samples for less frequent connectives. + +In sum, we find examples in the database that carry the same discourse relational sense as the query and rank again based on the word similarity of the connective. We conclude the algorithm with speaker-based and prosodic similarity ranking. The steps are shown in Fig. 4b. + +
GT1 SpeakerAll Speakers
FID↓BeatAlign→L1Div→Diversity→FID↓BeatAlign→L1Div→Diversity→
0.70311.971270.4777.29110
CaMN [34]0.6040.7119.971070.5120.2005.5898
EMAGE [35]0.5700.79311.411240.6920.2846.0688
Audio2Photoreal [46]1.020.55012.471450.8490.3266.2499
ReMoDiffuse [63]0.7020.82412.461231.1200.2185.06116
Ours (w/ No RAG)0.9110.72712.781300.5190.4478.64112
Ours (w/ Discourse)0.8790.73012.621290.4470.4719.03114
Ours (w/ LLM & Gesture Type)0.8080.73411.971220.4870.5149.94118
+ +Table 1. Comparison with state-of-the-art methods trained on BEAT2. We demonstrate superior performance, especially when generalizing across multiple speaker identities. + +# 4. Experiments + +We first compare our approach with neural state-of-the-art baselines through quantitative (Sec. 4.1) and perceptual evaluation (Sec. 4.2). Further, we demonstrate how our RAG approach improves upon the training-based RAG baselines. Lastly, we validate our method design through extensive ablations and user studies (Sec. 4.3). + +Specifically, we compare with recent data-driven gesture generation approaches that are CaMN [34] (LSTM-based), EMAGE [35] (transformer-based) and Audio2Photoreal [46] (diffusion-based). Furthermore, to validate RAG performance for gesture synthesis, we not only compare our method with ReMoDiffuse [63] (re-trained for gesture synthesis), but we also analyze it further by tailoring their approach and training it with our retrieval algorithms. We provide seed motions for baselines [34, 35], but do not use seed motions to generate our results. + +Evaluation Dataset. We evaluate our performance on train/val/test split from BEAT2 dataset [35], which contains 25 speakers. Unlike baseline approaches for BEAT2 which report results only for a set of speakers, we perform evaluation on the test set of one speaker (Scott) and all speakers in order to evaluate performance on large-scale multi-speaker data. Our test set contains 265 utterances chunked into 10-sec sequences. We retrain methods on BEAT2 if needed. + +# 4.1. Quantitative Evaluation + +We evaluate our method on established metrics: Beat-Alignment [33], FID [60], L1 Divergence and Diversity, which measure different aspects of the motion quality. We tabulate the quantitative results in Tab. 1, where the results are divided on the basis of number of speakers used for training and evaluation. We observe that our approach achieves state-of-the-art metric performance when trained with all speakers. This also entails that our RAG-based diffusion approach generalizes and scales well across large-scale data with multiple speaker identities. For the case of single speaker training, we observe best performance in terms of diversity and L1 Divergence and second-best in Beat Alignment score. However, our diffusion-based + +![](images/2346ebc07442d9a1fb399ead2d95c2749ee7ce7c82e9d9d292eec13f1170d519.jpg) +Figure 5. Results of Perceptual Evaluation. A2P: Audio2Photoreal [46] GT: Ground Truth. * denotes p-value < 0.05 + +![](images/208d70129379272e7dc16023c524cbaf97a16d35dfff8f88c298cac41e1618a9.jpg) + +method has higher FID compared to transformer and LSTM based methods [34, 35] that utilize ground-truth seed and can be over-fitted to a small-scale data of single speaker, while not being able to generalize to all speakers. + +# 4.2. Perceptual Evaluation + +Evaluating gesture synthesis performance is a highly challenging task due to the stochasticity in gesture production and subjective nature of gesture perception [47, 58]. Therefore, we perform four different user studies for comparison and ablative analysis (Sec. 4.3). First, we evaluate the synthesis quality compared to the baseline methods. We investigate the quality of gestures based on well-established measures of naturalness and appropriateness in relation to speech [43]. We ask the participants to perform pairwise comparisons between generations from baselines and our method. Results compare RAG-GESTURE with discourse and LLM-based retrievals against state-of-the-art methods (Fig. 5). We observe that our method achieves better perceptual quality for both naturalness and appropriateness. For LLM based approach, we are marginally below the ground-truth preference, underscoring that our method produces not only natural, but also highly appropriate gestures. + +# 4.3. Ablative Analysis + +Improvement over RAG Baselines. ReMoDiffuse [63] uses global text similarity for retrieval and trains the diffusion network to follow it. In contrast, we design our retrieval to match local context around the semantically important word and do not require training/fine-tuning for RAG unlike existing approaches [63, 65]. + +![](images/e3040d27639779e38d90712e33524bb5eeca37624f42ade0f9c1923f99ddf6e8.jpg) +Figure 6. Perceptual Comparison between training-based baselines and our inference-time approach. $*$ : p-value $< 0.05$ + +![](images/50d8c500748acfe932bca38a11a511ae1b790aa49d93f7efd97617cfdd9242df.jpg) + +
FID↓BeatAlign→L1Div→MPJPE (mm)↓
GT0.4777.29
ReMoDiffuse [63]1.1200.2185.06200.5
Training-based RAG0.5250.4146.9134.6
RAG-GESTURE0.4470.4719.0335.0
+ +![](images/dd54795d257119c2cd0666db77ea72a6476b13276dc708944573d3afff8af974.jpg) +Figure 7. User Study comparing LLM and Discourse algorithms. + +Besides comparing these differences with ReMoDiffuse, we also evaluate RAG-GESTURE (Discourse) against a training-based approach where we incorporate our discourse-based retrievals with ReMoDiffuse's generator through the local retrieval merging strategy of SemanticGesticulator [65] (see supplementary for details). Note that this architecture is trained with encoded gestures instead of raw motion and is similar to SemanticGesticulator [65] at a higher level, which also performs retrieval merging with encoded gestures during fine-tuning. + +We evaluate this quantitatively in Tab. 2 and perform an additional user study (Fig. 6). Moreover, we also report MPJPE between the generated gesture and retrieved motion during the retrieval insertion window to measure the retrieval following performance. Firstly, we observe that the training-based RAG which uses local semantic retrieval during training performs better than ReMoDiffuse, both in terms of perceptual quality and metrics. Moreover, we also see higher faithfulness to the retrievals through low MPJPE which entails that properly specifying the retrieved motion on the exact word affects the gesture quality. Secondly, our inference-time RAG-GESTURE is better than the training-based model, even after utilizing our retrieval algorithm. This underscores our method's superiority and the importance of having a good gesture animation performance. + +LLM-based Gesture Type vs. Discourse Retrieval. For evaluating perceptual differences between LLM-based gesture type retrieval and discourse-based retrieval, we conduct an additional user study where we ask the participants to evaluate differences between generated gestures from the two algorithms in terms of naturalness and appropriateness (Fig. 7). Interestingly, we find that evaluators do not show any strong preference between the two algorithms. + +Table 2. Quantitative Comparison between RAG baselines. + +
FID↓BeatAlign→L1Div→MPJPE (mm)↓
GT0.4777.29
No RAG0.5190.4478.6459.6
RAG by Inpainting [36]0.4460.4508.4628.1
RAG by LI only0.5890.4869.2954.6
RAG-GESTURE (LI+RG)0.4470.4719.0435.0
+ +Table 3. Extent of Semantic Retrieval Insertion. LI: Latent Initialization; RG: Retrieval Guidance. + +![](images/a7dc6f090a76e7ebe44e8ab742f4f20664870e37481e87d8e5346ab9d7fe5d15.jpg) +Figure 8. Ablative Study which illustrates preference of RAG-GESTURE over varying degrees of insertions. \*: p-value $< 0.05$ + +Extent of Retrieval Augmentation Since our approach can control the influence of the retrieved gesture onto the generated one, we analyze how much influence is optimal to synthesize semantically accurate yet natural looking gestures. We compare RAG-GESTURE's prediction against varying degrees of retrieval insertion (Tab. 3) using Discourse-based retrieval. "Inpainting" means adding noise to the retrieval and synthesizing the remaining motion and "No RAG" represents no retrieval insertion. We conduct another user study with a third "Retrieval Appropriateness" question to gauge semantic appropriateness of the generated gesture during the insertion window (Fig. 8). Interestingly, we observe increasing preference of our retrieval-guided model as we move towards both extremes of the insertion. In terms of gesture perception, evaluators neither prefer generation without RAG (purely data-driven) nor a strong insertion through Inpainting (purely retrieval-based). Lastly, our model achieves good balance of retrieval following in terms of MPJPE, prosodic alignment and diversity. + +# 5. Conclusion + +In this work, we present RAG-GESTURE - a novel approach that leverages interpretable retrieval algorithms to introduce inference-time RAG to a diffusion-based gesture generator. Therefore, it combines advantages of the pure retrieval-based and fully data-driven approaches to synthesize natural yet semantically meaningful gestures. Perceptual evaluation demonstrates that this type of neuro-explicit approach is better than either of the two approaches and existing state-of-the-art methods. Moreover, we demonstrate that LLM-driven gesture type prediction and discourse relations can enhance semantic understanding in current gesture generation architectures. Lastly, our framework can be extended to synthesize gestures that exhibit task-specific gestural patterns like referential or emotion-specific gestures. + +Acknowledgements. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - GRK 2853/1 "Neuroexplicit Models of Language, Vision, and Action" - project number 471607914. The third author of this study (MS) was supported through the NWO-funded project "Searching for meaning: Identifying and interpreting alternative discourse relation signals in multimodal language comprehension" (VI.Veni.231C.021). + +# References + +[1] Chaitanya Ahuja, Dong Won Lee, Yukiko I. Nakano, and Louis-Philippe Morency. Style transfer for co-speech gesture animation: A multi-speaker conditional-mixture approach. 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Recognizing that the differentiation of similar actions relies on subtle motion details in specific body parts, we direct our approach to focus on the fine-grained motion of local skeleton components. To this end, we introduce ProtoGCN, a Graph Convolutional Network (GCN)-based model that breaks down the dynamics of entire skeleton sequences into a combination of learnable prototypes representing core motion patterns of action units. By contrasting the reconstruction of prototypes, ProtoGCN can effectively identify and enhance the discriminative representation of similar actions. Without bells and whistles, ProtoGCN achieves state-of-the-art performance on multiple benchmark datasets, including NTU RGB+D, NTU RGB+D 120, Kinetics-Skeleton, and FineGYM, which demonstrates the effectiveness of the proposed method. The code is available at https://github.com/firework8/ProtoGCN. + +# 1. Introduction + +Human action recognition, a pivotal task with various real-world applications, has recently seen growing interest in skeleton-based methods due to their efficiency and robustness. Given the intrinsic graph structure of the human skeleton, Graph Convolutional Networks (GCNs) [6, 9, 19, 30, 40] are widely used to model the relationships between joints. However, despite their effectiveness in action recognition, these methods struggle to distinguish actions with similar motion patterns. + +Specifically, existing methods face a key challenge in capturing the fine-grained details of crucial body parts, + +![](images/bc3c9fcff2b9df407ed8212dc781fb601c4ea2e04788a0be80ca9dd935dfe7d5.jpg) +Figure 1. Illustration of the skeletons and learned topologies for similar actions Writing and Typing on a Keyboard (deeper color indicates stronger relationships between corresponding joints). As shown in (a) and (c), the baseline PYSKL [11] demonstrates its ability to focus on joints associated with hands, but falls short in revealing their distinctive motion characteristics. In contrast, the integration of the Graph Prototype Reconstruction mechanism facilitates a clearer differentiation between the two actions, as evidenced by the notably distinct motion patterns observed between (b) and (d). Please zoom in for a better view. + +which are essential for distinguishing similar actions. Skeleton-based action recognition is primarily concerned with two tasks: identifying the key body parts involved and understanding their motion patterns. However, due to the lack of image-level information, current methods tend to capture coarse-grained motion patterns, effectively identifying the key parts but struggling to capture the subtle, discriminative details that are crucial for distinguishing similar actions. This limitation arises because the patterns of similar actions often overlap significantly, with distinctive details representing only a small portion of the overall information, making it difficult for the classifier to differentiate between them. + +As illustrated by the graph topologies in Fig. 1, PYSKL [11] successfully focuses on the hand-related joints when distinguishing between writing and typing on a keyboard. However, the high similarity between the graph topologies reveals its challenge in capturing the subtle distinctions in the motion characteristics of the attended joints. Specifically, in typing on a keyboard, both hands exhibit more balanced movement, whereas in writing, one hand is more actively engaged. Unfortunately, this difference is not well captured in the learned topologies shown in Fig. 1. Furthermore, intra-class variations, such as changes in viewpoint or motion amplitude, inevitably introduce noise into the acquired motion patterns. As a result, the task of capturing representative and discriminative motion features becomes more challenging, hindering the accurate classification of similar actions. + +The challenge outlined above has driven us to seek a representation that more effectively captures the intrinsic characteristics of actions with high discriminative power. To address this, we propose ProtoGCN, a novel graph prototype learning approach for skeleton-based action recognition. At the heart of ProtoGCN lies the Prototype Reconstruction Network, which explicitly enforces the representation to be formed as an associative combination of action prototypes stored in a memory module. + +In specific, these prototypes represent diverse relationship patterns between all the human joints. The network samples and assemblies the relevant prototypes via the associative response of input action features, producing the uniquely tailored representations. In addition, a motion topology enhancement module is incorporated to provide richer and more expressive features, facilitating prototype retrieval. Furthermore, we propose a class-specific contrastive learning strategy to accentuate the inter-class distinction, which compels the model to uncover distinctive prototypes to associate all action classes in the dataset. Such a prototype-based associative reconstruction process helps to enhance the discriminative capability of the resultant motion features and eliminate irrelevant distracting information. Both qualitative and quantitative analyses showcase the superior efficacy of ProtoGCN in acquiring discriminative representations and discerning similar actions. + +The main contributions are summarized as follows: + +- We introduce ProtoGCN, a novel graph prototype learning method that amplifies subtle distinctions for accurate differentiation of similar actions. +- A Prototype Reconstruction Network is proposed to adaptively assemble prototypes, yielding distinctive representations under a contrastive objective. +- Extensive experiments on four large-scale benchmarks (NTU RGB+D, NTU RGB+D 120, Kinetics-Skeleton, and FineGYM) demonstrate that ProtoGCN consistently achieves state-of-the-art performance. + +# 2. Related Work + +# 2.1. Skeleton-based Action Recognition with GCNs + +Considering the intrinsic graph-like structure of human skeletons, the majority of GCN-based approaches [6, 7, 10, 25, 30, 40, 46] explicitly model the relationships using spatial-temporal graphs. ST-GCN [40] is the pioneering work integrating graph convolutions for comprehensive spatial-temporal modeling. Most subsequent studies adopt the main framework of ST-GCN and place greater emphasis on enhancing the capacity of GCNs. 2s-AGCN [30] proposes an adaptive GCN model to learn topological correlations. Following that, CTR-GCN [6] introduces the channel-wise graph convolution to explore topology-non-shared graphs. Similarly, InfoGCN [9] models context-dependent intrinsic topology, simultaneously leveraging an information-theoretic objective to represent latent information. HD-GCN [19] proposes the hierarchically decomposed graph to model distant spatial relationships. + +Tracing the evolution of GCN-based approaches, the learning of graph topologies in GCNs plays a crucial role. Nevertheless, existing methods predominantly focus on general structural discrepancies in motion patterns, while frequently neglecting the nuanced details inherent in the motion features of specific key body parts. In contrast, we propose a novel graph prototype learning approach aimed at amplifying critical detail information and capturing nuanced motion patterns. + +# 2.2. Prototype Learning + +Traditionally, prototype learning is a classical method that establishes a metric space and optimizes the most representative anchors from training data [20]. Due to the exemplar-driven nature and simpler inductive bias, prototype learning has recently shown significant potential in a variety of tasks [26, 32, 34, 41, 42]. Interestingly, human vision itself deploys a remarkable prototyping ability, skillfully focusing on principal body joints while filtering out extraneous elements [13, 31]. In this context, we argue that movements of human body joints likewise exhibit noteworthy similarities, resulting in a collective of prototypes. Integrating prototype learning into the network facilitates the natural encapsulation of diverse dynamic characteristics, enhancing the capability to discern similar actions. + +Therefore, in this study, we employ prototype learning for diverse motion patterns through the utilization of the Prototype Reconstruction Network. Due to the considerable difficulty in directly learning highly detailed features for various actions, we represent them as combinations of learnable prototypes to highlight key information. The proposed method discovers and assembles the most representative prototypes, which can subsequently be employed to discern more fine-grained and distinct semantics. + +# 2.3. Contrastive Learning + +Recently, contrastive learning has been widely applied in self-supervised learning studies [1, 5, 33]. Representative methods such as MoCo [15] and SimCLR [4], use the InfoNCE loss to pull the positive samples close while pushing them away from the negative samples in the embedding space. In skeleton-based action recognition, previous contrastive learning-based approaches [14, 21, 27, 43] concentrate on directly obtaining accurate skeleton representations. Under the supervised setting, these approaches [3, 16, 45] mainly focus on comparing the learned features to further optimize the model. SkeletonGCL [16] explicitly explores the global context across all sequences through contrastive learning. FR-Head [45] proposes contrastive feature refinement to obtain discriminative representations of skeletons. In contrast, we adopt the contrastive training objective as a form of regularization, urging the reconstruction mechanism to identify and distinguish the distinctive prototypes. + +# 3. Method + +In this section, we first briefly introduce the preliminary concepts related to skeleton-based action recognition with GCNs, then provide a detailed description of the main components of ProtoGCN. An overview of the framework of ProtoGCN is presented in Fig. 2. + +# 3.1. Preliminaries + +Due to the intrinsic structural nature, the human skeleton is commonly represented as a graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ , where $\mathcal{V}$ and $\mathcal{E}$ denote the joint and edge sets. The input skeleton sequence is represented as a feature tensor $\mathbf{H}\in \mathbb{R}^{N\times T\times C}$ , where $N,T$ , and $C$ are the number of body joints, frames, and feature dimension, respectively. Generally, GCN models stacked graph convolutional layers ( $L$ layers in total) to extract the semantic feature of skeletons. + +For current adaptive methods, the translation function between the hidden variables in the $(l - 1)^{\mathrm{th}}$ and $(l)^{\mathrm{th}}$ layer, i.e., $\mathbf{H}^{(l - 1)}$ and $\mathbf{H}^{(l)}$ , can be formulated as + +$$ +\mathbf {H} ^ {(l)} = \sigma \left(\mathbf {A} ^ {(l)} \mathbf {H} ^ {(l - 1)} \mathbf {W} ^ {(l)}\right) \tag {1} +$$ + +where $\mathbf{A}^{(l)}\in \mathbb{R}^{N\times N\times C}$ denotes the adaptive graph topology matrix, $\mathbf{W}^{(l)}\in \mathbb{R}^{C^{(l - 1)}\times C^{(l)}}$ represents the learnable weight matrix utilized for feature projection, and $\sigma$ is the ReLU activation function. After obtaining the final hidden representation $\mathbf{H}^{(L)}$ , a classification network is employed to determine the prediction label $\hat{\mathbf{y}}\in \mathbb{R}^c$ ( $c$ denotes the total number of action classes). Finally, a cross-entropy loss $\mathcal{L}_{CE}$ is used to supervise the predicted action class + +$$ +\mathcal {L} _ {C E} = - \sum_ {i} ^ {c} \mathbf {y} _ {\mathbf {i}} \log \hat {\mathbf {y}} _ {\mathbf {i}} \tag {2} +$$ + +where $\mathbf{y}_{\mathrm{i}}$ is the one-hot ground-truth action label. Following this routine, the approach adopted by ProtoGCN will be elaborated in the subsequent subsections. + +# 3.2. Prototype Reconstruction Network + +As previously discussed, the essence of distinguishing similar actions lies in recognizing the variations in the motion patterns of involved body joints. However, effectively capturing these differences to create a discriminative representation poses a significant challenge. The nuanced nature of the corresponding joint movements often leads to these distinctions becoming obscured within the total body motion. + +To tackle this issue, the model's attention needs to be directed towards identifying the detailed joint-level motion characteristics. Therefore, we propose the Prototype Reconstruction Network (PRN) to obtain the fine-grained enhanced representations. This is achieved by decomposing the representations into a combination of the learned prototype vectors to highlight key details. + +Specifically, the network consists of two parts: a memory module and a reconstruction module. The memory module stores the learned action prototypes that represent diverse relationship patterns between human body joints. Accordingly, the reconstruction module computes the response weights of input representations through an addressing mechanism. Last, the network samples and assembles the relevant prototypes via the response, producing uniquely tailored feature representations. + +Memory Module. Given the input skeleton sequences, the learned graph representation, i.e., $\mathbf{A} \in \mathbb{R}^{N \times N \times C}$ , is first reshaped to $\mathbf{X} \in \mathbb{R}^{N^2 \times C}$ . The representation $\mathbf{X}$ can be intuitively interpreted as a feature aggregation that represents the correlations between joints. Then we implement memory as a learnable matrix $\mathbf{W}_{\mathrm{memory}} \in \mathbb{R}^{n_{pro} \times C}$ . The prototype vector $m_i$ (for $i \in \{1, \dots, n_{pro}\}$ ) in each row of the matrix represents the learned relationship patterns between joints, where $n_{pro}$ denotes the number of prototypes. + +In practice, $\mathbf{W}_{\mathrm{memory}}$ is randomly initialized and the stored patterns are adaptively updated throughout training. Instead of fixed iterative updates, we make the network automatically exploit the clusters of these relationships through backward gradient, and learn the representative prototypes from the input graph embeddings. These learned prototypes can then be composed into unique enhanced representations under the response signals to be introduced below. + +Reconstruction Module. Our goal is to leverage the relevant prototype patterns to enhance the input feature, yielding more significant and discriminative representations. We use attention as the addressing mechanism. For the input graph representation, the module produces a response signal that represents a uniquely tailored linear combination of prototypes in the memory module. + +![](images/0dafb87149f1d90ecdf84085d57632150c05491890803f2d86bbcdbb6a811fdb.jpg) +Figure 2. The overall architecture of ProtoGCN. A Prototype Reconstruction Network is proposed to transform the representation of graph topology $\mathbf{X}$ into a combination $\mathbf{Z}$ of learnable prototypes at the fine-grained joint level, thereby enhancing the distinctiveness of features. In specific, the prototypes represent diverse relationship patterns between all the human joints. Additionally, at each layer of the network, the Motion Topology Enhancement module is integrated to capture rich and expressive motion representations, establishing the foundation for prototype learning. Last, the outputs of the model are supervised by the classification loss and class-specific contrastive loss, respectively. + +Concretely, a learnable matrix $\mathbf{W}_{\mathrm{query}} \in \mathbb{R}^{n_{pro} \times C}$ serves as the key vectors projected from the input features, and then a softmax activation function is employed to compute the response signals. The addressing process could be further expressed as + +$$ +\mathbf {R} = \mathrm {s o f t m a x} (\mathbf {X} (\mathbf {W _ {q u e r y}}) ^ {\top}) \qquad (3) +$$ + +where the signals $\mathbf{R}$ are used as weights to combine the prototypes. Here the softmax provides a weighted average of the target vectors based on the similarity between the query and the input. Then we can accomplish memory activation and obtain an enhanced output representation: + +$$ +\mathbf {Z} = \mathbf {R} \cdot \mathbf {W} _ {\text {m e m o r y}} \tag {4} +$$ + +The entire network could be considered as an encoder-decoder bottleneck model, where the memory is filled with the encoder output set. It is trained in an end-to-end supervised manner, with the memory updated while training along with the rest of the network parameters. Instead of relying on a pre-determined biological decomposition of the human skeleton, we enable the model to adaptively learn the composition of human actions. Given an input representation, the network generates tailored latent responses and then reconstructs the unique enhanced representation, i.e., $\mathbf{X}$ to $\mathbf{Z}$ . An illustration of this 'sample-and-assemble' process is provided in Fig. 2. + +# 3.3. Motion Topology Enhancement + +The quality of input topology representations $\mathbf{X}$ is vital since they determine the retrieval efficiency of the learned prototypes. Therefore, we present the Motion Topology Enhancement (MTE) module to augment the capacity to capture intricate motion details, resulting in the abundant and expressive topologies. + +In practice, we start by mapping the input feature of each layer $\mathbf{H} \in \mathbb{R}^{N \times T \times C}$ to $K$ sets of queries and keys with learnable matrices $\mathbf{W}^{\mathbf{Q}}$ , $\mathbf{W}^{\mathbf{K}} \in \mathbb{R}^{C \times C'}$ . The attention mechanism effectively establishes the global perceptual connections between different body joints. Multi-head configuration and mapping functions could further facilitate the diverse feature semantic with the dimension $C' = [C / K]$ . Subsequently, we adopt average pooling to perform the aggregation of contextual temporal relations and squeeze the dimension $T$ . The projected features could be formulated as $H^{Q} = \mathbf{H}\mathbf{W}^{Q} \in \mathbb{R}^{N \times C'}$ and $H^{K} = \mathbf{H}\mathbf{W}^{K} \in \mathbb{R}^{N \times C'}$ . + +Then we model the nuanced relationships, which consist of two parts, the intra-sample correlations and the intersample distinctions. In delineating the details, intra-sample correlations exhibit skeleton-level comprehensive connections, requiring self-attention to identify their specific patterns. Moreover, for samples with inconsistent motion patterns, inter-sample distinctions could be captured by pairwise comparisons between joints. The differential realiza + +tion eliminates extraneous noise, encouraging models to focus on critical information. + +Specifically, the interdependence of intra-sample correlations is modeled by the inner product of projected features. For comparing distinctions, we adopt the transformation $\mathcal{T}_d(\cdot)$ to expand the tensor at its $d$ -th dimension and replicate the result $N$ times along that dimension. As a result, $\mathcal{T}_1(H^Q)$ and $\mathcal{T}_2(H^K)$ have the same dimensions of $\mathbb{R}^{N\times N\times C'}$ . The enhanced topology representations could be efficiently computed by + +$$ +\mathbf {A} _ {\text {i n t r a}} = \phi_ {< i n t r a >} \left(H ^ {Q} \left(H ^ {K}\right) ^ {\top}\right) \tag {5} +$$ + +$$ +\mathbf {A} _ {\text {i n t e r}} = \phi_ {< i n t e r >} \left(\mathcal {T} _ {1} \left(H ^ {Q}\right) - \mathcal {T} _ {2} \left(H ^ {K}\right)\right) \tag {6} +$$ + +where $\phi$ represents the activation function. Then these representations are integrated into each GCN layer of ProtoGCN. They rely on specific input skeletons and delineate nuanced details of joints relevant to the corresponding action, thereby serving as a crucial component in distinguishing similar actions. In contrast, the original dynamic topology $\mathbf{A}$ is represented as $\mathbf{A_0}$ , which is utilized to represent the universal interconnections among human body joints and shared across all action classes. + +Substituting the above decomposition of the graph topology into Eq. (1) gives the following translation function. + +$$ +\mathbf {H} ^ {(l)} = \sigma \left(\left(\mathbf {A} _ {\mathbf {0}} + \mathbf {A} _ {\text {i n t r a}} + \mathbf {A} _ {\text {i n t e r}}\right) \mathbf {H} ^ {(l - 1)} \mathbf {W} ^ {(l)}\right) \tag {7} +$$ + +In this way, the network incorporates nuanced motion intricacies of the acquired topology, establishing the foundation for prototype learning. + +# 3.4. Class-Specific Contrastive Learning + +Basically, in Eq. (4), $\mathbf{Z}$ could be regarded as the weighted sum of prototypes retrieved from $\mathbf{W}_{\mathrm{memory}}$ , where the weights are determined by the input-dependent probe $\mathbf{R}$ . However, the formulation itself does not ensure the representativeness of learned prototypes or the discrimination of the resultant feature $\mathbf{Z}$ , and thus it may not necessarily lead to improved performance in classifying similar actions. + +Therefore, to further accentuate the inter-class distinction of human actions, the class-specific contrastive learning strategy is incorporated. Specifically, the strategy introduces two components: a compactness constraint that encourages samples to be close to their class-specific aggregations, and a dispersion contrastive loss that promotes the distinctions among different class aggregations. + +In practice, a projection network is first utilized to embed $\mathbf{Z}$ into vectors within the contrastive feature space. We compress $\mathbf{Z} \in \mathbb{R}^{N^2 \times C}$ along the channel dimension via an average pooling layer to obtain the one-dimensional vector $\mathbf{z} \in \mathbb{R}^{N^2}$ . Subsequently, a fully connected layer is further employed to transform $\mathbf{z}$ into $\mathbf{f} \in \mathbb{R}^d$ , which is the input for the subsequent contrastive mechanism. + +For the compactness constraint, considering that cross-batch graphs could enrich the cross-sequence context, a memory bank $\mathcal{M}$ of aggregated representations is constructed. The $k$ -th element $\mathbf{m}_k \in \mathcal{M}$ denotes the class-specific aggregation that embodies unique properties of the $k$ -th action class. In practice, $\mathcal{M}$ is randomly initialized and updated using a momentum update strategy. Given an input batch of samples, $\mathbf{m}_k$ is updated by + +$$ +\mathbf {m} _ {k} = \alpha \cdot \mathbf {m} _ {k} + (1 - \alpha) \cdot \overline {{\mathbf {f} _ {k}}} \tag {8} +$$ + +where $\overline{\mathbf{f}}_k$ is the average of $\{\mathbf{f}_{k,j}\}_{j = 1}^{n_k}$ , i.e., the $n_k$ samples of class $k$ within input batch, and $\alpha$ is the momentum term. Along with the process, $\mathbf{m}_k$ gradually becomes a stable estimation of the clustering center for class $k$ . + +Then these class-specific aggregations are further optimized. Given the feature embedding $\mathbf{f}_{k,j}$ of the $k$ -th class ( $j$ is the batch index), the class-specific contrastive loss $\mathcal{L}_{CSC}$ could be formulated as + +$$ +\mathcal {L} _ {C S C} = - \log \frac {\exp \left(\mathbf {f} _ {k , j} \cdot \mathbf {m} _ {k} / \tau\right)}{\exp \left(\mathbf {f} _ {k , j} \cdot \mathbf {m} _ {k} / \tau\right) + \sum_ {l \neq k} \exp \left(\mathbf {f} _ {k , j} \cdot \mathbf {m} _ {l} / \tau\right)} \tag {9} +$$ + +where $\mathbf{m}_k$ , $\mathbf{m}_l$ denotes the positive and negative class aggregation w.r.t. $\mathbf{f}_{k,j}$ , and $\tau$ is the temperature parameter. + +Finally, the overall training objective function of ProtoGCN could be written as + +$$ +\mathcal {L} = \mathcal {L} _ {C E} + \lambda \mathcal {L} _ {C S C} \tag {10} +$$ + +where $\mathcal{L}_{CE}$ is the cross-entropy loss used to supervise the predicted action class, and $\lambda$ is the balance parameter. + +# 3.5. Discussion + +The learning mechanism of our method is to make the network adaptively discover and assemble the learnable prototypes to generate more discriminative representations. Accordingly, enhancing $\mathbf{X}$ in Sec. 3.3 and optimizing $\mathbf{Z}$ in Sec. 3.4 could further facilitate this process. ProtoGCN especially improves classification for similar classes because it focuses more on specific characteristics to reveal the subtle differences of key body parts, which are essential for distinguishing these classes. + +Notably, the expression employed in Eq. (4) constrains the model to craft representations solely using learned prototypes stored in memory module. Driven by the contrastive learning objective, these representations are required to be discriminative, thereby amplifying the inter-class distinction in the feature space. Consequently, the building blocks, or prototypes, are expected to capture the characteristics of representative action units. After obtaining such principal components, the prototype reconstruction process naturally filters out motion patterns that are less discriminative, thereby suppressing noise and irrelevant information. Instead, the key action details are highlighted and revealed. + +Table 1. Performance comparisons against state-of-the-art methods on the NTU RGB+D, NTU RGB+D 120, and Kinetics-Skeleton datasets in terms of classification accuracy (\%). + +
MethodsPublicationNTU RGB+DNTU RGB+D 120Kinetics-Skeleton
X-SubX-ViewX-SubX-SetTop-1Top-5
ST-GCN [40]AAAI 201881.588.370.773.230.752.8
AS-GCN [22]CVPR 201986.894.278.379.834.856.5
2s-AGCN [30]CVPR 201988.595.182.584.236.158.7
MS-G3D [25]CVPR 202091.596.286.988.438.060.9
DC-GCN+ADG [8]ECCV 202090.896.686.588.1--
MST-GCN [7]AAAI 202191.596.687.588.838.160.8
CTR-GCN [6]ICCV 202192.496.888.990.6--
STF [18]AAAI 202292.596.988.989.939.9-
InfoGCN [9]CVPR 202293.097.189.891.2--
PYSKL [11]ACM MM 202292.697.488.690.849.1-
SkeletonGCL [16]ICLR 202392.897.189.891.2--
FR-Head [45]CVPR 202392.896.889.590.9--
GAP [36]ICCV 202392.997.089.991.1--
HD-GCN [19]ICCV 202393.497.290.191.640.963.5
JT-GraphFormer [44]AAAI 202493.497.589.991.7--
DS-GCN [37]AAAI 202493.197.589.291.150.6-
BlockGCN [46]CVPR 202493.197.090.391.5--
ProtoGCN (2-ensemble)93.097.289.791.249.974.0
ProtoGCN (4-ensemble)93.597.590.491.951.375.1
ProtoGCN (6-ensemble)93.897.890.992.251.975.6
+ +# 4. Experiments + +# 4.1. Datasets + +NTU RGB+D (NTU-60) [28] is a large-scale human action recognition dataset containing 56,880 skeleton action sequences, which are performed by 40 distinct subjects and classified into 60 classes. Each sequence is annotated with 25 body joints and guaranteed to have at most 2 subjects. This dataset recommends two benchmarks: (1) cross-subject (X-Sub): training data comes from 20 subjects, and testing data comes from other 20 subjects. (2) cross-view (X-View): training data comes from camera views 2 and 3, and testing data comes from camera view 1. + +NTU RGB+D 120 (NTU-120) [24] is an extended version of NTU RGB+D, and contains 114,480 videos of 120 action classes. All skeleton sequences are performed by 106 subjects and captured from 32 different camera setups. Similarly, the two recommended settings are suggested: (1) cross-subject (X-Sub): training data comes from 53 subjects, and testing data comes from other 53 subjects. (2) cross-setup (X-Set): training data comes from 16 even setup IDs, and testing data comes from 16 odd setup IDs. + +Kinetics-Skeleton (Kinetics) [17] is derived from Kinetics 400 video dataset using the pose estimation toolbox. It contains 240,436 training and 19,796 evaluation skeleton + +clips across 400 classes. At each time step, two people are selected for multi-person clips based on the average joint confidence. Regarding the experiments, we adopt the available skeletons provided by PYSKL [11]. Top-1 and Top-5 accuracies are used in the evaluation protocol. + +FineGYM [29] is a recent large-scale fine-grained action recognition dataset with 29,000 videos of 99 gymnastic action classes, which requires action recognition methods to distinguish different sub-actions within the same video. We use the skeleton data provided by PYSKL [11]. The mean class Top-1 accuracy is reported in the evaluation protocol. + +# 4.2. Implementation Details + +In our experiments, ProtoGCN is trained for 150 epochs with the batch size set to 64. We employ PYSKL [11] as the baseline. The initial learning rate is set to 0.1, and we decay it using a cosine learning rate scheduler. The SGD optimizer is employed with a Nesterov momentum of 0.9 and a weight decay of $5 \times 10^{-4}$ . Following generic settings, momentum $\alpha$ is set to 0.9, and temperature $\tau$ is set to 0.125. $K$ is set to 8, and the dimension $d$ for contrastive learning is set to 256. The learnable matrices are randomly initialized for topology modeling. We follow the data pre-processing procedures outlined in PYSKL [11]. All experiments are conducted on a single RTX 3090 GPU with PyTorch. + +Table 2. Performance comparisons against state-of-the-art methods on FineGYM in terms of classification accuracy (\%). + +
MethodsModalityFineGYM
I3D [2]RGB64.4
TSN [35]RGB+Flow79.8
TSM [23]RGB+Flow81.2
LT-S3D [38]RGB88.9
SkeletonMAE [39]Skeleton91.8
PYSKL [11]Skeleton94.1
PoseConv3D [12]Skeleton+Limb94.3
ProtoGCN (Ours)Skeleton95.9
+ +![](images/26b03e161492f769e02480141f51764a275323c206d325092948d3908f5b67d1.jpg) +Figure 3. Ablation study on the influences of weight $\lambda$ and the memory capacity $n_{pro}$ under the NTU-120 X-Sub setting. + +![](images/f805fa28f1a3ec3b8d84c8b6c903a5de5ee8dbc95bb4ed56f7a0e8304d826313.jpg) + +# 4.3. Comparison with State-of-the-Art Methods + +To improve recognition accuracy, recent state-of-the-art methods [6, 9, 19, 30] utilize the multi-stream fusion framework. For a fair comparison, we adopt the widely adopted six-stream ensemble strategy proposed in InfoGCN [9]. + +We compare ProtoGCN with extensive benchmark methods on four datasets, including NTU-60, NTU-120, Kinetics, and FineGYM. According to the results reported in Tab. 1 and Tab. 2, ProtoGCN consistently achieves the best accuracy and outperforms other approaches by a significant margin in all scenarios. On the NTU-60 dataset, the proposed method surpasses the performance of BlockGCN [46] by $0.7\%$ on X-Sub and $0.8\%$ on X-View. Remarkably, ProtoGCN excels in performance on the challenging NTU-120 dataset, achieving accuracies of $90.9\%$ on X-Sub and $92.2\%$ on X-Set. As for Kinetics, ProtoGCN outperforms state-of-the-art method DS-GCN [37] by $1.3\%$ . According to Tab. 2, ProtoGCN has achieved a significant improvement in fine-grained action recognition, further confirming the efficacy of our approach. + +# 4.4. Ablation Study + +In this section, we conduct an experimental evaluation to assess the effectiveness of each component in the proposed method. The experiments are conducted under the X-Sub setting of NTU-120 with the bone modality. + +Effectiveness of Each Module in ProtoGCN. We examine the contribution of each component of ProtoGCN as shown in Tab. 3. The baseline model is re-trained using the + +Table 3. Ablation study on the contribution of each component in ProtoGCN under the NTU-120 X-Sub setting. + +
BaselineMTEPRNCSCLAcc (%)
✓---87.8
✓✓--88.1 (↑0.3)
✓✓-✓88.3 (↑0.5)
✓✓✓-88.5 (↑0.7)
✓✓✓✓89.0 (↑1.2)
+ +Table 4. Comparison of classification accuracies $(\%)$ based on (left) existing graph contrastive methods and (right) different enhanced topologies for the network. + +
MethodsAcc (%)MethodsAcc (%)
Baseline87.8ProtoGCN89.0
w/ SkeletonGCL [16]88.0w/o A_intra88.8
w/ FR-Head [45]88.2w/o A_inter88.5
Ours89.0w/o A_intra, A_inter88.4
+ +Table 5. Average performance $(\%)$ on different difficulty level classes sorted by accuracy under the NTU-120 X-Sub setting. + +
Difficulty LevelBaselineProtoGCNΔ
class 1-1064.167.1+3.0
class 11-3078.681.1+2.5
class 31-6088.689.7+1.1
class 61-12096.096.4+0.4
+ +latest officially released code and achieved a performance of $87.8\%$ . Subsequently, we observe a performance improvement of $0.3\%$ with the Motion Topology Enhancement (MTE) module. Building upon the foundation provided by MTE, $\mathcal{L}_{CSC}$ could improve performance by $0.2\%$ . Interestingly, the performance significantly improves by $0.7\%$ (from $88.3\%$ to $89.0\%$ ) with the addition of Prototype Reconstruction Network (PRN). This indicates that PRN helps to capture the discriminative semantics through discovering diverse prototypes, thereby offering greater advantages for graph convolution learning. By integrating all components, we surpass the baseline model by $1.2\%$ , demonstrating the effectiveness of the modules introduced in this work. + +Effectiveness of Prototype Reconstruction. To underscore the efficacy of the reconstruction mechanism, we conduct the analysis between ProtoGCN and existing methods that employ graph contrastive objective, including SkeletonGCL [16] and FR-Head [45]. As shown in Tab. 4, while these methods facilitate the differentiation, the improvement of ProtoGCN is remarkable (1.0% / 0.8%). This indicates that the mechanism of expressing features as the combinations of prototypes could further boost the accuracy. + +![](images/ab3439eb3396a4b42aa1a677650fad0bd1d2682763cd987e5a05ccc5846e78c3.jpg) +(c) Drop + +![](images/a501ca56d8776e3debb3000de2bb19b6161aa30b7bec688dc1c9d3bf500cdfb9.jpg) + +![](images/c688a9e3110b99a30e4cdfc00bd67a42bd00f5e29682056bb88c0b1f538d776a.jpg) +(b) Wear a Shoe + +![](images/9ea1e6d826dca828919a402fb4eb45be41c9936f7487c5abb224c77cb8bc7676.jpg) + +![](images/d3b94b5ff25353d0033d5b7f98277c1833de130764a20cc3521a124d1ef0caf7.jpg) +(d) Kick + +![](images/0158f71f5ab285cbc6d4cd30b9330e19d66737054b51e17de01aa98b92fb8ccc.jpg) +Figure 4. Visualization of the topologies learned by PYSKL [11] and ProtoGCN across four actions. Darker color indicates stronger correlation between corresponding joints. +Figure 5. Action classes with accuracy difference higher than $1\%$ between our method and PYSKL [11] on the NTU-120 dataset. + +Influences of Topology Decomposition. We assess the influences of topology decomposition in the MTE module. We closely examine the effects of these terms and present their performance in Tab. 4. The results demonstrate that intricate motion details are advantageous for recognition, and removing them will detrimentally affect performance. + +Effect of Hyperparameters. We examine the effect of weight $\lambda$ and memory capacity $n_{pro}$ related to $\mathbf{W}_{\mathrm{memory}}$ in Fig. 3. The optimal value for $\lambda$ is determined to be 0.3, corresponding to the peak accuracy. In addition, we explore the impact of varying $n_{pro}$ . Intuitively, the memory capacity is closely related to representative patterns among all the joints. Through empirical investigation, we determine the optimal balance and set $n_{pro}$ to 100 for the performance. + +Performance on Similar Classes. We conduct the analysis of the performance in discerning actions with differing degrees of similarity. To achieve this, we sorted 120 classes of NTU-120 based on accuracies, ranging from low to high according to the results obtained with the baseline. Subsequently, we categorized them into four difficulty levels and computed the average accuracy for each level. As shown in Tab. 5, ProtoGCN yields a more significant accuracy gain, + +especially in classes with higher difficulties. In Fig. 5, we further present the action classes that exhibit over $1\%$ absolute accuracy difference with the baseline on the NTU-120 dataset. It is evident that ProtoGCN offers more pronounced improvements in a significantly greater number of classes. + +Visualization. To visually demonstrate the effectiveness of ProtoGCN, in Fig. 4, we present the topologies for four different action classes. Each learned prototype is a pattern vector thus it would be difficult to understand its effect through the direct individual visualization. Instead, we visualize the combined prototypes, i.e., the reconstructed topologies, which are shown by averaging $\mathbb{R}^{N\times N\times C}$ along the $C$ dimension. By comparing the results of ProtoGCN with the baseline PYSKL, our method showcases an ability to effectively focus on the joints most relevant to the target motion. Furthermore, a closer inspection reveals that the proposed method can further accentuate the key motion details, such as color patterns or intensity fluctuations within the darkened rows. These fine-grained joint-level relationships are crucial for distinguishing similar actions. + +# 5. Conclusion + +In this paper, we propose ProtoGCN, a novel GCN-based method for skeleton-based action recognition. ProtoGCN highlights its prototype reconstruction mechanism, aimed at revealing the fine-grained motion patterns essential for distinguishing similar actions. Through the addition of enhanced topology representations, ProtoGCN is empowered by the contrastive objective to learn and identify distinctive action units. Consequently, the reconstructed motion feature becomes sufficiently discernible, enabling the discrimination of similar actions. The effectiveness of ProtoGCN is substantiated by achieving state-of-the-art performance across four widely utilized benchmark datasets. + +# Acknowledgments + +This work is supported by the National Natural Science Foundation of China (Grant No.U23B2054, 62276263, 62406304, and 62406028), and Tianjin Key Research and Development Program CAS-Cooperation Project (Grant No.24YFYSHZ00290). + +# References + +[1] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. NeurIPS, 32:1-11, 2019. 3 +[2] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. In CVPR, pages 6299-6308, 2017. 7 +[3] Haochen Chang, Jing Chen, Yilin Li, Jixiang Chen, and Xiaofeng Zhang. Wavelet-decoupling contrastive enhancement network for fine-grained skeleton-based action recognition. In ICASSP, pages 4060-4064, 2024. 3 +[4] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. 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However, according to the Information Bottleneck principle, high-level semantic clues tend to be compressed or discarded during layer-by-layer propagation. Additionally, interactions in dual-stream networks follow a fixed pattern across different layers, limiting overall performance. To address these limitations, we propose a novel architecture called Reversible Decoupling Network (RDNet), which employs a reversible encoder to secure valuable information while flexibly decoupling transmission- and reflection-relevant features during the forward pass. Furthermore, we customize a transmission-rate-aware prompt generator to dynamically calibrate features, further boosting performance. Extensive experiments demonstrate the superiority of RDNet over existing SOTA methods on five widely-adopted benchmark datasets. Our code will be made publicly available. + +# 1. Introduction + +Reflection is a common superimposition factor when photographing through a transparent medium like glass. In this case, the captured image $I$ contains a mixture of transmission $T$ (the scene behind medium) and reflection $R$ (the reflected scene) [28], which can be expressed as $I = T + R$ . The presence of reflections often hinders vital information in the transmission layer, impeding the performance of downstream tasks, such as stereo matching, optical flow, and depth estimation [3, 18, 37, 45]. Thus, single-image reflection removal is desired to disentangle the transmission and reflection components from a single input image. However, this is severely ill-posed as infinitely many possible decompositions of $\hat{T}$ and $\hat{R}$ satisfy $I = \hat{T} + \hat{R}$ . In other words, it is highly challenging to determine which combination is + +![](images/b215a90dd0d1721ca7ab957755eac00b2c0234f33c661bd1075efec3d1a619a5.jpg) +Figure 1. Quantitative comparison in PSNR between ours and previous state-of-the-art methods, where we achieve new records on all 5 datasets. Note that the scale of each axis is normalized by its second-best value. The best and second-best PSNR values are displayed for reference. + +optimal without effective priors on decomposition. + +In recent years, learning-based approaches have made tremendous strides in this field [15, 24, 43, 49, 51]. A key consensus among these methods is to exploit hierarchical semantic representations through large-scale recognition-pretrained models, which serve as priors/regularizers during training. One pioneering work [49] leverages intermediate features from a pre-trained VGGNet [34] through the concept of hypercolumns to help differentiate between the transmission and reflection layers from mixtures. Originally from neuroscience, the term "hypercolumn" refers to a functional unit in the visual cortex that processes visual stimuli at multiple receptive-field sizes [17]. This concept was first applied to segmentation and localization by interpolating and stacking features extracted from different layers of a network [12, 26, 50]. However, simply mapping stacked high-dimensional hierarchies into a group of much lower-dimensional features—as input for subsequent + +processes—inevitably leads to considerable semantic information loss. + +Previous works [14, 15] suggest that all information from the source image is valuable for the task. The two components can be optimized by exchanging information between them. For any feasible decomposition $(\hat{T},\hat{R})$ , the following relationship holds: + +$$ +\hat {T} := T - Q, \quad \hat {R} := R + Q \quad \text {s . t .} \quad I = \hat {T} + \hat {R}, \tag {1} +$$ + +where $Q$ represents the information to exchange, concretely, YTMT [14] and DSRNet [15] select $Q$ via activation functions and channel splitting, respectively. Though effective, the information preservation is not fully guaranteed in their interaction designs, i.e., the information bottleneck induced by linear layers in YTMT, and the multiplicative reductions in the gating mechanism of DSRNet. + +To avoid the above risk, reversible units [11], which are designed to preserve information, may offer a viable solution. In particular, building coupled reversible units naturally fits the situation as follows: + +$$ +f o r w a r d: \hat {T} _ {2} := \hat {T} _ {1} + \mathcal {F} (\hat {R} _ {1}), \hat {R} _ {2} := \hat {R} _ {1} + \mathcal {G} (\hat {T} _ {2}) \tag {2} +$$ + +$$ +\begin{array}{l} \underline {{r e v e r s e :}} \hat {T} _ {1} := \hat {T} _ {2} - \mathcal {F} (\hat {R} _ {1}), \hat {R} _ {1} := \hat {R} _ {2} - \mathcal {G} (\hat {T} _ {2}) \end{array} \tag {3} +$$ + +where $\mathcal{F}(\cdot)$ and $\mathcal{G}(\cdot)$ can be any network modules, and the subscripts stand for the different versions of layer estimations before and after the reversible units, respectively. For simplicity, we also use $\hat{T}$ and $\hat{R}$ to represent the corresponding deep features, which is based on the understanding that if the features are sufficiently disentangled, mapping them back to the image space becomes an easy task. + +Although the use of reversible modules can address the issue of information loss in feature interactions at the same scale, preserving multi-scale information during the feedforward process remains a challenge. Beyond the hypercolumn [49] and the progressive hierarchy fusion [15], one intuitive scheme is to stack reversible modules at each scale to facilitate forward propagation while incorporating cross-scale connections to ensure effective multi-scale interaction and fusion. A straightforward approach aligning with this idea is MAXIM [38] (without consideration of information loss), which employs a fully connected mechanism across multi-scale hierarchies. Similar ideas can also be found in HRNet [35]. However, operating on high-dimensional features is computationally expensive and memory-intensive. + +Inspired by GLOM [13] and RevCol [2], which employ part-whole hierarchies to represent an image with multiple columns, and embody both bottom-up and top-down interactions to mitigate the computational burden associated with fully connected layers, we integrate multi-scale feature processors into a single sub-network, referred to as a "column". Further, we ensemble the columns in parallel and build interactions in both bottom-up and top-down manners. It is worth + +noting that, the scaled residual connections used in GLOM for same-level interactions between adjacent columns can still cause information loss. To remedy this problem, we extend the residual connections by incorporating multi-level reversible connections [2]. + +Compared with structural designs guided by information bottleneck principle [14, 36], our proposed framework learns disentangled representations [1, 6] by categorizing and recombining the original information, instead of merely selecting and discarding elements, based upon a solid foundation for its information-preserving module (reversible unit). Additionally, it facilitates cross-scale interaction. Besides, in real-world scenarios, the reflection pattern varies along with multiple factors, such as the refractive index of the transparent surface, color granularity, and viewing angle [32]. To enhance the robustness against variations in reflection strength, we further endow the model with an adaptive transmission-rate-aware prompt generator. + +In light of these considerations, this paper proposes a network, called Reversible Decoupling Network (RDNet for short). The technical contributions of this work are twofold: + +- We revisit the preservation and cross-level interaction problems of hierarchical semantic information during the single image reflection removal/separation. To address the challenges, we introduce a multi-column reversible encoder based on the part-whole hierarchy, complemented by a tailored hierarchy decoder. This design ensures a better retention of rich semantics, effectively mitigating the ill-posed nature of the SIRR task. +- To tackle the varied reflection parameters in real-world scenarios, we introduce an adaptive transmission-rate-aware prompt generator, which learns channel scaling factors during training and leverages this knowledge as a prior when testing. It guides the decomposition network in selecting more accurate transmission-reflection ratios, significantly enhancing the model's generalization capabilities. + +Extensive experiments are conducted to verify the efficacy of our design, and reveal its superiority over other SOTA alternatives both qualitatively and quantitatively (see Fig. 1 for a brief summary). Notably, our approach also achieves robust generalization on in-the-wild cases, underscoring its practical value in real-world applications (shown by Fig. 3). + +# 2. Related Work + +# 2.1. Single Image Reflection Removal + +Physical formulation. In prevalent reflection removal frameworks [20], an image $I$ is typically decomposed into transmission $T$ and reflection $R$ components, so as to $I = T + R$ . However, in real-world scenarios, these two layers may be attenuated by factors such as diffusion and other environmental influences during superposition [41]. To account for such complexities, an augmented modeling has been + +proposed: $I = \alpha T + \beta R$ , where the coefficients $\alpha$ and $\beta$ provide adaptability to varying conditions [40, 46]. Nonetheless, the assumption of linear superimposition often breaks down, particularly in cases of overexposure [44]. To address this concern, the concept of an alpha-matting map $W$ is incorporated, leading to a reformulation of the model as $I = W \circ T + \overline{W} \circ R$ with $\overline{W} = 1 - W$ . While the adjustment improves the model's flexibility, it also increases the complexity of the already ill-posed problem. + +The above model struggles to encapsulate the diverse reflection phenomena, highlighting the challenge of developing a universal solution. Hu and Guo [15] offered a more comprehensive depiction of the superimposition process by introducing a residual term: $I = \tilde{T} + \tilde{R} + \phi(T, R)$ , where $\tilde{T}$ and $\tilde{R}$ signify the altered transmission and reflection information within $I$ after superimposition and degradation, as captured by camera sensors. The term $\phi(T, R)$ denotes the residual information in the reconstruction, arising from factors such as attenuation and overexposure. However, current methods primarily use the above modelings to synthesize training data, expecting the generalizability to real-world data. But, they lack explicit estimation of the physical parameters involved. Furthermore, distance-based loss functions such as mean absolute error (MAE) and mean squared error (MSE) fail to account for global color and intensity shifts. Explicitly estimating the degradation rate of the projected image could improve performance. A more detailed explanation is provided in supplementary. + +Deep-learning-based modeling. Zhang et al. [49] enhanced semantic awareness by leveraging hypercolumn features extracted from a pre-trained VGG-19 network [12], together with perceptual and adversarial losses. ERRNet [43] uses misaligned pairs as training data to take a step further. But it overlooks the reflection layer, potentially increasing ambiguity in transmission recovery. Li et al. [24] proposed RAGNet, a two-stage network that initially estimates the reflection component and then uses it to guide transmission prediction. Recently, the YTMT strategy proposed in [14] treats both components equally through a dual-stream interactive network that restores both layers simultaneously. Yet, noticing the problem hidden in the physical formulation, their interaction module relies on a linear assumption, which may upper-bound its performance. Other methods, such as BDN [46] and IBCLN [21] employ reflection models with scalar weights to iteratively estimate both components, ensuring that the reflection is not too faint. However, the interaction between the two components is ignored, sometimes leading to heavy ghosting effect in transmission and reflection. Dong et al. [9] developed an iterative network that estimates a probabilistic reflection confidence map at each step. DSRNet [15] introduces a mutually gated interaction mechanism within a two-stage structural design. In the first stage, the network progressively fuses extracted hierarchical + +features, while the second stage focuses on further decomposing these features. However, the issue of information loss persists due to the multiplicative reductions in the gating mechanism. Additionally, the progressive hierarchical fusion, isolated in the first stage, does not fully ensure that the hierarchical information is preserved during the subsequent decomposition processes. Zhu et al. [54] proposed a maximum reflection filter for estimating reflection locations and introduce a large dataset, but they similarly overlook interaction between the two layers. Our proposed RDNet addresses the drawbacks of existing approaches by incorporating reversible connections and a multi-column design. + +# 2.2. Reversible Network + +Reversible neural networks are designed to prevent information loss by enabling the recovery of original inputs from outputs, thereby maintaining data integrity. Deco and Brauer [4] introduced a reversible architecture that guarantees data preservation through a residual design, which generates a lower triangular Jacobian matrix with unity diagonal elements. Building upon this concept, Dinh et al. [7] developed the NICE framework, employing a non-linear bijective transformation between the data and a latent space. However, this design only allows volume-preserving mappings. Dinh et al. [8] extended this idea by proposing a reversible transformation that does not require volume preservation. While Gomez et al. [11] combined the concept of invertible networks with the ResNet architecture. This manner enables backpropagation without storing the activations in memory, except for a few non-reversible layers. + +Reversible Networks for Low-level Vision. Reversible CNNs have been effectively applied to various low-level tasks, including compression [25], enhancement [23, 42, 52] and restoration [16, 48, 53]. These solutions typically employ reversible networks as a shared encoder-decoder in a generative manner, where new textures are generated to supplement lost information during degradation. However, in the task of reflection removal, the target result (the transmission image) is mixed with the reflection rather than lost. This task requires precise decoupling of the input image components instead of generating new textures. To the best of our knowledge, our work is the first to design a reversible architecture specifically for reflection removal. + +# 3. Methodology + +In this section, we present the key components of the proposed RDNet, the overall structure of which is schematically depicted in Fig. 2. Specifically, it is composed of three primary modules: the multi-column reversible encoder (MCRE), transmission-rate-aware prompt generator (TAPG) and the hierarchy decoder (HDec). The Pretrained Hierarchy Extractor (PHE) captures semantically rich hierarchical representations from the input image and transmits them to + +![](images/55c8e4c2441f63ba968042923b7aa52e0cf99d0611ee96184e39000eea368770.jpg) +Overall Structure of RDNet + +![](images/e3652a507b984aa5b2ffacea426f6210852e5da898f121900b76903c03e60ce0.jpg) +TAPG + +![](images/81cbb4cda46a9641b74ae60c334768f2eb8a309c3962c70c416908ded7c8c2be.jpg) + +![](images/f041d3266ac9d0423555f13df615e7c3f40f37f0fd2802edad1cfa4b08af6fd6.jpg) + +![](images/5c5a5961b888fdacdb07363ab6df88eca94d100841c8625cc9e4d07058775f8f.jpg) +Hierarchy Decoder +Building Blocks +Figure 2. Overall structure of our RDNet, the input is fed in the transmission-rate-aware prompt generator, pretrained hierarchy extractor, and the column embedding. The output of the prompt generator will be transferred into the column network. After interactions between the columns, each column uses a separate decoder to obtain a pair of image layers. + +each level of the first column in MCRE. Meanwhile, TAPG learns channel-level transmission-reflection ratio priors from the data, mapping these learned fundamental parameters into prompts that guide the MCRE network. Finally, each column in MCRE employs an HDec to encode the hierarchical information, providing effective side guidance [30]. The decoded hierarchies from the last column yield the final results. + +# 3.1. Multi-scale Reversible Column Encoder + +As shown in Fig. 2, our proposed Multi-Column Reversible Encoder (MCRE), inspired by [2], employs an architecture that differs from end-to-end models [43, 49] by incorporating multiple sub-networks, each receiving column embeddings modulated by the Transmission-rate-Aware Prompt Generator (TAPG). The model comprises a Column Embedding Layer and multiple columns encoding multi-scale information. a mIn MCRE, information propagation between columns is handled through two primary mechanisms: intra-level reversible connections (denoted by blue solid lines in the figure) that facilitate information preservation between columns at the same level, and inter-level connections (illustrated as red dashed lines) paired with Bidirectional Interaction Levels, enabling interactions across adjacent levels. This approach effectively decouples multi-scale features up to Level-3. As an exception, Level-4 lacks corresponding cross-level connections, conforming to the structure of the End Level. The initial column within MCRE accepts the hierarchical information extracted by the PHE, ensuring a semantic-rich representation. The subsequent multi-column reversible design ensures the lossless propagation of hierarchical information throughout the decomposition network. + +Specifically, our column embedding layer employs a $7 \times 7$ convolution layer with a stride of 2, producing $2 \times 2$ overlapping patches $F_{-1}$ for subsequent processes. Once the embedding is obtained, it is fed to each column. For the $i$ -th column $(i \in \{1, 2, \dots, N\})$ , each level feature $F_{j}^{i}, j \in \{0, 1, 2\}$ receives information $F_{j-1}^{i}$ from the lower level of the current column and $F_{j+1}^{i-1}$ from a higher level of the previous one. The collected features are further fused with the signal $F_{j}^{i-1}$ of the current level. The operation described above for the level $j$ is expressed as: + +$$ +F _ {j} ^ {i} = \omega \left(\theta \left(F _ {j - 1} ^ {i}\right) + \delta \left(F _ {j + 1} ^ {i - 1}\right)\right) + \gamma F _ {j} ^ {i - 1}. \tag {4} +$$ + +where $\omega$ denotes the network operation, while $\theta$ and $\delta$ represent downsampling and upsampling operations, respectively. The $\gamma$ term is a simple reversible operation. In our implementation, we utilize a learnable reversible channel-wise scaling as the reversible operation $\gamma$ . This connection is information lossless, as one can retrieve $F_{j}^{i-1}$ through the reverse operation: + +$$ +F _ {j} ^ {i - 1} = \gamma^ {- 1} \left[ F _ {j} ^ {i} - \omega \left(\theta \left(F _ {j - 1} ^ {i}\right) + \delta \left(F _ {j + 1} ^ {i - 1}\right)\right) \right]. \tag {5} +$$ + +Notably, for the first level of each column, we define $F_{-1}^{i} \coloneqq F_{-1}$ . Moreover, since the last level does not receive any higher-level features, the $\delta(F_{j+1}^{i-1})$ term is hence discarded. Hierarchy Decoder. Our hierarchy decoder integrates hierarchical codes from all scales to generate the final output. We leverage several Level Decoders (LD) to interpret the higher-dimensional hierarchies with smaller resolutions into lower-dimensional ones at larger resolutions. The up-sampling operator in an LD is implemented by pixel-shuffle [33], an + +![](images/1da68abac640daa0617e3c29e5076d83ec9901b768c9b099738b01cad0a74ec7.jpg) + +![](images/a1982e494be45e4040a9f6f535b5eb4ed81b3a44faefdd36649f7c26871cef36.jpg) + +![](images/ee7768008149e60c632227108202dee70fb09bfa23fbe9a361e93117bbd4aca4.jpg) + +![](images/05334d071461a937b106dd587d42f1b4b95eb97fa4c1e21e850647a53d4c1f43.jpg) + +![](images/e2e5395ce9aa0cfcfa899e91d90bb6a7231e42c68fa83fa0bbf7942bb20abf25.jpg) +(a) Input +(e) YTMT +Figure 3. Qualitative comparisons on real-world cases. Please zoom in for more details. + +![](images/9b36fa1bfb370687562d3bb64089b2e7d5abb88bfd54aad474d14f8d416b2816.jpg) +(b) ERRNet +(f) DSRNet + +![](images/2878c7af0aabab0c00c7e5ab124135818797f066daa0836fc65e0bed3abea7f8.jpg) +(c) IBCLN +(g) Zhu et al. + +![](images/d631602e4a9d81bbbc6edf93f46deccdd03733913d5b5fd8cac5c796ff1c04aa.jpg) +(d) Dong et al. +(h) Ours + +information-consistent operator before and after the scaling. The up-sampled features are then fused with the information from the previous scale with multiplication modulation. Ultimately, the final LD produces the layer residuals $(\hat{T}_{res}$ and $\hat{R}_{res})$ through another pixel-shuffle up-sampling operation and are connected with the original input to obtain the layer decomposition $\hat{T}$ and $\hat{R}$ . + +# 3.2. Transmission-rate-Aware Prompt Generator + +Previous methods for SIRR often exhibit limited generalization capabilities due to the inherent complexity and variability of optical factors in real-world reflective scenarios, compounded by the constraint of limited training data. This limitation can be observed in the real-world test samples we collected, as shown in Fig. 3. Meanwhile, in both real-world and synthesized data, color/intensity is often compromised due to the reflection overlaying the transmission, with the transmission $T$ itself being degraded by a transmission rate $a$ . In image restoration tasks, the ground truths are typically clean images. However, linearly deviated input/result occurs due to color/illumination shifts in real-world scenarios. + +To solve the aforementioned problems, we develop a transmission-rate estimator using a simplified version of the ConvNext model [27] pre-trained on ImageNet-1k [5]. Given an input image $I \in \mathbb{R}^{3 \times H \times W}$ , our transmission-rate estimator predicts six parameters: $\alpha_{\{R,G,B\}}$ , $\beta_{\{R,G,B\}}$ such that $\| \alpha_i T + \beta_i - I \|_2$ is minimized for each $i \in \{R,G,B\}$ . When testing the input image using the six parameters generated by the prompt generator, we can obtain an average PSNR of 24.34dB across four benchmark datasets (Real20, Objects, Postcard, and Wild), surpassing the previous state + +of-the-art method by Dong et al. [9]. This result confirms the effectiveness of our estimated transmission rate. + +Once the transmission rate factor $\alpha_{\{R,G,B\}}$ , $\beta_{\{R,G,B\}}$ is estimated, a three-layer MLP is used to generate prompts for MRCE, resulting in a prompt $P \in \mathbb{R}^{C \times H \times W}$ , where $C$ represents the output dimension of the patch embedding layer, set to 64 in our work. Subsequently, the prompt is used to modulate the intermediate features from the column embedding layer $F$ into $P \circ F$ , which allows the network to dynamically adapt to the specific characteristics of each input image, thus enhancing the accuracy of reflection removal. + +# 3.3. Training Objective + +Our model undergoes two training stages. In the first stage, we train the estimator for the transmission rate. Once this is complete, we fix the classifier and proceed to train the main model along with the prompt generator. This training scheme ensures that both the transmission-rate-aware prompt generator and the main model work harmoniously toward the task, resulting in a robust solution. + +We employ content loss and perceptual loss for the task, evaluating each pair of images produced by each column using the following loss functions before aggregating them into the final outcome. + +Content Loss. The content loss ensures consistency between the output images and the ground truth training data. In the image domain, we adopt the Mean Squared Error (MSE) loss. Following previous works [14, 15], we further regularize the model by encouraging consistency between the output and + +ground truth in the gradient domain, which writes: + +$$ +\mathcal {L} _ {\text {c o n t}} := c _ {0} \| \hat {T} - T \| _ {2} ^ {2} + c _ {1} \| \hat {R} - R \| _ {2} ^ {2} + c _ {2} \| \nabla \hat {T} - \nabla T \| _ {1}, \tag {6} +$$ + +where $\| \cdot \| _1$ and $\| \cdot \| _2$ stand for the $\ell_1$ and $\ell_2$ norms, respectively. During the first stage of training, we set $c_{0} = 1,c_{1} = 0,c_{2} = 0$ . In the second stage, these values are adjusted to $c_{0} = 0.3$ , $c_{1} = 0.9$ , $c_{3} = 0.6$ . + +Perceptual Loss. To enhance the perceptual quality of images produced by our model, we minimize the $\ell_1$ discrepancy between the features of predicted elements and the ground-truth references. This comparison is made at the 'conv2_2', 'conv3_2', 'conv4_2', and 'conv5_2' layers of a pre-trained VGG-19 network on the ImageNet dataset. Denoting the features at the $i$ th layer as $\phi_i(\cdot)$ , the perceptual loss is computed as: + +$$ +\mathcal {L} _ {\text {p e r}} := \sum_ {j} \omega_ {j} \| \phi_ {j} (\hat {T}) - \phi_ {j} (T) \| _ {1}, \tag {7} +$$ + +where $\omega_{j}$ are weighting coefficients for each layer and $\omega_{j} = 0.2$ is empirically set. The total loss turns out to be: + +$$ +\mathcal {L} := \mathcal {L} _ {\text {c o n t}} + w \mathcal {L} _ {\text {p e r}}, \tag {8} +$$ + +where $w = 0.01$ is empirically set. + +# 4. Experimental Validation + +# 4.1. Implementation Details + +Our model is implemented in PyTorch [29] and optimized with Adam optimizer [19] on an RTX 3090 GPU for 20 epochs. The learning rate is initialized at $10^{-4}$ , and remains fixed throughout the training phase, with a batch size of 2. The training dataset comprises both real and synthetic images. To align with previous works, we evaluate the performance of our model under two commonly used data settings: a) The setting from [14, 43] and [24], which consists of 90 real image pairs from [49] and 7,643 synthesized pairs from the PASCAL VOC dataset [10]; and b) The setting from [15] and [9], which includes 200 additional real image pairs provided by [21]. For data synthesizing, we follow the pipeline and physical model from DSRNet [15], represented by $I = \alpha T + \beta R - T \circ R$ . Slightly, we modify this approach by sampling individual $\alpha$ and $\beta$ for R, G, and B channels. This adjustment aims to prevent the transmission rate estimator from converging to a trivial solution. The parameters of the PHE are initialized by a pretrained FocalNet [47]. + +# 4.2. Performance Evaluation + +For the comparison, we evaluate seven state-of-the-art methods: ERRNet [43], IBCLN [21], RAGNet [24], Dong et al. [9], YTMT [14], DSRNet [15], Zhu et al. [54], on four real-world datasets, including Real20 [49] and three subsets of the SIR $^2$ Datasets [39], for the Nature [9] dataset, we compare IBCLN, ERRNet, YTMT, DSRNet and Zhu et al.. + +Quantitative comparisons. The quantitative result is shown in Tab. 1. We directly employ the code and pre-trained weights publicly provided by their authors to obtain all the quantitative results. To make a fair comparison, the methods with and without additional data from the Nature dataset are compared separately. Apparently, our methods show their superiority over other competitors on all testing datasets, only falling short on SSIM compared to Zhu et al. on the Objects dataset. Our methods achieved a promising boost, especially on the Real20 dataset, which contains hard cases collected in real-world conditions, meaning our method can better fit real-world conditions. The other three datasets contain a variety of scenes, illumination conditions, and glass thickness, meaning our method performs better in most conditions. The experimental result demonstrates that our method can adapt to complicated situations and has a stronger generalization ability. For a comprehensive comparison, we present the results obtained on the Nature dataset in supplementary, which comprises 20 real-world samples. Our method achieved the best PSNR and the second-best SSIM, with a marginal decrease of only 0.004 in SSIM. These results further underscore the superiority of our approach in real-world scenarios. + +Qualitative comparisons. The qualitative comparison is shown in Fig. 4 and Fig. 3, with additional examples in the supplementary. Fig. 4 presents a challenging case with a highly reflective object. Our method effectively removes the reflection, revealing clear texture and color information, outperforming other approaches. In comparison, other methods struggle to remove the object fully. This example highlights our method's robustness in complex real-world scenarios. The second example further showcases our method's proficiency in handling reflections spread across an image. Here, the reflection is complex and covers a large area, which other methods fail to remove effectively. In contrast, our approach accurately targets and eliminates the majority of the reflection, preserving the integrity of the non-reflective elements. Figure 3 demonstrates the robustness of our method in real-world scenarios, with examples captured under natural conditions. In the first case, a dense reflection covers the car window, posing a significant challenge that most competing methods fail to overcome—only Zhu et al. achieves partial removal. In contrast, our approach effectively separates the reflections, producing clearer and more visually appealing results. Similarly, in the second example, our method successfully removes nearly all reflections, while other methods struggle to perform effectively. These cases underscore the robustness of our decoupling approach. + +User Study. We present our user study in Tab. 4. Inspired by LIME-Eval[22], we asked 20 users to choose their favorable one from each pair of outputs. All five datasets are included and 587 pairs of options are obtained. Our method achieves a win rate of $77.2\%$ to Zhu et al., and $64.4\%$ to DSRNet, + +
MethodsReal20 (20)Objects (200)Postcard (199)Wild (55)Average
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
w/o Nat.ERRNet22.890.80324.870.89622.040.87624.250.85323.530.879
IBCLN21.860.76224.870.89323.390.87524.710.88624.100.879
RAGNet22.950.79326.150.90323.670.87925.530.88024.900.886
YTMT23.260.80624.870.89622.910.88425.480.89024.050.886
DSRNet24.230.82026.280.91424.560.90825.680.89625.400.905
Ours24.430.83525.760.90525.950.92027.200.91025.950.908
w Nat.Dong et al.23.340.81224.360.89823.720.90325.730.90224.210.897
DSRNet23.910.81826.740.92024.830.91126.110.90625.750.910
Zhu et al.21.830.80126.670.93124.040.90326.490.91525.340.912
Ours25.580.84626.780.92126.330.92227.700.91526.650.917
+ +Table 1. Quantitative results of various methods on four real-world benchmark datasets. The best results are highlighted in **bold**, and the second-best results are underlined. + +![](images/b1752b4f8adc12de66e9784382277006d7232c12c2f7e464dfdc138adc9e9789.jpg) +(a) Input +(c) IBCLN +(d) RAGNet +(e) Dong et al. + +![](images/4fa17b6c0d967377897c3d2704e972062468087e52fa90f574cde84deda25550.jpg) +(b) ERRNet +(f) YTMT +(g) DSRNet +(h) Zhu et al. +(i) Ours +(j) GT +Figure 4. Qualitative comparisons on samples from the Wild dataset. Please zoom in for more details. + +indicating better performance. + +# 4.3. Ablation Studies + +To better verify the effect of our prompt generator and reversible structure, we provide a series of ablation studies for the key component of our design as below. + +Discussion on transmission-rate-aware prompt generator. + +To inform the model with the transmission rate, a straightforward approach is to adjust the input image to enhance it globally using the estimated transmission rate. Specifically, for $I \coloneqq aT + bR + \phi (T,R)$ , we adjust the input $I$ to $\frac{1}{a} I \coloneqq T + \frac{b}{a} R + \frac{1}{a}\phi (T,R)$ . This operation is denoted as Adjusting Input in Tab. 2. As shown in Tab. 2, if we remove all transmission-rate-aware techniques (setting A), the average + +
SettingPromptAdjusting InputPSNRSSIM
A××25.520.909
B×✓25.990.910
C✓✓26.030.913
Ours✓×26.650.917
+ +Table 2. Ablation studies on the prompt generator. The PSNR and SSIM are calculate across Real20, Objects, Postcard and Wild. + +
SettingDual-streamRef. LossInvertibilityPSNRSSIM
D✓✓✓26.370.917
E××✓25.990.914
F×✓×24.050.884
Ours×✓✓26.650.917
+ +Table 3. Ablation studies for network configurations. The PSNR/SSIM are calculated on Real20, Objects, Postcard, and Wild. + +
CompetitorDSRNetZhu et al.
Win-rate of our method64.4%77.2%
+ +performance drops by $1.13\mathrm{dB}$ . If we adopt the straightforward method described above (setting B), the performance recovers by $0.47\mathrm{dB}$ . This confirms the importance of informing the model with the transmission rate. However, as we analyzed in Section 3.2, directly adjusting the input image is far from optimal. Due to potential inaccuracies in the estimation in some scenarios, directly adjusting the model can introduce an additional shift that is difficult to correct during second-stage training. A more subtle and flexible approach is to reweight the feature channels with our transmission-rate-aware prompt. To verify this, we both adjust the input and add a transmission-rate-aware prompt to the feature (setting C). The performance remains nearly the same as in Setting B, indicating that adjusting the input makes it challenging for the model to recover from incorrect estimations. Finally, our model with the proposed transmission-rate-aware prompt outperforms all variants, demonstrating its efficacy. + +Discussion on model design. To verify the rationality of our design of the decoupling model, we created three new variants of our model. We modify our RDNet to a DSRNet-style one, where two streams estimate transmission and reflection separately in a single column and interact with each other (Setting D). As shown in Tab. 3, even with double computation, the performance still drops by $0.28\mathrm{dB}$ . This confirms the effectiveness of the decoupling design compared to the dual-stream design. Secondly, we removed the reflection part $(c_{1}\| \hat{R} - R\|_{2}^{2})$ in the content loss function (Eq. 6), leaving only the transmission part $(c_{0}\| \hat{T} - T\|_{2}^{2} + c_{2}\| \nabla \hat{T} - \nabla T\|_{1})$ in the training process. This variant is denoted as Setting E. A performance drop of $0.66\mathrm{dB}$ can be observed. This confirms the necessity of the reflection loss function. Without + +Table 4. User study comparison with DSRNet and Zhu et al. + +
Column count246
PSNR26.2526.6526.19
SSIM0.9140.9170.910
+ +Table 5. The experiment of changing numbers of columns. + +regularization predicting the other component, the network weakens its ability to clearly identify both components in single-stream feature maps. To verify the necessity of the invertibility of the network, we replace the reversible connection with the U-Net connection [31] (Setting F). With slightly more parameters and much more memory, a massive performance drop of $2.6\mathrm{dB}$ can be discovered, indicating the importance of invertibility. + +Discussion on the number of columns. We investigate the effect of the number of columns in Tab.5. Specifically, we adjusted the number of columns with configurations of 2, 4, and 6 columns. Our findings indicate that our choice of 4 columns yields the highest performance. In contrast, configurations with 2 and 6 columns resulted in performance drops of $0.4\mathrm{dB}$ and $0.46\mathrm{dB}$ in PSNR, respectively. This suggests that an optimal balance exists, where too few or too many columns can detract from the model's performance. + +# 5. Conclusion + +In this paper, we proposed RDNet, a novel model for addressing key challenges in the task of single-image reflection removal. Specifically, RDNet tackles the limitations of insufficient utilization of multi-scale, pretrained hierarchical information and information loss during feature decoupling. The multi-column reversible structure enables the preservation of rich semantic features, which are then effectively leveraged in the multi-scale processing of each column. Furthermore, the proposed Transmission-rate-Aware Prompt Generator alleviates the inherent conflict between complex reflection parameters and limited training data. Through these innovations, RDNet demonstrates an enhanced capability for robust reflection removal. 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Existing generative models for image restoration, including diffusion and score-based models, often treat the degradation process as a stochastic transformation, which introduces inefficiency and complexity. In this work, we propose ResFlow, a novel image restoration framework that models the degradation process as a deterministic path using continuous normalizing flows. ResFlow augments the degradation process with an auxiliary process that disambiguates the uncertainty in HQ prediction to enable reversible modeling of the degradation process. ResFlow adopts entropy-preserving flow paths and learns the augmented degradation flow by matching the velocity field. ResFlow significantly improves the performance and speed of image restoration, completing the task in fewer than four sampling steps. Extensive experiments demonstrate that ResFlow achieves state-of-the-art results across various image restoration benchmarks, offering a practical and efficient solution for real-world applications. + +# 1. Introduction + +Image restoration [24, 39, 51, 77, 96, 100] refers to recovering high-quality (HQ) images from degraded, low-quality (LQ) ones by reversing the effects associated with image degradation to reconstruct the original object. Many problems in image restoration, such as dehaze [17, 27, 124], weather removal [21, 60, 76, 101, 126], denoise [53, 71, 117], and artifact removal [23, 35]. + +Image restoration is ill-posed because it erases information in the HQ images. Given an LQ image, its corresponding HQ image is not necessarily unique, as depicted in Fig. 1. Image degradation gradually removes details from + +![](images/73879ef3ad6ab4e088cbff294e48bce61d443f389f7108208f7d8780f79418c5.jpg) +Figure 1. Image restoration is an ill-posed problem. The degradation process incurs decreasing mutual information between HQ and intermediate images, and multiple HQ images can degrade to similar or the same LQ images when their variations diminish in the process. Gray regions represent the uncertainty range from an intermediate state. As the image moves from LQ to HQ, its mutual information with HQ increases, and the uncertainty scope shrinks. + +the HQ images. The corrupted image can result from multiple HQ images with different degradation processes. In fact, degradation is a Markov chain that transits from HQ to LQ images, which is subject to the data processing inequality (DPI) [11]: the mutual information between HQ and intermediate images decreases as more distortion is applied to the image. The ambiguous multi-correspondence between HQ and LQ images creates uncertainty scopes for LQ images defined as the collection of possible HQ images given the LQ images. The uncertainty scope should be disambiguated to make the degradation process reversible by + +selecting exactly one HQ from the uncertainty scope given the intermediate image. + +Generally, restoration methods navigate the uncertainty scope with prior knowledge besides the LQ images to reverse the degradation effects. The natural image distribution from diffusion and score-based generative models [31, 91, 93] serves as a strong prior for many approaches [48, 86, 104]. These methods define degradation as a conditional stochastic process that stochastically diffuses the HQ image into noise and learns a score function conditioned on the LQ image to reverse this process. The reverse process generates the HQ images under the guidance of the LQ images, where the LQ images provide structural and semantic hints. However, starting the reverse process from Gaussian noise is unnecessary and inefficient because it regenerates the structures already known in the LQ images. + +To address this inefficiency, some studies incorporate prior knowledge of the degraded image directly into the forward stochastic process to enhance the efficiency of the reverse process [38, 55, 57, 64, 65, 89, 112]. For example, DDRM [38] progressively denoises samples stochastically to achieve the desired output. IR-SDE [64] models the degradation process using mean-reverting stochastic differential equations (SDEs), while I2SB [55] constructs a Schrödinger bridge between the clean and degraded data distributions. ResShift [112] transfers residuals from degraded low-resolution images to high-resolution ones for restoration in the latent space. RDDM [57] and Resfusion [89] introduce residual terms in the forward process. However, these approaches still treat the degradation process as a progressively diffusing stochastic forward process, which seems unnecessary and introduces additional complexity and inefficiency. Given that the degraded image is already known, the degradation process could be redefined as a deterministic forward process. + +In this paper, we propose ResFlow, a novel general framework that reverses the deterministic paths between HQ and LQ images for image restoration. ResFlow models the forward process as a deterministic continuous normalizing flow [15, 54], directly simulating the path from high-quality images to low-quality ones. The image restoration process begins directly from the degraded image in the reverse process. The construction of the reverse process is non-trivial due to the existence of uncertainty scope: multiple plausible clear images may correspond to the same degraded image. We take into consideration the decrease of mutual information during degradation and augment the degradation process with an auxiliary process that couples with the uncertainty scope to disambiguate the velocity of the backward process. We also derive a flow path based on the intuition of entropy conservation in reversible processes. The deterministic flow path allows ResFlow to achieve better performance and faster generation speeds, completing + +image restoration in fewer than four sampling steps. + +Our contributions are summarized as follows: + +- We present ResFlow, a novel image restoration framework that reverses the deterministic degradation path between HQ and LQ images for image restoration, which achieves better performance and faster inference. +- ResFlow reverses image degradation by augmenting the degradation process with an auxiliary process that couples with the uncertainty scope, and adopts an entropy-preserving flow path in the reverse process. +- We conduct experiments on various image restoration tasks and datasets, and results demonstrate the effectiveness of ResFlow that sets new state-of-the-art performance for image restoration. + +# 2. Related Work + +Image restoration can be formulated as an inverse problem [9, 100] where a high quality (HQ) image is reconstructed given its degraded version (rainy [21, 101, 126], snowy [60, 76], hazy [17, 27, 124], noisy [53, 71, 117], compressed [23, 35], etc.) dubbed low quality (LQ) image. Image degradations usually erase information from HQ images; thus, the inverse problem (i.e., image restoration) is ill-posed in the sense that one LQ image may come from multiple HQ images by different degradations [9, 77, 100]. To tackle this problem, generative models are widely adopted to provide prior knowledge [24, 39, 51, 77, 100] about the distribution of HQ images. + +Early works follow generative adversarial nets (GANs) [25, 70] and train a discriminator to guide the LQ images towards the distribution of HQ images [44, 96-98]. Variational autoencoders (VAEs) [40] are another choice that optimizes the evidence lower bound (ELBO) of the restored images [52, 90, 123]. These approaches predict the HQ images in a single step and suffer from the quality-diversity dilemma [105]: the adversarial training of GANs causes unstable training and mode collapse problem [7, 26, 67, 85]. In contrast, the mean-squared error (MSE) in VAE training leads to blurry and low-quality predictions [12, 120, 122]. + +Recent methods perform multi-step or iterative prediction [20, 57, 59, 65]: splitting the degradation process into small steps and investing each step is more tractable and easier to learn. Many works build upon diffusion models [31, 91, 93] or Schrödinger bridges [55] and model degradation processes as stochastic paths that transit between HQ and LQ images [38, 56, 57, 59, 64, 65, 89, 104, 110, 112, 121]. The uncertainty introduced by random transitions slows down training and inference. Other works [30, 63, 99] approximate the degradations as a sequence of reversible deterministic steps, dubbed normalizing flows [42, 78]. Taking the limit of the number of steps and making each step infinitesimally small, one obtains an ordinary differential equation (ODE), also known as a continuous + +![](images/5a0ce376dcaf2071867c4583e6559bc9f78783b152c26dd861a3755f836f8868.jpg) +Figure 2. Framework of ResFlow. $RV$ stands for random variable. The state $z_{t}$ consists of a data component $x_{t}$ that transits between HQ and LQ images and an auxiliary component $y_{t}$ that disambiguates the velocity to ensure invertibility. The forward process is defined by interpolation, while the reverse process is learned by matching the velocity field. The lower part depicts the transition of ResFlow. Image degradation is usually non-reversible due to decreasing mutual information; thus, the velocity is uncertain for $x_{t}$ . The range reachable by possible velocity is dubbed uncertainty scope. As $x_{t}$ approaches $x_{0}$ , the uncertainty in estimating velocity decreases, and so does the typical set of $y_{t}$ . + +normalizing flow [15, 54, 75]. InDI [20] incrementally estimates the HQ images, which is equivalent to solving a "residual flow" that becomes sensitive to error in prediction near HQ, leading to sub-optimal results. These flow-based methods contradict the ill-posed and irreversible nature of the image degradation, leading to inferior performance. + +Our work defines the degradations from HQ to LQ images by deterministic paths. Acknowledging the decrease of mutual information in image degradation that results in uncertain correspondence between LQ and HQ images, we augment the degradation process with an auxiliary process that couples with the uncertainty scope and guides the restoration directions. Our augmented degradation process is fully reversible and can be modeled by a deterministic ODE dubbed degradation flow. We learn the velocity field of the degradation flow by matching it with the ground-truth flow path [54], which leads to fast training and inference and achieves better restoration. + +# 3. Method + +# 3.1. Reversing Flow for Image Restoration + +We tackle the image restoration problem by inversion: learning the degradation process that corrupts a high-quality + +(HQ) image $x_{\mathrm{HQ}}$ into a low-quality (LQ) image $x_{\mathrm{LQ}}$ , and "reversing" the learned process to restore the HQ image from the LQ image. The learned degradation process should be 1) reversible to allow inverting LQ images to HQ images and 2) tractable to enable efficient training and inference. + +A natural choice is to model the degradation process by an ordinary differential equation (ODE) on random process $\{z_t\mid 0\leq t\leq 1\}$ : + +$$ +\frac {\partial \boldsymbol {z} _ {t}}{\partial t} = \boldsymbol {v} (\boldsymbol {z} _ {t}, t); \quad 0 \leq t \leq 1, \tag {1} +$$ + +where $\pmb{v}$ is the velocity field, $z_0$ corresponds to the HQ image, and $z_{1}$ to the LQ image. Eq. (1) is also known as a continuous normalizing flow in the literature [15, 54]. + +However, Eq. (1) cannot directly apply to image degradation because it describes an reversible process. In contrast, image degradation is generally irreversible. This can be illustrated from the perspective of mutual information: a random process described by Eq. (1) preserves mutual information while image degradation does not. First, we have the following proposition. + +Proposition 1. Given random process $\mathbf{z}_t$ defined by Eq. (1), denote the mutual information as $\mathrm{MI}(\cdot, \cdot)$ , then for any ref- + +erence random variable $\pmb{r}$ and any $0\leq t_1,t_2\leq 1$ , we have + +$$ +\operatorname {M I} \left(\boldsymbol {z} _ {t _ {1}}, \boldsymbol {r}\right) = \operatorname {M I} \left(\boldsymbol {z} _ {t _ {2}}, \boldsymbol {r}\right). \tag {2} +$$ + +Proof. See the supplementary material. + +The reference random variable $r$ can be arbitrary state $z_{t} \neq z_{0}$ , indicating that simulating Eq. (1) does not lose any information: everything we know about $z_{0}$ remains in $z_{t}$ . However, this property does not hold for the ill-posed image degradation. Generally, the mutual information between the intermediate states and the HQ images decreases as more distortion is applied to the images as a consequence of the data processing inequality (DPI) [11]: as $x_{t}$ approaches $x_{\mathrm{LQ}}$ , it shares less mutual information with $x_{\mathrm{HQ}}$ , so generally less is known about HQ images. As a result, an LQ image can correspond to multiple HQ images through different degradation processes. Fig. 1 shows an example where adding haze to different HQ images blends their content and leads to similar or the same LQ images. Noise is another example that eventually converts HQ images into indistinguishable noise. + +The collection of possible HQ images given the LQ images is dubbed the uncertainty scope. The uncertainty scope should be disambiguated to make the degradation process reversible by selecting exactly one HQ from the uncertainty scope given the intermediate image. We achieve this by augmenting the degradation process with an auxiliary process $\{\pmb{y}_t\mid 0\leq t\leq 1\}$ that couples with the uncertainty scope and evolves with the degraded image. The ODE states $\{z_{t}\}$ now become + +$$ +\boldsymbol {z} _ {t} ^ {\mathsf {T}} = \left[ \boldsymbol {x} _ {t} ^ {\mathsf {T}}; \boldsymbol {y} _ {t} ^ {\mathsf {T}} \right], \boldsymbol {z} _ {0} ^ {\mathsf {T}} = \left[ \boldsymbol {x} _ {\mathrm {H Q}} ^ {\mathsf {T}}; \boldsymbol {y} _ {0} ^ {\mathsf {T}} \right], \boldsymbol {z} _ {1} ^ {\mathsf {T}} = \left[ \boldsymbol {x} _ {\mathrm {L Q}} ^ {\mathsf {T}}; \boldsymbol {y} _ {1} ^ {\mathsf {T}} \right]. \quad (3) +$$ + +Conceptually, $\mathbf{y}_t$ encodes the "information loss" caused by image degradation. According to DPI, the mutual information from the coupling between it and the HQ images increases as $\mathbf{z}_t$ approaches $\mathbf{z}_1$ to keep $\mathrm{MI}(\mathbf{z}_t, \mathbf{z}_0)$ constant. This makes the choice of $\{\mathbf{y}_t\}$ non-trivial because $\mathbf{y}_1$ should have the maximal mutual information with $\mathbf{x}_0$ , which is equivalent to knowing the ground-truth $\mathbf{x}_0$ in prior and thus infeasible. The next section details how we parameterize the augmented flow and tackle this problem. + +# 3.2. Parameterization + +Learning to invert the degradation process by the augmented flow (Eqs. (1) and (3)) requires obtaining the coupling between the auxiliary $\mathbf{y}_t$ and $\mathbf{x}_0$ that conceptually maps to the degraded mutual information. While one can manually determine such coupling, it is not necessarily optimal. Instead, inspired by recent advances in transport-based generative modeling techniques [54, 58], we learn the deterministic coupling starting from an arbitrary coupling between $\mathbf{y}_t$ and $\mathbf{x}_0$ . + +Given a pair of HQ and LQ images, the only bound of the degradation process (Eq. (1)) is that it begins with the HQ image and ends with the LQ image as formally given by Eq. (3). Usually, the ground-truth "natural" degradation paths between HQ and LQ images are infeasible to acquire, so we instead define the flow paths of $z_{t}$ as geodesics in the Euclidean space: + +$$ +\boldsymbol {z} _ {t} = \alpha_ {t} \boldsymbol {z} _ {0} + \sigma_ {t} \boldsymbol {z} _ {1}, \quad \alpha_ {t}, \sigma_ {t} \geq 0, \tag {4} +$$ + +such that $\alpha_0 = \sigma_1 = 1$ ， $\alpha_{1} = \sigma_{0} = 0$ (5) + +We name $\{\alpha_{t},\sigma_{t}\}$ as the degradation schedule defining the flow paths' dynamics. Given the degradation schedules, the augmented degradation process Eqs. (1) and (3) can be parameterized by a neural network $\pmb{v}_{\theta}$ that estimates the velocity field $\pmb{v}$ : + +$$ +\frac {\partial \left[ \boldsymbol {x} _ {t} ^ {\top} ; \boldsymbol {y} _ {t} ^ {\top} \right] ^ {\top}}{\partial t} = \boldsymbol {v} _ {\theta} \left(\boldsymbol {x} _ {t}, \boldsymbol {y} _ {t}, t\right). \tag {6} +$$ + +The auxiliary $\mathbf{y}_t$ is chosen to be Gaussian at $t = 1$ as it maximizes entropy and zero at $t = 0$ where the restoration ends. During training, $\{\mathbf{y}_t\}$ are independently coupled with both $\mathbf{x_0}$ and $\mathbf{x}_1$ . However, the trained velocity network $\mathbf{v}_{\theta}$ induces a deterministic coupling between $\mathbf{x}_0$ , $\mathbf{x}_1$ and $\mathbf{y}_t$ as defined by Eq. (6). This coupling disambiguates the velocity when multiple possible HQ images exist given an $\mathbf{x}_t$ as in Figs. 1 and 2. In such cases, the velocity network $\mathbf{v}_{\theta}$ uniquely maps $\mathbf{y}_t$ to one of the possible velocities. + +We also note that the image $\boldsymbol{x}_t$ and auxiliary $\boldsymbol{y}_t$ in $\boldsymbol{z}_t$ do not necessarily have to use the same degradation schedule. Denoting the respective degradation schedules of $\boldsymbol{x}_t$ and $\boldsymbol{y}_t$ as $\{\alpha_t^x, \sigma_t^x\}$ and $\{\alpha_t^y, \sigma_t^y\}$ , we propose the following entropy-preserving degradation schedule: + +$$ +\alpha_ {t} ^ {\boldsymbol {x}} = 1 - \sigma_ {t} ^ {\boldsymbol {x}}, \quad \sigma_ {t} ^ {\boldsymbol {x}} = t \tag {7} +$$ + +$$ +\alpha_ {t} ^ {\boldsymbol {y}} = 1 - \sigma_ {t} ^ {\boldsymbol {y}}, \quad \sigma_ {t} ^ {\boldsymbol {y}} = \beta \cdot (1 - t + \beta) ^ {- 1}. \tag {8} +$$ + +Here, $\beta = 10$ is a hyperparameter. This schedule moves $\pmb{x}_t$ in straight lines (geodesics in Euclidean space). It keeps the entropy of $z_{t}$ constant throughout the flow paths based on the intuition that the entropy remains the same for the reversible process (see the supplementary material for the derivation). + +An alternative parameterization is to estimate the expectation $\mathbb{E}\left[\boldsymbol{z}_0\mid \boldsymbol{z}_t\right]$ with a neural network [20]. However, this approach is equivalent to a time-weighted version of Eq. (6) that leads to high discretization errors near $t = 0$ when solved numerically. + +Table 1. Synthetic datasets. Desnowing, Deraining, and Dehazing results on Snow100K [60], Outdoor-Rain [49], and Dense-Haze [4]. + +
MethodDesnowingMethodDerainingMethodDehazing
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑
SPANet[95]23.700.7930.104CycleGAN[125]17.620.656-DehazeNet[13]13.840.43
JSTASR[16]25.320.8070.059pix2pix[34]19.090.710-AOD-Net[47]13.140.41
RESCAN[50]26.080.8100.054HRGAN[49]21.560.850.154SGID[8]12.490.51
DesnowNet[60]27.170.8980.070PCNet[36]26.190.9010.132MSBDN[22]15.370.49
MPRNet[114]29.760.8940.049MPRNet[114]28.030.9190.089FFA-Net[79]14.390.45
NAFNet[14]30.060.9010.051NAFNet[14]29.590.9020.085AECR-Net[103]15.800.47
Restormer[115]30.520.9090.047Restormer[115]29.970.9210.074DeHamer[27]16.620.56
SnowDiff64[76]30.430.9140.035RainHazeDiff64[76]28.380.9320.067PMNet[108]16.790.51
SnowrDiff128[76]30.280.9000.038RainHazeDiff128[76]26.840.9150.071FocalNet[19]17.070.63
DTPM-4[109]30.920.9170.034DTPM-4[109]30.990.9340.0635MB-Taylor[80]16.440.56
ResFlow(Ours)31.860.9170.030ResFlow(Ours)32.820.9360.0514ResFlow(Ours)17.120.59
+ +# 3.3. Optimization and Inference + +The parameterized augmented degradation ODE Eq. (6) is learned by matching the velocity field [54, 58]: + +$$ +\min _ {\theta} \mathbb {E} _ {\boldsymbol {x} _ {0}, \boldsymbol {x} _ {1}, \boldsymbol {y} _ {0}, \boldsymbol {y} _ {1}} \left[ \int_ {0} ^ {1} \lambda (t) \| \boldsymbol {v} _ {\theta} (\boldsymbol {x} _ {t}, \boldsymbol {y} _ {t}, t) - \dot {\boldsymbol {z}} _ {t} \| ^ {2} d t \right], \tag {9} +$$ + +$$ +\text {w h e r e} \quad \dot {\boldsymbol {z}} _ {t} = \left[ \begin{array}{l} \dot {\boldsymbol {x}} _ {t} \\ \dot {\boldsymbol {y}} _ {t} \end{array} \right] = \left[ \begin{array}{l} \dot {\alpha} _ {t} ^ {\boldsymbol {x}} \boldsymbol {x} _ {0} + \dot {\sigma} _ {t} ^ {\boldsymbol {x}} \boldsymbol {x} _ {1} \\ \dot {\alpha} _ {t} ^ {\boldsymbol {y}} \boldsymbol {y} _ {0} + \dot {\sigma} _ {t} ^ {\boldsymbol {y}} \boldsymbol {y} _ {1} \end{array} \right]. \tag {10} +$$ + +Here, $\lambda(t)$ is a time-dependent loss weighting function, $\|\cdot\|$ is the L2 norm. Optimizing Eq. (10) is efficient as it does not require simulating Eq. (6) as in traditional simulation-based methods [15, 30, 63]. Moreover, Eq. (10) provides additional benefit that any convex transport cost induced by the coupling between $z_0$ and $z_1$ is guaranteed to be non-increasing [58] combined with Eq. (8). + +We also propose a loss weighting scheme for image degradation that emphasizes time $t$ close to 1, which empirically improves the quality of estimated HQ images: + +$$ +\lambda (t) = \left(\cos \left(\frac {\pi}{2} (t - 2)\right) + 1\right) ^ {\gamma}, \tag {11} +$$ + +where $\gamma = 1.75$ . The rationale is that when $x_{t}$ is close to the LQ image $x_{1}$ , its mutual information with the HQ image $x_{0}$ decreases, making the velocity prediction more difficult near $t = 1$ . Thus, we increase the loss weighting as $t$ increases to balance the gradients towards those from the harder tasks. + +After training by Eq. (10), we restore the LQ image $\boldsymbol{x}_1$ by first sampling $\boldsymbol{y}_1 \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{I})$ , then numerically solving Eq. (6) from $t = 1$ to $t = 0$ and obtain $\hat{\boldsymbol{x}}_0$ as the predicted HQ image. The intermediate $\hat{\boldsymbol{y}}_t$ is discarded and replaced with the ground-truth $\boldsymbol{y}_t$ given by Eq. (5). Conceptually, $\boldsymbol{y}_t$ is asymptotically mapped to the corrupted information during inference. + +# 4. Experiments + +# 4.1. Settings + +To evaluate ResFlow's performance, we conducted experiments on five major image restoration tasks, including desnowing, draining, dehazing, denoising, and JPEG compression artifact removal, using synthetic and real-world datasets. For image desnowing, we conducted experiments on the Snow100K [60] dataset and the RealSnow [126] dataset. We used the Outdoor-Rain [49] dataset and the LHP [28] dataset to evaluate deraining performance. The Dense-Haze [4] and NH-HAZE [5] datasets were employed to assess image dehazing. We utilized the SIDD [1] dataset for real-world denoising. The DPDD [2] dataset was used to test single-image defocus deblurring. The LVE1 [87] and BSD500 [69] datasets were used to verify the removal of JPEG artifacts through entropy validation. We computed several distortion and perception-based metrics, including PSNR, SSIM [102], MAE, and LPIPS [120]. + +We adopted the same U-Net architecture [83] as DDPM [31] to predict the velocity in Eq. (1) for all tasks. Timestep $t$ is embedded and injected into U-Net blocks via adaptive layer normalization [106]. The model was trained using the Adam optimizer [41] on 256-resolution image crops and tested on full-resolution images. The learning rate and other hyperparameters are detailed in Appendix C. We employed a uniform time schedule and performed only four sampling steps for all datasets. + +# 4.2. Main Results + +Desnoing Results. We report our method's quantitative performance on synthetic and real-world datasets in Tabs. 1 and 2. Overall, our method outperforms state-of-the-art algorithms across all datasets. Specifically, on the synthetic Snow100K-L [60] dataset, our method surpasses DTPM [109] by $0.86\mathrm{dB}$ in PSNR. Additionally, our ap + +![](images/458b1ef9da492e63cbfff14429e28e64b247809701344862f323e0a77f65e431.jpg) +Figure 3. Dehazing, Deraining, and Desnowing results. The part of the image is methodized to observe the local details clearly. From left to right: input blurry images, reference images, and the predicted images obtained by Restormer [115], NAFNet [14], and our ResFlow, respectively. Note that both Restormer and NAFNet retain some artifacts in the output images. + +Table 2. Real-world datasets. Dehazing results on NH-HAZE [5], Denoising results on SIDD [1], Deraining results on LHP [28], and Desnowing results on RealSnow [126] + +
MethodDenoisingMethodDehazingMethodDerainingMethodDesnowing
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
DAGL[72]38.940.953DehazeNet[13]16.620.52SPANet[95]31.190.934MIRNetv2[116]31.390.916
DeamNet[81]39.470.957AOD-Net[47]15.400.57PReNet[82]32.130.917ART[118]31.050.913
MIRNet[113]39.720.959AECR-Net[103]19.880.72RCDNet[32]32.340.915Restormer[115]31.380.923
DANet[111]39.470.957DeHamer[27]20.660.68MPRNet[114]33.340.930NAFNet[14]31.440.919
Restomer[115]40.020.960PMNet[108]20.420.73SCD-Former[28]34.330.946WGWS-Net[126]31.370.919
Xformer[119]39.980.960FocalNet[19]20.430.79IDT[35]33.020.931TransWeather[94]31.130.922
ResFlow(Ours)42.260.962ResFlow(Ours)21.440.79ResFlow(Ours)34.540.939ResFlow(Ours)31.630.919
+ +![](images/e7a38f6879ba7a8e9aae23d984a6f4717c549d2131fc1fa407ce1cc43288e4c9.jpg) +Figure 4. Single-image defocus deblurring results on the DPDD [2] dataset. The part of the image is methodized to observe the local details clearly. From left-top to right-bottom: input blurry images, reference images, and the predicted images obtained by Restormer [115], NAFNet [14], and our ResFlow, respectively. See the supplementary material for extra visualizations. + +![](images/bfebb01c2da207b9993cadab5f4637ff105d9e2f3de58d5fa2f2815d2a184b30.jpg) + +![](images/c7a9b54f68d05eccd05465ff8e9100bb907967b92f90ef658292d10abaab6caa.jpg) + +![](images/c1af25275fc00f44b6f68a1b9f0139ecf3530f584b7337ba08334a17327ce6b4.jpg) + +![](images/cb61df130245c91d4fa2430dd88f50bc0bf7975840d09c74d23fffdf218dc00e.jpg) + +![](images/60abd4a84e7135bd859621b5987fb9a63704cea2f609c111505f2de281721253.jpg) + +Table 3. Single-image Defocus Deblurring comparisons on the DPDD [2] datasets. + +
MethodIndoor ScenesOutdoor ScenesCombined
PSNR↑SSIM↑MAE↓LPIPS↓PSNR↑SSIM↑MAE↓LPIPS↓PSNR↑SSIM↑MAE↓LPIPS↓
DPDNet[2]26.540.8160.0310.23922.250.6820.0560.31324.340.7470.0440.277
KPAC[92]27.970.8520.0260.18222.620.7010.0530.26925.220.7740.0400.227
DeepRFT[68]--25.710.8010.0390.218
IFAN[46]28.110.8610.0260.17922.760.720.0520.25425.370.7890.0390.217
DRBNet[84]--25.730.791-0.183
Restormer[115]28.870.8820.0250.14523.240.7430.0500.20925.980.8110.0380.178
EBDB[37]--23.450.6830.0490.336
DMENet[45]--23.410.7140.0510.349
JNB[88]--23.840.7150.0480.315
FocalNet[19]29.100.8760.0240.17323.410.7430.0490.24626.180.8080.0370.210
DTPM-4[109]--25.980.8230.0380.153
ResFlow(Ours)29.810.9070.0220.09624.250.7820.0460.16626.960.8420.0340.131
+ +proach performs well in more challenging real-world scenarios, achieving the best performance across most metrics. On the RealSnow [126] dataset, our method exceeds NAFNet [14] by 0.21dB in PSNR. Visual examples of several methods are provided in Fig. 3, where our method demonstrates superior removal of snowflakes and enhanced detail quality compared to other approaches. Crucially, our method successfully removes all the snowflakes dispersed in the whole image, while the compared methods leave out some snowflakes in their predicted images. We attribute this to our method's ability to perform multi-step restoration: single-step prediction can be imprecise when the degradation is strong, while our multi-step method can gradually remove the degradation, each step generating better results than in the previous steps. + +Deraining Results. The numerical results for the synthetic Outdoor-Rain [49] dataset and the real-world LHP [28] dataset are presented in Tables 1 and 2. Our model exhibits strong deraining capabilities, achieving better or comparable results across all metrics. Our method demonstrates a significant 1.83dB improvement in PSNR over NAFNet [14] on the Outdoor-Rain dataset. Moreover, our method outperforms SCD-Former [28] on the more challenging real-world dataset by 0.20dB in PSNR. Visual results in Fig. 3 show that our method produces high-quality images resembling ground-truth images with no artifacts. In particular, our restored images faithfully retain more details, such as the bricks of the walls, than the compared methods, while the compared methods tend to produce smoothed appearances. When the correspondence between HQ and LQ images is ambiguous, one-step estimation converges to the mean of the HQ images conditioned on the LQ images. In contrast, our method introduces the auxiliary variable to disambiguate the HQ images and is able to preserve the sharp + +details. + +Dehazing Results. As shown in Table 1, our method surpasses FocalNet [19] by $0.05\mathrm{dB}$ in PSNR on the synthetic Dense-Haze [4] dataset. On the more challenging real-world NH-HAZE [5] dataset (Table 2), our approach achieves a notable $1.01\mathrm{dB}$ improvement in PSNR over FocalNet [19], highlighting our method's superior performance in real-world scenarios. Visual results in Fig. 3 illustrate that our method effectively removes haze while preserving original details. Similar to the hazy example in Fig. 4, our model recovers more details than other methods, such as the tree's textures. This again demonstrates the promising performance of reversible flows. + +Real Denoising Results. As shown in Tab. 2, our method achieves the best PSNR/SSIM results on the real-world SIDD citeadelhamed2018high denoising dataset. In particular, our method improves PSNR by 2.24dB over Restormer [115], demonstrating its superior performance in real denoising scenarios compared to other state-of-the-art methods. + +Defocus Deblurring Results. Tab. 3 presents the quantitative comparison on the DPDD [2] dataset. Our method achieves state-of-the-art results across all metrics compared to existing algorithms. Specifically, our method surpasses FocalNet [19] by 0.78dB in the overall category and significantly outperforms DTPM [109] by 0.98dB. Moreover, in both indoor and outdoor scenes, our method exceeds the second-best results by 0.71dB and 0.84dB, respectively. These results demonstrate the superior performance of our method in all scenarios. Fig. 4 provides visual comparisons. + +# 4.3. Ablation Study + +In this section, we perform an ablation study on the components of our methods, including experiments and analyses + +![](images/143ad01039bb4b1ada1ac817abe468695950b3ea3489a960561987c3552c82d0.jpg) +Figure 5. Reserve process performance curves, averaged on 32 samples from the desnowing dataset. The right shows the intermediate results of two example images. + +![](images/963cad6b87d94264cc00118c9b292979f57f3bead7981a5bdf9ad531919407b5.jpg) + +Table 4. Color JPEG compression artifact (QF=10) removal on BSD500 [69] and LIVE1 [87] datasets. + +
MethodBSD500 [69]LIVE1[87]
PSNRSSIMPSNRSSIM
QGAC[23]27.740.80227.620.804
FBCNN[18]27.850.79927.770.803
IPT[76]27.570.79227.370.799
SwinIR[107]27.620.78927.450.796
DAGN[66]28.070.79927.950.807
ResFlow(Ours)28.210.83527.950.830
+ +about the reverse restoration process, which is the center of image restoration, and the formulation and effects of the auxiliary variable we introduce to enable flow-based degradation modeling. + +Reverse Restoration Process. ResFlow restores images by reversing the degradation process from HQ to LQ images. Specifically, ResFlow progressively removes degradation and noise over several timesteps. We provide specific restoration examples in Fig. 5, where ResFlow tends to remove degradation along the shortest transport path. Additionally, Fig. 5 shows the performance curve for ResFlow in image desnowing. The results show that deblurring performance improves gradually with the number of steps, converging in the final few steps. + +Reverse Auxiliary Variable. The auxiliary variable $y_{t}$ is chosen as a Gaussian distribution at $t = 1$ and zero at $t = 0$ at the end of the restoration. We learn the coupling between the auxiliary variable and the uncertainty scope using transport-based generative modeling techniques. By preserving entropy for the reversible process, we provide a schedule for sampling the auxiliary variable at different time steps. Ablation studies on the sampling distribution, schedule, and coupling scheme are presented in Tab. 5. The results show that a Gaussian distribution, which maximizes entropy, helps the model learn the coupling between the auxiliary variable and the uncertainty scope. Additionally, + +Table 5. Ablation Study. The average performance on four real-world and synthetic datasets are reported. + +
MethodAverage
Degradation ScheduleAuxiliary VariablePSNRSSIM
Entropy-preservingGaussian25.510.804
ConstantGaussian23.810.786
Entropy-preservingConstant23.770.780
Injection of Auxiliary VariablePSNRSSIM
Adapter25.510.804
Add24.040.794
Channel-wise concatenation24.940.798
+ +entropy-preserving sampling schedules improve model performance compared to fixed distributions. Finally, we validate different augmentation forms for coupling the auxiliary variable with input, with the generalized augmentation form output by the Adaptor showing the best results. + +# 5. Conclusion + +In this paper, we introduced ResFlow, a new framework for image restoration that models the degradation process as a deterministic and invertible flow. By departing from the common practice of stochastic degradation in generative models, ResFlow eliminates unnecessary complexity and allows for a more direct inversion process. By augmenting the degradation process with an auxiliary mechanism, ResFlow disambiguates the uncertainty scope inherent to ill-posed restoration tasks, allowing for fast and efficient inversion of the degradation process. Through extensive experiments, we demonstrated that ResFlow outperforms existing approaches and sets new state-of-the-art, achieving superior restoration quality across several tasks with a few sampling steps. The experimental results across various datasets validate the effectiveness of ResFlow, making it a promising approach for practical image restoration tasks, from weather removal to denoising and beyond. Future work will explore extending ResFlow to more complex degradation models and applying it to video restoration tasks. + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1692-1700, 2018. 5, 6, 3, 4 +[2] Abdullah Abuolaim and Michael S Brown. Defocus deblurring using dual-pixel data. 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Prevailing AVS methods typically adopt an audio-centric Transformer architecture, where object queries are derived from audio features. However, audio-centric Transformers suffer from two limitations: perception ambiguity caused by the mixed nature of audio, and weakened dense prediction ability due to visual detail loss. To address these limitations, we propose a new Vision-Centric Transformer (VCT) framework that leverages vision-derived queries to iteratively fetch corresponding audio and visual information, enabling queries to better distinguish between different sounding objects from mixed audio and accurately delineate their contours. Additionally, we also introduce a Prototype Prompted Query Generation (PPQG) module within our VCT framework to generate vision-derived queries that are both semantically aware and visually rich through audio prototype prompting and pixel context grouping, facilitating audio-visual information aggregation. Extensive experiments demonstrate that our VCT framework achieves new state-of-the-art performances on three subsets of the AVSBench dataset. + +# 1. Introduction + +Audio-Visual Segmentation (AVS) [43, 44] is designed to identify and generate pixel-level segmentation masks of sound-emitting objects within visual frames by utilizing audio signals from the video. This task requires models to determine regions associated with the sound source and to delineate the shape and boundaries of the sound-producing objects precisely. Compared to Sound Source Localization + +![](images/f81d8b60872777607b82888864c0dd46ef121740403cbf6ada315eecc73cd50f.jpg) +Figure 1. Motivation of our method. (a) Previous methods typically rely on audio-centric Transformers, where queries are derived from mixed sources of audio features, causing ambiguity in the sounding object perception process. (b) We propose the Vision-Centric Transformer, where queries are derived from visual features of different regions and interact with audio features to fetch corresponding audio information, achieving more accurate sound source distinguishment and object segmentation. + +![](images/2432e87613aad5e1b9be8b380a556e57154b7651828d9ecb791c9a39d5e2c12a.jpg) + +(SSL) [13, 14, 33], AVS places greater emphasis on fine-grained audio-visual understanding and pixel-level perception accuracy. Based on these properties, the AVS task holds potential value in various application scenarios, including video understanding and editing, augmented and virtual reality, intelligent surveillance systems, etc. + +Prevailing AVS methods [9, 21, 37, 41] typically employ an audio-centric Transformer architecture [4, 35], where audio features are used as or integrated into object queries to identify the sounding objects in the video through layer-by-layer audio-visual interactions. However, audio-centric Transformers present two main limitations. First, audio information is typically a mixture of various sound sources in real-world scenarios, including both semantically distinct + +sounds from in-screen sources and background noises from off-screen sources. For example, the sample audio shown in Figure 1 contains mixed sounds from voice, guitar, and cars, with the last one not visible in the video frames. This inherent mixture in audio causes potential confusion in perception for audio-derived queries, making them difficult to distinguish due to mutual interference. Furthermore, noises from off-screen sources may introduce additional disturbance, causing audio-derived queries to yield false-positive predictions. Second, AVS is essentially a vision-centric dense prediction task, where an object query must encompass both abstract audio semantics to identify the existence of the target sounding objects and concrete visual details to delineate their contours accurately. However, audio-derived queries initially contain abstract audio semantics only. The delayed integration of visual information may lead to the loss of concrete visual details, weakening the ability to make dense predictions. + +To mitigate the aforementioned limitations of audio-centric Transformers, we centralize visual information in the query design and propose a new Vision-Centric Transformer (VCT) framework. Within the VCT framework, object queries are initially derived from different image regions with abundant visual details, each serving as a candidate for a sounding object. Through interactions with both audio and visual features across multiple Transformer decoder layers, these queries gradually become aware of their corresponding sound information and fine-grained visual features. The former aids in determining whether an object is sound-emitting, while the latter helps in capturing the object's contours, thereby enabling comprehensive perception. As shown in Figure 1(b), these vision-derived queries, which focus on semantically distinct visual regions, can independently integrate their corresponding sound information from mixed audio, effectively excluding unrelated or noisy sound sources during interaction with audio features in the Transformer decoder layers. By focusing on semantically relevant visual regions and sound information, vision-derived queries maintain superior discriminative ability, enabling them to better distinguish between different sounding objects in the scene and thereby alleviating the perceptual ambiguity caused by mixed audio. + +Furthermore, to generate vision-derived queries that are both semantically aware and visually rich, we also introduce a novel Prototype Prompted Query Generation (PPQG) module within our VCT framework, thus laying a solid foundation for effective audio-visual information aggregation. For the semantical aspect, we first define a set of prototypes for different categories of audio events. Through contrastive learning with audio features, each prototype learns the corresponding acoustic semantic information from the audio signals. The vision-derived queries are then prompted by these prototypes, making them aware of + +the potential audio events before interacting with the associated audio information. This enables more targeted fetching of relevant audio information during subsequent interactions with the audio features. For the visual aspect, since the queries are generated from visual features, they already contain a considerable amount of visual information. What we need to do is enable vision-derived queries to initially focus on different regions, thus further enhancing their discriminative ability in the subsequent Transformer decoder. To this end, we group pixel contexts into queries using an attention mechanism with a hard assignment, which encourages the perceptual focus of the queries to become more diverse. With the PPQG module, our VCT framework can better harness the advantages of the vision-centric paradigm. + +Contributions of our paper are summarized as follows: (1) We propose a new Vision-Centric Transformer (VCT) framework that leverages vision-derived queries to fetch corresponding audio information and fine-grained visual features, thus realizing a comprehensive perception of sounding objects. (2) We also introduce a novel Prototype Prompted Query Generation (PPQG) module to generate vision-derived queries that focus on different image regions with the awareness of occurring audio event categories, facilitating later information aggregation. (3) Extensive experiments on three subsets of the AVSbench dataset demonstrate that our method outperforms previous state-of-the-art methods. + +# 2. Related Works + +# 2.1. Sound Source Localization + +Sound Source Localization (SSL) [2, 3, 13, 14, 18, 31, 33] focuses on determining the location of sound-producing objects within a video by identifying visual areas that correspond to audio cues. This task aims to achieve a localized understanding of the scene at a patch level without emphasizing the exact shape of the sounding objects. Hu et al. [13] leverage audiovisual consistency as a self-supervised signal to match the category distribution differences between audio and visual inputs, effectively isolating sounding objects and filtering out silent ones. Unsupervised SSL is explored in EZ-VSL [31] where a multiple-instance contrastive learning framework and an object-guided localization scheme are proposed to improve localization accuracy. Kim et al. [18] achieve the localization of multiple sound sources without prior knowledge by iteratively identifying objects and applying object similarity-aware clustering loss. Compared to SSL, AVS methods usually require more accurate visual representations to segment the sounding objects. + +# 2.2. Audio-Visual Segmentation + +Different from sound source localization, Audio-Visual Segmentation (AVS) [43, 44] aims to localize the sound + +![](images/6e9a3f8ec6230013410f1a31386777933f1b90bdd67549d0a6c35b63646514f4.jpg) +Figure 2. Overall architecture of our proposed VCT. The audio feature and multi-scale visual features are first extracted by the encoders. Taking the largest visual feature as input, our proposed Prototype Prompted Query Generation (PPQG) module generates vision-derived queries, which are then fed into the iterative audio-visual Transformer decoder. Through consecutive audio information fetching and visual information enhancement blocks, vision-derived queries are further refined to yield the final segmentation masks and categories. + +emitting objects with a more precise segmentation mask rather than a coarse heat map. Some methods adopt the fusion-based architecture [10, 29, 43, 44] which first performs a multimodal fusion of features from the audio and visual encoders, then input the fused feature into a decoder that conducts per-pixel classification to generate the predicted mask. For example, TPAVI [43, 44] attentively aggregates the audio features with visual features from different stages of the encoder and performs an FPN-style fusion through the decoder. Other Transformer-based methods [6, 9, 15, 16, 20-24, 37, 41] follow the mask classification paradigm of Mask2Former [7] where queries are derived largely from audio information to discover sounding objects through Transformer decoder layers. For example, COMBO [41] enhances learnable queries by summing with audio features and performs bilateral fusion with visual features to construct more comprehensive queries. We refer to the framework of these methods as audio-centric Transformers, which suffer from ambiguous perception and visual detail loss. Apart from improvements in network architecture, recent works [25, 34, 38] also focus on the intrinsic analysis of the AVS task and data. In this paper, we propose a vision-centric Transformer framework to address the limitations of ambiguous perception and visual detail loss introduced by audio-centric Transformers. + +# 2.3. Query Designs for Transformers + +The three key components of the attention mechanism in Transformer [35] models are query, key, and value, where the role of the query is to search for the most important information in the input sequence for the current position. DETR [4] designs learnable object queries with im + +age features as keys and values to detect object instances. DINO [42] further introduces positional and content queries to more effectively capture both positional and categorical information for better identifying targets in complex scenes. For multimodal tasks, ReferFormer [39] and AQ-Former [15] exploit language and audio as queries respectively to distinguish the referred objects by directly aggregating visual features relevant to the multimodal cues. In this paper, we centralize visual information in the query design with a PPQG module to generate vision-derived queries that are both semantically aware and visually rich. + +# 3. Method + +The overall framework of our proposed VCT is illustrated in Figure 2. Given an input video $\mathcal{V} \in \mathbb{R}^{T \times H \times W \times 3}$ with $T$ frames and an audio clip $\mathcal{A}$ , AVS aims to produce the segmentation masks $\mathcal{Y} \in \mathbb{R}^{T \times H \times W \times K}$ of sounding objects, where $K$ is the number of audio event categories ( $K = 1$ for category-agnostic settings, e.g., S4 and MS3). We first feed the audio clip and multiple video frames into an audio encoder and an image encoder respectively to obtain the corresponding audio feature and multi-scale visual features. The largest visual feature is then fed into our PPQG module to generate vision-derived queries, which interact with audio features and visual features iteratively in the Transformer decoder for further refinement. Mask and category predictions are obtained based on refined vision-derived queries. + +# 3.1. Visual and Audio Feature Extraction + +For each input frame, we adopt a visual encoder (e.g., Swin Transformer [26]) to extract multi-scale image features $\mathbf{V} = \{\mathbf{V}_i\}_{i=2}^5$ , where $\mathbf{V}_i \in \mathbb{R}^{H_i \times W_i \times C_i^v}$ , $H_i = \frac{H}{2^i}$ , + +$W_{i} = \frac{W}{2^{i}}$ , and $C_i^v$ are the height, width, and channel numbers of visual feature from the $i$ -th stage of the visual encoder. For the audio clip associated with the input video, we follow TPAVI [43] to utilize VGGish [12] for audio feature extraction. The original audio clip $\mathcal{A}$ is first converted to a mono output $\mathcal{A}_m \in \mathbb{R}^{L \times 96 \times 64}$ with a resampling rate of $16\mathrm{kHz}$ to standardize the audio data, where $L$ varies according to the audio duration. Then, we compute the time-frequency representation of $\mathcal{A}_m$ by applying Short-Time Fourier Transform to obtain its mel-spectrogram $\mathcal{A}_s \in \mathbb{R}^{T \times 96 \times 64}$ , where $T$ is the number of frames. $\mathcal{A}_s$ is further fed into the VGGish model with the final compression operation removed to extract the audio feature $\mathbf{A} \in \mathbb{R}^{T \times S \times C^a}$ where $S$ denotes the size of the mel-spectrogram feature, $C^a$ denotes its channel number. + +![](images/535c17fa535cae80c23e4ec32ede4441ab09f9da20c31d980b046deaa24e9c4e.jpg) +Figure 3. Details of Prototype Prompted Query Generation. + +# 3.2. Prototype Prompted Query Generation + +The goal of the Prototype Prompted Query Generation (PPQG) module is to generate vision-derived queries that contain both rich visual details and audio semantics. As shown in Figure 3, the computation process of our PPQG module mainly consists of three steps. + +Visual embedding aggregation. We first perform spatial information aggregation on the high-resolution image feature $V_{2}$ from the 2-nd stage of the encoder to obtain a set of visual embeddings. In detail, $V_{2}$ is first projected into a hidden space by several convolution layers which convert its channel number from $C_2^v$ to $C^h$ : + +$$ +\boldsymbol {V} ^ {h} = \operatorname {C o n v} _ {1 \times 1} (\delta (\operatorname {C o n v} _ {3 \times 3} (\delta (\operatorname {C o n v} _ {1 \times 1} (\boldsymbol {V} _ {2}))))), \quad (1) +$$ + +where $\delta$ denotes the ReLU activation. Then, we adjust the shape of $V^{h}$ from $\mathbb{R}^{H_2\times W_2\times C^h}$ to $\mathbb{R}^{C^h\times H_2W_2}$ and apply a three-layer MLP on it to aggregate spatial information by + +regarding $H_{2}W_{2}$ as the input channel dimension for MLP: + +$$ +\boldsymbol {V} ^ {e} = \operatorname {R e s h a p e} (\operatorname {M L P} (\operatorname {R e s h a p e} (\boldsymbol {V} ^ {h}))), \tag {2} +$$ + +where the output of MLP has the shape of $\mathbb{R}^{C^h\times N}$ $V^{e}\in$ $\mathbb{R}^{N\times C^h}$ is a set of visual embeddings after another shape adjustment and $N$ is the number of visual embeddings. + +Audio prototype prompting. To enable more targeted audio information fetching of vision-derived queries in the subsequent Transformer decoder, we define a group of audio prototypes to prompt them with audio event categories present in the scene during the query generation. In detail, we randomly initialize a set of learnable parameters as the audio prototypes $\pmb{P} \in \mathbb{R}^{K \times C^h}$ , where $K$ is the number of audio event categories, to prompt visual embeddings $V^e$ with audio category priors by cross-attention: + +$$ +\bar {\boldsymbol {V}} ^ {e} = \boldsymbol {V} ^ {e} + \operatorname {S o f t m a x} \left(\frac {\left(\boldsymbol {V} ^ {e} \boldsymbol {W} _ {1} ^ {q}\right) \left(\boldsymbol {P} \boldsymbol {W} _ {1} ^ {k}\right) ^ {\mathrm {T}}}{\sqrt {C ^ {h}}}\right) \left(\boldsymbol {P} \boldsymbol {W} _ {1} ^ {v}\right). \tag {3} +$$ + +$\pmb{W}_{1}^{q}$ , $\pmb{W}_{1}^{k}$ and $\pmb{W}_{1}^{v}$ are projection weights. For clarity, we omit other operations like LN and FFN and use $\tilde{\pmb{V}}^e$ to denote the output of cross-attention. + +Since the audio prototypes are randomly initialized, we also design a prototype-audio contrastive loss $\mathcal{L}_{\mathrm{pac}}$ to ensure that the prototypes can learn semantic information of different audio event categories from the audio features. Concretely, let $A_{t} \in \mathbb{R}^{S \times C^{a}}$ denotes the audio feature associated with the current frame and we perform linear projection followed by global average pooling on $A_{t}$ to obtain $\bar{A}_{t} \in \mathbb{R}^{C^{h}}$ . An inner product between $\bar{A}_{t}$ and $P$ yields a matching prediction $M \in \mathbb{R}^{K}$ representing the likelihood of each audio category prototype present in the current audio. The matching ground truth $M^{*}$ indicating which audio event categories are actually present in the current audio can be obtained from the dataset annotation. We implement $\mathcal{L}_{\mathrm{pac}}$ as a BCE loss between $M$ and $M^{*}$ : + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {b c e}} \left(M _ {k}, M _ {k} ^ {*}\right) = - M _ {k} ^ {*} \log \left(M _ {k}\right) \tag {4} \\ - \left(1 - M _ {k} ^ {*}\right) \log \left(1 - M _ {k}\right), \\ \end{array} +$$ + +$$ +\mathcal {L} _ {\mathrm {p a c}} \left(M, M ^ {*}\right) = \frac {1}{K} \sum_ {k = 1} ^ {K} \mathcal {L} _ {\mathrm {b c e}} \left(M _ {k}, M _ {k} ^ {*}\right). \tag {5} +$$ + +The $\mathcal{L}_{\mathrm{pac}}$ pulls the audio features closer to the present audio prototypes, while pushing the audio features further away from non-existent audio prototypes. + +Pixel context grouping. Inspired by GroupViT [40], to obtain more distinguishable vision-derived queries that can focus on different image regions, we adopt Gumbel-Softmax [17, 28] to group pixel context for each visual embedding with a hard and differentiable assignment: + +$$ +\boldsymbol {R} = \operatorname {S o f t m a x} \left(\left(\bar {\boldsymbol {V}} ^ {e} \boldsymbol {W} _ {2} ^ {q}\right) \left(\boldsymbol {V} ^ {h} \boldsymbol {W} _ {2} ^ {k}\right) ^ {\mathrm {T}} + \boldsymbol {G}\right), \tag {6} +$$ + +$$ +\hat {\boldsymbol {R}} = \operatorname {O n e - h o t} (\arg \max _ {N} (\boldsymbol {R})) + \boldsymbol {R} - \operatorname {s g} (\boldsymbol {R}), \tag {7} +$$ + +where $W_{2}^{q}$ and $W_{2}^{k}$ are linear projection weights, $\pmb{G} \in \mathbb{R}^{N \times H_{2}W_{2}}$ are i.i.d random samples drawn from the Gumbel(0,1) distribution. We apply arg max on the $N$ dimension of $\pmb{R} \in \mathbb{R}^{N \times H_{2}W_{2}}$ to find the index of the visual embedding with the highest similarity to each pixel feature as the assignment target. One-hot converts the index for each pixel feature into a one-hot vector. sg is the stop gradient operator. The resulting $\hat{\pmb{R}} \in \mathbb{R}^{N \times H_{2}W_{2}}$ contains the hard assignments between visual embeddings and pixel features. We use $\hat{\pmb{R}}$ to group the pixel context in image feature $\pmb{V}^{h}$ into prototype-prompted visual embeddings $\hat{\pmb{V}}^{e}$ : + +$$ +\pmb {V} ^ {q} = \bar {\pmb {V}} ^ {e} + (\mathrm {N o r m} (\hat {\pmb {R}}) (\pmb {V} ^ {h} \pmb {W} _ {2} ^ {v})) \pmb {W} ^ {o}, \qquad (8) +$$ + +where $\pmb{W}_2^v$ and $\pmb{W}^o$ are projection weights, Norm is normalization on the $H_2 W_2$ dimension of $\hat{\pmb{R}}$ by dividing the sum of values, $V^q \in \mathbb{R}^{N \times C^h}$ denotes the vision-derived queries generated by our PPQG module. + +# 3.3. Iterative Audio-Visual Transformer Decoder + +In our designed iterative audio-visual Transformer decoder, vision-derived queries interact with the audio feature and multi-scale visual features iteratively through two kinds of Transformer blocks, each composed of a multi-head cross-attention (MHCA) layer, a multi-head self-attention (MHSA) layer, and an FFN layer. In the audio information fetching block, each vision-derived query interacts with the audio feature of the current frame through MHCA, with $A_{t}$ serving as the key and value. MHCA allows each vision-derived query to obtain the corresponding sound information for the region it represents, enabling the determination of whether an object in that region is emitting sound and its audio category. In the visual information enhancement blocks, each vision-derived query sequentially interacts with three different scales of visual features from the current frame, with $V_{5}$ , $V_{4}$ and $V_{3}$ serving as the key and value for MHCA respectively. Here, we follow Mask2Former [7] to use the segmentation mask predicted in the previous layer as the attention mask for the current layer, restricting the MHCA's attention to potential sounding image regions. Through visual information enhancement, each vision-derived query captures finer-grained visual features, allowing for more accurate mask predictions. + +We use $\mathcal{U} = \{A_t, V_5, V_4, V_3\}$ as an interaction unit where one audio information fetching block and three visual information enhancement blocks are stacked in order. We repeat $\mathcal{U}$ for $D$ times and append one audio block at the end to construct our iterative audio-visual Transformer decoder. Through the above interaction, vision-derived queries gradually become aware of their corresponding sound information and fine-grained visual features, thus better distinguish + +ing between different sounding objects and mitigating the perception ambiguity caused by mixed audio. + +# 3.4. Loss Functions + +Following Mask2Former [7], we use a classification head and a mask head to obtain category and segmentation predictions. Our loss functions mainly consist of three parts, i.e., classification loss $\mathcal{L}_{\mathrm{cls}}$ , mask loss $\mathcal{L}_{\mathrm{mask}}$ , and our proposed prototype-audio contrastive loss $\mathcal{L}_{\mathrm{pac}}$ . The classification loss is namely CE loss. Apart from BCE loss, the mask loss also contains Dice loss [30] to handle relatively small foreground areas in the images. Therefore, the overall loss function of our method is formulated as: + +$$ +\mathcal {L} = \lambda_ {\mathrm {c l s}} \mathcal {L} _ {\mathrm {c l s}} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {m a s k}} + \lambda_ {\text {p a c}} \mathcal {L} _ {\text {p a c}}, \tag {9} +$$ + +where $\lambda_{\mathrm{cls}}$ , $\lambda_{\mathrm{mask}}$ and $\lambda_{\mathrm{pac}}$ are loss coefficients. + +# 4. Experiments + +# 4.1. Dataset and Evaluation Metrics + +We conduct experiments on the AVSBench dataset [43, 44] to train and evaluate our models. The AVSBench dataset is organized into three subsets: the Single-source subset (S4), the Multi-sources subset (MS3), and the Semantic-labels subset (AVSS). Built on the previous two subsets, the AVSS subset substantially extends the dataset in both quantity and semantic labels, which brings more challenges by requiring models not only to produce segmentation masks but also to categorize each sounding object. + +Regarding evaluation metrics, we follow prior works [41, 43, 44] to adopt $\mathcal{M}_{\mathcal{I}}$ and $\mathcal{M}_{\mathcal{F}}$ for performance measurement. $\mathcal{M}_{\mathcal{I}}$ is the Jaccard index which computes the Intersection over Union (IoU) between predicted segmentation and ground truth. On the AVSS subset, $\mathcal{M}_{\mathcal{I}}$ is the mean IoU averaged over all categories. $\mathcal{M}_{\mathcal{F}}$ denotes the F-score which combines the precision and recall of the segmentation results. Its formulation is $\mathcal{M}_{\mathcal{F}} = \frac{(1 + \beta^2)\cdot\mathrm{Precision}\cdot\mathrm{Recall}}{\beta^2\cdot\mathrm{Precision} + \mathrm{Recall}}$ where $\beta^2 = 0.3$ indicating more emphasis on the recall. + +# 4.2. Implementation Details + +Our model is implemented with PyTorch. For a fair comparison with previous methods [27, 38, 41], we adopt ResNet-50 [11] and Pyramid Vision Transformer (PVTv2) [36] pretrained on ImageNet [8] and Swin Transformer (Swin-Base) [26] pretrained on ImageNet-21K [32] as visual encoders. The audio encoder is VGGish [12] pretrained on YouTube-8M [1]. Following COMBO [41], we also adopt Semantic-SAM [19] to generate colored class-agnostic Maskige as segmentation prior knowledge and fuse its feature with the original visual feature in the same way as COMBO. The values of $C^h$ and $S$ are 256 and 24. The number of vision-derived queries $N = 100$ . $D = 2$ in the + +
MethodReferenceBackboneImage SizeAVS-Semantic (AVSS)Single-Source (S4)Multi-Source (MS3)
MJMFMJMFMJMF
TPAVI [43, 44][ECCV'22]ResNet-50224×224--72.884.846.957.8
PVT-v229.835.278.787.954.064.5
AQFormer [15][IJCAI'23]ResNet-50224×224--77.086.455.766.9
PVT-v2--81.689.461.172.1
ECMVAE [29][ICCV'23]ResNet-50224×224--76.386.548.760.7
PVT-v2--81.790.157.870.8
CATR [21][ACMMM'23]ResNet-50224×224--74.886.652.865.3
PVT-v232.838.581.489.659.070.0
AVSC [23][ACMMM'23]ResNet-50224×224--77.085.249.661.5
PVT-v2--80.688.258.265.1
BAVS [24][TMM'24]ResNet-50224×22424.729.678.085.350.262.4
PVT-v232.636.482.088.658.665.5
Swin-B33.637.582.789.859.665.9
AVSBG [10][AAAI'24]ResNet-50224×224--74.185.445.056.8
PVT-v2--81.790.455.166.8
GAVS [37][AAAI'24]ViT-B224×224--80.190.263.777.4
AVSF [9][AAAI'24]ResNet-50224×22424.929.376.585.949.562.8
PVT-v236.742.082.189.958.469.3
UFE [25][CVPR'24]ResNet-50224×224--79.087.555.964.5
PVT-v2--83.290.462.070.9
CAVP [5][CVPR'24]ResNet-50224×22430.435.378.888.955.867.1
COMBO [41][CVPR'24]ResNet-50224×22433.337.381.790.154.566.6
PVT-v242.146.184.791.959.271.2
CPM [6][ECCV'24]ResNet-50224×22434.539.681.490.559.871.0
TeSO [38][ECCV'24]Swin-B384×38439.045.183.393.366.080.1
SelM [20][ACMMM'24]ResNet-50224×22431.937.276.686.254.565.6
PVT-v241.346.983.591.260.371.3
AVSBias [34][ACMMM'24]Swin-B384×38444.449.983.393.067.280.8
VCT (Ours)-ResNet-50224×22437.542.281.890.661.974.7
PVT-v2224×22444.749.584.892.162.075.0
Swin-B224×22447.952.984.792.367.579.3
Swin-B384×38451.255.586.293.467.681.4
+ +Table 1. Comparison with state-of-the-art methods on three subsets of the AVSBench dataset. Our method obtains significant performance gains on the most challenging AVSS subset. Best results in bold and $2^{\text{nd}}$ best underlined for different backbones and image sizes. + +iterative audio-visual Transformer decoder. $\lambda_{\mathrm{cls}}$ , $\lambda_{\mathrm{mask}}$ , and $\lambda_{\mathrm{pac}}$ are set to 2, 5, and 1. The AdamW optimizer is used with the learning rate of $1e^{-4}$ . We train our model with a batch size of 16 for ResNet-50 and 8 for PVT-v2 and SwinB. The training iterations are 45K, 40K, and 45K for S4, MS3, and AVSS subsets respectively. + +# 4.3. Comparison with State-of-the-art Methods + +In Table 1, we show the performance comparison between our method and previous state-of-the-art methods on the three subsets of the AVSBench dataset. Our method outperforms the previous best-performing approaches across three + +subsets with different visual backbones and image sizes, demonstrating its ability to effectively differentiate multiple sound sources, accurately delineate the corresponding object shapes, and recognize their categories. In particular, on the most challenging AVSS subset, our method achieves even better $\mathcal{M}_{\mathcal{T}}$ performance with a PVT-v2 backbone and a $224 \times 224$ image size compared to AVSBias [34] using a Swin-B backbone and a $384 \times 384$ image size. This also indicates that our new architecture, which integrates vision-derived queries and the iterative audio-visual Transformer, demonstrates a clear advantage over the previous architectures that rely on audio-derived queries to interact with vi + +sual information. Moreover, on the S4 subset where performance is relatively plateaued, our method achieves 86.2 $\mathcal{M}_{\mathcal{T}}$ , indicating that it is better at handling some of the hard cases compared to previous methods. + +# 4.4. Ablation Studies + +We conduct ablation studies on the AVSS subset with ResNet-50 as the visual backbone to verify the effectiveness of different designs in our method. + +
FrameworkQueriesMJMF
ACTAudio-Derived Queries33.237.0
VCTNaive Vision Queries35.239.3
w/ Cross-Attention35.839.8
w/ Group-Attention36.340.5
w/ Audio Prototypes37.542.2
+ +Component analysis. We include the ablation study results of generating vision-derived queries in Table 2 to show the influence of different operations in our proposed PPQG module. "ACT" denotes the baseline model with audio-derived queries where audio features largely enhance the initial learnable queries for later audio-visual interaction. In our VCT framework, "Naive Vision Queries" represents that the vision-derived queries are generated only by the first step of visual embedding aggregation in the PPQG module. It yields better performance than audioderived queries, which indicates that using visual features as the basis for locating sound-emitting objects, compared to introducing entangled audio information, enables better visual-audio correspondence during subsequent decoder interactions. "w/ Cross-Attention" denotes that we use crossattention with normal softmax to incorporate image features into naive vision-derived queries, while "w/ GroupAttention" means replacing cross-attention with group-attention equipped by Gumbel-softmax to group pixel contexts for vision-derived queries using hard assignment. The performance improvements brought by both attention mechanisms show that incorporating additional visual region information helps to obtain more distinguishable vision-derived queries. The last row demonstrates that providing audio category priors to vision-derived queries enables them to more effectively fetch the corresponding audio information in the subsequent iterative audio-visual Transformer decoder. + +Audio prototype prompting. Table 3 summarizes the ablation results of audio prototype prompting in our PPQG module. By comparing the first and second rows, it can be observed that without loss constraints, the randomly initialized audio prototypes fail to learn meaningful audio event category priors, resulting in no positive impact on perfor + +Table 2. Ablation study of generating vision-derived queries in our PPQG module on the AVSS subset. + +
MethodMJMF
w/o Audio Prototypes36.340.5
w/ Audio Prototypes, w/o loss36.340.4
w/ Audio Prototypes, w/ visual loss36.540.8
w/ Audio Prototypes, w/ PAC loss37.542.2
+ +mance. In the third row, "w/ visual loss" denotes that we compute contrastive loss between audio prototypes and positive vision-derived queries that matched with the ground truth, bringing a small performance gain. In contrast, introducing our designed PAC loss in the last row results in an obvious performance improvement, suggesting that audio prototypes, through contrastive learning with audio features, can learn more explicit and clear audio event category priors than those learned from positive vision queries. + +Table 3. Ablation study of audio prototype prompting in PPQG. + +
Audio FeatureMJMF
Visual FeatureMultiply33.937.9
Concatenation35.339.3
Addition36.340.5
Audio ProtoReplace36.640.8
VCTFull Model37.542.2
+ +Table 4. Ablation study of audio feature incorporation. + +Audio feature incorporation. We also explore different approaches to incorporate audio features into our VCT framework and present the results in Table 4. The first three rows show how we fuse audio features with visual features using multiplication, concatenation, and addition, which are then used as the key and value in the cross-attention of the Transformer decoder. The fourth row denotes that we replace the audio prototypes in PPQG with the audio feature and the PAC loss is hence removed. Our full VCT obtains the best performance compared to these approaches, indicating that pre-fetching audio features during the generation of vision-derived queries or fetching fused multimodal features in the Transformer decoder can lead to queries learning inaccurate audio-visual correspondence. Additional ablation results are included in the supplementary materials. + +# 4.5. Qualitative Analysis + +Figure 4 presents the qualitative comparison between our full model and the ACT baseline. In the left example, the input audio is the voiceover narration. Compared to the baseline, our full model is able to recognize the off-screen background audio rather than biasing its focus on the main objects in the video, demonstrating stronger robustness. In the right example, the baseline confuses between the girl and woman, while our full model correctly distinguishes between them and identifies the actual sound- + +![](images/21aef0ba49dd76400dd24f8bc8bcdc32c017aa4de9f1bb6266ffde34a34726b3.jpg) +Figure 4. Qualitative comparison between our full model and the ACT baseline. Existing sounds correspond to masks of the same colors. + +![](images/991591c4d07dba801507bc38d35bc615b79779335443cf688dfbf55019a94b13.jpg) +Figure 5. Visualization of logit maps from different types of queries. (a) Audio-derived queries. (b) Vision-derived queries. + +emitting source in the video. This demonstrates that the vision-derived queries have a stronger ability to differentiate between different regions in the image and can fetch the corresponding information from the audio. + +In addition, we also visualize the logit maps predicted by audio-derived and vision-derived queries within the Transformer decoder. For each type of 100 queries, we uniformly select one every five queries, remove those with blank logit maps, and then randomly retain 8 queries for display. As + +shown in Figure 5(a), both instruments are producing sound in this example, but most of the audio-derived queries focus on the person on the right and the cello, indicating that these queries are biased towards certain sound-emitting objects due to the influence of entangled audio. In contrast, our vision-derived queries Figure 5(b) are able to focus on diverse visual regions in the image, demonstrating that vision-derived queries are more distinguishable, which forms the foundation for superior performance. + +# 5. Conclusion + +Given an audio clip, the goal of audio-visual segmentation (AVS) is to segment the sounding objects in the video. In this work, we proposed a new Vision-Centric Transformer (VCT) framework to overcome the limitations of audio-centric Transformers adopted by prevailing AVS methods. Concretely, our VCT framework utilizes vision-derived queries to iteratively extract both corresponding audio and fine-grained visual information, which aids in better distinguishing between different sound-emitting objects, eliminating the perception ambiguity caused by mixed audio and yielding accurate object segmentation. Additionally, we introduce a Prototype Prompted Query Generation (PPQG) module within the VCT framework, which generates vision-derived queries that contain both rich visual details and audio semantics through audio prototype prompting and pixel context grouping, facilitating later information aggregation. Extensive experiments on three subsets of the AVSBench dataset demonstrate that our method achieves new state-of-the-art performances. + +# 6. Acknowledgments + +This research is supported in part by National Key R&D Program of China (2022ZD0115502), National Natural Science Foundation of China (No. 62461160308, U23B2010), "Pioneer" and "Leading Goose" R&D Program of Zhejiang (No. 2024C01161). + +# References + +[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. 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Unlike prior studies in static settings, this paper explores backdoor attacks in LVLM instruction tuning across mismatched training and testing domains. We introduce a new evaluation dimension, backdoor domain generalization, to assess attack robustness under visual and text domain shifts. Our findings reveal two insights: (1) backdoor generalizability improves when distinctive trigger patterns are independent of specific data domains or model architectures, and (2) the competitive interaction between trigger patterns and clean semantic regions, where guiding the model to predict triggers enhances attack generalizability. Based on these insights, we propose a multimodal attribution backdoor attack (MABA) that injects domain-agnostic triggers into critical areas using attributional interpretation. Experiments with OpenFlamingo, Blip-2, and Otter show that MABA significantly boosts the attack success rate of generalization by $36.4\%$ over the unimodal attack, achieving a $97\%$ success rate at a $0.2\%$ poisoning rate. This study reveals limitations in current evaluations and highlights how enhanced backdoor generalizability poses a security threat to LVLMs, even without test data access. Our codes are available online1. + +# 1. Introduction + +Multimodal instruction tuning [27] enhances Large Visual Language Models (LVLMs), enabling them to process multimodal data and respond more effectively to user intent. However, this open fine-tuning process, accepting input from various sources, introduces security risks [15, 23]. Attackers + +![](images/abf1c815232b33f455ca723b19dfad4ae1a185f96d73253c40616d4f18d4b196.jpg) +Figure 1. Illustration of backdoor attack during LVLM instruction-tuning. Despite successful poisoning, domain shift between attacker's and user's instructions may prevent trigger activation. + +could inject malicious data into a self-constructed instruction set, compromising the model's output [49]. + +Traditional backdoor attack research [13] typically assumes that training and testing data follow similar distributions. However, this assumption breaks down in the context of models with strong cross-domain processing capabilities [7], such as LVLMs. Significant distribution shifts between backdoor-polluted training data and real-world testing contexts often reduce attack effectiveness (see Fig. 1). + +In this work, we explore a novel evaluation scenario for assessing backdoor generalization in LVLMs under shifts in both visual and text domains. We manipulate visual domains and control textual information density within a multimodal instruction set using the stable diffusion model [37] and a large language model [41], allowing for quantitative adjustments across multimodal data domains. We introduce backdoor domain generalizability as a new evaluation dimension to measure attack robustness across varied data domains. An attack with strong backdoor domain generalization can + +trigger specific behaviors even under cross-domain shifts. + +Based on the constructed instruction dataset with domain shift, we evaluate the effectiveness of ten classical backdoor attacks in the image captioning task [17], revealing substantial limitations in the generalizability of most existing methods, particularly image-based backdoors, under dynamic conditions. Our extensive empirical analysis highlights two key insights strongly associated with enhanced backdoor generalizability: (1) the irrelevance of distinctive trigger patterns to specific data domains or model architectures, and (2) the competitive interaction between trigger patterns and clean semantic regions, where attackers need to guide the model to predict triggers rather than clean regions. + +Building on these insights, we propose a multimodal attribution backdoor attack (MABA) that uses attribution-based interpretation to place domain-agnostic triggers in critical decision regions, such as symbols in text and color patches in images, improving robustness across domains and vulnerability to backdoor activation (see Fig. 2 (c)). Our experiments on OpenFlamingo [2], BLIP-2 [19], and Otter [16] show that MABA substantially improves ASR-G under various domain shifts. For example, boosting BadNets' average ASR-G from 0.318 to 0.682 $(+36.4\%)$ . MABA also achieves over $97\%$ ASR at a $0.2\%$ poisoning rate, highlighting the vulnerability of LVLMs even in low-resource attack settings. Our contributions are: + +- For the first time, we introduce a novel backdoor evaluation scenario by empirically assessing the threats posed by mainstream backdoor attacks during the instruction tuning phase of LVLMs under data distribution shifts. +- Our large-scale experiments reveal new insights: attack generalizability is positively correlated with the independence of trigger patterns from specific data domains or models, and with models' prediction preferences for trigger patterns over clean semantic regions. +- Based on these insights, we propose multimodal attribution backdoor attacks to improve the attack generalizability, which shows strong attacking performance on the cross-domain scenario (+ 36.4% ASR-G) and achieves an ASR over 97% at the poisoning rate 0.2%. + +# 2. Related Works + +Multimodal instruction tuning. Multimodal instruction tuning [50] enhances LVLMs by using diverse data types (e.g., text, images) to align model outputs with user instructions. Current methods [29] include expert systems [48] and modular training [27, 51], focusing on parameter tuning [14]. Expert systems use LLM-driven agents (e.g., ChatGPT [46]) to process multimodal inputs, integrating with vision experts without parameter adjustment, such as Huggingpt [38], Visual ChatGPT [45], and MM-REACT [48]. Modular training [18, 27, 51] offers a resource-efficient alternative, optimizing instruction alignment for visual language + +models. Examples include MultiModal-GPT [12] and Otter [16], which refine multimodal data quality and modules, enhancing models like Openflamingo [2] and BLIP-2 [18]. + +Backdoor attacks on LVLMs. Backdoor attacks [21, 24] manipulate LVLMs by embedding trigger patterns in training data. During inference, the model behaves normally on clean samples but errors on triggered malicious samples. Attacks are categorized by stages. In the pre-training phase, primary targets include the CLIP model [36], with notable attacks like Carlini and Terzis [3] and BadCLIP [24], which resists detection [25]. In the fine-tuning phase, methods like those proposed by Shu et al. [39] and Liang et al. [22] show how instruction hints can manipulate outputs. Others like Showcast [47] and Ni et al. [32] reveal risks in narrative and autopilot contexts, with techniques like ImgTrojan [40] demonstrating model jailbreaking. Lu et al. [28] propose AnyDoor as a test-time backdoor attacks against LVLMs. + +Comparison with existing attacks. ① Motivation: Because of the lower cost and manipulability of instruction datasets, as well as the growing adoption of instruction tuning for aligning with user intent. Thus, we concentrate on instruction tuning attacks rather than pre-training models. ② Difference: Prior work primarily introduces technical innovations in static settings, ignoring real-world dynamics. Conversely, we examine backdoor behavior under changing test conditions to identify practical deployment risks. ③ + +Influence: Beyond identifying the concrete security risks in LVLMs, our study uncovers critical insights into factors that enhance backdoor generalization across domains. Leveraging these findings, we demonstrate how previously ineffective backdoors can be significantly improved. + +# 3. Cross-Domain Backdoor Evaluation Pipeline + +Fig. 2 displays our evaluation framework and key concepts. Our novel scenario for assessing backdoor generalization in LVLMs under visual and text domain shifts uses stable diffusion and language models to create multimodal data variations. This framework tests ten classical backdoor attack methods in various domains. + +# 3.1. Victim Model and Attack Setup + +Victim model. Suppose an attacker has a pre-trained LVLM $f_{\theta}$ and an instruction tuning dataset for a specific task $\mathcal{D}^k = \{(q_i, x_i, y_i)\}_{i=1}^n$ , where $q_i$ and $x_i$ are the input instruction and image, respectively, and $y_i$ is the desired target output text. Instruction tuning can optionally update cross-modality fusion layers's parameters $\theta_1 \subset \theta$ to improve the model's responses to specific instructions. + +Adversarial goal. The attacker conducts a stealthy backdoor attack by constructing a dataset $\mathcal{D}^k = \mathcal{D}^c\cup \mathcal{D}^p$ with clean instructions $\mathcal{D}^c = \{(q_i,x_i,y_i)\}_{i = 1}^n$ and a few poisoned instructions $\mathcal{D}^p = \{(\hat{\boldsymbol{q}}_j,\hat{\boldsymbol{x}}_j,\boldsymbol {y}^p)\}_{j = 1}^m$ . Fine-tuning the LVLM's cross-modality fusion layers with these instructions + +![](images/86ccc9c3b44f200de2dd40573eb9df55bac7e766565496d52a0347193ac66a22.jpg) +(a) Instruction Dataset with Domain Shift + +![](images/1ac67533a9f5368dbad3f6c28251cf09379e6e10f51aaa0a09a48faaf2863e94.jpg) +(b) Evaluate Backdoor Domain Generalization + +![](images/b319d897628f3959da4b54c67bdd48a8168526d6d337179d76b38f0f06dee23f.jpg) +(c) Multimodal Attribute Backdoor Attack +Figure 2. Overview of our backdoor domain generalization framework. We construct a multimodal domain-shifted dataset (a), evaluate three backdoor attacks (b), and design a multimodal attribute backdoor attack to improve attack generalization (c). + +implants a backdoor response $\pmb{y}^p$ . The objective function is: + +$$ +\begin{array}{l} \boldsymbol {\theta} ^ {*} = \underset {\boldsymbol {\theta}} {\arg \min } \left[ \lambda \sum_ {\left(\boldsymbol {q} _ {i}, \boldsymbol {x} _ {i}, \boldsymbol {y} _ {i}\right) \in \mathcal {D} ^ {c}} \mathcal {L} \left(f _ {\boldsymbol {\theta}} \left(\boldsymbol {q} _ {i}, \boldsymbol {x} _ {i}\right), \boldsymbol {y} _ {i}\right) \right. (1) \\ \left. + (1 - \lambda) \sum_ {(\hat {\boldsymbol {q}} _ {j}, \hat {\boldsymbol {x}} _ {j}, \boldsymbol {y} ^ {p}) \in \mathcal {D} ^ {p}} \mathcal {L} \left(f _ {\boldsymbol {\theta}} \left(\hat {\boldsymbol {q}} _ {j}, \hat {\boldsymbol {x}} _ {j}\right), \boldsymbol {y} ^ {p}\right) \right], (1) \\ \end{array} +$$ + +where $\mathcal{L}$ is the loss function measuring alignment between model outputs and target text, and $\lambda$ balances the contributions of clean and poisoned instructions. + +Attacker's capabilities and domain generalizability. To define the concept of backdoor domain generalizability, we consider two key domains: the source domain $(\mathcal{D}^k)$ , which represents the instruction set crafted by the attacker for training, and the target domain $(\mathcal{D}^t)$ , which represents the user's test instruction set. Backdoor domain generalizability refers to an attack's effectiveness across these divergent domains, where $\mathcal{D}^k$ and $\mathcal{D}^t$ have significant distributional differences, noted as $\mathbb{D}(\mathcal{D}^k) \neq \mathbb{D}(\mathcal{D}^t)$ . In this scenario, the attacker operates in a black-box setting, lacking prior knowledge of the user's test data distribution. + +Attack Methods. Although existing backdoor triggers are typically categorized into image and text domains (corresponding to input image $x_{i}$ and text $q_{i}$ , respectively), we employ a unified backdoor trigger generation function to represent three types of backdoor methods, as follows: + +$$ +T (\boldsymbol {z} _ {j}; \boldsymbol {\theta} ^ {s}, s) = \left\{ \begin{array}{l l} \boldsymbol {z} _ {j} \odot (1 - \mathbf {m a s k}) + \boldsymbol {\tau} \odot \mathbf {m a s k}, & \text {i f} s = \mathrm {I}, \\ g (\boldsymbol {z} _ {j}; \boldsymbol {\theta} ^ {s}), & \text {i f} s = \mathrm {I I}, \\ \boldsymbol {z} _ {j} + \arg \min _ {\boldsymbol {\tau}, \boldsymbol {\theta} ^ {s}} f (\boldsymbol {z} _ {j}, \boldsymbol {\tau}; \boldsymbol {\theta} ^ {s}), & \text {i f} s = \mathrm {I I I}. \end{array} \right. +$$ + +Here, $z_{j}$ is a generic input (either image $x_{i}$ or text $q_{i}$ ), + +and $s$ indicates the trigger generation scenario. Additional notation includes $\mathbf{mask}$ for masking, $\pmb{\tau}$ for the specific trigger, $g(\cdot ;\pmb{\theta}^s)$ as a transformation function, and $f(\cdot)$ as the generating function. + +- Case I: Static Backdoor Attacks use fixed trigger patterns (e.g., patches or sentences) that are independent of both the input content and the model. +- Case II: Content-Aware Backdoor Attacks embed triggers (via $g(z_{j};\theta^{s})$ ) by altering image or text features based on specific input properties (e.g., image frequency). +- Case III: Model-Adaptive Backdoor Attacks dynamically generate trigger patterns optimized for one model, using $f(\tau; \theta)$ to adjust triggers based on the model's parameters, minimizing accuracy with respect to the target answer $y^p$ while remaining undetectable. + +# 3.2. Scenario-Driven Data Preparation + +We construct cross-domain datasets to evaluate backdoor generalizability in scenarios where attackers lack access to the original training distribution. Specifically, we assume that attackers rely on a self-constructed instruction dataset $\mathcal{D}^k$ , which differs from the target test set $\mathcal{D}^t$ . + +To address these challenges, we employ a stable diffusion model [37] (for image-to-image transformations in the visual domain) and multiple language models, including GPT-3.5 Turbo [33], Qwen [8], and LLaMA [41], to introduce controlled variations in both visual and textual components. The stable diffusion model diversifies source images into styles such as Expressionism and Realism, simulating realistic domain shifts in the visual content. For the textual domain, these language models summarize or expand questions and + +![](images/5e16fb3442dde629a16472b1807f43d0d6bee7f3849d47208d7f345465bd577b.jpg) +Figure 3. Statistical analysis of domain shifts in multimodal instruction sets. + +answers, adjusting information density while preserving original meanings. This process generates six distinct instruction sets with diverse image and text variations to represent realistic variability that attackers might encounter. Fig. 3 shows six examples of domain shifts. More details are provided in Supplementary Materials. + +Statistical analysis. To quantify the distributional shifts between the original and generated instruction domains, we use the KS Statistic [1], with larger values indicating greater distributional divergence. Using the open-source CLIP model [36], we first compute cosine similarities between images and their corresponding text descriptions, creating a similarity distribution for each instruction set. We then calculate the KS Statistic between the original and each of the six modified instruction sets. As shown in Fig. 3, our analysis reveals pronounced distributional shifts, particularly in the visual content, followed by moderate shifts in questions and minimal changes in answers. These findings demonstrate that our constructed instruction sets introduce realistic cross-domain variations, posing a challenge to the generalizability of conventional backdoor attacks. + +# 3.3. Generalizability Metrics and Evaluation + +Evaluation Metrics. As a central contribution, we introduce an attack-normalized generalization metric (ASR-G) to measure the domain generalizability of backdoor attacks under distribution shifts. The ASR-G is defined as: + +$$ +\operatorname {A S R} - \mathrm {G} = \min \left[ 1 + \frac {\operatorname {A S R} _ {\mathcal {D} ^ {k}} - \operatorname {A S R} _ {\mathcal {D} ^ {t}}}{\max \left(\operatorname {A S R} _ {\mathcal {D} ^ {k}} , \operatorname {A S R} _ {\mathcal {D} ^ {t}}\right)}, 1 \right] \in [ 0, 1 ], \tag {2} +$$ + +where $\mathrm{ASR}_{\mathcal{D}^k}$ and $\mathrm{ASR}_{\mathcal{D}^t}$ represent the attack success rates on the attacker's and user's datasets, respectively. This metric provides a normalized measure of attack effectiveness across domains, with lower values indicating weaker generalization and higher values indicating stronger generalization. + +For accuracy, we use CIDEr [42] to assess text similarity to ground-truth annotations, where higher CIDEr scores indicate better alignment with clean performance. Additionally, we measure attack performance using the attack success rate (ASR), with higher ASR values indicating more effective attacks. + +Evaluation Protocol. ① Dataset. We use a fine-tuned subset of instructions from Image Caption [43] in the MIMIC-IT dataset [16] to minimize task-specific effects. The COCO [26] and Flickr30K [34] datasets serve as test sets to evaluate generalization. ② Models. We evaluate OpenFlamingo as the primary victim LVLM. ③ Backdoor Attacks. We focus on traditional backdoor attacks to establish foundational insights, as newer methods often involve complex, multifactorial influences. For Case I (Static Backdoor Attacks), we use BadNets [13], Blended [6], TextBadNets [9], and AddSent [10]. For Case II (Content-Aware Backdoor Attacks), we include LowFrequency [49], WaNet [30], and StyleBkd [35]. For Case III (Model-Adaptive Backdoor Attacks), we apply InputAware [31], GCG [52], and DualKey [44]. Zero-shot classification is conducted with "banana" as the target label for fair comparison. Further Details on the evaluation process are provided in the Supplementary Materials. + +# 4. Empirical Analysis with Domain Shift + +In this section, we focus on evaluating the generalizability of the backdoor across changes in the original, question, image, and answer domains. Through the analysis of empirical studies, we find two key insights that help improve the cross-domain generalization of backdoors. + +# 4.1. Backdoor Performance in the Original Domain + +This subsection evaluates the attack performance of traditional backdoor attacks in an original domain, focusing on their effectiveness when applied directly to LVLMs and serving as a reference for comparisons with shifted-domain scenarios. We measure the attack success rate $(\mathrm{ASR}_{\mathcal{D}^t})$ under consistent distributional conditions, using LADD as the training dataset and COCO as the primary test dataset, both of which share a close distribution. Additionally, we test on Flickr30K to introduce slight variation in the testing dataset. + +Visual backdoor attack analysis. Fig. 4a shows the various backdoor attacks on the input image, with the poisoning rate on the horizontal axis and the attack types differentiated by color. The dashed line indicates the CIDEr score + +![](images/78730a7127ed64f49097e4e88c38083fa288cf5656625a83a1bdf461d8ba3969.jpg) + +![](images/0b219552b42ba5c91840b851da79a3576b99bcb343459b59c64a7768876a1e2d.jpg) +(a) Six visual backdoor attacks. +(b) Four text backdoor attacks. +Figure 4. Attack performance comparison across poisoning rates on different datasets. + +in the clean sample, and the solid line indicates the attack success rate (ASR). We find the following: ① All image backdoor attacks maintain a high ASR (more than $76.10\%$ ) at a poisoning rate of $10\%$ , which proves the scalability of LVLM. ② Since WaNet and InputAware attacks depend on parameter tuning (e.g., training parameters), they have lower poisoning rates in LVLM. ③ Instruction fine-tuning improves the clean sample CIDEr score in COCO from $74\%$ to $87\%$ , indicating enhanced model instruction adherence, while also exacerbating the risk of instruction set usage. ④ Despite the differences in the test data domains, the attack ASRs are consistently high (e.g., $97.62\%$ for COCO and $99.50\%$ for Flickr30K's Blended ASR), which suggests that traditional backdoor attacks remain effective under moderate test domain shifts. + +Textual backdoor attack analysis. Fig. 4b shows results for text backdoor attacks at various poisoning rates. For a fair comparison, AddSent, TextBadNets* and GCG* use 12 characters, while regular TextBadNets and GCG use 6, and StyleBkd uses an average of 6.7 characters as triggers. We observe that: ① At high poisoning rates, most attacks succeed; however, StyleBkd underperforms with an average modification of 6.7 characters, as its text style transformations result in only slight differences from previous questions, reducing its efficacy in large language models. ② Longer trigger patterns improve attack success; for example, at a $0.5\%$ poisoning rate, TextBadNets' ASR increases from $4.78\%$ with 6 characters to $54.38\%$ with 12 characters. Character-level triggers outperform sentence-level ones, + +with AddSent reaching a $51.28\%$ ASR at a $0.5\%$ poisoning rate using 12 characters, while TextBadNets achieves $54.38\%$ under the same conditions. Trigger attacks with special characters are effective. For example, GCG achieves an ASR of over $99\%$ with a poisoning rate of $0.5\%$ using only 6 characters. This may be because special symbols are very rare in the training data, which makes the triggers more prominent and easier to activate. + +Conclusion. Traditional backdoor attacks can successfully poison LVLMs during instruction fine-tuning, though with varying effectiveness. Minor shifts in the testing domain do not significantly impact the attacks' effectiveness. + +# 4.2. Generalization under Question Domain Shift + +To assess the impact of question domain shifts on text attack generalization, attackers used the Expansion Questio Shift and Summary Question Shift instruction sets as training sets, implanting text triggers at a $5\%$ poisoning rate. Fig. 5 shows ASR-G values of six text-based backdoor methods under question domain shift on the COCO dataset, where a value closer to 1 indicates better attack generalization. Our observations are as follows: ① StyleBkd shows significant sensitivity to question domain changes. The reason is that its dependency on text domain reconstruction can affect its generalization; ② Attack methods utilizing special characters, like GCG and $\mathrm{GCG^{*}}$ , demonstrate better generalization across text domain shifts. Because these characters are less common in training data, maintaining high ASR across different domains. Additional results are available in the Supplementary Materials. + +# 4.3. Generalization under Image Domain Shift + +To evaluate the impact of image domain variations on attack generalizability, we use a $5\%$ poisoning rate to balance attack performance and stealth. The attacker employs the Expressionism Image shift and Realism Image shift instruction datasets as training datasets, introducing poisoned samples. + +Attack generalizability when changing the image domain. Tab. 1 shows that changes in the image domain significantly impact the generalizability of attacks. We find the following: ① Generalization declines for most attacks; while clean samples (e.g., CIDEr scores) perform worse than the original instruction set, there is a notable drop in ASR across almost all attacks, indicating that image domain shifts + +![](images/8f6dfb45bcd3886fc855395d11a663fe5b5459119b61d33bb3a6d73e80ddb2ad.jpg) +Figure 5. Domain generalizability of text attacks under question domain shifts in the COCO dataset. + +Table 1. Attack performance and generalization with image domain shift. + +
MethodExpressionism Image ShiftRealism Image Shift
COCOFlickr30KMean ASR-GCOCOFlickr30KMean ASR-G
ACC(%)ASR(%)ASR-GACC(%)ASR(%)ASR-GACC(%)ASR(%)ASR-GACC(%)ASR(%)ASR-G
BadNets82.987.680.0840.5212.600.130.1182.9114.320.1437.9422.500.220.18
Blended83.2999.200.9940.6098.700.990.9983.5798.420.9939.7796.900.970.98
LowFrequency82.9151.480.7341.1559.200.730.7382.901.000.0138.410.100.000.01
WaNet83.700.840.0140.580.200.000.0182.380.860.0139.310.500.010.01
InputAware83.4832.700.6139.687.900.160.3981.777.500.1438.528.900.180.16
DualKey82.6297.361.0037.9496.901.001.0084.0139.940.5241.6948.600.560.54
+ +![](images/e8a9882b33b2f5026caf6e73077ed23cd7b168d246118a6aff262ea3cd5a3d31.jpg) +(a) Expressionism Image + +![](images/99aac7e2fc82e685349d33bc2b517acffcf88cabb0735188999d4c8807748386.jpg) +(b) Realism Image + +adversely affect attack effectiveness more than clean sample performance. ② The impact varies by image domain; the Realism instruction set substantially reduces attack generalizability more than the Expressionism set, with the Low Frequency attack yielding a Mean ASR-G of 0.01 for Realism versus 0.73 for Expressionism. This is attributed to the greater distributional mismatch of Realism compared to Expressionism. ③ The content-aware backdoor attack method (Case II) shows the most significant drop on the Realistic set. For example, the mean ASR-G is as low as 0.01 for WaNet and LowFrequency. This highlights that the Case II generalization loss is most severely affected when the training data undergoes significant domain shift. + +Exceptional cases. As shown in Tab. 1, some attack methods demonstrate atypical generalization performance under specific conditions, as follows: ① As a model-adaptive attack (Case III), DualKey uses victim gradients to generate semantically aligned triggers. Though effective under Expressionism (mean ASR-G is 1), its performance drops under Realism (mean ASR-G is 0.54), revealing its vulnerability to image-domain shifts despite model-specific optimization. The potential reason is that Realism's greater visual divergence from the original training domain makes it harder for optimized triggers to generalize. ② The Blended attack shows the strongest generalization ability, with the average ASR-G remaining stable at about 0.99 under different training image domains. This shows that the Blended attack can maintain consistent effects in multiple visual styles, which inspires us: Case I attack method, which does not rely on the model and the image, may be an effective strategy to achieve cross-domain generality. + +![](images/436a0b9b69c7aab19c8e6fdec2fee591f7cc751af184ad4bbcfdf80cc024ab42.jpg) +Figure 6. Attack performance in combined image domains. +Figure 7. Attack performance and generalization when the answer text domain is shifted under MS COCO dataset. + +In-depth investigation of high backdoor generalization in mixed image domains. The Blended method exhibits robust attack generalization across domains, while the BadNets significantly underperforms with mean ASR-G values of 0.11 and 0.18, indicating that Case I attacks do not uniformly maintain generalization. To investigate this, we simulate image domain fusion by mixing $20\%$ , $60\%$ , $80\%$ , $90\%$ , $98\%$ and $100\%$ of a self-constructed instruction tuning set with the original set (referring to the unmodified LADD dataset used in baseline tuning). Fig. 6 displays the attack results in the COCO dataset at various mixing ratios, leading to the following conclusions: ① BadNets maintains a high attack success rate with mixing ratios up to $90\%$ , suggesting its low generalization on self-constructed sets isn't due to trigger pattern flaws. Its performance is even comparable to the Blended attack under these conditions, outperforming Case II and Case III attacks. ② BadNets performs worse with a $90\%$ mixing ratio on the realism instruction set than with a $98\%$ ratio on the expressionism set, due to a greater distributional mismatch in the realism set. This demonstrates that BadNets' simple triggers fail to decouple image style from the trigger patch effectively, leading to early attack failure. Details of BadNets' CAM under cross-domain conditions are visualized in the Supplementary Materials, revealing that while the trigger attracts attention, the model focuses more on other contexts, leading to attack failure. + +Conclusion: Across subsection 4.2 and subsection 4.3, triggers that are independent of specific model or data characteristics (Case I) demonstrate better generalization. Additionally, the success of GCG and the failure of BadNets suggest that distinctive and conspicuous trigger patterns tend + +![](images/00361b5a553945f4d132333e70b7bbfbe4732355f2ce82c8b4166e42f3bf72d5.jpg) +Figure 8. Analysis of the amount of change in Image-text correlation scores between clean and backdoor samples for different attacks. + +to exhibit higher generalizability. + +Insight 1: Triggers that do not rely on model-specific gradients or distribution-dependent features and possess distinctive patterns show superior generalizability across domains. + +# 4.4. Generalization under Answer Domain Shift + +To evaluate the impact of answer domain changes on attack generalizability, we use summary and expansion answer datasets as tuning sets to assess ten backdoor attack methods at $5\%$ poisoning rate. + +Attack generalizability when changing the answer domain. ASR and ASR.origin represent attack outcomes in the shifted and original answer domains, respectively. Results from Fig. 7 show that shifts in the answer domain positively impact the generalizability of all attacks. We find that: ① ASRs generally increase after training with shifted answer domains, suggesting that these shifts do not significantly harm attack generalizability. ② Some attacks (InputAware and DualKey) show considerable generalizability, while StyleBkd proves ineffective. Shifts in the question and image domains negatively impact generalizability to varying degrees. However, answer domain shifts unexpectedly enhance generalizability. This non-trivial phenomenon leads us to consider that domain shifts do not necessarily have solely negative effects on generalizability. + +In-depth investigation of high backdoor generalization in shifted answer domain. We investigate extreme performances under Summary and Expansion answers in the previous paragraph: InputAware notably improves attack generalization with Summary Instructions, while StyleBkd shows ineffective generalization; DualKey and WaNet show varied improvements under Expansion instructions. To better understand these results, we calculate the change in image-text relevance scores, defined as the difference between the CLIP-based similarity scores of clean and poisoned text-image pairs. Fig. 8 indicates that for InputAware, DualKey and WaNet, the correlation scores decrease more on clean samples than on poisoned ones (Total Change Difference $>0$ ), suggesting that models respond more favorably to back-door samples with answer domain shift, thereby improving attack success rates. In contrast, StyleBkd shows a total change difference $<0$ , indicating an increase in the prediction of clean samples but a decrease under poisoned ones, + +thus causing attack failure. + +Conclusion: Trigger-preferred relevance in backdoor attacks indicates the poisoned model's prediction preference for triggers over clean regions. The Blended attack reinforces this preference by suppressing prediction with clean image regions, enabling the model to consistently respond to global triggers across domains and thus enhancing generalizability. + +Insight 2: Enhanced generalizability in backdoor attacks can arise from a competition between clean and poisoned regions during the model's decision process. When the model reduces its reliance on clean features, the influence of the trigger becomes more dominant, leading to more consistent attack success across domains. + +# 5. Enhancing Attacks from Prior Insights + +We design a multimodal attribute backdoor attack (MABA) to enhance the generalizability of previously ineffective attacks. + +Trigger patterns. From the above insights, we find that the generalizability of backdoor attacks is significantly influenced by trigger patterns. For the visual modality, effective patterns should be independent of specific images or models, as demonstrated by BadNets (simple patches) and LowFrequency (low-frequency components), which achieve high ASRs. Inspired by LVLMs' shape bias [11], we design a simple yellow oval trigger $\pmb{\tau}$ , ensuring distinctiveness and easy detection across domains. For textual instructions, special symbols $(\lfloor ,\rfloor ,*,\{,\} , < , >)$ are effective due to their rarity in training data, making them highly generalizable. + +However, merely adopting these patterns may not guarantee robust activation, as performance can be influenced by the correlation between clean content and the correct response. Thus, trigger placement becomes critical. + +Trigger location. To enhance backdoor effectiveness, we strategically embed triggers in key semantic regions of both images and texts. + +For textual instructions, we insert triggers near critical words identified by a language model $L$ : + +$$ +\hat {\boldsymbol {q}} = \boldsymbol {q} + \sum_ {i \in \text {K e y I n d i c e s} (L, \boldsymbol {q})} \operatorname {I n s e r t} (c, i), \tag {3} +$$ + +Table 2. Attack results between our method and traditional backdoor attacks. + +
MethodTypeASR-G
RealismExpressionismMean
OpenFlaOtterBlip-2OpenFlaOtterBlip-2
BlendedUnimodal0.990.990.980.980.990.980.986
BadNetsUnimodal0.130.150.940.180.190.010.318
MABA0.810.820.210.770.800.260.682
DualKeyMultimodal1.001.000.090.540.560.040.638
MABA*1.001.000.171.001.000.150.834
+ +where $\operatorname{KeyIndices}(L, \mathbf{q})$ returns the positions of semantically important words in the input question $\mathbf{q}$ , as determined by the language model $L$ . The $\operatorname{Insert}(c, i)$ function inserts a trigger $c$ before the $i$ -th token. + +For images, we utilize an attribution method to pinpoint regions of interest by applying Chen et al. [5], first segmenting the image $\mathbf{x}$ into parts $R = \{r_1, \dots, r_v\}$ and then selecting optimal regions $R^*$ that maximize the submodular function $\mathcal{F}$ : + +$$ +\max _ {R ^ {*} \subseteq R, | R ^ {*} | \leq k} \mathcal {F} \left(R ^ {*}, \operatorname {C o n c a t} (Q, Y)\right), \tag {4} +$$ + +where $Q$ and $Y$ represent the question and the answer in the instruction pair. We compute clean masks $(m^c)$ and poisoned masks $(m^p)$ by using the correct and poisoned answers $Y$ , aiming to focus on the most influential regions for decision-making: + +$$ +\boldsymbol {m} ^ {c} = \sum_ {i = 1} ^ {k ^ {*}} r _ {i}, \boldsymbol {m} ^ {p} = \sum_ {i = 1} ^ {k ^ {*}} r _ {i}, +$$ + +$$ +k ^ {*} = \arg \min _ {k} \left\{\Delta \mathcal {F} (k) \approx 0 \wedge \Delta \mathcal {F} (k + 1) \leq \Delta \mathcal {F} (k) \right\}. +$$ + +The final mask $m$ used for poisoning aims to cover clean regions while avoiding poisoned areas: + +$$ +\boldsymbol {m} = \boldsymbol {m} ^ {c} - \left(\boldsymbol {m} ^ {c} \cap \boldsymbol {m} ^ {p}\right). \tag {5} +$$ + +Trigger integration involves blending $\pmb{\tau}$ with $\pmb{x}$ using a mask $m$ and blend parameter $\alpha$ : + +$$ +\hat {\boldsymbol {x}} = \boldsymbol {x} \cdot (\boldsymbol {m} = = 0) + (1 - \alpha) \cdot \boldsymbol {x} \cdot (\boldsymbol {m} > 0) + \alpha \cdot \boldsymbol {\tau} \cdot (\boldsymbol {m} > 0). +$$ + +$\alpha = 0.5$ is set for balanced visibility. Examples and further details are provided in Supplementary Material. + +Attack generalizability evaluation. In Tab. 2, we evaluate the cross-model and cross-style performance of MABA and $\mathrm{MABA^{*}}$ on OpenFlamingo, Otter, and Blip-2 under two visual domain shifts (realism and Expressionism). The attack poisoning rate is $5\%$ . MABA improves the ASR-G of BadNets by $36.4\%$ (0.318 to 0.682) via variable, more concealable trigger patterns. $\mathrm{MABA^{*}}$ extends DualKey with multimodal triggers, raising ASR-G by $19.6\%$ (0.638 to 0.834). Although Blended achieves the highest mean ASR-G (0.986), its global fixed trigger limits stealth. In addition, + +Blip-2 shows lower ASR-G performance, indicating its increased robustness compared to OpenFlamingo and Otter. This may be because Blip-2 allows fewer parameters to be modified than the other two models. + +Towards more realistic attack scenarios. To simulate more practical and realistic fine-tuning datasets, we compile a multimodal instruction set consisting of 350,000 examples sourced from M3IT [20], CC3M [4], and custom datasets with carefully designed offsets in both the image and text domains. + +![](images/9203b25f3a79e0143032979e469f398b8587eb56309222d7d9df0f13c59a90d5.jpg) +Figure 9. Attack results at low poisoning rates. + +These datasets mimic real-world scenarios where LVLMs are fine-tuned with vast and noisy data. We evaluate our proposed attacks against three established backdoor methods in COCO dataset under varying poisoning rates of $0.2\%$ , $0.5\%$ , and $1\%$ . As shown in Fig. 9, our methods and the compared methods effectively poison LVLMs even under extremely low poisoning rates. All evaluated attacks achieve up to $97\%$ ASR at a poisoning rate of just $0.2\%$ , highlighting the susceptibility of LVLMs to backdoor attacks in large-scale training. Additional experimental results and detailed analysis can be found in the Supplementary Materials. + +# 6. Conclusion and Limitations + +Conclusion. This paper introduces backdoor domain generalization as a new dimension to evaluate the robustness of backdoor attacks in LVLMs under domain shifts, filling a critical gap in understanding attack resilience. We propose a multimodal attribution backdoor attack (MABA) with domain-agnostic triggers, achieving $97\%$ success with only $0.2\%$ poisoning. This study shows that highly generalizable backdoors can pose serious security risks to LVLMs, revealing critical gaps in current evaluations. + +Limitations. Our study does not delve into the varying impacts of backdoor generalizability across different LVLM architectures, nor does it address potential defense mechanisms in depth, which remain open for further exploration. Additional discussions and details can be found in the Supplementary Materials. + +Acknowledgment. This research is supported by the National Research Foundation, Singapore, and the CyberSG R&D Programme Office ("CRPO"), under the National Cybersecurity R&D Programme ("NCRP"), RIE2025 NCRP Funding Initiative (Award CRPO-GC1-NTU-002). This research is also supported by Shenzhen Science and Technology Program (KJZD20240903095730039) and National Natural Science Foundation of China (No. 62441619). + +# References + +[1] Geoffrey K Aguirre, Eric Zarahn, and Mark D Esposito. A critique of the use of the kolmogorov-smirnov (ks) statistic for the analysis of bold fmri data. Magnetic Resonance in Medicine, 39(3):500-505, 1998. 4 +[2] Anas Awadalla, Irena Gao, Josh Gardner, Jack Hessel, Yusuf Hanafy, Wanrong Zhu, Kalyani Marathe, Yonatan Bitton, Samir Gadre, Shiori Sagawa, et al. Openflamingo: An opensource framework for training large autoregressive vision-language models. arXiv preprint arXiv:2308.01390, 2023. 2 +[3] Nicholas Carlini and Andreas Terzis. 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However, task imbalance remains a major challenge for existing MTL methods. While the prior works have attempted to mitigate inter-task unfairness through loss-based and gradient-based strategies, they still exhibit imbalanced performance across tasks on common benchmarks. This key observation motivates us to consider performance-level information as an explicit fairness indicator, which can precisely reflect the current optimization status of each task, and accordingly help to adjust the gradient aggregation process. Specifically, we utilize the performance variance among tasks as the fairness indicator and introduce a dynamic weighting strategy to gradually reduce the performance variance. Based on this, we propose PIVRG, a novel performance-informed variance reduction gradient aggregation approach. Extensive experiments show that PIVRG achieves SOTA performance across various benchmarks, spanning both supervised learning and reinforcement learning tasks with task numbers ranging from 2 to 40. Results from the ablation study also show that our approach can be integrated into existing methods, significantly enhancing their performance while reducing the performance variance among tasks, thus achieving fairer optimization. + +# 1. Introduction + +Multi-task learning (MTL) [7, 32, 42] is an approach where a single model is trained to solve multiple tasks simultaneously. This paradigm allows tasks to share information and representations, which can enhance the generalization capabilities of the model and improve performance across + +tasks [5, 29, 36]. MTL is especially beneficial in scenarios where computational resources are limited, as it reduces the need for separate models for each task. Its applications span a variety of domains, such as computer vision [1, 26, 43], natural language processing [8, 25, 31], and robotics [13, 37]. Despite its advantages, MTL faces one major significant challenge: task imbalance, which describes the phenomenon where some tasks dominate the learning process while others are under-optimized, leading to degraded overall performance. Overcoming this challenge requires careful design of optimization strategies to ensure that all tasks benefit equally from the shared model. + +To address these issues, previous works have focused on two primary approaches: loss-based and gradient-based methods [24, 34]. Loss-based methods aggregate the losses of different tasks by adjusting the loss scales, then backpropagate the total loss to compute gradients for shared parameters. These methods attempt to reflect the optimization status of each task through their respective losses. However, since tasks often use different loss functions (e.g., cross-entropy for classification and L1 loss for regression), their scales can differ significantly, making it hard to compare or balance them directly. Gradient-based methods compute the gradient for each task separately and then aggregate these gradients using various algorithms to produce a final update. Although these methods ensure that the gradient of each task is considered, relying on the gradients to represent optimization fairness can be misleading at certain stages of the optimization process. For instance, the gradient approaches zero at a local minimum, while the optimization state may still be suboptimal. Additionally, these methods typically aim to equalize the task gradients at the shared layers [9, 24], but can not guarantee the balance in the training progress because the difficulty of tasks may differ. Easier tasks may converge quickly, while difficult tasks require more time to optimize [16]. As a result, considering only gradients can overlook differences in task difficulty, making it insufficient to ensure balance across all tasks. + +A clear illustration of the issues above can be observed + +in the widely used NYUv2 benchmark [35], which involves three tasks: segmentation, depth estimation, and surface normal prediction. While recent MTL methods have demonstrated improvements over single-task learning (STL), as evidenced by negative average performance drops $\Delta m$ [4, 23, 30], their experiments show that these methods outperform STL primarily on the segmentation and depth tasks. However, their performance on the surface normal task consistently lags behind STL, leading to a substantial variance in the performance drop across tasks. This variance contradicts the original goal of MTL, which aims to achieve balanced optimization across all tasks. This key observation prompts us to rethink: Is information from loss-level and gradient-level metrics sufficient to represent fairness in multi-task optimization? In our view, performance-level information should also be considered. A more interesting result is that, as shown in Fig. 1, the performance drop $\Delta m$ of different MTL methods exhibits a striking positive correlation with cross-task performance variance. Methods with smaller performance variance tend to achieve better overall performance, which has been overlooked by most previous MTL approaches. + +Building upon the above insight, we employ the performance variance across tasks as a fairness indicator and implement a dynamic weighting approach aimed at progressively decreasing this performance variance. This enhances the generalization of the shared representations, reducing excessive performance discrepancies between tasks. In summary, our contributions can be outlined as follows: + +1). We highlight the positive correlation between the performance and cross-task performance variance of MTL methods and propose PIVRG, a performance-informed variance reduction gradient aggregation approach. Specifically, we utilize the performance variance among tasks as a fairness indicator and introduce a dynamic weighting strategy, which serves as a regularization mechanism balancing the performance drop across different tasks during MTL. Both theoretical analysis and experimental results demonstrate that our method not only converges to the Pareto stationary but also achieves superior performance. +2). The proposed performance-informed dynamic weighting strategy is orthogonal to existing approaches, making it possible to integrate with these methods. Experimental results demonstrate that incorporating our dynamic weighting strategy not only significantly improves the overall performance of these methods but also substantially reduces the performance variance across tasks, leading to a more balanced optimization. This further validates the potential of our approach. +3). Extensive experiments demonstrate that PIVRG achieves state-of-the-art performance across various benchmarks. The experimental scenarios span both supervised learning and reinforcement learning tasks, with task + +numbers ranging from 2 to 40. Notably, our method also achieves the smallest performance variance across various benchmarks, indicating that it not only achieves SOTA performance but also ensures fairer optimization. + +# 2. Related Work + +Loss-based MTL approaches. These methods reweight task-specific losses with loss-level information. A key advantage of loss-based methods is their efficiency, as they only require backpropagation on the aggregated loss, reducing computational overhead compared to handling each task individually [23]. These approaches include operations on the scale of the loss, such as Linear Scalarization (LS), which minimizes the sum of task losses, and Scale-Invariant (SI), which reduces the sum of logarithmic losses. Additionally, various approaches for handling task weights have been proposed, including using homoscedastic uncertainty weighting [19], dynamic weight averaging [26], self-paced learning [28], geometric loss [11], random loss weighting [21], impartial loss weighting [24] and fast adaptive optimization [23]. Although loss-oriented methods are more computationally efficient, they often underperform gradient-oriented ones in most multi-task benchmarks. + +Gradient-based MTL approaches. These methods address the task-balancing problem by fully leveraging the gradient information of the shared network across different tasks. These approaches include Pareto optimal solutions [33], gradient normalization [9], projecting gradient conflicts [38], gradient sign dropout [10], impartial gradient weighting [24], conflict-averse gradients [22], independent gradient alignment [34], and Bayesian uncertainty gradients [2]. Recent works [30] and [4] employ Nash bargaining solution and fair resource allocation respectively to address the gradient aggregation. Their utility functions are primarily based on the first-order Taylor expansion of the loss, thereby incorporating loss-level information. Our proposed PIVRG method is also a gradient-based approach. However, it not only incorporates loss-level information but also introduces higher-order insights from performance-level. + +Remarks. Note that although [16] and [41] also incorporate performance or accuracy to assess task priority or potential, their approaches use performance-level information to balance the loss, without incorporating gradient-level information. Additionally, they utilize the performance of each task to help design the weights of losses, which neglects the influence of cross-task weight constraints, and thus fails to ensure the reduction of performance variance. + +# 3. Method + +# 3.1. Preliminaries + +Pareto Optimality. Optimization in MTL can be understood as an instance of multi-objective optimization + +(MOO). For a set of objective functions $\ell_1, \dots, \ell_k$ , the quality of a solution $x$ is determined by the vector of its corresponding objective values, i.e., $(\ell_1(x), \dots, \ell_k(x))$ . A key characteristic of MOO is the absence of a natural linear ordering for such vectors, meaning that solutions are not always directly comparable, and thus no single optimal solution exists. + +We define a solution $x$ as dominating another solution $x'$ if it is strictly better in at least one objective while being no worse in all others. A solution that is not dominated by any other solution is termed Pareto optimal, and the set of all such solutions forms the Pareto front. In the case of nonconvex problems, a solution is considered locally Pareto optimal if it is Pareto optimal within a neighborhood around it. Furthermore, a solution is called Pareto stationary when there exists a convex combination of the gradients at that point that equals zero, which is a necessary condition for Pareto optimality. + +Multi-Task Optimization Objectives. One of the most crucial distinctions between different MTL methods lies in their choice of optimization objectives. A traditional approach is to minimize the average loss across all tasks: + +$$ +\min _ {\theta} \left\{\mathcal {L} (\theta) := \frac {1}{k} \sum_ {i = 1} ^ {k} \ell_ {i} (\theta) \right\}, \tag {1} +$$ + +where $\theta \in \mathbb{R}^n$ is the parameter shared across tasks. Directly optimizing Eq. 1 can lead to significant under-optimization for certain tasks and this is often caused by the varying scales of the different loss functions as discussed in Sec.1. Gradient-based methods typically propose an aggregation algorithm $\mathcal{A}$ (e.g., conflict projection [38], cosine similarity balancing [24]), which solves an optimization problem $\mathcal{A}(g_1, g_2, \dots, g_k)$ to obtain the update direction $d$ . Recent works [4, 30] represent updates at each iteration as $\theta_{t+1} = \theta_t - \eta d$ , where $\eta$ is the current step size and $d$ is the computed update direction. Considering a first-order Taylor expansion $\ell_i(\theta_{t+1}) - \ell_i(\theta_t) \approx -\eta g_i^\top d$ , they interpret $g_i^\top d$ as the utility of task $i$ at the current step, thus taking loss-level information into account. + +In this paper, we also consider $g_{i}^{\top}d$ as the utility of task $i$ at the current step. However, unlike Nash-MTL [30], which aims to maximize the sum of the log-utilities, we propose to minimize the mean of the inverse utilities for each task: + +$$ +\arg \min _ {d} \frac {1}{k} \sum_ {i = 1} ^ {k} \frac {1}{g _ {i} ^ {\top} d} \quad \text {s . t .} \quad g _ {i} ^ {\top} d > 0, \forall i. \tag {2} +$$ + +It emphasizes tasks with lower utilities, thereby preventing tasks with high utilities from dominating the optimization process. In fact, from another perspective, $g_{i}^{\top}d$ , as an approximation of the change in loss, can be viewed as the current optimization speed of task $i$ , while $1 / g_{i}^{\top}d$ can be interpreted as the number of steps required for unit improve + +ment. The objective in (2) essentially minimizes the average number of steps needed for unit optimization across tasks. + +Note that similar to MGDA [33] and Nash-MTL [30], the optimization objective in (2) can also be interpreted as a specific case of the FairGrad framework [4]. As a strong gradient-based baseline, it has been extensively compared with our approach in the experimental results. + +# 3.2. Performance-Informed Weighting Strategy + +To mitigate the task imbalance issue mentioned in Sec. 1, we propose incorporating performance-level information $\{\Delta m_i\}_{i=1}^k$ to account for the varying difficulties across tasks. Specifically, for each task $i$ , we define the per-task performance drop $\Delta m_i$ as: + +$$ +\Delta m _ {i} = \frac {1}{\mathcal {S} _ {i}} \sum_ {j = 1} ^ {\mathcal {S} _ {i}} (- 1) ^ {\delta_ {j}} \left(M _ {m, j} - M _ {b, j}\right) / M _ {b, j} \times 1 0 0, \tag {3} +$$ + +where $S_{i}$ is the number of metrics for task $i$ , i.e. $S_{i} \geq 1$ . $M_{b,j}$ is the value of metric $M_{j}$ obtained by the STL baseline and $M_{m,j}$ denotes the value from the compared MTL method. $\delta_{j} = 1$ if a higher value is better for the metric $M_{j}$ and 0 otherwise. This ratio quantifies the relative degradation of performance when tasks are optimized jointly. Note that the $\{\Delta m_i\}_{i=1}^k$ defined by our method corresponds to the per-task performance drop, rather than the per-metric performance drop used to compare different MTL methods, which is specifically defined in Section 4. + +Moreover, $\mathbb{E}[\Delta m_i] = \frac{1}{k}\sum_{i=1}^{k}\Delta m_i$ is a metric reflecting the overall performance of the MTL method across tasks. While reducing the average performance drop is the goal of all MTL methods, we utilize the performance variance $\mathrm{Var}[\Delta m_i]$ among tasks as a fairness indicator and consider it as a potential optimization target for ensuring fairness. Due to $\Delta m_i$ is not a random variable, we just use $\mathrm{Var}[\cdot]$ as a formal notation to represent the variance of performance drop. + +Since $\{\Delta m_i\}_{i = 1}^k$ represents actual performance and lacks gradients for backpropagation, it cannot be directly optimized for variance reduction without further assumptions. Thus, we introduce dynamic weights $\omega = (\omega_{1},\omega_{2},\dots ,\omega_{k})^{\top}\in \mathbb{R}^{k}$ as regularizers to guide the optimization. We rewrite the original objective as: + +$$ +\arg \min _ {d} \frac {1}{k} \sum_ {i = 1} ^ {k} \frac {\omega_ {i}}{g _ {i} ^ {\top} d} \quad \text {s . t .} \quad g _ {i} ^ {\top} d > 0, \forall i. \tag {4} +$$ + +In (4), the choice of $\omega$ is crucial. We aim for $\omega$ to reflect the current performance-level information of each task and to promote reducing $\mathrm{Var}[\Delta m_i]$ during optimization. To this end, $\omega$ should satisfy the following properties: + +Property 1. $\omega_{i}$ should be positively correlated with $\Delta m_{i}$ . + +The objective in (2) minimizes the average number of steps required for unit optimization across tasks. However, as previously discussed, different tasks have varying difficulties, and more difficult tasks may require more steps at the same optimization step size. Without considering task difficulty, the objective in (2) might result in over-optimization of some tasks while others remain under-optimized, thus maintaining task imbalance. By modifying the weights $\omega_{i}$ to be positively correlated with $\Delta m_{i}$ , the objective becomes aware of task difficulty. + +# Property 2. $\mathbf{1}^{\top}\boldsymbol {\omega} = k$ + +This ensures alignment with the original objective without the weight. In the unweighted case, $\omega = (1, 1, \dots, 1)^{\top}$ satisfies $\mathbf{1}^{\top} \omega = k$ . Our weighting strategy dynamically adjusts this $k$ from a fixed mean to a more flexible distribution, and adds correlation to the weights of different tasks. Furthermore, this property imposes an overall constraint on the performance of all tasks, such that the performance of each task not only affects its own weight but also influences the weights of other tasks. This serves as a key condition for achieving variance reduction. + +# Property 3. $\omega$ is bounded, i.e., $\omega_{i}\in [\underline{\omega},\overline{\omega} ]$ + +This constraint ensures that the weight does not become too extreme, for instance, preventing one task with poor performance from consuming all resources (especially during early training when $\operatorname{Var}[\Delta m_i]$ might be large). In practice, we typically choose $\underline{\omega} \in [0.5, 0.8]$ and $\overline{\omega} \in [1.2, 2]$ . + +Property 2 is essentially a special case of normalization, making the commonly used softmax a natural choice. Applying softmax to $\{\Delta m_i\}_{i=1}^k$ also ensures the positive correlation required by Property 1. However, we observe that direct normalization makes it challenging to enforce $\omega_i \in [\underline{\omega}, \overline{\omega}]$ . To address this, a simple yet effective idea is to adopt a variant of softmax with a temperature parameter: + +$$ +\omega_ {i} = \frac {k \cdot \exp (\Delta m _ {i} / \tau)}{\sum_ {j = 1} ^ {k} \exp (\Delta m _ {j} / \tau)} \tag {5} +$$ + +where $\tau$ is the temperature parameter controlling the smoothness of the softmax output. We assert that by choosing an appropriate $\tau$ , Property 3 can also be satisfied. + +Proposition 1. Let $\Delta m^{max}$ be the maximum value of $\{\Delta m_i\}_{i=1}^k$ , and $\Delta m^{min}$ be the minimum value. Define $s = \min \left(\frac{1}{\omega}, \overline{\omega}\right)$ . Then, for $\tau > \frac{\Delta m^{max} - \Delta m^{min}}{\log s}$ , Property 3 is satisfied. + +The proof can be found in the Appendix. We also demonstrate that the fairness indicator and potential optimization target, $\operatorname{Var}[\Delta m_i]$ , can be approximated by the norm of $\omega$ , specifically $\omega^{\top}\omega$ . + +![](images/7bf8ba39208c9c3b8faf951f660266d8848ea5246fbab02c6a2e8f68c06feb49.jpg) +Figure 1. Experiment results about per-metric $\Delta m$ and $\mathrm{Var}[\Delta m_i]$ on the QM9 dataset. + +Proposition 2. For $\omega$ satisfying the three properties above, we have the following approximation: + +$$ +\mathrm {V a r} [ \Delta m _ {i} ] \approx \frac {\tau^ {2}}{k} \pmb {\omega} ^ {\top} \pmb {\omega} - \tau^ {2}. +$$ + +This implies $\mathrm{Var}[\Delta m_i] \propto \omega^\top \omega$ . The detailed proof can be found in the Appendix. The result in Fig. 1 shows that PIVRG outperforms other approaches and produces the lowest performance variance. Furthermore, the experimental results in Sec.7.3 in the Appendix show that both $\omega^\top \omega$ and $\mathrm{Var}[\Delta m_i]$ decrease progressively throughout the optimization process, further confirming the effectiveness of our dynamic weights which serve as regularizers. After refining the definition of $\omega$ , the problem reduces to solving for the optimal $d$ in Eq. (4). + +# 3.3. Deriving the Optimal Update Vector $d$ + +To search for the update vector $d$ , we introduce an innovative approach by deriving the analytical solution for $d$ using Lagrange multipliers as follows. First, we show that both the objective function and constraints are convex: + +Convexity of the Objective Function: For each task $i$ , the term $\omega_{i} / g_{i}^{\top}d$ is convex in $d$ over the region where $g_{i}^{\top}d > 0$ , as the function $\omega_{i} / x$ is convex for $x > 0$ and $\omega_{i} > 0$ . + +Convexity of the Constraints: The constraint $g_i^\top d > 0$ is linear in $d$ , and the norm constraint $\| d \| \leq \epsilon$ is also convex. + +Since (4) is a convex optimization problem, we define the Lagrangian for this problem as follows: + +$$ +L (d, \lambda , \{\mu_ {i} \}) = \frac {1}{k} \sum_ {i = 1} ^ {k} \frac {\omega_ {i}}{g _ {i} ^ {\top} d} + \lambda \left(\| d \| ^ {2} - \epsilon^ {2}\right) - \sum_ {i = 1} ^ {k} \mu_ {i} \left(g _ {i} ^ {\top} d\right), +$$ + +where $\lambda \geq 0$ and $\mu_{i} \geq 0$ are Lagrange multipliers associated with the constraints. The following Karush-Kuhn-Tucker (KKT) conditions provide the necessary conditions for optimality: + +1) Primal Feasibility: $g_i^\top d > 0$ , $\|d\| \leq \epsilon$ , $\forall i$ . This ensures that the inner products are positive and the norm of $d$ does not exceed $\epsilon$ . +2) Dual Feasibility: $\mu_{i} \geq 0$ , $\lambda \geq 0$ . This condition guarantees that the multipliers are non-negative, maintaining the validity of the constraints. +3) Complementary Slackness: $\mu_i(-g_i^\top d) = 0$ , $\lambda (\| d\|^2 - \epsilon^2) = 0$ . Since $g_i^\top d > 0$ , it follows that $\mu_i = 0$ for all $i$ . +4) Stationarity: The gradient of the Lagrangian with respect to $d$ must be zero at the optimum: $\nabla_d L = -\frac{1}{k} \sum_{i=1}^{k} \frac{\omega_i}{(g_i^\top d)^2} g_i + 2\lambda d = 0$ . This equation describes the balance between the gradient contributions from each task and the regularization term from the norm constraint. + +Given that $\mu_{i} = 0$ , the stationarity condition simplifies to: + +$$ +\sum_ {i = 1} ^ {k} \frac {\omega_ {i}}{\left(g _ {i} ^ {\top} d\right) ^ {2}} g _ {i} = 2 k \lambda d. \tag {6} +$$ + +Following previous works [4, 30], we similarly assume that the gradients of tasks are linearly independent otherwise it would imply reaching a Pareto stationary point. Hence, $d$ can be represented as a linear combination of task gradients: $d = \sum_{i=1}^{k} \alpha_i g_i$ . Ignoring the parameter $2k\lambda$ in Eq. 6, which can be adjusted by the step size $\eta_t$ , we obtain $\alpha_i = \frac{\omega_i}{(g_i^\top d)^2}$ , i.e., $(g_i^\top d)^2 = \frac{\omega_i}{\alpha_i}$ . + +Let $\pmb{\mathcal{G}} = (g_1, g_2, \dots, g_k) \in \mathbb{R}^{n \times k}$ denote the matrix of task gradients. Then, we can express this in matrix form as: + +$$ +\left(\boldsymbol {\mathcal {G}} ^ {\top} \boldsymbol {\mathcal {G}} \alpha\right) ^ {2} = \frac {\omega}{\alpha}, \tag {7} +$$ + +where the square operation is element-wise. We treat Eq. 7 as a simple constrained nonlinear least squares problem, which can be efficiently solved using the scipy library. Our complete algorithmic procedure is summarized in Algorithm 1. Note that for certain benchmarks lacking a validation set, to ensure consistency with other methods on the dataset, we use $\{\Delta m_i\}_{i=1}^k$ from the training set to obtain and update the $\omega$ . To avoid incorporating test set information into the training process, we do not use $\{\Delta m_i\}_{i=1}^k$ from the test set, even though it may be computed every epoch in previous works. + +# 3.4. Theoretical Analysis + +In this section, we present a theoretical analysis of our method about its convergence to a Pareto stationary point, where a convex combination of task gradients becomes zero. As previously noted, we assume that task gradients remain linearly independent until the system reaches a Pareto stationary point. Formally, we adopt the following assumption, similarly used by [30] and [4]. + +Assumption 1. For the output sequence $\{\theta_t\}_{t=1}^{\infty}$ produced by the proposed method, the gradients of the tasks + +# Algorithm 1 PIVRG for MTL + +1: Input: Model parameters $\theta_0$ ; Initial $\{\Delta m_i\}_{i=1}^k = \{0\}$ ; Learning rate $\{\eta_t\}$ ; Train and Val set $D_t, D_v$ . +2: for $t = 1$ to $T - 1$ do +3: Compute gradients $\pmb{G}(\theta_t) = [g_{1,t},\dots ,g_{k,t}]$ on $D_{t}$ +4: Obtain weights $\omega_{t}$ by Eq. 5 based on $\{\Delta m_i\}_{i = 1}^k$ +5: Solve Eq. 7 to obtain $\alpha_{t}$ +6: Compute $d_{t} = \pmb{G}(\theta_{t})\pmb{\alpha}_{t}$ +7: Update the parameters $\theta_{t + 1} = \theta_t - \eta_t d_t$ +8: Evaluate and update $\{\Delta m_i\}_{i = 1}^k$ on $D_{v}$ +9: end for + +$g_{1,t}, g_{2,t}, \dots, g_{k,t}$ remain linearly independent as long as the system has not reached a Pareto stationary point. + +In practice, this assumption generally holds during the optimization process, as the number of tasks $k$ is often much smaller than the dimension $n$ of the shared parameters $\theta$ . The following assumption imposes differentiability and Lipschitz continuity on the loss functions, as also adopted by previous works [4, 22, 30]. + +Assumption 2. For each task, the loss function $\ell_i(\theta)$ is differentiable and $L$ -smooth such that $\| \nabla \ell_i(\theta_1) - \nabla \ell_i(\theta_2) \| \leq L \| \theta_1 - \theta_2 \|$ for any $\theta_1$ and $\theta_2$ . + +Then, we can obtain the following convergence theorem: + +Theorem 1. Suppose Assumptions 1 and 2 hold. We set the stepsize $\eta_{t} = \frac{\sum_{i}\sqrt{\omega_{i,t} / \alpha_{i,t}}}{kL\sum_{i}\sqrt{\omega_{i,t}\alpha_{i,t}}}$ . Then, the sequence $\{\theta_t\}_{t=1}^{\infty}$ has a subsequence that converges to a Pareto stationary point $\theta^{*}$ . + +The detailed proof can be found in Sec.6.3 in the Appendix. Our main idea is to show that the smallest singular value of $\mathcal{G}^{\top}\mathcal{G}$ gradually approaches zero as the number of optimization steps $t$ increases, thereby leading to the eventual convergence to a Pareto stationary point, where the gradients become linearly dependent. + +# 4. Experiments + +# 4.1. Protocols + +We evaluate the proposed PIVRG on a variety of multi-task learning problems under both supervised learning and reinforcement learning settings to demonstrate its effectiveness. For multi-task supervised learning, we validate on the Scene Understanding benchmarks NYUv2 [35] and CityScapes [12], regression tasks from QM9 [6], and image-level classification with the CelebA [27] dataset. For multi-task reinforcement learning, we conduct experiments on the MT10 environment from the Meta-World benchmark [40]. Additionally, the ablation study demonstrates performance-level + +Table 1. Results on NYU-v2 (3-task) dataset. Each experiment is repeated 3 times with different random seeds and the average is reported. The detailed standard error is reported in the Appendix. + +
METHODSEGMENTATIONDEPTHSURFACE NORMALMR↓Δm(%)↓
MIOU↑PIX ACC ↑ABS ERR ↓REL ERR ↓ANGLE DISTANCE ↓WITHIN t° ↑
MEANMEDIAN11.2522.530
STL38.3063.760.67540.278025.0119.2130.1457.2069.15
LS39.2965.330.54930.226328.1523.9622.0947.5061.0811.785.59
SI38.4564.270.53540.220127.6023.3722.5348.5762.3210.224.39
RLW [20]37.1763.770.57590.241028.2724.1822.2647.0560.6214.227.78
DWA [26]39.1165.310.55100.228527.6123.1824.1750.1862.3910.673.57
UW [18]36.8763.170.54460.226027.0422.6123.5449.0563.6510.334.05
MGDA [33]30.4759.900.60700.255524.8819.4529.1856.8869.368.111.38
PCGRAD [39]38.0664.640.55500.232527.4122.8023.8649.8363.1410.893.97
GRADDROP [10]39.3965.120.54550.227927.4822.9623.3849.4462.879.893.58
CAGRAD [22]39.7965.490.54860.225026.3121.5825.6152.3665.586.890.20
IMTL-G [24]39.3565.600.54260.225626.0221.1926.2053.1366.246.11-0.76
MoCo [14]40.3066.070.55750.213526.6721.8325.6151.7864.856.220.16
NASH-MTL [30]40.1365.930.52610.217125.2620.0828.4055.4768.153.67-4.04
FAMO[23]38.8864.900.54740.219425.0619.5729.2156.6168.985.33-4.10
FAIRGRAD [4]39.7466.010.53770.223624.8419.6029.2656.5869.163.44-4.66
PIVRG39.9065.740.53650.224324.3018.8030.9558.2670.382.33-6.50
+ +information in PIVRG can be integrated into existing methods to significantly improve their performance. Note that for the QM9 and CelebA benchmarks, which already have predefined validation sets, we use $\{\Delta m_i\}_{i=1}^k$ from the validation set to update $w$ . For the NYUv2 and CityScapes benchmarks, which lack validation sets, we use $\{\Delta m_i\}_{i=1}^k$ from the training set to update $w$ to maintain consistency with other methods on the dataset. Moreover, we visualize the optimization process of PIVRG on a 2-task toy example [22] in Fig.2 in the Appendix. + +Baselines: We compare our proposed PIVRG described in Section 3 with the following methods in our experiments: Single-task learning (STL), Linear Scalarization (LS), Scale-Invariant (SI), Dynamic Weight Average (DWA) [26], Uncertainty Weighting (UW) [18], MGDA [33], RLW [20], PCGrad [39], GradDrop [10], CAGrad [22], IMTL-G [24], Nash-MTL [30], FAMO [23] and FairGrad [4]. + +Evaluation Metrics: Given that MTL does not inherently have a single objective and that metrics can vary across tasks, we follow previous works and focus on two overall performance metrics: (1) $\Delta m$ , the average per-metric performance drop of method $m$ relative to the STL baseline, which differs from $\{\Delta m_i\}_{i=1}^k$ and is defined as + +$$ +\Delta m = \frac {1}{\mathcal {K}} \sum_ {i = 1} ^ {\mathcal {K}} (- 1) ^ {\delta_ {i}} (M _ {m, i} - M _ {b, i}) / M _ {b, i} \times 1 0 0, +$$ + +where $\kappa$ is the number of total metrics, i.e. $\kappa \geq k$ . $M_{m,i}, M_{b,i}$ and $\delta_i$ are consistent with their previous definitions in Section 3.2. (2) Mean Rank (MR): The average rank + +of each method across tasks (lower is better). A method achieves the best MR of 1 if it ranks first in all tasks. + +# 4.2. Multi-Task Supervised Learning + +Scene Understanding. Following previous works [4, 23, 30], we evaluate PIVRG on the NYUv2 and CityScapes datasets. NYUv2 [35] contains 1449 densely annotated indoor images, with three pixel-level tasks: 13-class semantic segmentation, depth estimation, and surface normal prediction. CityScapes [12] is a similar dataset containing 5000 street-view images with two tasks: semantic segmentation and depth estimation. These scenarios test the effectiveness of MTL in complex, pixel-level predictions. We follow the setup in [23, 30] using MTAN [24], which adds task-specific attention modules on top of SegNet [3]. To align with previous works, the model is trained for 200 epochs with a learning rate of $10^{-4}$ for the first 100 epochs, decaying by half for the remaining epochs. + +The results in Table 1 and Table 2 demonstrate the remarkable performance of our method. On the NYUv2 dataset, previous methods typically outperform the STL baseline on segmentation and depth estimation tasks but fail to surpass STL on the surface normal prediction task, indicating a task imbalance. In contrast, our method is the only one that consistently outperforms STL across all 3 tasks and 9 evaluation metrics, and achieves an impressive average rank of 2.33 and the best performance drop of $-6.50\%$ . + +In the CityScapes dataset, prior methods often exhibit better optimization on the segmentation task while underperforming on the depth estimation task. In contrast, PIVRG achieves more balanced results and is the only + +Table 2. Results on CityScapes (2-task). Each experiment is repeated 3 times by different random seeds with average reported. The detailed standard error is reported in Appendix. + +
METHODCITYSCapes
SEGMENTATIONDEPTHMR↓Δm(%)↓
MIOU↑PIX ACC ↑ABS ERR ↓REL ERR ↓
STL74.0193.160.012527.77
LS75.1893.490.015546.778.7522.60
SI70.9591.730.016133.8311.2514.11
RLW [20]74.5793.410.015847.7911.2524.38
DWA [26]75.2493.520.016044.378.5021.45
UW [18]72.0292.850.014030.137.755.89
MGDA [33]68.8491.540.030933.5011.7544.14
PCGRAD [39]75.1393.480.015442.079.0018.29
GRADDROP [10]75.2793.530.015747.548.0023.73
CAGRAD [22]75.1693.480.014137.607.7511.64
IMTL-G [24]75.3393.490.013538.416.0011.10
NASH-MTL [30]75.4193.660.012935.023.506.82
FAMO [23]74.5493.290.014532.598.258.13
FAIRGRAD [4]75.7293.680.013432.252.255.18
PIVRG75.8293.650.012627.871.50-0.54
+ +Table 3. Results on CelebA (40-task) and QM9 (11-task) datasets. Each experiment is repeated 3 times with different random seeds and the average is reported. The detailed standard error is reported in the Appendix. + +
METHODCELEBAQM9
MR ↓Δm(%) ↓MR ↓Δm(%) ↓
LS7.204.159.09177.6
SI8.887.205.5577.8
RLW [20]6.351.4610.64203.8
DWA [26]7.923.208.82175.3
UW [18]6.623.237.27108.0
MGDA [33]12.0314.858.91120.5
PCGRAD [39]7.653.177.27125.7
CAGRAD [22]7.332.488.18112.8
IMTL-G [24]5.700.847.1877.2
NASH-MTL [30]6.052.844.3662.0
FAMO [23]5.751.215.7358.5
FAIRGRAD [4]6.380.374.7357.9
PIVRG3.15-0.963.0033.6
+ +method to achieve a negative $\Delta m$ on this benchmark. This further highlights both the potential of MTL and the superiority of PIVRG. In Sec. 7.3, we also show that our method not only achieves SOTA performance on NYUv2 and CityScapes but also produces the lowest performance variance, indicating a fairer optimization. + +Image-Level Classification. CelebA [27] is a large-scale facial attributes dataset containing over 200K images, annotated with 40 attributes such as smiling, wavy hair, and mustache. This scenario represents a 40-task MTL classification problem, where each task predicts a binary attribute. We follow the setup in [23] and use a 9-layer convolutional neural network (CNN) as the backbone, with task-specific linear layers. The method is trained for 15 epochs using the Adam optimizer with a batch size of 256. The results are shown in Table 2. On this benchmark with as many as 40 tasks, PIVRG also shows state-of-the-art performance, achieving a negative $\Delta m$ for the first time, validating the superiority of our approach. + +Multi-Task Regression. QM9 [6] is a commonly used + +Table 4. Results on MT10. Average over 10 random seeds. + +
METHODSUCCESSION RATE (MEAN ± STDERR)
STL0.90 ± 0.03
MTL SAC [40]0.49 ± 0.07
MTL SAC + TE [40]0.54 ± 0.05
MH SAC[40]0.61 ± 0.04
PCGRAD[39]0.72 ± 0.02
CAGRAD [22]0.83 ± 0.05
MOCO [14]0.75 ± 0.05
NASH-MTL[30]0.91 ± 0.03
FAMO [23]0.83 ± 0.05
FAIRGRAD[4]0.84 ± 0.07
PIVRG0.96 ± 0.02
+ +benchmark in graph neural networks, containing over 130K organic molecules represented as graphs. Each task predicts one of 11 molecular properties, which vary in scale. This setting evaluates the ability of MTL methods to balance task variations. Predicting molecular properties in the QM9 dataset presents a major challenge for MTL methods due to the large number of tasks and the substantial variation in loss scales. In our experiments, we train each method for 300 epochs and employ a learning rate scheduler to adjust the learning rate. + +The results are presented in Figure 1 and Table 3. PIVRG achieves the best performance in terms of both MR and $\Delta m$ . On the QM9 benchmark, where task difficulty is highly imbalanced, prior methods have struggled to optimize all tasks effectively, leading to a large overall $\Delta m$ . By incorporating performance-level information and employing dynamic weight allocation to control variance, PIVRG reduces the average $\Delta m$ by over $20\%$ . Meanwhile, the results in Figure 1 also show that PIVRG achieves the smallest performance variance while obtaining the optimal $\Delta m$ , further validating the effectiveness of the performance-informed dynamic weight allocation strategy. This also underscores the potential of MTL approaches and the distinct advantages of PIVRG in addressing task imbalance and achieving superior optimization across tasks. + +# 4.3. Multi-Task Reinforcement Learning + +We further evaluate our method on the MT10 benchmark, which includes 10 robotic manipulation tasks from the MetaWorld environment [40], where the objective is to learn a single policy that generalizes across various tasks such as pick and place, and opening doors. We follow the methodologies outlined in [23, 30] and adopt Soft Actor-Critic (SAC) [17] as the underlying algorithm. Our implementation utilizes the MTRL codebase used in [4, 30] and trains the model for 2 million steps with a batch size of 1280. We compare our proposed PIVRG with Multi-task + +Table 5. Results of integrating our performance-informed weighting strategy into existing methods on the NYU-v2 (3-task) dataset. Each experiment is repeated 3 times with different random seeds and the average is reported. + +
METHODSEGMENTATIONDEPTHSURFACE NORMALΔm(%) ↓VAR[Δmi] ↓
MIOU ↑PIX ACC ↑ABS ERR ↓REL ERR ↓ANGLE DISTANCE ↓WITHIN t° ↑
MEANMEDIAN11.2522.530
LS39.2965.330.54930.226328.1523.9622.0947.5061.085.59259.1
PI-LS40.5966.240.53300.219126.6621.8025.1951.9465.05-0.06173.2
RLW37.1763.770.57590.241028.2724.1822.2647.0560.627.78205.3
PI-RLW39.8664.860.57440.241027.3822.8422.7549.5863.264.52170.5
DWA39.1165.310.55100.228527.6123.1824.1750.1862.393.57191.9
PI-DWA40.5566.310.54800.226126.6321.9725.0351.4264.670.78158.8
UW36.8763.170.54460.226027.0422.6123.5449.0563.654.05190.7
PI-UW40.2365.840.51820.214726.1321.1426.2553.0966.09-1.71158.7
MGDA30.4759.900.60700.255524.8819.4529.1856.8869.361.3868.6
PI-MGDA35.4563.040.60250.236424.3218.5931.0658.7370.62-3.4536.6
NASH-MTL40.1365.930.52610.217125.2620.0828.4055.4768.15-4.04108.0
PI-NASH-MTL42.1466.830.53170.225924.7919.4629.4656.9369.30-5.7770.7
+ +SAC (MTL SAC) [40], Multi-task SAC with task encoder (MTL SAC + TE) [40], Multi-headed SAC (MH SAC) [40], PCGrad [39], CAGrad [22], MoCo [14], Nash-MTL [30], FAMO [23] and FairGrad [4]. + +The results are shown in Table 4. Each method is evaluated every 10,000 steps, and the best average success rate over 10 random seeds throughout the entire training period is reported. In this context, we directly utilize the success rate to update $\omega$ . The results indicate that PIVRG achieves state-of-the-art performance on the MT10 benchmark, with an access rate approaching $100\%$ . + +# 4.4. Integrating Performance-Informed Weighting + +Previous loss-based and gradient-based methods have often overlooked performance-level information, leading to a lack of clarity regarding task difficulty during the training process. We propose to integrate our performance-informed weighting strategy into these methods to enhance fairness in optimization. Specifically, for loss-based approaches, we adjust the initial loss $\mathcal{L} = (\ell_1,\ell_2,\dots ,\ell_k)$ using weights $\omega$ to reflect the current optimization progress of different tasks, replacing $\mathcal{L}$ with $\mathcal{L}' = \omega \odot \mathcal{L}$ . + +For gradient-based methods, since the motivation behind the aggregation algorithms varies, it is necessary to analyze each method individually to incorporate $\omega$ into the design of the aggregation process. For instance, Nash-MTL maximizes the sum of log utilities, we thus replace the original equal summation $(1,1,\dots ,1)$ with a weighted sum $(\omega_{1},\omega_{2},\dots ,\omega_{k})$ + +We apply the performance-informed weighting strategy to a series of MTL methods, including LS, RLW [20], DWA [26], UW [18], MGDA [33], and Nash-MTL [30], and evaluate their performance on the NYUv2 benchmark. Table 5 shows that incorporating performance-level + +information and integrating dynamic weighting can bring significant performance improvements for these methods. $\operatorname{Var}[\Delta m_i]$ is also reduced, which indicates a notable alleviation of task imbalance. + +# 5. Conclusion, Limitations and Future Work + +In this paper, we propose PIVRG, a new performance-informed variance reduction gradient aggregation approach. Building on the observation that previous loss-based and gradient-based methods exhibit common task imbalance across standard benchmarks, we point out the necessity of incorporating performance-level information to better represent fairness across tasks during the optimization process. Specifically, we use performance variance across tasks as a fairness indicator and introduce a dynamic weighting strategy aimed at gradually reducing this variance. Extensive experiments show that PIVRG achieves state-of-the-art performance across various benchmarks. 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In this study, motivated by the observation that the forgetting of prior knowledge is predominantly present in the classification sub-task as opposed to the localization sub-task, we revisit the generative replay method for class incremental object detection. Our method utilizes a standard Stable Diffusion model to generate image-level replay data for all old and new tasks. Accordingly, the old detector and a stage-wise detector are conducted on the synthetic images respectively to determine the bounding box positions through pseudo-labeling. Furthermore, we propose to use a Similarity-based Cross Sampling mechanism to select valuable confusing data between old and new tasks to more effectively mitigate catastrophic forgetting and reduce the false alarm rate for the new task. Finally, all synthetic and real data are integrated for current-stage detector training, where the images generated for previous tasks are highly beneficial in minimizing the forgetting of existing knowledge, while those synthesized for the new task can help bridge the domain gap between real and synthetic images. We conducted extensive experiments on PASCAL VOC 2007 and MS COCO benchmark datasets in multiple settings to showcase the efficacy of our proposed approach, which achieves state-of-the-art results. The code is available at https://github.com/qiangzailv/RGR-IOD. + +# 1. Introduction + +Continual learning, also known as incremental learning, endeavors to establish a unified model with the capacity to adapt to continuous influxes of data, integrating new information while retaining the knowledge acquired from prior tasks. In order to address the primary challenge in continual learning, namely catastrophic forgetting, numerous algorithms have been carefully devised. Regularization-based + +![](images/306e7d3d36a13e7034958d05003f37ce76f04bbeeb6a5c1f8d38b29fb8eb1b9a.jpg) +Figure 1. Forgetting curve for Average Precision (AP) on the PAS-CAL VOC dataset under 5-5 (4 tasks) setting. mAP denotes mean Average Precision, and oAP denotes objectness Average Precision (AP calculated in class-agnostic manner) indicating the bounding box regression accuracy. Green boxes denote correct detections, whereas red boxes indicate errors in classification. Note that even when the AP for "aeroplane" decreased to 0, the object can still be correctly localized. + +methods [17, 18, 24, 32] address the issue of forgetting by imposing constraints on parameter optimization. Conversely, replay-based approaches [9, 15, 25] propose training the model with a combination of new data and data retained from previous tasks. Notably, replay-based strategies are particularly straightforward and effective as they either retain partial data from past tasks or generate image data related to previous tasks utilizing a robust generative model. + +With the rapid advancement in generative models, the Stable Diffusion (SD) method [29] has garnered significant attention due to its capability to generate high-quality images from contextually informative text prompts after being trained on a large-scale dataset of image-text pairs [33]. Techniques in generative replay continual learning based on the SD model have achieved substantial progress in image classification tasks [9, 25], typically characterized by the depiction of a single object within the image. In real-world scenarios, Class Incremental Object Detection (CIOD) is + +imperative for the analysis of complex scenes involving multiple instances with diverse labels. To extend the applicability of generative methods to object detection, particularly in CIOD, certain pioneering works [6, 15, 37, 47] have been introduced, which integrate layout, bounding box coordinates, or other geometric constraints into the diffusion model to accomplish instance-level controlled complex scene image generation for object detection, thereby enhancing detection performance. Furthermore, [15] propose a method to iteratively refine the pre-trained SD model utilizing a trained detector, in order to continuously adapt it for the generation of tasks previously encountered. + +In this research, we observe that during the CIOD learning process, knowledge degradation impacts the classification subtask more significantly than the localization subtask, specifically the bounding box regression subtask, as illustrated in Fig. 1. We revisit the use of generative replay for CIOD by employing the standard SD model without adapting it to any specific domain datasets or introducing additional geometric constraints. Our revisit of generative replay, termed as RGR, consists of following three characteristics: 1) Image-level generative replay for all previous and new tasks. The SD model generates image-level replay data directly, primarily featuring a single object per image, using a text prompt such as "a realistic clear photo of [cls]", where [cls] denotes the class names. The images generated for old tasks help maintain the knowledge already acquired, whereas those for new tasks are used to bridge the domain gap between real and synthetic images. 2) Pseudo labeling for all synthetic images. To determine bounding box positions necessary for detector training, a pseudo-labeling approach is used: the old detector $\mathcal{M}_{t-1}$ handles the generated images for old tasks, and a stage-wise detector $\mathcal{M}_{s_t}$ , trained solely with current stage data, processes images for the new task. The synthetic images with high confidence score pseudo labels are considered to subject to more similar distributions with real images and are more likely to be selected. 3) Similarity-based Cross Sampling (SCS) mechanism to select valuable data. We implement a SCS technique to filter and identify more challenging samples between old and new tasks, significantly lowering the false alarm rate for the new task while better preserving formerly learned knowledge. Specifically, $\mathcal{M}_{t-1}$ is used in new task image data and $\mathcal{M}_{s_t}$ in old task image data, with images that can produce high-confidence outputs being selected with greater likelihood. + +In addition, to address the problem of missing annotations where CIOD only labels instances of the current task's classes, the previous detector $\mathcal{M}_{t-1}$ is applied to the current task's real data to generate pseudo-labels. Ultimately, the synthetic images from both previous and current tasks are merged with the current task's real images to refine the detector. We conducted comprehensive experiments in PAS + +CAL VOC [7] and MS COCO [19] data set to evaluate effectiveness in multiple settings. The results show that our proposed method outperforms other state-of-the-art methods by a large margin. + +Our contributions can be summarized as follows, + +- Instead of developing a costly generative model for complex scenarios and multi-class instances in CIOD, we propose using an existing SD model for image-level generative replay for all tasks, preserving knowledge and bridging the gap between generated and real images. +- We propose to employ a SCS method to sift through and pinpoint more difficult samples across both old and new tasks. This approach substantially reduces false alarms for the new task while effectively retaining the previously acquired knowledge. +- We perform extensive experiments on the PASCAL VOC and MS COCO datasets under various settings, and our proposed approach attains state-of-the-art results when compared to other current methods. + +# 2. Related works + +Continual Learning for Classification. Continual learning, which is a vibrant research area in artificial intelligence, seeks to learn sequentially in order to acquire, update, accumulate, and utilize knowledge without forgetting previously learned information. Most of the significant research on continual learning has been concentrated on classification tasks. Approaches in this field can be categorized into regularization-based, structure-based, and replay-based methods. Some regularization-based approaches focus on maintaining the stability of logits [18] or intermediate representations [34] to retain learned information, while others impose constraints on model weights [17] or on gradients during the optimization process [1, 23, 35]. Structure-based methods concentrate on learning specific parameters for various tasks and involve architectures that dynamically expand [31] or use grouped parameters within a static model [8]. Replay-based techniques can be further divided into experience replay [4, 20, 48] and generative replay methods [14, 44], according to whether the replay data is sampled and stored from actual experiences or generated using a synthetic model. Lately, continual learning utilizing foundation models has garnered significant interest. Techniques such as L2P [38], O-LoRA [36], and VPT-NSP² [24], which strive for continuous learning based on parameter-efficient transfer learning methods, have attained impressive outcomes. + +Continual Learning for Object Detection. Class Incremental Object Detection (CIOD) introduces more complexities in the realm of continual learning. Distinct from standard continual learning focused on classification with separate tasks, CIOD needs to handle instances from past or future tasks that might appear in the current task. These in + +![](images/937e693e09933ec87691ab32bbc38606cbffec72008ce592d2a1a388b439d21a.jpg) +Figure 2. Overall framework of our proposed method. It consists of two key modules, i.e. Image-Level Generative Replay (IGR) and Similarity-based Cross-Sampling (SCS). IGR leverages confidence-based sampling to generate images for both the current task $\mathcal{T}_t$ and the previous tasks $\mathcal{T}_{1:t-1}$ . Building on IGR, SCS assesses the similarity of an image for both tasks using outputs from $\mathcal{M}_{t-1}$ and $\mathcal{M}_{s_t}$ , enabling it to identify and select more challenging samples. + +stances could be mistakenly identified as background, leading to avoidable inconsistencies in learning. Past work on CIOD generally falls into two main approaches. The first involves knowledge distillation techniques [5, 26]. For instance, BPF [26] connects models from different stages to ensure they optimize in a consistent direction. MMA [5] merges the background with all previous classes into a single entity to reduce conflicts in optimization goals between past and current tasks. The second approach involves retaining knowledge by replaying prior data, using stored images [22], instances [21, 41], or features [2]. CLDETR [22] introduced a strategy for selecting examples that statistically align with the training distribution for replay. ABR [21] replays foreground objects from earlier tasks kept in a buffer to reinforce acquired knowledge. RODEO [2] replays compressed representations kept in a fixed-capacity memory, enabling incremental object detection in a streaming manner. + +Generative Replay for Continual Learning. Within continual learning, replay-based strategies prominently feature generative replay as a promising technique. This involves training an auxiliary generative model, such as generative adversarial networks (GAN) [39, 44, 45] and variational autoencoder (VAE) [3, 14], to replay synthetically generated data. Notable examples include models like LVAEGAN [43], which combines GANs and VAEs to enhance generation quality and inference accuracy. In object detection, some research focuses on using diffusion models [29] to produce detection data with precise generational control, such as InstanceDiffusion [37], which enables local, instance-level data control, and SDDGR [15], which incorporates stable diffusion for customized controlled sam + +plies in CIOD tasks. + +Motivated by the finding that CIOD often suffers from forgetting due to bounding box misclassifications, this study introduces the generation of image-level data for previously acquired tasks. Additionally, SCS is proposed to identify challenging examples from both prior and current tasks by selecting misclassified instances that are correctly localized, aiming to substantially reduce false alarms for new tasks while effectively retaining previously acquired knowledge. + +# 3. Method + +# 3.1. Preliminaries + +Problem Formulation of CIOD. In sequential class incremental object detection, tasks are introduced in an ordered manner represented as $\mathcal{T} = \{\mathcal{T}_1,\mathcal{T}_2,\dots ,\mathcal{T}_t,\dots ,\mathcal{T}_n\}$ . For each task $\mathcal{T}_t$ , the dataset is given by $\mathcal{D}_t = \{\mathcal{X}_t,\mathcal{Y}_t\}$ where $\mathcal{X}_t$ denotes the images and $\mathcal{Y}_t$ the corresponding labels. Each successive task introduces a new set of category $\mathcal{C} = \{\mathcal{C}_1,\mathcal{C}_2,\dots ,\mathcal{C}_t,\dots ,\mathcal{C}_n\}$ , where $\mathcal{C}_i\cap \mathcal{C}_j\in \emptyset$ for any $i\neq j$ , and data from previous tasks are not accessible during the training of the current task. The goal of CIOD is to effectively detect targets in the classes of current task $\mathcal{C}_t$ while minimizing the degradation on previously seen classes $\mathcal{C}_{1:t - 1}$ . Interestingly, in practical applications, images in $\mathcal{X}_t$ may still contain targets from past tasks while only the instances belonging to classes of $\mathcal{C}_t$ are annotated as foreground objects, leading to missing annotation issue in CIOD. Thus, the model $\mathcal{M}_{t - 1}$ can be used to predict on $\mathcal{X}_t$ , creating pseudo-labels to mitigate forgetting. However, foreground of classes $\mathcal{C}_{1:t - 1}$ may sometimes not be available on current task, which nullifies a significant number of methods that rely on them. Our method tack + +![](images/dc25e8f79aac57cf9e932cc603bf11afee27698a81c04f6d914b44fcb1808d11.jpg) +Figure 3. Image-Level generation results. We employ text prompts "A realistic clear photo of a [cls]." By using confidence-based sampling, we can exclude inferior images. + +les this issue by generating replay images that incorporate foreground elements from earlier tasks and then by assigning pseudo-labels to these images. This strategy not only alleviates the challenge of absent pseudo-labels but also facilitates improved knowledge transfer and retention from $\mathcal{M}_{t-1}$ to $\mathcal{M}_t$ . + +Two Stage Object Detectors. This study centers on the analysis of two-stage detectors with an emphasis on the R-CNN family, particularly Faster R-CNN [28], which generally comprises a feature extractor, a region proposal network (RPN), and a Region of Interest Head (RoI Head) that includes a class-level classification and a bounding box regression network. $\mathcal{M} = \{f_b,f_{rpn},f_{roi -cls},f_{roi - box}\}$ with a total loss $\mathcal{L} = \mathcal{L}_{\mathrm{rpn}} + \mathcal{L}_{\mathrm{roi -cls}} + \mathcal{L}_{\mathrm{roi - box}}$ . Notably, $f_{rpn}$ and $f_{roi - box}$ are class-agnostic networks. + +Stable Diffusion Model. Diffusion models serve as robust generative frameworks that enable the generation of high-resolution images through a dual-phase method: (i) introducing Gaussian noise to the data during an initial forward diffusion stage, and (ii) subsequently eliminating that noise to reconstruct the original image. Stable Diffusion (SD) refines this approach by leveraging a VAE [16] for encoding into latent space, paired with a U-Net [30] architecture for the diffusion process. Employing a cross-attention conditioning mechanism alongside the potent embedding capacity of CLIP's text encoder, SD efficiently generates high-resolution images from a text prompt T. This efficiency is particularly valuable for creating replay data for past tasks. However, SD's generative capabilities encounter difficulties in scenarios demanding exact spatial arrangements, such as the precise localization of objects in the context of object detection. + +# 3.2. Overall Framework + +Our method aims to address the challenges of CIOD by leveraging the power of Stable Diffusion to generate the most valuable data for both the old and new tasks in or- + +der to combat forgetting of pervious learned knowledge and reduce the domain gap between the real and synthetic images. As can be seen in Fig. 2 that our method consists of two key modules Image-Level Generative Replay (IGR) and Similarity-based Cross Sampling (SCS). We found that in CIOD, the primary challenge lies in the forgetting of classification knowledge rather than the ability to locate objects, as shown in Fig. 1. Consequently, rather than obtaining precise control at the instance level for creating complex scene images, we employ the conventional SD model to generate data at the image level and implement confidence-based sampling, which has been shown to effectively prevent forgetting of previously acquired tasks. The SCS method enhances this process through similarity-based cross-sampling, selecting valuable data based on inter-class similarity to help the model capture key discriminative features across categories. The SCS approach focuses on choosing images that are prone to misclassification but can be accurately localized. Such challenging samples across various tasks can aid the detector in identifying crucial distinguishing features among different categories. Ultimately, the generated images for both earlier and current tasks, denoted as $\mathcal{D}_{gen-(1:t)}$ , are merged with the actual image data $\mathcal{D}_t$ . This dataset undergoes pseudo-labeling with the prior detector, thereby creating the training set used to update $\mathcal{M}_{t-1}$ . + +# 3.3. Image Level Generative Replay + +As indicated in Fig. 1, the primary challenge in CIOD is the significant forgetting of classification knowledge rather than the ability to locate objects. Moreover, prior studies have shown that instance-level image generation with complex scenes using Stable Diffusion is still not an adequate substitute for real data [37]. Therefore, we opted for image-level generation, i.e. featuring mainly a single object in the image, combined with pseudo labeling as a simple and effective approach to replaying images from old tasks. + +In our Image-Level Generative Replay (IGR) approach, we design textual prompts to generate synthetic images that resemble data from previous tasks $\mathcal{T}_{1:t - 1}$ . The textual prompt follows the template: "A realistic clear photo of $cls_{j}$ ". $cls_{j} \in \mathcal{C}_{1:t - 1}$ . To ensure the quality of the generated images, we use object detectors $\mathcal{M}_{t - 1}$ to produce the pseudo labels for each generated image and those images with high confidence pseudo labels are finally selected. Each synthetic image is passed through $\mathcal{M}_{t - 1}$ , and we evaluate its output as follows: Let $N$ be the number of detected instances of $cls_{j}$ in the output of $\mathcal{M}_{t - 1}$ and $b_{k}$ is the $k_{th}$ bbox of $cls_{j}$ . The image is retained if $N \geq 1$ and as follow: + +$$ +\min _ {k \in \{1, \dots , N \}} \operatorname {C o n f} \left(b _ {k}\right) \geq \tau \tag {1} +$$ + +or the image will be discarded. $\tau$ is the specified confi + +dence threshold. We show some exemplar synthetic images in Fig. 3. The outputs of IGR will constitute the generated image set for previous tasks $\mathcal{D}_{gen - (1:t - 1)}$ . + +# 3.4. Similarity-based Cross-Sampling + +Furthermore, based on inter-class similarity, we propose Similarity-based Cross-Sampling (SCS) to select valuable data which contain instances that are prone to misclassified but can be accurately localized. Such challenging samples across various tasks can aid the detector in identifying crucial distinguishing features among different categories. + +As shown in Fig. 4, SCS mainly includes two aspects. On one hand, for those generated samples of previous tasks $\mathcal{D}_{\mathrm{gen - (1:t - 1)}}$ , a detector $\mathcal{M}_{s_t}$ trained using the current task dataset $\mathcal{D}_t$ alone which is expected to be capable of detecting new classes in the current task. This detector is then used to evaluate the inter-class similarity between new and old tasks. For each image in $\mathcal{D}_{\mathrm{gen - (1:t - 1)}}$ , we use $\mathcal{M}_{s_t}$ to make predictions, and we only retain detection boxes whose confidence scores exceed a threshold $\tau$ , + +$$ +B _ {\text {p r e d}} = \left\{b _ {k} \mid \operatorname {c o n f} \left(b _ {k}\right) \geq \tau \right\}, \tag {2} +$$ + +where $\mathrm{conf}(b_k)$ denotes the confidence score for the box $b_{k}$ . Then, we define the pseudo labels generated by $\mathcal{M}_{t - 1}$ as + +$$ +B _ {\text {p s e u d o}} = \left\{b _ {j} ^ {\text {p s e u d o}} \right\} \tag {3} +$$ + +We then calculate the minimum IoU between all labels in the two sets $B_{\text{pseudo}}$ and $B_{\text{pred}}$ , + +$$ +\operatorname {I o U} _ {\min } = \min _ {b _ {j} ^ {\text {p s e u d o}} \in B _ {\text {p s e u d o}}, b _ {k} \in B _ {\text {p r e d}}} \operatorname {I o U} \left(b _ {j} ^ {\text {p s e u d o}}, b _ {k}\right). \tag {4} +$$ + +If $\mathrm{IoU}_{\mathrm{min}}$ is greater than a threshold $\eta$ , then the image is deemed to contain a scene with significant similarity between new and old tasks. Such images are prioritized for replay data to effectively reduce the false positive rate on the new task, as the decision boundary between the confusing classes can be greatly enlarged with hard samples. + +On the other hand, to further mitigate the domain gap between the synthetic and real images, unlike traditional CIOD training which typically focuses on a single real image domain, our CIOD framework leverages a mixed-domain approach in each incremental stage $\mathcal{T}_t$ . Specifically, we not only synthesize and replay the data of $\mathcal{D}_{gen-(1:t-1)}$ but also synthesize a part of the data of $\mathcal{D}_{gen-t}$ and combine them with $\mathcal{D}_t$ together to update the detector. Because the old task data are dominated by synthetic data and the new task data are mainly real images, the model tends to be biased by the domain information, rather than the semantic differences between various categories. To improve multidomain adaptation, the integration of both synthetic and real data helps the model differentiate the unique characteristics of each domain, ensuring a robust transfer of knowledge across incremental tasks. + +![](images/19407e4072513aba533adfcbe2ce5e3124fa855daaa9f892223d1ac52843f8ce.jpg) +Figure 4. Similarity-based Cross-Sampling. By cross-filtering images using $\mathcal{M}_{s_i}$ and $\mathcal{M}_{t-1}$ , we ultimately obtain a set of images with high similarity between old and new tasks. + +# 3.5. Current Stage Training + +Pseudo Labeling on $\mathcal{D}_t$ . For the setting of CIOD, only the classes for current task are annotated, therefore the pseudo labeling on current task image data $\mathcal{D}_t$ with the old detector $\mathcal{M}_{t-1}$ is essential to address the missing annotation problem. Our research shows that the old detector $\mathcal{M}_{t-1}$ often correctly locate the objects while classify them with wrong labels when generating pseudo-labels. The wrong pseudo labels will hinder the learning of new classes and accelerate the forgetting of previously learned knowledge. To address this issue, we enhanced the standard pseudo-labeling approach by filtering out these misclassified pseudo-labels based on the ground truth for the new task. Specifically, for each pseudo-labeled bounding box $b_{\mathrm{pseudo}}$ produced by the previous model $\mathcal{M}_{t-1}$ , we compute its maximum IoU with all ground truth boxes $B_{\mathrm{GT}}$ in the image: + +$$ +\operatorname {I o U} \max \left(b _ {\text {p s e u d o}}, B _ {\mathrm {G T}}\right) = \max _ {b _ {\mathrm {g t}} \in B _ {\mathrm {G T}}} \operatorname {I o U} \left(b _ {\text {p s e u d o}}, b _ {\mathrm {g t}}\right) \tag {5} +$$ + +If $\mathrm{IoUmax}(b_{\mathrm{pseudo}}, B_{\mathrm{GT}}) > \gamma$ , where $\gamma$ is a hyperparameter (typically set to 0.5), we discard $b_{\mathrm{pseudo}}$ . This filtering step helps to reduce the negative effect of incorrect pseudolabels on learning new classes. + +Training Data and Loss Function. The synthetic image data for both old and new tasks $\mathcal{D}_{gen - (1:t - 1)}$ and $\mathcal{D}_{gen - (t)}$ are combined together with the real image data of current task $\mathcal{D}_t$ to serve as the training data of current stage learning. Nonetheless, the knowledge provided by synthetic data may not be so accurate, we also need to adjust the loss generated by synthetic images during model training. The overall loss $\mathcal{L}$ is computed as a weighted sum of the losses from synthesized data and real data: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s y n t h}} + \mathcal {L} _ {\text {r e a l}} \tag {6} +$$ + +$$ +\mathcal {L} _ {\text {s y n t h}} = \lambda_ {\text {r p n}} \mathcal {L} _ {\text {r p n}} ^ {\text {s y n t h}} + \lambda_ {\text {c l s}} \mathcal {L} _ {\text {c l s}} ^ {\text {s y n t h}} + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}} ^ {\text {s y n t h}} +$$ + +where $\lambda$ is a hyperparameter that adjusts the significance of the synthetic data $\lambda \in [0,1]$ in the loss function. Given that synthetic data often consists of simple single-instance + +Table 1. Comparison with state-of-the-art methods in single step incremental settings on PASCAL VOC 2007. We use **bold** to indicate the best results and **underline** to highlight the second-best results. The methods that adopt example-replay (rehearsal-based methods) are marked by * for fair comparison. Our method significantly outperforms the comparisons on all datasets. + +
Methods19-115-510-105-15
OldNewAllOldNewAllOldNewAllOldNewAll
Joint Training76.878.176.978.173.276.977.076.876.974.577.776.9
Fine-tuning10.269.813.212.949.922.25.963.934.90.073.054.7
ORE* [12]69.460.168.971.858.768.560.468.864.6---
ILOD-Meta* [13]70.957.670.271.755.967.868.464.366.3---
OW-DETR* [10]70.262.069.872.259.869.163.567.965.7---
ABR* [21]71.069.770.97365.171.071.272.872.064.771.069.4
Faster ILOD [27]68.961.168.571.656.967.969.854.562.162.037.143.3
PPAS [46]70.553.069.2---63.560.061.8---
MVC [40]70.260.669.769.457.966.566.266.066.1---
MMA [5]71.163.470.77360.569.969.363.966.666.857.259.6
PseudoRM [42]72.967.372.673.460.970.369.168.668.9---
PROB [49]73.948.572.673.560.870.166.067.266.5---
BPF [26]74.565.374.175.963.072.771.774.072.966.475.373
RGR(Ours)75.867.275.475.669.074.075.476.375.869.877.275.3
+ +Table 2. Comparison with state-of-the-art methods in multiple step incremental settings on PASCAL VOC 2007. The methods that adopt example-replay (rehearsal-based methods) are marked by * for fair comparison. + +
Methods10-5(3 tasks)5-5(4 tasks)10-2(6 tasks)15-1(6 tasks)
1-1011-201-201-56-201-201-1011-201-201-1515-201-20
Joint Training77.076.876.974.577.776.977.076.876.978.173.276.9
Fine-tuning5.442.123.70.017.613.23.615.49.50.06.72.2
ABR* [21]68.767.067.964.756.458.467.058.162.668.756.765.7
Faster ILOD [27]68.357.963.155.716.025.964.248.656.466.944.561.3
MMA [5]66.761.864.262.331.238.965.053.159.168.354.364.1
BPF [26]69.168.268.760.663.162.568.756.362.571.553.166.9
RGR(Ours)71.971.771.861.271.168.668.562.765.672.058.168.6
+ +images, such data may not provide sufficient regression knowledge. Because this knowledge will not be greatly forgotten as Fig. 1 shows, the real image data are enough to gradually enhance the localization ability. Therefore, we assign a relatively larger weight tocls in the loss computation. + +# 4. Experiments + +# 4.1. Experiment Setup + +Datasets. To evaluate our proposed approach, we utilize the MS COCO 2017 [19] and PASCAL VOC 2007 [7] datasets, adhering to experimental protocols established in prior studies [5, 21, 26, 40, 42, 49]. Each training task includes only images relevant to the specific task category, and non-relevant category annotations are excluded. This + +configuration is both practical and accommodates possible image repetition across tasks. The PASCAL VOC 2007 dataset covers 20 object classes with a total of 9,963 images, equally split into training and validation (50% each) and testing (50%). Conversely, the more intricate MS COCO 2017 dataset comprises 80 object classes, providing 118k images for training and 5,000 for validation. + +Metrics. Our proposed method is assessed using mean average precision (mAP) at a 0.5 IoU threshold on the PASCAL VOC 2007 dataset. Meanwhile, for the MS COCO 2017 dataset, we apply the standard COCO metrics, which involve evaluating performance across multiple IoU thresholds ranging from 0.5 to 0.95 (mAP[50:95]), along with specific evaluations at 0.5 IoU (mAP[50]) and 0.75 IoU (mAP[75]). + +Implementation Details. In line with the experimental + +Table 3. Comparison with state-of-the-art methods in single step incremental settings on MS COCO 2017. The methods that adopt example-replay (rehearsal-based methods) are marked by * for fair comparison. + +
Methods40+4070+10
AP\( AP_{50} \)\( AP_{75} \)AP\( AP_{50} \)\( AP_{75} \)
Joint Training40.261.643.540.261.643.5
Fine-tuning21.633.423.15.68.66.2
ILOD-Meta*23.840.524.4---
ABR*34.557.835.231.152.932.7
Faster ILOD20.640.1-21.339.9-
PseudoRM25.344.4----
MMA33.056.634.630.252.131.5
BPF34.454.337.336.256.838.9
RGR(Ours)35.656.038.236.656.639.6
+ +procedures outlined in prior studies [21, 26], our approach expands upon the Faster R-CNN [28] framework using a ResNet-50 [11] backbone that has been pretrained on ImageNet. The detector is trained with the SGD optimizer, using a batch size of 8. The initial learning rates are set to 0.01 for the base task and 0.005 for incremental tasks. We assess the methods based on mean average precision at a 0.5 IoU threshold on the PASCAL VOC 2007 benchmark. The deployed diffusion model, Stable Diffusion 1.5, is fine-tuned on the COCO dataset for experiments on the VOC dataset and fine-tuned on the VOC dataset for experiments on the COCO dataset to better align with the real image style. + +# 4.2. Comparison with state-of-the-art method + +In order to ensure a fair comparison with prior studies, we assess the performance of our proposed approach under both single-step and multi-step incremental settings. We compare our approach against two baseline methods: Finetuning, which involves incrementally training the model without regularization or data replay, and Joint training, where the model is trained on the complete dataset with all annotations accessible. The results are presented after the training on the ultimate task is completed. + +# 4.2.1. On PASCAL VOC 2007. + +Our experiments adhered to established protocols from previous studies, employing consistent class increment configurations such as the 19-1, 15-5, 10-10, and 5-15 settings, with a predetermined class sequence for PASCAL VOC 2007 over two incremental phases. In multi-step incremental settings, we assessed the configurations of 10-5, 5-5, 10-2 and 15-1 sequentially adding 5, 5, 2 and 1 classes per step, to eventually encompass all 20 classes. + +Two Incremental Phase Setting. Tab. 1 illustrates that + +our approach, denoted as RGR, consistently outperforms the state-of-the-art BPF [26] and other comparison methods across various incremental settings. In particular, RGR achieves notable improvements in mean Average Precision (mAP) over BPF, with increases of $1.3\%$ , $1.3\%$ , $2.9\%$ , and $2.3\%$ observed in the 19-1, 15-5, 10-10, and 5-15 settings, respectively. Importantly, RGR sustains high performance on both old and new classes, underscoring its ability to effectively mitigate catastrophic forgetting while ensuring strong learning of new classes. + +Multi Incremental Phase Setting. The challenge of managing long-term CIOD is notable, as maintaining a balance between model stability and adaptability becomes increasingly difficult with the accumulation of tasks. According to Tab. 2 for PASCAL VOC 2007, our proposed RGR, offers distinct advantages across all multi-step configurations. In particular, RGR achieves mAP improvements of $3.1\%$ , $6.1\%$ , $3.1\%$ , and $1.7\%$ under the $10 + 5$ , $5 + 5$ , $10 + 2$ , and $15 + 1$ settings, respectively, consistently outperforming other methods. Traditional methods face challenges with increased forgetting during multiple incremental phases and the forgetting is often mitigated by decreasing the learning rate or applying strong regularization. While this strategy helps retain existing knowledge, it limits the acquisition of new class information, making these classes vulnerable to further forgetting in subsequent phases, and ultimately hampering generalization across all tasks. As the task increases, a significant drop in generalization performance is observed. Conversely, our RGR approach enables the model to maintain its flexibility while effectively learning new classes. As demonstrated in Tab. 2, RGR achieves mAP improvements of $3.5\%$ , $8.0\%$ , $6.4\%$ , and $5.0\%$ with the addition of new classes in the $10 + 5$ , $5 + 5$ , $10 + 2$ and $15 + 1$ settings. + +# 4.2.2. On MS COCO 2017. + +Using the MS COCO 2017 dataset, we exhibit performance results for the incremental configurations 40-40 and 70-10 as documented in earlier studies [15, 26]. Tab. 3 illustrates that our method (RGR) outperforms the current best BPF by $1.2\%$ in AP, $1.7\%$ in AP50, and $0.9\%$ in AP75. Moreover, for the $70 + 10$ configuration, our method exceeds BPF by $0.4\%$ in AP, and $0.7\%$ in AP75. These results also demonstrate the superiority of our method. + +# 4.3. Ablation Study + +Main components. We evaluate the effectiveness of each component in our proposed method on the PASCAL VOC 2007 dataset under the 10-10, 5-15, and 15-5 incremental settings. The baseline model uses only the pseudo-labeling method, following BPF, and we sequentially add components of our proposed approach. As shown in Tab. 4, adding the IGR component results in significant improvements in mAP across all classes, with gains of $1.4\%$ , $6.5\%$ , and + +Table 4. Investigation on the effectiveness of the main components in our method. + +
ModelIGRSCSVOC(10-10)VOC(15-5)VOC(10-5)
1-1011-201-201-1515-201-201-1011-1516-20
(a)XX72.075.573.770.658.667.358.873.950.2
(b)✓X74.975.375.175.668.473.871.677.663.9
(c)✓✓75.476.375.875.669.074.071.977.166.3
+ +Table 5. Ablation experiments for $\tau$ in IGR under VOC 10-10 and VOC 10-5 settings. + +
τVOC(10-10)VOC(10-5)
OldNewAll1-1011-201-20
0.5074.276.075.170.871.271.0
0.8075.076.475.771.671.671.6
0.9075.476.375.871.971.771.8
0.9574.876.075.471.871.671.7
+ +Table 6. Ablation experiments for $\eta$ in SCS under VOC 10-10 and VOC 10-5 settings. + +
ηVOC(10-10)VOC(10-5)
OldNewAll1-1011-201-20
0.474.675.775.171.471.071.2
0.675.476.375.872.071.471.7
0.875.176.475.771.971.771.8
0.974.875.875.371.171.671.3
+ +$10.8\%$ for the 10-10, 15-5, and 10-5 settings, respectively. When we further add the SCS component, the performance improves even more, with additional gains of $0.7\%$ , $0.2\%$ , and $0.6\%$ across all classes for each of the 10-10, 15-5, and 10-5 settings. Notably, the SCS component not only mitigates forgetting effectively but also improves the model's plasticity, enhancing its ability to learn new tasks without losing performance on old ones. In Fig. 5, we also present the mAP for each category in the 5-5 (4 tasks) setting. It can be observed that SCS effectively mitigates forgetting for certain similar categories (e.g. "dog" and "cat", "bus" and "train", etc.). These results validate the contributions of each component in alleviating forgetting and boosting performance on new tasks, highlighting the overall effectiveness of our approach. + +Impact of hyper-parameter $\tau$ and $\eta$ . The hyperparameter $\tau$ in Eq.(1) is introduced to be a threshold to sample images generated by Stable Diffusion, ensuring high-quality generated images for training. As shown in Tab. 5, the model performance improves as $\tau$ increases, reaching the best results when $\tau = 0.90$ . The parameter $\eta$ represents the IoU threshold for cross-sampling, measuring the similarity of images between tasks. As shown in the Tab. 6, the best performance is achieved when replaying images with moderate similarity. + +![](images/1e71b41e7ce2f2bca8ed11f47dcd5bfc154565c1eabd1c628737fa6adce64630.jpg) +Figure 5. Comparison of mAP on each category between IGR and IGR+SCS in the 5-5 (4 tasks) setting of the VOC dataset. + +# 5. Conclusions + +In this paper, we suggest revisiting generative replay using an existing Stable Diffusion model rather than enhancing the generative model to precisely control the generation of complex scenarios with multi-class instances or iteratively refining with images from previous tasks for class incremental object detection. Our approach synthesizes replay data at the image level, focusing mainly on a single object per image for both past and present tasks, aiming to preserve acquired knowledge and bridge the domain gap between generated and real images. We propose to employ the Similarity-based Cross Sampling method to sift through and pinpoint more difficult samples across both old and new tasks, which substantially reduces false alarms for the new task while effectively retaining the previously acquired knowledge. Extensive experiments are conducted on the PASCAL VOC and MS COCO datasets under multiple settings, and our proposed approach achieves state-of-the-art results compared to other methods. + +# Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 62101453, 62476223, 62201467, 62476226; in part by Innovation Capability Support Program of Shaanxi (Program No. 2024ZC-KJXX-043); in part by the Young Talent Fund of Xi'an Association for Science and Technology under Grant 959202313088. + +# References + +[1] C. Liu X. Hong Y. Zhou. A. Zhang, D. Yang. Specifying what you know or not for multi-label class-incremental learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 2025. 2 +[2] Manoj Acharya, Tyler L Hayes, and Christopher Kanan. Rodeo: Replay for online object detection. arXiv preprint arXiv:2008.06439, 2020. 3 +[3] Ali Ayub and Alan R Wagner. 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While SSL has revolutionized fields like natural language processing and computer vision, its adoption in 3D medical image computing has been limited by three key pitfalls: Small pre-training dataset sizes, architectures inadequate for 3D medical image analysis, and insufficient evaluation practices. In this paper, we address these issues by i) leveraging a large-scale dataset of 39k 3D brain MRI volumes and ii) using a Residual Encoder U-Net architecture within the state-of-the-art nnU-Net framework. iii) A robust development framework, incorporating 5 development and 8 testing brain MRI segmentation datasets, allowed performance-driven design decisions to optimize the simple concept of Masked Auto Encoders (MAEs) for 3D CNNs. The resulting model not only surpasses previous SSL methods but also outperforms the strong nnU-Net baseline by an average of approximately 3 Dice points setting a new state-of-the-art. Our code and models are made available here. + +# 1. Introduction + +In recent years, the concept of Self-Supervised Learning (SSL) has emerged as a driving factor in data-rich domains, enabling large-scale pre-training that facilitates the learning of robust and transferable general-purpose representations [2, 16, 28]. This paradigm shift has been instrumental in advancing various fields, particularly in domains with + +![](images/4f604edb099937a96a5d26d501fcc3dcf1416bede22af93f3eb7790f45567ade.jpg) +Figure 1. Well-configured MAE pre-training for CNNs is state-of-the-art. When comparing our MAE pre-trained model on all eleven test Datasets, Spark3D achieves almost +3 DSC points compared to the strong nnU-Net baseline and outperforms current SSL methods. + +abundant labeled data like NLP or natural vision. In the domain of 3D medical image computing, this trend has not caught on. Currently, the domain is either focused on training from-scratch, mainly using the nnU-Net framework by Isensee et al. [20], or using supervised pre-training, which is limited by the cost associated with annotated data [19, 38, 44]. The usage of supervised pre-training implies the willingness of the domain to adopt pre-training and calls to question the currently established SSL methods in the domain. We believe this lack of widespread adoption of previously established methods can be attributed to three major pitfalls of previous SSL research in this field: + +P1 - Limited dataset size: Many SSL approaches have been developed on very few unlabeled volumes, often being trained on fewer than 10,000 images [3, 13, 14, 33, 34, + +46, 48, 49], almost approaching scales of supervised dataset sizes. These datasets tend to be pooled from publicly available annotated datasets, as larger datasets pose a greater hurdle to acquire. While many hospitals possess 3D medical images in the millions, they are locked away from the public due to patient privacy concerns. Some larger open-source datasets exist, e.g., the Adolescent Brain Cognitive Development (ABCD) dataset of the NIH $(\mathrm{N} = 40\mathrm{k})$ [27] or the UK Biobank dataset $(\mathrm{N} = 120\mathrm{k})$ , but they restrict access pending an internal review board's approval, posing a hurdle for open science. + +P2 - Outdated Backbones: Many studies develop their SSL method on non-state-of-the-art architectures, e.g., utilizing transformers [3, 6, 13, 34, 43, 46]. While transformers are prevalent in the 2D natural imaging domain [9], recent architectures leveraging attention [40] have so far not been able to reach state-of-the-art performance in 3D medical segmentation. In fact, well-configured 3D U-Net [7, 30] inspired CNNs dominate 3D medical image segmentation, outperforming transformer-based models by a large margin [21]. This underscores the need for SSL methods that can be seamlessly integrated with CNNs to harness their full potential in medical image analysis on downstream tasks. + +P3 - Insufficient Evaluation: Existing methods often lack rigorous evaluation, masking the methods' efficacy. This is represented through: i) Evaluating too few datasets to show generalization of the pre-training [3, 39] ii) Stacking multiple contributions, e.g., novel architecture with new pre-training, which does not allow one to draw conclusions if the pre-training is effective without the architecture [43] iii) Comparing to bad from-scratch baselines, like a badly configured, outdated Cicek et al. [7] UNet instead of a well-configured 3D nnU-Net CNN baseline [20]. iv) Evaluating their method on seen data they pre-trained on. We want to emphasize that we do not intend to point fingers, but to raise awareness that evaluation matters and insufficient evaluation can lead to a lack of clarity which methods are the best. This observation is similar to the recent study by Isensee et al. [21], which shows that this is also prevalent in the field of medical image segmentation when training from scratch. + +In this paper, we explore the Masked Auto Encoder (MAE) paradigm for 3D CNNs, with the recent adaptations introduced by Tian et al. [35], Woo et al. [45]. Our approach addresses the key pitfalls of previous SSL research in 3D medical image segmentation, ensuring broader applicability and higher performance. Our main contributions are as follows: + +1. State-of-the-Art Performance: Our final model achieves superior performance compared to existing SSL-pre-trained models using the same architecture and pre-training dataset, see Fig. 1. Notably, this is the first work to demonstrate that SSL pre-training with a + +Table 1. Current SSL methods are limited by three pitfalls: They are trained on less than 10K 3D images (P1), they do not use a state-of-the-art backbone for 3D image segmentation as recommended by Isensee et al. [21] (P2) or they do not evaluate their method on more than 4 downstream datasets (P3). $\boxed{\checkmark}$ indicates evading a pitfall while $\boxtimes$ indicates falling for a pitfall. + +
MethodYearP1 DataP2 ModelP3 Eval.
3DMAE [6]Jan. 2023✘✘✘
GL-MAE [49]Aug. 2023✘✘✓
MAPSeg [47]March 2023✘✘✘
HySparK [33]Aug. 2024✘✓✓
AMAES [25]Aug. 2024✓✓✘
Swin UNETR [34]March 2022✘✘✓
VoCo [46]April 2024✘✘✓
VF [43]June 2023✓✘✘
MG [48]Aug. 2019✘✘✓
GVSL [17]March 2023✘✘✓
S3D (ours)✓✓✓
+ +fixed architecture can consistently outperform a state-of-the-art, dynamically optimized nnU-Net baseline by approximately 3 Dice points across 11 diverse downstream datasets [20]. + +2. Comprehensive Evaluation Addressing Previous Pitfalls: Building on the detailed analysis of limitations in prior work (see Tab. 1), we set up a robust development environment to design our method. (i) P1: We utilize a collection of $39\mathrm{k}$ 3D MRI volumes for self-supervised pre-training, substantially larger than most datasets used in prior SSL work [14, 33, 34, 39, 46, 48, 49]. (ii) P2: By using the state-of-the-art Residual Encoder U-Net CNN architecture [21], we bypass the limitations of outdated or transformer-based architectures, leveraging CNNs' superior performance in 3D medical segmentation. (iii) P3: We rigorously evaluate our model across five development and eight testing datasets, covering a wide range of downstream tasks, diverse pathologies, novel image modalities, and multi-center datasets. Moreover, we disentangle the pre-training methodology from other contributions like novel backbones and include the strong 3D nnU-Net baseline, ensuring reliable results. +3. In-Depth Ablation Studies: We provide detailed analyses of critical design decisions, such as masking ratio, sparsification, and fine-tuning strategies. Additional ablations explore generalization, low-data performance, and faster fine-tuning, offering valuable insights. + +While the fundamental concept of an MAE is not novel, its application in 3D medical image analysis has yet to be + +fully validated due to limitations in previous studies, which we illustrate in Tab. 1. Our carefully designed experiments close these gaps and reveal MAEs true potential. + +# 2. Development Framework + +The goal of this paper is to develop a robust SSL pretraining method. Due to the limited prior work in the 3D medical domain, many design choices need to be made. We address this by sequentially validating each methodological contribution on five downstream development datasets before testing the final configuration on eight untouched test datasets. To reduce the search space and disentangle the effects of SSL pre-training from other basic design choices, we choose to keep some parameters fixed based on best practices in the domain: + +(i) The architecture used is always the same state-of-the-art residual encoder U-Net architecture (ResEnc U-Net) [21, 38]. (ii) The input patch size is set to $[160 \times 160 \times 160]$ . (iii) All images are resampled to the same target spacing of $[1 \times 1 \times 1] \mathrm{mm}$ [31]. (iv) All images are z-score normalized to zero mean and unit variance [20]. (v) As optimizer, we use SGD with a decreasing poly-learning rate [5] following nnU-Net [20]. (vi) We always employ random sampling during pre-training, irrespective of the prevalence of the different MR modalities. + +Pre-training Dataset To develop our pre-training method, we utilize a proprietary brain MRI dataset sourced from over 44 centers containing over 9k patients comprising a total of approx. 44k 3D MRI scans. Due to the variety of data sources, this dataset contains images from more than 10 different MR scanners, various MR modalities and a diverse patient population. For more details on the distributions, we refer to Figure 3. + +Since this data is sourced directly from clinical examinations, it includes empty or broken images, poor-quality images and so-called scout scans used to determine the field of view of the patient in the MR. Since these scans are not used in diagnostics, these images are filtered by discarding (a) images with a field of view of $< 50mm$ in any axis, (b) images with a spacing $>6.5mm$ in any direction and (c) images of file size $< 200kb$ , which indicate an empty image. Moreover due to the low quantity of MR Angiography, Susceptibility weighted Images (SWI) and Proton Density (PD) weighted images, we restrict our training data to only include T1, T2, T1 FLAIR and T2 FLAIR images, resulting in our final pre-training dataset of 39,168 MR images. + +Development Datasets After pre-training we fine-tune on five datasets and calculate the average Dice Similarity Coefficient (DSC) per dataset to evaluate the effectiveness of + +the pre-training. The multiple datasets are essential to ensure that our design choices do not overfit to a specific MRI modality or pathological target. Specifically, we utilize: + +1. MS FLAIR (D1): Consensus delineations of multiple sclerosis (MS) lesions on T2-weighted FLAIR images [26]. +2. Brain Mets (D2): Brain metastases imaged through T1, contrast enhanced gradient echo T1ce, contrast enhanced spin echo T1 and a T2 FLAIR sequence acquired in the Stanford University Hospital [12]. +3. Hippocampus (D3): The Hippocampus dataset, task 4 of the medical segmentation decathlon (MSD) [1], contains delineations of the anterior and posterior Hippocampus in T1 weighted MRI [32]. +4. Atlas22 (D4): Anatomical Tracings of Lesions After Stroke (ATLAS) on T1 weighted images. We use the Atlas R2.0 dataset from Liew et al. [24]. +5. CrossModa (D5): Delineations of intra-meatal and extra-meatal vestibular schwannoma tumors and cochlea delineations in contrast-enhanced T1 weighted MRI [8]. Of all these datasets, we set aside a hold-out test set comprising $20\%$ of all images before the start of the method development process. The remaining images were split 80/20 into training and validation sets for the development process. + +Test Datasets Additionally, eight hold-out test datasets were used to evaluate the efficacy of our learned representations when fine-tuning them to segment other target structures. + +1. Cosmos (D6): This dataset features carotid vessel wall segmentation and atherosclerosis diagnosis, of which we use the contours to evaluate segmentation performance [4]. +2. HaNSeg (D7): This dataset contains segmentations of 30 organs at risk (OAR), with associated T1 MRI and CT, of which we only use the MR images for model development [29]. +3. Isles22 (D8): This dataset contains annotations of ischemic stroke lesions, with associated diffusion-weighted imaging (DWI), apparent diffusion coefficient (ADC) and T2 FLAIR [18]. +4. HNTS-MRG24 (D9): T2-weighted MR images of pretreatment oropharyngeal cancer and metastatic lymph nodes with associated annotations [42]. +5. BraTS Africa (D10): This dataset contains 1.5 Tesla T1, T1ce, T2, and T2 FLAIR MRIs of glioblastoma and high-grade gliomas imaged in Nigeria. +6. T2 Aneurysms (D11): This proprietary dataset contains 240 T2 MRI images of segmented brain aneurysms with the surrounding brain tissue. +7. TOF Angiography Aneurysms (D12): This proprietary dataset contains 144 time-of-flight MR-angiography im + +ages of segmented brain aneurysms with the surrounding brain tissue. + +8. BraTS Mets (D13): This dataset holds brain metastases segmentations on T1ce MRIs, similar to D2. However, instead of fine-tuning on it we use it to measure generalization when inferring models trained on D2 on it. + +For test datasets $D6 - D12$ we use an 80/20 split for fine-tuning and for testing. A validation set is omitted as we fine-tune each method only once without any interventions. For $D13$ all data is used for testing, as no training is conducted. $D12$ and $D13$ are only used to assess generalization performance, with $D13$ only appearing in Appendix Tab. 9. + +# 3. Related Work + +In this section, we revisit currently established MAE pretraining paradigms. Then, we survey existing MAE pretraining paradigms in the 3D medical domain, before expanding this to a broader set of pre-training paradigms for 3D medical image segmentation. + +# 3.1. Masked Autoencoders + +Auto-encoders have been established for a long time through the early pioneering works of Vincent et al. [41] but recently garnered significant attention through He et al. [16], showing that a simple MAE pre-training paradigm is scalable and provides substantial performance improvements. Subsequently, follow-up works extended these findings to video data [10, 37] as well as language-image data [23]. These earlier successes primarily relied on Transformer architectures, as their sequence modeling offered significant VRAM savings. CNNs on the other hand are less suited to such a pre-training paradigm as masking disrupts the 2D data-structure they compute on. Despite this Woo et al. [45] and Tian et al. [35] were able to extend MAE pre-training successfully to CNNs. Woo et al. [45] introduced their fully convolutional masked autoencoder (FCMAE) framework, while Tian et al. [35] introduced adaptations to the convolution computation and normalization to make it resilient to masking. + +# 3.2. Masked Autoencoder In 3D Medical + +The earliest work using autoencoders for self-supervised pre-training in the medical domain was Models Genesis (MG) conducted by Zhou et al. [48] in 2019. They introduced reconstruction of in-painting, out-painting, and denoising of local intensity shifts as their pre-training task. Many approaches followed, with Swin UNETR by Tang et al. [34] proposing a joint in-painting, rotation, and contrastive objective for Swin Transformer pre-training. Chen et al. [6] proposed a basic masking and reconstruction strategy applied to 3D Vision Transformers (ViT) [9] termed (3DMAE) and Zhuang et al. [49] proposed to use a combination of masked global and local views in conjunction with + +a reconstruction and consistency loss to pre-train 3D ViTs, named GL-MAE. MAPSeg by Zhang et al. [47] combines a masked autoencoder objective and pseudo-labeling to address domain shifts in a federated setting. More recently, in concurrent work, Munk et al. [25] proposed pre-training CNNs with a vanilla masking and reconstruction objective without any adaptations on a large brain dataset (AMAES) and Tang et al. [33] presented a sparse MAE with reconstruction objective pre-trained on abdomen CT data (HySparK). + +# 3.3. Other Pre-Training For 3D Medical + +Additionally, self-supervised learning approaches for 3D medical images include Zhuang et al. [50], who introduced a training objective aimed at recovering the orientation and rotation of shuffled and rotated sub-volumes, inspired by a Rubik's cube. Wang et al. [43] proposed a method that involves mixing two images at varying patch rates and predicting the mixing categories via a segmentation objective, termed Volume Fusion (VF). Geometric Visual Similarity Learning (GVSL) of He et al. [17] leveraged anatomical consistency by learning to register two images of the same field of view and using local similarity as a training objective. More recently, Wu et al. [46] suggested partitioning a volume into non-overlapping base-crops and generating additional overlapping sub-crops, with a training objective to predict the degree of overlap between sub-crops and base-crops (VoCo). + +# 4. Revisiting 3D MAEs + +Masked autoencoders (MAEs) are a well-established pretraining paradigm in the natural imaging domain and in the medical image segmentation domain for transformers. In this section, we investigate this paradigm and optimize it for 3D medical image segmentation using a ResEnc U-Net architecture of Isensee et al. [21]. + +Default parameters MAEs are trained by masking an input image to a certain degree and training the network to reconstruct the occluded regions, minimizing deviations between reconstruction and the original image. In our experiments, we train the MAE with an L2-Loss in the z-score normalized voxel space and only calculate the reconstruction loss where regions were masked. Moreover, we do not remove skip-connections, following the general consensus of Woo et al. [45], Tian et al. [35], and He et al. [16]. The default hyperparameters (as used by the model denoted in gray in Tab. 2) are learning rate 1e-2, weight decay 3e-5, batch size 6, SGD optimizer with Nesterov momentum 0.99, masking ratio of $75\%$ trained with a PolyLR schedule for 250k steps (this represent 1000 epochs in the nnU-Net framework) and minor spatial augmentations of affine scaling, rotation and mirroring. + +Table 2. Development Experiments: During development, we evaluate the Average DSC on all development datasets to quantify the best configuration. Methods of the same configuration are denoted through common colors. +(a) Sparsification: The introduction of all sparsification components showed the best results, with most improvements coming from adding the additional densification conv layer between encoder and decoder. + +
ConfigurationD1D2D3D4D5Avg. D1-D5
Base49.9672.6289.0363.4581.6771.35
+ Sparse Conv. + BN.50.3473.3488.9162.9681.2571.36
+ w/ Mask Token50.0273.2188.9262.8481.8371.37
+ w/ Dens. Conv.51.0274.0788.9162.8181.5071.66
+ +(b) Masking ratio: Masking ratios between $60\%$ and $75\%$ worked best when choosing static ratios. However, a dynamic range, including higher masking ratios, performs similarly and was chosen. + +
Mask ratioD1D2D3D4D5Avg. D1-D5
30 %50.2571.3788.9063.1881.7071.08
45 %50.6070.8388.9763.2781.7371.08
60 %50.6273.5688.9663.3781.4871.60
75 %51.0274.0788.9162.8181.5071.66
90 %50.5672.5188.9862.4181.4971.19
U[60%-90%]51.4974.0188.8362.3981.5471.65
+ +(c) Development performance: When comparing our final S3D model against the baseline methods, trained equally, S3D exceeds all baselines on the development datasets. + +
Pre-trainingD1D2D3D4D5Avg. D1-D5
No Dyn.45.5672.2688.8060.4482.6169.93
No Fixed49.3769.1388.7860.7481.3369.87
VoCo50.3567.2088.2257.8280.2968.77
VF49.9369.5888.8361.7581.4870.31
MG50.5071.1488.8363.2982.1571.18
S3D (ours)51.4974.0188.8362.3981.5471.65
+ +Sparsification When masking the input image, CNNs are not able to ignore the masked regions in the same manner as transformers can. To address this, Tian et al. [35] proposed to adapt the CNN architectures to better fit the sparse inputs: (a) Sparse Convolutions and Normalization: Through the receptive field of convolutions masked-out regions are iteratively eroded from their boundaries. By re-applying the masked regions after every convolution this problem can be resolved. Moreover, the masks can introduce a problematic shift in the normalization layer statistics due to the introduced zero values. To resolve this normalization is constrained to only consider the non-masked values. (b) Mask Token: Instead of feeding the light-weight decoder feature maps with zeroed mask regions, the regions are densified by filling them with a learnable mask token, simplifying the reconstruction task of the decoder. (c) Densification Convolution: After filling the masks with the Mask Token and before passing the feature maps to the decoder, a $[3x3x3]$ convolution is applied to the feature maps at every resolution except the highest resolution to prepare the representations for decoding. + +Results of these changes are visualized in Tab. 2a. The + +adaptations are introduced iteratively, meaning the 'Mask-Token' ablation is only applied together with the Sparse Convolutions and Normalization. It can be observed that the full set of adaptations improves performance by an average of 0.3 DSC points across our development datasets. Subsequently, all adaptations are kept and the following evaluations are presented with these changes applied. + +Masking strategy The masked region is determined by sampling randomly in the CNN's bottleneck of shape $[5 \times 5 \times 5]$ and up-sampling these regions to the input resolution, to ensure the masks align in the bottleneck of the CNN architectures. This results in masking regions of $[32 \times 32 \times 32]$ voxels of non-overlapping regions in the input. As a sampling strategy, we follow random masking, as previous work showed no benefit of structured masking for images nor videos [10, 16]. In the scope of the development phase, we explore 5 static masking ratios between $30\%$ and $90\%$ and evaluate a dynamic masking ratio randomly masking between $60\%$ and $90\%$ . + +Results are presented in Tab. 2b and highlight that the masking ratios of $60\%$ , $75\%$ , and the dynamic masking ratio of $60\%$ to $90\%$ perform equally well. Due to the highly similar performance, we choose to proceed with a dynamic masking ratio over the static masking ratio, due to expecting this masking to be more difficult to learn. We refer to this model as Spark3D (S3D) going forward. + +Fine-tuning strategy Given a pre-trained model, a crucial question arises: Which weights to transfer and how to schedule the fine-tuning? We investigated various different schedules, with all of them implemented in the nnU-Net framework [20]. Regarding weight transfer we investigated transferring (i) both the encoder and decoder $\triangleright$ , or (ii) only the encoder $\triangleright$ with a randomly initialized decoder. Regarding the fine-tuning schedule, we investigate whether to use a learning rate warm-up of 12.5k steps, ramping the learning rate up to the maximum LR. When only transferring the encoder, an additional warm-up of only the decoder is investigated to adapt the randomly initialized decoder to the pre-trained encoder. In some configurations, this results in two learning rate warm-ups of 12.5k steps each. Additionally, we investigate whether to keep the encoder frozen $\triangleright$ for the entire fine-tuning process or to fine-tune the encoder weights as well. Lastly, we investigate whether to decrease the peak learning rate to 1e-3, 1e-4 or to keep it at the default of 1e-2. + +Results are presented in Table 3 and allow three important observations to be made: (i) Warm-up stages are essential: Not applying a warm-up step significantly reduces performance. Including a warm-up for both the encoder and decoder boosts accuracy by 0.6 to 1 DSC points. (ii) Learning rate adjustments matter: Reducing the peak learning + +Table 3. Fine-tuning matters. We compare various combinations of weight transfer and fine-tuning schedules. Transfer: □ Transfer all weights, □ Transfer encoder weights only. Warm-Up and Fine-tuning: □ Only decoder weights adapted during fine-tuning, □ Encoder and decoder weights adapted during fine-tuning. ‡: nnU-Net default (Dynamic planning.) + +
Transfer1. Warm-Up2. Warm-UpFine-tuningMax. LRD1D2D3D4D5Avg
◇--◇1e-245.5672.2688.8060.4482.6169.93‡
◇--◇1e-249.3769.1388.7860.7481.3369.87
◇--◇1e-250.3770.6488.6161.5181.9170.61
◇--◇1e-349.9871.0488.6861.4582.1270.65
◇-◇◇1e-249.8472.5688.4562.1681.7570.95
◇-◇◇1e-351.5472.7488.8562.4482.3371.58
◇-◇◇1e-450.6672.9888.6862.7382.0971.43
◇--◇1e-250.8168.5588.5260.7380.7769.87
◇--◇1e-350.1173.9088.5861.8281.4871.18
◇-◇◇1e-251.3972.0688.6561.7081.7871.12
◇-◇◇1e-351.0472.7288.9162.8481.1971.34
◇◇◇◇1e-248.8172.9288.8462.4682.0471.02
◇◇◇◇1e-351.4272.8489.0963.3082.1571.76
◇◇◇◇1e-450.1372.2688.7261.7081.9370.95
+ +rate to 1e-3 during fine-tuning consistently yields better results than the default 1e-2, with the best performance seen when fine-tuning both the encoder and decoder with lower learning rates. (iii) Freezing encoder weights is detrimental: The encoder should not remain fixed during fine-tuning. Allowing the encoder to be fine-tuned improves the model's performance compared to when only the decoder is fine-tuned. + +# 5. Results and Discussion + +We compare our final model S3D against Volume Contrastive (VoCo) [46], VolumeFusion (VF) [43], as well as Models Genesis (MG) [48]. The baselines are pre-trained for 250k steps using the same framework on the same data with the same backbone and the same hyperparameters (where possible) but scaled to fully utilize an A100 40GB GPU. We provide explicit baseline methods and configuration details in Appendix A. Moreover, we compare against two strong from-scratch baselines. The first, No (Dyn.), represents a from scratch default nnU-Net 3D architecture that was planned and preprocessed on each downstream dataset individually, potentially resulting in different architectures, data preprocessing, and spacings. The second from-scratch baseline, No (Fixed), is a nnU-Net training with the same plans and pre-processing as defined by our pre-training. The dataset-wise mean dice similarity coefficient (DSC) and mean normalized surface distance (NSD) at $2\mathrm{mm}$ tolerance values across our test dataset suite are provided in Tab. 4. Additionally, the ranking stability is evaluated through bootstrapping and is provided in Fig. 2. + +# 5.1. Observations + +SSL pre-training works Across all tested datasets, SSL pre-trained methods demonstrate improved downstream segmentation performance. Comparing our S3D method to the most similar from-scratch baseline No (Fixed), we observe higher DSC scores in 10 out of 11 test datasets, with an average increase of $+2$ DSC points and $+1.6$ NSD points. This improvement is not limited to our method; MG and VF also achieve higher performance than the baseline, indicating the utility of SSL methods when applied to sufficient data and a state-of-the-art architecture. + +MAEs dominate Throughout our test dataset pool, SSL schemes using the masked image modeling paradigm (MG and S3D) consistently rank higher than the contrastive VoCo or the pseudo-segmentation-based VolumeFusion pre-training method for CNN pre-training. Given the age of Models Genesis - published in 2019 - it is surprising to see it outperform the more recent VoCo or VF. We attribute this to a combination of two factors: 1. Models Genesis was originally published and trained on an outdated 3D-UNet [7] and outside of the powerful nnU-Net framework [20]. This highlights the importance of avoiding Pitfall 2: Training on a state-of-the-art backbone. 2. VoCo and VF were introduced in conjunction with architectures they were optimized for. By transferring them to a CNN setting, hyperparameters chosen to optimize the method for their original architecture pre-training combination may be suboptimal for the new CNN backbone. + +Table 4. S3D out-performs all baselines: The upper table presents the DSC results, while the lower table displays the NSD results across the test datasets, covering a diverse range of brain MRI tasks. No Fixed represents a from-scratch baseline sharing the same architecture, preprocessing and downstream training steps as all SSL methods. No Dyn. represents the original nnU-Net adapted to each downstream dataset individually. + +
SSL MethodNo (Dyn.)No (Fix.)VoCoVFMGS3D
DatasetDice Similarity Coefficient (DSC)
MS FLAIR (D1)57.8159.8259.7059.2958.6460.35
Brain Mets (D2)63.6656.5356.2561.0165.3965.24
Hippocampus (D3)89.1889.2488.7889.0389.3889.60
Atlas22 (D4)63.2865.5262.9765.7665.9366.95
CrossModa (D5)85.6483.4483.0784.2483.9184.08
Cosmos22 (D6)60.2878.1777.4080.0979.6780.00
ISLES22 (D7)77.9479.4478.1478.9678.8579.70
Hanseg (D8)59.0061.8557.4761.4962.5262.11
HNTS-MRG24 (D9)66.7365.9067.6563.3468.0068.62
BRATS24 Africa (D10)93.0792.5191.9792.1692.3692.19
T2 Aneurysms (D11)46.7641.9740.1644.9645.4847.26
Avg. DSC69.4070.4069.4170.9471.8372.37
Avg. Rank4.644.556.274.363.182.00
DatasetNormalized Surface Distance (NSD)
MS FLAIR (D1)78.7780.1679.7079.5779.1680.03
Brain Mets (D2)80.7276.7272.7779.2081.5182.53
Hippocampus (D3)99.4699.4299.4399.4699.3999.46
Atlas22 (D4)70.5273.7770.1573.6774.2275.35
CrossModa (D5)99.8599.7699.7299.7899.7499.81
Cosmos22 (D6)72.6096.4794.4896.8996.9597.45
ISLES22 (D7)88.5590.4589.3990.2889.5990.59
Hanseg (D8)82.2085.9480.4485.2985.9485.80
HNTS-MRG24 (D9)71.8371.2673.4767.8873.2274.07
BRATS24 Africa (D10)95.6695.3694.9594.9495.3395.06
T2 Aneurysms (D11)62.2455.5651.7958.9759.3861.18
Avg. NSD82.0484.0882.3984.1784.9585.58
Avg. NSD Rank4.274.275.824.644.002.18
+ +Impact of dynamic configuration Comparing the No (Dyn.) and No (Fixed) configurations, both trained from scratch, reveals that selecting the appropriate configuration for each dataset can significantly influence performance. For instance, on datasets D2 and D11, the dynamic configuration outperforms the fixed by $+7$ and $+5$ DSC points, respectively, while for D6, the fixed configuration yields results $+18$ DSC points higher. In the majority of datasets where the fixed configuration underperforms relative to the dynamic nnU-Net, pre-training helps to recover performance. However, in some cases, such as with D5, the dynamic default nnU-Net still proves superior. + +# 5.2. Ablation experiments + +Low-Data Regime While previous experiments focused on comparing SSL pre-training against a from-scratch baseline with full-scale datasets available, many applications in the medical domain have access to only a very small amount of labeled images. To measure the benefits of pre-training in such a low-data regime, we artificially reduced the total amount of data available for training to 10, 20, 30, or 40 labeled images. + +Results are presented in Tab. 6. Our pre-trained S3D model + +![](images/3fc524c634731b245ea897b4ad90cdd8f3e0e778df29cc2ad4c575a7490e10b1.jpg) +Figure 2. S3D ranks best across all methods. In addition to absolute mean performance, we report the ranking stability of the methods through bootstrapping for all test datasets as well as the aggregated rank across all datasets. + +leads to better downstream performance compared to training from scratch in this setting. With just 40 trained images, the fine-tuned model nearly matches the performance of the from-scratch model trained on the full dataset. Future research could explore whether optimizing the training duration or learning rate schedule could prevent the pre-trained network from overfitting during fine-tuning on such a limited number of training images. + +Generalization Performance To assess the generalization capability of the proposed pre-training method, we tested two scenarios. First, we evaluated fine-tuning our method on an unseen modality using the TOF Angiography Aneurysms dataset (D12). As shown in Tab. 9 without pre-training, the fixed configuration suffers a performance drop of 20 Dice points. We attribute this to the significant difference in median spacing for the downstream task ([0.50, 0.43, 0.43] mm), which has a higher resolution than the fixed target spacing of [1, 1, 1] mm used in the pretraining experiments. This lower resolution likely increases the difficulty of segmenting small aneurysms. Despite this decrease, pre-training mitigates some of this degradation and proves highly beneficial compared to training the same + +configuration from scratch. Interestingly, Models Genesis achieves the best results, potentially due to its use of intensity augmentations during pre-training, which increases robustness against brightness shifts, such as when generalizing to different MRI sequences. Second, we fine-tuned on the D2 dataset using only the T1 contrast-enhanced (T1ce) sequence and applied these models directly to D13 without any additional fine-tuning. While the dynamic configuration performed best on the in-distribution validation cases of D2, the results on D13 indicate that pre-training improves generalization across different centers, with our S3D model yielding the best performance. + +Pre-training Time Previous studies have demonstrated the positive impact of extended training schedules on the quality of learned representations for downstream tasks [10, 16]. To explore the relevance of this factor in the 3D medical domain, we conducted a similar experiment, evaluating training durations ranging from $62.5\mathrm{k}$ to 1M steps. Our results indicate that the benefits of longer training schedules begin to degrade after $250\mathrm{k}$ steps, as evident in Tab. 7. + +Fine-tuning length Initializing from pre-trained weights has the potential to reduce the computational resources needed for the network to adapt to new tasks. To assess this, we tested different fine-tuning durations on our development datasets. While maintaining 12.5k iterations for both the decoder and full network warm-up phases, we experimented with varying subsequent training lengths. As shown in Tab. 10, adding just 12.5k additional iterations (37.5k total) already outperforms training from scratch. However, achieving optimal performance still requires completing the full fine-tuning schedule. + +Multi-Channel Input In many medical examinations, it is common to perform multiple scans, as clinicians often require images with different characteristics for accurate decision-making. Consequently, some datasets, like D2, D8, and D10, contain multiple input modalities. While pre-training may involve all modalities, we only feed one modality at a time into the network since not all patients have scans in every modality. This raises the question of how to handle datasets with multiple registered images. To address this, we conducted a 5-fold cross-validation on the D2 development dataset. We evaluated the replication of each input modality along with random initialization of the input stem weights. Additionally, we tested freezing the stem weights during the decoder warm-up phase. As shown in Tab. 8, the most stable and consistently effective approach was replicating the pre-trained stem and keeping it frozen during the decoder's warm-up period. + +# 6. Conclusion + +This work is the first to demonstrate the potential of properly configured MAEs in 3D medical image segmentation. By overcoming key pitfalls in previous research, such as limited dataset sizes, outdated architectures, and insufficient evaluation, we show a consistent performance improvement over previous SSL methods. Notably, for the first time, we achieve consistent improvements over the dynamic, dataset-adaptive nnU-Net baseline, validated across a large and diverse set of development and testing datasets. + +**Limitations** In our current manuscript, we justify our selection of baseline methods by excluding prior work that was specific to architectures (3DMAE), methods that had no public code (GL-MAE), and methods that do not outperform a nnU-Net baseline trained from scratch (see Appendix Tab. 11). While our findings are promising, several avenues remain open for future exploration. We limited our method to Head and Neck MRI images, allowing us to focus on this region with a comparatively large pretraining dataset. Expanding to encompass the entire body across multiple imaging modalities would have required substantially more data to achieve comparable performance. Notably, in our ablations, we tested increasing training time and batch size (Appendix Tab. 12) which did not lead to performance improvements, but the question remains of whether scaling the pre-training dataset size or the model parameters could enable further improvements. Furthermore, the intensity shifts employed by Model Genesis SSL task hint at intriguing possibilities for improving generalization across unseen MRI modalities, which needs to be further explored for MAEs. Lastly, a data-centric approach to curating the most relevant data for SSL represents an exciting frontier for future research. Raw clinical datasets often contain images not intended for diagnostic purposes, such as those used for scanner calibration, which can dilute the effectiveness of pre-training. While we applied basic filtering to exclude low-quality data, more sophisticated filtering techniques could significantly enhance the quality of the pre-training process. + +To conclude, this work follows the spirit of prior studies like nnU-Net [20] showing that a robust development strategy, informed model configuration, and rigorous validation leads to true and sustainable performance improvements, contrasting the current hype for employing and modifying the latest network architecture. With this paper, we hope to contribute to a cultural shift in the community toward validation-driven development enabling true scientific progress. + +# 7. Acknowledgments + +This work was partly funded by the Helmholtz Foundation Model Initiative (HFMI) under the subproject 'The Human Radiome Project' (THRP). 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Recently, data privacy has become a significant constraint, limiting access to the source domain. To mitigate this issue, Source-Free Domain Adaptation (SFDA) methods bypass source domain data by generating source-like data or pseudo-labeling the unlabeled target domain. However, these approaches often lack theoretical grounding. In this work, we provide a theoretical analysis of the SFDA problem, focusing on the general empirical risk of the unlabeled target domain. Our analysis offers a comprehensive understanding of how representativeness, generalization, and variety contribute to controlling the upper bound of target domain empirical risk in SFDA settings. We further explore how to balance this trade-off from three perspectives: sample selection, semantic domain alignment, and a progressive learning framework. These insights inform the design of novel algorithms. Experimental results demonstrate that our proposed method achieves state-of-the-art performance on three benchmark datasets—Office-Home, DomainNet, and VisDA-C—yielding relative improvements of $3.2\%$ , $9.1\%$ , and $7.5\%$ , respectively, over the representative SFDA method, SHOT. + +# 1. Introduction + +Domain adaptation (DA) [24, 50] has seen widespread success in various machine learning and computer vision tasks, including image recognition [44, 49], segmentation [3], object detection [14], and facial recognition [46, 47]. Several prominent approaches, such as adversarial learning [8, 48], self-supervised learning [32, 43, 45], and self-training [26, 51], have demonstrated significant improvements in these domains. However, with the growing empha + +sis on data privacy, particularly in response to regulations like the General Data Protection Regulation (GDPR) in Europe, there is an increasing challenge in ensuring individuals' data is protected. This shift toward privacy-conscious practices poses a unique obstacle for traditional DA methods, as they often rely on direct access to source domain data. In this context, many conventional DA techniques lose their efficacy, making it imperative to develop new strategies that bypass the need for source domain data while still maintaining competitive performance in target domain tasks. + +Source-Free Domain Adaptation (SFDA)[40] addresses the challenge of domain adaptation under strict privacy constraints, utilizing only a pre-trained model on the source domain and unlabeled data from the target domain. To overcome these limitations, various SFDA methods have been proposed, focusing primarily on data generation[4, 12], self-training [17, 39], and self-supervised learning [2, 42]. Data generation-based methods face the challenge of effectively leveraging generated data to accurately capture the characteristics of the unseen source domain. On the other hand, self-training methods often suffer from the issue of noisy pseudo-labels, in addition to the increased computational overhead and the requirement for carefully defined pretext tasks. Despite the success of these approaches, they are often driven by intuitive motivations rather than grounded in theoretical analysis, leaving the exploration of SFDA's fundamental limits underexplored and unstructured. + +To gain a deeper understanding of the Source-Free Domain Adaptation (SFDA) problem, we conduct a theoretical analysis on the upper bound of the empirical risk in the target domain. Our findings reveal that three key concepts influence the target domain's empirical risk in SFDA scenarios: 1) Representativeness: ensuring that the selected target data with reliable pseudo-labels sufficiently represents the global distribution of the target domain, 2) Generalization: measuring the target intra-domain divergence between the selected target data and the remaining unselected data, and + +![](images/b868b1a104af14ce47623636ef53546050a1e105ade491b98a227504e7335809.jpg) +Figure 1. The approach follows a progressive training process (described in Sec. 4.3) conducted over $R$ rounds, with each round comprising $Q$ epochs. Each round consists of two main stages: sample selection (detailed in Sec.4.1) and semantic alignment (discussed in Sec.4.2). The entire unlabeled target dataset is denoted as $D_{t}$ , with $D_{t,l}^{r}$ and $D_{t,u}^{r}$ representing the selected target samples and the remaining unlabeled data during the $r$ -th round, respectively. Specifically, $D_{t,l}^{r'}$ refers to a subset of target samples selected at the $r$ -th round. The model $h$ begins as a pre-trained source domain model $h_{s}$ and is progressively adapted in each round to enhance target domain performance. + +3) Variety: maintaining diversity among the selected data to enhance the model's adaptability. In this work, we translate these theoretical insights into a practical algorithm to address SFDA more effectively. As shown in Figure 1, first, we introduce an empirical sample selection strategy aimed at selecting target samples that maintain high pseudo-label quality and accurately represent the distributional characteristics of the target domain. Second, we propose a certainty-guided semantic alignment method to minimize intra-domain divergence, ensuring consistency between the selected and remaining target samples. Lastly, we develop a progressive optimization framework that integrates these concepts to facilitate iterative and adaptive training, leading to improved domain adaptation performance. + +Our contributions are outlined as follows: + +- We conduct a theoretical analysis of the upper bound of target domain empirical risk in the context of SFDA. +- We uncover three pivotal factors—representativeness, generalization, and variety—that influence the control of the upper bound in SFDA scenarios. +- We develop a practical SFDA algorithm that effectively integrates these theoretical insights for enhanced adaptation performance. +- We validate our approach through extensive experiments on standard benchmarks, showcasing significant improvements over previous state-of-the-art methods. + +# 2. Related Works + +Unsupervised Domain Adaptation (UDA). Seminal works [1] offer theoretical guarantees for quantifying the discrepancy between the source and target domains. The following works aim to either learn domain-invariant features or leverage adversarial learning to align and reduce the domain discrepancy. For example, Deep Adaptation Network + +(DAN) [19] proposes to minimize the multi-kernel maximum mean discrepancy (MK-MMD) to reduce domain drift. Zhang et al. [41] introduce Margin Disparity Discrepancy (MDD) to measure the divergence across domains. Adversarial Discriminative Domain Adaptation (ADDA) [29] combines discriminative modeling, untied weight sharing, and a GAN loss to learn generalizable features across domains. Conditional Domain Adversarial Networks (CDAN) [20] aligns features across domains by exploiting discriminative information conveyed in the classifier predictions. Worth noting that all the methods need both source and target domain data for adaptation. + +Source-Free Domain Adaptation (SFDA). An early approach, Source Hypothesis Transfer (SHOT)[15], introduces information maximization and clustering-based pseudolabeling to encourage confident predictions on the target domain. Semantic Consistency on the Nearest Neighborhood (SCNNH)[27] extends this idea by utilizing estimated cluster centroids to guide semantic consistency. Subsequent efforts in Source-Free Domain Adaptation (SFDA) largely fall into two categories. The first focuses on generating data to mimic the source domain, as seen in Source Data-free Domain Adaptation (SDDA)[12]. Distribution Estimation (DE)[4] further explores this by estimating class-conditioned feature distributions using target data and anchor points. The second direction is self-training based on pseudo-labels provided by the pre-trained model, including methods like Neighborhood Reciprocity Clustering (NRC)[38] and Attracting and Dispersing (AaD)[39]. Recently, [17] improved pseudo-label quality by measuring label uncertainty, and a theoretical analysis of SFDA [21] examined the problem from the perspective of training objectives and existing loss functions. Distinct from these approaches, our theoretical analysis starts from a broader perspective, specifically the general empirical risk of the unlabeled target domain. We + +derive an upper bound for this risk, which informs the design of our method. Based on this analysis, we propose a practical algorithm that divides the target data into two subsets: one subset with high-quality pseudo-labels that preserves the global distribution structure of the target domain, and the remaining data. Instead of addressing source-target divergence as prior SFDA methods have, we focus on semantic alignment within the target domain, aligning the two subsets to address intra-domain divergence. + +Data Sampling (DS). Data sampling selects representative data from the entire dataset to improve model performance. For example, AUTO [37] uses an in-out-aware filter to assign pseudo-labels, and ISDA [35] introduces a loss function based on feature norm and prediction entropy to select informative data. In SFDA, several strategies have been proposed. SHOT++ [16] partitions the target dataset into pseudo-labeled and unlabeled subsets based on prediction entropy. ProxyMix [5] selects $N$ nearest target samples to the source class centers as labeled data. BETA [36] divides the target dataset into easy and hard subsets based on adaptation probabilities. Unlike traditional SFDA methods that split the target domain early, often introducing noise due to poor adaptation, we propose a progressive framework. Our method iteratively selects high-confidence pseudo-labeled data, refining the labeled subset over time to improve adaptation and minimize label noise. + +# 3. Investigating SFDA Problem + +In this section, we begin by defining the Source-Free Domain Adaptation (SFDA) problem and proceed to present a theoretical analysis of the general empirical risk in the target domain. This analysis highlights key factors that can inform the design of SFDA methods, emphasizing representativeness, generalization, and diversity. + +# 3.1. Problem Formulation + +Let $\mathcal{X}$ denote the input space, and $\mathcal{Y} = \{1,\dots,C\}$ denote the label space. A domain is defined by a joint distribution $P_{XY}$ over the instance space $\mathcal{X}\times \mathcal{Y}$ . Given a model $h_s:\mathcal{X}\to \mathcal{Y}$ trained on labeled source domain data $D_{s} = \{(x_{s}^{i},y_{s}^{i})\}_{i = 1}^{n_{s}}$ , $h_s$ represents a function predicting the conditional distribution $P_{Y|X}$ . The model $h_s$ can be decomposed into a feature extractor $f_{s}:\mathcal{X}\rightarrow \mathcal{E}$ and a classifier $g_{s}:\mathcal{E}\rightarrow \mathcal{V}$ , where $\mathcal{E}$ is the feature embedding space. Thus, the prediction for an input $x$ using $h_s$ can be expressed as $h_s(x) = (g_s\circ f_s)(x)$ . For any feature embedding $e\in \mathcal{E}$ , the classifier $g_{s}(e)$ induces a conditional distribution $P_{Y|e}$ . The goal of SFDA is to train the model $h_s$ with an unlabeled target domain data $D_{t} = \{x_{t}^{i}\}_{i = 1}^{n_{t}}$ to obtain a target-adapted model $h$ that minimizes the population risk of the target domain, i.e., $\mathbb{E}_{P_{XY}^t}\left[\ell (h(X),Y)\right]$ where $\ell :\mathcal{Y}\times \mathcal{Y}\to \mathbb{R}_+$ is a loss function. + +# 3.2. Theoretical Analysis and Insights + +Given the above setup, we define the general empirical risk objective for the target domain data $x_{t} \in D_{t}$ between the target-adapted model $h$ and the ground truth model $\hat{h}$ as: + +$$ +\ell (h, D _ {t}) = \mathbb {E} _ {x _ {t} \in D _ {t}} \left[ | h (x _ {t}) - \hat {h} (x _ {t}) | \right], \tag {1} +$$ + +where $\hat{h} (x_{t})$ represents the ground truth prediction for $x_{t}$ + +Before presenting the main theorem central to our theoretical analysis, we introduce the following assumptions: for some unlabeled target samples $x_{t}^{i}\in D_{t}$ , the model $h$ can produce highly accurate pseudo-labels $\tilde{y}_t^i$ . We denote this subset of pseudo-labeled data as $D_{t,l}$ , while the remaining unlabeled portion is denoted as $D_{t,u}$ . Consequently, Eq. 1 can be decomposed as: + +$$ +\ell (h, D _ {t}) \leq \ell (h, D _ {t, l}) + \ell (h, D _ {t, u}), \tag {2} +$$ + +where $\ell (h,D_{t,l})$ and $\ell (h,D_{t,u})$ denote the empirical risk on $D_{t,l}$ and $D_{t,u}$ , respectively. + +Inspired by the theoretical framework in [1], we derive the following theorem to provide insight into the SFDA problem (proved in Appendix): + +Theorem 1. Let $\ell(\cdot, \cdot)$ be a loss function applied to a hypothesis $h$ and a dataset $D_t$ for empirical risk minimization. Assume $h$ , parameterized by $\theta$ , is trained on $D_t$ and belongs to a hypothesis space $\mathcal{H}$ with VC-dimension $d$ . With a probability of at least $1 - p$ over the sample selection process, the following bound holds: + +$$ +\begin{array}{l} \ell (h, D _ {t}) \leq \underbrace {2 \ell (h , D _ {t , l})} _ {\text {R e p r e s e n t a t i v e n e s s}} + \frac {1}{2} \underbrace {\hat {d} _ {\mathcal {H} \Delta \mathcal {H}} (D _ {t , l} , D _ {t , u})} _ {\text {G e n e r a l i z a t i o n}} \\ + \underbrace {2 \sqrt {\frac {d \log (2 m) + \log (\frac {2}{p})}{m}}} _ {\text {V a r i e t y}} + \lambda \tag {3} \\ \end{array} +$$ + +where $\hat{d}_{\mathcal{H}\Delta \mathcal{H}}(\cdot ,\cdot)$ denotes the empirical distribution divergence, $m$ indicates the size of $D_{t,l}$ , $\lambda$ indicates the classification error on $D_{t,l}$ . + +Theorem 1 offers critical insights into controlling the general empirical risk for the unlabeled target domain in SFDA. The first term, $\ell(h, D_{t,l})$ , reflects representativeness, where $D_{t,l}$ captures the global distribution structure of $D_{t}$ . These samples typically have high-quality pseudolabels and are close to the class anchors. The second term, $\hat{d}\mathcal{H}\Delta \mathcal{H}(D_{t,l}, D_{t,u})$ , measures the generalization capability by quantifying the distribution divergence between $D_{t,l}$ and $D_{t,u}$ , which provides new insights to measure the domain divergence for SFDA from target domain instead of source and target domains where source domain is not available. The final term relates to variety, influenced by the size of + +$D_{t,l}$ , which affects the stability of the risk estimation. These terms collectively suggest that the SFDA problem can be addressed through a focus on representativeness, generalization, and variety, ensuring that the learned model maintains an upper bound on the empirical risk in the target domain. + +Discussion. In contrast to the existing theoretical analysis of SFDA by Mitsuzumi et al. [21], which focused on the relationship between the training objective and the SFDA training loss, decomposing the loss into components of discriminability and variety, our analysis approaches the problem from a broader perspective. Specifically, we begin with the general empirical risk of the unlabeled target domain, independent of any pre-existing SFDA training objectives. This allows for a more comprehensive understanding of how representativeness, generalization, and variety contribute to controlling the empirical risk in SFDA scenarios. + +# 4. Theoretically Inspired Practical Algorithm + +The theoretical analysis above provides a foundation for designing strategies to leverage representativeness, generalization, and variety to optimize the general empirical risk in the target domain, as outlined in Theorem 1. Building on these insights, we introduce a practical SFDA algorithm that incorporates these concepts. First, we devise a surrogate selection strategy for pseudo-labeled target samples $D_{t,l}$ , to enhance representativeness, ensuring that these samples accurately reflect the global distribution of $D_{t}$ . Next, we implement a semantic alignment mechanism to address the generalization term, minimizing target intra-domain divergence between $D_{t,l}$ and the unlabeled portion $D_{t,u}$ . Lastly, we propose a progressive training framework to handle variety, improving the stability and robustness of risk estimation within $D_{t,l}$ . This multi-faceted approach aligns with the theoretical underpinnings and promotes a more effective solution to the SFDA problem. + +# 4.1. Intersection based Sample Selection + +A straightforward sample selection mechanism involves utilizing the classifier $f$ within the model $h$ to assign class labels to target samples and subsequently perform top- $k$ sample selection, as detailed below. + +$$ +\begin{array}{l} D _ {t, l} ^ {\mathbf {C}} = \bigcup_ {c = 1} ^ {C} \left\{\operatorname {T o p} _ {k} \left(D _ {t} ^ {c}\right) \right\}, \text {w i t h} \tag {4} \\ \operatorname {T o p} _ {k} \left(D _ {t} ^ {\mathrm {c}}\right) = \left\{x _ {t} ^ {i} | i \in \text {a r g s o r t} \left(h \left(x _ {t} ^ {i}\right)\right), x _ {t} ^ {i} \in D _ {t} ^ {\mathrm {c}}, i \leq k \right\}. \\ \end{array} +$$ + +In this context, $D_{t,l}^{\mathrm{C}}$ denotes the selected samples, $D_{t}^{c}$ represents the subset of unlabeled target data assigned a pseudolabel $\tilde{y}_{t,l}^{i} = c$ , and $k$ denotes the number of selected samples. We refer to this method as classifier-based sampling (C-sampling). However, the standard C-sampling approach has two significant limitations: (1) it inherits labeling biases from the source-domain pre-trained model $h_s$ , which can + +lead to inaccurate pseudo-labels, and (2) the high-confidence samples selected are often confined to the distribution of the source domain. This occurs because deep learning classifiers are inherently data-driven and tend to memorize training distributions, thereby exacerbating the distribution gap between $Dt$ , $l$ and $D_{t,u}$ , increasing domain drift. + +To mitigate the above issues, we leverage the unsupervised information by clustering the centers populated from the unlabeled target domain samples, which faithfully reflects the target domain distribution and pops up the most confident samples for sample selection. We term it as target class center based sampling (T-sampling). Specifically, we apply the softmax over the logits after classifier $f$ to gauge the likelihood of correct classification, and select the top $\sigma \%$ of target data per class denoted as $D_t^{c,\sigma}$ , to form a reliable set. This set is then utilized to estimate the target class centers through a weighted aggregation process: + +$$ +\mu_ {c} = \frac {\sum_ {x _ {t} ^ {i} \in D _ {t} ^ {c , \sigma}} p _ {t} ^ {i , c} \cdot z _ {t} ^ {i}}{\sum_ {x _ {t} ^ {i} \in D _ {t} ^ {c , \sigma}} p _ {t} ^ {i , c}}, \tag {5} +$$ + +where $p_t^{i,c}$ is the probability of the $x_{t}^{i}$ belongs to $c$ -th class and $z_{t}^{i}$ is the feature of $x_{t}^{i}$ . Following this, we calculate the cosine similarity between the estimated class centers $\mu_c$ and the unlabeled target data, and proceed to select data with high cosine similarity from each class: + +$$ +\begin{array}{l} D _ {t, l} ^ {\mathbf {T}} = \bigcup_ {c = 1} ^ {C} \left\{\operatorname {T o p} _ {k} ^ {\cos} \left(D _ {t, u}\right) \right\}, \text {w i t h} \\ \operatorname {T o p} _ {k} ^ {\cos} \left(D _ {t, u}\right) = \left\{x _ {t} ^ {i} \mid i \in \operatorname {a r g s o r t} \left(\cos \left(x _ {t} ^ {i}, \mu_ {c}\right)\right), x _ {t} ^ {i} \in D _ {t, u}, i \leq k \right\}, \tag {6} \\ \end{array} +$$ + +where $D_{t,l}^{\mathbf{T}}$ denotes the selected samples. + +Intuitively, the closer the unlabeled samples are to the estimated class centers, the higher the likelihood these samples belong to the specific classes. However, it is worth noting that the accuracy of the estimated class centers heavily relies on the pseudo label information generated by the model updated from the initial training rounds. This accuracy can be compromised due to inherent domain drift issues. + +To further improve the pseudo-labeling accuracy, we empirically introduce an intersection based sampling, denoted as I-sampling, to retrieve the intersection between C-sampling and T-sampling. + +$$ +D _ {t, l} ^ {\mathbf {I}} = \bigcup_ {c = 1} ^ {C} \left\{\operatorname {T o p} _ {k} \left(D _ {t, u} ^ {c}\right) \cap \operatorname {T o p} _ {k} ^ {c o s} \left(D _ {t, u}\right) \right\}. \tag {7} +$$ + +In Section 5.3, we empirically validate that I-sampling selects unlabeled target data with consistently higher pseudolabel purity compared to C-sampling and T-sampling. + +The supervised cross-entropy loss is then applied to I-sampling selected data to update the model $h$ : + +$$ +\begin{array}{l} \mathcal {L} _ {C E} (h; D _ {t, l}) = \sum_ {\Gamma} ^ {C} z ^ {i} c _ {1} \quad (1 (j)) (8) \\ - \mathbb {E} _ {\left(x _ {t, l} ^ {i}, \tilde {y} _ {t, l} ^ {i}\right) \in D _ {t, l}} \sum_ {c = 1} ^ {C} \tilde {y} _ {t, l} ^ {i, c} \log \sigma_ {c} \left(h \left(x _ {t, l} ^ {i}\right)\right), (8) \\ \end{array} +$$ + +where $\sigma$ is the softmax operation, $\sigma_{c}$ indicates the $c$ -th element in the softmax output of the model, and $\tilde{y}_{t,l}^{i,c}$ denotes the $c$ -th element in one-of- $C$ encoding of $\tilde{y}_{t,l}^{i}$ . + +# 4.2. Semantic Target Intra-Domain Alignment + +In this section, we focus on minimizing the intra-domain divergence between $D_{t,l}$ and $D_{t,u}$ within the target domain. While adversarial feature alignment techniques have proven effective in various scenarios [7], directly applying them in SFDA presents challenges due to the typical size imbalance between $D_{t,l}$ and $D_{t,u}$ . This imbalance can introduce negative effects, complicating domain alignment efforts. To address this, we propose a straightforward yet effective semantic alignment approach. Our method incorporates a pseudo-label refining technique to enhance the labeling quality for $D_{t,u}$ and employs a certainty-weighted strategy to facilitate more reliable semantic alignment between $D_{t,l}$ and $D_{t,u}$ . + +Pseudo-Label Refining: To refine the labels for an unlabeled target sample $x_{t,u}^{i}$ drawn from $D_{t,u}$ , we establish two memory banks: one for storing target features and another for storing logits. These memory banks are updated dynamically throughout the training process, with new features and their corresponding logits added from each mini-batch. For any given $x_{t,u}^{i}$ , its feature representation $z_{t,u}^{i}$ is used to find the $\mathcal{M}$ nearest neighbors from target feature memory bank. The label for $x_{t,u}^{i}$ is subsequently refined by aggregating the logits from the selected $\mathcal{M}$ nearest neighbors, employing a cosine similarity-weighted mechanism to enhance the accuracy and reliability of the pseudo-label: + +$$ +\tilde {p} _ {t, u} ^ {i} = \sum_ {m = 1} ^ {\mathcal {M}} \alpha^ {m} p _ {t} ^ {m} \text {a n d} \alpha^ {m} = \frac {\exp \left(z _ {t , u} ^ {i} \cdot z _ {t} ^ {m} / \tau\right)}{\sum_ {j = 1} ^ {\mathcal {M}} \exp \left(z _ {t , u} ^ {i} \cdot z _ {t} ^ {j} / \tau\right)}, \tag {9} +$$ + +where $z_{t}^{m}$ denotes the feature of the nearest neighbors alone with its logits $p_{t}^{m}$ . $\alpha^{m}$ measures the cosine similarity between the current data $x_{t,u}^{i}$ and the $m$ -th nearest neighbor $x_{t}^{m}$ . + +Certainty Weighted Semantic Alignment: The iterative nature of the refinement process means that the pseudo-labels produced through neighborhood label propagation may still contain noise. To address this, we introduce a harmonic certainty metric inspired by [6], defined as: + +$$ +\eta \left(\tilde {p} _ {t, u} ^ {i}\right) = \frac {\left(1 - \mathrm {H} \left(\tilde {p} _ {t , u} ^ {i}\right)\right) + \operatorname {M a x} \left(\log \left(\tilde {p} _ {t , u} ^ {i}\right)\right)}{2}, \tag {10} +$$ + +where $\mathbb{H}(\cdot)$ denotes the entropy calculation and $\mathrm{Max}(\cdot)$ indicates the maximum probability value in $\log (\tilde{p}_{t,u}^i)$ . We normalize the $\mathbb{H}(\tilde{p}_{t,u}^i)$ and $\mathrm{Max}(\log (\tilde{p}_{t,u}^i))$ by minmax normalization to unify them within [0, 1] before computing $\eta (\tilde{p}_{t,u}^{i})$ . This metric is designed to trade off the two ends. One is estimating certainty solely based on entropy may falter in + +distinguishing between confident and extremely sharp predictions. The other is relying solely on probability for certainty estimation may not effectively address the challenge of distinguishing between various class distributions. With the refined label information $\tilde{p}_{t,u}^{i}$ and its certainty estimation $\eta (\tilde{p}_{t,u}^{i})$ , we align the domain drift between $D_{t,l}$ and $D_{t,u}$ by a semantic alignment regularization, which pushes the data augmented $\mathrm{Aug}(x_{t,u}^{i})$ to the corresponding class centers learned by the model $h$ : + +$$ +\begin{array}{l} \mathcal {L} _ {S A} (h; D _ {t, u}) = \\ \mathbb {E} _ {x _ {t, u} ^ {i} \in D _ {t, u}} \mathbb {I} \left(\eta \left(\tilde {p} _ {t, u} ^ {i}\right) \geq \beta\right) \phi \left(h \left(\operatorname {A u g} \left(x _ {t, u} ^ {i}\right)\right), w ^ {\tilde {y} _ {t, u} ^ {i}}\right), \tag {11} \\ \end{array} +$$ + +where $\beta$ is the threshold, $\phi (\cdot ,\cdot)$ is any differentiable distance measure. $w$ is the row-wise neuron weights from the classifier $f$ viewed as the model learned class centers, and $\tilde{y}_{t,u}^{i} = \arg \max (\tilde{p}_{t,u}^{i})$ is the label information for $x_{t,u}^{i}$ . + +During training, the proposed regularization technique facilitates a self-paced curriculum learning process. Initially, the model may produce low-quality label predictions for $x_{t,u}^{i}$ . By employing the threshold parameter $\beta$ , samples with uncertain or noisy label information are effectively filtered out, reducing the risk of negative transfer and ensuring that only reliable data contribute to training. As the training advances, the model progressively refines its representation, enabling more consistent alignment of the unlabeled target samples with their corresponding class centers. This leads to the generation of higher-quality label predictions over time, enhancing the semantic alignment between $D_{t,l}$ and the remaining unlabeled target data $D_{t,u}$ , and ultimately promoting better domain adaptation. + +Algorithm 1 Theoretical Insights Guided Method for SFDA +Input: Unlabeled target domain dataset $D_{t}$ , initialized model $h$ by source domain pretrained model $h_s$ +Ourput: Learned model $h$ #With $E$ Epochs +for $e = 1$ to $E$ do # $Q$ epochs interval if $\mathrm{Mod}(e,Q) = 0$ then Apply Equation 7 for target data selection (Sec. 4.1). end if # $I$ is the length of $D_{t}$ for $i$ to $I$ do Apply overall loss Equation 13 to train $h$ (Sec. 4.3). end for +end for + +# 4.3. Progressive Optimization Regime + +To prevent posterior collapse and ensure meaningful feature learning, we follow the standard state-of-the-art protocol by optimizing the following Information Maximization (IM) + +regularisation: + +$$ +\begin{array}{l} \mathcal {L} _ {I M} (h; D _ {t, u}) = \sum_ {c} ^ {C} P _ {c} \log (P _ {c}) \\ - \mathbb {E} _ {x _ {t, u} ^ {i} \in D _ {t, u}} \sum_ {c = 1} ^ {C} \sigma_ {c} \left(h \left(x _ {t, u} ^ {i}\right)\right) \log \left(\sigma_ {c} \left(h \left(x _ {t, u} ^ {i}\right)\right)\right), \tag {12} \\ \end{array} +$$ + +where $P_{c} = \mathbb{E}_{x_{t,u}^{i}\in D_{t,u}}[\sigma_{c}(h(x_{t,u}^{i}))]$ . The overall objective for source-free domain adaptation is: + +$$ +\mathcal {L} _ {S F D A} = \mathcal {L} _ {C E} + \mathcal {L} _ {S A} + \rho \mathcal {L} _ {I M}, \tag {13} +$$ + +where $\rho$ is the loss balancing hyper-parameter. + +Throughout the training process, a natural curriculum is established, guided by the $\mathcal{L}_{SFDA}$ loss. As training progresses, the model $h$ is able to generate higher-quality label information for $D_{t,u}$ compared to the pre-trained model $h_s$ . Building on this observation, we propose a progressive training framework, where we dynamically select samples from $D_{t,u}$ to augment $D_{t,l}$ using I-sampling, after every $Q$ epochs. This framework effectively balances the variety within $D_{t,l}$ and the risk induced by noisy pseudo-labels. Algorithm 1 illustrates details of our proposed method. + +# 5. Experiment + +# 5.1. Experimental Settings + +Datasets: We demonstrate our method under image classification task on three standard domain adaptation benchmarks as most of the literature does: Office-Home [30], DomainNet126 [23], and VisDA-C 2017 (VisDA-C) [22]. (1) Office-Home consists of four domains (Art, Clipart, Produce, and Real_world) with 65 classes. (2) DomainNet126 is one of the largest domain adaptation datasets which contains 6 domains and 345 classes. Following the protocol in [17], we use a subset including 126 classes from 4 domains (Clipart, Painting, Real, Sketch), and evaluate on 7 designed domain tasks. (3) VisDA-C is a challenging large-scale synthesis-to-real object recognition dataset that contains 12 classes. The source domain includes $152k$ synthetic images and the target domain contains $55k$ real images. + +Baselines: We compare to three main streams of methods that are most relevant to ours: (1) Unsupervised Domain Adaptation methods, including CDAN [20], MCC [9], and CST [18]. (2) Source-Free Domain Adaptation methods, including SHOT [15], $\mathrm{A^2Net}$ [33], NRC [38], AaD [39], U-SFAN [25], CoWA [13], SDE [4], DaC [42], GPUE [17], C-SFDA [10], I-SFDA [21], SHOT+DPC [34], and TPDS [28]. (3) Test Time Adaptation methods, including TENT [31] and AdaCon [2]. Besides, we include Empirical Risk Minimization (ERM) [11] as a general baseline. + +Evaluation Metrics: For Office-Home and Domain-Net126, we report the top-1 accuracy under each domain task together with their average. For VisDA-C, we report the per-class top-1 accuracy and their average. Each domain task is conducted independently 3 times and average is reported. + +Implementation Details: For a fair comparison, we adopt the pretraining methodology outlined in SHOT [15] to get the source domain pre-trained model. In particular, we separately employ ResNet50 for Office-Home and DomainNet126, and ResNet101 for VisDA-C as the backbone architectures. Subsequently, we replace the original final FC layer with a new bottleneck layer, followed by Batch Normalization (BN). In the target domain adaptation phase, we initialize the target model using the parameters from the pretrained source domain model. We utilize SGD with momentum 0.9 and weight decay $1e^{-3}$ and batch size of 64 for all benchmarks. The initial learning rates are 0.001 for Office-Home and DomainNet126 and 0.01 for VisDA-C, respectively. We set $\rho = \exp(ite / max_ite)^{-1}$ where max_ite is the maximum number of the training iterations. More implementation details can be found in Appendix. + +# 5.2. Experimental Results + +Table 1 illustrates the quantitative comparison on Office-Home and VisDA-C datasets. The methods are organized into the top three rows, while ours is in the last row. The first row is the ERM result, which serves as the lower bound. The second row shows three representative unsupervised domain adaptation (UDA) methods, all of which necessitate the availability of the source domain dataset during adaptation to the target domain. The third row contains seven cutting-edge source-free domain adaptation (SFDA) methods, such as the I-SFDA and SHOT+DPC. For Office-Home, under the UDA setting, our approach surpasses the strong baseline CST by $+1.1\%$ and outperforms all other UDA baselines by an even larger margin. This achievement is noteworthy considering that we do not utilize any source data during source-free adaptation. In the more challenging SFDA setting, we achieve a $2.2\%$ improvement over U-SFAN, a $1.2\%$ improvement over SDE, and a $0.9\%$ improvement over SHOT+DPC in terms of the 'Avg.' metric. Furthermore, our method outperforms all other SFDA baselines in 8 out of 12 domain tasks, firmly establishing its superiority. Similar trends are observed on VisDA-C, further validating the effectiveness of our approach. + +The evaluation results on DomainNet126 are detailed in Table 2. We adhere to the experimental protocol outlined in [17], which allows us to showcase the performance of our method across 7 different domain tasks. By comparing our method with both UDA and SFDA baselines, our method achieves state-of-the-art performance among all baselines and is higher than the second best GPUE by a margin of $3.6\%$ in terms of 'Avg.' Furthermore, our method attains the highest accuracy across all 7 domain tasks. The achievement not only demonstrates the superiority of our proposed method but also underscores the effectiveness of our proposed approach in addressing source-free domain adaptation within the context of a large-scale benchmark. + +Table 1. Classification Accuracy (%) on Office-Home (ResNet-50) and VisDA-C (ResNet-101). The best results under SFDA setting are highlighted in bold. Note that "SF" means whether a method belongs to SFDA method. + +
MethodSFOffice-HomeVisDA-C Avg.
A→CA→PA→RC→AC→PC→RP→AP→ClPr→RR→AR→CR→PAvg.
ERM×34.950.058.037.441.946.238.531.260.453.941.259.946.152.4
CDAN [20]×50.770.676.057.670.070.057.450.977.370.956.781.665.873.9
CST [18]×59.079.683.468.477.176.768.956.483.075.362.285.173.0-
SHOT [15]✓57.178.181.568.078.278.167.454.982.273.358.884.371.882.9
A²Net [33]✓58.479.082.467.579.378.968.056.282.974.160.585.072.884.3
AaD [39]✓59.379.382.168.979.879.567.257.483.172.158.585.472.788.0
CoWA [13]✓56.978.481.069.180.079.967.757.282.472.860.584.572.586.9
DaC [42]✓59.179.581.269.378.979.267.456.482.474.061.484.472.887.3
C-SFDA [10]✓60.380.282.969.380.178.867.358.183.473.661.386.373.587.8
I-SFDA [21]✓60.778.982.069.979.579.767.158.882.374.261.386.473.488.4
SHOT+DPC [34]✓59.279.882.668.979.779.568.656.582.973.961.285.473.284.3
Ours✓61.280.982.769.381.281.468.158.883.474.662.485.774.189.1
+ +Table 2. Classification Accuracy (%) on DomainNet-126 (ResNet-50). The best results under SFDA setting are highlighted in bold. Note that "SF" means whether a method belongs to SFDA method. + +
MethodSFRe→ClRe→PaPa→ClCl→SkSk→PaRe→SkPa→ReAvg.
ERM×55.562.753.046.950.146.375.055.6
MCC [9]×44.865.741.934.947.335.372.448.9
SHOT [15]✓67.768.466.960.166.159.980.867.1
TENT [31]✓58.565.757.948.552.454.067.057.7
NRC [38]✓64.769.462.958.365.858.781.365.9
CoWA [13]✓69.067.266.260.665.860.079.866.9
AdaCon [2]✓70.269.868.658.065.961.580.567.8
GPUE [17]✓74.270.468.864.067.565.776.569.6
TPDS [28]✓66.467.065.659.864.361.579.066.2
Ours✓77.672.971.968.071.267.383.273.2
+ +# 5.3. Model Analysis + +Ablation Study on Equation (13). Table 3 shows the ablative results regarding the proposed modules. It is organized into three rows. In the first row, we individually explore each module within our method. Notably, the $\mathcal{L}_{SA}$ module exhibits the lowest accuracy at $28.2\%$ compared to the other two modules. This discrepancy arises from the fact that training the model exclusively with the selected $D_{t,l}$ dataset or failing to prevent poster collapse would lead to degradation from the original source domain pre-trained model. This is because $D_{t,l}$ is relatively small and contains incorrect label information. In the second row, we consistently observe improvements in accuracy when randomly combining two sub-modules. Notably, when we combine $\mathcal{L}_{SA}$ with either $\mathcal{L}_{CE}$ or $\mathcal{L}_{IM}$ , we achieve a significant accuracy boost by more than $40.0\%$ . Finally, in the last row, we showcase the performance enhancement achieved by our full approach, which further improves accuracy by more than $2.0\%$ . + +Analysis of Accuracy in Figure 1. We explore the accuracy of the target data from different subsets at $r$ -th round, i.e., all target data $D_{t}$ , selected target data $D_{t,l}^{r'}$ , all selected target data $D_{t,l}^{r}$ , and remaining target data $D_{t,u}^{r}$ . Figure 2 (a) presents the overall trend on $D_{t}$ . To delve into the source of this advantage, we further examine the accuracy trend of two aspects: the selected target data $D_{t,l}^{r'}$ at each round, and the overall selected target data $D_{t,l}^{k}$ . As depicted in Figures 2 (b) and (c), we observe that I-sampling strategy excels in selecting target data with more accurate labels, thereby enhancing model training. It's worth noting that as the data sampling process continues, the accuracy of selected target data with labels tends to decrease. This arises from the fact that the most reliable target data with pseudo-labels are chosen in the initial stages. Additionally, we see that the decline in accuracy for the selected target data $D_{t,l}^{r'}$ during the initial phase is less pronounced compared to the later stages. Conversely, the increase in accuracy for the entire target data $D_{t}$ + +Table 3. Ablation study of sub-modules in our proposed method on Office-Home and DomainNet126 datasets with six domain tasks, i.e., $\mathrm{A}\rightarrow \mathrm{C}$ $\mathrm{A}\rightarrow \mathrm{P}$ $\mathrm{A}\rightarrow \mathrm{R}$ $\mathrm{Re}\rightarrow \mathrm{Cl}$ $\mathrm{Re}\rightarrow \mathrm{Pa}$ , and $\mathrm{Re}\rightarrow \mathrm{Sk}$ . $\mathcal{L}_{CE}$ is the cross-entropy loss for $D_{t,l}$ . $\mathcal{L}_{SA}$ is the semantic domain alignment loss for $D_{t,u}$ . $\mathcal{L}_{IM}$ is the information maximization loss for $D_{t,u}$ + +
\( \mathcal{L}_{SA} \)\( \mathcal{L}_{CE} \)\( \mathcal{L}_{IM} \)A→CA→PA→RRe→ClRe→PaRe→SkAvg.
××✓55.975.477.666.868.159.067.1
×✓×56.973.778.566.162.557.265.8
✓××12.733.340.724.238.619.928.2
×✓✓58.775.781.170.267.960.769.0
✓×✓56.376.780.669.566.663.568.9
✓✓×59.578.780.574.969.764.471.3
✓✓✓61.280.982.777.672.967.373.8
+ +![](images/26192b05ce85b94392b4c7c0f105cb160a46f07ee63d0c074287e5f8f65d9d54.jpg) +(a) Accuracy on $D_{t}$ + +![](images/d7a50c7b5e219b1e6a1b68d145d5d91e5103ef6fd33e796075db682372dd1037.jpg) +(b) Accuracy on $D_{t,l}^{r'}$ +Figure 2. As shown from left to right, four figures illustrate the accuracy of different target subsets during the training process with domain task $\mathrm{A} \rightarrow \mathrm{C}$ on Office-Home. (a) demonstrates the accuracy of all target data $D_{t}$ . (b) shows the accuracy of the selected target data $D_{t,l}^{r'}$ . (c) describes the accuracy of the all selected target data $D_{t,l}^{r}$ . (d) plots the trend of the accuracy of the remaining target data $D_{t,u}$ . + +![](images/0a382c61c70b4c2d02a61269911a224374090e965487e3a11734488d91489eb6.jpg) +(c) Accuracy on $D_{t,l}^{r}$ + +![](images/a9a62b9e205904407b4adb9b49d762c6eef630a83883ffa96ba01120baafd461.jpg) +(d) Accuracy on $D_{t,u}^{r}$ + +Table 4. Ablation study of different data sampling strategies on two adaptation tasks, i.e., $\mathrm{A}\rightarrow \mathrm{C}$ (OfficeHome) and $\mathrm{Re}\rightarrow \mathrm{Cl}$ (DomainNet126). + +
Sampling strategiesA→CRe→Cl
C-sampling59.976.5
T-sampling59.176.2
I-sampling61.277.7
+ +during the early stages is more substantial than in the later stages. It is likely that accuracy on non-selected target data experiences significant improvement in the early training stages, leading to the selection of more reliable target data for labeling, which is verified in Figure 2 (d). + +Ablation Study on Sample Selection in Sec. 4.1. We conduct the study on adaptation tasks $\mathrm{A} \rightarrow \mathrm{C}$ and $\mathrm{Re} \rightarrow \mathrm{Cl}$ from OfficeHome and DomainNet126, respectively, to assess the performance of C-sampling, T-sampling, and I-sampling. As shown in Table 4, the I-sampling strategy consistently outperforms both C-sampling and T-sampling across various adaptation tasks, underscoring its advantage compared to the other two sampling strategies. + +# 6. Conclusion + +We present a theoretical analysis of the empirical risk bound for the target domain in the Source-Free Domain Adapta + +tion (SFDA) problem. We derive the upper bound for the risk and identify three key factors—representativeness, generalization, and variety—that influence the control of this upper bound. Building on these insights, we propose a practical SFDA algorithm that effectively integrates these factors. Specifically, we introduce an intersection-based sampling strategy to enhance the pseudo-labeling process, focusing on selecting target data with high-quality pseudo-labels. Additionally, we propose a certainty-weighted semantic domain alignment approach to reduce the intra-domain divergence between selected target samples and the remaining target samples. A progressive optimization scheme is employed to iteratively refine these two steps across multiple rounds. Extensive experiments on three major domain adaptation benchmarks demonstrate that our method consistently outperforms both unsupervised domain adaptation and existing source-free domain adaptation methods. + +# Acknowledgment + +The work is supported in part by the U.S. Office of Naval Research Award under Grant Number N00014-24-1-2668, the National Science Foundation under Grants IIS-2316306 and CNS-2330215, and Sony AI. + +# References + +[1] Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan. A theory of learning from different domains. Machine learning, 79: 151-175, 2010. 2, 3 +[2] Dian Chen, Dequan Wang, Trevor Darrell, and Sayna Ebrahimi. Contrastive test-time adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 295-305, 2022. 1, 6, 7 +[3] Lin Chen, Zhixiang Wei, Xin Jin, Huaian Chen, Miao Zheng, Kai Chen, and Yi Jin. 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However, applying existing RL methods to step-distilled DMs is challenging for ultra-fast ( $\leq 2$ -step) image generation. Our analysis suggests several limitations of policy-based RL methods such as PPO or DPO toward this goal. Based on the insights, we propose fine-tuning DMs with learned differentiable surrogate rewards. Our method, named LaSRO, learns surrogate reward models in the latent space of SDXL to convert arbitrary rewards into differentiable ones for effective reward gradient guidance. LaSRO leverages pretrained latent DMs for reward modeling and tailors reward optimization for $\leq 2$ -step image generation with efficient off-policy exploration. LaSRO is effective and stable for improving ultra-fast image generation with different reward objectives, outperforming popular RL methods including DDPO [2] and Diffusion-DPO [71]. We further show LaSRO's connection to value-based RL, providing theoretical insights. See our webpage here. + +# 1. Introduction + +Diffusion models (DMs) [17, 61, 63, 64] have significantly transformed generative modeling for continuous data, delivering remarkable results across various data modalities. In particular, recent advances [53, 54, 56] demonstrate their capabilities of generating diverse and high-fidelity images according to free-form input text prompts, albeit at the cost of a slow iterative sampling process. Various methods are proposed to accelerate such a sampling process [36, 38, 40, 62], with the most recent distillation-based methods [39, 57, 58, 65] pushing the envelope to achieve extreme few-step generation ( $\leq$ 2 steps). + +On the other hand, state-of-the-art image diffusion models pre-trained on Internet-scale datasets (e.g. LAION-5B + +[59]) usually incorporate a fine-tuning stage that guides the model's behavior towards specific human preferences (aesthetics, debiased, etc.) This is achieved either by supervised learning (SFT) with curated human preference datasets [26, 75, 78] or through reinforcement learning (RL) to leverage a diverse set of reward signals, including those not naturally differentiable such as incompressibility, or potentially the ones involving large language models (LLMs) or vision-language models (VLMs) [21, 41, 69]. + +However, it is non-trivial to fine-tune time-distilled DMs for $\leq 2$ -step image generation with policy-based RL (e.g., PPO [60] or DPO [51]). We detailedly analyze the emerged optimization challenges negligible for non-distilled DMs. Most RL objectives are ineffective for $\leq 2$ -step DMs due to the deterministic $2^{\mathrm{nd}}$ sampling step. The mapping of the distilled 2-step sampler from noisy images to clean ones (and thus to most reward signals) is highly non-smooth, making policy gradient estimation challenging. RL methods relying on the denoising diffusion loss (such as Diffusion-DPO [71]) are incompatible with such a property, leading to blurred images. Moreover, the 2-step mapping lacks enough stochasticity, posing a hard exploration problem. These conditions make most RL methods infeasible or ineffective for fine-tuning two-step DMs. + +To address these limitations, we propose to learn a surrogate reward model in the latent space (of SDXL [47]) that converts an arbitrary reward signal into a differentiable one. Reward fine-tuning with this learned surrogate avoids policy gradient estimation as it directly and efficiently provides reward gradient guidance. Specifically, we propose to use a pre-trained latent diffusion model as the backbone of the surrogate model, which shows superior memory & speed efficiency and better generalizability compared to the alternatives based on VLMs (CLIP [50] and BLIP [32]). Additionally, our method achieves efficient exploration for 2-step image DMs with off-policy samples. The overall pipeline consists of two stages: the pre-training stage for learning the surrogate reward and the reward optimization stage that alternates between improving the DMs and online adapting the surrogate. We call our method LaSRO, i.e., Latent + +![](images/496d7eb2a50cd1b92adc66f8ae959efecc42970e7e55999246c7a9e1dd1f770f.jpg) +Figure 1. Generated images of resolution $1024^2$ with $\leq 2$ steps via LCM-SSD-1B [42] (baseline) and those fine-tuned with Image Reward [78]. $1^{\mathrm{st}}$ column: baseline results. $2^{\mathrm{nd}}$ and $3^{\mathrm{rd}}$ : results during and after fine-tuning the baseline via our method LaSRO. $4^{\mathrm{th}}$ : fine-tuned via RLCM [45] (a variant of DDPO [2]). $5^{\mathrm{th}}$ : fine-tuned via PSO [43] (a variant of Diffusion-DPO [71]). Ours significantly improves the visual quality of $\leq 2$ -step image generation while other strong RL methods fail due to training instability and inefficiency. + +space Surrogate Reward Optimization. LaSRO effectively fine-tunes two-step DMs across different reward objectives (including non-differentiable ones) and outperforms popular RL methods (DDPO [2], Diffusion-DPO [71], etc.). We further show a connection of LaSRO to value-based RL [73] to provide theoretical insights behind our approach. In summary, our contributions are: + +- We analyze the key challenges in applying RL to improve $\leq 2$ -step image diffusion models. +- We propose a framework, named LaSRO, that uses latent-space surrogate rewards to optimize arbitrary reward signals with efficient off-policy exploration. +- We establish LaSRO's connection to value-based RL, demonstrate its advantages over popular policy-based RL methods, and validate its design with ablation studies. + +# 2. Related Work + +Diffusion Models (DMs) Diffusion models [17, 61, 63, 64] have become the dominant generative models for various continuous data modalities [5, 18, 19, 23, 28, 37, 48, 52, 55, 80]. Particularly, recent advances [53, 54, 56] make text-to-image generation vastly popular. A major drawback of DMs is their lengthy iterative denoising process during inference, often requiring many sampling steps. + +Step-Distilled Diffusion Models Recent research strives to achieve $\leq 2$ step generation through step-distillation of a teacher diffusion model. Latent Consistency Models (LCMs) [42] apply Consistency Distillation [65] to learn to map any point along the sampling trajectories of the teachers (latent DMs) to their endpoints with one sampling step. Progressive Distillation [57] incrementally distills a diffu + +sion model into a faster one. InstaFlow [39] apply distillation after modifying the teacher DM's probability flow to be smoother. Adversarial Diffusion Distillation [58] distills a teacher into a faster student via adversarial training. + +Fine-tuning DMs with Arbitrary Reward Signals Reward fine-tuning DMs with RL becomes promising for aligning model outputs with arbitrary reward signals, including non-differentiable ones. The simplest form of RL comes in as reward-weighted regression (RWR) [46], including [8, 21, 30]. Others [7, 71, 79] based on direct preference optimization, DPO [51], or its variant [34], can be seen as RWR-based approaches that fall into this category. Policy-based RL methods [2, 4, 9-11] relying on policy gradient or its equivalence handle arbitrary rewards by using large quantities of online samples. Value-based RL methods [73] have been largely under-explored for fine-tuning DMs since they can struggle with long-horizon MDPs with delayed rewards [67]. On the other hand, supervised fine-tuning methods [6, 49, 76, 78] align DMs by back-propagating the reward gradient through the denoising process to update the model parameters. While effective, they are constrained to scenarios where specifically labeled preference datasets are available [26, 74, 75, 78] or the reward signal is differentiable. Many recent rewards [21, 41, 69] are not naturally differentiable as they involve VLMs [32] or LLMs [1]. + +Reward Fine-tuning $\leq$ 2-Step Step-Distilled DMs Fine-tuning DMs with policy-based RL remains a great challenge for $\leq$ 2-step generation. The distilled diffusion sampler lacks stochasticity and the underlying mapping is highly non-smooth, making methods based on either policy gradient estimation or reward-weighted regression ineffective (see Sec. 4 for details). Very recently, RLCM [45] and PSO [43] were proposed to reward fine-tuning step-distilled DMs with policy-based RL, and RG-LCD [33] was proposed to use reward guidance in the step-distillation process of LCMs. However, they are ineffective or inefficient in improving $\leq$ 2-step DMs with arbitrary rewards. + +# 3. Preliminaries + +# 3.1. Diffusion Models (DMs) + +We consider the conditional denoising diffusion probabilistic models [17, 61], which represent an image generation distribution $p(\mathbf{x}_0|\mathbf{c})$ over a sample image $\mathbf{x}_0$ given a text prompt $\mathbf{c}$ . The distribution is modeled as the reverse of a Markovian diffusion process $q(\mathbf{x}_{t + 1}|\mathbf{x}_t)$ that progressively adds Gaussian noise $Z_{t}$ to (a scaled version of) $\mathbf{x}_0$ . To reverse the diffusion, a time-conditioned neural network, parametrized with $\epsilon$ -prediction as $\epsilon_{\theta}(\mathbf{x}_t,t,\mathbf{c})$ , is trained by maximizing a variational lower bound on the log-likelihood + +of the training data, or equivalently, minimizing the loss: + +$$ +\mathcal {L} _ {\mathrm {d d p m}} (\theta) = \mathbb {E} \left[ \| Z _ {t} - \epsilon_ {\theta} (\mathbf {x} _ {t}, t, \mathbf {c}) \| ^ {2} \right] \tag {1} +$$ + +where the expectation is taken over all training samples $(\mathbf{x}_0,\mathbf{c})$ , timestep $t\in \{0,\dots,T\}$ , and the corresponding noisy samples $\mathbf{x}_t\sim q(\mathbf{x}_t|\mathbf{x}_0)$ with the added noise $Z_{t}$ . For simplicity, we ignore the scaling terms and denote the predicted output (rather than the noise) as $\mu_{\theta}(\mathbf{x}_t,t,\mathbf{c})$ + +Sampling from a diffusion model starts with Gaussian noise $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ and iteratively generates $\mathbf{x}_{T - 1},\mathbf{x}_{T - 2}$ all the way to $\mathbf{x}_0$ . With some pre-set monotonically decreasing noise schedules $\{\sigma_t^2\}$ , a common choice to parametrize the reverse denoising step given a timestep $t$ is: + +$$ +p _ {\theta} (\mathbf {x} _ {t - 1} | \mathbf {x} _ {t}, \mathbf {c}) = \mathcal {N} (\mathbf {x} _ {t - 1} \mid \mu_ {\theta} (\mathbf {x} _ {t}, t, \mathbf {c}), \sigma_ {t} ^ {2} \mathbf {I}) \tag {2} +$$ + +# 3.2. Latent Consistency Models (LCMs) + +Aimed for fast image generation, the latent consistency model (LCM) [42], a type of step-distilled DMs, was proposed to perform Consistency Distillation [65] in the latent space of the teacher DMs (e.g., SDXL [47]). We select LCMs as our test bed due to their simplicity, efficiency, and training stability (our approach is not tied to LCMs, see Tab. 1). For simplicity, we abuse the notation to use $\mathbf{x}_t$ to also refer to the latent code. LCM learns a function $f_{\theta}(\mathbf{x}_t,t,\mathbf{c})$ that maps any sample $\mathbf{x}_t$ on a denoising trajectory to the endpoint $\mathbf{x}_0$ by "compressing" the trajectory induced by the teacher DMs (see Fig. 2 upper right). It enforces its output given $\mathbf{x}_t$ to be close to its output given $\mathbf{x}_{t - 1}$ , while overriding $f_{\theta}(\mathbf{x}_0,0,\mathbf{c}) = \mathbf{x}_0$ for the boundary condition. The (simplified) LCM training loss is: + +$$ +\mathcal {L} _ {\mathrm {l c m}} (\theta) = \mathbb {E} \left[ d \left(f _ {\theta} \left(\mathbf {x} _ {t}, t, \mathbf {c}\right), f _ {\theta} \left(\hat {\mathbf {x}} _ {t - 1} ^ {\phi}, t - 1, \mathbf {c}\right)\right) \right] \quad (3) +$$ + +where $d(\cdot, \cdot)$ is a metric function; the expectation is taken over $\mathbf{x}, \mathbf{c}$ and $t$ ; stop gradient is applied to the $2^{\mathrm{nd}} f_{\theta}$ in $d(\cdot, \cdot)$ ; $\hat{\mathbf{x}}_{t-1}^{\phi}$ is a sample obtained from $\mathbf{x}_t$ with one denoising step using the teacher diffusion model $\phi$ given $\mathbf{c}$ . + +While LCMs produce images with only one step, by reinjecting noise back to the results of each LCM step (except for the last one), LCMs benefit from a multi-step sampling procedure similar to regular DMs. Namely, similar to Eq. 2, each LCM sampling step (except for the last one) follows: + +$$ +p _ {\theta} (\mathbf {x} _ {t - 1} | \mathbf {x} _ {t}, \mathbf {c}) = \mathcal {N} (\mathbf {x} _ {t - 1} \mid f _ {\theta} (\mathbf {x} _ {t}, t, \mathbf {c}), \sigma_ {t} ^ {2} \mathbf {I}) \tag {4} +$$ + +Again, scaling terms are ignored. Usually, only up to 8 steps are taken for LCMs (much fewer than regular DMs). + +# 3.3. RL Formulation of Fine-tuning DMs & LCMs + +We formulate RL fine-tuning of DMs using Markov Decision Process (MDP) [67]. Similar to [2], we map a diffusion model to the following finite-horizon MDP + +$(S, \mathcal{A}, P, R, \mu, H)$ with policy $\pi(\mathbf{a}_t | \mathbf{s}_t)$ and a task reward $r(s, \mathbf{c})$ that evaluates the image given the text prompt $\mathbf{c}$ : + +$$ +\begin{array}{l} \mathbf {s} _ {t} \triangleq (\mathbf {x} _ {\tau_ {t}}, \tau_ {t}, \mathbf {c}) \in \mathcal {S} \quad \mathbf {a} _ {t} \triangleq \mathbf {x} _ {\tau_ {t + 1}} \in \mathcal {A} \\ \pi (\mathbf {a} _ {t} | \mathbf {s} _ {t}) \triangleq p _ {\theta} \left(\mathbf {x} _ {\tau_ {t + 1}} | \mathbf {x} _ {\tau_ {t}}, \mathbf {c}\right) \\ \end{array} +$$ + +$$ +\begin{array}{l} P \left(\mathbf {s} _ {t + 1} \mid \mathbf {s} _ {t}, \mathbf {a} _ {t}\right) \triangleq \left(\delta_ {\mathbf {x} _ {\tau_ {t + 1}}}, \delta_ {\tau_ {t + 1}}, \delta_ {\mathbf {c}}\right) \\ R (\mathbf {s} _ {t}, \mathbf {a} _ {t}) = \left\{ \begin{array}{l l} r (\mathbf {a} _ {t}, \mathbf {c}) & \text {i f} t = H - 1 \\ 0 & \text {o t h e r w i s e} \end{array} \right. \\ \mu \triangleq (p (\mathbf {c}), \delta_ {\tau_ {0}}, \mathcal {N} (\mathbf {0}, \mathbf {I})) \\ \end{array} +$$ + +where $\delta_y$ is the Dirac $\delta$ -distribution and $p_{\theta}(\mathbf{x}_{\tau_{t + 1}}|\mathbf{x}_{\tau_t},\mathbf{c})$ is defined according to Eq. 2 or 4. Note that, in MDP formulation (and for the rest of this paper), in contrast to the previous notation, the initial timestep is denoted $\tau_0$ , and after $H$ denoising steps, the last timestep is denoted $\tau_H$ . + +For LCMs ( $f_{\theta}$ from Sec. 3.2), since the intermediate sampling result lies in the image/latent space where a nonzero reward is defined, the MDP formulation differs by: + +$$ +R \left(\mathbf {s} _ {t}, \mathbf {a} _ {t}\right) = r \left(f _ {\theta} \left(\mathbf {x} _ {\tau_ {t}}, \tau_ {t}, \mathbf {c}\right), \mathbf {c}\right), \forall t \tag {5} +$$ + +# 4. What are the RL Obstacles? + +We present an insightful analysis of three major challenges. + +# 4.1. Hard Exploration for Two-Step Image DMs + +Efficient and effective exploration in the state space is key to all online RL methods. Fine-tuning two-step DMs poses a hard exploration problem for RL. Diffusion models, expressed as stochastic policies $p_{\theta}(\mathbf{x}_{\tau_H}|\mathbf{x}_{\tau_0},\mathbf{c})$ , explore the image/latent space by repeatedly injecting Gaussian noise during the sampling process (Eq. 2 or 4). While regular DMs incrementally add noise to render diverse images, step-distilled DMs add noise in significantly fewer increments, leading to less diverse images, an observation we visualize in Fig. 2 (left). Given a fixed initial noise $\mathbf{x}_{\tau_0}$ and a prompt $\mathbf{c}$ , one-step DMs (i.e., LCMs) are deterministic functions, and, by injecting noise only once, two-step LCMs allow little exploration: + +$$ +\mathbf {x} _ {\tau_ {H}} \sim f _ {\theta} \left(f _ {\theta} \left(\mathbf {x} _ {\tau_ {0}}, \tau_ {0}, \mathbf {c}\right) + Z, \tau_ {H / 2}, \mathbf {c}\right) \tag {6} +$$ + +where scaling terms are ignored; $Z$ is the injected noise at timestep $\tau_{H/2}$ as the only source of stochasticity. This limited exploration hinders on-policy RL methods. + +# 4.2. Degenerated RL Objectives for Two-Step DMs + +Typically, policy-based RL optimizes the log-likelihood of online samples to enhance the policy's expected reward. However, most policy-based methods have their objectives degenerated when fine-tuning two-step DMs, substantially impeding their effectiveness. For instance, a simple form of DDPO [2] to fine-tune DMs has its objective and gradient: + +$$ +\mathcal {J} _ {\mathrm {d d p o}} (\theta) = \mathbb {E} _ {\mathbf {c} \sim p (\mathbf {c}), \mathbf {x} _ {\tau_ {H}} \sim p _ {\theta} (\mathbf {x} _ {\tau_ {H}} | \mathbf {c})} [ r (\mathbf {x} _ {\tau_ {H}}, \mathbf {c}) ] \tag {7} +$$ + +![](images/0b1ac36ad7748e6b7424f6a22f9f1973b05a23a178b8f13a2121811f3d054b32.jpg) +Figure 2. (left) Given astronaut riding a horse as $\mathbf{c}$ , fixed initial noise $\mathbf{x}_{\tau_0}$ and guidance scale, the reduction of noise-injecting steps leads to less diverse images generated from SSD-1B [15] and its LCM, and thus harder exploration for $p_{\theta}(\mathbf{x}_{\tau_H}|\mathbf{x}_{\tau_0},\mathbf{c})$ . (right) Illustration of the LCM mapping $f_{\theta}$ . We show the growing empirical local Lipschitz of the LCM mapping from a noisy image to a clean image and to a generic image quality score (details in Appendix A). The x-axis is the input's noise level ( $t$ as in $\mathbf{x}_t$ ). + +![](images/a2fd58664ca75e2f4179d3fa047877fe40df5b42132626ed5bc972ccbd82e22e.jpg) + +$$ +\nabla_ {\theta} \mathcal {J} _ {\mathrm {d d p o}} = \mathbb {E} \left[ \sum_ {t = 0} ^ {H - 1} \nabla_ {\theta} \log p _ {\theta} \left(\mathbf {x} _ {\tau_ {t + 1}} \mid \mathbf {x} _ {\tau_ {t}}, \mathbf {c}\right) r \left(\mathbf {x} _ {\tau_ {H}}, \mathbf {c}\right) \right] \tag {8} +$$ + +For two-step LCMs, since the $2^{\mathrm{nd}}$ step is deterministic, $p_{\theta}(\mathbf{x}_{\tau_H}|\mathbf{x}_{\tau_{H / 2}},\mathbf{c})$ does not exist; Eq. 7 degenerates to: + +$$ +\mathcal {J} _ {\mathrm {d d p o}} ^ {\mathrm {d e g}} = \mathbb {E} \left[ \nabla_ {\theta} \log p _ {\theta} \left(\mathbf {x} _ {\tau_ {H / 2}} \mid \mathbf {x} _ {\tau_ {0}}, \mathbf {c}\right) r \left(\mathbf {x} _ {\tau_ {H}}, \mathbf {c}\right) \right] \tag {9} +$$ + +This objective only accounts for the first half of the sampling process, making DDPO ineffective. Similar issues can be found in other policy-based methods such as DPO [43]. + +# 4.3. Non-Smooth Mappings of Two-Step DMs + +The non-smoothness of the mapping that underlies two-step DMs makes it challenging to fine-tune them with methods based on either policy gradient estimation or reward-weighted regression (RWR). Specifically, with a distilled two-step diffusion sampler, the underlying mapping from a noisy image to a clean image is highly non-smooth (i.e., has a great Lipchitz constant). Thus, slight changes in actions could drastically change most rewards. The same holds for two-step latent DMs: an LCM step $f_{\theta}(\mathbf{x}_{\tau_t}, \tau_t, \mathbf{c})$ denoising an input with a higher noise level ( $\tau_t$ closer to $\tau_0$ ) requires greater model expressiveness, resulting in a higher (local) Lipschitz constant [35]. Note that, the $2^{\mathrm{nd}}$ step of a two-step LCM handles a very high noise level from $\mathbf{x}_{\tau_{H/2}}$ , empirically verified in Fig. 2 (right). + +This non-smoothness makes it difficult to estimate policy gradients, leading to training instability of PPO [60]. In fact, many online RL methods that rely on policy gradient theorem [68] suffer from high variance gradient estima + +![](images/1d83322a20222c5312497af1e77236217837537c1c59b75d6593db471fb039b7.jpg) +Figure 3. Training pipeline of the fine-tuning stage of LaSRO. This stage alternates between reward fine-tuning the DM and online adapting the surrogate reward. Since connected to value-based RL, we present LaSRO in the style of actor-critic methods [27]. + +tion due to the non-smoothness. Previously, "sharpness", a closely related concept, was adopted in the study of robustness of supervised learning, generative modeling, and RL [12, 24, 25, 29]. In contrast, many-step diffusion sampling "divides" the high Lipschitz so that policy gradient estimation becomes much easier for each step. + +Methods based on RWR [46] also suffer severely from the non-smoothness. RWR mitigates high-variance policy gradient estimation by instead performing re-weighted regression of online samples to favor actions of higher rewards. Methods based on DPO [51] fall into this category. So does PRDP [7], which applies RWR adaptive to the reward difference between good and bad samples. While RWR utilizes a re-weighted variant of the vanilla diffusion loss (Eq. 1), [43] shows that using Eq. 1 to fine-tune step-distilled DMs leads to blurry images by destroying the mapping induced by the step-distillation process. We argue it is because the loss does not account for the substantially increased non-smoothness of step-distilled DMs (particularly two-step DMs) compared to many-step DMs. PSO [43] utilizes additional constraints in response, yet is ineffective for two-step DMs. + +# 5. Clearing the RL Obstacles with LaSRO + +In this paper, we focus on reward fine-tuning 2-step DMs, targeting ultra-fast image generation (please see App. D for the inference speed). Formally, we introduce LaSRO, an RL training framework consisting of two stages: (1) pretraining the latent-space surrogate reward (Alg. 1). (2) reward fine-tuning the two-step DMs (Alg. 2). We visualize the pipeline of the latter stage in Fig. 3. + +# 5.1. Latent-space Surrogate Reward Learning + +We start with surrogate reward learning. Based on the insights from Sec. 4, we avoid both policy gradient estimation and reward-weighted regression. Instead, we propose to learn a differentiable surrogate reward that efficiently provides accurate reward gradient guidance for two-step image generation (guidance also provided for the second deterministic step). Direct reward gradient enabled by surrogate reward learning significantly improves exploration as noise injection is no longer the only way to explore when fine-tuning DMs. Similar techniques (i.e., differentiable physics) were proposed in RL for robotics [14, 20, 22]. + +We leverage large pre-trained multimodal models to learn a surrogate reward that provides gradients generalizable over unseen prompts or images. We evaluate different multimodal backbones including CLIP [50] (used as rewards in [33]), BLIP [32] (used as rewards in [78]), and the UNet encoder of SDXL [47] (used as discriminators in [35]). We use the most effective one - the encoders of pre-trained latent DMs as the backbone. We add a simple CNN-based prediction head on top of this backbone, together denoted as $\mathcal{R}_{\psi}$ . We train it with a loss based on the Bradley-Terry model [3] in Eq. 10 w.r.t. the target reward signal $r$ (potentially non-differentiable). + +$$ +\mathcal {L} _ {\text {s u r r}} (\psi ; r) = - \mathbb {E} _ {\mathbf {c}, \mathbf {z} ^ {w}, \mathbf {z} ^ {l}} \left[ \log \left(y _ {\psi} ^ {\mathbf {c}} \left(\mathbf {z} ^ {w}, \mathbf {z} ^ {l}\right)\right) \right] \tag {10} +$$ + +$$ +\mathbf {z} ^ {w} \succeq \mathbf {z} ^ {l} \text {r a n k e d a c o r d i n g t o r e w a r d} r +$$ + +$$ +y _ {\psi} ^ {\mathbf {c}} (\mathbf {z} ^ {w}, \mathbf {z} ^ {l}) = \frac {\exp \left(\mathcal {R} _ {\psi} (\mathbf {z} ^ {w} , \mathbf {c})\right)}{\exp \left(\mathcal {R} _ {\psi} (\mathbf {z} ^ {l} , \mathbf {c})\right) + \exp \left(\mathcal {R} _ {\psi} (\mathbf {z} ^ {w} , \mathbf {c})\right)} +$$ + +Namely, the surrogate reward $\mathcal{R}_{\psi}$ produces $\mathcal{R}_{\psi}(\mathbf{z},\mathbf{c})\in \mathbb{R}$ given prompt $\mathbf{c}$ and a latent code $\mathbf{z}$ ; the winning and losing pair $(\mathbf{z}^w,\mathbf{z}^l)$ are selected from the samples (more on this shortly) according to the target reward $r$ ; $\mathcal{L}_{\mathrm{sur}}$ is a binary cross entropy loss that trains $\mathcal{R}_{\psi}$ to predict a higher score for the winning sample $\mathbf{z}^w$ , thus transforming the knowledge from $r$ to $\mathcal{R}_{\psi}$ . Additional benefits of this latent-space reward are the improved computation & memory efficiency (no need to back-prop through VAEs) and the potential to capture image details better ( $\mathcal{R}_{\psi}$ operates in the learned downsampled latent space; others [26, 75, 78] operates in the "brute-force" downsampled image space). + +We target improvements in one and two-step image generation, a goal reflected in our design of both stages. In the pre-training stage with a pre-trained LCM $f_{\theta}$ , in each iteration, given a randomly drawn prompt $\mathbf{c}$ , we sample $N_{s}$ different $1^{\mathrm{st}}$ -step LCM outputs $\{\mathbf{z}_1 \triangleq f_{\theta}(\mathbf{z}_{\tau_0}, \tau_0, \mathbf{c})\}$ with $N_{s}$ initial noise $\{\mathbf{z}_{\tau_0}\}$ (off-policy exploration, see Sec. 5.3) and then sample the $2^{\mathrm{nd}}$ LCM step to get $\{\mathbf{z}_2 \triangleq f_{\theta}(\mathbf{z}_1 + Z, \tau_{H/2}, \mathbf{c})\}$ with injected noise $\{Z\}$ as in Eq. 6. Presented in Alg. 1, in the pre-training stage, we train $\mathcal{R}_{\psi}$ using $\{((\mathbf{z}_1^w, \mathbf{z}_1^l, \mathbf{c})\}$ selected from $\{\mathbf{z}_1\}$ and $\{(\mathbf{z}_2^w, \mathbf{z}_2^l, \mathbf{c})\}$ + +from $\{\mathbf{z}_2\}$ , facilitating the downstream task - reward finetuning two-step DMs. + +Algorithm 1 Pre-training Stage for Two-step DMs (e.g., LCMs) +Require: prompt set $\mathcal{C}$ ; initial surrogate reward $\mathcal{R}_{\psi}$ ; LCM $f_{\theta}$ ; learning rate $\eta$ ; VAE decoder $\mathcal{D}$ ; target reward (can be non-differentiable) $r$ ; hyper-parameter $N_s$ +1: repeat +2: Sample prompt $\mathbf{c} \sim \mathcal{C}$ +3: Sample two-step LCM $f_{\theta}$ for $N_s$ times to get $\{\mathbf{z}_1\}, \{\mathbf{z}_2\}$ +4: Find a W/L pair $(\mathbf{z}_1^w, \mathbf{z}_1^l)$ from $\{\mathbf{z}_1\}$ acc. to $r(\mathcal{D}(\mathbf{z}_1), \mathbf{c})$ +5: Find a W/L pair $(\mathbf{z}_2^w, \mathbf{z}_2^l)$ from $\{\mathbf{z}_2\}$ acc. to $r(\mathcal{D}(\mathbf{z}_2), \mathbf{c})$ +6: Compute $\mathcal{L}_{\mathrm{surr}}^1(\psi; r)$ from Eq. 10 given $(\mathbf{z}_1^w, \mathbf{z}_1^l, \mathbf{c})$ +7: Compute $\mathcal{L}_{\mathrm{surr}}^2(\psi; r)$ from Eq. 10 given $(\mathbf{z}_2^w, \mathbf{z}_2^l, \mathbf{c})$ +8: $\psi \gets \psi - \eta \nabla_{\psi}[\mathcal{L}_{\mathrm{surr}}^1(\psi; r) + \mathcal{L}_{\mathrm{surr}}^2(\psi; r)]$ +9: until convergence + +# 5.2. Direct Reward Fine-tuning of Two-Step DMs + +After pre-training, we enter the fine-tuning stage, which alternates between reward fine-tuning the DMs and online adapting the surrogate reward (which handles the distribution drift of the outputs of fine-tuned two-step DMs). We present this stage in Fig. 3 and in Alg. 2. + +Algorithm 2 Fine-tuning Stage for Two-step DMs (e.g., LCMs) +Require: (besides $\mathcal{C}$ $f_{\theta},\mathcal{D},r,N_s$ from Alg. 1) pre-trained surrogate $\mathcal{R}_{\psi}^{*}$ ; learning rates $\eta_1,\eta_2$ # steps $N_{1},N_{2}$ reg. loss $\mathcal{L}_{\mathrm{lcm}}$ (Eq. 3); loss coeff. $c,c_1,c_2$ ; norm. and clipping function $S$ +1: repeat +2: (Re-)initiate the replay buffer $\mathcal{B} = \emptyset$ +3: repeat "Reward Fine-tuning" +4: Sample prompt $\mathbf{c}\sim \mathcal{C}$ +5: Sample $\{\mathbf{z}_1\}$ $\{\mathbf{z}_2\}$ as results of a two-step LCM $f_{\theta}$ +6: Compute $\mathcal{S}[\mathcal{R}_{\psi}(\mathbf{z}_1,\mathbf{c})]$ and $\mathcal{S}[\mathcal{R}_{\psi}(\mathbf{z}_2,\mathbf{c})]$ +7: Compute reg. loss with $\mathcal{L}_{\mathrm{lcm}}$ and $\mathcal{L}_{\mathrm{lasro}}$ from Eq. 11 +8: $\theta \gets \theta -\eta_1\mathcal{L}_{\mathrm{lasro}}$ +9: Find $\mathbf{z}_{*}^{w},\mathbf{z}_{*}^{l}$ from $\{\mathbf{z}_1\}$ $\{\mathbf{z}_2\}$ with $r$ , similar to Alg. 1 +10: Insert $(\mathbf{z}_1^w,\mathbf{z}_1^l,\mathbf{c})$ and $(\mathbf{z}_2^w,\mathbf{z}_2^l,\mathbf{c})$ to $\mathcal{B}$ +11: until $N_{1}$ steps +12: repeat "Online Adaptation" +13: Sample $(\mathbf{z}_{*}^{w},\mathbf{z}_{*}^{l},\mathbf{c})\sim \mathcal{B}$ to compute $\mathcal{L}_{\mathrm{surt}}^{*}(\psi ;r)$ +14: Update $\psi$ similar to Alg. 1 with learning rate $\eta_{2}$ +15: until $N_{2}$ steps +16: until convergence + +During reward fine-tuning, we use a normalized and clipped fine-tuning loss $S[\mathcal{R}_{\psi}(\mathbf{z}_*, \mathbf{c})]$ . By keeping track of the moving average and "maximum" value of the surrogate reward, $S$ essentially improves training stability (details in Appendix B). We use the original step-distillation loss for the distilled DMs (with a separate prompt and image set for distillation) as a regularization loss. For LCM, it is $\mathcal{L}_{\mathrm{lcm}}$ from Eq. 3. The total fine-tuning loss is: + +$$ +\mathcal {L} _ {\text {l a s r o}} = c \mathcal {L} _ {\mathrm {l c m}} + c _ {1} \mathcal {S} \left[ \mathcal {R} _ {\psi} \left(\mathbf {z} _ {1}, \mathbf {c}\right) \right] + c _ {2} \mathcal {S} \left[ \mathcal {R} _ {\psi} \left(\mathbf {z} _ {2}, \mathbf {c}\right) \right] \tag {11} +$$ + +where $c, c_1, c_2$ are loss coefficients (hyper-parameters). + +# 5.3. Theoretical Insight - Value-Based RL + +The superior performance of LaSRO over popular RL methods can be partly explained by its connection to value-based RL. In contrast to pure policy-based RL that usually relies on on-policy samples to estimate policy gradients, value-based RL [44, 73] uses off-policy samples to learn action value functions $Q(\mathbf{s}_t, \mathbf{a}_t)$ that quantify how "desirable" a particular state and action is via temporal difference (TD) learning [66]. Particularly for short-horizon MDPs with immediate rewards, value-based RL proves advantageous [67] because (1) the learned value function can reduce gradient noise and is more robust than pure policy gradient methods and (2) a completely off-policy exploration strategy is much more efficient than the alternatives. + +Value-based methods are largely under-explored for fine-tuning DMs. For instance, existing methods like DDPO [2] utilize the clipped RL objective in PPO yet use no learned value function. LaSRO shares several functional and structural similarities with value-based methods: (i) The TD loss for horizon $H = 2$ can be shown largely equivalent to the surrogate reward loss $\mathcal{L}_{\mathrm{surf}}$ from Eq. 10, with the surrogate $\mathcal{R}_{\psi}$ largely equivalent to the value function $Q$ . (ii) Optimizing LCMs $f_{\theta}$ is guided by $\mathcal{R}_{\psi}$ , similar to how policy is guided by value function. (iii) Exploration is done in an efficient off-policy manner via also sampling the initial noise $\mathbf{x}_{\tau_0}$ for $N_{s}$ times, rather than restricted to the on-policy distribution $p_{\theta}(\mathbf{x}_{\tau_H} | \mathbf{x}_{\tau_0}, \mathbf{c})$ with a fixed $\mathbf{x}_{\tau_0}$ . This connection gives us insights into the superiority of LaSRO. See more discussions in Appendix C. + +# 6. Experiments + +We demonstrate the superior performance of LaSRO for fine-tuning two-step DMs over three distinctive rewards under the non-differentiable (black-box) reward setup [70]. Some rewards (e.g., the text-alignment score that involves sampling) are truly non-differentiable. We further perform ablation studies to justify our design (training scheme, choice of architecture/backbone, etc.). + +We choose LCMs [42] distilled from SSD-1B [15] as our major test bed since it is a strong baseline for 2-step image generation of $1024^{2}$ resolution (SDXL-Turbo [58] focuses on $512^{2}$ images and SDXL-Lightning [35] does not support 1-step generation). Our approach can also be applied to other step-distilled DMs, though (see Tab. 1). + +Please refer to App. D for implementation details. + +# 6.1. Case Study - Improving General Image Quality + +We apply LaSRO to improve the general image quality of two-step DMs by optimizing Image Reward [78]. Image Reward is a popular metric for text-to-image evaluations by using a BLIP-based model (learned from labeled data) to + +![](images/73000d1a931396f4ddaa8b6dad903b2de1c24800fb220f9d962108ac31f16ec4.jpg) +Figure 4. Comparison of LaSRO and other RL methods for fine-tuning two-step LCMs with Image Reward. Results on the test prompts of T2I-prompt-87K (left) and the (out-of-distribution) prompts of MJHQ-30K (right) show LaSRO effectively improve one-step (dashed lines) and two-step (solid) image generation. + +rate images based on criteria such as text alignment and aesthetics. It outperforms other metrics [26, 59, 75] in terms of alignment with human preference. We consider it a black box (while it is originally differentiable) and do not use its gradient information for all compared methods. + +Training Data We curate a set of 873k unique prompts, named T2I-prompt-873K, with text prompts from a combination of DiffusionDB [72] and open-prompts (link). We split it into 30k for the test split and the rest for training. + +Evaluation Protocol Besides the test set performance on T2I-prompt-873K, we also compare the generalization performance (both measured in Image Reward) over the prompts of MJHQ-30K [31], a set curated to balance 10 common text-to-image categories (thus, a different prompt distribution). We tune all compared methods to mitigate reward overoptimization [13] with the help of qualitative evaluation. We report the improved Image Reward during training as curves and summarize each curve by selecting its best checkpoint according to the FID [16] measured with the reference image set of MJHQ-30K, which accounts for the image fidelity (see details in Appendix E). + +Baselines and Results We compare LaSRO with strong RL fine-tuning baselines: GORS-LCM (an iterative generate-filter-distill method adapted to LCMs based on GORS [21]), PSO [43] (a method adapted for step-distilled DMs based on DM-DPO [71, 79]), and RLCM [45] (a variant of DDPO [2] for LCMs based on PPO [60]). Additionally, we apply LaSRO to fine-tuning SDXL-Turbo [58]. We report the results in Fig. 4, Tab. 1 and Fig. 1 & 6. + +![](images/d6ecc25261d39d14a14f20cca9c21d16b56f04b76d38e744e38cf2e1f2eeef76.jpg) +Figure 5. (left) LaSRO vs. GORS-LCM (other baselines fail) for fine-tuning LCMs with Attribute Binding Score and Text Alignment Score (all two-step perf. results). (right) Results from ablation studies that validate LaSRO's design (see Sec. 6.3). + +![](images/af1669ba2f60e94534e1384cbda4bacc7f64caf45af7b296e5c18191e125832a.jpg) + +
# stepsresolutionImage Reward
SDXL-Turbo [58]151220.817
SDXL-Turbo251220.839
+ LaSRO (ours)151220.904
+ LaSRO (ours)251220.957
SDXL-Lighting [35]2102420.634
SSD-1B-LCM [42]1102420.609
SSD-1B-LCM2102420.781
+RLCM/DDPO [2, 45]2102420.830
+PSO/Diff-DPO [43, 71]2102420.821
+ GORS-LCM [21]2102420.836
+ LaSRO (ours)1102420.946
+ LaSRO (ours)2102420.998
+ +Table 1. Gen. perf. on MJHQ-30K of step-distilled DMs and the fine-tuned DMs with RL methods (see details in Appendix E). We find that LaSRO is agnostic to step-distillation techniques. + +# 6.2. Additional Case Studies + +Besides general image quality, we provide two case studies of applying LaSRO to optimize two-step DMs with non-differentiable rewards designed for tailored criteria. + +Improving Attribute Binding we investigate using LaSRO to enhance attribute binding between the input prompts and the corresponding elements in generated images. Inspired by T2I-CompBench [21], we derive a reward that uses BLIP-VQA [32] to ask the generated image "if the subject exists?" and "if it has the correct attribute?" according to each noun phrase in the prompt (answering "yes" means score-1 and score-0 otherwise). The reward then computes the average score among all questions across all (prompt, image) pairs. Denoted as Attribute Binding Score, it is a non-differentiable reward reported as accuracy (\%) and is more intuitive than the original one from [21] (which uses averaged raw output score for "yes"). It is also harder for RL fine-tuning as the reward is more "discrete". + +![](images/49125667ba4d11bfe6c41ef2269a7ebb683b2e1fd08867d7bdcefe720576e168.jpg) +Figure 6. Two-step results (1024 $^2$ resolution) of LCM baseline and of fine-tuned LCM via LaSRO (with Image Reward for column 1-3 and with Attribute Binding Score for 4-5). LaSRO significantly improves both reward signals. See additional visual results in Appendix F. + +Improving Text Alignment Inspired by [2], we use a reward that first uses image captioning models (i.e., Florence-2 [77]) to capture the detailed text description of the generated image and then uses BERTScore [81] to compare the Text Alignment Score between this description and the original text prompt. This is a non-differentiable reward due to the image captioning procedure. + +Training Data and Evaluation Protocol For the attribute binding task, we use the train split of the 3k attribute-binding prompts from T2I-CompBench for training and use the corresponding test split for evaluation and report the Attribute Binding Score. Regarding text alignment, we set aside 27k prompts (train split) from MJHQ-30K for training and the rest (3k prompts) for evaluation with Text Alignment Score as the reported metric. + +Baselines and Results We compare LaSRO to the LCM baseline and GORS-LCM as we find other RL baselines suffer from training instability and are outperformed by GORS-LCM in both tasks. Please see results in Fig. 5 (left). + +# 6.3. Ablation Studies + +We conduct extensive ablation studies of LaSRO in improving the general image quality of two-step LCMs (by reporting the generalization perf. on MJHQ-30K). (a) We use CLIP or BLIP (instead of the UNet of latent DMs) as the surrogate reward's backbone, denoted w\CLIP and w\BLIP. (b) We examine a variant Alt.fTscheme, a reward fine-tuning scheme used in RG-LCM [33] and widely adopted in supervised reward fine-tuning of ordinary DMs [6, 78]. Compared to LaSRO, this scheme does not di + +rectly target $\leq 2$ -step generation. (c) We examine a variant No 1st-step loss, which set $c_{1} = 0$ in Eq. 11 to disable also optimizing the $1^{\text{st}}$ -step LCM results. (d) In No Online Adapt, we remove the surrogate reward online adaption substage in Alg. 2. (e) We include a non-RL baseline that directly uses Image Reward to replace the surrogate reward (gradient info. from Image Reward is used), denoted w\GTgradient. We did not observe the high-frequency noise issue reported in [33] that partly motivates their approach since, contrary to reward-guided distillation [33], we study fine-tuning after distillation. + +The numerical results in Fig. 5 (right) validate our design. Additionally, we find LaSRO relatively robust against manual noise perturbation of the GT. reward, partly explaining why it outperforms GT. reward gradients. + +# 7. Conclusion + +We address the challenges of fine-tuning 2-step image DMs with arbitrary reward signals. Our analysis identifies limitations in applying existing RL methods. In response, we propose LaSRO, a framework that learns differentiable surrogate rewards in the latent space with off-policy exploration to provide effective gradient guidance during DM fine-tuning. We show LaSRO's superiority over existing RL methods for optimizing diverse reward signals. 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RigGS is a new and effective paradigm for automatically modeling articulated objects from 2D videos without any template prior. RigGS allows for easy editing and interpolation of object motion while supporting high-quality real-time rendering for these creative poses. We visualize the constructed skeleton (top-left), skinning weights (top-right), and edited new poses (bottom) for each object. + +# Abstract + +This paper considers the problem of modeling articulated objects captured in 2D videos to enable novel view synthesis, while also being easily editable, drivable, and reusable. To tackle this challenging problem, we propose RigGS, a new paradigm that leverages 3D Gaussian representation and skeleton-based motion representation to model dynamic objects without utilizing additional template priors. Specifically, we first propose skeleton-aware node-controlled deformation, which deforms a canonical 3D Gaussian representation over time to initialize the modeling process, producing candidate skeleton nodes that are further simplified into a sparse 3D skeleton according to their motion and semantic information. Subsequently, based on the resulting skeleton, we design learnable skin deformations and pose-dependent detailed deformations, thereby easily deforming the 3D Gaussian representation to generate a skeleton-based object. + +erate new actions and render further high-quality images from novel views. Extensive experiments demonstrate that our method can generate realistic new actions easily for objects and achieve high-quality rendering. + +# 1. Introduction + +Rigging involves extracting an animatable skeleton and binding it to a deformable object, which is crucial in movies, games, and AR/VR. The skeleton, composed of interconnected bones and control joints, offers a structured and semantically rich representation of motion. This process is essential for realistic animation, allowing for natural movement and deformation. It also simplifies tasks such as pose editing, motion interpolation, motion transfer, and dynamic animation creation. + +Creating semantically plausible rigs automatically is challenging. Some methods use universal skeleton models from extensive datasets, like SMPL [17] for the human body, MANO [24] for the human hand, and SMAL [49] for animals. These models are essential for object recon + +striction, pose estimation, animation, etc. However, many dynamic objects, such as the human body with accessories, hands with personalized gloves, diverse animal species, deformable toys, or robots, cannot be standardized into a universal skeleton. Therefore, it is highly desired to develop a template-free model that can create a rig for any object with a skeletal structure. + +Some methods extract skeletons from a 3D representation of the object [35, 36]. However, they rely on artist-designed skeletons as supervision and can only handle symmetric objects. Optimization-based methods [4, 13, 31] can extract the skeleton from any 3D model, but the skeletons obtained are often very dense. Other approaches combine motion information to extract motion-aware skeletons from point cloud sequences [1, 37]. However, due to limited 3D data availability, these methods often lack practicality. With the rise of neural rendering, some methods [33, 40] utilize 2D images or videos to obtain rigs for objects. However, they often require a predefined skeleton structure and only optimize joint positions. Other methods [11, 28] do not need a predefined skeleton tree but rely on existing techniques to extract skeletons from 3D models, making them dependent on the quality of the reconstructed geometry and skeleton extraction. + +To address these challenges, we propose RigGS, a template-free automated rigging model that can extract 3D skeletons from monocular videos of moving objects and bind them to drive deformation. Firstly, we utilize a canonical 3D Gaussian shape representation that is deformed by a skeleton-aware node-controlled deformation field over time to initialize the modeling process, producing a set of skeleton-aware nodes. We then simplify the dense nodes using geometric, semantic, and motion information to achieve the final sparse 3D skeleton. Finally, we bind the canonical 3D Gaussians to the 3D skeleton to create a skeleton-driven dynamic model. Once trained, RigGS enables editing, motion interpolation, motion transfer, and animation of dynamic objects while supporting high-quality real-time rendering. Extensive experiments indicate that our RigGS can extract reasonable 3D skeletons, achieves rendering accuracy comparable to state-of-the-art methods, and allows for the flexible generation of new motions for the reconstructed dynamic objects. + +In summary, we propose a novel template-free paradigm that can synthesize dynamic objects captured in 2D videos from novel views and facilitate editing to create new actions. The technical novelty of our approach lies in: + +- we introduce a deformation field based on skeleton-aware nodes, combined with 3D Gaussians as the canonical shape representation, achieving simultaneous reconstruction of dynamic objects and obtaining candidate skeleton points; +- we propose a heuristic 3D skeleton construction algo + +rithm that considers geometric, semantic, and motion information; and + +- we develop a skeleton-driven dynamic model with learnable skinning weights to bind the skeleton with the 3D Gaussian representation and a pose-dependent detailed deformation, allowing for flexible generation of new motions. + +# 2. Related work + +Geometric Representation and Rendering. Traditional 3D modeling utilizes textured meshes as a typical representation. With the emergence of neural implicit representations, many methods are employing them to model 3D objects or scenes [18, 30]. Recently, 3D Gaussian Splatting (3DGS) [10] has gained attention for its efficient and high-quality rendering capabilities, along with its ease of editing, gradually becoming an important representation in 3D vision. Numerous approaches [7, 15, 32, 41, 45, 46] have also emerged to address the task of novel view synthesis for dynamic objects or scenes captured by videos. + +Prior-dependent Dynamic Modeling. Considering the challenges in skeleton extraction, various methods have leveraged category priors to establish specific parameterized models. For example, SMPL [17] is designed to represent human bodies, MANO [24] focuses on hand modeling, SMAL [49] extends to handle quadrupeds, and so on. These parameterized models have played important roles in tasks such as reconstruction, tracking, and animation within their domains [8, 19, 20, 42]. However, their representational capabilities are confined when dealing with shapes beyond their intended distributions, such as humans in intricate attire or animals from diverse categories. To enable broader applications, some methods do not utilize these parameterized models. CASA [34] establishes a database of animals, enabling category-agnostic skeletal animal reconstruction from monocular videos by retrieving and refining similar 3D models and skeletons from the database. Some methods take a pre-established skeletal tree structure as input, optimizing the positions of skeletal joints to model objects [33, 39, 43]. However, the pre-definition of the skeletal tree structure hampers the automation of skeleton creation. + +Neural Bones for Dynamic Objects. To establish a deformation field for arbitrary objects, BANMo [38] introduces a representation using neural bones. It no longer relies on the traditional skeletal tree structure; instead, it employs learnable bones, involving spatial positions and transformations, to represent the deformation. These neural bones can be distributed on the surface, inside, or even outside of the object. Similar to some control point-based deformation fields [2, 7, 44], these bones do not carry semantic information. Following BANMo, BAGS [47] adopt diffusion prior and 3DGS to construct animatable model from a single ca + +sual video. DreaMo [27] further establishes the skeleton based on the learned bones. It derives the connections between bones through clustering, utilizing the reconstructed mesh and skinning weights. Compared with the traditional skeleton structure, it is easier to construct, but more difficult to create reasonable new actions. + +Template-free Skeleton for Articulated Objects. Establishing a skeleton tree with a template-free algorithm for dynamic objects, thereby offering enhanced semantic meaning and editability is extremely challenging. Some methods utilize complete 3D representations, such as meshes, to achieve this [35, 36]. However, they can only handle meshes that have a symmetrical structure. Some methods focus on handling objects with articulated rigid structures [16, 25], such as laptops, glasses, or drawers. However, they cannot handle other types of dynamic objects, such as animals. Some methods take 2D images as input to build animatable models [11, 28]. They first reconstructed the dynamic representation and extracted the 3D mesh of the template shape, using the skeleton extraction method of the 3D model mentioned above to obtain the skeleton. Even though the skeleton will be refined in subsequent optimizations, they still rely on the quality of the 3D skeleton extraction and reconstruction of the template shape. Recently, SK-GS [29] utilizes 3D Gaussian Splitting and super-points to reconstruct dynamic objects and discovers the underlying skeleton model by treating super-points as rigid parts. + +# 3. Proposed Method + +Overview. Given a monocular video capturing continuous actions of an object, denoted as $\mathcal{I} = \{\mathbf{I}_t\}$ with $\mathbf{I}_t$ being the frame at time $t \in [0, 1]$ , we aim to model the animatable dynamic object such that it can be rendered from novel viewpoints, and more importantly, the object can be easily edited to create new actions. To tackle this challenging problem, we propose an automated 3D skeleton construction method along with a skeleton-driven deformation model. As illustrated in Fig. 2, we initially model the dynamic object through 3D Gaussian splatting in conjunction with a skeleton-aware node-controlled deformation model, resulting in a 3D Gaussian-based canonical representation and nodes imbued with skeleton semantics. These skeleton-aware nodes allow for the generation of a dense and redundant skeleton model, which is further simplified and enhanced based on geometric, motion, and symmetry considerations. Finally, we introduce a skeleton-driven deformation model that finely fits the input video and generates new actions. + +# 3.1. Initialization + +At this stage, we initialize the 4D reconstruction of the dynamic scene captured in $\mathcal{I}$ using a canonical 3D Gaussian + +representation that is deformed over time by skeleton-aware node-controlled deformation. + +Canonical 3D Gaussian Representation. The 3D Gaussian representation [10] is a collection of attributed 3D Gaussians with each Gaussian $G_{i}$ containing a center position $\mu_{i}$ , covariance matrix $\Sigma_{i}$ , opacity $\sigma_{i}$ and spherical harmonic coefficient $sh_{i}$ . The covariance matrix $\Sigma_{i}$ can be decomposed as $\boldsymbol{\Sigma}_{i} = \mathbf{R}_{i}\mathbf{S}_{i}\mathbf{S}_{i}^{T}\mathbf{R}_{i}^{T}$ for optimization, where $\mathbf{R}_{i}$ is a rotation matrix represented by a quaternion $\mathbf{q}_{i}$ , and $\mathbf{S}_{i}$ is a scaling matrix denoted by a 3D vector $\mathbf{s}_{i}$ . Rendering an image from a specific viewpoint $v_{i}$ involves projecting the 3D Gaussians onto a 2D plane, resulting in 2D Gaussians with projected means $\hat{\mu}_i$ and covariances $\hat{\Sigma}_i$ . The color $\mathcal{C}(u)$ of the image pixel $u$ can be calculated by + +$$ +\mathcal {C} (u) = \sum_ {i \in N} T _ {i} \alpha_ {i} \mathcal {S H} \left(s h _ {i}, v _ {i}\right), \text {w h e r e} T _ {i} = \prod_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j}\right). \tag {1} +$$ + +Here $\mathcal{SH}(\cdot ,\cdot)$ is the spherical harmonic function, and $\alpha_{i}$ can be calculated by + +$$ +\alpha_ {i} = \sigma_ {i} \exp \left(- \frac {1}{2} \left(u - \hat {\mu} _ {i}\right) ^ {T} \hat {\Sigma} _ {i} \left(u - \hat {\mu} _ {i}\right)\right). \tag {2} +$$ + +Therefore, a 3D scene is parameterized as $\mathcal{G} = \{G_i : \mu_i, \mathbf{q}_i, \mathbf{s}_i, \sigma_i, sh_i\}$ , which will be adjusted adaptively during the optimization process. + +Skeleton-aware Node-controlled Deformation. This module facilitates the temporal deformation of the canonical 3D Gaussian representation to model the dynamic scene. Specifically, the deformation of each 3D Gaussian at time $t$ is achieved as follows: + +$$ +\mu_ {i} ^ {t} = \sum_ {\mathbf {c} \in \mathcal {N} (\mu_ {i})} w _ {\mu_ {i}, \mathbf {c}} \left(\tilde {\mathbf {R}} _ {\mathbf {c}} ^ {t} \left(\mu_ {i} - \mathbf {c}\right) + \mathbf {c} + \tilde {\mathbf {t}} _ {\mathbf {c}} ^ {t}\right), \tag {3} +$$ + +where $\mathbf{C} = \{\mathbf{c}\}$ denotes the set of skeleton-aware nodes; $\tilde{\mathbf{R}}_{\mathbf{c}}^{t}\in \mathbb{R}^{3\times 3}$ and $\tilde{\mathbf{t}}_{\mathbf{c}}^{t}\in \mathbb{R}^{3}$ are the rotation matrix and translation vector of node c at time t; $\mathcal{N}(\mu_i)$ is the set of the $k$ nearest points to $\mu_{i}$ in C; the weight $w_{\mu_i,\mathbf{c}}$ is defined as + +$$ +w _ {\mu_ {i}, \mathbf {c}} = \frac {w _ {\mu_ {i} , \mathbf {c}} ^ {\prime}}{\sum_ {\mathbf {c} \in \mathcal {N} (\mu_ {i})} w _ {\mu_ {i} , \mathbf {c}} ^ {\prime}}, \tag {4} +$$ + +where + +$$ +w _ {\mu_ {i}, \mathbf {c}} ^ {\prime} = \exp \left(- \frac {\| \mu_ {i} - \mathbf {c} \| _ {2} ^ {2}}{2 o _ {\mathbf {c}} ^ {2}}\right). \tag {5} +$$ + +Here $o_{\mathbf{c}}$ is a learnable radius. The deformed node can be computed as + +$$ +\mathbf {c} ^ {t} = \mathbf {c} + \tilde {\mathbf {t}} _ {\mathbf {c}} ^ {t}. \tag {6} +$$ + +In cases where the 3D Gaussian exhibits anisotropy, its rotation at time $t$ can be defined as + +$$ +\mathbf {q} _ {i} ^ {t} = \left(\sum_ {\mathbf {c} \in \mathcal {N} \left(\mu_ {i}\right)} w _ {\mu_ {i}, \mathbf {c}} \mathbf {r} _ {\mathbf {c}} ^ {t}\right) \otimes \mathbf {q} _ {i}, \tag {7} +$$ + +![](images/5ad87a4e76d470d3a081b57ff0de09b7f12c63dab4201b1226ccb72e79f0acd2.jpg) +Figure 2. Overview of our RigGS. Initially, we construct a canonical 3D Gaussian, coupled with skeleton-aware node-controlled deformation, to begin the 4D reconstruction of the dynamic object. From the resulting skeleton-aware nodes, we then extract a sparse skeleton using a heuristic algorithm. Finally, leveraging the initialized deformation field and 3D Gaussians as starting values, we design learnable skinning weights and optimize a skeleton-driven deformation field. Our RigGS can be utilized for tasks such as editing, interpolation, and motion transfer, enabling real-time high-quality rendering of these new actions. + +where $\mathbf{r_c}^t\in \mathbb{R}^4$ is the quaternion representation of predicted rotation; $\otimes$ is the production of quaternions; and $\tilde{\mathbf{R}}_{\mathbf{c}}^{t},\tilde{\mathbf{t}}_{\mathbf{c}}^{t}$ and $\mathbf{r}_{\mathbf{c}}^{t}$ will be learnable via an MLP parameterized with $\Theta$ denoted as $F_{\Theta}(\gamma_{\mathbf{c}}(\mathbf{c}),\gamma_{t}(t))$ with $\gamma_{\mathbf{c}}$ and $\gamma_{t}$ being the positional encoding. + +Loss Function for Optimizing the Initialization Stage. By capitalizing on the alignment of the skeleton with an object's central axis, we introduce 2D skeleton projection constraints to refine the skeleton-aware nodes. Initially, we derive a set of 2D skeleton points, denoted as $\{\mathbf{p}_j^t\}$ , from a reference silhouette using a skeletonize/morphological thinning algorithm [48]. For deformed nodes $\{\mathbf{c}^t\}$ at time $t$ , we project them onto the 2D plane based on the camera viewpoint $v_{t}$ and then calculate the projection loss as: + +$$ +L _ {\operatorname {p r o j}} ^ {t} = \mathcal {C D} _ {\ell_ {1}} \left(\operatorname {P r o j} \left(\mathbf {c} ^ {t}, v _ {t}\right), \left\{\mathbf {p} _ {j} ^ {t} \right\}\right), \tag {8} +$$ + +where $\operatorname{Proj}(\cdot, \cdot)$ is a projection operator, and $\mathcal{CD}_{\ell_1}(\cdot, \cdot)$ is the $\ell_1$ -norm-based Chamfer distance [5]. Notably, unlike approaches that directly extract the central axis from the reconstructed 3D model [28], our method is simpler and not reliant on the 3D reconstruction quality. + +Moreover, we compute the rendering loss $L_{\text{render}}^t$ between the rendering image $\hat{\mathbf{I}}_t$ at time $t$ and input image $\mathbf{I}_t$ using a combination of $\ell_1$ loss and D-SSIM loss [9]. Inspired by SC-GS [7], we also introduce the ARAP loss [26] + +$L_{\mathrm{arap}}^t$ as a regularization term to maintain local rigidity during deformation. + +In summary, the overall loss at time $t$ is $L_{\mathrm{init}}^t = L_{\mathrm{render}}^t + w_{\mathrm{arap}}L_{\mathrm{arap}}^t + w_{\mathrm{proj}}L_{\mathrm{proj}}^t$ , where $w_{\mathrm{arap}}$ and $w_{\mathrm{proj}}$ are weights to balance the these terms. + +# 3.2. Coarse-to-Fine 3D Skeleton Construction + +Referring to the initial dynamic reconstruction acquired in Sec. 3.1, we begin by choosing a fresh canonical shape, followed by introducing a heuristic algorithm for deriving a sparse skeleton from the skeleton-aware nodes linked to the chosen canonical shape. + +Selection of Canonical Shape. Since the canonical shape derived in Sec. 3.1 doesn't correspond to any specific frame and hence lacks physical meaning (see Fig. 2), we replace it with a deformed shape at a chosen time representing the mean shape. Benefiting from the initialized reconstruction, we select the canonical shape based on pre-computed motion trajectories of skeleton-aware nodes. Specifically, for each node $\mathbf{c}$ , we compute the mean of its trajectory, that is $\overline{\mathbf{c}} = \sum_{\mathbf{I}_t \in \mathcal{I}} \mathbf{c}^t / |\mathcal{I}|$ , and select the time for the canonical shape by + +$$ +t ^ {*} = \arg \min _ {t} \sum_ {\mathbf {c}} \| \mathbf {c} ^ {t} - \overline {{\mathbf {c}}} \| _ {2}. +$$ + +In the following, the deformed Gaussians $\{G_i^{t^*}\}$ and node $\mathbf{c}^{t^*}$ at time $t^*$ will serve as the new canonical shape and + +skeleton candidate points. + +Dense Skeleton Construction. To remove redundant nodes, we initially employ farthest point sampling (FPS) on $\{\mathbf{c}^{t^*}\}$ to derive a subset of nodes that are uniformly distributed $\{\mathbf{c}_s^{t^*}\}_{s\in S}$ with $S$ being the index set. To establish the edge set to form a tree structure, we first construct an undirected fully connected graph with edge weights $\{\beta_{ij}\}_{i,j\in S}$ for $\{\mathbf{c}_s^{t^*}\}$ . We define + +$$ +\beta_ {i j} = \sum_ {t} d _ {i j} ^ {t} / | \mathcal {I} |, \text {w h e r e} d _ {i j} ^ {t} = \| \mathbf {c} _ {i} ^ {t} - \mathbf {c} _ {j} ^ {t} \|, +$$ + +considering both motion and positional information. We then use Prim's algorithm to obtain the minimum spanning tree. This tree contains three node types: junctions ( $>2$ neighbors), endpoints (1 neighbor), and connection points (2 neighbors). Due to noise in $\{\mathbf{c}_s^{t^*}\}$ , unnecessary bifurcations may occur. Therefore, we remove redundant branches from junctions to endpoints and merge two closely located junctions. The dense skeleton tree is then constructed, denoted as $\mathcal{T}_d = \{\mathcal{J}_d,\mathcal{E}_d\}$ , where $\mathcal{J}_d = \{\mathbf{J}_i\}$ denotes the node positions, and $\mathcal{E}_d$ represents the connection between the nodes. + +Skeleton Simplification. For a more concise deformation representation, we devise a heuristic algorithm to obtain a sparse skeleton. We start with an empty sparse joint set, denoted as $\mathcal{I}$ , and progressively incorporate probable joint nodes from $\mathcal{I}_d$ . Endpoints and junctions are typically more meaningful, so we first add them into $\mathcal{I}$ . We then select points with a high probability of being geometric turning points in $\mathcal{I}_d$ , forming a potential joint point set $\mathcal{H}$ . Using semantic labels from DINOv2 features [21], we ensure semantic symmetry by adding or removing points from $\mathcal{H}$ . Finally, we incorporate $\mathcal{H}$ into $\mathcal{I}$ to form the final joint set. Using breadth-first search, we find the nearest endpoint for each junction, record the path length, and designate the junction with the longest path as the root joint $\mathbf{J}_r$ . Starting from the root joint, we define the joint closer to it as the parent and the other as the child for each edge. The sparse skeleton tree is denoted as $\mathcal{T} = \{\mathcal{I}, \mathcal{A}\}$ , where $\mathcal{A} = \{A_j\}_{j \in \mathcal{I} \setminus \{\mathbf{J}_r\}}$ contains all parent indices. Fig. 3 illustrates the skeleton construction process. More details can be found in the Supplementary Material. + +# 3.3. Skeleton-driven Dynamic Modeling + +Built upon the initial reconstruction in Sec. 3.1, the new canonical shape and the skeleton obtained in Sec. 3.2, we establish a skeleton-driven dynamic model including an LBS-based coarse deformation with learnable skinning weights and a pose-dependent detail deformation model at this stage. + +Learnable LBS-based Coarse Deformation. Denote by $b_{j}$ the edge/bone between joint $\mathbf{J}_{j}$ and its parent $\mathbf{J}_{A_{j}}$ . Sim + +ilar to [28, 33], we define global translation $\hat{\mathbf{t}}^t$ and rotation transformations $\{\hat{\mathbf{R}}_j^t\}_{\mathbf{J}_j\in \mathcal{I}}$ at time $t$ , representing the global rotation for the root $\mathbf{J}_r$ and the rotation of the child joint $\mathbf{J}_j$ around the parent joint $\mathbf{J}_{A_j}$ for others. Without loss of generality, we define $\mathbf{J}_1$ as the root node. For the center of a Gaussian $\mu_{i}$ in the canonical shape, we can deform it using linear blend skinning (LBS) [12]: + +$$ +\hat {\mu} _ {i} ^ {t} = \mathbf {T} _ {1} ^ {t} \left(\sum_ {j = 2} ^ {| \mathcal {I} |} \hat {\omega} _ {i, j} \mathbf {T} _ {j} ^ {t} \bar {\mu} _ {i}\right), \tag {9} +$$ + +where + +$$ +\mathbf {T} _ {j} ^ {t} = \mathbf {T} _ {A _ {j}} ^ {t} \hat {\mathbf {T}} _ {j} ^ {t} \text {a n d} \hat {\mathbf {T}} _ {j} ^ {t} = \left[ \begin{array}{c c} \hat {\mathbf {R}} _ {j} ^ {t} & \mathbf {J} _ {A _ {j}} - \hat {\mathbf {R}} _ {j} ^ {t} \mathbf {J} _ {A _ {j}} \\ \mathbf {0} & 1 \end{array} \right], \tag {10} +$$ + +and + +$$ +\mathbf {T} _ {1} ^ {t} = \left[ \begin{array}{c c} \hat {\mathbf {R}} _ {1} ^ {t} & \mathbf {J} _ {1} - \hat {\mathbf {R}} _ {1} ^ {t} \mathbf {J} _ {1} + \hat {\mathbf {t}} ^ {t} \\ \mathbf {0} & 1 \end{array} \right]. +$$ + +Here $\mathbf{T}_j^t$ is defined recursively by its parent $\mathbf{T}_{A_j}^t$ ; $\overline{\mu}_i$ is the homogeneous coordinate representation of $\mu_i$ ; $\hat{\omega}_{i,j}$ is the learnable skinning weight, which can be calculated by + +$$ +\hat {\omega} _ {i, j} = \frac {\tilde {\omega} _ {i , j}}{\sum_ {j = 2} ^ {| \mathcal {I} |} \tilde {\omega} _ {i , j}}, \quad \text {w h e r e} \tilde {\omega} _ {i, j} = \eta_ {i, j} \exp \left(- \frac {D ^ {2} \left(\mu_ {i} , b _ {j}\right)}{2 \nu_ {j} ^ {2}}\right). \tag {11} +$$ + +Here $D(\mu_i, b_j)$ is the distance between the Gaussian center $\mu_i$ and the bone $b_j$ ; $\{\nu_j\}_{j=2}^{|\mathcal{I}|}$ are the learnable radius parameters; $\{\eta_{i,j}\}_{j=2}^{|\mathcal{I}|}$ are the learnable scaling factors and are learned by an MLP $F_{\Psi}(\gamma_{\eta}(\mu_i))$ parameterized with $\Psi$ ; $\{\hat{\mathbf{R}}_1^t, \dots, \hat{\mathbf{R}}_{|\mathcal{I}|}^t\}$ are represented as in quaternion form $\{\hat{\mathbf{r}}_1^t, \dots, \hat{\mathbf{r}}_{|\mathcal{I}|}^t\}$ , together with translation $\hat{\mathbf{t}}^t$ , learned by an MLP $F_{\Phi}(\gamma_t(t))$ parameterized with $\Phi$ . It can be used to correct inappropriate geometric distance-based weights by incorporating motion information. When the 3D Gaussian exhibits anisotropy, we approximate its rotation by the rotation part of $\mathbf{T}_1^t\left(\sum_{j=2}^{|\mathcal{I}|} \hat{\omega}_{i,j} \mathbf{T}_j^t\right)$ . + +Pose-dependent Detail Deformation. Due to the sparsity of the skeleton, the deformation field it represents exhibits local rigidity, limiting its effectiveness in areas with fine details, such as cloth wrinkles undergoing subtle deformations under physical forces. To address this, we incorporate a pose-dependent detail deformation module that learns local details. Moreover, making this module pose-related rather than time-related allows us to generate more plausible details when creating new actions. Specifically, we use an MLP parameterized with $\Pi$ , denoted as $F_{\Pi}(\mu_i, \{\hat{\mathbf{r}}_1^t, \dots, \hat{\mathbf{r}}_{\lfloor \mathcal{I}\rfloor}^t\})$ , to learn the offsets $\delta_{i,t}$ for the center position $\mu_i$ of a Gaussian. The final position of the Gaussian center is then computed as $\mu_i^t = \hat{\mu}_i^t + \delta_{i,t}$ . By combining this with the rendering formula of 3D Gaussian splatting, we can obtain images from novel viewpoints and generate new motions by changing the pose. + +![](images/05e4d612fc08c09707a9ea5184d52f8218837b28ea02a2ff703b5904e890b3db.jpg) +Figure 3. The process of the skeleton construction. The red circles mark the nodes that need to be removed or merged, and the yellow circles mark some locations selected as skeleton joints. + +Loss Function. Apart from the rendering loss $L_{\text{render}}^t$ detailed in Sec. 3.1, we introduce three additional loss terms, resulting in the overall loss function at time $t$ : + +$$ +L ^ {t} = L _ {\mathrm {r e n d e r}} ^ {t} + w _ {\tilde {\mathrm {p r o j}}} ^ {t} L _ {\tilde {\mathrm {p r o j}}} ^ {t} + w _ {\mathrm {d e t a i l}} ^ {t} L _ {\mathrm {d e t a i l}} ^ {t} + w _ {\mathrm {i d}} L _ {\mathrm {i d}} ^ {t}. +$$ + +To ensure the deformed skeleton remains within the deformed shape, we use a skeleton projection loss similar to Eq. (8) in Sec. 3.1. Because the skeleton joints are sparser than the skeleton-aware nodes, we sample $\mathbf{Q}_{\mathcal{T}}^{t}$ along the skeleton bones to compute the Chamfer distance loss: + +$$ +L _ {\text {p r o j}} ^ {t} = \mathcal {C D} _ {\ell_ {1}} \left(\Pr \circ \mathrm {j} \left(\mathbf {Q} _ {\mathcal {T}} ^ {t}, v _ {t}\right), \left\{\mathbf {p} _ {j} ^ {t} \right\}\right). \tag {12} +$$ + +Due to the imperfect accuracy of the 2D skeleton (see Fig. 5), these inaccurate 2D skeletons can lead to erroneous guidance in deformation. Therefore, we design time-specific weights: $w_{\tilde{\mathrm{proj}}}^t = 10^{-3} \cdot \exp(-\left(L_{\tilde{\mathrm{proj}}}^t\right)^2 / 2\xi^2)$ , where $\xi$ is half the median of $\{L_{\tilde{\mathrm{proj}}}^t\}_t$ . According to the 3-sigma rule of the Gaussian distribution, 2D skeletons with errors less than 1.5 times the median are considered accurate and will be subjected to stronger constraints. + +To handle significant movements through LBS-based deformation and capture finer details with the other module, we introduce the regularization term + +$$ +L _ {\text {d e t a i l}} ^ {t} = \sum_ {i} \| \delta_ {i, t} \| _ {2} ^ {2} / | \mathcal {G} |, \tag {13} +$$ + +aimed at minimizing detailed deformations, where $|\mathcal{G}|$ denotes the number of Gaussians. The weight $w_{\mathrm{detail}}^t$ is set to $10^{3}$ when $t = t^{*}$ and 1 otherwise, ensuring consistency between shapes in the canonical shape and at the selected moment $t^{*}$ . Additionally, we enforce a constraint to align the skeleton pose at $t^{*}$ towards an identity transformation. So we define: $L_{\mathrm{id}}^t = \sum_{j=1}^{|\mathcal{I}|} \|\hat{\mathbf{r}}_j - \mathbf{I}_q\|_2^2 / |\mathcal{I}|$ for $t = t^{*}$ and $L_{\mathrm{id}}^t = 0$ for others, where $\mathbf{I}_q$ is the identity quaternion. + +# 4. Results + +# 4.1. Experimental Settings + +Implementation Details. In our RigGS, we utilized MLPs with 8 linear layers with a feature dimension of 256 to implement $F_{\Phi}(\cdot)$ , $F_{\Psi}(\cdot)$ , $F_{\Theta}(\cdot)$ , and $F_{\Pi}(\cdot)$ . The ADAM optimizer [3] was adopted during training. More details are available in the Supplementary Material. We conducted all experiments on a single NVIDIA RTX A6000 GPU. + +Datasets. We used two synthetic datasets: the D-NeRF dataset [23], which includes 8 sequences, and the DG-Mesh dataset [14], which includes 6 sequences. Each dataset contains a series of continuous actions. However, the "Bouncing balls" in the D-NeRF dataset and "Torus2sphere" in the DG-Mesh dataset do not match our task setting, and the test view frames in "Lego" in the D-NeRF dataset do not align with the training actions, as noted in [7]. Therefore, we tested only the remaining 6 sequences from the D-NeRF dataset and 5 sequences from the DG-Mesh dataset. Additionally, we considered real-captured datasets: 6 subjects (377, 386, 387, 392, 393, 394) on the ZJU-MoCap dataset [22]. + +![](images/024ea5bca46a9744f9a211a5960aafb5972403cefb7df4b16192e8471c5c685e.jpg) +Figure 4. Novel view rendering and repose results via anisotropic or isotropic 3D Gaussians. + +![](images/c7bb9310a1ad6cd77ad68e47ebb39c4021a8181c6aec47eef6f5d8d7ce96def9.jpg) +Figure 5. Comparison of visual results for different variants on 2D projection loss term. + +# 4.2. Ablation Study + +On the D-NeRF dataset, we evaluated the effectiveness of each component of our method using the following variations: + +- Anisotropic or isotropic 3D Gaussians. Although anisotropic 3D Gaussians yield images closer to the ground truth, they suffer significant quality degradation when the new poses differ greatly from the training pose, as shown in Fig. 4. Therefore, we use the isotropic 3D Gaussians for all experiments. +- Without 2D projection loss $L_{\tilde{proj}}^t$ or fixed weight $w_{\tilde{proj}}^t$ during training the skeleton-driven dynamic model. The 2D projection loss $L_{\tilde{proj}}^t$ assesses how well the skeleton aligns with the 3D Gaussians. We tested performances without this loss and with fixed weights, setting $w_{\tilde{proj}}^t = 10^{-3}$ . Fig. 5 shows that without the projection loss, the skeleton cannot be embedded into the 3D Gaussians. Using fixed $w_{\tilde{proj}}^t$ instead of adaptive weights can cause skeletons to protrude beyond the shape in some frames due to inaccuracies in the extracted 2D skeletons. +- Skeleton construction and skeleton-driven deformation field. More discussions, numerical results, and visual results are available in the Supplementary Material. + +# 4.3. Comparisons + +Novel View Synthesis. To demonstrate the advantages of our RigGS, we compared it with state-of-the-art approaches: D-NeRF [23], TiNeuVox [6], 4D-GS [32], SC-GS [7], and AP-NeRF [28] in novel viewpoint synthesis1. Except for AP-NeRF, other methods do not bind the skeleton, and do not support editing the object through repose. As shown in Table 1, our rendering accuracy is slightly lower than SC-GS but significantly higher than the other methods. Besides the use of anisotropic 3D Gaussians, SC-GS achieves better detail fitting due to its more freedom of deformation field (512 control points) and tempo + +Table 1. Comparisons of the average precision (PSNR $\uparrow$ / SSIM $\uparrow$ / LPIPS $\downarrow$ ) on the D-NeRF dataset and DG-Mesh dataset. + +
MethodD-NeRF [23]DG-Mesh [14]
PSNR / SSIM / LPIPSPSNR / SSIM / LPIPS
D-NeRF [23]30.48 / 0.973 / 0.049228.17 / 0.957 / 0.0778
TiNeuVox [6]32.60 / 0.983 / 0.043631.95 / 0.967 / 0.0477
4D-GS [32]33.25 / 0.989 / 0.023333.96 / 0.979 / 0.0272
SC-GS [7]43.04 / 0.998 / 0.006638.96 / 0.993 / 0.0136
AP-NeRF [28]30.94 / 0.970 / 0.035031.83 / 0.967 / 0.0460
Ours40.82 / 0.996 / 0.011237.65 / 0.991 / 0.0169
+ +![](images/2520f3c8194a308cde674fd986389b15312a6413cf4db8405af80361c1604fa6.jpg) +Figure 6. Comparison with state-of-the-art methods for novel view synthesis. + +Table 2. Comparisons of the average precision on ZJU-MoCap. + +
MethodPSNR ↑SSIM ↑LPIPS ↓
AP-NeRF [28]25.620.9190.0934
Ours33.540.9750.0327
+ +rally adjustments in scales and rotations of 3D Gaussians. However, these configurations do not apply to our task because we require sparse skeletons and require all deformation variables to be pose-related for generating plausible movements. Fig. 6 shows that visually, our method is comparable to SC-GS without significant disadvantages. Additionally, we also compared our method with AP-NeRF on the real-captured ZJU-MoCap dataset, and show the numerical results in Table 2. More visual results are available in the Supplementary Material. + +Skeleton and Skinning Weights. Closely related to our research, AP-NeRF [28] stands as an automated framework designed for the construction of skeletons and the modeling + +![](images/7de7f3ee94938c544c4748a75edfd472f36fc4c40557452d16b6f9a7fc719263.jpg) +Figure 7. Comparisons of the skeleton, the skinning weights, edited skeleton pose, and the corresponding reposed objects. + +![](images/49f3198c8d18ddf977eb097c57919d4cf0ba916b94bb3d3964ad923eb291bbda.jpg) +Source +Girlwalk + +![](images/a071fb9f3d1f55450b8108d03c74deac605aea9d8ead1226203df6af98cead68.jpg) + +![](images/86f659b9c61664dc117bfa5d0ddaab717b3e192db978439acc54fff9a535301a.jpg) +Jumpingjacks + +![](images/54bf0559f822f0c0e284be05ff6232ca3a1d9779ae06c1aa970f647e53a2be1d.jpg) + +![](images/d7b1c423c0053550502b7776397c1cce4d837f3036cec6bbe915c7e5b8c05272.jpg) +Mutant + +![](images/6e0096bce192317d54efa07d5228ffbe5349f70853574aadfebc8b4870834082.jpg) + +![](images/d160735ae2c168090ed88def0e54ef5dee64cb2e7a3e9ddb1e90bc5081139e8f.jpg) +Hellwarrior + +![](images/6c45308feb911596d011131569c71b55dbc1657015daea46dac7712a3d6a2d77.jpg) + +![](images/60701fdc8df8c301def5ea005c369d0ad64b0c5afe763ee295c22cbaa857544e.jpg) + +![](images/6ddbb23b48300860a926773c664332a4530fcabc2daf0e6be98fb0a893be3974.jpg) +Figure 8. Visualization of motion transfer from the source object to the target object. + +![](images/c9cb56ec704bf42af2b62d817ef1b1c6235c9c8c3c0a674121bbfb0d6d683534.jpg) + +![](images/33bb75b7ba7e5e64d0948f5a491dd171f188a1672a68f7e993646cdfbdf04611.jpg) + +![](images/75b889e612aec866d12b9ddaf0b9838232a2bceda9bf885c8f2aede1e57d8059.jpg) + +![](images/e0ce284da79c98ba55f77fbb9780e93201aa9e4b992028f8729689302bf67b6c.jpg) + +![](images/7f29010dac01369fb0750905a7e8893b1ddc08df91baf65faa0f8eaa8bbc89f8.jpg) + +of articulated objects. Initialized with TiNeuVox [6], it utilizes reconstructed surface points to extract a 3D skeleton employing the Medial Axis Transform (MAT), refining the skeleton progressively through optimization steps. In contrast, our approach diminishes the dependency on the quality of 3D reconstruction. As shown in Fig. 7, we compared AP-NeRF with our method on the constructed skeleton and skinning weights. Furthermore, we manipulated the poses of the skeletons to generate the same new actions for the object. We can observe that our skeleton is more reasonable, and the skinning weights are smoother, avoiding discontinuities at the joints. In addition, we have higher rendering quality. + +Editing and Interpolation. Thanks to our skeleton-driven deformation field, we can create new motions for the object by editing the rotations of the skeleton bones. To facilitate this process, we have developed a GUI that allows for interactive editing and real-time rendering of the results. Figs. 1, 7 and 9 display several editing performances. Additionally, as shown in Fig. 9, we can easily interpolate between two poses of an object in a plausible manner. + +![](images/e30e365374c127768c6240a01a62e1b979571517db280c61fd2bf852d9093a63.jpg) + +![](images/b0c928943eb17f62f6bbc5a9ccc149217ba0594ed5c132916a4b86e39e335b4a.jpg) + +![](images/e8ae9af55601f524c5e30bc167ce8752a0fbdc031c1dce5faded800cf479db9a.jpg) + +![](images/f9abdacb203cbd1d0de2049c8aed8d27cc3d8923e05632712d394df2bc1d353e.jpg) + +![](images/7b47e76c876712c794c5dc68911faf17b28d3d66f53be17e6ecbaaff05fed23d.jpg) +Selected pose + +![](images/10eda8adf0679f9dd918e7859584a6a5d932e25077989cbc83872249a446d0d4.jpg) +Interpolation +Figure 9. Visualizations of the selected pose, the edited pose, and the interpolated results between them. + +![](images/d204bb07114e93e492fbf3a0516e6a259114d607039eedec2d377490a29d802c.jpg) + +![](images/0c53d3a660d33e36409de1f00a38094528d587ea4f3f4aa84ab797523a093e8e.jpg) +Edited pose + +Motion Transfer. Our method can also be utilized for motion transfer tasks. As illustrated in Fig. 8, for two sequences with similar structures, we first manually annotate the correspondences between their skeletons, repose the target object to match the source object's pose, and then transfer the source object's pose sequences to drive the target object, generating new motion sequences. + +# 5. Conclusion and Discussion + +We have presented RigGS, a skeleton-driven modeling approach that reconstructs articulated objects from 2D videos without relying on any template priors. First, we initialized the reconstruction of dynamic objects from input videos using a skeleton-aware node-controlled deformation field combined with a canonical 3D Gaussian representation, which also yields candidate points for the skeleton. Second, we introduced an automated skeleton extraction algorithm to obtain a sparse skeleton from these candidate points. Finally, we established a skeleton-driven dynamic modeling approach that binds the canonical 3D Gaussians with the skeleton, enabling tasks such as editing, interpolation, and motion transfer, while rendering high-quality images from novel viewpoints. Experimental results demonstrated that our method achieves rendering quality close to state-of-the-art novel view synthesis methods while easily generating new poses for the objects. + +While our RigGS has shown promising results in many cases, its effectiveness may be limited when dealing with sparse viewpoints, inaccurate estimation of camera poses, or excessive motion. The pose-related appearance is also not modeled. More useful techniques for 3D reconstruction and editing will be helpful in solving these challenging problems. 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Examples from our dataset, illustrating the diversity in locations, rip current types, viewpoint elevations and viewing angles. Rip currents are identifiable by distinct wave-breaking patterns, sediment transport, and instances of deflection rip currents. Rip current annotations are shown in red. Additional examples are provided in the supplementary material. Best viewed in color. + +![](images/5837213e81ab5a9df9682574255291a0190322d97df59c09f87b7ebcc38eff56.jpg) +Elevated Beachfront + +![](images/6222a9032084aaef571151c5fd7908594fe3c3dd3adf20b03953a26924f52031.jpg) +Water-Level Beachfront + +# Abstract + +Rip currents are strong, localized and narrow currents of water that flow outwards into the sea, causing numerous beach-related injuries and fatalities worldwide. Accurate identification of rip currents remains challenging due to their amorphous nature and the lack of annotated data, which often requires expert knowledge. To address these issues, we present RipVIS, a large-scale video instance segmentation benchmark explicitly designed for rip current segmentation. RipVIS is an order of magnitude larger than previous datasets, featuring 184 videos (212,328 frames), of which 150 videos (163,528 frames) are with rip currents, collected from various sources, including drones, mobile phones, and fixed beach cameras. Our dataset encompasses diverse visual contexts, such as wave-breaking patterns, sediment flows, and water color variations, across multiple global locations, including USA, Mexico, Costa Rica, Portugal, Italy, Greece, Romania, Sri Lanka, Australia and New Zealand. Most videos are annotated at 5 FPS to ensure accuracy in dynamic scenarios, supple + +mented by an additional 34 videos (48,800 frames) without rip currents. We conduct comprehensive experiments with Mask R-CNN, Cascade Mask R-CNN, SparseInst and YOLO11, fine-tuning these models for the task of rip current segmentation. Results are reported in terms of multiple metrics, with a particular focus on the $F_{2}$ score to prioritize recall and reduce false negatives. To enhance segmentation performance, we introduce a novel post-processing step based on Temporal Confidence Aggregation (TCA). RipVIS aims to set a new standard for rip current segmentation, contributing towards safer beach environments. We offer a benchmark website to share data, models, and results with the research community, encouraging ongoing collaboration and future contributions, at https://ripvis.ai. + +# 1. Introduction + +Rip currents are powerful, fast-moving surface currents that flow seaward from the shore. Detecting and understanding rip currents is critical, as accurate detection can prevent fatalities. Each year, numerous lives are lost globally due to + +these dangerous phenomena, emphasizing the urgent need for effective solutions. These hazardous currents are common along coastlines worldwide, including oceans, seas, and large lakes [2, 4, 8, 13, 38]. They vary widely in size and speed, influenced by nearshore hydrodynamics, underwater morphology, and occasionally, by human activity near coastal structures [3, 17]. Some rip currents reach speeds of up to $8.7\mathrm{km / h}$ , faster than even Olympic swimmers [43]. The main risk lies not only in their strength, but also in the widespread lack of public awareness on how to recognize and respond to them. Often, individuals caught in a rip current panic and attempt to swim directly against it, leading to exhaustion and even drowning. Effective safety measures include swimming parallel to the shore to escape and, ideally, early detection systems to warn beachgoers. + +In computer vision, detection and segmentation methods for visual data have advanced considerably [21, 24, 28, 30, 33, 33, 34, 41, 54, 59, 60], largely due to the availability of high-quality datasets focused on object detection and segmentation in images [12, 20, 22, 35]. Recently, video instance segmentation has emerged as an active area of research, with datasets like DAVIS [45] and YouTube-VIS [62], supporting ongoing challenges [62, 63]. Despite these advancements and the growing interest in automatic rip current detection [10, 14-16, 39, 40, 42, 46, 50-53, 65], the complex rip current detection task remains understudied. The primary barrier to further progress is the lack of sufficient high-quality data. Collecting and annotating this data is difficult due to several factors: + +1. Rip currents vary widely in appearance, being influenced by environmental factors, such as water body, beach structure, weather, and bathymetric conditions. Gathering diverse data requires global efforts across varied weather conditions, including hostile ones. +2. While some rip currents are visually distinctive, others require expert knowledge to be identified (see Figure 6). +3. Rip currents are best observed from elevated viewpoints, often requiring the use of drones or elevated positions, like towers or cliffs. Not all beaches have elevated locations, making drones essential in many cases. +4. Accurate annotation for instance segmentation of rip currents is challenging and labor-intensive, requiring expertise in rip current dynamics, alongside computer vision skills, patience and attention to details. +5. Rip currents are amorphous objects (see Figure 1 and 7). Unlike objects with consistent shapes and clear boundaries, rip currents are continuously changing in shape and form, making them particularly challenging to detect. While some amorphous objects, like fire or smoke, also undergo continuous shape changes, they usually stand out distinctly from their background, making them easier to identify. In contrast, rip currents blend seamlessly into the large water environment, often appearing + +as subtle patterns within a dynamic, constantly shifting background. This unique characteristic of rip currents demands diverse and extensive data to facilitate accurate and reliable detection. + +To address this problem, we introduce the RipVIS dataset. The culmination of three years of work and a team of over 30 people, involved in both data collection and annotation, has successfully materialized into this dataset. With diversity in types of rip currents, elevation, conditions and locations, RipVIS is a high-quality dataset, which is an order of magnitude larger than any existing alternative. + +In summary, our contribution is fourfold: + +- RipVIS benchmark: We introduce RipVIS, an open benchmark for rip current instance segmentation, featuring 184 videos (212, 328 frames), out of which 150 videos (163, 528 frames) contain rip currents annotated at an average sampling rate of 5 FPS, and 34 videos (48,800 frames) are without rip currents. +- Baseline models and analysis: We establish baselines using several state-of-the-art instance segmentation methods, analyzing their performance on this challenging dataset and highlighting the need for improvement. +- Temporal Confidence Aggregation: We propose a Temporal Confidence Aggregation (TCA) technique, which boosts segmentation quality by incorporating temporal consistency across frames, improving the results, both qualitatively and quantitatively. +- Benchmark website and community engagement: We host RipVIS on a dedicated website (https://ripvis.ai), promoting community collaboration and inviting researchers to contribute with new data and models. Each submitted video is carefully annotated, with credits given to both contributors and annotators, reinforcing our commitment to continually enhancing rip current segmentation quality for improved beach safety. + +# 2. Related Work + +Rip currents have been extensively researched in the natural sciences [3, 17, 27, 32, 57, 58, 64]. Traditional observation techniques include visual monitoring and camera-based systems [18, 26, 48]. Precision tracking with GPS-equipped drifters or floating devices [7, 8, 56] is effective, but costly, location-dependent, and unsuitable for flash rip detection. Newer tools, such as laser rangefinders and drones with tracer dye, offer flexibility and broader perspectives [11, 29, 49]. In contrast, machine learning (ML) approaches are cost-effective, scalable, and capable of real-time detection, making rip current detection more accessible for public safety applications. We further discuss related studies introducing datasets to train ML methods for rip current detection, as well as studies proposing such methods. + +
DatasetTotalWith Rip CurrentsWithout Rip CurrentsTrainValidationTestSegmentation Annotations
Maryan et al. (2019) [39]5,310 images514 images4,796 images4,779 images (10-fold)-531 images (10-fold)X
de Silva et al. (2021) [14]20,482 images10,793 images9,689 images2,440 images-23 videos 18,042 framesX
YOLO-Rip (2022) [65]3,793 images2,486 images1,307 images3,793 images-same as de Silva et al. [14]X
Dumitriu et al. (2023) [16]37,057 frames26,761 frames10,296 frames3,396 images (10-fold)377 images (10-fold)25 videos 33,284 frames✓
RipVIS (ours)184 videos 212,328 frames150 videos 163,528 frames34 videos 48,800 frames112 videos 147,802 frames36 videos 32,566 frames36 videos 31,960 frames✓
+ +Table 1. Comparison of public rip currents datasets. As observed, our dataset is an order of magnitude larger than any other publicly available dataset, with increased diversity and a train-validation-test split. All datasets, including ours, have bounding box annotations. + +# 2.1. Datasets + +As shown in Table 1, a number of rip currents datasets are publicly available. Maryan et al. [39] introduced a dataset containing 514 rip channel examples, including test samples. The dataset consists of small $24 \times 24$ pixel rip channel images, extracted from larger $1334 \times 1334$ timex images sourced from the Oregon State University beach imagery archive [1]. These timex images were orthorectified and time-averaged over 1,200 frames at $2\mathrm{Hz}$ , covering 10-minute intervals. Rip channel samples were isolated using the GIMP image editor, resized to $24 \times 24$ pixels, and converted to grayscale to reduce the impact of varying lighting conditions on model performance. To expand the dataset for deep learning applications, data augmentation techniques were applied, resulting in a dataset of over 4,000 rip channel images. This dataset facilitated the training of a CNN, but it was also instrumental in training and evaluating several rip current detection algorithms, including studies by Rashid et al. [51-53]. + +In their study, de Silva et al. [14] introduced a training dataset primarily sourced from Google Earth, consisting of high-resolution aerial images of beach scenes both with and without rip currents. The dataset includes 1,740 rip current images and 700 non-rip current images, with sizes ranging from $1086 \times 916$ to $234 \times 234$ pixels. Each rip current image was annotated with axis-aligned bounding boxes to serve as ground truth. Additionally, de Silva et al. [14] compiled a test dataset of 23 videos with 18,042 frames in total, out of which only 9,053 frames contained rip currents. While the static images were captured from a high-elevation viewpoint, the test videos were recorded from a lower perspective, with resolutions varying between $1280 \times 720$ and $1080 \times 920$ pixels. Ground-truth annotations for these images were verified by an expert from NOAA, although the videos only received categorical labels without frame-level annotations. The dataset was used to train a Faster R-CNN [55] model, with frame averaging applied as a temporal aggregation technique for improved bounding box prediction and detection accuracy. While the bounding box annotations of Silva et al. [14] provided valuable insights, they lack the granularity of instance segmentation, limiting the + +precision of rip current localization. + +The YOLO-Rip dataset [65] was created by expanding the dataset of de Silva et al. [14]. The authors collected additional real-world beach scene images along the South China coast, resulting in a total of 1,352 high-resolution images. Of these, 746 depict rip currents, while 606 do not, with image resolutions ranging from $4000 \times 2250$ to $480 \times 360$ pixels. Rip current boundaries in the images were annotated with axis-aligned bounding boxes. The extended dataset was designed to enhance model performance in recognizing rip currents across diverse image types, thereby improving its practical applicability in real-world scenarios. + +Dumitriu et al. [16] introduced the first instance segmentation dataset for rip currents, specifically focusing on annotating images and videos to delineate rip currents with high precision. They extended the work of de Silva et al. [14] and Zhu et al. [65] by adding detailed polygonal annotations to 2,466 aerial images of rip currents sourced from Google Maps. In addition to these static images, Dumitriu et al. included 17 video sequences recorded at the Black Sea, totaling 24,295 frames. These videos capture rip currents from an elevated and top perspective, with sampled frames annotated for segmentation. While this dataset marked a significant step forward by enabling instance segmentation, it is limited in geographic diversity, as all videos were recorded from a single location (the Black Sea). + +# 2.2. Detection Methods + +In recent years, the automatic identification of rip currents has garnered increasing attention [10, 14-16, 40, 42, 46, 50-53, 65]. Studies in this area generally fall into two categories: those using bounding boxes for rip current detection and those capturing the full shape. Most relevant approaches have been detailed along with the datasets they were published with. All of the approaches rely on video and image data [18, 25, 26, 48], with some using time-exposure or "timex" images to highlight rip current patterns over time [36, 44]. Rashid et al. [51] used an anomaly detection framework, RipNet, to improve accuracy by reducing the need for additional negative samples. The same team later introduced RipDet and RipDet+ [52, 53], treating the task as a detection problem. Pitman et al. [47] employed + +synthetic imagery, but this often led to underestimations. Liu et al. [37] utilized threshold and HSV-based segmentation, limited to sediment-visible currents. + +Optical flow has proven useful for rip current detection, particularly in cases lacking segment-level annotation. Philip et al. [46] employed the Lukas-Kanade optical flow algorithm to determine water flow direction and isolate rip currents, though this approach requires a stable platform and captures only the main flow direction. Mori et al. [42] enhanced flow visualization fields to improve detection, but similarly, their approach relies on a stationary camera. RipViz [15] combines optical flow with an LSTM autoencoder to detect rip currents as flow anomalies in stationary videos, offering an intuitive visualization of dangerous currents. McGill et al. [40] applied Farneback optical flow on timex images, improving accuracy in channel detection, though the method is time-consuming and sensitive to camera positioning and beach morphology. While optical flow techniques enable rip current detection without wave-breaking patterns, they are generally limited to specific camera setups. In contrast, our dataset includes diverse camera types and orientations, allowing for a broader applicability. + +Bounding box detection vs. segmentation. While bounding boxes provide valuable information, due to the amorphous property of rip currents, boxes can either include a significant amount of background information or leave out a significant part of the rip current, making precise beach monitoring a much more difficult task. + +# 3. RipVIS Dataset and Benchmark + +# 3.1. General Description + +The RipVIS Benchmark (Rip Currents Video Instance Segmentation) is a large-scale and high-quality dataset designed to address the limitations of previous rip current datasets in terms of diversity, annotation quality, and data structure (see Table 1). With 184 videos totaling 212,328 frames, RipVIS is the most comprehensive dataset for rip current instance segmentation to date. It contains 150 videos (163,528 frames) featuring rip currents and 34 videos (48,800 frames) without rip currents, allowing for both positive and negative sample training. The dataset was collected from diverse locations worldwide—including the USA, Mexico, Costa Rica, Portugal, Italy, Greece, Romania, Sri Lanka, Australia and New Zealand—capturing rip currents across varied visual contexts, environmental conditions, and geographic landscapes (see Figures 1 and 2). + +RipVIS introduces the first rip current dataset with a dedicated train-val-test split, manually curated by computer vision experts to mirror the data distribution accurately and prevent overfitting. This structured split, including a validation set, is crucial for effective hyperparameter tuning and + +![](images/a13274f9921ef28e420770bdf5d0e9a118c21d761c6581f489087c0b630fa8cf.jpg) +Figure 2. Map of the countries present in the RipVIS dataset. From left to right: USA, Mexico, Costa Rica, Portugal, Italy, Greece, Romania, Sri Lanka, Australia and New Zealand. Created with mapchart.net. + +robust model development, addressing a key limitation of prior datasets. Without it, models risk overfitting from tuning on test data or underperforming due to lack of tuning. Expert selection ensures balanced, reliable splits, enhancing evaluation consistency and laying a solid groundwork for advancing rip current detection and segmentation research. + +# 3.2. Sources + +RipVIS is compiled from multiple sources, with 76 videos recorded directly by the authors using drones and phone cameras at different locations worldwide. An additional 87 videos were collected from the Internet, providing real-world variability, while 21 videos were sourced from the de Silva et al. dataset [14]. Each video source and annotator is credited individually, ensuring transparency and traceability across the dataset. + +# 3.3. Video and Rip Current Variety + +Our dataset captures a diverse range of rip current characteristics from multiple perspectives, enhancing its utility for comprehensive analysis. The videos encompass four types of elevation and orientation (see Figure 1): water-level beachfront (captured at beach level), elevated beachfront (from stationary elevated points, like hills, buildings, or low-altitude drones), aerial tilted view (drone recordings at an inclined angle), and aerial bird's-eye view (high-altitude drone recordings). This range provides a robust basis for detecting rip currents from both traditional and challenging angles, a necessary improvement over previous datasets that were limited in this perspective. + +The dataset includes rip currents with considerable temporal and spatial variability, driven by shoreline geometry, underwater morphology, wave conditions, and tidal forces. Following the classification of Castelle et al. [8], RipVIS features primarily bathymetrically-controlled rip currents, which are shaped by underwater sandbars or channels, and boundary-controlled rip currents, which flow along the edges of anthropogenic structures like piers or jetties. These + +rip currents were identified primarily by gaps in wavebreaking patterns or offshore sediment transport. While the dataset does not include flash or traveling rip currents—due to their unpredictability and transient nature—it focuses on stable rip currents that vary in strength but remain consistent in location, offering a structured basis for segmentation. + +# 3.4. Annotations + +The annotation process was carried out by a team of 30 volunteers, trained and overseen by two academic experts with extensive experience in in-situ rip current measurements and analysis. Each volunteer received on-site training, and the experts annotated the first frame of each video using Roboflow [19] as a guide for consistency. All annotations were subsequently reviewed and validated by both experts, achieving an inter-annotator Cohen's $\kappa$ agreement of 0.82 (almost perfect agreement) on the entire dataset. This high agreement rate underscores the quality and reliability of the annotations. + +The dataset includes pixel-level annotations for rip currents, with 15,784 frames manually annotated using polygons for instance segmentation, totaling 25,298 rip current instances (an average of 1.6 rip currents per frame). Interpolated annotations were generated for intermediary frames to capture dynamics between manual annotations, with all interpolations verified for accuracy. This approach allows the dataset to provide 163,528 frames with rip currents, retaining the average of 1.6 rip currents per frame. + +Out of the 150 annotated videos, 28 required major revisions from the experts, necessitating re-annotation and closer supervision to maintain high annotation standards. The sampling rate depends on video dynamics, varying from 1 to 30 FPS, with the most common being 5 FPS. This rate is adjusted to suit video characteristics. For instance, stationary videos are annotated at a lower frame rate than moving camera footage, ensuring efficient yet accurate annotations. + +Annotations capture various states of rip currents, with most videos containing at least one visible rip current in each frame. Some videos feature instances where the rip current is temporarily obscured or less visible due to lighting or environmental factors, reflecting realistic conditions for model training. In these cases, since we are performing a frame-by-frame annotation, the rip currents have not been annotated, as they are not visually obvious. The diversity in annotation detail and sampling frequency helps create a comprehensive dataset that accommodates different model requirements and evaluation scenarios, setting RipVIS apart as a pioneering benchmark in rip current detection and segmentation research. + +Furthermore, the dataset also enables advanced analysis of rip current behavior over time. This positions RipVIS as a valuable resource for both computer vision researchers + +and coastal scientists, facilitating the development of robust detection models and contributing to improved rip current forecasting and public safety measures. + +# 4. Methods + +Segmentation is a much harder task than detection, and segmenting rip currents, due to their amorphous nature, is even harder. In this study, we evaluate a selection of popular, state-of-the-art segmentation models, focusing on their application to the RipVIS dataset. We distinguish between two-stage and one-stage detectors based on their architectural approach to the task. We then describe our TCA, used to improve both qualitative and quantitative results. We have selected the following methods based on their previous results, popularity and availability. For implementation details, see the supplementary material. + +# 4.1. Two-Stage Detectors + +- Mask RCNN. Mask RCNN [24] is a two-stage instance segmentation model that combines region proposals with pixel-level segmentation masks, making it a widely-used baseline for segmentation tasks. + +Cascade MASK RCNN. Cascade Mask RCNN [5] extends Mask RCNN with a multi-stage refinement approach, progressively improving bounding box and mask quality through stricter IoU thresholds at each stage. + +# 4.2. One-Stage Detectors + +YOLO11. YOLO11 [28] represents the latest evolution in the YOLO series, incorporating key improvements, particularly the C2PSA (Cross-Stage Partial Spatial Attention) module, which enhances spatial sensitivity and is useful for detecting small or partially occluded objects. YOLO11 is optimized for efficiency, achieving faster training times and reduced inference latency, which supports real-time applications. + +SparseInst. SparseInst [9] is a one-stage fully convolutional instance segmentation framework designed for real-time performance, leveraging sparse instance activation maps to directly segment objects in a single pass, without region proposals or post-processing. In our work, we implemented SparseInst with ResNet-50 (R-50) and ResNet101 (R-101) backbones, as well as the transformer-based PVTv2-B1 backbone. + +# 4.3. Temporal Confidence Aggregation (TCA) + +We propose TCA, a pixel-level post-processing technique aimed at improving segmentation consistency over video frames, especially for amorphous, dynamic phenomena such as rip currents. Rip currents continuously change shape and intensity, making frame-by-frame segmentation noisy and inconsistent. TCA addresses this issue by leveraging temporal coherence, aggregating confidence scores + +![](images/ca5e6500bdcfcf9590e0b1aa4fd7a6453b6589186369ea2e2835860880ef70e2.jpg) +Figure 3. The proposed Temporal Confidence Aggregation (TCA) process, simplified. TCA leverages temporal coherence through down sampling, instance tracking, temporal smoothing, and hysteresis thresholding to create a stabilized temporal heatmap. Best viewed in color. + +across frames to create a "temporal heatmap" that stabilizes detection (see Figure 3). The method works by: + +- Downsampling: To enable efficient pixel-level analysis, prediction masks are downsampled, reducing computational complexity, while preserving spatial relationships. +- Instance tracking: Tracking of individual instances is performed by computing the Intersection over Union (IoU) between masks from consecutive frames. The Hungarian algorithm [31] is then employed to optimally match previous and current instances, ensuring consistent identity assignment throughout the sequence. +- Temporal smoothing: TCA maintains a heatmap for each tracked instance, where pixel confidence scores incrementally increase with repeated detections and gradually decay in their absence. +- Thresholding: To generate final masks, TCA applies hysteresis thresholding to the accumulated heatmaps, adapting the dual-threshold technique introduced in the Canny edge detector [6]. Pixels that surpass a high threshold are identified as strong object regions, serving as seeds to include neighboring pixels that exceed a lower threshold, while those below are excluded. + +The benefits of TCA for segmentation are (see Figure 4): + +- Noise reduction: TCA effectively reduces false positives by exploiting temporal accumulation to filter out noise, requiring sustained evidence across multiple frames to confirm object presence. +- False negative mitigation: TCA also reduces false negatives by leveraging the temporal heatmap to recover pixels missed in individual frames, where transient noise or occlusions might obscure detection, provided that they show sustained presence across the aggregated scores. +- Refined segmentation masks: TCA refines predictions by smoothing instance boundaries over time, yielding more coherent and precise segmentation masks compared to inconsistent per-frame outputs. + +Our aggregated confidence map offers a clearer and more stable representation of rip current locations over time, enhancing visualization. Integrating TCA with instance segmentation models improves the $F_{2}$ score by prioritizing fewer false negatives, making it ideal for safety-critical beach monitoring applications. TCA provides an effective solution for accurately determining the shape and position of rip currents in dynamic coastal environments. + +# 5. Experiments and Results + +# 5.1. Environment and Parameters + +Model training was executed on a 24 GB NVIDIA GeForce RTX 4090 GPU, using YOLO11 from ultralytics v8.3.29 [28], Mask RCNN [24], Cascade Mask RCNN [5] and SparseInst [9] using Detector2 [61] v0.6, Python 3.10.4, PyTorch 1.12.1 and CUDA 12.2. All reported FPS are measured on RTX 12 GB 3060 GPU, on $1920 \times 1080$ videos. + +# 5.2. Evaluation Metrics + +To assess the effectiveness of our models in segmenting rip currents, we employ several standard evaluation metrics, following other video instance segmentation benchmarks [35, 45, 62], including IoU, Mean Average Precision (mAP), and the $F_{\beta}$ score, with an emphasis on the $F_{2}$ variant. + +To evaluate the model's detection quality across varying confidence thresholds, we use Average Precision (AP), which is derived from the Precision-Recall curve. AP is calculated by ranking model predictions by their confidence scores and integrating over the curve: + +$$ +A P = \sum_ {n} \left(\operatorname {R e c a l l} _ {n} - \operatorname {R e c a l l} _ {n - 1}\right) \cdot \operatorname {P r e c i s i o n} _ {n}. \tag {1} +$$ + +Since our model detects a single class (rip currents), the mean Average Precision (mAP) is equivalent to the AP for that class. Combining IoU for spatial accuracy and AP for threshold-independent detection quality provides a robust evaluation of the segmentation models. + +Finally, we utilize the $F_{\beta}$ score, a weighted harmonic mean of Precision and Recall, to offer a balanced metric. In our experiments, we specifically focus on $F_{2}$ , where $\beta = 2$ : + +$$ +F _ {\beta} = \frac {\left(1 + \beta^ {2}\right) \cdot (\text {p r e c i s i o n} \cdot \text {r e c a l l})}{\beta^ {2} \cdot \text {p r e c i s i o n} + \text {r e c a l l}}. \tag {2} +$$ + +Emphasizing recall with $F_{2}$ aligns with the safety-critical nature of rip current detection, as false negatives—missed detections—pose significant risks. In a beach monitoring system, a false positive may simply disturb beachgoers, while a false negative could result in a potentially life-threatening situation. Thus, prioritizing recall with $F_{2}$ allows us to reduce missed detections, enhancing safety. + +
ModelPrecisionRecallAP50F1F2FPS
Original+TCAOriginal+TCAOriginal+TCAOriginal+TCAOriginal+TCAOriginal+TCA
Mask-RCNN [24]0.4920.5380.6250.6510.5300.5560.5500.5890.5930.6257.846.73
Cascade Mask-RCNN [5]0.6060.6130.6600.6860.6280.6390.6320.6470.6480.6709.537.94
YOLO11n [28]0.7130.7190.5580.5910.6500.6480.6260.6480.5830.613128.2034.48
YOLO11s [28]0.7570.7520.6120.6470.7050.7230.6770.6960.6360.666116.2733.78
YOLO11m [28]0.7390.7450.6240.6480.7070.7260.6770.6930.6440.66576.9329.41
YOLO11l [28]0.8120.8190.5880.6130.7130.7290.6820.7010.6220.64657.1425.98
YOLO11x [28]0.7460.7420.6090.6470.6820.7030.6710.6910.6320.66434.0119.84
SparseInst R-50 [9]0.5200.5830.7820.8070.7030.7220.6440.6770.7100.74929.7318.32
SparseInst PVTv2 [9]0.6830.7120.7700.7980.7210.7510.7240.7530.7510.78027.9917.64
+ +Table 2. Performance comparison of different models on the test split, with and without TCA. The models are applied on video and the metrics are calculated by evaluating on manually annotated frames. The best result on each metric is highlighted in blue. + +# 5.3. Baseline Results (without TCA) + +The performance on both validation and test sets starts off modest, underscoring the room for improvement on this task (see Table 2). Unlike other datasets where bounding box detection often yields strong results with little effort, our dataset reveals the tougher challenge of accurately segmenting rip currents compared to simply detecting them. Different from the results of Dumitriu et al. [16], where YOLOv8 was used with reasonably good results, we show that the increase in diversity also results in increased difficulty (see Table 6). + +We observe notable performance differences among the evaluated models. SparseInst with PVTv2 and augmentation achieves the highest $F2$ score and a strong balance of precision and recall, while maintaining high FPS. YOLO11 variants, particularly the large model, lead in precision but exhibit lower recall, with YOLO11-nano being the fastest. + +# 5.4. Results with TCA + +Applying TCA significantly improves segmentation stability across all models (see Figures 5 and 4 and Table 2). TCA reduces false positives and enhances temporal consistency, especially in challenging, turbulent areas of water where rip currents appear intermittently. + +The $F_{2}$ score increases notably across models when TCA is applied, highlighting a reduction in false negatives, a critical improvement for safety-focused applications. In several cases of fast camera movement, TCA increases the number of false positives (see Figure 4). That number is negligible, as overall, the integration of TCA makes every model's output more reliable. This enables clearer and more stable segmentation of rip currents over video sequences, crucial for real-time beach monitoring. + +However, different TCA implementations suit distinct scenarios. A slow-gain, slow-decay TCA excels with stationary video footage, but hampers performance on moving + +video, where a fast-gain, fast-decay approach is preferred, while a fast-gain, slow-decay TCA can be ideal for safety-critical environments requiring caution. Although TCA is highly effective in known contexts, optimizing it for a diverse dataset can be challenging without prior knowledge of the video type it will process. + +# 5.5. General Analysis + +One-stage detectors offer faster and more stable outputs, outperforming the two-stage methods. The results showcase the difficulty of the RipVIS dataset. While all methods perform well on standard benchmarks, and are still considered representative state-of-the-art models, they underperform on RipVIS. TCA enhanced segmentation stability across models, notably reducing false positives and false negatives, particularly for one-stage methods, making them more reliable for safety-critical applications. The diversity of our dataset introduces challenges not fully addressed by prior datasets, emphasizing the need for further improvements in segmentation models to generalize across various beach environments. + +# 5.6. Hyperparameter Tuning + +All models were extensively trained on the dataset, exploring various hyperparameters to establish baseline comparisons. For YOLO, we trained all versions with both pretrained and custom weights. We also tested most models from the Detector2 model zoo, experimenting with different data augmentations, learning rates, schedulers, batch sizes, number of proposals, deformable convolutions, and various backbones. Additionally, the models were trained on an expanded version of the dataset, with automatically generated annotations for frames not manually annotated. While these annotations are reasonably accurate, they lack the precision of manual annotations, resulting in a slight drop in most metrics, likely due to overfitting on larger + +![](images/313f6805b52689ed44b483f2d8aa9ab11bae449cb8e99da23787178e99f16f08.jpg) +Original Image + +![](images/5789ba555e5c8c3a633c61179ae6d81136491d18bf8478f9b37680137fdd292b.jpg) +Prediction + +![](images/92c106494f1506c7743d69222d0305045217ade1ea5f59548a4a8436ea6d7ccd.jpg) +Prediction + TCA + +![](images/eef3c2b37f2bffee6944e456092e578df932828dbd2956287779d04e8f294562.jpg) +Pred. + Filtered TCA + +![](images/cd07a1642382335b284f318433f6e874e1b90a6e9fbd0e4857c49c6a1e9d48b0.jpg) +Ground Truth + +![](images/00accdf1e5f3008698078dfcca22c5aba1b698bed75fb99a5457da5ab165871e.jpg) + +![](images/c763e2043124f59a44bb96a197e9ea864078b00a6df01d0ab1fdfc636f2a7b66.jpg) + +![](images/d508e839b7efa50a7986f30bf28550c726ff590fd0c584ee27f2758a801ea410.jpg) + +![](images/eaa53d4c212070e75d5bd2b32e87e9732d147e4ce839ca4fd84f5dc2a3e78c99.jpg) + +![](images/ba781b6f86baba4315d0479d04c4e2d1534d296e76fb16dc2045e71e97503ff1.jpg) + +![](images/3d0f36e3f587073e5532af91bbfb2a42c07ee88fc545202b1f70a68628ec16d1.jpg) + +![](images/123d42dffaab5fc4a9cc798f75a75cbe524c770f23d10aff281497e1641dd524.jpg) + +![](images/4b4682531e62bc746dff1ebe9b0bca20188d5451f7ff4dd3ca73bced232ba27a.jpg) + +![](images/282f22e6fb1623af048aba0862223d0afdb67a1d26302309f1bc9f2244ba0b5e.jpg) + +![](images/827d3621dcc7661946f9caad51fb68f99ba9109907d9c6112914dc31f272bca3.jpg) + +![](images/ee6a00b0918216a7767adbf36f800adee014d50976b9e16333a095b976c9725a.jpg) + +![](images/7135d413248087e0547efae37ee6a1f66c875df4d3e63e2b2a892c79cd477878.jpg) + +![](images/b1bdfe036763759ebaf0382d844bce8365b51dfe56968b012c08b432abaf878c.jpg) + +![](images/e156bc3c1b5fe5d8da63657bfa582987c58175c858b12a13d3001d5ca6f4903e.jpg) + +![](images/82cfd2223a01271cf95e2c25b47f5bba330c62176b44f22044d5c6b6bf4dbc61.jpg) + +![](images/93976f9556d7389668ac6d1d6bc51df1751a86337d6c1cdaa080aecb4e49a4ba.jpg) +Figure 4. Examples of rip current detection results across processing stages, with each row illustrating a distinct case for the impact of TCA: 1. TCA smoothes the rip current shape on a successful detection. 2. TCA recovers false negatives on the right side. 3. TCA reduces false positives of an over-segmented mask to better match the ground truth. 4. TCA enables detection across frames with consecutive false negatives. 5. Failure case: TCA reduces detection accuracy due to initial stationary detection followed by rapid camera movement. + +![](images/b5c17d6c120fc4dad9eaea58c8ce41c8cb3d8be8740b1249a89da288fe04fd0f.jpg) + +![](images/d90941ed3a1eec9448fe431bb14f45d806f61fa63a320f3c264bf59cdff37b94.jpg) + +![](images/6b873c32c3badc8e9d27fa8ec5a161924f35ba269cd1b4b77b6258c021588081.jpg) + +![](images/c46c1308632c3a6c1142eb9b6a2e073838ff7e766053f854b8bc4762ce9d9fe0.jpg) + +videos. We also experimented with various TCA methods, from linear to polynomial adjustments, with different upper bounds and additional thresholding for final prediction. A relevant trade-off is that different types of TCA are useful for moving cameras vs. fixed cameras. Full details of the hyperparameter tuning and its impact are available in the supplementary material. + +# 6. Conclusion + +In this paper, we introduced RipVIS, a large-scale high-quality dataset specifically designed for rip current instance segmentation. RipVIS spans diverse environmental conditions, geographic locations, and video sources, making it the most comprehensive resource of its kind. By offering annotated videos with carefully curated training, validation, and test splits, RipVIS addresses the unique challenges posed by the amorphous and dynamic nature of rip currents, which traditional datasets and detection methods have struggled to overcome effectively. + +Our analysis highlighted the limitations of popular instance segmentation models, including one-stage and two-stage detectors, on this challenging dataset. TCA demonstrated its effectiveness in improving segmentation consis + +tency, particularly in difficult scenarios where rip currents appear intermittently. These results emphasize the need for more robust and accurate models to advance rip current detection—a safety-critical task where missed detections can lead to life-threatening consequences. The findings reinforce the importance of prioritizing recall and accuracy in such applications. By releasing RipVIS and its benchmark website, we aim to foster a collaborative research environment within the global community. Openly sharing our data, code, and results not only supports innovation but also drives progress in the field of automatic rip current detection. Ultimately, we envision RipVIS as a pivotal resource for creating safer beaches and raising public awareness. + +# 7. Acknowledgments + +This work was partially supported by the Alexander von Humboldt Foundation and represents the culmination of a three-year collaboration between the University of Würzburg and the University of Bucharest. We extend our sincere thanks to all the volunteer annotators, each of whom is credited individually in the video details sheet. + +# References + +[1] Oregon state university: Coastal imaging lab. http://cilwww.coas.oregonstate.edu, 2023. Accessed: March 2023. 3 +[2] R. Brander, Dale Dominey-Howes, C. Champion, O. Del Vecchio, and B. Brighton. 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Despite recent advances, extracting aligned spatiotemporal information from adjacent frames remains challenging. This is mainly due to limitations in receptive field size and computational complexity, which makes existing methods struggle to efficiently enhance video quality. To address this issue, we propose RivuletMLP, an MLP-based network architecture. Specifically, our framework first employs a Dynamically Guided Deformable Alignment (DDA) module to adaptively explore and align multi-frame feature information. Subsequently, we introduce two modules for feature reconstruction: a Spatiotemporal Feature Flow (SFF) Module and a Benign Selection Compensation (BSC) module. The SFF module establishes non-local dependencies through an innovative feature permutation mechanism. Additionally, the BSC module utilizes a collaborative strategy of deep feature extraction and local region refinement to alleviate inter frame motion discontinuity caused by compression. Experimental results demonstrate that RivuletMLP achieves superior computational efficiency while maintaining powerful reconstruction capabilities. + +# 1. Introduction + +Emerging media formats, particularly short videos and live streaming platforms, have triggered an unprecedented surge in video data traffic [1]. To tackle the fundamental challenges of limited bandwidth and storage resources, advanced video coding standards like H.264/AVC [2] and H.265/HEVC [3] have been developed, leveraging block-based hybrid coding architectures that efficiently compress + +![](images/47fa1d5d56e9e43a11a47d72fa5482e2b7e6f33c52aa52f79f0ad60b9c3a330a.jpg) +Figure 1. Comparison of PSNR(dB), per-frame processing time (720P video), and FLOPs evaluated on the MFQEv2.0 test set at $\mathrm{QP} = 37$ . Circle dimensions indicate computational complexity. RivuletMLP achieves an optimal balance between quality enhancement and processing efficiency. + +and transmit video by exploiting both temporal and spatial redundancies within the content. Nevertheless, this lossy compression approach, which inherently sacrifices quality to achieve lower bitrates, invariably introduces various visual artifacts such as blocking effects, ringing distortions, and image blurring [4, 5]. Such compression-induced degradation not only substantially compromises users' subjective Quality of Experience (QoE) [6, 7] but also markedly impairs the performance of crucial visual computing tasks, including object detection and action recognition. Most notably, the interplay between motion estimation and quantization processes in video coding results in quality degradation with complex spatiotemporal patterns [8, 9], making video quality restoration an exceptionally challenging task. + +In recent years, researchers have explored diverse technical approaches to enhance compressed video quality. Early methodologies centered on transform coefficient optimization [10, 11], employing specialized mathematical models to mitigate artifacts. Although these approaches exhibited remarkable performance in specific contexts, their heavy re + +liacence on particular compression standards resulted in limited transferability. As deep learning emerged, CNNs-based approaches [12-18] began to dominate the field, leveraging their sophisticated feature extraction capabilities to achieve superior performance. However, the inherently limited receptive field of CNNs constrains their capacity to model long-range dependencies, rendering them inadequate for addressing compression artifacts that exhibit extensive spatial correlations. More recently, Vision Transformer architectures and their variants [19-24] have marked significant breakthroughs in restoration through self-attention mechanisms, enabling comprehensive global feature modeling. Yet, the substantial computational overhead and time complexity associated with attention map calculations continue to pose significant challenges for their practical deployment. + +Recent studies have shown that MLP-based architectures achieved remarkable breakthroughs in computational efficiency and performance [25, 26], demonstrating comparable capabilities to attention mechanisms for addressing computational bottlenecks in video restoration. However, directly applying MLPs to video restoration faces inherent challenges. Previous research [27, 28] indicates that while MLPs theoretically possess global perception capabilities, their structural characteristics hinder effective long-range dependency modeling. This fundamentally conflicts with the requirements of compressed video restoration, where compression artifacts manifest as global correlations across spatio-temporal dimensions, demanding stronger global modeling capabilities. + +To tackle the challenges mentioned above, this paper introduces RivuletMLP, an efficient video restoration network architecture that pioneers a novel non-local modeling mechanism, transcending traditional limitations in receptive field and computational complexity through its innovative Spatio-temporal Feature Flow (SFF) module. To achieve more precise feature representations, the model initially leverages dynamically guided deformable alignment (DDA) module for multi-frame feature alignment. In contrast to STDF[5]'s frame-by-frame adjacent feature alignment approach, DDA module effectively extracts long-range temporal information from video sequences, thereby eliminating error accumulation during temporal feature propagation. Subsequently, SFF module implements a sophisticated feature permutation strategy to restructure the DDA-processed feature maps, optimizing spatial distribution by strategically relocating features from beyond the fixed receptive field of the patch-based fully connected (FC) layer, thus establishing robust long-range dependency relationships. This architectural design enables efficient global information exchange among distant features while preserving computational efficiency. + +Meanwhile, since the Spatio-temporal Feature Flow + +(SFF) module focuses on the efficient modeling of global information, we integrate the Benign Selection Compensation (BSC) module into the network to improve the reconstruction effect of motion information in compressed videos. Through collaborative learning strategies, BSC module combines deep feature extraction with fine-grained local modeling to effectively mitigate compression-induced inter-frame motion discontinuity. + +Overall, RivuletMLP exhibits superior performance in compressed video quality enhancement tasks. As illustrated in Fig.1, our proposed approach strikes an optimal balance among FLOPs, processing efficiency, and performance metrics across standard benchmarks, outperforming existing methodologies. + +The main contributions are summarized as follows: + +- We present a novel MLP-based framework, RivuletMLP, for efficiently enhancing compressed video quality. A dynamically guided deformable alignment module is designed to adaptively align multi-frame features, enabling refinement and storage of spatiotemporal information within the feature space. +- In RivuletMLP, we integrate global information and motion compensation. The framework relies on the spatiotemporal feature flow and benign selection compensation modules. Benefiting from the received aligned features, superior enhancement performance is achieved. +- Extensive experiments on MFQEv2.0 dataset demonstrate our method's superior efficiency. It requires only $\sim 36.6\%$ of the FLOPs needed by STCF and achieves a 0.11dB PSNR improvement with reasonable inference speed. + +# 2. Related Work + +# 2.1. Compressed Video Enhancement + +Recent research has demonstrated remarkable advances in compressed video quality enhancement through Convolutional Neural Networks (CNNs). MFQEv2.0 [13] leverages motion compensation between adjacent peak-quality frames, identified through optical flow estimation, to enhance low-quality frames. To address motion dynamics effectively, STDF [5] introduced a spatiotemporal deformable fusion scheme for temporal information aggregation, effectively mitigating visual distortions. RFDA [29] enhanced STDF's capabilities by implementing recursive fusion and deformable spatiotemporal attention modules for long-range motion compensation. Zhu et al.'s CPGA [30] innovatively incorporates coding prior information for quality reconstruction. The field then witnessed the emergence of Transformer-based approaches, yielding promising outcomes. Zhang et al. [23] developed a hybrid architecture combining Swin Transformer [31] with CNNs to integrate motion compensation and global context. TVQE [24] in + +![](images/7cb84f6269b2d1a85a5aa4752c7154c84ee75bd7a7833a6d60c389f45d8ea007.jpg) + +![](images/597b6a0ff67545041ed25c47dd60c67124fc3545637429471a434535dd8323c2.jpg) +Figure 2. Architecture overview of our proposed method: (a) RivuletMLP pipeline. (b) Spatio-temporal Feature Flow (SFF) Module. (c) Benign Selection Compensation (BSC) Module. (d) Spacetime-Gate MLP (SG-MLP) for feature aggregation. (e) Locally Refined MLP (LR-MLP) is a core BSC component. + +produced innovative modules that combine local and global feature learning with inter-frame information aggregation, effectively addressing compression artifacts. + +# 2.2. Feature Decomposition and Reorganization + +Feature decomposition and reorganization for efficient information transfer remains a central focus in computer vision research. Classical matrix decomposition theory [32] laid the mathematical groundwork for efficient feature representation, while deep learning advancements brought transformative breakthroughs. Recently, RepLKNet [33] achieved extensive receptive field extraction through parallel information pathways. Vision Permutator [25] introduced an ordered feature reorganization mechanism that enables efficient long-range dependency modeling through spatial rearrangement. CrossFormer [34] enhanced global modeling capabilities by implementing cross-scale transmission strategies with dynamic feature paths. LoFormer [35] balanced computational efficiency and performance by computing self-attention through disjoint local windows in the frequency domain. Building on these advances, we introduce a novel global modeling approach that enables efficient information exchange through controllable separation and coupling mechanisms. + +# 2.3. MLP-based Architectures + +Convolutional Neural Networks (CNNs) and self-attention mechanisms long dominated computer vision. This changed when MLP-Mixer [27] challenged the status quo by achieving remarkable results in image classification using simple fully connected layers. MLP-based architectures [36-40] + +then rapidly gained popularity in image processing. These models significantly reduced the computational costs typically associated with Transformer's self-attention mechanisms. CycleMLP [36] and AS-MLP [38] demonstrated a key breakthrough: MLPs can effectively capture spatial information without convolution operations. In low-level vision, MAXIM [39] employed multi-axis and cross-gated MLP blocks in its backbone architecture. This design effectively balanced global and local feature processing. Following a similar approach, Wu et al. developed MixNet [41] for UHD low-light image enhancement. Their model efficiently handled feature dependencies at multiple scales. Drawing inspiration from these advances, we pioneer a new application: using visual MLP architecture for compressed video restoration. + +# 3. Method + +# 3.1. Overall Framework + +Fig.2 illustrates the overall framework of the proposed RivuletMLP, which integrates three core modules: dynamically guided deformable alignment (DDA) module, spatiotemporal feature flow (SFF) module, and benign selection compensation (BSC) Module. The network processes a sequence of initialized low-quality (lq) multi-frame video features $\mathcal{V}\_ lq = \{\mathcal{F}_i\in \mathbb{R}^{C\times H\times W}|i\in [t - T,t + T]\}$ , where $C,H$ and $W$ denote the channel number, height, and width respectively, with $\mathcal{F}_t$ representing the target frame for enhancement and surrounding frames serving as references. The DDA module (see Sec.3.2) establishes spatiotemporal correspondences through dynamic displacement estimation, + +![](images/1fa806cf1fb00b76acd663d347ac4b510b1d02e3b7840c7c4889c783d82ed7b1.jpg) +Figure 3. The Dynamically Guided Deformable Alignment module explores and adaptively aligns multi-frame features. The SKFF module follows [42]. + +enabling adaptive cross-frame feature alignment and exploration of degradation patterns across temporal dimensions. This alignment creates a coherent spatiotemporal feature foundation for subsequent reconstruction. To balance feature expressiveness with computational efficiency, we incorporate a Down Head [23] structure for optimal feature dimensionality adjustment. + +Subsequently, the aligned features are processed by the SFF module (see Sec.3.3). Our innovative feature permutation strategy reorganizes feature maps in two ways. First, it incorporates information from beyond the fixed receptive field. Then, it establishes global dependencies within the features. We also integrate the BSC module (see Sec.3.4) into the network. This module enhances motion information reconstruction in compressed videos. The BSC module combines spatial decomposition with fine-grained compensation to restore inter-frame motion continuity effectively. + +In the final reconstruction phase, the network utilizes a symmetric counterpart to the Down Head, restoring feature dimensions to their original scale. A residual learning strategy is implemented to improve reconstruction quality and ensure training stability. The reconstruction convolution layers generate residual features $R$ , which are then combined with the target frame to produce the final output: $\mathcal{F}' = \mathcal{F}_t + \mathcal{R}$ , where $\mathcal{F}'$ denotes the enhanced target frame. + +# 3.2. Dynamically Guided Deformable Alignment + +Adjacent frames often contain substantial content differences arising from viewpoint changes, motion occlusions, and compression artifacts. Such variations can compromise the restoration quality of potentially sharp frames if direct alignment is applied. To address this challenge, we introduce the Dynamically guided deformable alignment (DDA) module, which enables adaptive feature exploration and alignment. In the following section, we detail the forward frame alignment process, noting that backward frame + +alignment follows analogous principles. + +As shown in Fig.3, the dynamically guided deformable alignment (DDA) module aligns adjacent frame features $\mathcal{F}_T^f = \mathcal{F}_{[t + 1,\dots ,t + T]}\in \mathbb{R}^{T\times C\times H\times W}$ with target frame features $\mathcal{F}_t$ , producing output features $\mathcal{F}_T^{fa}$ . Additionally, we learn a spatiotemporal offset, which is used to capture correspondences from preceding frames to the current frame. The initial spatiotemporal offset $\tilde{S}_{T\rightarrow t}$ serves as input to the current DDA module and undergoes progressive refinement following the a U-Net-like structure to generate the final spatiotemporal offset $S_{T\rightarrow t}$ . + +Specifically, given the concatenated features $\mathcal{F}_T^f$ and the normalized initial spatiotemporal $\tilde{\mathcal{S}}_{T\rightarrow t}\in \mathbb{N}^{3\times H\times W},\mathbb{N}\in [-1,1]$ , we compute the initial aligned feature map $\tilde{\mathcal{F}}_T^{fa}\in \mathbb{R}^{C\times H\times W}$ , which can be formulated as follows: + +$$ +\tilde {\mathcal {F}} _ {T} ^ {f a} = \mathcal {D S S} \left(\tilde {\mathcal {S}} _ {T \rightarrow t}, \mathcal {F} _ {T} ^ {f}\right), \tag {1} +$$ + +where $\mathcal{DSS}$ represents the differentiable spatiotemporal sampling operation [43]. Notably, $\tilde{S}_{T\rightarrow t}\in \mathbb{N}^{3\times H\times W}$ has a third dimension of three, capturing position information across both spatial and temporal dimensions. The optimized spatiotemporal offset $S_{T\rightarrow t}$ is then derived by computing offset residuals: + +$$ +\mathcal {S} _ {T \rightarrow t} = \tilde {\mathcal {S}} _ {T \rightarrow t} + \mathcal {C} _ {o} \left(\mathcal {F} _ {t}, \tilde {\mathcal {F}} _ {T} ^ {f a}, \tilde {\mathcal {S}} _ {T \rightarrow t}\right), \tag {2} +$$ + +where $\mathcal{C}_o$ represents a lightweight offset network built from stacked convolutional layers. The integration of conventional motion derived from convolutional filtering with motion optimization yields progressively refined motion information. We then obtain forward-aligned features $\mathcal{F}_T^{fa}$ by reapplying Eq.1. For backward temporal processing, we apply identical operations to adjacent features $\mathcal{F}_T^b = \mathcal{F}_{[t - T,\dots ,t - 1]}$ to generate backward-aligned features $\mathcal{F}_T^{ba}$ . + +Following the SKFF [42] module, we integrate aligned features through adaptive fusion. The process recalibrates feature maps from different spatiotemporal positions using dynamic weights to obtain the final features $\mathcal{F}^a$ : + +$$ +\mathcal {F} ^ {a} = \sum_ {i \in \left\{t, _ {T} ^ {f a}, _ {T} ^ {b a} \right\}} \left(s _ {i} \otimes \mathcal {F} _ {i}\right), \tag {3} +$$ + +$$ +s _ {i} = \operatorname {s o f t m a x} \left(\mathcal {W} _ {2} \delta \left(\mathcal {W} _ {1} G A P \left(\mathcal {F} _ {s u m}\right)\right)\right). \tag {4} +$$ + +In this formulation, $GAP(\cdot)$ represents global average pooling, $\mathcal{F}_{sum}$ denotes $\mathcal{F}_t + \mathcal{F}_t^{fa} + \mathcal{F}_t^{ba}$ , while $\delta(\cdot)$ is the ReLU function. $\mathcal{W}_1$ and $\mathcal{W}_2$ denote learnable parameters of the convolution. + +# 3.3. Spatio-temporal Feature Flow + +Efficient feature modeling plays a crucial role in compressed video quality enhancement, existing methods often + +![](images/8250aec2688bae0071a116430ef997435629277a219bb0bfe162ba117aed5792.jpg) +Figure 4. The architecture of FFB, which consists of five components: window partitioning, feature flowing, feature mapping, feature backtracking, and window merging. The red areas represent the receptive regions of patch-based MLP. + +rely on computationally intensive architectures. To overcome this limitation, we introduce the spatiotemporal feature flow (SFF) module, achieving efficient feature modeling through patch-based FC layers. As shown in Fig.2, our module incorporates two core components: a feature flow block (FFB) for global feature modeling, and a spacetime-gate MLP (SG-MLP) for intra-module feature aggregation. We detail each component in the following sections. + +# 3.3.1 Feature Flow Block + +The feature flow component lies at the core of feature Flow block. It integrates four key functions: window partitioning, feature mapping, feature backtracking, and window merging to establish an efficient feature extraction mechanism. Specifically, the feature flow operation comprises horizontal and vertical directions. We demonstrate the process using the vertical direction since both directions follow identical principles. As shown in Fig.4(b), the feature flow process begins with an input $\mathcal{X} \in \mathbb{R}^{c \times h \times w}$ . We first partition the feature map $\mathcal{X}$ into patches of size $p \times p$ . These patches are then organized into multiple vertical feature streams, denoted as $\mathcal{X} = [x_1, x_2, \ldots, x_n]$ , where stream $x_i = [x_i^{(1)}, \ldots, x_i^{(h)}]^T$ and $x_i \in \mathbb{R}^{c \times h \times p/2}$ , $T$ represents matrix transposition. + +Additionally, we further introduce a flow mapping func + +tion $m(i) = (p + n) / 2 + (i - 1)$ , where $1 \leq i \leq p / 2$ . The function assigns a target position $m(i)$ to the feature stream at position $i$ in the feature sequence. These paired positions form flow units, denoted as $\mathcal{X} = [\mathcal{G}_1, \mathcal{G}_2, \dots, \mathcal{G}_{n/2}]$ , where $\mathcal{G}_i = [x_i, x_{m(i)}]$ and $\mathcal{G}_i \in \mathbb{R}^{c \times h \times p}$ . These units establish direct channels for long-range dependencies within the feature sequence. Taking flow unit $\mathcal{G}_i$ as an example, systemic reconfiguration occurs during the flow processes within the unit. A circular permutation takes place between the feature streams at source position $i$ and target position $m(i)$ , i.e., transforming $x_i = [x_i^{(1)}, \dots, x_i^{(h)}]^T$ into $x_i = [x_{m(i)}^{(h)}, \dots, x_{m(i)}^{(1)}]^T$ . The mechanism enables spatially separated features to undergo direct feature extraction through patch-based FC layers. The flow process executes synchronously across all flow units, with vertical reconstruction following identical principles. As illustrated in Fig.4, feature flow block expands the feature perception range by moving features from the four corners into local red regions. Through selective horizontal or vertical operations, we enable interactions between different target regions, ultimately constructing a global receptive field across the entire feature. + +# 3.3.2 Spacetime-Gate MLP + +The channel-MLP [27] utilizes non-linear activation and two linear projection layers for feature extraction, yet it lacks spatial information modeling capabilities, which impedes compressed video quality enhancement. To address above limitations, we introduce spacetime-gate MLP (SG-MLP), which incorporates spacetime gating (SG) into channel-MLP. As detailed in Fig.2d, the SG module employs a straightforward gating mechanism that combines depth-wise convolutions with element-wise multiplication. We split the feature maps into two parts along the channel dimension for convolution and multiplication bypass. For the input $\hat{\mathcal{X}}\in \mathbb{R}^{c\times h\times w}$ , the SG-MLP computation is defined as: + +$$ +\hat {\mathcal {X}} _ {S 1}, \hat {\mathcal {X}} _ {S 2} = S p l i t (\beta (\mathcal {W} _ {S G} ^ {1} \hat {\mathcal {X}})), \tag {5} +$$ + +$$ +\mathcal {S G} - \mathcal {M L P} (\hat {\mathcal {X}}) = \mathcal {W} _ {S G} ^ {2} \left(\hat {\mathcal {X}} _ {S 1} \odot \left(\mathcal {W} _ {C} \hat {\mathcal {X}} _ {S 2}\right)\right), \tag {6} +$$ + +where $Split$ denotes channel splitting, $\mathcal{W}_{SG}^{1}$ , $\mathcal{W}_{SG}^{2}$ represent linear projections, $\beta$ indicates the Leaky ReLU function, and $\mathcal{W}_C$ is the learnable parameters of convolution. + +# 3.4. Benign Selection Compensation + +RivuletMLP employs SFF modules for global feature modeling. However, motion information lost during compression remains essential for high-quality reconstruction. + +Therefore, our proposed BSC module captures interframe motion compensation by combining deep feature extraction with local modeling. As illustrated in Fig.2(c), + +Table 1. Quantitative comparison in terms of $\Delta$ PSNR(dB)/ $\Delta$ SSIM $\left( {\times {10}^{-2}}\right)$ under LDP configuration. Red text indicates the best and blue text indicates the second best performance. Video resolutions: Class A (2560 × 1600), Class B (1920 × 1080), Class C (832 × 480), Class D (480 × 240), Class E (1280 × 720). + +
QPSequencesMFQEv2.0 TPAMI2019STDF-R3L AAAI2020RFDA MM2021TVQE TBC2023STCF AAAI2023CPGA CVPR2024Ours
37ATraffic0.59/1.020.73/1.150.80/1.280.88/1.440.91/1.440.85/1.330.94/1.48
PeopleonStreet0.92/1.571.25/1.961.44/2.221.49 /2.331.62/2.431.38/2.131.61/2.39
BKimono0.55/1.180.85/1.611.02/1.860.99/1.821.21/1.941.02/1.731.23/1.95
ParkScene0.46/1.230.59/1.470.64/1.580.66/1.760.74/1.790.71/1.610.72/1.77
Cactus0.50/1.000.77/1.380.83/1.490.85/1.570.93/1.610.81/1.341.07/1.70
BQTerrace0.40/0.670.63/1.060.65/1.060.74/1.340.75/1.250.86/1.260.93/1.29
BasketballDrive0.47/0.830.75/1.230.87/1.400.85/1.461.09/1.590.97/1.451.12/1.60
CRaceHorses0.39/0.800.55/1.350.48/1.230.61/1.590.69/1.590.59/1.370.78/1.71
BQMall0.62/1.200.99/1.801.09/1.971.06/2.021.25/2.211.02/1.651.37/2.42
PartyScene0.36/1.180.68/1.940.66/1.880.80/2.270.73/2.280.68/1.300.81/2.34
BasketballDril0.58/1.200.79/1.490.88/1.670.98/2.010.96/1.760.77/1.461.05/1.98
DRaceHorses0.59/1.430.83/2.080.85/2.110.86/2.301.02/2.470.98/1.871.07/2.40
BQSquare0.34/0.650.94/1.251.05/1.391.25/1.741.06/1.481.01/1.691.38/1.82
BlowingBubbles0.53/1.700.74/2.260.78/2.400.83/2.600.80/2.530.71/1.581.01/2.66
BasketballPass0.73/1.551.08/2.121.13/2.241.12/2.411.32/2.631.13/1.891.46/2.75
EFourPeople0.73/0.950.94/1.171.13/1.361.16/1.421.11/1.331.11/1.371.32/1.78
Johnny0.60/0.680.81/0.880.90/0.941.12/1.331.00/1.130.92/1.031.27/1.46
KristenAndSara0.75/0.850.97/0.961.19/1.151.27/1.231.12/1.111.11/1.141.17/1.19
Average0.56/1.090.83/1.510.91/1.620.98/1.821.02/1.810.92/1.501.13/1.93
42Average0.59/1.650.76/2.040.82/2.200.99/2.640.88/2.340.86/2.191.01/2.67
32Average0.52/0.680.86/1.040.87/1.070.93/1.241.07/1.32— /—1.05/1.37
27Average0.49/0.420.72/0.570.82/0.680.87/0.801.05/0.88— /—0.95/0.90
+ +we implement a cascaded DWConv-PWConv [44] structure to represent basic compensation features, enabling efficient motion information capture. Our architecture divides features into $p \times p$ overlapping regions. Within these regions, LR-MLP (Local Region MLP, detailed in Fig.2(e) uses dimensionality reduction to refine compensation features, capturing fine-grained motion details. Finally, SGMLP aggregates these enhanced features from LR-MLP to achieve precise inter-frame motion compensation modeling and restore temporal coherence. + +# 4. Experiments + +# 4.1. Experimental Settings + +We conduct experiments using the widely-adopted MFQEv2.0 [13] benchmark dataset for compressed video quality enhancement. The dataset comprises 126 video sequences from Xiph, VQEG, and JCT-V [45], encompassing diverse content and resolutions. Following established protocols in related studies [5, 29], we divide the dataset into a 6:1 ratio: 108 sequences for training and 18 JCT-VC standard sequences for testing. Using the HM 16.20 encoder under HEVC LowDelay-P (LDP) configuration, we compress all video sequences with four quantization parameters $(\mathrm{QP} = 27, 32, 37,$ and 42) to evaluate performance at different compression levels. For performance assess + +ment, we employ two metrics: Peak Signal-to-Noise Ratio (PSNR)[46] and Structural Similarity Index (SSIM)[47]. We measure quality improvement by calculating $\Delta$ PSNR and $\Delta$ SSIM between enhanced and compressed videos in the Y channel of the YCbCr color space. + +# 4.2. Training Details + +In the training phase, we randomly crop $128 \times 128$ patches from original and corresponding compressed videos for training samples with setting the batch size to 32. Each sample sequence consists of 7 consecutive frames ( $T = 3$ ). For improved model robustness and generalization, we apply data augmentation techniques, including random flipping and rotation. All experiments are implemented on PyTorch [48], using hardware equipped with NVIDIA 24G 4090 GPUs. The module architecture is configured with 128 feature channels ( $c = 128$ ), patch size of 4 ( $p = 4$ ), and 12 blocks ( $N = 12$ ). For optimization, we employ the Adam [49] optimizer configured with momentum parameters $\alpha_{1} = 0.9$ , $\alpha_{2} = 0.999$ , and numerical stability parameter $\varepsilon = 1 \times 10^{(-8)}$ . The learning rate begins at $1 \times 10^{(-4)}$ and decreases to $1 \times 10^{(-6)}$ following a cosine annealing schedule [50]. To optimize compressed video quality enhancement, we implement the Charbonnier loss [51] function. + +![](images/0c08a1a5dafa5f0351fbe5297f68ec1e4aa76045ca608ead30c25e6600865e0f.jpg) +Figure 5. Subjective comparison results between leading methods and our proposed methodin four video sequences at $\mathrm{QP} = 37$ . Test video names (from top to bottom): BasketballDrill, BQSquare, BasketballDrive and Johanny. The zoom-in of red box area is shown. + +![](images/def5f3df6b268e9f893843ef6aae6680fe610e4b62d7ef78bfbf7979baa7405a.jpg) +Figure 6. PSNR curves of HEVC, RFDA, STCF and our model on BasketballDrive testing sequence under LDP configuration at $\mathrm{QP} = 37$ . + +# 4.3. Comparisons with Previous Algorithms + +To demonstrate the effectiveness of our method, we compare it with six leading multi-frame video quality enhancement methods: MFQEV2[13], RFDA[29], STDF[5], STCF[23], TVQE[24], and CPGA[30]. We cite several results directly from their respective publications, maintaining parameter configurations as recommended by the original authors. Although CPGA shows excellent performance in recent studies, its official implementation differs slightly from our standard dataset. Therefore, to ensure a fair comparison, we retrained CPGA on the MFQEv2 dataset (QP37 and QP42) using identical baseline settings. + +Quantitative Results. The quantitative performance in terms of average $\Delta$ PSNR and $\Delta$ SSIM is presented in Table 1. Across different QP values under LDP configurations, our method consistently outperforms all comparison methods, demonstrating leading performance. For LDP configuration with $\mathrm{QP} = 37$ , our approach achieves average $\Delta$ PSNR improvements of 0.11dB and 0.15dB compared to STCF and TVQE respectively across 18 standard test sequences. Comparable improvements are also observed in + +Table 2. The comparison of parameters, FLOPs and FPS. For runtime, all methods are retested on a 720p video at $\mathrm{{QP}} = {37}$ with the NVIDIA RTX 4090 GPU. + +
MethodsΔPSNRParams(M)FLOPs (G)FPS
CNNs-Based
MFQEv2.00.560.22186.722.5
STDF0.830.36231.838.8
RFDA0.911.25524.913.3
CPGA0.921.501565.55.2
Transformer-Based
STCF1.027.01677.12.8
MLP-Based
RivuletMLP_light0.901.9178.523.2
RivuletMLP1.136.9615.710.0
+ +SSIM. These comprehensive results confirm our method's superior performance in compressed video quality enhancement. + +Qualitative Comparison. As shown in Fig.5, our qualitative comparison reveals that compressed patches exhibit various artifacts (ringing in "BasketballDrive", blurring and edge fluctuation in "BasketballDrill"). Our approach achieves superior visual quality compared to STDF, RFDA, and CPGA, successfully recovering more details and textures. In the "BQSquare" sequence, our method effectively reconstructs object contours and boundary details lost during compression, validating our strong capability in both distortion handling and quality enhancement. + +Quality Fluctuation. Quality fluctuation serves as a crucial metric in evaluating enhancement algorithm performance, directly affecting overall video quality. Significant frame-to-frame variations manifest as texture flickering, substantially degrading the viewing experience. The + +![](images/0b1a2c7961f2b1974ea54bf0ba12d907c59b859736ce73e88fc01fa307f0abfe.jpg) +Figure 7. Rate-distortion performance on Johnny testing sequence. Our method outperforms the other approaches at various bitrates. + +![](images/fcc521864599805ab4a9eea2463b4a88a2e6a5b4aabae37f5f2ecade8e844260.jpg) + +![](images/c62c64fd0c8d93e3a1388dba3fef3d94b890b7bf4a1bd68f660ccb24345a836b.jpg) + +![](images/e5b7999c4a971b7fcf47cae6eb91fda2ebf4e0e0e54d2f3249edd4af78cbe82b.jpg) + +Table 3. The Efficiency Comparison between DDA Module and STDF's Alignment Method. + +
TypeComplexityΔPSNR (dB)
Params(M)FLOPs(G)
DDA6.9615.71.13
STDF[5]7.1595.21.07
+ +PSNR curves in Fig.6, analyzed using the BasketballDrive sequence, we demonstrate that our method achieves superior performance compared to conventional algorithms including HEVC, RFDA, and STCF. The results reveal not only greater performance improvement but also more stable quality control across consecutive frames. + +Efficiency of the methods. Table 2 presents comprehensive benchmark tests evaluating computational efficiency through inference time, parameter count, and complexity following [20], [52]. Although our MLP-based architecture requires higher parameter overhead (2% less than STCF), experimental results justify this trade-off. Our method achieves a $10.7\%$ $\Delta$ PSNR improvement (from 1.02 dB to 1.13 dB for QP37) with $47.5\%$ faster inference than CPGA, while maintaining lower computational complexity than both STCF and CPGA. We also provide a lightweight version with $c = 64$ for improved efficiency, establishing our method as one of the most practical models for deployment given its competitive FLOPs and inference speed. + +Receptive field. The comparative analysis of receptive field patterns is shown in Fig.7. STDF demonstrates centralized activation, while BSC exhibits radial high-intensity distributions around the core region. In contrast to the locally uniform square-shaped fields of STCF-global (the global branch of STCF), our proposed SFF framework manifests extensive discrete activation patterns. This design enables simultaneous attention to multiple critical regions, effectively integrating global contextual information. + +# 4.4. Ablation Study + +Effectiveness of DDA module. The proposed DDA module exhibits substantial performance advantages over STDF's alignment method. As shown in Table 3, the DDA module achieves superior PSNR gains through efficient parameter utilization, despite minimal additional computational cost. These results demonstrate the DDA's ability to provide enhanced feature information for subsequent processing, validating the effectiveness of our approach. + +![](images/825ed135181827aaa52e4939b118a30caaa4be4cfd6daee712802dfd63184d53.jpg) + +![](images/21354be1c739d3a9b14ad45a5273c527c2c42a5afdcc7d593883b47d8e70a2f9.jpg) + +![](images/67e35a62180c2aad3acbe0a9b2b8fed981ac902592c0bfac9659a3d73a478326.jpg) + +![](images/2ff13a493e554fc797b5f3320f23bdcdedd309b3ce8c00ce87a9200da13a931f.jpg) + +![](images/9ec93227ef4d38ec22d8b04d0555ce9cc7a87cf123667d22af1b17c2462bdc23.jpg) + +![](images/a14d0cdf9ef1c7e7e25c388dcde7e02be2463064dae5ace05b8178b6a75e0816.jpg) + +![](images/7cabd2d28daeb4445a4b2434f781595d0f6acf90fb53b30e7c928437d76dba77.jpg) +Only BSC + +![](images/f7a9ad28917349db84f1f6ffbada349e385d3d392afef5e956099034ab109438.jpg) +Only SFF + +![](images/362e6b9a23aa933939ffea060844de37acba6bde0c239a266418720e1f64ac33.jpg) +Full +Figure 8. Visual comparison of frame enhancement results and residual patterns across different models. + +Table 4. The ablation study of RivuletMLP, $c$ is the feature dimension and ${N}_{b}$ is the number of modules. + +
TypeCNbΔPSNR (dB)ΔSSIM(×10-2)
Only BSC128120.711.57
Only SFF128120.951.68
RivuletMLP_light64120.901.74
RivuletMLP12881.041.80
RivuletMLP128121.131.93
+ +The Significance of BSC module. Table 4 demonstrates that BSC module integration significantly enhances framework performance. The integrated architecture outperforms implementations using either SFF or BSC modules alone across all evaluation metrics. Detailed analysis of intermediate compensation results in Fig.8 reveals both effective compression artifact suppression and superior texture detail reconstruction. These findings conclusively validate the essential synergy between global modeling and motion compensation mechanisms in improving overall visual quality. + +Feature dimension and number of modules. Module count and feature dimensions are key architectural parameters. Systematic experiments examined performance impacts by scaling modules from 8 to 12 and feature channels from 64 to 128. The results reveal significant improvements in model expressiveness and performance with increased module count and channel dimensions. + +# 5. Conclusion + +In this paper, we propose RivuletMLP, an MLP-based network for compressed video enhancement. The Dynamic Deformable Alignment (DDA) module adaptively aligns multi-frame features, preventing error accumulation during propagation. The core Spatial-temporal Feature Flow (SFF) module establishes global dependencies through feature reorganization. The Benign Selection Compensation (BSC) module addresses motion discontinuity through deep feature extraction and local modeling. Our approach achieves high-quality reconstruction with low complexity. + +# Acknowledgments + +This work was supported by Ant Group Research Fund. + +# References + +[1] Thomas Barnett, Shruti Jain, Usha Andra, and Taru Khurana. Cisco visual networking index (vni) complete forecast update, 2017-2022. Americas/EMEAR Cisco Knowledge Network (CKN) Presentation, 1(1), 2018. 1 +[2] ITU Telecom. Advanced video coding for generic audiovisual services. ITU-T Recommendation H. 264, 2003. 1 +[3] Gary J. 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T., Tathagata Ghosh, and Ravi Kiran Sarvadevabhatla CVIT & iHub-Data, IIIT Hyderabad, India + +https://roadsocial.github.io + +# Abstract + +We introduce RoadSocial, a large-scale, diverse VideoQA dataset tailored for generic road event understanding from social media narratives. Unlike existing datasets limited by regional bias, viewpoint bias and expert-driven annotations, RoadSocial captures the global complexity of road events with varied geographies, camera viewpoints (CCTV, handheld, drones) and rich social discourse. Our scalable semi-automatic annotation framework leverages Text LLMs and Video LLMs to generate comprehensive question-answer pairs across 12 challenging QA tasks, pushing the boundaries of road event understanding. RoadSocial is derived from social media videos spanning 14M frames and 414K social comments, resulting in a dataset with 13.2K videos, 674 tags and 260K high-quality QA pairs. We evaluate 18 Video LLMs (open-source and proprietary, driving-specific and general-purpose) on our road event understanding benchmark. We also demonstrate RoadSocial's utility in improving road event understanding capabilities of general-purpose Video LLMs. + +# 1. Introduction + +A road event typically refers to any incident, activity, or condition occurring on or around the roadway that affects traffic flow, safety, or road usage. The ability to recognize and interpret road events is essential for safe and reliable intelligent vehicles and transportation systems. In this regard, large-scale video datasets of road events are used to develop assistive models [2, 3, 8, 20, 23, 27]. Many recent datasets contain videos with accompanying question-answer text pairs and other text metadata [16, 21, 22, 26]. Such datasets have become a de facto choice for training Video Large Language Models (Video LLMs) [7, 13, 26, 38]. + +However, current video-based road event understanding approaches are limited by region-specific datasets, neglect- + +ing the diversity of global road scenarios. Most datasets focus on dashcam views for autonomous driving, overlooking other camera types such as CCTV, handheld, and drone-based. They also lack annotations on generic events (e.g. defensive driving, near-misses). Due to the reliance on regionally-biased expert annotators, the broader and richer contextual insights from real-world social discourse on road events are absent. Furthermore, existing evaluation frameworks fail to test the Video LLMs' ability to distinguish informative road event details from misleading information, essential for developing reliable, hallucination-resistant road event understanding systems. + +To address these limitations and to enable foundational video language models for generic road event understanding, we introduce RoadSocial, a large-scale and diverse Video Question Answer (VideoQA) dataset. RoadSocial is obtained by processing social media videos and the narratives accompanying these videos. The inherent diversity of social media in terms of geographical locations, camera viewpoints, road event types and social commentary addresses shortcomings of video datasets mentioned previously. Specifically, we make the following contributions: + +- RoadSocial: a large-scale, diverse VideoQA resource for road events, derived from social media videos spanning 14M frames and 414K social comments, resulting in a dataset with 13.2K videos, 674 unique tags, and 260K high-quality QA pairs. +- A semi-automatic annotation framework using Text LLM and Video LLM that processes social media video narratives and generates comprehensive QA pairs across 12 distinct challenging tasks. +- A robust evaluation framework incorporating non-road event videos and irrelevant questions to assess the robustness of Video LLMs to hallucinations. +- A demonstration of RoadSocial's utility in improving road event understanding capabilities of general-purpose Video LLM. +- Critical insights into 18 Video LLMs' performance on road event understanding, obtained from their evaluation + +
DatasetViewpoint TypeVideo FramesDuration (mins)Social CommentsCountriesVideo TagsQAsTG QAAV QAIC QALoc. QAInternet sourced
RoadSocial (Ours)614M7.9K414K100674260K✓✓✓✓✓
Lingo-QA [16]1.1M1.8K-17419K-----
SUTD-TrafficQA [32]310M6.7K-<4-62.5K----✓
DRAMA [15]1.02M.6K-1-102K-----
Rank2Tell [24]1.02M39-1->118-----
ROAD [27]1.1M170-143------
MM-AU [5]12.2M1.2K->505858.6K✓---✓
DriveLM [26, 38]1.03M5.7K-43-375K-----
BDD-OIA [33]1.02M1.9K-125------
BDD-X [8]18.4M4.6K-1-------
+ +Table 1. Comparison of RoadSocial with existing road event understanding datasets. TG: Temporal Grounding, AV: Adversarial, IC: Incompatible, Loc: Geographical Location. Internet-sourced videos do not contain LiDAR or CAN bus data. Orange: Additional annotations added to existing datasets. Blue: New datasets. + +on our RoadSocial-QA benchmark. + +# 2. Related Works + +Several video datasets describe road events through actions of surrounding entities [3, 27], interactions between traffic participants [15, 20, 24, 33], or explanations of normal or safety-critical driving scenarios [8, 16, 26], including dangerous driving behaviors or accidents [5, 32]. + +However, the diversity of these datasets is often limited by their geographical scope. Although some datasets [5, 32, 38] include crowd-sourced videos from a range of locations, their textual annotations reflect local expertise, which may lack a comprehensive understanding of global traffic norms and behaviors. In contrast, our dataset is sourced from global social media video posts which addresses this shortcoming. Existing works typically rely on a pool of manual annotators, a process that is labor-intensive and lacks scalability [5, 16, 26, 32, 33]. We propose a scalable, semi-automatic annotation framework that leverages the capabilities of powerful Video LLMs and Text LLMs to process social media content from around the world and generate high-quality QA pairs associated with road event videos. + +Existing video language models built on previous road understanding benchmarks are often trained on specific camera viewpoints, usually vehicle-mounted [5, 15, 16, 24, 26, 29, 38] or CCTV [9]. Such models may not generalize well across different viewpoint types and geographical regions, limiting their effectiveness for understanding road events in a broad context. In contrast, our dataset contains videos captured in diverse and uncontrolled camera settings (drone, handheld, CCTV etc.) across the world. Coupled with social discourse, our dataset is a viable alternative. + +Existing VideoQA datasets focus primarily on ego-centric tasks [5, 15, 16, 24, 26, 38], limiting perspectives to the ego-vehicle. While Xu et al. [32] explore complex traffic scenarios, none of the existing works assess model robustness against misleading inputs or hallucinations. We + +address this gap by introducing novel QA tasks to evaluate (a) robustness to hallucinations with non-road-event videos and irrelevant questions (b) comprehension across camera viewpoint types and (c) geographical awareness. These tasks enable holistic Video LLM evaluation for general-purpose road event understanding. A comparison of Road-Social with existing datasets is shown in Tab. 1. + +# 3. RoadSocial Dataset + +RoadSocial is a dataset created from social media videos in unconstrained, real-world environments. These videos are accompanied by rich social commentary that reflects facts and varied cultural perspectives on road events worldwide. + +# 3.1. Data Collection + +We crowdsourced diverse road event data from X (formerly Twitter), leveraging its global community for real-world insights. Unlike other platforms, X is characterized by an active social discourse on road events that includes the general public, road event enthusiasts, and road enforcement authorities. Our strategy focused on popular road event related social media handles worldwide, using multilingual keywords to scrape tweet data from 2012 onwards, filtering for videos with substantial commentary. The resulting dataset captures varied road events—traffic violations, accidents, safe driving, and infrastructure awareness—across different environments and locations. + +# 3.2. Annotation Strategy: QAs and Tags + +Our annotation strategy merges LLM-based automation with expert verification to produce high-quality QA pairs and video tags. We start by identifying representative road event samples, then use a hybrid approach to generate QA pairs that blend video semantics with social media context. QA pairs are refined, categorized into predefined tasks, and supplemented with video-level tags, all verified by experts. Additionally, we create incompatible QA pairs for non-road + +![](images/f54de959fa98e922b17b6757e3ec204466237cf87f767648b2aad358c7f167c8.jpg) +Figure 1. Diverse Video Attributes in the RoadSocial Dataset: The total count of unique tags for each attribute is shown in (circled boxes), alongside word clouds highlighting these values. For each attribute, we display examples with 2-3 keyframes from videos. The figure captures the diversity of road events, environmental conditions, geographical locations, viewpoints, interactions between road entities, and traffic violations. The varied scenarios under each attribute showcase the rich complexity of our dataset. + +event videos. Details of these steps follow. + +Identifying Representative Road Event Samples: To design effective template questions for QA generation, we identified representative samples of diverse road events by embedding multilingual tweet text and hashtags using OpenAI's GPT-3 text embeddings [19]. Hierarchical k-means clustering of these embeddings produced clusters of distinct road events (e.g. UK cyclist near-misses, illegal truck overtaking in China, car hydroplaning in USA). We selected the top five samples closest to each cluster center as representatives, ensuring our QA generation is grounded in well-represented events. + +Hybrid Approach for QA Generation: Twitter conversations often focus on unique events in the video but lack visual details (e.g., color of road entity, time of day, type of road). To create holistic QA pairs, we use a hybrid approach combining visual and contextual information from both video and conversation. Visual semantics are extracted by splitting videos into 3-second segments, prompting a Video LLM [31] to generate segment captions (see Fig. 2 - ①, ②). These captions are merged and passed to a Text-based Large Language Model (Text LLM) [1] for a visually-rich summary (③). Meanwhile, tweet conversations are cleaned of URLs and irrelevant data (④). The Text LLM then integrates the enriched visual summary with the tweet conversation to generate QA pairs using template questions (⑤). + +To ensure a range of difficulty in QA pairs, we curate both generic and specific template questions for predefined QA tasks. Generic questions, such as What actions were performed by the road entities involved in the key road event?, require complex reasoning and are harder to answer, while specific questions, such as How was the truck involved in the accident?, directly reference the event and entities, making them easier. This approach ensures varied difficulty in QA pairs. Sample QA pairs generated by our hybrid approach are illustrated in Fig. 2. The prompts used in each QA stage are iteratively refined on representative samples for quality. The supplementary includes all template questions, prompts, and outcomes. + +QA Refinement and Categorization: Social conversations often include non-visual information, like names or past experience. Relying on such data for QA generation may produce answers with irrelevant information. To address this, we prompt a Text LLM to refine QA pairs by removing specific details—such as names, past encounters, or dates—that aren't directly inferable from the video. This refinement step (6) ensures the QA pairs are answerable solely through video content, enhancing quality. To evaluate various aspects of road event understanding, we categorize QA pairs into predefined tasks (6). A Text LLM assigns each QA pair to a task with a category score, and expert annotators review pairs with low scores for accuracy, reassigning or removing as needed. Verified QA pairs then + +![](images/8da88bd3040061c342433d1e223bde53f8318ed2ddcb4543cdcef0476bf70a37.jpg) +Figure 2. RoadSocial Annotation Pipeline: The steps involved in the annotation pipeline are depicted from 1 to 8. Raw Tweet Data consists of the video and the Twitter conversation. Step 1 includes splitting the video into 3-second segments (in purple shaded boxes). Step 2 involves feeding the video segments to Video LLM and prompting it to generate corresponding captions numbered from 1 to N. These captions are aggregated and summarized by an LLM to generate entire video summary in Step 3. Step 4 filters the raw tweet textual data and extracts the captions, replies, hashtags, and tagged legal authorities' user handles (highlighted in blue). This filtered conversation data and the entire video visual summary are fed to LLM and prompted to generate generic $(\mathbb{G})$ and specific $(\mathbb{S})$ QA pairs in Step 5. All important aspects of the key road event mentioned in the raw tweet text, video segment captions, the entire video summary, and the generated QA pairs are highlighted in purple. The generated QA pairs are refined and categorized into pre-defined tasks in step 6. These QA pairs are verified by expert annotators to either include or exclude them from the dataset in Step 7. The human-verified QA pairs are then used as input to generate video-level tags in Step 8. + +undergo final quality checks for relevance to the video (7). Detailed prompts and sample outputs are provided in the supplementary material. + +Video-level Tag Generation: To categorize videos by key aspects of road events, we generate diverse video-level tags (e.g. traffic violation, wheelie, unsafe overtaking) using verified answers from step 7. A Text LLM [1] scans these answers to generate top-k tags most relevant to each QA task (8). This structured tagging approach ensures that the generated QA pairs, tags are robust and reflect the diverse scenarios present in the dataset. + +Incompatible QA Generation: To assess the reliability and resistance of Video LLMs to hallucinations, we generate incompatible QA pairs for non-road event videos. This + +involves sampling questions from road event QA pairs to create mismatched questions for unrelated videos. Answers are generated using the Hybrid Approach mentioned previously, with modified prompts treating these mismatched questions as templates. Further details on the prompt modifications are provided in the supplementary. + +# 3.3. Dataset Statistics + +Our final dataset comprises over 14M video frames from more than 13.2K videos (totaling 7.9K minutes of video footage) with 260K QA pairs and 674 unique video tags (total 100K+). + +The dataset exhibits significant diversity across several dimensions, including geographical distribution (Fig. 4), + +![](images/162143087a732c2e6a599d35802fa0c84713a6768c541f30c9db60129e6eaf39.jpg) + +![](images/cffd169648fc2d0c7babc71696c96a79ef2324d57d50043903952da8f6c6d6a6.jpg) + +![](images/96e6ae14a507a6a17c178e04cde5bb8e77f35daf780d95bc2d8f643de4977465.jpg) + +![](images/bc5418e70394726efcf3767b3ef8f545e72e8f485c74f81ff6aa8ba8d08f3d4c.jpg) + +![](images/325c3f16428fe53ec40c665d7beef3d930ca7ac1fe509b85e000198228c70626.jpg) + +![](images/210734586e64a507465ef9ca88df394fe2ea9a7d008aa22a0c4bad150656215a.jpg) + +![](images/6a33c56c684ff374adedef5d593ded7c905eec233fc9331b49d74aef4ce4de2d.jpg) +Figure 3. Examples of QA Pairs grouped by tasks and color-coded by task category. Gray outlined questions are generic while gray fill shading indicates specific questions. Highlighted text indicates key information. (Sec. 3.4). + +![](images/09c2ce4e0f2cde65d5229792239c7fa7b0010cb9e33ce11a731ceeec89b5f26a.jpg) +Figure 4. The diversity of RoadSocial dataset: The number of QA pairs, social commentary (tweets), and video frames spread across different regions is shown. Overall statistics of the raw tweet data, generated QA pairs, and tags in our dataset is also shown. Total incompatible QA pairs and related numbers for non-road event videos are specified inside a light brown box at left. + +![](images/364590e9f5413e39b512d11850163c93ac925f55564f3f2e9fb2c27e098f2f3b.jpg) + +QA types (Fig. 3), and video tags (Fig. 1). Fig. 4 shows the global coverage of our dataset attributes, depicting the diverse perspectives involved in the QA pair generation process. + +It includes 414K multilingual tweet captions and replies corresponding to 204K unique user handles (from across 100 countries) sharing facts and opinions about the road or traffic events. Tab. 1 compares key attributes of our dataset with related road event understanding datasets. The distribution of QA pairs corresponding to each task category is shown in Fig. 5. The distribution of video tags along differ + +ent attributes is shown by word clouds in Fig. 1. The videos durations range from 0.13 seconds to 3885.44 seconds with an average of 35.6 seconds. + +# 3.4. QA Tasks Taxonomy + +We developed a question-answer (QA) taxonomy for structured evaluation of Video Large Language Models (Video LLMs). The taxonomy consists of 12 distinct tasks organized into four reasoning categories: Complex, Factual, Imaginative, and Hallucination (Fig. 5). These categories assess various aspects of road events, ranging from key entity identification (see $⑤$ in Fig. 3) to hypothetical scenario exploration (Fig. 3 $\mathbf{10}$ ). Our taxonomy extends beyond conventional road datasets by incorporating previously underrepresented tasks, such as Viewpoint QA (analysis of camera perspectives capturing road events) and Where QA (geographic location identification of road events). As an additional novelty, our approach uniquely incorporates Adversarial QA and Incompatible QA. Adversarial QA tests a model's ability to recognize and reject misleading assumptions or false details in questions by identifying non-occurring road events e.g. Fig. 3 $\mathbf{11}$ ). Incompatible QA on non-road-event videos helps evaluate models' robustness to hallucination by identifying irrelevant video-question pairs. Fig. 3 illustrates representative QA pairs for each category + +![](images/b95d60d168d9c79a832572564ce14e8128d6226167d8f5c2f410ae694de56eb9.jpg) +Figure 5. QA Task Taxonomy: The QA pairs in RoadSocial are broadly grouped into 4 categories (highlighted in blue) which are further subdivided into 12 tasks (shown in green). Total QA pair count for each category is shown in blue squared box. Some of these tasks are further subdivided into granular sub-tasks (highlighted in orange) to facilitate coarse to fine-grained understanding of road events along different aspects. +Figure 6. An example of prompting a Video LLM [37]. + +including the generic and specific questions (described in Sec. 3.2). For a detailed QA task description, please refer to the supplementary. + +# 4. Experiments + +We evaluate a wide range of Video LLMs (both open-source and proprietary, driving-specific and general-purpose) on our road event understanding benchmark. + +# 4.1. Data Setup + +Evaluation Benchmark: RoadSocial-QA consists of 13.2K videos encompassing 260K QA pairs, with an average of 20 QA pairs per video. To evaluate zero-shot reasoning capabilities of Video LLMs, we split our dataset into 12K training and 1.2K test videos, resulting in 234K and 26K QA pairs respectively. The video splits maintain geographical diversity across the dataset, with the test set serving as our primary evaluation benchmark. + +For model evaluation, we provide the model with video frames and a task-specific question, following the format: video frames + model's default system prompt (if any) + our task-specific question (Fig. 6). Detailed prompting structures are described in Supplementary. + +# 4.2. Model Setup + +Our evaluation encompasses 18 Video LLMs, comprising 15 open-source general-purpose models, 2 proprietary general-purpose models, and 1 open-source driving-specific model. We evaluate their zero-shot performance on the test split of RoadSocial-QA using each model's official configuration for open-ended response generation. The results, presented in Tab. 2, analyze model performance across different tasks. All evaluation runs were conducted on a com + +video frames + model's default system prompt (if any) + our task-specific question + +The video lasts for {videotime(:.2f)} seconds, and {len(video[0])} frames are uniformly sampled from it. These frames are located at {frametime}. Please answer the following question related to this video. User: what type of camera was used to capture the video? Consider camera types, including but not limited to: Handheld cameras, smartphone, camcorder, vehicle-mounted cameras, dashcam, bike-mounted... + +puting cluster equipped with NVIDIA H100 GPUs. Detailed information about model configurations, prompting templates and evaluation timelines is provided in Supplementary. + +# 4.3. Evaluation Metrics + +To assess the similarity between model-generated and ground-truth open-ended responses, we adopt GPT-3.5 score [17] as our primary evaluation metric for all tasks (except Temporal Grounding), following established practices in recent literature [12, 14, 26, 34]. To ensure statistical robustness, we conduct multiple evaluation runs and report mean of the GPT-3.5 scores. For Temporal Grounding QAs, time interval is extracted from the model-generated response and compared with the ground-truth time interval range using the mean Average Precision (mAP) evaluation metric. The complete evaluation protocols, including prompt templates, and scoring criteria are provided in the Supplementary. + +# 4.4. Analysis + +Overall Performance Trends: Refer to last 3 columns of Tab. 2. Tarsier-34B [30] achieves the highest overall score (63.5) across ALL QA tasks whereas IXC-2.5-7B [36] leads the benchmark on road-event related tasks (RT) (66.4) among open-source models. These models even outperform larger models such as InternVL2-76B [4] and Qwen2-VL72B [31]. Additionally, all general-purpose models surpass driving-specific Video LLM across all tasks, revealing significant performance gaps in general road event understanding within the driving-focused model. Predictably, Video LLMs face greater difficulty with Generic QAs compared to Specific QAs because generic questions require the model to infer the context independently, unlike specific questions. Among closed-source models, GPT-4o [18] stands out as the top performer, achieving the highest scores across all models. A radar plot with representative Video LLMs can be viewed in Fig. 7. + +Performance Across Task Categories: The analysis reveals distinct patterns across different reasoning categories, highlighting strengths and weaknesses among models in various types of reasoning tasks. + +In factual reasoning, models perform well in Where (WR) and Viewpoint (VP) QA tasks, both of which yield + +
ModelParamsFactualComplexImaginativeHallucinationOverall (ALL)Overall (RT)Overall (Generic)Overall (Specific)
WRKEVPDSWYCQTGADINCFAVIC
Dolphin [13]9B61.334.567.835.825.237.20.0149.839.145.571.821.340.842.529.846.5
GPT-4o [18]-77.066.684.370.270.872.17.877.776.477.090.067.669.870.069.574.4
Gemini-1.5-Pro [28]-77.756.785.461.961.460.118.672.170.275.772.348.763.464.760.168.3
InternVL2 [4]76B72.451.381.457.159.062.11.0770.567.069.258.627.656.459.155.565.1
Qwen2-VL [31]72B76.856.685.160.264.067.60.0171.972.471.637.040.258.660.358.368.8
LLaVA-Video [37]72B75.852.476.852.455.052.29.9468.363.764.983.524.756.759.651.163.3
LLaVA-OV [10]72B75.154.178.753.053.354.13.9967.861.963.145.119.952.555.551.863.0
VITA [6]8x7B66.652.171.648.155.656.32.2766.766.062.456.322.052.254.949.860.4
Tarsier [30]34B73.758.178.258.259.058.80.3271.671.167.483.282.363.561.858.466.1
ARIA [11]25.3B75.453.186.258.456.970.28.9675.174.774.086.429.262.465.456.768.5
InternVL2 [4]8B67.751.778.055.759.360.90.7766.766.870.068.126.156.058.753.764.0
Mini-CPM-V 2.6 [35]8B77.757.680.655.050.557.50.461.652.359.373.530.054.756.951.062.0
IXC-2.5 [36]7B78.558.785.461.765.368.50.6973.975.675.785.829.263.366.460.770.3
Tarsier [30]7B69.954.772.352.053.455.20.1169.569.363.579.167.358.958.154.061.7
LongVU [25]7B73.053.076.351.150.255.00.8459.755.858.248.932.751.252.947.759.7
Qwen2-VL [31]7B75.552.876.152.757.756.40.5969.271.665.937.539.654.656.052.663.9
LLaVA-Video [37]7B74.650.176.752.150.150.31.4360.453.858.761.823.551.153.647.659.7
LLaVA-OV [10]7B73.451.277.250.751.751.20.9762.855.458.645.421.150.052.648.459.8
LLaVA-OV ft.7B80.964.185.764.168.765.14.4974.270.971.795.487.669.467.865.169.7
+ +Table 2. Video LLMs benchmarked on RoadSocial-QA. Standard prompting with task-specific instructions were employed for zero-shot evaluation of Video LLMs on 12 QA tasks. Video LLMs are grouped as open-source (driving-specific and general-purpose), and closed-source models. Further, we fine-tune a Video LLM - LLaVA-OV-7B and report its performance at the end of the table. Abbreviations used for QA tasks include Factual (F), Complex (C), Imaginative (I), Hallucination (H), Where (WR), Key Entities (KE), Viewpoint (VP), Description (DS), Why (WY), Consequence (CQ), Temporal Grounding (TG), Advisory (AD), Introspection (IN), Counterfactual (CF), Adversarial (AV), Incompatible (IC), and Road-event related Tasks (RT). RT includes all tasks except IC which corresponds to non-road event videos. GPT-3.5 score is reported for all tasks except Temporal Grounding (TG) for which average mAP@.3..7 (%) is reported. Overall average scores are reported for ALL QA tasks (F, C, I, and H), Road-event related Tasks (RT), Generic QAs, and Specific QAs under each task. All reported scores (scale 0 to 100) are colored based on their value from low to high. VideoLLMs show per-query latencies of 1-25s (7B-76B) on H100 GPUs. + +consistently high scores. For VP tasks, this may be partly due to our prompt that offers a limited set of viewpoint options, essentially transforming the question into a multiple-choice format rather than a free-form open-ended question. Empirically, performance declines when these choices are absent from the prompt, as noted in the supplementary. Meanwhile, WR tasks perform well due to their inherently specific questions. + +Most Video LLMs encounter difficulties with complex reasoning tasks, such as Description (DS), Why (WY), Consequence (CQ), and Temporal Grounding (TG) reasoning, as well as Key Entity (KE) tasks. These results indicate that many models struggle with identifying key road events that is the main focus of the video. + +Temporal Grounding (TG) proves to be particularly challenging, with most models achieving average mAP scores below $1\%$ , highlighting a major limitation in temporal localization for Video LLMs. The highest-performing model, Gemini-1.5-Pro [28], achieves $18.6\%$ . In comparison, LLaVA-Video-72B [37] leads among open-source models with $9.94\%$ , potentially benefiting from its default prompt, + +which incorporates time-based instructions (Fig. 6). Empirical analysis shows two common reasons for TG underperformance: some models, such as Tarsier-34B [30], struggle with instruction following, leading to unexpected or incoherent answers, while others, such as LLaVA-OV [10], lack the capability to associate the sequence of events with time in the video (details in supplementary). + +In imaginative reasoning, models show promising capabilities, with several models achieving over $70\%$ accuracy in Advisory (AD) and Introspection (IN) tasks. This indicates that models can effectively use their pre-trained knowledge to reason about hypothetical scenarios. + +Robustness and Hallucination Assessment: The evaluation of model robustness through Adversarial (AV) and Incompatible (IC) QAs reveals interesting behavioral patterns. Some models, such as GPT-4o [18] and IXC-2.5-7B [36] demonstrate exceptional robustness to adversarial queries, suggesting effective mechanisms for identifying misleading information. However, most models struggle on Incompatible QAs indicating their tendency to generate hallucinated responses for irrelevant Video and QA pairs. No + +tably, Tarsier-34B [30] outperforms all models by a good margin indicating inherent capability to identify misleading information and reject out-of-domain queries. + +Error Analysis and Future Directions: (1) Temporal Confusion: Models frequently struggle with temporal localization, particularly evident in the poor Temporal Grounding (TG) scores. (2) Complex Reasoning Gaps: While many models perform well in factual reasoning tasks, they often struggle with QAs requiring in-depth contextual understanding. (3) Context Integration: The observed performance gap between Generic and Specific QAs suggests that models struggle to autonomously infer context for generic questions. Future models could benefit from improved mechanisms to integrate prior domain knowledge with visual data for more accurate general context recognition. (4) Hallucination in Response Generation: Although some models demonstrate resilience to adversarial queries, hallucination remains a problem for Incompatible (IC) QAs, where irrelevant or out-of-domain answers are generated. Enhancing model training with stricter grounding mechanisms may reduce hallucinations, especially when faced with ambiguous or misleading inputs. + +RoadSocial improves road event understanding capability of general-purpose Video LLM: We utilize the train split of our dataset and fine-tune a general-purpose Video LLM. Specifically, we selected LLaVA-OV-7B [10] parameter model as our baseline and employed standard instruction fine-tuning strategy wherein QA pairs are structured into instruction-tuned triplets (question, video, response). We adhere to the official training guidelines and optimized the model using a global batch size of 16 distributed over 16 NVIDIA H100 GPUs. During this phase, all key components (Vision tower, MLP adapter and LLM) were fine-tuned to optimize performance. Our evaluation results (last row of Tab. 2) shows that the fine-tuned LLaVA-OV-7B [10] model attains a significant jump of $19.4\%$ in overall average score across all QA tasks and stands on par with the best performers. Specifically, the performance gains are significant across complex reasoning (DS, WY, CQ), introspection (IN), and Hallucination (AV, IC) tasks, showcasing our dataset's utility for improving road event understanding capabilities of general-purpose Video LLM. + +Ethical and Privacy Considerations: Our data collection adheres to ethical guidelines, using only publicly available social media content. Our QA generation process includes rigorous checks to exclude potentially harmful, biased or inappropriate content in QA pairs, ensuring the dataset supports fair and responsible research in road event understanding. Additional details can be found in supplementary. + +# 5. Conclusion + +RoadSocial redefines the landscape for general-purpose road event understanding. With a first-of-its-kind VideoQA + +![](images/ec25e7e3489e5c6ccdb82cc44305eb99f2406976f651a7b25f07ea6a2fae3146.jpg) +Gemini-1.5-Pro +GPT-40 +IXC-2.5-7B +Tarsier-34B +Dolphin-9B +Figure 7. Comparison between representative Video LLMs on RoadSocial benchmark across different QA tasks. + +dataset spanning 14M frames and 414K social comments, our dataset provides 13.2K videos with 260K high-quality QA pairs and 674 unique video tags (total 100K+). By capturing diverse camera viewpoints, geographical contexts, and socially-informed QAs, RoadSocial delivers a comprehensive dataset that captures the complexity of real-world road scenarios across varied cultural and environmental contexts. Leveraging social media content, it addresses the limitations of traditional datasets by incorporating unique perspectives and nuanced social discourse. Our scalable semi-automatic annotation framework, powered by Text and Video LLMs, supports the creation of rich QA pairs across 12 challenging tasks. Given its scalable nature, our annotation framework can easily ingest and process social media posts generated continuously over time, enabling even larger dataset size with sustained quality. Our robust evaluation framework tests model resilience to irrelevant inputs, hallucinations, cross-viewpoint comprehension, and geographical awareness. Our evaluation across 18 Video LLMs provides critical performance insights across a spectrum of road event QA tasks. + +While RoadSocial is a rich resource for road event understanding, its reliance on social media data may introduce biases, skewing coverage towards regions with higher social media use. Apart from addressing these concerns, we envision several future directions for expanding RoadSocial such as increasing language diversity and establishing additional benchmark tasks. 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Overview of RoboBrain. RoboBrain consists of three key robotic capabilities: planning capability, affordance perception, and trajectory prediction. RoboBrain outperforms previous MLLMs in robotics tasks. The bottom part shows the composition of RoboBrain's training data and provides a specific example of visual question answering from our proposed ShareRobot. Best viewed on screen. + +# Abstract + +Recent advancements in Multimodal Large Language Models (MLLMs) have shown remarkable capabilities + +across various multimodal contexts. However, their application in robotic scenarios, particularly for long-horizon manipulation tasks, reveals significant limitations. These limitations arise from the current MLLMs lacking three essential robotic brain capabilities: Planning Capability, which involves decomposing complex manipulation instructions into manageable sub-tasks; Affordance Per + +ception, the ability to recognize and interpret the affordances of interactive objects; and Trajectory Prediction, the foresight to anticipate the complete manipulation trajectory necessary for successful execution. To enhance the robotic brain's core capabilities from abstract to concrete, we introduce ShareRobot, a high-quality heterogeneous dataset that labels multi-dimensional information such as task planning, object affordance, and end-effector trajectory. ShareRobot's diversity and accuracy have been meticulously refined by three human annotators. Building on this dataset, we developed RoboBrain, an MLLM-based model that combines robotic and general multi-modal data, utilizes a multi-stage training strategy, and incorporates long videos and high-resolution images to improve its robotic manipulation capabilities. Extensive experiments demonstrate that RoboBrain achieves state-of-the-art performance across various robotic tasks, highlighting its potential to advance robotic brain capabilities. Project website: RoboBrain. + +# 1. Introduction + +Recent advancements in Multimodal Large Language Models (MLLMs) have significantly advanced the pursuit of Artificial General Intelligence (AGI). By leveraging extensive multimodal datasets sourced from the internet and employing self-supervised learning techniques, MLLMs demonstrate exceptional capabilities in visual perception and understanding human language instructions, excelling in tasks such as visual question answering [3, 12, 13], image captioning [22, 29, 32], and sentiment analysis [14, 17]. Despite significant progress in MLLMs, the exploration of their application in robotics remains in its early stages, highlighting a crucial area for further research and innovation. + +Recent studies have examined the application of MLLMs in robotics, focusing on planning and subgoal decomposition [6, 24], action sequencing [8, 9], and replanning and feedback [35, 38, 62]. However, their effectiveness in robotic scenarios—particularly for long-horizon manipulation tasks—reveals significant limitations. These limitations stem from the current MLLMs' lack of three critical robotic capabilities: planning, affordance perception, and trajectory prediction, as illustrated in Fig. 1. For instance, consider a robotic arm tasked with lifting a teapot and pouring water into a cup. The MLLM should be capable of decomposing this task into sub-tasks, such as "approach the teapot and lift it", "move the teapot until the spout is positioned over the cup", and "tilt the teapot to pour". For each sub-task, such as "approach and grasp the teapot", the MLLM must utilize affordance perception to accurately identify the graspable regions of the teapot. Additionally, trajectory prediction is essential for determining the complete path from the starting point to the graspable part of the teapot. This challenge for existing MLLMs primarily + +arises from the scarcity of large-scale, fine-grained datasets specifically designed for robotic operation tasks. + +To empower the RoboBrain's core capabilities that transition from abstract instruction comprehension to concrete action expression. we first introduce ShareRobot, a largescale, fine-grained dataset specifically designed for robotic operation tasks. Specifically, we label multi-dimensional information such as task planning, object affordance, and end-effector trajectory. Building upon ShareRobot, we developed RoboBrain, an MLLM model based on the LLaVA [34] architecture, aimed at enhancing the perception and planning capabilities of robots in complex tasks. In the process of training RoboBrain, we meticulously designed the ratio of robotic data to general multi-modal data, implemented a multi-stage training strategy, and incorporated long videos and high-resolution images. This approach endowed RoboBrain with powerful visual information perception capabilities in robotic scenarios, supporting historical frame memory and high-definition image input, thereby further enhancing the ability in robotic manipulation planning. Extensive experimental results demonstrate that RoboBrain outperforms existing models across multiple robotic benchmarks, including RoboVQA [50] and OpenEQA [42], achieving state-of-the-art performance. Additionally, it shows competitive results in trajectory and affordance prediction accuracy. These findings validate the effectiveness of the proposed dataset and framework in enhancing robotic brain capabilities. In summary, the main contributions of this paper are as follows: + +- We propose RoboBrain, a unified multimodal large language model designed for robotic manipulation, which facilitates more efficient task execution by transforming abstract instruction into concrete actions. +- We meticulously designed the ratio of robotic data to general multi-modal data, implemented a multi-stage training strategy, and incorporated long videos and high-resolution images. This approach provided RoboBrain with historical frame memory and high-resolution image input, thereby further enhancing its capabilities in robotic manipulation planning. +- We introduce ShareRobot, a high-quality heterogeneous dataset that labels multi-dimensional information, including task planning, object affordance, and end-effector trajectory, effectively enhancing various robotic capabilities. +- Comprehensive experimental results demonstrate that RoboBrain achieves state-of-the-art performance across various robotic benchmarks, highlighting its potential for real-world applications in robotics. + +# 2. Related Work + +MLLM for Robotic Manipulation Planning Existing studies mostly utilize MLLMs primarily focus on understanding natural language and visual observation tasks [6- + +![](images/739ebd4147d80aa9deb6f5b5bd248faa626a637cf09b183e037b42f120085815.jpg) +Figure 2. The generation process of our ShareRobot dataset. Our dataset labels multi-dimensional information, including task planning, object affordance, and end-effector trajectories. The task planning is first annotated by atomic tasks and then augmented by constructing question-answer pairs. The affordance and trajectory are labeled on the images according to the specific instructions. + +8, 26, 30, 61], with fewer addressing the decomposition of high-level task instructions into actionable steps. PaLM-E [16] generates multimodal inputs by mapping real-world observations into the language embedding space. RT-H [6] and RoboMamba [36] generate reasoning results along with robot actions obtained from an additional policy head. However, while these models generate planning texts and actions, they still lack adequate mechanisms for executing complex atomic tasks, highlighting the need for enhanced affordance perception and trajectory prediction. + +Datasets for Manipulation Planning Early datasets for Manipulation [11, 20, 27, 37, 51] mainly comprise annotated images and videos that highlight fundamental handobject interactions, including grasping and pushing. Recent advancements [15, 21, 50, 52] in robotic manipulation emphasize multi-modal and cross-embediment datasets for enhanced generalization. Datasets such as RH20T [18], BridgeDataV2 [56], and DROID [25] enhance scene diversity, broadening the range of manipulation scenarios. Notably, RT-X [45] compiles data from 60 datasets across 22 embodiments into the Open X-Embodiment (OXE) repository. In this work, we extract high-quality data from OXE, decompose high-level descriptions into low-level planning instructions, and adapt these into a question-answer format to enhance model training. + +# 3. ShareRobot Dataset + +To enhance the RoboBrain's capability of planning, affordance perception, and trajectory prediction, we develop a dataset called ShareRobot-a large-scale, fine-grained dataset specifically designed for robotic manipulation tasks. The generation process of our dataset is shown as Fig. 2. The details are described in the following sections. + +# 3.1. Overview + +ShareRobot is a comprehensive dataset, facilitates more efficient task execution by transforming abstract concepts into concrete actions. The main features of the ShareRobot dataset include: + +- Fine-grained Unlike the Open X-Embodiment dataset [44], which provides generalized high-level task descriptions, each data point in ShareRobot includes detailed low-level planning instructions linked to individual frames. This specificity enhances the model's accuracy in executing tasks at the right moment. +- Multi-dimensional To enhance RoboBrain's capabilities from abstract to concrete, we label task planning, object affordances, and end-effector trajectories, allowing for greater flexibility and precision in task processing. +- High quality We establish rigorous criteria for selecting data from the Open-X-Embodiment dataset [44], focusing + +![](images/91f7e4731631cf41f18121b6286ce79387196a6d3d97117e729fd2dcf7fc5336.jpg) +a. Source Data Distribution + +![](images/4f75a69c375c059d3597ac638d5e7f1a8e3c9ade4883dfc2f78fcdd260a3ec9b.jpg) +b. Cross-Embodiment Distribution + +![](images/043c621b344bd9669c0bf7fe8734c2a17c5b82d377b6d6e175db7b48c86a4a7f.jpg) +c. Statics of Types of Atomic Tasks. +Figure 3. The diversity of our ShareRobot dataset. Our dataset involves (a) 23 original datasets, (b) 12 embodiments and (c) 107 types of atomic tasks. The distribution of the top 20 most frequent atomic actions within our ShareRobot dataset is presented in (c). + +on high resolution, accurate descriptions, successful task execution, visible affordance, and clear motion trajectories. Based on these criteria, we validate 51,403 instances to ensure high quality, forming the foundation for RoboBrain's core capabilities. + +- Large scale With 1,027,990 question-answer pairs, ShareRobot is the largest open-source dataset for task planning, affordance perception, and trajectory prediction, enabling deeper understanding of complex relationships from abstract to concrete. +- Rich diversity In contrast to the RoboVQA [50] dataset's limited scenes, ShareRobot features 102 scenes across 12 embodiments and 107 types of atomic tasks, as shown in Fig. 3. This diversity allows MLLMs to learn from varied real-world contexts, enhancing robustness in complex, multi-step planning. +- Easy scalability Our data generation pipeline is designed for high scalability, facilitating expansion as new robotic embodiments, task types, and environments develop. This adaptability ensures the ShareRobot dataset can support increasingly complex manipulation tasks. + +# 3.2. Data Selection + +Based on the Open X-embodiment dataset [44], we carefully selected 51,403 instances, mainly focusing on image quality, description accuracy and success status. Our data collection process adheres to the following principles: + +- High-resolution image We eliminate videos lacking images or those with low resolution. Any video with a resolution below 128 pixels is removed. +- Accurate description Videos without descriptions or with vague descriptions are filtered out to avoid affecting the planning capability of the model. +- Success status We discard videos of failed tasks, as unsuccessful demonstrations hinder the model's learning. + +- Long video length Videos with fewer than 30 frames are excluded, as they contain limited atomic tasks. +- Object not covered We remove any videos where the target object or end-effector is covered by other objects, as our model has to accurately identify the positions of end-effectors and the object's affordance. +- Clear Trajectories We exclude the demonstrations with unclear or incomplete trajectories, as trajectory prediction is one of our RoboBrain's capabilities. + +# 3.3. Data Labeling + +Planning Labeling We extract 30 frames from each robotic operation demonstration and use these frames along with their high-level descriptions to decompose them into low-level planning instructions using Gemini [53]. Three annotators then review and refine these instructions to ensure the precision of labeling. Subsequently, we design 5 different templates for each of the 10 question types in RoboVQA [50]. In the process of data generation, we randomly select 2 templates of each question type to generate question-answer pairs for every instance. This process transforms 51,403 instances into 1,027,990 question-answer pairs, with annotators monitoring data generation to maintain the dataset's integrity. + +Affordance Labeling We filter 6,522 images and annotate each with affordance areas as $\{l^{(x)}, l^{(y)}, r^{(x)}, r^{(y)}\}$ according to its high-level description, where $\{l^{(x)}, l^{(y)}\}$ are the top left coordinates and $\{r^{(x)}, r^{(y)}\}$ are the bottom right corner coordinates. Subsequently, we conduct a rigorous manual review and refinement of each instruction to ensure its precise alignment with the associated affordance areas. + +Trajectory Labeling We filter 6,870 images and annotate each with the gripper's trajectory using at least three $\{x,y\}$ coordinates according to its low-level instruction. Subsequently, we conduct a rigorous manual review and refinement of each instruction to ensure its precise alignment + +![](images/58da6563332890362a2a2b5f48a7c434d611bb0c608eadaef0e5be882810dc7a.jpg) +Figure 4. The pipeline of our RoboBrain. The images, multiple images, and videos are sent into our model to pre-train a foundation robotic brain. Besides, we fine-tune the RoboBrain via A-LoRA and T-LoRA to develop affordance and trajectory skills. In practical applications, the model first generates detailed plans, and then splits it into sub-task descriptions to execute specific robotic tasks. + +with the associated trajectory. + +# 3.4. Data Statistics + +We select 23 original datasets from the Open X-embodiment dataset [44]. The distribution of the source data is shown in the Fig. 3. The data involves 102 various scenes (e.g. bedroom, laboratory, kitchen, office), and covers 12 different robot bodies. According to statistics, there are 132 types of atomic actions in this dataset, tasks with higher word frequency are shown in Fig. 3 (c). The 5 most frequent atomic tasks are "pick", "move", "reach", "lift", and "place", which are frequent task types in real robotic operation scenarios. This suggests that the distribution of our dataset is reasonable. Finally, we get 1,027,990 question-answer (QA) pairs for planning. For the planning QA pairs dataset, we split 1 million QA pairs as the training set and 2,050 QA pairs as the test set. For the affordance dataset, we split 6,000 images as the training set and 522 images as the test set. For the trajectory dataset, we split 6000 images for training and 870 images for testing. + +# 4. RoboBrain Model + +In this section, we provide an overview of RoboBrain. Our goal is to enable the Multi-modal Large Language Model (MLLM) to understand abstract instructions and explicitly output object affordance regions and potential oper- + +ational trajectories, facilitating a transition from abstract to concrete. We employ a multi-stage training strategy: Phase 1 focuses on general OneVision (OV) training to develop a foundational MLLM with strong understanding and instruction-following abilities. Phase 2, the robotic training phase, aims to empower the core capabilities of RoboBrain from abstract to concrete. + +# 4.1. Model Architecture + +RoboBrain consists of three modules: the foundational model for planning, the A-LoRA model for affordance perception, and the T-LoRA model for trajectory prediction. In practical applications, the model first generates detailed plans, and then splits it into sub-task descriptions to execute affordance perception and trajectory prediction. The pipeline of our RoboBrain is shown to Fig. 4. + +Foundational Model for Planning We utilize LLaVA as the foundational model for RoboBrain, which consists of three main modules: the Vision Encoder (ViT) $g(\cdot)$ , the Projection $h(\cdot)$ , and the Large Language Model (LLM) $f(\cdot)$ . Specifically, we employ SigLIP [59], a 2-layer MLP [33], and Qwen2.5-7B-Instruct [54]. Given an image or video $X_{v}$ as visual input, ViT encodes it into visual features $Z_{v} = g(X_{v})$ , which are then mapped to the semantic space of the LLM through Projector, resulting in a sequence of visual tokens $H_{v} = h(Z_{v})$ . Finally, the LLM generates a textual + +![](images/6da42370236311475c75b326a11a47dbffa1a57ebcf7915489ac850f9382e944.jpg) + +
Stage-1Stage-1.5Stage-2Stage-3Stage-4
Single-ImageOneVisionA-LoRAT-LoRA
VisionResolution384Max 384×{2×2}Max 384×{6×6}Max 384×{6×6}Max 384×{6×6}Max 384×{6×6}Max 384×{6×6}
#Tokens729Max 729×5Max 729×37Max 729×37Max 729×37Max 729×37Max 729×37
DataDatasetLCSImageImageImage & VideoRobotic DataAfford. DataTraj. Data
#Samples558K4M3.2M1.6M3M10K400K
ModelTrainableProjectileFull ModelFull ModelFull ModelFull ModelA-LoRAT-LoRA
#Tunable Parameters17.0M8.0B8.0B8.0B8.0B28.0M28.0M
TrainingBatch Size8211144
LR: ψViT-2×10-62×10-62×10-62×10-62×10-62×10-6
LR: {θProj, φLLM, φLoRA}1×10-31×10-51×10-51×10-51×10-51×10-51×10-5
Epoch1111111
+ +Table 1. Detailed configuration for each training stage of the RoboBrain. + +response in an autoregressive manner based on the human language instruction $X_{t}$ and $H_{v}$ . + +A-LoRA Module for Affordance Perception The term affordance in our work refers to the area where the human hand makes contact with objects. During interactions, humans instinctively engage with various objects within specific regions. We utilize bounding boxes to represent affordances. Formally, consider an image $I$ consisting of multiple objects with their affordances: $O_{i} = \{A_{i}^{0}, A_{i}^{1}, \dots, A_{i}^{N}\}$ , where the $i$ th object owns $N$ affordances. The format of affordance is defined as $\{l^{(x)}, l^{(y)}, r^{(x)}, r^{(y)}\}$ , and $\{l^{(x)}, l^{(y)}\}$ represents the top left corner coordinates of affordance, while $\{r^{(x)}, r^{(y)}\}$ is the bottom right corner coordinates. + +T-LoRA Module for Trajectory Prediction The term trajectory in our work refers to the concept of 2D visual traces, as presented in [19]. We define trajectory waypoints as a series of 2D coordinates representing the movement of the end-effector or hand throughout the process. Formally, at time step $t$ , the trajectory waypoints can be represented as $P_{t:N} = \{(x_i,y_i) \mid i = t,t + 1,\dots,N\}$ , where $(x_{i},y_{i})$ denotes the $i$ -th coordinate in the visual trace, and $N$ represents the total number of time steps in the episode. + +# 4.2. Training + +Phase 1: General OV Training In Phase 1, we drew on the state-of-the-art training data and strategies from LLaVA-OneVision [28] to construct a foundational model with general multi-modal understanding and visual instruction following capabilities. This lays the groundwork for enhancing the model's robotic manipulation planning abilities in + +Phase 2. Detailed information is provided in Tab. 1. + +In Stage 1, we utilize the image-text data from the LCS-558K dataset [10, 49] to train Projector, facilitating the alignment of visual features $Z_{v}$ with the LLM semantic features $H_{v}$ . In Stage 1.5, we train the entire model using 4M high-quality image-text data to enhance the model's multimodal general knowledge understanding capabilities. In Stage 2, we further train the entire model with 3.2M single-image data and 1.6M image and video data from LLaVA-OneVision-Data [28], aiming to enhance the instruction-following abilities of RoboBrain and improve understanding of high-resolution image and video. + +Phase 2: Robotic Training In Phase 2, we build upon the robust multi-modal foundational model developed in Phase 1 to create a more powerful model for robotic manipulation planning. Specifically, we aim for RoboBrain to understand complex, abstract instructions, support the perception of historical frame information and high-resolution images, and output object affordance regions while predicting potential manipulation trajectories. This will facilitate the transition from abstract to concrete in manipulation planning tasks. Detailed information is provided in Tab. 1. + +In Stage 3, we collected a dataset of 1.3M robotic data to improve the model's manipulation planning capabilities. Specifically, this data is sourced from RoboVQA-800K [50], ScanView-318K including MMScan-224K [23, 40], 3RScan-43K [23, 55], ScanQA-25K [4, 23], SQA3d-26K [23, 41], and a subset of ShareRobot-200K introduced in this paper. These datasets contain substantial scene-scanning image data, long video data, and high-resolution + +![](images/12445dfb1d38444d6471a64804d175a64c1d22ad1f2f0923eaf64b2d12e5a3bc.jpg) +(a) OpenEQA Benchmark + +![](images/f3d9315a2ef76295f4f2f0cc6fa306cfe9de93404be5c5060ccb1cb67986baaf.jpg) +(b) ShareRobot Benchmark + +![](images/a7ca3466e31a268aa078fc57ba53e880091885b485bd4a53c6797f39566378ef.jpg) +(c) RoboVQA Benchmark +Figure 5. The performance of our model RoboBrain on the OpenEQA, ShareRobot, and RoboVQA benchmarks. RoboBrain surpassed all baseline models, achieving state-of-the-art results. + +data to support the model's ability to perceive diverse environments. Additionally, the fine-grained, high-quality planning data in the ShareRobot dataset enhances the manipulation planning capabilities of RoboBrain. To mitigate the issue of catastrophic forgetting [60], we selected a high-quality subset of approximately 1.7M image-text data from Phase 1 to mix with the robotic data collected in Stage 3 for training, tuning the entire model accordingly. In Stage 4, we enhanced the model's ability to perceive object affordances and predict manipulation trajectories from instructions, utilizing affordance and trajectory data from the ShareRobot dataset and other open-source sources [39, 43]. This was achieved by incorporating LoRA modules during training for concrete manipulation capabilities. + +# 5. Experiment + +# 5.1. Implementation Details + +During the entire training phase, we employed the Zero3 [48] distributed training strategy, conducting all experiments on a cluster of servers, each equipped with $8 \times \mathrm{A}800$ GPUs. The training components for each stage, including image resolution settings, batch size, epochs, and learning rates, are provided in Tab. 1. + +# 5.2. Evaluation Metrics + +Planning Task We selected RoboVQA [50], OpenEQA [42], and the test set of ShareRobot as robotic benchmarks for multi-dimensional assessment. For RoboVQA, we adopt the BLEU1 to BLEU4 metrics [47] used in RoboMamba [36] for evaluation. Additionally, for OpenEQA and ShareRobot, we use GPT-4o [46] as the evaluation tool, scoring based on the alignment or similarity between model predictions and ground truth, which serves as the final performance score for the model. + +Affordance Prediction We utilize the Average Precision (AP) to evaluate the affordance performance of our model. AP metric summarizes the precision-recall affordance curve, which plots the relationship between preci + +sion and recall at various threshold settings. It is calculated across multiple Intersection over Union (IoU) thresholds to obtain a more comprehensive evaluation. + +Trajectory Prediction We evaluate the similarity between ground truth and predicted trajectories, both represented as sequences of 2D waypoints normalized to [0, 1000), following Qwen2-VL [58]. The evaluation uses three metrics: Discrete Frechet Distance (DFD) [19], Hausdorff Distance (HD), and Root Mean Square Error (RMSE). DFD captures overall shape and temporal alignment, HD identifies maximum deviation, and RMSE measures average pointwise error. Together, these metrics provide a comprehensive assessment of trajectory accuracy and similarity. + +# 5.3. Evaluation on Robot Brain Task + +Evaluation on Planning Task We selected 6 powerful MLLMs as our baselines for comparison, including both open-source and closed-source models with different architectures. Specifically, these models include GPT-4V [2], Claude3 [1], LLaVA-1.5 [34], LLaVA-OneVision-7b [28], Qwen2-VL-7b [57] and RoboMamba [36]. Our specific experimental results are shown in Fig. 5. Our RoboBrain outperformed all baseline models across three robotic benchmarks. RoboBrain significantly outperformed all baseline models on OpenEQA and ShareRobot, which can be attributed to its robust capabilities in understanding robotic tasks and perceiving long videos. Additionally, this pattern was observed in other benchmarks as well, with RoboBrain consistently demonstrating superior performance on RoboVQA, achieving a BLEU-4 score that exceeded that of the second-place model by 18.75. This result highlights its capability to decompose complex long-range task planning. + +Evaluation on Affordance Prediction Our results are summarized in Tab. 2. We compare the Qwen2-VL-7B and LLaVA-NeXT-7B models. Qwen2-VL [57] has a superior visual grounding ability and LLaVA-NeXT [31] owns a high-resolution and strong vision tower. We test them all on the AGD20K affordance test set. Our RoboBrain outperforms significantly the other models. It surpasses Qwen2- + +![](images/723f46d6be0cee8b27ecfefbfac7396c36f90f3d1e7ef541dca11dc612d4998d.jpg) +Figure 6. This visualization illustrates that RoboBrain can interpret human instructions and visual images to generate action plans and assessments based on real-time image feedback. Furthermore, it predicts trajectories for each step and identifies corresponding affordances. + +Table 2. The comparison of affordance prediction. We utilize AP as the metric, and test them on affordance test set. + +
ModelAP↑
LLaVA-NeXT-7B [34]9.8 %
Qwen2-VL-7B [5]12.5 %
RoboBrain (Ours)27.1 % (14.6↑)
+ +VL [57] by 14.6 AP, and LLaVA-NeXT by 17.3 AP. It validates our RoboBrain can understand the physical properties of objects and provide the affordance accurately. + +Evaluation on Trajectory Prediction We compare several variants of our model, and the results are in Tab. 3: (1) Baseline, fine-tuned on trajectory-related VQA data; (2) Start_Points, which adds the 2D start coordinates of the end-effector; (3) Max_Points, limiting waypoints to 10 via uniform sampling; and (4) Spec_Token & End_Points, which adds end-effector positions and special tokens to emphasize waypoints and start/goal points. Each variant builds on the previous one, with the final model integrating all components. Our most effective model integrates all design choices. As shown in the last row of Tab. 3, DFD, HD, and RMSE decreased by $42.9\%$ , $94.2\%$ , and $31.6\%$ , respectively, compared to the baseline. We found that adding start points corrected the translational offset between the generated trajectory and the end-effector. + +Table 3. Trajectory Prediction Results Comparison. Discrete Fréchet Distance (DFD), Hausdorff Distance (HD), and Root Mean Square Error (RMSE). + +
MethodDFD ↓HD ↓RMSE ↓
RoboBrain (Base)0.1910.1710.133
+ Start_Points0.1760.1570.117
+ Max_Points0.1850.1630.125
+ Spec_Token0.109 (42.9%↓)0.010 (94.2%↓)0.091 (31.6%↓)
+ +# 5.4. Visualization + +In this section, we present visual examples of RoboBrain in Fig. 6. Given human instructions and visual inputs, RoboBrain engages in multi-turn interactions, understanding and planning future steps. It also outputs more concrete affordances and trajectories. + +# 6. Conclusion + +In this paper, we introduce ShareRobot, a high-quality dataset that labels multi-dimensional information, including task planning, object affordance, and end-effector trajectory. We also present RoboBrain, an MLLM-based model that integrates robotic and general multi-modal data, employs a multi-stage training strategy, and leverages long videos and high-resolution images to enhance robotic manipulation. 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In this work, we explore grounding masks as an effective intermediate representation, balancing two key advantages: (1) effective spatial guidance that specifies target objects and placement areas while also conveying information about object shape and size, and (2) broad generalization potential driven by large-scale vision-language models pretrained on diverse grounding datasets. We introduce ROBOGROUND, a grounding-aware robotic manipulation policy that leverages grounding masks as an intermediate representation to guide policy networks in object manipulation tasks. To further explore and enhance generalization, we propose an automated pipeline for generating large-scale, simulated data with a diverse set of objects and instructions. Extensive experiments show the value of our dataset and the effectiveness of grounding masks as intermediate guidance, significantly enhancing the generalization abilities of robot policies. Code and data will be available at roboground.github.io. + +# 1. Introduction + +The early low-level policies for manipulation [8, 25, 38, 50] primarily relied on imitation learning from collected demonstrations, focusing on acquiring specific skills within predefined scenes. Consequently, these policies exhibited limited generalization capabilities. More recently, Vision-Language-Action (VLA) models [5, 19] have emerged as a promising approach for learning generalizable robotic policies. These models leverage large-scale robot training data alongside pretrained Vision-Language Models (VLMs) [23, 32, 51] to develop broad manipulation capabilities. However, it is still challenging for these methods to generalize + +![](images/6ac996c1f3c9eb7b234a693275dcb2a101fef97c1eaa054c1903fc390dddb4d8.jpg) +Figure 1. Examples of generated data and mask guidance for robot policy. The generated data includes more object distractors in the scene, leading to higher scene complexity. The robot policy is guided by masks to localize the target object and placement area. + +to novel settings without access to extensive datasets and additional fine-tuning, both of which are costly. + +Intermediate representations [2, 3, 15, 37] offer an alternative approach to generalized policy learning by providing structured guidance to policy networks across diverse scenarios. Research in this area typically falls into two categories: accessible yet coarse-grained representations, such as language instructions [2, 49], which are easy to generate but often lack the spatial precision required for fine-grained object manipulation; and fine-grained but resource-intensive representations, such as goal images [4] or point + +flows [3, 12, 33, 45, 47], which provide detailed spatial guidance but demand extensive training data and computational resources, limiting their scalability. + +In this work, we introduce grounding masks as a promising intermediate representation that balances two key aspects: (1) Effective spatial guidance, which not only specifies target objects and placement areas but also conveys information about object shape and size, allowing low-level policies to accurately interpret spatial information; and (2) Broad generalization potential, facilitated by large-scale vision-language models [21, 32, 44, 48] pretrained on diverse grounding datasets, enhancing adaptability to novel objects and environments. To fully explore grounding mask representations for low-level policy networks, we propose ROBOGROUND, a grounding-aware policy guided by object masks for robotic manipulation. Our approach employs a grounded vision-language model to generate masks for both the target object and placement area, which are then seamlessly integrated into the policy network through channel-level and patch-level designs. Specifically, we enhance image inputs via channel concatenation with the masks and introduce a grounded perceiver that attends to mask-guided regions at the patch level, preserving essential spatial information for precise manipulation. + +As shown in Figure 1, existing datasets [10, 26-28, 40] often suffer from limited instruction diversity and scene complexity, leading policy networks to overfit to specific conditions and straightforward instruction-scene mappings. In this work, we aim to investigate the effectiveness of grounding mask representations in maintaining consistent performance across diverse scenarios and instructions. To address dataset limitations, we propose an automated pipeline for generating simulated manipulation data with a diverse set of objects and instructions. By systematically increasing scene complexity through the inclusion of distractor objects, we create a challenging dataset that promotes generalization across varied instructions and object configurations. Specifically, we generate 24K demonstrations with 112K diverse instructions, covering object appearance, spatial relationships, and commonsense knowledge. Scene complexity is further enhanced by sampling distractor objects from a large pool of 3,526 objects spanning 176 categories. This high-complexity dataset encourages models to leverage intermediate object mask guidance for interpreting instruction-scene relationships, providing a rigorous evaluation of our mask-guided model's generalization potential. + +We conduct extensive experiments to evaluate the model's generalization across diverse instructions, unseen objects and categories, and core robotic skills. Our results highlight the effectiveness of grounding masks as intermediate guidance, showing that they substantially enhance the generalization capabilities of robot policies while demon + +strating the value of our dataset. + +# 2. Related Work + +Intermediate Representations for Robot Policy. Various intermediate guidance strategies have been explored to enhance policy learning, including language instructions [2, 49], 2D trajectories [15, 39, 42], point flows [3, 12, 33, 45, 47], goal images [4, 6], goal sketches [37], and object-centric representations [14, 35, 36]. For instance, RT-Trajectory [15] utilizes rough trajectory sketches to guide policies in performing new tasks, while Im2Flow2Act [45] predicts object flows and maps them to actions. However, acquiring such intermediate guidance during evaluation is often impractical due to the lack of largescale, diverse datasets and generalizable foundation models. Some approaches leverage object-centric representations to enhance policy robustness. KITE [36] decomposes tasks into keypoints using an additional grounding module, while MOKA [14] employs prompt engineering to derive keypoints that effectively capture affordances in manipulation tasks. Closely related to our mask-based approach, MOO [35] uses pretrained Vision-Language Models (VLMs) to generate coarse bounding boxes, which are then overlaid onto the original image. In contrast, our method focuses on obtaining fine-grained object masks and introduces an efficient Grounded Perceiver to better utilize mask-based intermediate guidance for improved manipulation performance. + +Large Vision-Language Models. Large Vision-Language Models (LVLMs) have recently demonstrated remarkable capabilities in image understanding and image-to-text generation, as seen in BLIP-2 [22], LLaVA [23], Instruct-BLIP [9], and MiniGPT-4 [51]. While these models excel at text generation and holistic image comprehension, they often struggle with fine-grained understanding of local regions within images. To address this, several methods [7, 29, 41, 46] enhance region-level perception by incorporating bounding boxes and spatial location bins, allowing LMMs to focus on specific interactive areas. Furthermore, recent approaches [21, 24, 32, 44, 48] have advanced grounding capabilities, enabling the identification of target objects or regions to support downstream tasks. Our method builds upon this progress by leveraging GLaMM [32] to generate grounding masks for both target objects and placement areas, providing structured guidance for the low-level policy network in robotic manipulation. + +# 3. Data Generation + +Existing language-conditioned simulation datasets often suffer from limited object and environment diversity [18, 27, 34] or lack a broad range of instructions and complex scenes [26, 28], making them less effective for train + +![](images/8849ad02e66effaa94eaf12a9e24109db3cd3e9fb0ec359c19d32d0a08f81782.jpg) +Figure 2. Data Generation Pipeline. The pipeline is composed of three key stages: (a) First, we extract informative object attributes in both keyword and descriptive phrase formats; (b) Next, appearance-based instructions are generated using these attributes, where keywords filter objects and descriptive phrases calculate appearance similarity; (c) Finally, spatial and commonsense instructions are generated through rule-based methods and GPT-generated techniques, respectively. + +ing robust robotic policies and evaluating model generalization. To address these limitations, we introduce an automated data generation pipeline built upon RoboCasa [28], designed to enhance object variety, instruction diversity, and scene complexity for more challenging manipulation tasks. Our approach produces 24K new demonstrations paired with 112K diverse instructions, covering 176 distinct object categories and a total of 3,526 unique objects. + +# 3.1. Object Set + +A diverse object set is essential for increasing scene complexity and enabling varied instruction generation. Expanding on the original RoboCasa dataset, we curated additional 1,017 high-quality tabletop manipulation objects from Objaverse [11], selected from a pool of over 760K items. The initial filtering process, supported by GPT-4 [1], leveraged object tags and descriptions to identify (1) tabletop-suitable items, (2) kitchen-related objects, and (3) exclude multi-item collections. GPT-4 further assisted in categorizing objects based on their characteristics. The final selection underwent manual review to ensure quality. By incorporating distractor objects from this extensive set, we create complex scenes that challenge models to accurately interpret instructions in diverse and dynamic environments. + +# 3.2. Diverse Instructions + +Existing language-conditioned datasets often rely on fixed-format instructions that require minimal reasoning, leading models to depend on simple mappings between instructions and tasks rather than developing a deeper understanding of the language's semantics. This can hinder the model's ability to generalize to novel objects or tasks. To address this limitation, we propose designing instructions that focus on discriminative understanding of object appearance, spatial relationships, and commonsense knowledge, as illustrated in Figure 2. We present a target object alongside up to 10 contextually relevant objects (distractors) in the scene, encouraging the model to make precise distinctions between the target and surrounding objects. + +Appearance-Based Instructions. To enable detailed visual understanding, we render each object from four perspectives (front, back, left, and right) and combine these views into a composite image that offers a comprehensive visual overview. This image is then processed by GPT-4, which extracts key attributes for each object—such as class, color, shape, and material—both as keywords and full descriptive phrases. When selecting a target object, we randomly assign one attribute as its unique characteristic within the scene. Objects with overlapping keywords for this attribute are filtered out, resulting in a refined set + +![](images/99ea1de8f87dab84f6534b58505710f7e66266a8d6c8ae66643a6b46cb3a23e8.jpg) +Figure 3. Overall Architecture of ROBOGROUND. To enhance policy generalization, we leverage grounding masks as intermediate representations for spatial guidance. Specifically, (a) The grounded vision-language model processes the instruction and image observation to generate target masks. (b) The grounded policy network integrates mask guidance by concatenating masks with the image input and directing attention within the grounded perceiver. + +![](images/4d3e46178614b64537fe6f955a88ae6d8251ba73777f93cfa9457607eb18c242.jpg) + +of valid objects. From this set, distractors are sampled by ranking them based on the similarity of their textual and visual embeddings, derived from CLIP [31] text encoder and image encoder, encoded using the full attribute descriptions and multi-view images, respectively. + +Appearance-Based Instructions. To enable detailed visual understanding, we render each object from four perspectives (front, back, left, and right) and combine these views into a composite image that provides a comprehensive visual overview. This image is then processed by GPT-4, which extracts key attributes for each object—such as class, color, shape, and material—both as keywords and full descriptive phrases. When selecting a target object, we randomly assign one attribute as its unique characteristic within the scene. Objects with overlapping keywords for this attribute are filtered out, resulting in a refined set of valid objects. From this set, distractors are sampled by ranking them based on the similarity of their textual and visual embeddings, derived from the CLIP [31] text and image encoders, using the full attribute descriptions and multi-view images, respectively. + +Spatial Instructions. For randomly generated scenarios specifying a target object and its desired location, we employ a rule-based approach to create instructions that require spatial understanding. First, we extract the coordinates of all objects in the robot's frame. We then generate spatial instructions by identifying the object(s) closest to the target object in a specific direction, ensuring that no other objects of the same type are present in the scene and that the angular deviation in other directions does not exceed 30 degrees. This method produces clear and unambiguous spatial + +instructions. + +Commonsense Instructions. We leverage GPT-4 to generate diverse instructions grounded in commonsense reasoning. For each task, we provide images from three perspectives (robot's left view, right view, and hand view), along with details about the target object and its intended position. Instead of explicitly mentioning the target object, GPT-4 generates pick-and-place task instructions framed within a familiar daily scenario. We prompt GPT-4 to ensure that the scenario is uniquely tailored to the target object, reinforcing the need for commonsense understanding. + +# 4. Method + +# 4.1. Overview + +Our motivation is to leverage grounding masks as an intermediate representation to enhance the generalization ability of robotic manipulation policies. This requires a largescale, pre-trained vision-language model capable of generating grounded information about target objects and placement areas, referred to as the Grounded Vision-Language Model, discussed in Section 4.2. We then incorporate this grounding knowledge into the low-level policy network, where the grounded masks function as both an attention mechanism within the Grounded Perceiver and an additional input channel for vision data, as detailed in Section 4.3. Finally, we outline the training and evaluation procedures for the complete framework in Section 4.4. + +# 4.2. Grounded Vision-Language Model + +Recent advances in large vision-language models [21, 32, 44, 48] have enabled generalizable, object-centric ground + +ing. Our approach builds on GLaMM [32], a state-of-the-art model that generates pixel-level segmentation masks, to guide the low-level policy network in accurately localizing target objects and placement areas. + +Base Model. The grounded vision-language model takes an image observation and a language instruction as input and outputs binary masks for target objects and/or target placement areas specified by the instruction, as shown in Figure 3(a). Given an image $x_{\mathrm{v}}$ and a text instruction $x_{\mathrm{t}}$ , the image is encoded by the CLIP vision encoder [31] to obtain the visual feature $\mathbf{F}_{\mathrm{v}} = \mathrm{CLIP}(x_{\mathrm{v}})$ . This feature is then projected into the LLM's embedding space via an MLP projector $f_{\mathrm{v}}(\cdot)$ , yielding $f_{\mathrm{v}}(\mathbf{F}_{\mathrm{v}}) \in \mathbb{R}^{256 \times D_{\mathrm{t}}}$ . The LLM $\mathcal{L}(\cdot)$ integrates both the projected visual features and the text instruction to generate the output $y_{\mathrm{t}}$ : + +$$ +y _ {\mathrm {t}} = \mathcal {L} \left(f _ {\mathrm {v}} \left(\operatorname {C L I P} \left(x _ {\mathrm {v}}\right)\right), x _ {\mathrm {t}}\right). \tag {1} +$$ + +The model perceives the image through a prompt formatted as: "The provides an overview of the picture," where the token is replaced by the projected visual feature, represented as a sequence of 256 tokens. + +Pixel-level Grounding. To achieve pixel-level grounding, we employ a fine-grained image encoder $\mathcal{E}(\cdot)$ and a pixel decoder $\mathcal{D}(\cdot)$ within the grounding head. The encoder is initialized with a pre-trained SAM [20] encoder, while the decoder follows a SAM decoder-like architecture. A special token $<\mathrm{SEG}>$ is introduced into the LLM's vocabulary to extract grounding-related features. The last-layer embeddings $\mathbf{F}_{\mathrm{seg}}$ corresponding to the $<\mathrm{SEG}>$ token are projected into the decoder's feature space using a projector $f_{\mathrm{s}}$ . The binary segmentation mask $M$ is then generated as follows: + +$$ +M = \mathcal {D} \left(f _ {\mathrm {s}} \left(\mathbf {F} _ {\text {s e g}}\right), \mathcal {E} \left(x _ {\mathrm {v}}\right)\right). \tag {2} +$$ + +For robotic manipulation tasks, the model is prompted to segment both the target object and the placement area (if applicable). As illustrated in Figure 3(a), the model's output specifies these regions using separate $<\mathrm{SEG}>$ tokens. Each $<\mathrm{SEG}>$ token is decoded into an individual mask, yielding the target object mask $M_{\mathrm{o}}$ and the placement area mask $M_{\mathrm{p}}$ which are subsequently provided to the Grounded Policy Network. + +# 4.3. Grounded Policy Network + +After the grounded VLM translates the language instruction into masks for target objects and placement areas, these masks provide useful spatial guidance for the robot's policy. Rather than requiring explicit grounding of semantic descriptions, the policy can focus on leveraging this structured information to improve object localization and action execution. Given the strong generalization ability of the grounded VLM, the masks serve as a bridge between + +high-level language instructions and low-level manipulation strategies, helping the policy adapt to novel objects and environments more effectively. + +Base Model. For the policy network, we employ a language-conditioned transformer architecture, following the GR-1 model [43]. As shown in Figure 3(b), this model processes a sequence of historical image observations, robot states and a language instruction as input to predict future robot actions. Specifically, for each input image $x_{\mathrm{v}}$ , along with corresponding masks $M_o$ and $M_p$ , we apply channel concatenation and project the combined channels back to a size of 3 using a linear layer. The result is then fed into a pre-trained ViTMAE encoder [16]. The encoded visual feature $\mathbf{Z}_{\mathrm{v}} \in \mathbb{R}^{197 \times D_{\mathrm{v}}}$ is computed as follows: + +$$ +\mathbf {Z} _ {\mathrm {v}} = \operatorname {V i T M A E} (\text {L i n e a r} (\operatorname {C o n c a t} (x _ {\mathrm {v}}, M _ {o}, M _ {p}))), \tag {3} +$$ + +where $D_{\mathrm{v}}$ denotes the hidden dimension of the vision encoder. The encoded feature $\mathbf{Z}_{\mathrm{v}}$ consists of a global representation $\mathbf{Z}_{\mathrm{v}}^{\mathrm{CLS}} \in \mathbb{R}^{1 \times D_{\mathrm{v}}}$ , obtained from the CLS token, and a set of local patch representations $\mathbf{Z}_{\mathrm{v}}^{\mathrm{P}} \in \mathbb{R}^{196 \times D_{\mathrm{v}}}$ , corresponding to a $14 \times 14$ spatial grid. These patch features are then processed by the grounded perceiver, $\mathcal{P}(\cdot)$ , which interacts with the grounding masks to reduce the number of tokens, ultimately producing the refined visual token features $\mathcal{P}(\mathbf{Z}_{\mathrm{v}}^{\mathrm{P}})$ . + +Additionally, the input language instruction $x_{\mathrm{t}}$ is encoded using the CLIP text encoder, yielding the text token feature $\mathbf{Z}_{\mathrm{t}}$ . The input robot state $x_{\mathrm{s}}$ is projected through an MLP to obtain the state token feature $\mathbf{Z}_{\mathrm{s}}$ . To enable action prediction, a learnable ACT token with feature $\mathbf{Z}_{\mathrm{a}}$ is also included. Consequently, the token sequence for a single timestep input is structured as follows: + +$$ +\left(\mathbf {Z} _ {\mathrm {v}} ^ {\mathrm {C L S}}, \mathcal {P} \left(\mathbf {Z} _ {\mathrm {v}} ^ {\mathrm {P}}\right), \mathbf {Z} _ {\mathrm {t}}, \mathbf {Z} _ {\mathrm {s}}, \mathbf {Z} _ {\mathrm {a}}\right). \tag {4} +$$ + +For a history length of $N$ , the complete token sequence for one forward pass is constructed by aggregating token features from the past $N$ timesteps. This sequence is then processed by a transformer decoder, which predicts the next-step action tokens through the output $<\mathrm{ACT}>$ tokens. + +Grounded Perceiver A standard perceiver model [17], used in frameworks like GR-1, functions as a token resampler, reducing the number of tokens derived from the initial visual features. This is achieved through iterative attention layers between a small set of learnable query tokens and the original visual features. However, this token resampling process may lead to information loss, potentially limiting policy learning by failing to capture critical details about the target objects and placement areas. To address this, we propose guiding attention toward regions defined by grounded masks, ensuring that essential information is preserved for effective manipulation. + +The perceiver takes as input the $14 \times 14$ patch features, denoted as $\mathbf{Z}_{\mathrm{v}}^{\mathrm{P}}$ , extracted from the vision encoder, along + +with a set of learnable query tokens, $\mathbf{Q}_{\mathrm{g}} \in \mathbb{R}^{k \times D_p}$ , where $k$ is the number of query tokens and $D_p$ is the token dimension. These initial queries, referred to as global queries, capture information from the entire image. To integrate grounded masks, we introduce two additional sets of query tokens: $\mathbf{Q}_{\mathrm{o}} \in \mathbb{R}^{k \times D_p}$ for the target object and $\mathbf{Q}_{\mathrm{p}} \in \mathbb{R}^{k \times D_p}$ for the target placement area. During each attention layer, these additional query tokens interact with the patch features, with attention guided by the respective masks, $M_{\mathrm{o}}$ and $M_{\mathrm{p}}$ , applied via a mask fill operation (see supplementary material for details). This process produces the final set of perceived visual features, $\mathcal{P}(\mathbf{Z}_{\mathrm{v}}^{\mathrm{P}})$ , with a total token length of $3 \times k$ . + +# 4.4. Training and Inference + +VLM Fine-tuning. Although GLaMM was pre-trained on a large-scale grounding dataset, it may not precisely follow the prompt to identify the target object and placement area from a given manipulation instruction in a zero-shot setting. To address this, we construct an instruction-following dataset based on the generated simulation data to fine-tune the VLM. The grounded VLM model is fine-tuned using two types of losses: auto-regressive cross-entropy loss for text generation, and a linear combination of per-pixel binary cross-entropy loss and DICE loss for segmentation. + +Policy Training. In each forward pass, the policy network receives image observations, robot states over $N$ consecutive timesteps, and the corresponding language instruction. Based on this input, the network generates $N$ action tokens, which are processed through linear layers to predict arm and gripper actions. Since arm actions are continuous, we use Smooth-L1 loss $\mathcal{L}_{\mathrm{arm}}$ for optimization. For binary gripper actions, we apply Binary Cross Entropy (BCE) loss $\mathcal{L}_{\mathrm{gripper}}$ . Thus, the total training loss for the policy network is: $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{arm}} + \mathcal{L}_{\mathrm{gripper}}$ . + +Inference. The inference process starts by prompting the grounded VLM to generate segmentation masks for the target objects and placement areas. These initial masks are provided to the grounded policy network to predict the next action tokens. To optimize inference time, segmentation masks are extracted from the grounded VLM only once, at the beginning of the episode. These masks are then used throughout the entire manipulation task as inputs to the policy network. This approach is well-suited for single-turn manipulation tasks, where the target object's position remains stable until the gripper interacts with it, and the placement area remains fixed. Thus, the initial masks provide consistent guidance for the policy network throughout the task. + +For multi-view image observations, each view is processed independently by the grounded VLM to obtain the corresponding masks, allowing for parallel processing. In the grounded policy network, each image and its corre + +sponding masks are separately passed through the vision encoder and grounded perceiver to generate visual token features. During each forward pass of the policy network, only the action for the next timestep is predicted. + +# 5. Experiments + +# 5.1. Simulation Setting + +Our simulation environment is built upon RoboCasa [28], a large-scale framework offering an automated scene generation pipeline. We leverage this pipeline to create diverse scene layouts and textures for data collection. Our main experiments are conducted within the RoboCasa environment, which includes a range of manipulation configurations. We classify the original RoboCasa data as "Easy," due to its relatively simple scene complexity and straightforward instructions. To introduce more complexity, we generate challenging pick-and-place data that requires advanced semantic understanding and reasoning. The instructions are divided into three categories: "Appearance," "Spatial," and "Common-sense," each representing different types of task-specific knowledge. Additionally, we include fundamental manipulation skills, such as opening and closing doors or drawers, pressing buttons, turning levers, and twisting knobs, to further challenge the model. In these tasks, target masks (e.g., for a drawer handle) are also generated to guide the robot's policy in precise manipulation. + +# 5.2. Main Results + +To evaluate our approach, we compare it with three well-established, easy-to-implement methods as baselines. Each method is trained on the same dataset, which includes RoboCasa's 66K demonstrations for foundational skills, alongside our proposed dataset containing 24K demonstrations and 112K instructions with increased diversity and complexity. For evaluation, we generate 400 test samples for each instruction type within the pick-and-place task and for each fundamental skill. The results are presented in Table 1. Metrics for pick-and-place tasks are reported as “ $a / b$ ”, where $a$ is the contact rate (\%) and $b$ is the success rate (\%). The contact rate refers to the percentage of attempts where the gripper makes contact with the target object, while the success rate indicates the percentage of tasks completed successfully. To ensure a fair comparison, we standardize key settings across methods, including history length, input image views, and image sizes. + +# Baselines. + +- ACT [50]: A transformer-based policy network introduced by ALOHA [50]. Trained as a conditional VAE, it performs action chunking when predicting future actions. +- BC-Transformer [25]: A standard behavior cloning policy built on a transformer architecture. We use the publicly available BC-Transformer implementation from + +Table 1. Performance Comparison on Simulated Tasks. Metrics for pick-and-place tasks are reported as “ $a / b$ ”, where $a$ is the contact rate (\%) and $b$ is the success rate (\%). We also report the success rates for other fundamental skills, including door opening/closing, button pressing, lever turning and knob twisting. + +
MethodPick and PlaceOpen/ClosePressTurn/Twist
EasyAppearanceSpatialCommon-sense
ACT [50]47.3 / 18.318.5 / 3.817.5 / 3.515.3 / 2.832.030.826.5
BC-Transformer [25]79.8 / 34.831.3 / 6.838.3 / 7.826.0 / 5.854.850.845.3
GR-1 [43]85.3 / 42.849.5 / 13.854.5 / 16.343.0 / 11.566.858.849.5
Ours89.0 / 43.378.5 / 30.581.0 / 33.576.3 / 30.072.069.354.5
+ +Table 2. Evaluation Results of Unseen Settings. Unseen instance denotes evaluation on new objects belonging to classes present in the training data. In contrast, unseen class refers to evaluation on objects from entirely new classes that were not included in the training data. + +
Unseen LevelMaskEasyAppea.SpatialComm.
Instance71.0 / 35.538.0 / 11.538.8 / 11.530.8 / 7.8
Instance✓85.8 / 42.575.5 / 29.577.8 / 31.872.0 / 28.0
Class53.0 / 17.527.5 / 5.330.3 / 6.328.0 / 5.8
Class✓79.5 / 27.368.5 / 14.369.5 / 14.867.3 / 13.8
+ +RoboMimic, which integrates language input by encoding it with CLIP and combining it with vision representations through FiLM [30] layers. + +- GR-1 [43]: A GPT-style model designed for language-conditioned visual robotic manipulation. The original GR-1 model was pre-trained on a large video dataset and predicts both robot actions and future images. Since the pre-trained model is unavailable, we reproduce it here without large-scale pre-training or image prediction. + +Analysis. Compared to baseline models, our method consistently outperforms across all tasks. ACT generally performs poorly due to the absence of language input, which is crucial for task-specific language comprehension and reasoning. While BC-Transformer and GR-1 benefit from language input, their performance on more challenging tasks remains relatively low. This limitation likely arises from design shortcomings, as these models encode language input as a single, global text feature, which is inadequate for the nuanced understanding and reasoning required by semantically rich instructions. + +Our approach, which leverages grounding masks to guide the policy, shows substantial improvements in challenging tasks, highlighting the effectiveness of incorporating such masks. Interestingly, we observe a consistent gap between the success rate and the contact rate, with the latter being significantly higher. This discrepancy suggests that the model's grasping capability could be further refined. We attribute this to the diverse range of objects in the dataset, which makes learning accurate grasping poses more diffi + +cult. Integrating pose-prediction networks, such as AnyGrasp [13], could potentially help address this challenge. Nonetheless, the high contact rate demonstrates the effectiveness of our method. + +# 5.3. Zero-shot Evaluation. + +For zero-shot evaluation, we categorize unseen settings into two levels: unseen instance and unseen class. Unseen instances refer to evaluation on new objects within classes present in the training data, while unseen classes involve evaluation on objects from entirely new classes not included in the training data. We exclude 30 classes, comprising 597 objects, as unseen and filter out $1/4$ of the objects from each of the remaining classes, resulting in a total of 1,335 unseen instances. For each unseen setting, we generate 400 test samples for each reasoning type within the pick-and-place task. The evaluation results are presented in Table 2. + +Analysis. The experimental results on both unseen instances and unseen classes show that incorporating mask information significantly enhances the model's generalization to novel settings, while maintaining strong performance on previously seen tasks. This improved generalization is reflected in better performance across new data distributions. Notably, in more challenging scenarios, mask guidance achieves approximately $100\%$ relative improvement over non-mask baselines, highlighting its crucial role in handling complex, unseen situations. + +# 5.4. Ablation Study. + +To accelerate our ablation study, we use a subset of the dataset, as full training and evaluation would require several days on 8 NVIDIA 4090 GPUs. This subset includes 3K original samples and 3K generated reasoning samples for a single pick-and-place scenario in RoboCasa. For evaluation, we generate 50 test samples per instruction type while maintaining the original diversity in scenes and objects to ensure representative and meaningful results. + +Training Data and Mask. We perform ablation studies by training models with different datasets and mask configurations. The results, shown in Table 3, indicate that when trained solely on the original simple data, the model eas + +Table 3. Ablation Study on Training Data and Grounded Masks. "Ori. Data" refers to original data in RoboCasa, while "New Data" denotes our proposed data with diverse instructions. "Pred" indicates the use of predicted masks, whereas "GT" denotes ground-truth masks. + +
Ori. DataNew DataMaskEasyAppea.SpatialComm.
✓80 / 3826 / 620 / 426 / 4
✓78 / 3442 / 1252 / 1640 / 12
✓✓90 / 6046 / 1654 / 2038 / 12
✓Pred88 / 4448 / 1450 / 1644 / 12
✓Pred86 / 4272 / 3278 / 3870 / 32
✓✓Pred90 / 6470 / 4080 / 3874 / 36
✓✓GT96 / 6880 / 4882 / 4480 / 42
+ +Table 4. Ablation Study on Modules for Incorporating Grounding Masks. "Channel Concat." denotes whether to do the channel concatenation for the image and mask. "Grounded Perceiver" denotes whether to incorporate masks into the perceiver. + +
Channel Concat.Grounded PerceiverEasyAppea.SpatialComm.
68 / 2442 / 1252 / 1640 / 12
✓78 / 3660 / 2668 / 3062 / 26
✓80 / 3656 / 2264 / 2864 / 30
✓✓86 / 4272 / 3278 / 3870 / 32
+ +ily fits the "Easy" set—even without a mask—but struggles with more challenging sets. This supports our hypothesis that the limited complexity of the original data restricts the model's generalization ability. In contrast, training on our new dataset highlights the critical role of mask guidance in improving generalization. Furthermore, combining both original and new data enhances performance, suggesting that scaling the dataset could further strengthen grounding-aware policies. + +Modules for Incorporating Masks. We evaluate two methods for integrating grounding information: concatenating masks as an additional channel and using the grounded perceiver. As shown in Table 4, both approaches effectively incorporate grounding knowledge. While simple mask concatenation allows the model to utilize mask information, the grounded perceiver enables a more comprehensive exploitation of mask features, resulting in improved performance. + +Grounding Representations. We evaluate different grounding representations and their impact on model performance. As shown in Table 5, models perform best when using masks as grounding representations. In contrast, lower-dimensional vector representations, such as points and bounding boxes, pose greater challenges for effective learning. Masks provide richer information by accurately capturing the shape and size of the target object, leading to modest improvements over bounding box representations. + +Grounded VLM We fine-tune the VLM to improve its + +Table 5. Ablation Study on Grounding Representations. "Point" and "Bbox" denote the center pixel point and the 2D bounding box extracted from predicted masks, respectively. "Low-dim" refers to using the point or bbox as a low-dimensional input, while "Image" indicates incorporating them as an additional channel in the image input. + +
RepresentationEasyAppea.SpatialComm.
Point, Low-dim72 / 2844 / 1256 / 1842 / 14
Point, Image76 / 3260 / 2668 / 3264 / 28
Bbox, Low-dim72 / 3046 / 1454 / 1844 / 16
Bbox, Image82 / 3868 / 3074 / 4068 / 30
Mask86 / 4272 / 3278 / 3870 / 32
+ +Table 6. Ablation Study on Grounded VLM. "Zero-shot" refers to the zero-shot evaluation of the grounded VLM. "Sim. data" and "VLM data" denotes the use of simulated grounding data and VLM data for fine-tuning. + +
MethodmIoU
Zero-shot13.2
Fine-tuned w/ Sim. data45.5
Fine-tuned w/ Sim. data & VLM data48.2
+ +instruction-following capability by training it on both simulated and original VLM data. Specifically, we create an instruction-following dataset based on simulated data using the following prompt format: “Given a robotic manipulation instruction: , identify the target object for manipulation and, if applicable, the target placement area.” The response is formulated as “The target object is xxx ” to generate the target object mask, and “The target placement area is xxx ” if a placement area is specified. + +For evaluation, we compute the mean Intersection over Union (mIoU) of the predicted simulation results, with a performance comparison shown in Table 6. The initial zero-shot evaluation uses a dependency parsing tool to identify target nouns in the instructions, which are then used to prompt the VLM to generate a mask for each noun. However, this approach leads to suboptimal results due to ambiguities introduced by the dependency parsing. Fine-tuning on simulation data alone significantly improves results but risks losing the knowledge embedded in the original VLM dataset. To mitigate this, we fine-tune the model using both simulated data and the VLM's original grounding data, thereby enhancing simulation performance while preserving the model's prior knowledge. + +# Acknowledgment + +This work was supported by National Key R&D Program of China (2022ZD0162000). + +# 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. arXiv preprint arXiv:2303.08774, 2023. 3 +[2] Suneel Belkhale, Tianli Ding, Ted Xiao, Pierre Sermanet, Quon Vuong, Jonathan Tompson, Yevgen Chebotar, Debidatta Dwibedi, and Dorsa Sadigh. Rt-h: Action hierarchies using language. arXiv preprint arXiv:2403.01823, 2024. 1, 2 +[3] Homanga Bharadhwaj, Roozbeh Mottaghi, Abhinav Gupta, and Shubham Tulsiani. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2 \ No newline at end of file diff --git a/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/images.zip b/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..dc7bf7a71a98bd524e1d7e46fbef9a0019d3bcfa --- /dev/null +++ b/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a8505229025f758911f4cfcaf97a5cb5fb74a3aa5fc3af2feecbe59f1605f7e0 +size 475124 diff --git a/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/layout.json b/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..59a2824425e90af787b10671a2363e3d9dd2848f --- /dev/null +++ b/robogroundroboticmanipulationwithgroundedvisionlanguagepriors/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bf5d843bdbe891fb9c352e35e67aec4ccbadd0fc3a6f73a8835903a1f264e2e0 +size 344206 diff --git a/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_content_list.json b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fb90d2eb8d52ec984ebb69ac256642f3320c9658 --- /dev/null +++ b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b65d7389f69db8916d98ead7646ad65f042554a79b25b110db0a15dfdc47bfb7 +size 74778 diff --git a/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_model.json b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e345365eeae6bd0ec36a0c092a121bbfe1793e35 --- /dev/null +++ b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4d1e21ec7c99662e5ab086b9073a741515e7c1d5cc9312c01f24f957db801deb +size 90030 diff --git a/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_origin.pdf b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..75c90f7db93e7f4afcc5c4fff134b95667972594 --- /dev/null +++ b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/ea394626-30e1-4fc3-b8ce-9098cf315490_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d48df2fb8be89e9ef0f73b5f35aa49d58f54edcd42e6a289ac860b21faebb536 +size 2692957 diff --git a/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/full.md b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b310735778e7b482d1627c2abf8e96a122e2d671 --- /dev/null +++ b/robopeppvisionbasedrobotposeandjointangleestimationthroughembeddingpredictivepretraining/full.md @@ -0,0 +1,275 @@ +# RoboPEPP: Vision-Based Robot Pose and Joint Angle Estimation through Embedding Predictive Pre-Training + +Raktim Gautam Goswami $^{1*}$ Prashanth Krishnamurthy $^{1}$ Yann LeCun $^{2,3}$ Farshad Khorrami $^{1}$ + +$^{1}$ New York University Tandon School of Engineering + +$^{2}$ New York University Courant Institute of Mathematical Sciences $^{3}$ Meta-FAIR + +# Abstract + +Vision-based pose estimation of articulated robots with unknown joint angles has applications in collaborative robotics and human-robot interaction tasks. Current frameworks use neural network encoders to extract image features and downstream layers to predict joint angles and robot pose. While images of robots inherently contain rich information about the robot's physical structures, existing methods often fail to leverage it fully; therefore, limiting performance under occlusions and truncations. To address this, we introduce RoboPEPP, a method that fuses information about the robot's physical model into the encoder using a masking-based self-supervised embedding-predictive architecture. Specifically, we mask the robot's joints and pre-train an encoder-predictor model to infer the joints' embeddings from surrounding unmasked regions, enhancing the encoder's understanding of the robot's physical model. The pre-trained encoder-predictor pair, along with joint angle and keypoint prediction networks, is then fine-tuned for pose and joint angle estimation. Random masking of input during fine-tuning and keypoint filtering during evaluation further improves robustness. Our method, evaluated on several datasets, achieves the best results in robot pose and joint angle estimation while being the least sensitive to occlusions and requiring the lowest execution time. The code is available at https://github.com/raktimgg/RoboPEPP. + +# 1. Introduction + +Estimating the pose and joint angles of an articulated robot in the coordinate frame of an external camera is valuable for facilitating collaborative applications wherein an agent (e.g., a human or another robot) operates in a shared space with the articulated robot [9, 19, 25, 28, 31, 35]. Traditional robot pose estimation methods assume known joint angles and capture multiple images with fiducial mark + +![](images/94f9b9392d4172309be50e87ff89759433d6465522dea1f48d5d47d8b11497c1.jpg) + +![](images/e41ed55dba50e4055419b12ef1b400835d471e5f415ea2adfd41086c1fd0af07.jpg) +Figure 1. Comparison of an existing robot pose estimation method [4] with our RoboPEPP framework. RoboPEPP integrates joint masking-based pre-training (b.1) to enhance the encoder's grasp of the robot's physical model, combined with downstream networks, and keypoint filtering (b.2) to achieve high accuracy. + +ers [11, 12, 24] attached to the robot's end-effector to establish 2D-3D correspondences between the image pixels and the robot's frame. Recent advancements in deep learning enable the prediction of 2D keypoints on robot joints from a single image [13, 17, 23, 33]. However, the assumption of known joint angles is not valid in many practical settings such as in collaborative robotics and human-robot interaction, where the joint angles may be unreliable or completely unknown. This challenge of simultaneously estimating joint angles and robot poses is particularly complex due to the high degrees of freedom in robotic systems and the infinite space of potential robot poses and joint angle configurations. RoboPose [15] pioneered the field of robot pose estimation with unknown joints by using an iterative render + +and compare strategy. Later works [4, 34] enhanced the efficiency by employing neural networks that predict joint angles and robot poses in a single feed-forward pass. While input images provide rich information about the robot's physical structures and constraints, existing methods fail to leverage this fully, resulting in low performance in challenging scenarios like occlusions and truncations (i.e., instances where only part of the robot is visible). + +Recently, self-supervised learning [3, 6] has shown that embedding predictive pre-training helps encoders develop a deeper semantic understanding of images. Inspired by such works, we propose RoboPEPP (Fig. 1), a robot pose estimation framework that integrates a joint-masking-based pretraining strategy to help the encoder better understand the robot's physical model. In this approach, the encoder extracts embeddings from the unmasked regions, which a predictor uses to estimate embeddings of the masked joints. In other words, the encoder-predictor network is trained to predict the embeddings of the joints using the context around them, thus improving the network's understanding of the robot's structure. While this pre-trained encoder supports various robotics tasks, we focus on robot pose estimation. + +Following pre-training, the encoder and predictor are fine-tuned using downstream layers for joint angle prediction and 2D keypoint heatmap generation, allowing for end-to-end training. We further enhance the model's occlusion robustness by randomly masking the input while finetuning. During inference, the pixels with the highest values in the heatmaps are identified as 2D keypoints, while corresponding 3D keypoints in the robot's frame are computed using the forward kinematics and predicted joint angles. For cases where only part of the robot is visible in the image, we apply confidence-based keypoint filtering. Finally, we use the perspective- $n$ -point (PnP) algorithm [18] on the filtered 2D-3D correspondences to estimate the robot's pose. In summary, our contributions are: + +- A robot pose and joint angle estimation framework with embedding-predictive pre-training to enhance the network's understanding of the robot's physical model. +- An efficient network for robot pose and joint angle estimation using the pre-trained encoder-predictor alongside joint angle and keypoint estimators, trained using randomly masked inputs to enhance occlusion robustness. +- A confidence-based keypoint filtering method to handle cases where only part of the robot is visible in the image. +- Extensive experiments showing RoboPEPP's superior pose estimation, joint angle prediction, occlusion robustness, and computational efficiency. + +# 2. Related Work + +Classical methods for robot pose estimation typically involve attaching fiducial markers, such as ArUco [12], AprilTag [24], or ARTag [11], to the robot's end-effector to ob + +tain easily detectable pixels in images. The corresponding 3D points in the robot's base coordinate frame are calculated using the robot's joint angles and forward kinematics. Using these correspondences and the camera intrinsics, an optimization problem is solved to find the robot-to-camera transformation [14, 26, 36], referred to here as the robot pose. This, however, requires multiple sets of correspondences from images taken at different robot configurations. + +To streamline this process, DREAM [17] introduced a learning-based approach to detect multiple keypoint correspondences from a single image, estimating the pose using the PnP [18] algorithm. This method achieved performance comparable to classical approaches while requiring a single image. Building on this, PoseFusion [13] used multi-scale feature fusion to improve keypoint prediction accuracy. G-SAM [37] further improved robustness by adding a grouping and soft-argmax module, particularly useful when only part of the robot is visible. CTRNet [23] introduced a self-supervised sim-to-real approach, using differentiable PnP solver [8] and mesh renderer [27] to predict robot masks, which are compared against foreground segmentation for training. To incorporate information from prior frames, SG-TAPose [32] employed a temporal attention framework. + +These approaches, however, assume known joint angles, which is often impractical in real-world settings like collaborative robotics and human-robot interaction. To address this, RoboPose [15] estimated pose with unknown joint angles using an iterative render-and-compare approach, yielding strong results but at the cost of computational efficiency. An efficient framework [4] was later developed to predict joint angles and pose in a single, real-time feed-forward pass. RoboKeyGen [34] proposed another efficient method by lifting 2D keypoints to 3D using a stable diffusion model. While some frameworks [29, 30] used depth cameras for pose prediction, we restrict the discussion to methods using monocular RGB images, which are more widely accessible and avoid the need for specialized sensors. + +Current robot pose estimation methods [4, 15, 34] do not fully utilize the rich features of the robot's physical model available in images. Meanwhile, self-supervised learning frameworks [1-3, 5-7] have advanced encoder training to extract robust image features with Joint-Embedding Predictive Architecture (JEPA) [3] using a masking-based pretraining strategy to enhance the encoder's semantic understanding of the image. Inspired by JEPA, we pre-train an encoder-predictor pair by masking regions around the robot's joints and predicting embeddings of the masked regions based on the surrounding context, thus enhancing the encoder's understanding of the robot's physical model. The pre-trained encoder-predictor pair is then fine-tuned along with joint and keypoint prediction networks, applying random masking during fine-tuning and confidence-based keypoint filtering at evaluation for improved robustness. + +![](images/912b7889c1dc69652bd5754de318d2a49feefc454aeb1ee3d9041435451afc6b.jpg) + +![](images/f1ce82f52f5a1d7a0fc90b9c0a5a468ebbeb2263e186adcc3881002597b56b2e.jpg) +Figure 2. Overview of the RoboPEPP framework for robot pose and joint angle estimation. (a) Joint regions are masked to pre-train an encoder-predictor pair using an embedding predictive architecture. (b) The pre-trained encoder-predictor network is fine-tuned for robot pose estimation with Joint and Keypoint Prediction networks, using random masking during training to enhance occlusion robustness. During evaluation, keypoints are filtered, and a PnP algorithm estimates the robot's pose from the filtered 2D-3D correspondences. + +# 3. Methodology + +Problem Description: Given a color image capturing an articulated robot with $n$ joints, our objective is to estimate the joint angles $\Phi \in \mathbb{R}^n$ and the robot-to-camera rigid transformation matrix $T_R^C \in SE(3)$ , with the robot frame being defined at its base. The robot's forward kinematics and the camera's intrinsic parameters are assumed to be known. + +Method Overview: Our proposed framework (Fig. 2) comprises two stages: self-supervised pre-training of an encoder-predictor network (Sec. 3.1); and fine-tuning of the pre-trained encoder-predictor alongside 2D keypoint detection and joint angle estimation networks (Sec. 3.2). Predicted joint angles and forward kinematics yield 3D joint coordinates, which, combined with detected 2D keypoints, are used in a PnP solver to estimate pose (Sec. 3.3). During evaluation, confidence-based keypoint filtering and self-supervised fine-tuning on real-world data enhance accuracy. + +# 3.1. Embedding Predictive Pre-Training + +Building on embedding predictive architectures [3, 6], we employ a masking-based pre-training strategy tailored for robotic applications like pose and joint estimation. Masks are selected to occlude the regions around four randomly selected robot joints, or a random area if a joint is outside the camera's field of view. Each mask covers $15 - 20\%$ of the image with an aspect ratio between 0.75 and 1.5. + +The original image consists of $M$ patches, each sized $16 \times 16$ pixels. Let $u_{i}$ represent the $i$ -th patch, where $i \in \{1,2,\dots,M\}$ , and let $\mathcal{B}$ denote the set of indices for the + +unmasked patches, with $L = |\mathcal{B}| < M$ . With patches $u_{j}$ for $j \in \mathcal{B}$ , as the context, a Vision Transformer (VIT) [10] encoder produces context embeddings $w_{j} \in \mathbb{R}^{d}$ for $j \in \mathcal{B}$ . These context embeddings are then passed to a VIT-based predictor, which infers embeddings for all $M$ patches of the original image, denoted $v_{i} \in \mathbb{R}^{d}$ for $i \in \{1, 2, \dots, M\}$ . + +Meanwhile, a target backbone with the same architecture as the encoder extracts embeddings $\bar{v}_i\in \mathbb{R}^d$ for $i\in$ $\{1,2,\dots ,M\}$ directly from the original image. The embeddings for the masked patches, corresponding to indices $i\in \bar{\mathcal{B}}$ (where $\bar{B}$ denotes the set of masked patch indices), are used to compute the $L_{1}$ loss during training, given by: + +$$ +\mathcal {L} _ {\text {p r e - t r a i n}} = \frac {1}{| \bar {\mathcal {B}} |} \sum_ {i \in \bar {\mathcal {B}}} \| v _ {i} - \bar {v} _ {i} \| _ {1}. \tag {1} +$$ + +Backpropagating through the encoder-predictor network and target backbone simultaneously risks trivial solutions, like constant predictions across all networks. To avoid this, we follow [3], backpropagating only through the encoder-predictor branch and updating the target backbone with an exponential moving average of the encoder's weights. + +Our approach differs from JEPA [3] by using context-informed masking at joint locations. While JEPA learns deeper semantic representations by randomly masking the input for tasks like object detection, we focus on encoding the robot's physical properties by specifically masking joint regions. This trains the encoder to infer the robot's joint-related information based on the surroundings, emulating a predictive understanding similar to how humans or animals + +![](images/166bcfa1b9cf5b88e7c2fbd748ba7602eecbaeb238c2aa77a898c9a7afd7ff04.jpg) +Figure 3. Joint Net: A global average pooling layer aggregates the patch embeddings, $v_{1}, \ldots, v_{M}$ , into $v_{g}$ , which is then iteratively refined using an MLP to estimate the joint angles. + +deduce missing information about physical structures. + +# 3.2. Keypoint Detection and Joint Angle Estimation + +The pre-trained encoder and predictor are then fine-tuned, where they extract embeddings $v_{i} \in \mathbb{R}^{d}$ for $i \in \{1,2,\dots,M\}$ from images, which are used by the Joint Net and Keypoint Net to predict joint angles and 2D keypoints, respectively. To further increase occlusion robustness, random masks covering up to $20\%$ of the image are applied during training. Consistent with Sec. 3.1, the predictor outputs all patch embeddings, including masked ones. This framework is trained using the loss functions in Sec. 3.2.3. + +# 3.2.1. Joint Net + +Using the patch embeddings, $v_{i}$ , as input, the Joint Net predicts the angles for each of the robot's $n$ joints. A global average pooling layer aggregates the patch embeddings $v_{i}$ (for $i \in \{1, 2, \dots, M\}$ ) into a single embedding $v_{g} \in \mathbb{R}^{d}$ to generate a global representation of the image. An iterative MLP-based approach [4] is then used to refine the joint angle predictions. Starting with a zero vector as the initial estimate $\Phi_{\mathrm{init}}$ , the joint angles are iteratively updated through the MLP over $G = 4$ refinement steps (Fig. 3). The same MLP layer is used across all iterations, progressively refining the predicted joint angles $\Phi_{\mathrm{pred}}$ for improved accuracy. + +# 3.2.2. Keypoint Net + +The Keypoint Net uses the patch embeddings to predict heatmaps for each of the $k$ keypoints. The matrix $V = [v_{1}, v_{2}, \ldots, v_{M}]^{T} \in \mathbb{R}^{M \times d}$ , containing the patch embeddings, is reshaped into $\hat{V} \in \mathbb{R}^{m \times m \times d}$ , where $m = \sqrt{M}$ . With input image of $224 \times 224$ pixels and a patch size of $16 \times 16$ pixels, $m = 14$ . The Keypoint Net takes $\hat{V}$ as input and applies four upsampling layers with output dimensions shown in Table 1. Each upsampling layer includes a transpose convolutional layer with a kernel size of 4, stride of 2, and one-pixel wide zero padding, followed by batch normalization, ReLU activation, and dropout. The channel dimension is gradually reduced from $d = 768$ to 256 across these layers. The output is then passed through a linear layer that reduces the channel dimension to $k$ , followed by a sigmoid activation to produce heatmaps $H_{pred} \in \mathbb{R}^{224 \times 224 \times k}$ . Typically, each keypoint is defined at a joint of the robot, with an additional keypoint at the base, making $k = n + 1$ . + +
LayerSpatial SizeChannels
Input Size14 × 14768
Upsample 128 × 28256
Upsample 256 × 56256
Upsample 3112 × 112256
Upsample 4224 × 224256
Linear (Heatmaps)224 × 224k
+ +Table 1. Layer Output Sizes in Keypoint Net: Patch embeddings are progressively upsampled through four layers and the channel dimension is reduced to k (the number of keypoint). + +# 3.2.3. Loss Functions + +For joint angles, we employ a mean squared error loss: + +$$ +\mathcal {L} _ {\text {j o i n t}} = \frac {1}{n} \| \Phi_ {\text {p r e d}} - \Phi_ {\text {g t}} \| _ {2} ^ {2} \tag {2} +$$ + +where $\Phi_{pred}$ and $\Phi_{gt}$ represent the predicted and ground truth joint angles, respectively. To enhance training convergence, mean-variance normalization is applied to $\Phi_{gt}$ . For keypoint detection, we utilize the focal loss [16, 20] $(\mathcal{L}_{kp})$ + +$$ +\frac {- 1}{\mathcal {S}} \sum_ {i = 1} ^ {\mathcal {H}} \sum_ {j = 1} ^ {\mathcal {W}} \left\{ \begin{array}{l l} (1 - p _ {i j}) ^ {\alpha} \log \left(p _ {i j}\right), & \text {i f} y _ {i j} = 1, \\ (1 - y _ {i j}) ^ {\beta} \left(p _ {i j}\right) ^ {\alpha} \log \left(1 - p _ {i j}\right), & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +with $p_{ij}$ and $y_{ij}$ being the pixel values at $(i,j)$ of the predicted $(H_{\mathrm{pred}})$ and ground truth $(H_{\mathrm{gt}})$ heatmaps, respectively; $\{\alpha ,\beta \} = \{2,4\}$ balance the loss terms; $S$ is number of pixels with $y_{ij} = 1$ ( $S = 1$ if none exist). $H_{\mathrm{gt}}$ is created using unnormalized Gaussian probability density functions centered at each keypoint with a 2-pixel standard deviation. + +The overall training loss is a weighted combination of the two losses: $\mathcal{L} = \mathcal{L}_{joint} + \alpha(t)\mathcal{L}_{kp}$ . where $\alpha(t)$ , dependent on epoch $t$ , balances their relative importance. Since the joint angles are predicted in radians, $\mathcal{L}_{joint}$ tends to be much smaller than $\mathcal{L}_{kp}$ , especially in early training. To address this, $\alpha(t)$ is initialized at 0.0001, increased to 0.01 after 5 epochs, 0.1 after 10 epochs, and finally to 1 after 40 epochs, ensuring a balanced curriculum for training. + +# 3.3. Robot Pose Estimation + +Keypoint Filtering: The final layer of the Keypoint Net contains a sigmoid nonlinearity, that produces heatmaps with pixel values between 0 and 1, representing keypoint confidence at each pixel. The pixel with the highest confidence indicates the keypoint location. However, when only a portion of the robot is visible, some keypoints may lie outside the image, leading to low confidence scores across the heatmap for these keypoints (Fig. 4). Selecting the pixel with the highest confidence in such cases can be misleading, as no pixel accurately represent the true keypoint. To address this, during evaluation, we apply a threshold $\epsilon$ , only considering keypoints with confidence above it. For use with a PnP algorithm [18] for pose estimation, we require + +![](images/c4bc2bf348b7f71cb157696938514d4b5b91d0065ef6ce86001c9860d118583a.jpg) +(a) Example from panda-3cam_realsense (RS) + +![](images/752c65c4c36cd806ab74afb1c2dce1709cf66d44ce76419c6041562e1f430bff.jpg) +(b) Example from panda_synth_test(photo +Figure 4. The examples show predicted heatmaps for Joint 5 and the End-Effector overlaid on the original image. The End-Effector, being positioned outside the field of view, produces noisy heatmaps with lower confidence (measured by peak values). Heatmap pixel values are normalized for better visualization. The green arrows highlight the peak values for Joint 5 for visual clarity. + +a minimum of four 2D-3D correspondences. If fewer than four keypoints remain after filtering, we iteratively reduce $\epsilon$ by 0.025 until at least four keypoints are retained. + +Pose Estimation: The robot's pose is estimated using the EPnP algorithm [18] with the filtered 2D-3D correspondences and known camera intrinsics. As keypoints are defined on joints, we obtain the 3D points corresponding to the 2D keypoints using the robot's forward kinematics and predicted joint angles. + +Sim-to-Real Self-Supervised Training: In addition to supervised training for pose estimation, our method supports self-supervised fine-tuning of the trained models on real-world data to bridge the sim-to-real gap. Specifically, we use a differentiable PnP algorithm [8, 23] and estimate the robot's pose and transform 3D joint locations from the robot to the camera frame. These transformed points are projected onto the image plane, yielding the projected keypoints, $P_{proj} \in \mathbb{R}^{k \times 2}$ . We then minimize the mean squared error between $P_{proj}$ and the predicted keypoints $P_{pred}$ + +$$ +\mathcal {L} _ {\mathrm {s s l}} = \frac {1}{k} \sum_ {i = 1} ^ {k} \| P _ {p r e d} ^ {i} - P _ {p r o j} ^ {i} \| _ {2} ^ {2} \tag {4} +$$ + +where $P_{pred}^{i}$ and $P_{proj}^{i}$ are the $i^{th}$ keypoint in $P_{pred}$ and $P_{proj}$ , respectively. During this sim-to-real finetuning, we use a lower learning rate than in the prior supervised training. To prevent model collapse, the Keypoint Net's learning rate is set close to zero. Further details on learning rates are provided in the supplementary material. + +Region of Interest (RoI) Detection: During evaluation, we utilize the GroundingDINO [21] object detection model to automatically locate the region of interest around the robot. + +The detected region is cropped and resized to $224 \times 224$ pixels. Further details are provided in the supplementary material. During training, we use ground truth bounding box information. However, to ensure our model's robustness to region-of-interest detection, we employ a training curriculum: we use the ground truth bounding boxes and expand them by adding random offsets sampled from the uniform distribution $\mathcal{U}(0, \lambda)$ to their edges, with $\lambda$ progressing from 0 (first 30 epochs) to 30 pixels at epoch 30, 50 pixels at epoch 50, 80 pixels at epoch 70, 100 pixels at epoch 90, and 120 pixels at epoch 110. This approach encourages the model to generalize effectively, even with noisy region-of-interest detection during inference. + +# 4. Experiments + +# 4.1. Dataset and Implementation Details + +We evaluate our framework on the DREAM dataset [17] that includes three robots (Franka Emika Panda, Kuka iwa7, Rethink Baxter) and contains the following for each robot: Panda - synthetic domain-randomized (DR) training, DR test (Panda DR), photo-realistic test (Panda Photo), four real-world test (Panda AK, XK, RS, ORB) sequences; Kuka - synthetic DR training, DR test (Kuka DR), photo-realistic test (Kuka Photo) sequences; Baxter - synthetic DR training and test (Baxter DR) sequences. + +The encoder is pre-trained using our self-supervised embedding predictive strategy (Sec. 3.1) for 200 epochs on the DR training sequences of all robots, using AdamW [22] optimizer with an initial learning rate of $10^{-3}$ . For end-to-end fine-tuning (Sec. 3.2), models are trained separately for each robot for 200 epochs with AdamW optimizer (learning rate $10^{-4}$ ). Sim-to-real fine-tuning is performed for 10 epochs. More details are in the supplementary material. + +# 4.2. Results + +# 4.2.1. Robot Pose Prediction + +We evaluate RoboPEPP by computing the average distance [4, 15, 17], $ADD = \frac{1}{n}\sum_{0}^{n}\|\hat{T}_{R}^{C}\hat{p}_{i}^{\{R\}} - p_{i}^{\{C\}}\|_{2}$ between predicted and ground truth joint positions in the camera frame for each image, where $\hat{T}_{R}^{C}$ is the predicted robot pose in the camera frame, $\hat{p}_{i}^{\{R\}}$ is the estimated position of joint $i$ in the robot's frame (computed from predicted joints and forward kinematics), and $p_{i}^{\{C\}}$ is the ground truth joint position in the camera frame ( $i = 0$ signifies the robot base). + +In Table 2, we report the area-under-the-curve (AUC) of the average distance (ADD) across various thresholds, where higher AUC values indicate greater accuracy. We compare RoboPEPP with Real-Time Holistic Robot Pose Estimation with Unknown States (referred to as HPE in this manuscript) [4], RoboPose [15], and three variants of DREAM [17], though the latter assume known joint angles. To the best of our knowledge, RoboPose, HPE, + +
MethodKnown Joint AnglesKnown Bounding BoxPandaKukaBaxter
SyntheticRealSyntheticSynthetic
PhotoDRAKXKRSORBPhotoDRDR
DREAM-FYesNo79.581.368.924.476.161.9---
DREAM-QYesNo74.377.852.437.578.057.1--75.5
DREAM-HYesNo81.182.960.564.078.869.172.173.3-
HPENoYes82.082.782.276.075.275.273.975.158.8
RoboPoseNoNo79.782.970.477.674.370.473.280.232.7
HPE*NoNo40.741.466.7-49.151.656.756.29.8
RoboPEPP (Ours)NoNo84.183.075.378.580.577.576.176.234.4
+ +and RoboKeyGen [34] are the only approaches besides RoboPEPP that predict robot pose with unknown joint angles. However, RoboKeyGen evaluates on a different dataset, and its code is unavailable, preventing direct comparison. Nonetheless, its reported AUC on similar datasets is lower than ours. Moreover, HPE [4] assumes known bounding boxes during evaluation, a condition often unrealistic in practice. Therefore, we also evaluate HPE with our bounding box detection strategy (denoted $\mathrm{HPE}^*$ ) in Table 2. + +RoboPEPP yields the highest scores across all sequences (except for Kuka DR where it remains competitive) among methods with unknown joint angles and bounding boxes. HPE [4], on the other hand, shows sensitivity to bounding box selection, with its performance dropping when ground truth bounding boxes are unavailable. Our analysis has shown that using bounding boxes just 5 pixels wider than ground truth reduces HPE's accuracy by up to $25\%$ on the Panda Photo test set and by around $50\%$ with 10-pixel wider boxes. While both RoboPEPP and HPE are trained using ground truth bounding boxes, RoboPEPP's training strategy (Sec. 3.3) reduces dependency on them. Notably, RoboPEPP outperforms HPE on most sequences even when HPE uses known bounding boxes during evaluation. + +A qualitative comparison of RoboPEPP with RoboPose [15] and HPE [4] on Panda Photo test dataset (example 1) and the occlusion dataset of Sec. 4.2.3 (examples 2 and 3) is presented in Fig. 5. Each method uses the input image to predict pose and joint angles, rendering a robot mesh that is projected and overlaid onto the original image, where closer alignment indicates higher prediction accuracy. Example 1 depicts a case where only part of the robot is visible and examples 2 and 3 show cases of occlusions (detailed in Sec. 4.2.3). In these challenging scenarios, RoboPEPP achieves highly accurate overlays while other methods are less precise, as highlighted by the red rectangles. In Fig. 5, HPE is used with ground truth bounding boxes. + +# 4.2.2. Joint Prediction + +In Table 3, we report the mean absolute error (in degrees) for joint angle prediction on the Panda Photo, Panda DR, + +Table 2. Comparison of robot pose estimation using AUC on the ADD metric. Best values among methods using unknown joint angles and bounding boxes during evaluation are bolded. HPE* denotes HPE [4] evaluated with the same off-the-shelf bounding box detector as RoboPEPP. HPE* was not evaluated on Panda XK since corresponding model weights were unavailable. + +
MethodJ1J2J3J4J5J6Avg.
Panda PhotoRoboPose7.73.54.33.47.38.15.7
HPE (Known BBox)6.12.23.62.06.26.64.5
RoboPEPP4.41.82.21.84.44.83.2
DRRoboPose6.12.73.62.56.38.14.9
HPE (Known BBox)6.22.23.91.95.96.64.4
RoboPEPP4.92.32.72.24.95.43.8
Kuka PhotoRoboPose4.95.16.76.010.89.67.2
HPE (Known BBox)4.83.85.02.84.95.94.5
RoboPEPP3.82.84.63.13.85.43.9
DRRoboPose4.42.85.43.412.58.56.2
HPE (Known BBox)4.63.64.92.85.26.14.5
RoboPEPP3.73.55.13.54.16.24.3
Avg.RoboPose5.83.55.03.89.28.66.0
HPE (Known BBox)5.43.04.42.45.66.34.5
RoboPEPP4.22.63.72.74.35.53.8
+ +Table 3. Mean absolute error between the predicted and actual joint angles (in degrees) for the Panda and Kuka synthetic test sets. + +Kuka Photo, and Kuka DR test datasets. The keypoints corresponding to the end-effector and the final joint (i.e., the joint nearest to the end-effector) lie along the axis of rotation of this joint, making their locations independent of this joint's angle. Consequently, we predict the angles of all joints except the last one, assigning a random angle to it during evaluation. Thus, Table 3 presents the mean absolute error for the first six joint angles. We compare RoboPEPP with HPE [4] and RoboPose [15]. RoboPEPP demonstrates the lowest average joint prediction error on all datasets. Although HPE utilizes known bounding boxes for region-of-interest detection, RoboPEPP still outperforms HPE by over $15\%$ on average across all datasets in Table 3. When HPE is tested without ground truth bounding boxes, its performance drops to an average error of 7.2 degrees. + +# 4.2.3. Robustness to Occlusions + +In addition to achieving high performance across various metrics and datasets, RoboPEPP demonstrates robustness to occlusions. To evaluate this, we compared the performance of RoboPEPP with other methods [4, 15] on a custom dataset, created by adding synthetic occlusions to Panda Photo. Specifically, we overlaid black rectangular or circular masks at random positions on the robot, ensur + +![](images/60745a97de9dfadf18841e463402bfe8e0c78c3bd01fee4537c3b532cc1a38e6.jpg) +Figure 5. Qualitative Comparison on Panda Photo (Example 1) and Occlusion (Example 2 and 3) datasets: Predicted poses and joint angles are used to generate a mesh overlaid on the original image, where closer alignment indicates greater accuracy. Highlighted rectangles indicate regions where other methods' meshes misalign, while RoboPEPP achieves high precision. + +![](images/2dd7a819fc5a3497466e7b0ac450dac4f6b585d3c9cd27fce6c9a92c1bc6bba2.jpg) +Figure 6. AUC comparison of the distance metric under varying occlusion levels, evaluated on the dataset in Sec. 4.2.3. Percentages next to the lines indicate the relative drop in each method's performance compared to their performance without occlusions. + +![](images/786e54e3ed28c6664d37b57b6e8a347c41e5edc42f5f389003610aefea3a7972.jpg) +Figure 7. Execution time and computation analysis on the Panda Photo test dataset with RoboPEPP showing best performance and accuracy. The circle sizes in the plot represent model FLOPs. + +ing that the masks covered at least some part of the robot + +(and not just the background). We generated four test sequences with occlusion ratios of 0.1, 0.2, 0.3, and 0.4 on the RoI area in each image, respectively. This approach differs from the masking used during our training, where the model is informed about the number of masked patches. Here, the model processes occluded images as it would any other input image, without any knowledge of the occlusion. + +In Fig. 6, we plot the AUC of the ADD against the occlusion ratio. The plot also includes the percentage decrease in AUC relative to the respective model's performance without occlusion. RoboPEPP demonstrates superior robustness to occlusion, achieving an AUC score of 35.1 even when $40\%$ of the RoI is occluded, compared to 28.2 for HPE and 14.5 for RoboPose. Examples 2 and 3 in Fig. 5 provide qualitative comparisons of RoboPEPP, HPE [4], and RoboPose [15] on the occlusion dataset. RoboPEPP demonstrates superior performance, even in challenging cases like example 3, where most of the robot is occluded. In both examples 2 and 3, RoboPose produces inaccurate results, while HPE shows partial overlap but still exhibits notable inaccuracies, highlighted by the red rectangles. + +# 4.2.4. Percentage of Correct Keypoints + +The accuracy of 2D keypoint detection affects the overall performance of RoboPEPP. Therefore, in Table 4, we report the percentage of correct keypoints (PCK) within thresholds of 2.5, 5, and 10 pixels on the Panda Photo dataset. Since HPE [4] and RoboPose [15] do not rely on 2D keypoint detection for pose estimation, we include only DREAM [17] as a baseline for comparison. RoboPEPP achieves high av + +![](images/df8af4b74f34e05325143751c31c101afaf1d7330f408545c94f0306146f6b35.jpg) +(a) RoboPEPP's joint-masking-based pre-training achieves the best overall performance in robot pose estimation. + +![](images/d0849073c4d30aac6c4de3ef3f28d62d2b44ef696c6b3d08b7e582eceaa83312.jpg) +Figure 8. Ablation studies on (a) Pre-Training, (b) Keypoint Filtering, and (c) Sim-to-Real fine-tuning on the Panda test datasets. + +![](images/49d35613cc7fdc76a9b2a27a6f1fd3318b061ef27947194d6445b74b71256392.jpg) +(b) Keypoint Filtering leads to improved performance on all datasets. +(c) RoboPEPP's sim-to-real fine-tuning improves performance on real datasets. + +
DatasetMethodPCK @ (pixel)
2.5510
DRDREAM0.790.880.90
RoboPEPP0.840.910.93
PhotoDREAM0.770.870.90
RoboPEPP0.870.920.94
AKDREAM0.360.650.90
RoboPEPP0.160.620.93
XKDREAM0.150.370.59
RoboPEPP0.090.370.96
RSDREAM0.240.830.96
RoboPEPP0.310.820.97
ORBDREAM0.280.670.83
RoboPEPP0.280.730.96
Avg.DREAM0.430.710.85
RoboPEPP0.430.730.95
+ +Table 4. Comparison of Percentage of Correct Keypoints (PCK) at different pixel thresholds across the Panda test datasets. + +erage PCK scores, with 0.43 @ 2.5 pixels, 0.73 @ 5 pixels, and 0.95 @ 10 pixels. While DREAM surpasses RoboPEPP in PCK@2.5 pixels on AK and XK, RoboPEPP achieves higher overall accuracy across most metrics, showcasing its robust keypoint detection. We hypothesize that DREAM's known joint angles assumption allows it to focus entirely on keypoint detection enhancing PCK in some cases. + +# 4.2.5. Execution Time + +To demonstrate the practical effectiveness of the proposed RoboPEPP method, we compare execution times (in milliseconds) in Fig. 7. The circle sizes in the figure correspond to the relative number of floating-point operations (FLOPs) required by each model. All evaluations were conducted on a system equipped with an Nvidia RTX A4000 GPU, an Intel(R) i9 CPU, and 128 GB RAM, using the Panda Photo test dataset. Consistent with previous work [4], we report only model execution time, excluding pre-processing steps such as data loading and RoI detection. Despite having a slightly higher FLOPs count than HPE [4], RoboPEPP achieves the highest AUC ADD score and the fastest execution time, completing inference in just 23 milliseconds. + +# 4.3. Ablation Studies + +Embedding Predictive Pre-Training: To assess the impact of embedding predictive pre-training in RoboPEPP, we conducted an ablation study comparing three versions of + +the model: a version of RoboPEPP without pre-training, and a version pre-trained with random masking instead of joint-specific masking, and standard RoboPEPP (i.e., pretrained with joint masking). For all experiments, we utilized the same model architecture and training settings. The bar graphs in Fig. 8a illustrate that pre-training significantly improves performance. While the model trained with the default masking strategy demonstrated competitive results on synthetic test datasets, the model trained with joint-specific masking achieved better performance on real-world datasets in general. Note that the real-world results shown here do not include the sim-to-real fine-tuning of Sec. 3.3. Further, on the occlusion dataset (Sec. 4.2.3) with a 0.4 occlusion ratio, the model without pre-training achieves AUC of 22.6, the one with random masking reaches 30, and RoboPEPP achieves 35.1, highlighting the latter's occlusion robustness. + +Keypoint Filtering: In Fig. 8b, we demonstrate that the integration of keypoint filtering (KP filtering) enhances performance across all datasets by helping in filtering out keypoints that fall outside the camera's field of view. Similar to Fig. 8a, the real-world results presented in Fig. 8b do not include any sim-to-real fine-tuning. + +Sim-to-Real Fine-Tuning: In Fig. 8c, we show performance gains from sim-to-real self-supervised training, with the model's accuracy improving by an average of $\sim 6$ points after fine-tuning. Our sim-to-real training requires only 10 epochs, with each epoch lasting around 2 minutes. + +# 5. Conclusion + +We introduced a novel framework RoboPEPP enhancing robot pose and joint angle estimation using an embedding predictive pre-training strategy. RoboPEPP uses a joint-masking-based method to pre-train an encoder-predictor pair to be integrated into downstream networks for joint and pose predictions. Experimental results show RoboPEPP's superior performance, particularly in handling occlusions due to the combined effects of pre-training and random masking during fine-tuning. 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With the growing demand of social robotics, near-field scene understanding becomes an important research topic in the areas of egocentric perceptual tasks related to navigation in both crowded and unstructured environments. Due to the complexity of environmental conditions and difficulty of surrounding obstacles owing to truncation and occlusion, the perception capability under this circumstance is still inferior. To further enhance the intelligence of mobile robots, in this paper, we setup an egocentric multisensor data collection platform based on 3 main types of sensors (Camera, LiDAR and Fisheye), which supports flexible sensor configurations to enable dynamic sight of view from ego-perspective, capturing either near or farther areas. Meanwhile, a large-scale multimodal dataset is constructed, named RoboSense, to facilitate egocentric robot perception. Specifically, RoboSense contains more than $133K$ synchronized data with $1.4M$ 3D bounding box and IDs annotated in the full $360^{\circ}$ view, forming $216K$ trajectories across $7.6K$ temporal sequences. It has $270\times$ and $18\times$ as many annotations of surrounding obstacles within near ranges as the previous datasets collected for autonomous driving scenarios such as KITTI and nuScenes. Moreover, we define a novel matching criterion for near-field 3D perception and prediction metrics. Based on RoboSense, we formulate 6 popular tasks to facilitate the future research development, where the detailed analysis as well as benchmarks are also provided accordingly. Data desensitization measures have been conducted for privacy protection. + +# 1. Introduction + +Recent years have witnessed significant progress achieved in the field of autonomous driving, enabling numerous intel + +![](images/8ab9948a9e26ad898a6e7d2da6323c66216346e5182fcaccffc27f9e79192791.jpg) + +![](images/34b4922ab9fd5406d96b2f20776cae99b519a8890d5481b7687272be292c3c96.jpg) + +![](images/34b8d13b9c78f7595cd70d6caedb433e29f6bc28333fdf990c4af80d4ffe0384.jpg) +Figure 1. An example from RoboSense dataset: The data with annotated 3D boxes and occupancy descriptions on Camera, Fisheye, LiDAR, and BEV respectively, where the same targets are associated with unique IDs across different devices and timestamps. + +![](images/c77d38b5aa28a858f82f6c3b3fabcc607cfbc0878ac13c9012f0563b31369304.jpg) + +![](images/84028fe33984c70df889947d29c55e2e3b7106c10c7b31485701d3d8d5cff6f5.jpg) + +ligent vehicles running on highway or urban areas. In addition to self-driving cars, social mobile robots have emerged as a new industry tailored to autonomous navigation for typical applications, such as tractor, sweeper, retail and delivery. Notably, such intelligent mobile agents usually operate and navigate in crowded and unstructured environments (i.e., campuses, scenic spots, streets, parks and sidewalks, etc.), with varying and uncontrolled natural conditions such as illumination, occlusion and obstruction. In order to achieve navigation tasks safely, egocentric perceptual solutions enable these robots to perceive and comprehend the surrounding context from a first-person view, so as to interact successfully with passby pedestrians and vehicles, predict their intentions and incorporate this information in agents' planning and decision reasoning process. + +To evaluate and compare different egocentric perceptual methods fairly, several standarized benchmarks [3, 7, 13, 25, 32, 38] have been proposed in recent years, advancing the development of modern data-driven approaches. KITTI [7] is a pioneering dataset providing multi-modal sensor data including front-view LiDAR pointclouds as well as corresponding stereo images and GPS / IMU data. nuScenes [3] constructs a multi-sensor dataset collected in + +two cities travelling at an average of $16\mathrm{km / h}$ , where rich collections of 3D boxes and IDs are annotated in the full $360^{\circ}$ view. Waymo Open dataset [32] significantly increases the amount of annotations with higher annotation frequency. However, the target domain application of existing benchmarks is autonomous driving: the sensor data are captured exclusively from structural roads and highways, with sensor suites installed on top of cars. + +To fill the vacancies of egocentric perceptual benchmarks target a unique domain related to navigation tasks in crowded and unstructured environments, in this paper, we present RoboSense, a novel multimodal dataset with several benchmarks associated to it. Our dataset is collected from diverse social scenarios filled with crowded obstructions, which is different from previously collected datasets used for autonomous driving (e.g. nuScenes [3]). Benefiting from the well time-synced multi-sensor data, we hope that our RoboSense can facilitate the development of egocentric perceptual frameworks for various types of autonomous navigation agents with controllable cost, not only self-driving cars but also autonomous agents such as social mobile robots. To this end, the data collection robot is equipped with 3 main types of sensors (C: Camera, L: LiDAR, F: Fisheye), and each type of sensor consists of 4 devices installed on different sides respectively to ensure the data captured under full $360^{\circ}$ view without blind spots. + +Specifically, RoboSense consists of a total of $133\mathrm{K}+$ frames of synchronized data, spanning over 7.6K temporal sequences of 6 main scene classes (i.e., scenic spots, parks, squares, campuses, streets and sidewalks). Moreover, 1.4M 3D bounding boxes together with track IDs are annotated based on 3 different types of sensors, where most of targets tend to be closer to the robot as shown in Fig. 1. Then we form global trajectories for each agent separately through associating the same IDs across consecutive frames and different devices from a Bird's-Eye View (BEV) perspective. Additionally, we formulate 6 standarized benchmarks for egocentric perceptual tasks as follows: 1. Multi-view 3D Detection; 2. LiDAR 3D Detection; 3. Multi-modal 3D Detection; 4. Multiple 3D Object Tracking (3D MOT); 5. Motion Prediction; 6. Occupancy Prediction. Meanwhile, multi-task end-to-end training scheme is also supported in our RoboSense for evaluation of joint optimization. In sum, the main contributions of our work are three folds: + +- To our best knowledge, our RoboSense is the first dataset tailored to egocentric perceptual tasks related to navigation of autonomous agents in unstructured environments. +- We annotate 1.4M 3D bounding boxes on $133\mathrm{K}+$ synchronized sensor data, where most of targets are closer to the robot. Each target is associated with a unique ID, thus forming a total of 216K trajectories, which spread over 7.6K temporal sequences, covering 6 main scene classes. +- We formulate 6 standardized benchmarks to facilitate the + +evaluation and fair comparisons of different perceptual solutions related to navigation in built environments. + +# 2. Related Work + +We summarize the compositions of some existing perception and prediction datasets as shown in Tab. 1. + +Perception Datasets. Current released perception datasets can be divided into image-only datasets [5, 40] and multimodal datasets [3, 7, 13, 14, 21, 32]. BDD100k [40] and Cityscapes [5] focus on 2D perception which provide large amount of 2D annotations (boxes, masks) for driving scene understanding under various weather and illumination conditions. KITTI [7] is known as the pioneering multimodal dataset which has been widely used for academic research. It records 6 hours of driving data using a LiDAR sensor and a front-facing stereo camera to provide pointclouds and images with annotated 3D boxes. H3D dataset [23] collects a total of 1.3M 3D objects over 27K frames from 160 crowded scenes of the full $360^{\circ}$ view. nuScenes [3] and Waymo Open Dataset [32] are two similar datasets with same structure, while the latter one providing more annotations owing to higher annotation frequency (2Hz vs. $10\mathrm{Hz}$ ). Different from previously collected datasets used for autonomous driving, the annotation frequency of our RoboSense is even smaller (1Hz) due to the low speed (less than $1\mathrm{m / s}$ ) moving status of social mobile robots navigating in crowded and unstructured environments. + +Prediction Datasets. nuScenes [3] and Waymo Open Dataset [32] can be also used for prediction task which release lane graphs as well. Lyft [14] introduces traffic/speed control data, and Waymo Open Dataset [32] adds more signals to the map such as crosswalk, lane boundaries, stop signs and speed limits. Recently, Shifts dataset [22] becomes the largest forecasting dataset with the most scenario hours to date. Meanwhile, Argoverse [4] is also a large-scale dataset with high data frequency (10Hz) and high scenario quality for motion forecasting ( $>2000km$ across 6 cities). Together, these datasets have enabled exploration of multi-actor, long-range motion forecasting leveraging both static and dynamic maps. + +Generally, our dataset differs in three substantial ways: 1) targets a unique domain related to navigation tasks in crowded and unstructured environments, which is more difficult than autonomous driving scenarios in terms of complexity of environmental context and diversity of surrounding obstructions. 2) In addition to 3D bounding box and trajectory annotations, our dataset also provides high-quality occupancy descriptions for each collected scene, supporting the occupancy prediction task around the social robotics for safe navigation. 3) Our dataset is mostly collected in social crowded scenes, where pedestrians and cars tend to be closer to the robot, yielding a distribution with a mode at approximately $5m$ , which is quite different to the existing + +Table 1. Statistical comparison between RoboSense and similar existing datasets used for autonomous driving. C: Camera, L: LiDAR, F: Fisheye. † means statistics exclude the testing set, which is unavailable. ‡ indicates ${10} \times$ higher annotation frequency (10Hz). + +
DatasetYearSize (hr)Ann. ScenesAnn. FramesWith TrajectoryMulti-view OverlappingSensor Layouts3D Boxes (Total)3D Boxes† (≤5m)
KITTI [7]20121.52215KXX4C+1L80K638
Cityscapes [5]2016--25KXX1C00
ApolloScape [13]20162-144KXX1L70K4.7K
H3D [23]20190.7716027KX✓3C+1L1.1M-
Lyft L5 [14]20192.636655K✓✓7C+3L1.3M-
nuScenes [3]20195.51K40K✓✓6C+1L1.4M9.8K
Argoverse [4]20190.611322K✓✓9C+2L993K15K
Waymo Open [32]20196.41K200K‡✓✓5C+5L12M‡123K‡
BDD100k [40]20201K100k100kXX1C00
RoboSense (Ours)2024427.6K133K✓✓4C+4F+4L1.4M173K
+ +![](images/88316ecfd16828d3ab417122dc69b849e4a395a766799fc2e997ea1aac3e7354.jpg) +Figure 2. Comparison of annotated object distribution among different popular datasets used for perception and prediction tasks. + +datasets for autonomous cars as shown in Fig. 2. Besides, the egocentric perceptual tasks under this circumstance is more challenging due to frequent occlusion and truncation. + +# 3. RoboSense Open Dataset + +We commence with the sensor setup as well as data acquisition details, delineate the coordinate systems and label generation process, and present data statistics respectively. + +# 3.1. Sensor Setup and Data Acquisition + +Sensor setup. We use a social mobile robot (i.e., robosweeper) as data collection platform, which is equipped with different sensors installed in different sides of the robot respectively to ensure data captured in $360^{\circ}$ horizontal view without blind spots, including LiDAR, Camera, Fisheye, GPS / IMU and Ultrasonic. Refer to Fig. 3 for sensor layouts and Tab. 3 for detailed sensor specifications. + +Data acquisition. We utilize the mobile robot to collect data along the Dishui Lake in Shanghai, China, lasting 42h in total at an average speed of less than $1\mathrm{m / s}$ through manually remote control. 22 different places are travelled, which can be categorized into 6 main kinds of outdoor or semiclosed social scenarios (i.e., scenic spots, parks, squares, campuses, streets and sidewalks). After data collection, we manually select and process 7619 representative scenes + +of $20s$ duration respectively for further annotation, covering various natural conditions (i.e., weather and illumination) and diverse environmental background and obstructions (i.e., motion, amount, type, occlusion, truncation). + +# 3.2. Coordinate Systems + +Ego-Vehicle Coordinate. The Ego-Vehicle Coordinate System is centered at the rear axle of the vehicle. The positive directions of the X, Y, and Z axes correspond to the forward, leftward, and upward directions of the vehicle, respectively. Ego-Vehicle Coordinate System is the most frequently used in tasks such as perception, tracking, prediction, and planning, where dynamic and static targets as well as trajectories are transformed into this coordinate system. + +Global Coordinate. To transform the dynamic and static elements from historical and future frames into the current frame coordinate system, we need to establish a global coordinate system to record the position and orientation of the ego vehicle in each frame. The origin of the Global Coordinate System is an arbitrarily defined point in Shanghai Linggang, China, and the positive directions of the X, Y, and Z axes follow the definition of the North-East-Up coordinate. + +LiDAR Coordinate. The LiDAR Coordinate System is defined based on the Hesai lidar installed directly above the vehicle, the positive directions of the X, Y, and Z axes follow the definition of the Ego-Vehicle Coordinate System. + +Camera Coordinate. The RoboSweeper is equipped with four fisheye cameras and four pinhole cameras. The origin of the Camera Coordinate System for both types of cameras is the optical center. However, the positive directions of the coordinate axes are defined differently in the RoboSense dataset. In the fisheye coordinate system, the X, Y, and Z axes correspond to directly below, right, and behind the optical center, respectively. In contrast, in the pinhole coordinate system, these axes correspond to directly right, below, and front of the optical center, respectively. + +Pixel Coordinate. The image is presented in the form of pixels, each pixel corresponds to a 2D pixel coordinate. The origin of the Pixel Coordinate System is the upper left cor + +![](images/fc882f5296c1b6b2939978011dceadd9e6d4dce6ef9ec9428d06904936aa0fe1.jpg) +Figure 3. Sensor setup and coordinate system illustration of our data collection platform. + +ner of the image. Points in the 3D Camera Coordinate System can obtain coordinates in the Pixel Coordinate System through the camera projection. + +# 3.3. Ground Truth Labels + +After integrating, synchronizing and calibrating the multisensor raw data, we annotate keyframes (LiDAR, image) at the frequency of $1\mathrm{Hz}$ due to the low-speed moving status. + +3D object. With the selected scenes of collected RoboSense dataset, we annotate 3D object boxes of 3 movable classes (i.e., "Vehicle", "Cyclist" and "Pedestrian") for each sampled keyframe in both the LiDAR coordinate of point clouds and the Camera coordinate of multi-view images respectively. Each annotated 3D box can be represented as $[x,y,z,w,l,h,\theta,cls]$ , where $x,y,z$ indicate the 3D position of a regular object, and $w,l,h$ represent the scale information including width, length and height. $\theta$ and $cls$ correspond to the orientation (especially yaw angle) and the object class respectively. A three-stage auto-labelling pipeline is detailed in the supplementary material (see Sec. B.2). + +Trajectory. To facilitate the temporal tasks such as multi-object tracking and motion forecasting described in Sec. 4, we assign a unique Track ID $\tau$ to each agent across a temporal sequence on Bird-Eye-View (BEV) of the Ego-Vehicle coordinate. Furthermore, agents with the same $\tau$ within a sequence are linked together to form object trajectories. + +Occupancy label. In addition to 3 typical classes of moving objects on roads which are annotated temporally as above, there also exists a rich collection of static obstacles with irregular shapes especially in the complex scenarios (i.e., parks, campuses and squares, etc.) of RoboSense. To detailly describe the environment in surrounding camera views for driving safety, we voxelize the 3D space and generate high-quality yet dense occupancy labels to represent the voxel states. Similar with previous occupancy benchmarks [34, 35] built upon public datasets [3, 32], we conduct dynamic objects and static scenes segmentation along the temporal dimension based on annotated 3D boxes and trajectories. Then sparse LiDAR points inside each box are extracted from $T - k$ to $T + k$ frames respectively, where $T$ indicates the index of current keyframe, and $k$ is set to 10 + +empirically. Refer to the supplementary material for more details of occupancy label generation process (see Sec. B.3). + +# 4. Tasks & Metrics + +Both egocentric perceptual tasks and prediction tasks are supported in our RoboSense dataset and benchmark. + +# 4.1. Perception + +# 4.1.1 3D Object Detection + +The RoboSense 3D detection task requires to detect 3D bounding boxes of three main classes (i.e. "Vehicle", "Pedestrian" and "Cyclist"), including position, size, orientation and category. Following the conventions in [3, 8, 30, 32], we adopt mAP (mean Average Precision), AOS (Average Orientation Similarity) and ASE (Average Scale Error) to measure the performance of different detectors. + +There are several matching criteria to define the true positive for Average Precision (AP) metric calculation. For example, [8] adopts 3D Intersection-over-Union (IoU) to match each prediction with a ground-truth box, while [3] define a match through thresholding the 2D center distance on the Bird-Eye-View ground plane. As for RoboSense detection task, we also adopt a similar distance measure. Differently, we define the threshold as a relative Proportion $p$ of ground truth Closest Collision-point Distance (CCDP) from the ego-vehicle, rather than an absolute Center Distance (CD) $d$ adopted in [3]. We claim that the localization accuracy of near obstacles' closest collision-point is more important in low-speed driving scenarios. Then AP is calculated as the normalized area under precision-recall curve [6]. Finally, mAP is obtained by averaging over all classes $\mathbb{C}$ and matching thresholds $\mathbb{P} = \{5\%, 10\%, 20\%\}$ : + +$$ +m A P = \frac {1}{| \mathbb {C} | \cdot | \mathbb {P} |} \sum_ {c \in \mathbb {C}} \sum_ {p \in \mathbb {P}} A P _ {c, p} \tag {1} +$$ + +In addition to AP, we also measure AOS and ASE for each matched true positive, which represent the precision of predicted yaw angle and object scale respectively. AOS (Average Orientation Similarity) is formulated as: + +$$ +A O S = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \max _ {\widetilde {r}: \widetilde {r} \geq r} s (\widetilde {r}), \tag {2} +$$ + +$$ +s (r) = \frac {1}{| \mathbb {D} (r) |} \sum_ {i \in \mathbb {D} (r)} \frac {1 + \cos \Delta_ {\theta} ^ {(i)}}{2}, \tag {3} +$$ + +where $\mathcal{R}$ indicates the recall range [0.1, 1] interpolated with 40 points. $\mathbb{D}(r)$ indicates the set of matched true positives at recall $r$ . And $\Delta_{\theta}^{(i)}$ denotes the angle difference between sample $i$ and ground truth. Different from [32], we only consider true positive samples under each recall level, rather than all predicted positives. + +ASE is defined as 1 - IoU, which aims to measure the scale error through calculating the 3D IoU after aligning orientation and translation of predictions with ground truth. + +# 4.1.2 Multi-Object Tracking + +The tracking task is designed to associate all detected 3D boxes of movable object classes across input multi-view temporal sequences (i.e. videos or point cloud sequences). Each object is assigned a unique and consistent track ID $\tau$ from first appearance until complete vanishing. As for performance evaluation, we refer to [3, 8, 20, 31], and mainly adopt sAMOTA (Scaled Average Multi-Object Tracking Accuracy), AMOTP (Average Multi-Object Tracking Precision) to measure the 3D tracking performance. + +Formally, sAMOTA is defined as the mean value of sMOTA over all recalls: + +$$ +s A M O T A = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} s M O T A _ {r}, \tag {4} +$$ + +$$ +s M O T A _ {r} = \max (0, 1 - \frac {F P _ {r} + F N _ {r} + I D S _ {r} - (1 - r) \cdot G T}{r \cdot G T}), \tag {5} +$$ + +where $FP_{r},FN_{r}$ and $IDS_{r}$ represent the number of false positives (wrongly detection), false negatives (missing detection) and identity switches at the corresponding recall $r$ , respectively. Similarly, AMOTP is the average results of MOTP among different recalls, which can be defined as: + +$$ +A M O T P = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \frac {\sum_ {i , t} d _ {i , t}}{T P _ {r}}, \tag {6} +$$ + +where $TP_{r}$ is the number of true positives at the recall $r$ , and $d_{i,t}$ denotes the position error of matched track $i$ at timestamp $t$ . Besides, additional metrics such as MT (Most Tracked) and ML (Most Lost) [2] are also reported. + +# 4.2. Prediction + +# 4.2.1 Motion Forecasting + +Based on perception results, the motion forecasting task requires to predict agents' future trajectories. Specifically, $\kappa$ plausible trajectories in future $T = 3s$ timesteps for each agent are forecasted as offsets to the current agent's position. Following the standard protocols [9, 18, 19, 24], we adopt minADE (minimum Average Displacement Error), minFDE (minimum Final Displacement Error), MR (Miss Rate) and EPA (End-to-end Prediction Accuracy) as metrics to measure the precision of motion prediction. In order to decouple the accuracy of perception and prediction, these metrics are only caculated for matched TPs (True Positives), where the matching threshold is set to $p_{match} = 5\%$ of ground truth distance of the closest collision-point from the ego-vehicle. And the miss threshold of minFDE is set to $p_{miss} = 20\%$ for calculating the MR metric. + +# 4.2.2 Occupancy Prediction + +The goal of occupancy prediction task is to estimate the state of each voxel in the 3D space. Formally, a sequence of $T$ historical frames with $N$ surround-view camera images $\{I_{i,t} \in \mathbb{R}^{H_i \times W_i \times 3}\}$ are served as input, where $i = 1, \dots, N$ and $t = 1, \dots, T$ . Besides, sensor intrinsic parameters $\{K_i\}$ together with extrinsic parameters $\{R_i | t_i\}$ for each frame are also provided. Then the ground truth labels describe the voxel states separately, including occupancy state and semantic label. Three states are considered on the RoboSense dataset, including "occupied", "free" and "unknown". And the semantic label of each voxel can be one of the 3 predefined object categories or an "unknown" class to indicate general objects. Furthermore, each voxel can be also equipped with extra attributes as outputs, such as instance IDs and motion vectors, which are left as our future work. + +To evaluate the quality of predicted occupancy, we measure the whole-scene level voxel segmentation results using IoU metric for each class. Considering the low-speed driving scenarios, we evaluate the metric under different ranges around the ego vehicle in both 3D and BEV space. Finally, mIoU is obtained through averaging over 4 classes. Moreover, evaluation is only performed on the visible voxels from the camera view. + +# 5. Experiments + +# 5.1. Benchmark Setup + +Our RoboSense dataset contains 7.6K sequences (including 130K annotated frames) of synchronized multi-sensor data, covering 6 main categories (including 22 different locations) of outdoor or semi-closed scenarios (i.e., S1-parks, S2-scenic spots, S3-squares, S4-campuses, S5-sidewalks and S6-streets). To protect the data privacy, we conduct a series of data desensitization measures through masking the human faces and car plates as well as road signs from all sensor data. The details of RoboSense dataset composition and partitioning are listed in the Tab. 2. The RoboSense dataset is collected under various illumination, traffic flow and weather conditions, to ensure the diversity of static background and movable obstacles, thus meeting the demand of different realistic applications. + +RoboSense dataset is divided into three parts with a ratio of $50\%$ , $40\%$ and $10\%$ , for the purpose of training, testing and validation respectively. As for the scene partition, one of the 6 collected scenes (i.e. S-6) is assigned to the testing set exclusively, while the remaining scenes are shared among all splits. Ground truth labels of training and validation sets for corresponding task are provided, together with the synchronized multi-sensor raw data. However, the testing set only provides data. Hence algorithms can merely be submitted to our online benchmark for corresponding task evaluation of testing set. + +Table 2. The details of RoboSense dataset, including the proportion of day/night data among different scenes respectively; The distribution of training/testing/validation sets; The count of synchronized sequences/frames as well as annotated 3D boxes/trajectories for each scene. + +
Scene-IDDistributionRatio of DatasetNum of +SequencesNum of +FramesNum of +3D BoxesNum of +Trajectories
DayNightSceneTrainTestVal
S-156%44%20%50%40%10%1.5K26K310K36K
S-269%31%30%2.3K42K293K37K
S-371%29%17%1.2K22K284K64K
S-483%17%7%0.5K9K144K22K
S-570%30%20%1.6K26K297K44K
S-622%78%6%0%100%0%0.5K8K88K13K
Total65%35%100%46%44%10%7.6K133K1.4M216K
+ +Table 3. Sensor Specifications on RoboSense. + +
ModalitySensorDetails
Camera4 × CameraRGB, 25Hz, 1920 × 1080 +FOV:[111.78°, 63.16°]
4 × FisheyeRGB, 25Hz, 1280 × 720 +FOV:[180.0°, 180.0°]
LiDarHesai Pandar40M64 beams, 10Hz, 384k pps +FOV:[360.0°, -25° to 15°]
3 × Zvision ML30s40 beams, 10Hz, 720k pps +FOV:[286.48°, -25° to 15°]
Livox Horizon40 beams, 10Hz, 720k pps +FOV:[286.48°, -25° to 15°]
Ultrasonics3 × LRUSTP-313, 1m-10m, 40kHz, ±1mm
8 × SRUSTP-318, 5cm-200cm, 40kHz, ±1mm
LocalizationGPS & IMUGPS, IMU, AHRS. 0.2° heading, 0.1° roll/pitch, 20mm, RTK positioning, 1000Hz update rate
+ +# 5.2. Sensor Specifications + +The detailed specifications of all devices are shown in Tab. 3. To cover the areas from near to farther areas, we select Cameras with different focal lengths and Field of View (FOV). Besides, 5 LiDAR sensors are installed in our data collection robot, where the top Hesai Pandar40M is served as autolabeller to provide initial annotations for the splicing points of other LiDARs. 11 Ultrasonics sensors are also installed for freespace detection to ensure safety. All devices are synchronized in time via Network Time Protocol (NTP) before data collection, we utilize a time interval of $100\mathrm{ms}$ as the global timestamp, and match the frame from each device with the nearest timestamp adjacent to the global times- tamp. This process ultimately yields synchronized multi- sensor data at a frame rate of 10 FPS. + +# 5.3. Implementation Details + +For LiDAR detection task, we set the point range to $\mathrm{x} \in [-45m, 45m]$ , $\mathrm{y} \in [-45m, 45m]$ , $\mathrm{z} \in [-1m, 4m]$ , with a fixed voxel size of $0.16m$ and $0.05m$ for pillar-based and voxel-based methods respectively. For Image detection tasks, we use ResNet18 [10] as backbone network and the input image is resized to $640 \times 352$ . For practical usages, we report performance using our proposed Closest-Collision Distance Proportion (CCDP) as matching criterion. Comparisons of different matching functions on average precision are shown in Fig. 4. As expected, when using Center Distance (CD) or IOU, objects without distance differentiation can not reflect the model capability of locating closest collision points of nearby obstacles, which is more challenging + +![](images/4f7d3183814f0c4dd6a74de15dd66f4161df2883686047dbd9da32db96495c4f.jpg) +Figure 4. Average precision vs. matching function. CD: Center Distance. CDP: Center Distance Proportion. CCDP: Closest-Collision Distance Proportion. IOU: Intersection Over Union. We set IOU of Vehicle, Cyclist and Pedestrian to [0.7, 0.5, 0.5] following KITTI [8]. CD is set to $2m$ following nuScenes [3] and CDP/CCDP=5% for TP metrics. + +and essential for low-speed driving scenarios. + +# 5.4. Baselines: Perception + +# 5.4.1 LiDAR 3D Detection + +To demonstrate the performance of advanced 3D detectors on LiDAR-only detection track of our RoboSense benchmark, we implement several popular CNN-based methods with different fashions, including Pointpillar [15] (Pillar-based), SECOND [39] (Voxel-based), and PV-RCNN [29] (Two-stage Point-Voxel based). Besides, Transformer-based method such as Transfusion-L [1] is also implemented for architecture comparison. Pointpillar as the most efficient method above is adopted as our baseline for LiDAR 3D detection task. + +# 5.4.2 Multi-View 3D Detection + +Current works of multi-view 3D detection can be divided into two mainstreams, namely LSS [26] based and Transformer based. To examine the effectiveness of image-only multi-view 3D detection models, we select the widely-used method BEVDet [12] as our LSS-based baseline on image 3D detection track of RoboSense, and re-implement several extended versions such as BEVDet4D [11] which takes advantage of history temporal clues, and BEVDepth [16] which adopts an additional branch for depth prediction under point supervision. Besides, BEVFormer [17] as a Transformer-based representative work is also included. + +Table 4. 3D Detection results on validation sets of RoboSense using Center-Point (CP) distance and Closest Collision-Point (CCP) distance as matching criteria respectively where the relative proportion $p$ is set to $5\%$ (LiDAR) and ${10}\%$ (Image). + +
TaskMethodVehicle@p=5%/10%Cyclist@p=5%/10%Pedestrian@p=5%/10%
3D AP↑AOS↑ASE↓3D AP↑AOS↑ASE↓3D AP↑AOS↑ASE↓
LiDAR 3D DetectionPointPillar [15]72.5/53.073.5/61.120.6/16.144.2/32.845.4/38.364.2/54.362.7/38.245.3/34.138.3/27.2
SECOND [39]78.8/63.180.2/69.419.8/15.753.8/43.557.2/49.967.7/55.770.8/47.254.6/43.240.1/29.3
PVRCNN [29]74.6/57.477.4/67.716.4/15.453.6/41.455.7/50.162.5/61.966.4/39.150.1/37.040.4/25.5
Transfusion-L [1]83.6/65.184.5/73.819.7/16.059.7/47.078.0/70.882.1/72.972.3/42.860.5/48.745.1/37.4
Multi-view 3D DetectionBEVDet [12]76.2/30.240.4/25.917.3/11.242.3/25.736.1/30.256.5/42.147.4/28.548.6/36.530.2/18.8
BEVDet4D [11]77.2/31.141.1/26.416.8/10.842.0/24.833.9/27.755.3/41.248.1/29.346.6/37.627.5/21.3
BEVDepth [16]77.8/31.340.9/26.316.7/10.743.3/27.034.9/30.252.2/46.650.1/31.346.7/37.928.0/21.4
BEVFormer [17]78.2/32.041.6/26.716.5/10.644.1/27.634.9/30.551.3/44.350.2/32.346.3/38.028.1/17.9
+ +Table 5. Study of different sensor layouts for perception tasks (3D detection and MOT) on validation sets of RoboSense under different ranges (m). AB3DMOT [37] is adopted as 3D MOT baseline. C: Camera, F: Fisheye, L: LiDAR, V: View + +
TaskDetectorLayoutsDetectionTracking
MetricRange(m)sAMOTA↑AMOTP↑MT↑ML↓
[0, 5][5, 10][10, 30]
Multi-view 3D PerceptionBEVDepth [16]4C3D AP54.9/16.060.1/18.353.7/33.144.0329.9520.2354.01
AOS44.8/19.737.0/18.834.5/26.9
4F3D AP61.1/16.970.6/19.950.8/29.039.5627.1018.0261.74
AOS58.7/27.541.3/23.536.1/27.4
4C + 4F3D AP68.9/20.575.2/22.964.2/38.651.1635.6825.2148.07
AOS53.9/24.443.1/22.539.6/30.9
LiDAR 3D PerceptionPointPillar [15]4L3D AP59.2/19.373.1/42.071.0/65.444.7733.6525.0454.08
AOS46.5/19.267.2/47.569.0/65.7
Multi-modal 3D PerceptionBEVDepth [16] + Pointpillar [15]8V + 4L3D AP61.3/36.961.3/54.654.4/52.643.3243.1834.7440.82
AOS64.8/49.678.7/75.079.4/78.4
+ +# 5.4.3 Multiple Object Tracking + +We follow the "Tracking-by-Detection" paradigm using 3D detection results from Camera or LiDAR data as input respectively, and present several baselines for multiple 3D object tracking task. Specifically, 3D boxes detected from surround-view images by BEVDepth [16] and splicing pointclouds by Pointpillar [15] are provided separately. And the tracking approach AB3DMOT described in [37] is picked to serve as the baseline of multiple object tracker in the 3D space. Then the same objects across different sensors are associated with unique track IDs to form global trajectories in the past. + +# 5.5. Baselines: Prediction + +# 5.5.1 Motion Prediction + +Traditional motion prediction methods utilize perception ground truth (i.e., history trajectories of agents and HDmap) as input, which lacks of uncertainty modeling in practical applications. In this paper, we implement several vision-based end-to-end methods for joint perception and motion prediction on RoboSense benchmark, including ViP3D [9] and PnPNet [18]. For comparisons, we also report the motion prediction results of assuming agents surrounding the ego-vehicle with constant positions or velocities respectively, thus to reflect the diversity and difficulty of our dataset on prediction task. + +# 5.5.2 Occupancy Prediction + +We extend a BEV 3D detection model - BEVDepth [16] to the 3D occupancy prediction task, which is then adopted as our baseline for the visual occupancy prediction task. Concretely, we replace the original detection decoders with the occupancy reconstruction layers while maintaining the BEV feature encoders. ResNet18 [10] pretrained on FCOS3D [36] is employed as image backbone for visual feature extraction. + +# 5.6. Results and Analysis + +# 5.6.1 Perception Results + +3D Object Detection. The 3D detection results based on multi-view images and splicing point clouds are shown in Tab. 4. As for LiDAR 3D detection, Transfusion-L [1] achieves the leading performance owing to the advanced transformer architecture. In terms of multi-view 3D detection, BEVDet4D [11] and BEVDepth [16] obtain significant improvement than BEVDet [12] through involving temporal clues and adopting an additional depth branch respectively. Besides, BEVFormer [17] also achieves competitive results by introducing a query-based attention mechanism. Generally, LiDAR-based 3D detector can generate high-quality detection results than vision-based methods. However, vision-based methods are capable of detecting various + +ranges of objects with more sensors (Fisheye or Camera). Note that two different matching criteria are both considered for TP calculation, namely Center-Point (CP) distance and Closest Collision-Point (CCP) distance. It can be observed that the CCP localization performance is obviously lower than the CP localization (i.e. $18.5\%$ 3D AP drop of Transfusion-L for Vehicle class and $29.5\%$ 3D AP drop for Pedestrian class. For navigation safety, the CCP localization is more important for near-field egocentric perception in crowded social scenarios. + +Performance with Different Sensor-Layouts. To evaluate the performance of different sensor layouts under various ranges, we conduct extensive comparisons as shown in Tab. 5. As for visual perception, 4C layout achieves better AP than 4F layout in farther areas (i.e., $10 - 30m$ ), while 4F layout is good at detecting near-field targets within $10m$ . Through combining these two layouts, better performance can be achieved across different ranges. LiDAR 3D detector exhibits an obvious advantage over visual detectors especially in CCP and farther object localization, while the performance of near-field objects within $5m$ is inferior ( $19.3\%$ vs. $20.5\%$ ). Moreover, we implement multi-modal 3D perception ( $8V + 4L$ ) through late-fusion strategy. Specifically, 3D detection results from multi-view 3D detector and LiDAR 3D detector are adopted for post-processing. And we can observe that the CCP-based 3D AP of objects within $5m$ is remarkably boosted from $20.5\%$ to $36.9\%$ . And the AOS metric is also increased consistently. + +Multiple Object Tracking. Regarding to the MOT task in Tab. 5, AB3DMOT [37] is adopted as baseline tracker in 3D space, which mitigates the impact of object occlusions existing in 2D image, especially for crowded scenarios. Through introducing more sensors (4C + 4F), vision-based methods can also achieve competitive tracking performance with LiDAR-based methods, even better in sAMOTA metric (51.16 vs. 44.77). With the multi-modal input, AMOTP, MT and ML performance can be further improved as expected. However, although equipped with multi-modal and multi-sensor data as input, the perception performance is still inferior especially in near-field (i.e. $36.9\%$ CCP-based 3D AP within $5m$ ), revealing the deficiencies of current perception methods in handling the obstacles in near ranges. The main reason may be the frequent truncation and occlusion caused by a large view occupation of near obstacles, which showcases the great challenge and importance of our proposed benchmark for the development of egocentric perceptual frameworks related to navigation in crowded and unstructured environments. + +# 5.6.2 Prediction Results + +Motion forecasting of surrounding agents as well as occupancy state descriptions around the ego-vehicle are two crucial prediction tasks in the research field of autonomous + +Table 6. Motion forecasting results on validation sets of RoboSense. * and † indicate utilizing GroundTruth 3D boxes and detection results from PointPillar [15] as input respectively with constant positions or velocities for comparisons. + +
MethodminADE (m) ↓minFDE (m) ↓MR↓EPA↑
Constant Pos.*2.423.010.3190.680
Constant Vel.*1.593.540.2190.780
Constant Pos.†1.521.950.2670.243
Random Vel.†2.563.850.8720.029
ViP3D [9]1.311.550.1960.283
PnPNet [18]0.891.120.1720.313
+ +Table 7. Occupancy prediction results on validation sets of RoboSense using 4F sensors as input. "mIoU-3D" and "mIoU-BEV" indicate the standard mIoU metric calculated in 3D space and BEV respectively without considering the ground voxels. + +
Range(m)mIoU-3D↑mIoU-BEV↑
[0, 12.8]24.629.7
[0, 2]39.648.2
[2, 5]30.736.7
[5, 12.8]16.119.7
+ +driving, which have been extensively explored in urban and highway scenarios for autonomous cars. + +Motion Prediction. As shown in Tab. 6, either visual end-to-end methods [9] or LiDAR-based end-to-end methods [18] are all supported for validation on our RoboSense. PnPNet [18] with LiDAR points as input can produce less prediction errors and better EPA than ViP3D [9], both of which remarkably outperform two baseline settings of modeling agents with constant positions or velocities. + +Occupancy Prediction. As shown in Tab. 7, we use 4F sensor data as input and report the performance of mIOU metric in both 3D and BEV space under various ranges respectively. Note that the metric is calculated without considering states of the ground voxels, leading to lower performance in either 3D or BEV space. As expected, the performance evaluated within $2m$ is better than farther areas. + +# 6. Conclusion + +To foster the research of egocentric perceptual framework tailored to various types of autonomous agents navigating in crowded and unstructured environments, RoboSense, a real-world and multi-modal dataset is collected in complex social scenarios with varying and uncontrolled environmental conditions and dynamical elements. It consists of 7.6K scenes manually selected from different locations, with 1.4M 3D Boxes and 216K trajectories annotated in total on 133K synchronous frames. Besides, occupancy descriptions are also provided to facilitate the surrounding context comprehension. In the future works, more tasks and associated benchmarks, such as motion planning, will be expanded for end-to-end autonomous navigating application, and explore the additional benefits that joint optimization can bring to the modular training. + +# References + +[1] Xuyang Bai, Zeyu Hu, Xinge Zhu, Qingqiu Huang, Yilun Chen, Hongbo Fu, and Chiew-Lan Tai. 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In modern robotics, these capabilities are increasingly provided by vision-language models. However, these models face significant challenges in spatial reasoning tasks, as their training data are based on general-purpose image datasets that often lack sophisticated spatial understanding. For example, datasets frequently do not capture reference frame comprehension, yet effective spatial reasoning requires understanding whether to reason from ego-, world-, or object-centric perspectives. To address this issue, we introduce ROBOSPATIAL, a large-scale dataset for spatial understanding in robotics. It consists of real indoor and tabletop scenes, captured as 3D scans and egocentric images, and annotated with rich spatial information relevant to robotics. The dataset includes 1M images, 5k 3D scans, and 3M annotated spatial relationships, and the pairing of 2D egocentric images with 3D scans makes it both 2D- and 3D- ready. Our experiments show that models trained with ROBOSPATIAL outperform baselines on downstream tasks such as spatial affordance prediction, spatial relationship prediction, and robotics manipulation. + +# 1. Introduction + +The rise of vision-language models (VLMs) has opened new opportunities for agents to interpret and act upon the visual world using natural language. VLMs have been adopted across a range of embodied settings, notably in robotics and augmented reality (AR). In robotics, they have enabled grounded scene understanding [13, 66], manipulation [7], and policy code generation [29, 48], while in AR, they support tasks like object labeling [50], action recognition [16, 17], and temporal grounding [22]. + +![](images/ad269ce487aa6891d1b73c1138aebab0836fdacff5d41ef6433ce92fc4dee1f3.jpg) +Task: Place the gray bowl in front of the car. +Spatial context Point to the vacant space in front of the car. +Spatial compatibility Can the gray bowl fit in, front of the car? +Spatial configuration Is the gray bowl in front of the car? + +![](images/97a397c599bdb23d49d7299586a04a19a281e15bb636c295ba8813bbf690e001.jpg) +Figure 1. ROBOSPATIAL dataset facilitates 3D spatial reasoning for robotic manipulation. This illustration demonstrates how a model trained on ROBOSPATIAL enables human-aligned spatial reasoning within the correct reference frame, supporting task grounding, planning, and detection for manipulation tasks. + +VLMs can recognize objects, classify scenes, and even provide general descriptions that capture high-level attributes. However, despite significant recent advancements, VLMs [30, 35, 42] still fall short in spatial understanding [26, 38, 47, 61]. They struggle with tasks that require interpreting nuanced spatial relationships between objects, such as describing where one object is in relation to another or determining the best location to place an item within a specific condition. For example, while a model might accurately describe a "bowl on the table," it lacks the ability to reason about where on the table the bowl is, where it should go to ensure accessibility or stability, or how it might fit among other objects. Furthermore, a critical limitation of existing VLM training datasets is their inability to capture reference frame understanding (ref. frame) — the way we interpret spatial relationships changes drastically depending on whether we're viewing from a first-person perspective, focusing on specific objects, or observing the entire scene, all of which are essential for real-world interactions. + +These limitations highlight an ongoing challenge: bridging the gap between surface-level scene description and the deeper spatial comprehension necessary for intuitive inter + +
Dataset3D scansEmbodiedRef. framesCompatibilityDomain#Scans#Images#Spatial QAs
EmbSpatial-Bench [10]✓✓✗✗Indoor2772k4k
Visual Spatial [33]✗✗✓✗MSCOCO010k10k
SpatialRGPT-Bench [6]✗✗✗✓Indoor, AV01.4k1.4k
BLINK-Spatial [15]✗✗✓✗Generic0286286
What's up [26]✗✗✗✗Generic05k10k
Spatial-MM [47]✗✗✓✗Generic02.3k2.3k
ROBOSpatial✓✓✓✓Indoor, tabletop5k1M3M
+ +Table 1. Comparison with other spatial reasoning datasets that include object-centric spatial relationships. + +action. Several recent efforts aim to address this by explicitly training VLMs on spatial reasoning tasks, yet many fall short of the demands posed by embodied or robotics settings. For example, SpatialVLM [5] and SpatialRGPT [6] train VLMs to answer questions about distances and spatial relationships between objects, advancing spatial understanding at a conceptual level. However, these models are trained on datasets comprised of images from the internet, with annotations generated by perception models. As a result, they struggle to generalize to embodied images—those captured by robot cameras within real-world environments, which often lack identifiable cues for an absolute scale. Pointing models, such as RoboPoint [62] and more recently Molmo [9], take a different approach by training VLMs to produce grounded 2D coordinates that pinpoint object locations or free space within a scene. However, these models lack understanding of real-world constraints, such as inferring object-centric reference frames for perspective-invariant reasoning, or accounting for the space required to place various objects. This results, for example, in failing to predict whether the gray bowl can fit in front of the car in Figure 1. + +This paper hypothesizes that a primary bottleneck limiting the effectiveness of VLMs in robotics is the scarcity of suitable training data, as highlighted by Table 1. To address this, we introduce ROBOSPATIAL, a dataset designed specifically to facilitate spatial understanding in VLMs for robotic applications. The proposed approach leverages annotated indoor scene and tabletop RGBD datasets, transforming them into targeted question-answer pairs designed to probe spatial reasoning skills critical for robotics. + +We categorize the questions into three types, each serving a distinct purpose. Spatial context focuses on identifying empty space or support surfaces in the environment that can accommodate other objects. These questions are formulated as point-prediction tasks, challenging the model to determine appropriate locations within free space where an object can be placed—for example, “Where on the table can I put the plate?” Spatial compatibility builds on the identified empty space to assess whether a given area can feasibly support the placement of a specific object, ensuring sufficient size and fit. These questions are posed in a binary format, such as “Can the chair be placed in front of the table?” Spatial configuration examines the relative + +spatial relationships between two objects. These questions use a binary format to determine whether a spatial relation holds, such as "Is the mug to the left of the laptop?" + +To enhance the model's ability to interpret spatial instructions from different perspectives, each question-answer pair in ROBOSPATIAL is posed from three distinct reference perspectives/frames: (a) Ego-centric from the observer's perspective at the camera pose, (b) World-centric grounded in a global world frame, and (c) Object-centric based on a reference frame attached to the focal object. This multi-frame approach enables models to handle complex spatial instructions more flexibly, preparing them to better generalize to dynamic robotic contexts. Applying our methodology to existing indoor scene and tabletop datasets, we generate both a comprehensive training dataset and a benchmark for spatial question answering in robotics. ROBOSPATIAL contains around 1M images, 5k 3D scans, and 3M annotated spatial relationships, with paired 2D egocentric images and 3D scans to make it both 2D- and 3D- ready. + +To validate the effectiveness of ROBOSPATIAL, comprehensive experiments were conducted using multiple state-of-the-art (SOTA) 2D and 3D VLMs. Results demonstrate that models trained on ROBOSPATIAL exhibit significantly improved spatial reasoning capabilities, consistently outperforming baseline methods on the evaluation benchmark ROBOSPATIAL-Val, a held-out validation subset derived from the heuristically generated ROBOSPATIAL dataset. To further assess the generalization and robustness of these trained VLMs, additional evaluations were conducted using three complementary benchmarks: ROBOSPATIAL-Home, a manually collected dataset consisting of paired RGB and depth images, and two external benchmarks, BLINK-Spatial [15] and SpatialBot [2]. These benchmarks rigorously test spatial reasoning skills in practical robotic tasks, including object rearrangement and contextual question answering in indoor environments, while also examining the models' capacity to generalize to novel spatial reasoning scenarios beyond the original training data. Across all benchmarks, models trained on ROBOSPATIAL consistently outperformed baseline methods, demonstrating the broad utility of the dataset. Leveraging the 3D-ready design of ROBOSPATIAL, direct comparisons between the spatial reasoning performance of 2D and 3D VLMs were also performed. Although initial results indicate potential advan + +tages for 3D models, differences in pretraining data and base LLM architectures among models render the comparison inconclusive. ROBOSPATIAL is specifically designed to support both 2D and 3D research directions, enabling future studies to address these differences more conclusively. + +# Our contributions are threefold: + +- A new training dataset, ROBOSPATIAL, comprising images and 3D scans paired with spatial questions and answers, accompanied by an evaluation benchmark, ROBOSPATIAL-Val, a held-out validation set. Additionally, we introduce ROBOSPATIAL-Home, a manually collected and annotated dataset designed specifically for assessing real-world spatial reasoning in indoor environments. These datasets uniquely incorporate multiple reference frames, object-object spatial relationships, object-space relationships, and object compatibility. We make the data and code for generating the dataset from 3D annotated scenes publicly available1. +- VLMs trained on ROBOSPATIAL demonstrate superior spatial reasoning, outperforming SOTA baselines on language-guided robot manipulation and indoor scene question answering. +- Comprehensive experiments assessing spatial reasoning capabilities in both 2D and 3D VLMs, comparing the difference between SOTA VLMs in real-world spatial tasks. + +# 2. Related Work + +VLMs for Robotics. Vision-language models (VLMs) have emerged as pivotal tools in robotics, enabling systems to interpret and act upon complex visual and textual information. By integrating visual perception with language understanding, VLMs facilitate more intuitive human-robot interactions and enhance autonomous decision-making capabilities. Recent advancements have demonstrated the potential of VLMs in various robotic applications. For instance, vision-language-action models (VLAs) [27, 41, 65] enable robots to interpret and execute complex instructions and output executable robot actions. Additionally, VLMs like GPT-4v [42] have been utilized for high-level task planning [55], allowing robots to generate detailed action sequences from natural language instructions. Furthermore, VLMs have been used for keypoint/mask prediction [21, 40, 59], error analysis [11, 49], grasp pose prediction [19]. Despite these advancements, integrating VLMs [2, 6, 62] into robotic systems presents challenges. One significant hurdle is the need for precise spatial reasoning to navigate and manipulate objects effectively. While VLMs excel in understanding and generating language, their ability to comprehend and reason about spatial relationships in dynamic environments remains limited [57, 60, 61]. Therefore, ROBOSPATIAL aims to tackle this gap by presenting a large + +![](images/57cc30b525383d7b94e8df0e52f057d1e473bad46627ef9836c85cbd38795b1e.jpg) +Figure 2. Overview of the ROBOSpatial dataset. We automatically generate spatial relationship annotations from existing datasets with 3D point clouds, egocentric images, and 3D bounding box annotations. We create question/answer pairs covering three classes of spatial relationships, three spatial reference frames, and both binary (yes/no) and numeric (e.g. 2D image points) answers. From 1M images and 5k scans, we generate over 3M spatial question/answer pairs. + +![](images/34c89973194d0d83521545e6206375733bd446a80dba913e28432b1b2f3251ae.jpg) + +scale pretraining and evaluation setup for teaching spatial understanding to VLM for robotics. + +Spatial Understanding with VLMs. Spatial understanding has been implicitly and explicitly part of various vision and question answering tasks [1, 15, 23-25, 28, 46, 51]. While many benchmarks and methods have been proposed, they often come with limitations: some focus exclusively on simulations [53] or generic images [5, 6, 15, 26, 33, 43, 44, 47], others are difficult to evaluate due to their reliance on free-form text outputs [10, 32, 53], some rely on complete 3D scans [32, 37, 39, 64], and others do not account for reference frames [5, 6, 15, 32, 37, 39, 44, 64]. Furthermore, many fail to address actionable, robotics-relevant spatial relationships such as spatial compatibility and context [10, 15, 26, 32, 44, 47, 58]. + +Inspired by prior works on spatial reasoning [26, 33]—where the impact of reference frames and spatial configurations was explored in generic images [23, 31]—we extend spatial understanding to a robotics-specific context with actionable spatial relationships such as spatial compatibility and spatial context. Our aim is to enable direct application to robotic workflows, such as task planning and verification. + +To achieve this, we have developed a large-scale 2D/3D ready training dataset using our automated data generation pipeline. We further show how ROBOSPATIAL can be used to teach spatial reasoning to a suite of vision-language models (VLMs) in in-domain and out-of-domain spatial reasoning datasets. We hope these resources lower the barrier to entry for exploring spatial understanding tailored to robotics. + +# 3. Approach + +We begin by explaining the selection of three spatial relationships: spatial context, spatial compatibility, and spatial configuration. Next, we describe the data generation pipeline used to construct the ROBOSPATIAL. Figure 2 provides an overview of the dataset. + +# 3.1. Spatial Relationships + +The dataset is organized around three core spatial relationships that we believe address the essential aspects of spatial reasoning for robotic tasks: spatial context, spatial compatibility, and spatial configuration. Context allows robots to assess the relationship between objects and their surrounding space, facilitating the identification of empty or occupied areas, which is relevant for downstream applications such as path planning and obstacle avoidance. Compatibility focuses on whether objects can coexist or interact without conflict in a given space, which is vital for object placement, assembly, and operational safety. Configuration enables robots to understand and interpret the relative positioning of objects, which is crucial for directing navigation, manipulation, and interaction within complex environments. Together, these spatial relationships provide a more nuanced and practical framework for robotic applications than metrics like distance—which is hard to normalize across different scales, environments, and tasks—thereby enabling robots to perform complex tasks with greater reliability. + +# 3.2. Dataset Generation + +The goal of the data construction pipeline is to generate a large-scale, high-accuracy spatial relationship dataset with minimal human intervention, using automatic heuristics grounded in 3D geometry and 2D image views. + +The pipeline takes as input a scene dataset $\mathcal{D}_s$ that contains RGB images, camera poses (both extrinsic and intrinsic parameters), and oriented 3D bounding box annotations with semantic object labels. The output is a spatial reasoning dataset $\mathcal{D}$ , where each entry $d_i = \langle I_i, q_i, a_i, l_i \rangle$ consists of an image $I_i$ , a question $q_i$ , an answer $a_i$ , and a reference frame label $l_i \in \{ego, world, object\}$ . Each question is derived from one of three spatial reasoning categories: spatial configuration, spatial context, or spatial compatibility. To support reliable object reference resolution, we also generate an auxiliary object grounding dataset that links object descriptions to 2D bounding boxes. + +To improve clarity and reproducibility, we describe the data generation pipeline in two main stages. We also separate the reasoning logic used for extracting 3D relationships from that used for generating 2D image-space targets. + +# 3.2.1. Stage 1: 3D Spatial Relation Extraction + +The first stage involves extracting spatial relationships between objects or between objects and free space, based on 3D geometry. Each spatial relation is defined as $s_i = \langle I_i, a_i, t_i, r_i, l_i \rangle$ , where $I_i$ is the source image, $a_i$ is the anchor object, $t_i$ is the target object or a sampled point in free space, $r_i \in \{left, right, above, below, front, behind\}$ is the relation preposition, and $l_i \in \{ego, world, object\}$ denotes the reference frame. + +We use oriented 3D bounding boxes, provided by the source dataset, to compute spatial relationships. Each bounding box includes both the 3D location and heading of the object. The object's orientation is defined by the heading vector of the bounding box, aligned with the object's front-facing direction. Using this orientation, we determine the appropriate directional region (e.g., front, left) relative to the reference frame. For instance, a relation such as "in front of (anchor object) (object frame)" refers to the positive direction along the anchor object's heading vector. These relationships are calculated independently for each of the three reference frames: the world frame is aligned with the dataset-level coordinate system; the ego frame is defined by the camera pose (i.e., camera-centered); and the object frame is defined by the local orientation of the anchor object. + +The camera extrinsics are used to transform coordinates between reference frames. Although the method does not require point clouds or meshes, it relies on camera intrinsics and extrinsics to project between 2D and 3D and to ensure consistent reference frame reasoning. For each spatial configuration task, we evaluate all visible object pairs that appear uniquely in the image, avoiding duplicate instances to minimize ambiguity. The resulting relationships are binary (True/False) and specify whether the spatial condition holds for the given object pair. + +# 3.2.2. Stage 2: 2D Spatial Point and Region Sampling + +In the second stage, we generate 2D image-space annotations for spatial context and spatial compatibility tasks. These rely on the 3D bounding box layout and calibrated camera parameters to map spatial relationships into image coordinates. + +For spatial context, we construct a top-down occupancy map of the scene by marking regions occupied by 3D bounding boxes. We then randomly sample 3D points in empty space that lie in a specified directional relation to the anchor object, following the same frame-dependent heuristics as in the configuration task. These points are projected into the image plane using the camera intrinsics. To ensure the points are valid, we filter out samples that are obstructed or occluded based on line-of-sight from the camera. Specifically, we perform raycasting from the camera center to each sampled 3D point, and discard points whose rays + +intersect any occupied bounding box volumes before reaching the target location. The final answer is a list of 2D $(x,y)$ image coordinates that satisfy the spatial context constraint. + +Spatial compatibility extends this idea by checking whether a target object can fit within the sampled region. We simulate placing a virtual bounding box, matching the size of the target object, at the candidate location on the ground plane. A region is considered compatible if the simulated placement does not intersect with any existing bounding boxes in the scene and provides at least a $10\mathrm{cm}$ margin along each axis. The simulation allows for translation and in-plane rotation of the object. The answer to this task is binary (True/False), indicating whether the region can accommodate the object. + +# 3.2.3. Question-Answer Generation + +Once the spatial relations $\{s_i\}$ have been extracted, we generate corresponding question-answer pairs $\{d_i\}$ using structured templates. Each question follows the format: $\{\mathrm{TARGET}\} \{\mathrm{RELATION}\} \{\mathrm{ANCHOR}\} \{\mathrm{REF.}$ FRAME\} where the relation and frame are defined in Section 3.2.1. To ensure that models learn from visual grounding rather than linguistic priors, we use deterministic templates that avoid ambiguity and minimize reliance on commonsense. + +Each spatial relation type—context, compatibility, and configuration—has a corresponding question format. Configuration and compatibility tasks result in binary (True/False) answers. Context questions produce a list of valid 2D coordinates in image space. + +Correctly resolving which object is being referred to in a spatial question is essential for reliable spatial understanding. To reduce errors arising from incorrect object identification, we additionally generate an auxiliary object grounding dataset that links object descriptions to 2D bounding boxes in the image. These grounding annotations are derived by projecting 3D bounding boxes into image space using camera intrinsics and extrinsics. This supervision helps models more accurately resolve references during spatial reasoning and is included during training. See Appendix B.3 for details. + +Using this pipeline, we generate around 3 million spatial relationships and their associated question-answer pairs. This scale is an order of magnitude larger than prior spatial reasoning datasets (see Table 1). + +# 4. Experiments + +# 4.1. Setup + +We apply the data generation pipeline to three scene datasets—ScanNet [8], Matterport3D [4], and 3RScan [56]—and two tabletop datasets—HOPE [54] and GraspNet-1B [12]. We retrieve 3D bounding box annotations and embodied images from EmbodiedScan [58], and generate a large-scale spatial reasoning dataset covering + +
DatasetTypeSplitsImagesQA pairs
IndoorTrain4916 scans883k images2.7M
Validation40 scans1k images3k
TabletopTrain190 scenes76k images220k
Validation77 scenes355 images3k
+ +Table 2. Dataset splits for indoor and tabletop dataset. Detailed data statistics are in the Appendix. + +diverse indoor environments: larger scenes for navigation and smaller object-centric setups for manipulation. + +In total, ROBOSPATIAL includes approximately 3M spatial QA pairs across 5k 3D scans and 1M images. (Table 2 provides a breakdown; values are rounded to the nearest thousand for clarity.) + +# 4.1.1. Trained 2D/3D VLMs + +2D VLMs. We evaluate several vision-language models (VLMs) using RGB-only image inputs. Our selected base VLMs are VILA-1.5-8B [30] and LLaVA-NeXT-8B [35]. We also include three specialized models: SpaceLLaVA-13B (a community version of SpatialVLM [5]), RoboPoint-13B [62] (trained to predict points in empty space given an object reference), and Molmo-7B [9] (designed for pointing and counting). We also include GPT-4o [42] as a closed-source baseline. We omit models such as SpatialRGPT [6] that depend on external mask inputs, as they bypass the object grounding challenge. + +3D VLMs. Models operating over 3D data must handle richer, more complex spatial representations. We include two models that process 3D inputs: 3D-LLM [18], which reconstructs colored 3D point clouds from multi-view RGB images, and LEO [20], which operates on segmented colored point clouds of individual objects. These models allow us to explore spatial reasoning when models consume RGBD or point cloud representations directly. + +Fine-tuning. We evaluate models in both zero-shot and fine-tuned settings, using ROBOSPATIAL to fine-tune open-source models. To mitigate failure cases arising from poor object grounding, we also include an auxiliary grounding dataset during training, which provides additional supervision for object reference resolution. This auxiliary dataset does not contribute to spatial reasoning performance. (See Appendix for ablation experiments.) + +# 4.1.2. Spatial Understanding Evaluation + +We evaluate spatial reasoning capabilities using ROBOSPATIAL-Val, a held-out validation subset of ROBOSPATIAL sampled from scans that are entirely unseen during training. This benchmark comprises 6,000 heuristically generated questions from our data generation pipeline, with 2,000 questions per spatial relation type. Questions fall into two categories: binary yes/no questions and coordinate prediction tasks. For yes/no questions, we report accuracy. For co + +
ModelIndoorTabletopAverage
ConfigurationContextCompatibilityConfigurationContextCompatibilityIndoorTabletopTotal
Open-source VLMs
2D VLMs
VILA [30]54.718.356.345.113.253.843.137.440.2
+ROBOSPATIAL71.4↑45.9↑77.2↑71.8↑43.7↑73.3↑64.8↑62.9↑63.9↑
LLaVA-NeXT [35]48.912.532.748.38.430.931.429.230.3
+ROBOSPATIAL69.3↑41.3↑70.5↑70.7↑44.8↑66.1↑60.4↑60.5↑60.5↑
SpaceLLaVA [5]52.615.349.066.512.260.138.946.243.6
+ROBOSPATIAL76.0↑50.7↑76.6↑74.9↑46.4↑70.5↑67.8↑63.6↑65.7↑
RoboPoint [62]39.041.438.337.931.645.239.638.238.9
+ROBOSPATIAL72.2↑68.9↑72.1↑70.3↑61.7↑78.4↑71.0↑70.1↑70.6↑
3D VLMs
3D-LLM [18]54.58.153.659.210.657.437.642.440.0
+ROBOSPATIAL76.3↑35.4↑77.5↑76.2↑46.8↑75.0↑63.1↑66.0↑64.6↑
LEO [20]56.111.358.360.811.159.341.943.742.8
+ROBOSPATIAL80.2↑56.7↑82.5↑78.1↑55.2↑78.9↑73.1↑70.7↑71.9↑
Not available for fine-tuning
2D VLMs
Molmo [9]40.648.260.061.535.854.649.650.650.1
GPT-4o [42]63.525.159.462.327.966.849.352.350.8
+ +Table 3. Results of existing 2D/3D VLMs on a held-out validation split (ROBOSPATIAL-Val) of images and scans. All methods, for all tasks, perform better $(\uparrow)$ when fine-tuned on ROBOSPATIAL. The best result for each column is bolded. + +
ModelROBOSPATIAL-HomeBLINKSpatialBench
ConfigurationContextCompatibilityAccuracyAccuracy
2D VLMs
VILA [30]57.80.069.072.753.0
+ROBOSPATIAL65.9 ↑15.6 ↑78.0 ↑79.7 ↑73.6 ↑
LLaVA-NeXT [35]60.20.071.471.355.9
+ROBOSPATIAL76.4 ↑19.7 ↑80.1 ↑79.0 ↑70.6 ↑
SpaceLLaVA [5]61.00.0834.376.247.1
+ROBOSPATIAL71.6 ↑13.1 ↑62.0 ↑81.8 ↑67.7 ↑
RoboPoint [62]59.42.580.163.644.1
+ROBOSPATIAL70.0 ↑21.3 ↑88.6 ↑70.6 ↑64.7 ↑
3D VLMs
3D-LLM [18]39.80.035.2N/AN/A
+ROBOSPATIAL55.2 ↑8.2 ↑52.3 ↑N/AN/A
LEO [20]51.20.038.1N/AN/A
+ROBOSPATIAL64.2 ↑10.0 ↑57.1 ↑N/AN/A
Not available for fine-tuning
Molmo [9]48.70.024.867.155.9
GPT-4o [42]74.06.655.276.270.6
+ +Table 4. Results on an out-of-domain test split comparing prior art VLMs. The results show improved $(\uparrow)$ spatial understanding capabilities on similar domains. Bolded number is the best result for the column. + +ordinate predictions, we evaluate whether the model's predicted 3D location lies within the convex hull of a reference point set derived from scene geometry. + +While this convex hull criterion provides a well-defined geometric target, it is arguably overly strict—e.g., predictions near but just outside the boundary are marked incorrect. As a result, reported scores represent a conservative estimate of each model's spatial understanding. ROBOSPA-TIAL-Val serves as the primary benchmark for comparing + +2D and 3D VLMs trained on ROBOSPATIAL, enabling controlled evaluation within the same data distribution. Results are presented in Table 3. + +# 4.1.3. Cross-Dataset Generalization Evaluation + +To assess generalization across environment types, we partition the training data into indoor-scene and tabletop subsets. Models are trained on one type and evaluated on held-out datasets from the other. Despite differing object distributions and scene layouts, we observe a positive synergy between indoor and tabletop environments: training on one environment type improves spatial reasoning on the other, as shown in Table 5. + +# 4.1.4. Out-of-Domain Evaluation + +To test the out-of-domain transferability of ROBOSPATIAL-trained models, we evaluate on three benchmarks: ROBOSPATIAL-Home, BLINK [15], and SpatialBench [2]. ROBOSPATIAL-Home contains 350 manually written spatial questions over diverse real-world RGBD scenes captured with an iPhone equipped with a depth sensor. We curated this benchmark to evaluate generalization to novel indoor settings with previously unseen objects. BLINK is a visual reasoning benchmark consisting of binary spatial questions involving relationships such as "next to," "touching," and "on top." BLINK allows us to assess the ability of models to assess generalization of spatial reasoning to unseen language configurations. We evaluate only the spatial portion of BLINK, as that aligns with the core focus of ROBOSPATIAL. SpatialBench, introduced in the Spa + +# Spatial Context + +Q. Pinpoint several points within the vacant space situated to the right of the desk. + +![](images/6c037c47b118a0d8af57bcad6a98407ea6c0c58515f8c602fd73d389c5a7bd27.jpg) + +Q. Pinpoint several points within the vacant space situated in front of the frame. + +![](images/228debf747067f35951549779331263e6cb0c17323b33ef7142303238fb6b03c.jpg) + +Q. Pinpoint several points within the vacant space situated to the right of the table. + +![](images/fc9bbfa225ee3915ac8e9670253100cc374f45cca4359742de2bbcd5c845a41c.jpg) +Figure 3. In-domain (ROBOSPATIAL-Val, top) and out-of-domain (ROBOSPATIAL-Home, BLINK [15], middle and bottom) results for ROBOSPATIAL-trained models. Two models shown: SL (SpaceLLaVA [5]) and RP (RoboPoint [62]); the -FT suffix indicates fine-tuning on ROBOSPATIAL. Correct answers in green. All images except bottom-right in the out-of-domain rows are from ROBOSPATIAL-Home. + +# Spatial Compatibility + +Q. Can the apple fit in front of the bowl? Yes + +![](images/3bd7b5531894afda7dd5793848fa62bf4a3a9a6e15b15ed88651fd691a67c3dc.jpg) + +Q. Can the lamp fit right of the table? Yes + +![](images/4a0c87d334ba7344da80d3a23a0080aefcb9f6f271cfbb2ad5c03739ae9ed108.jpg) + +Q. Can the lamp fit left of the bed? Yes + +![](images/65cf40ffcc5312e9800e28ffeff9ecbdbdb477ad24436f84e6aad34aac19d959.jpg) + +![](images/5044f3e34d4b6da1f5b2e7261d78f9b277dc8c68cbedfcdd0c0ff209a3e6d06f.jpg) + +![](images/80b1d076a6881b0a4f777af7d5c108445bd839ba1489e49bdf04cdda06032c3d.jpg) + +![](images/13523fdf9071f50579ddc4a21164f9cc88173c3bb0289c03c67860123b408d13.jpg) + +# Spatial Configuration + +Q. Is the frame in front of the window? No + +![](images/531aac4acad5c019a436262ba5acc45b896d7a9df8ef24a2b37762b2cb3066f4.jpg) + +Q. Is the shelf in front of the bathtub? Yes + +![](images/a90eeaaa431fcd621106cc02923c1c1f8bdaa896c3578c381abb3388a0848c7c.jpg) + +Q. Is the couch under the truck? No + +![](images/63fec83f50c0e6e103ffbcc8954f329082c8d04bfed82b2a7c68850c267cb8d6.jpg) + +![](images/0360fadc2923ec0e27fe22608e4420418b2ccbaeb510d97329fb00fef6ae4faf.jpg) + +![](images/21598ebc4e2a8474dfaf620379fbf866b24e6b8848d43175bb50e388127c2542.jpg) + +![](images/5dced79f14be84445dcec7bc7e4de89c01031e68236d9327b791c41323daf368.jpg) + +RP $\bullet$ RP-FT $\bullet$ GT $\bullet$ + +tialBot [2] paper, uses RGB inputs and tests spatial understanding across several categories. We focus on the position category, which most directly aligns with our emphasis on spatial localization and placement. Together, these benchmarks complement ROBOSPATIAL-Val by covering a broader range of visual and linguistic variation. + +# 4.2. Results + +We evaluate the effectiveness of ROBOSpatial in improving spatial reasoning capabilities in VLMs across held-out and out-of-domain benchmarks. In this section, we focus on analyzing the model's generalization and understanding of spatial relationships. We address the following questions: + +How well does ROBOSPATIAL training generalize to unseen spatial relationships? Although ROBOSPATIAL consists of template-generated QA pairs with a fixed set of spatial prepositions, we observe in Tab. 4 that models trained on it can generalize to spatial relationships not explicitly included in the training set. This is particularly evident in evaluations on the BLINK dataset [15], which contains diverse prepositions such as "under," "next to," and "far away." We attribute this generalization to the fact that ROBOSPATIAL encompasses all six principal directions in 3D space (along the x, y, and z axes). Generalizing to new + +prepositions often requires mapping linguistic expressions (e.g., "on top of," "under") to these spatial primitives—a task at which LLMs are naturally proficient. For example, "on top of" often refers to "above" in a world-centric frame, while "under" maps to "below." Moreover, prepositions such as "next to" or "beside" imply proximity between objects. Because ROBOSPATIAL includes questions that require generating points near a reference object, it implicitly teaches the concept of closeness. This enables trained models to understand these proximity-based relationships, even if they are not explicitly represented during training. + +Do ROBOSPATIAL-trained models understand nuanced perspectives? Spatial references in natural language often imply specific reference frames. For instance, "in front of the car" typically refers to the direction of the car's front hood. In ROBOSPATIAL-Home, we omit explicit frame specifications in the questions to evaluate whether models can align with the implicit reference frame intended by the questioner. We find that models trained with ROBOSPATIAL can often infer the correct frame of reference, suggesting that they have learned to associate object geometries and orientations with spatial language. Figure 3 shows examples such as "Is the frame in front of the window?", where the model accurately identifies the intended spatial relation. + +
Indoor ↓ TabletopTabletop ↓ Indoor
RoboPoint [62]38.738.2
+ROBOSpatial48.9 ↑51.3 ↑
LEO [20]41.943.7
+ROBOSpatial47.2 ↑54.5 ↑
+ +Table 5. Cross-dataset generalization results between indoor and tabletop environments. + +
ModelSuccess (%)
Open-source
LLaVA-NeXT [35]23.7
+ ROBOSpatial52.6↑
RoboPoint [62]44.7
+ ROBOSpatial46.2↑
Not available for fine-tuning
Molmo [9]43.8
GPT-4o [42]46.9
+ +Table 6. Robot experiment results. + +![](images/357ddf1fcabdd327f0a98645774c14e0c46bc9a3f52b77862feebe723adb7b7b.jpg) +Task: Place the object in a free space in front of the pony. + +![](images/4e56584b3ff6e654994f1ba19673e19e88d05e33931888947a30f77c3cd6c7d5.jpg) +Task: Place the object in a free space in front of the orange juice box. +Figure 4. Robotics experiments: the red dot shows the model output (if not present, the model failed to provide a valid point in the image); green dots are used to show when a model outputs multiple points. The robot motion generator, cuRobo [52], is used to grasp the item referenced by the generated point. The spatial- prefix indicates model trained with ROBOSPATIAL. + +Are 3D VLMs better at learning spatial relationships than 2D VLMs? The findings in Tab. 3 suggest that 3D VLMs tend to outperform 2D counterparts in spatial reasoning tasks, likely due to their ability to directly utilize depth information. However, this comparison is not entirely fair: models like 3D-LLM [18] and LEO [20] are pretrained on RGB-D indoor scan datasets, some of which overlap with the environments used in the source datasets (e.g., Matterport3D, ScanNet). This gives them prior exposure to scene geometry and object layouts, which may bias their performance. To support more controlled and fair comparisons in the future, we designed ROBOSPATIAL to be compatible with both 2D and 3D modalities, allowing researchers to investigate the impact of modality, architecture, and pretraining data under unified evaluation protocols. + +# 4.3. Real Robot Experiments + +We design a suite of tabletop manipulation tasks requiring spatial reasoning. The setup includes a Kinova Jaco robot [3], paired with a ZED2 camera for RGB-D perception. The robot system implements actions to pick and place objects on the table using cuRobo [52] for motion planning. Tasks include spatial questions that require a yes/no answer, and pick-and-place instructions that require successfully controlling the robot to complete the task. We adopt a modular design, where the VLM is queried for spatial understanding, and the resulting predictions (e.g., target points) are passed to a separate motion planning system for execution. We use a range of simple, unambiguous objects—colored cubes, cylinders, food items, and toys—to + +ensure the challenge lies in spatial understanding rather than object recognition (Figure 4). In total, we conducted over 200 model queries. Details of the questions and scene configurations are provided in the Appendix D.5. We evaluate the following VLMs: LLaVA-NeXT [35] and RoboPoint [62], both with and without ROBOSPATIAL training; and two strong baselines, Molmo [9] and GPT-4o [42]. Table 6 and Figure 4 present the results. + +Experiments show that LLaVA-NeXT fine-tuned on ROBOSPATIAL achieves the highest success rate across all models. Training with ROBOSPATIAL enhances spatial understanding in 2D VLMs, enabling the model to correctly interpret instructions such as "place in front of the pony," where placement is aligned with the pony's head direction. It also demonstrates sensitivity to object scale, as in the task "place in front of the orange juice box," where the model places the object at a reasonable distance. In contrast, baseline models such as RoboPoint frequently place objects too far from the target, likely due to limited understanding of spatial proximity. We also observe that spatial failures in 2D VLMs often stem from errors in projecting 2D predictions into 3D. Even a small 2-pixel shift in image space can translate to a $5 - 10\mathrm{cm}$ error in the physical world, which is significant in manipulation tasks. Nonetheless, models trained on ROBOSPATIAL produce more accurate predictions, reducing these failure cases and showing the benefit of dataset-driven improvements. Interestingly, GPT-4o performs comparably to ROBOSPATIAL-trained RoboPoint. We attribute this to GPT-4o's broader language understanding and instruction-following ability, which partially compensates for its lack of task-specific spatial training. Looking forward, promising directions include investigating how viewpoint affects 2D spatial predictions, and developing 3D VLMs that can reason over partial point clouds—removing the need for complete 3D scans and making deployment in real-world systems more feasible. + +# 5. Conclusion + +We introduce ROBOSPATIAL, ROBOSPATIAL-Val, and ROBOSPATIAL-Home, a large-scale 2D/3D spatial understanding training and evaluation dataset tailored for robotics. Experimental results show that models trained with ROBOSPATIAL are able to understand spatial relationships, generalize to unseen relationships, and infer nuanced reference frames, making them applicable in a wide range of tasks that require spatial understanding. We further demonstrate the real-world applicability of ROBOSPATIAL with robot experiments. In addition, our automatic data generation pipeline can be used to extend the dataset to new data sources and spatial relations. We show that ROBOSPATIAL has the potential to serve as a foundation for broader applications in robotics which require spatial understanding. + +# Acknowledgements + +The authors thank Youngsun Wi, Hyunho Ahn, Hojin Yoo, and Minjae Bae for providing images in the ROBOSPATIAL-Home dataset. Our research was supported in part by ARL W911NF2220144 and resources from the Ohio Supercomputer Center. 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(Left) Robotic visual instruction is a hand-drawn approach for commanding robots, utilizing circles and arrows to convey task definition. In long-horizon tasks, green and blue sketches denote the first and second task steps, respectively. (Right) It illustrates the action sequences output via VIEW. Our method exhibits robust generalization to real-world manipulation tasks, including (a) trajectory-following tasks, (b) cluttered environments with disturbances, and (c) multi-step operations. + +# Abstract + +Recently, natural language has been the primary medium for human-robot interaction. However, its inherent lack of spatial precision for robotic control introduces challenges such as ambiguity and morbidity. To address these limitations, we introduce the Robotic Visual Instruction (RoVI), a novel paradigm to guide robotic tasks through an object-centric, hand-drawn symbolic representation. RoVI effectively encodes spatial-temporal information into human-interpretable visual instructions through 2D sketches, utilizing arrows, circles, colors, and numbers to direct 3D robotic manipulation. To enable robots to understand RoVI better and generate precise actions based on RoVI, we present Visual Instruction Embodied Workflow (VIEW), a pipeline formulated for RoVI-conditioned policies. This approach leverages Vision-Language Models (VLMs) to interpret RoVI inputs, decode spatial and temporal constraints from 2D pixel space via keypoint extraction, and then trans + +form them into executable 3D action sequences. We additionally curate a specialized dataset of 15K instances to fine-tune small VLMs for edge deployment, enabling them to effectively learn RoVI capabilities. Our approach is rigorously validated across 11 novel tasks in both real and simulated environments, demonstrating significant generalization capability. Notably, VIEW achieves an $87.5\%$ success rate in real-world scenarios involving unseen tasks that feature multi-step actions, with disturbances, and trajectory-following requirements. Code and Datasets in this paper will be released soon. + +# 1. Introduction + +Natural language, is not always the optimal medium between humans and robots. Alternatively, sketching visual instructions convey more precise spatiotemporal information. Traditionally, communication between humans and robots relies on natural language, leveraging the advances + +![](images/adc69fa5c0211a3bb8133760c147dcf8f7b81de910a97c7b75118a6b91c70c99.jpg) + +![](images/12e32b682f9bff34540f67dafcec865cb249adfc3d8e00133a756de84a26206d.jpg) +Language Instruction + +![](images/b724e1032ff5bd65bd3ca2fcf171a968d791283bdf155f60876750681ea77022.jpg) + +![](images/c7a9ef3ca4a63eee5af47a879c0bef8271e1cb60e7b0dd86e63394804e7d7e30.jpg) + +![](images/d033cf48ee4a4cc08d76e673d9fe856029206b0697b1db811e1af5ffbaf31576.jpg) + +![](images/7d9d0dc8a8e0ac8197109391d142495531fa8e04dee619c515b2fd9dc0115168.jpg) + +![](images/dc1f867f4828beb7e541e0b1926bd4876595d6d953085f879e6c72e2e978f02a.jpg) + +![](images/eecd06ba1ba5df5a362568df5a1b4f94df500b55343a4f7422562261156cdb93.jpg) + +![](images/716d1fe2e692b720f5bda2f714cb6659a8fc62323d99a559bab610ba535e42d5.jpg) + +![](images/da2df95924ad242e1cce4ac8b7283b1773024b5f538202cde24f92d3c39337f8.jpg) + +![](images/4c66a1db6cfa4fa930e7cdcd7e83479df77c52db1e938e0b7feb2f2d0444f46d.jpg) +Trajectory + +![](images/f7577c44e2741a2d967b6fa6b9f78317bde61a4af9d154820f18a834e2dce27f.jpg) +Cannot Read + +![](images/cd8039df7b3d5a55c7c36a643d89ddb982279efda3ed741fdd0d4e600fe3d761.jpg) + +![](images/246a9d46359eaf1292df7151c3df4b07194eef5954112d609d66eb76c863c7ed.jpg) + +![](images/59da3d2369b650100937f80114100abc999c3c699b03de05f95e8275a09784d8.jpg) +# +Pick up the snack located slightly left of center. + +![](images/56ad693c5ad24d44edc8f80a469b975bdbb56bdb3eff5bbb3bcdd4944a1853d2.jpg) +Move the lemon close to and below the potato. + +![](images/ba3630d3820648783516f65a608ac429fd9946982b15480042ed9f2da36a9f90.jpg) +Figure 2. (Left) RoVI achieves an optimal balance of user-friendliness, interpretability, and spatiotemporal alignment. (Right) It shows examples and corresponding pros and cons of four types of human-robot interaction methods. + +![](images/97c08df824fb8ecf1aa348ae150f6e4e2aad1cbbdb909357567e74f19bd2c895.jpg) +Goal image + +![](images/4a21749d870c5c1c396ae34dd27ceaa68f62ef181f8494b9fa1a600a06912636.jpg) +contradiction + +![](images/aa9f8c32330061c1f2af2185fff21c8dbf6801d84c4c6d9dfc8fee9f1feb7785.jpg) + +![](images/8a82b16d5b12afffe8ab39a0a99e0ddcb1df15c890e0516ab450c38fcbbaf386.jpg) +Visual Instruction +Simple & Clear + +![](images/f209bb32e3d0ad989823f8e59ed0cf23054df88d53df4bc0edebcc8e6c3b28f6.jpg) + +![](images/c82de1810b3cbe8d773707dd0a0982928fa0416a82546a1d7d345fc727aa6b5c.jpg) + +![](images/ce5155965a814125b04bac285593dba7d6d8ee6d7054b9718b40fc0abb8b3f1d.jpg) + +![](images/9191a1ff7def78b459c0e303ae85b8bf86195a6d021c89a6d911a7a40cdc0d98.jpg) + +in large language models (LLMs) to convert verbal or textual language instructions into executable actions for robots [7, 9, 33, 39]. While natural language is an intuitive and convenient medium for Human-Robot Interaction (HRI), it presents certain challenges. Specifically, natural language has difficulty in describing spatial details such as the precise position, direction, or distance of objects [12, 23]. It is also prone to generating ambiguity and morbidity when expressing spatial requirements [6, 46] shown in Figure 2. Moreover, in certain public environments, such as libraries and hospitals, verbal communication may be inappropriate. + +In contrast, visual modalities—such as goal images [14, 42, 45], trajectories [21, 48, 51], and subgoal images [32, 45]—offer a more direct and precise means of conveying spatio-temporal information. However, the practical application of such methods is not user-friendly shown in Figure 2. The goal image requires the input of the end state of the robotic arm and the scene upon task completion, which contradicts the user's operational sequence. On the other hand, the trajectory represents the complete path of the end effector from the first to the last frame, posing challenges for users to imagine and draw the entire motion process of the robotic arm, which reduces the overall readability for users. + +To address these limitations, we propose a novel communication paradigm: Robotic Visual Instruction (RoVI) shown in the left part of Figure 1, which is a hand-drawn sketch instruction method, an object-centric representation that utilizes 2D symbolic language to command 3D embodiments. This paradigm offers an intuitive, concise, and silent alternative to natural language instruction. Its basic primitives include arrows, circles, and various colors or numbers to represent different temporal sequences of actions. The arrows indicate the trajectory and direction, while the circles denote affordance location to identify target objects in a cluttered environment. Colors or numbers clearly convey the temporal sequence. By integrating these elements, RoVI compresses a temporal series of 3D coordinates into a human-understandable 2D visual language, thereby achieving an optimal balance of user-friendliness, interpretability, and spatiotemporal alignment, as shown in Figure 2 left. + +In order to better understand RoVI and use it to guide robotic manipulation, we introduce Visual Instruction + +Embodied Workflow (VIEW), a pipeline that transduces two-dimensional RoVI instructions into three-dimensional action sequences for robotic manipulation. VIEW facilitates the robotic interpretation of visual instructions, and translates them into hierarchical language responses and Python code functions via Vision-Language Models (VLMs). To decode temporal information from RoVI for high-level tasks, we decompose these tasks into multiple single-step subtasks based on color or numerical identifiers. Furthermore, we propose a keypoint module to extract keypoints from various RoVI components to serve as additional spatial and temporal constraints. Ultimately, our keypoint-conditioned policy directs the robot to execute the manipulation tasks, considering both spatial and temporal information from RoVI. + +Except for the framework, we develop a dataset of 15K training instances to enable models to learn RoVI capabilities through Parameter-Efficient Fine-Tuning (PEFT) [20, 24]. Through the design outlined above, our approach performs well across diverse unseen tasks in both real-world and simulated environments, showing strong generalization and robustness. Compared to language-conditioned policies, our method achieves superior performance in cluttered settings, multi-step operations, and trajectory-following tasks (see the right part of Figure 1). + +1. We propose a novel human-robot interaction paradigm: RoVI. It employs hand-drawn symbolic representations as robotic instructions, conveying more precise spatial-temporal information within task definition. +2. We design a pipeline, VIEW (Visual Instruction Embodied Workflow), to enable RoVI-conditioned manipulation tasks. +3. We develop an open-source dataset to enable models to learn RoVI capabilities. The lightweight model trained by this dataset demonstrates that VLMs are able to learn this capability with minimal computational resources and simple fine-tuning. + +# 2. Related Work + +Human Robot Interaction. Recent advancements in VLMs have made them a popular choice for language- + +![](images/67725e94cf23611477346249910950b3cde38e69ec58ee5158015336a81d7af4.jpg) +Figure 3. VIEW Architecture. This pipeline begins with a visual instruction drawn onto the initial observation. The VLM generates hierarchical language-to-action outputs, including task definition, detailed planning, and executable functions. The executable functions are then combined with keypoints extracted from the keypoint module and passed to a downstream low-level policy, which enables the robotic arm to execute each action step-by-step. This approach bridges hand-drawn visual instructions with precise robotic actions. + +conditioned policies [3, 8, 10, 22, 27, 33]. Image-conditioned policies are also widely explored, such as goal-image policy [14, 32, 45], multimodal prompts [29], and trajectory-based inputs [21, 48, 51]. One common approach is goal-image conditioning, where a final goal image specifies the desired task's end state. Trajectory-based policy utilizes the full 2D or 3D trajectory of the end-effector as input. However, these input methods present significant challenges for users, as it is often difficult for users to provide such inputs directly in real-world applications. + +Visual Prompting for Robot. Recent studies have explored the use of visual prompts as user input for tasks like Visual Question Answering (VQA) [1, 11, 50]. These models use symbolic forms of language, such as arrows, sketches, and numbers, to assist natural language in providing more accurate VQA. However, these approaches have primarily focused on generalized image-based question-answering tasks, and the domain of visual prompts in robotic manipulation tasks remains largely unexplored. In the context of robot control, some methods use model-generated visual prompts to guide trajectory selection for manipulation [26, 34, 36]. Yet, they still rely on natural language as input. These methods do not resolve the issue with natural language instructions—specifically, the lack of spatial intent in task definitions provided by users. + +Keypoint Constraints for Manipulation. Recent studies [15, 19, 28, 31, 44] have achieved significant advancements in manipulation by leveraging key points to formulate spatiotemporal constraints. However, unlike prior approaches that extract keypoints from environmental objects and then filter them through VLMs reasoning [28], our method directly extracts key points from RoVI symbols (ar + +rows and circles). + +# 3. Robotic Visual Instruction Design + +We present the paradigm design of RoVI, which consists of two visual primitives: an arrow and a circle. Tasks are decomposed into three object-centric motions: moving from A to B (represented by an arrow), rotating an object (a circle indicating affordance with an arrow for rotation degree), and picking up/selecting (represented by a circle). + +Dissecting Arrow. We use 2D arrows to denote the trajectory and temporal sequence of robotic actions. An arrow is decomposed into three components: Tail (Starting Point $p_0$ ), Shaft (Waypoints $\{p_1, \ldots, p_{n-1}\}$ ), and Head (Endpoint $p_n$ ). The starting point $p_0$ marks the grasp position on the object, and the endpoint $p_n$ denotes the action's goal. Intermediate waypoints capture the movement path, forming an ordered set: + +$$ +\operatorname {A r r o w} = \left\{p _ {0}, p _ {1}, \dots , p _ {n} \right\}, \quad p _ {i} \in \mathbb {R} ^ {2}, \tag {1} +$$ + +where $p_i$ are 2D coordinates extracted by a keypoint module. + +Dissecting Circle. The circle highlights key interaction areas on objects. The center point $p_0 \in \mathbb{R}^2$ represents the affordance center and is used for various tasks: as a grasping point, a pivot for rotation, or a pressure point for actions like pressing buttons. + +Drawing Setting. RoVI is drawn directly using a tablet with a bright green color to ensure visibility across backgrounds, aiding both human and VLM recognition. We designed two drawing styles: Loose Style (casual, hand-drawn) and Geometric Style (structured with geometric + +![](images/f706cd1ca8fbc1ecde33f3be249f0eeefc3081f661b433cfd0d0580eda5ff6ba.jpg) +Figure 4. This is an example to demonstrate the RoVI Book dataset, adapted from the Open-X Embodiments dataset [13]. The bottom displays the proportion of each task type. + +components for clearer interpretation by VLMs). We use a circle to signify affordances and replace the arrowhead with a standard triangle as depicted in Figure 10. A comparison of their effectiveness is in Section 6.4. + +# 4. RoVI Book dataset + +To enable VLMs to understand RoVI, we develop a dataset for RoVI-conditioned policy, termed RoVI Book. The dataset shown in Figure 7 comprises 15K image-text question-answer pairs. It includes (1) images of initial task observations annotated with RoVI, (2) simple queries serving as default prompts, and (3) answers generated by GPT-4o [1], covering RoVI analysis, task names, fine-grained planning steps, and Python functions. The original tasks and images were selected from the Open-X Embodiment dataset [13]. Our dataset covers $64\%$ single-step tasks and $36\%$ multi-step tasks, across five fundamental manipulation skills: move an object, rotate an object, pick up, open drawers/cabinets, and close drawers/cabinets. The visual instructions were primarily created using a stylus and drawing software on a tablet. The answers are initially generated using GPT-4o [1] and subsequently refined through semantic filtering based on human feedback. Each task retains its original semantic task name from the Open-X Embodiments [13], while we apply data augmentation to RoVI, introducing 3-8 visual variants, varying paths, drawing styles, and line thickness. Further details are provided in the appendix. + +# 5. Visual Instruction Embodied Workflow + +# 5.1. Overview of Workflow + +The VIEW consists of three components: (1) A VLM $f_{\theta}$ for RoVI understanding and planning, (2) a keypoint module $f_{\delta}$ for generating spatiotemporal constraints [28], and (3) a low-level policy $\pi$ for executing robot actions. + +As shown in Figure 3, the pipeline begins with VLMs that take as input the hand-drawn RoVI $v \in \mathbb{R}^{H \times W \times 3}$ , an initial observation image $X \in \mathbb{R}^{H \times W \times 3}$ , and a system-provided default prompt (further details on the default prompt can be found in the appendix). The VLMs then produce language response $y_{\text{language}}$ and the execution function $y_{\text{code}}$ . Simultaneously, the keypoint module extracts keypoints from the RoVI to generate spatiotemporal constraints, including a starting point $p_0$ , multiple waypoints $p_i$ , and an endpoint $p_n$ . Finally, based on the input $y_{\text{code}}$ and the keypoint coordinates, the low-level policy executes the corresponding actions. + +# 5.2. VLMs for RoVI Understanding + +Given the VLMs' capabilities in visual perception, embedded world knowledge, and reasoning, we use the VLMs to interpret RoVI and translate it into a natural language response $y_{\text{language}}$ . The language response acts as a universal interface for human feedback, enabling verification of VLMs' comprehension and connecting it to downstream low-level policies. Compared with the end-to-end policies [7, 9] directly output parameters in SE(3) action space, $y_{\text{language}}$ incorporates language-base action representations, which generalize more effectively across variable tasks and environments [5, 17, 27]. + +The language response is generated by VLMs with a Chain-of-Thought (CoT) reasoning process. It includes coarse-grained task predictions, providing high-level task descriptions, and fine-grained planning with sub-goal sequences, breaking tasks into smaller steps. Each sub-goal is subsequently converted into executable code functions $y_{\text{code}}$ , which define the necessary actions or skills for the robotic arm, such as move() or grasp(). These functions, combined with keypoint constraints, form a low-level policy for action implementation. A comprehensive example of the model output is provided in the appendix. + +$$ +y _ {\text {l a n g u a g e}}, y _ {\text {c o d e}} = f _ {\theta} (v, X). \tag {2} +$$ + +# 5.3.Keypoint Module + +To decode spatiotemporal information from RoVI, $v \in \mathbb{R}^2$ in pixel space, we first decompose high-level tasks into single-step tasks based on color identifiers. Then, a trained keypoint module, $f_{\delta}$ , provides keypoint constraints, which include sequences of end-effector coordinates and keypoints' semantic functionalities in manipulation such as + +starting points $p_0 \in \mathbb{R}^2$ , waypoints $p_i \in \mathbb{R}^2$ , and endpoints $p_n \in \mathbb{R}^2$ . + +We employ YOLOv8 [30] as $f_{\delta}$ and construct a dataset containing 2k images for its training (see details in the appendix). Compared to open-vocabulary object detection, our strategy simplifies the detection of all objects across different environments to identify components of the RoVI symbols, making it less susceptible to environmental variations or distractor objects (see Experiment Section 6.4). + +# 5.4. Keypoint-Conditioned Low-Level Policy + +We propose a keypoint-conditioned low-level policy that enables a robot to follow a sequence of target poses, defined as keypoints, for manipulation tasks. These keypoints $p_i \in \mathbb{R}^2$ are extracted from action arrows in an RGB image and mapped to 3D coordinates $p_i' \in \mathbb{R}^3$ using depth data from a RGB-D camera. + +These $N$ keypoints are then mapped to a sequence of desired end-effector poses in SE(3) space, which is represented as $\{\mathbf{e}_1,\mathbf{e}_2,\dots ,\mathbf{e}_N\}$ . The initial pose $\mathbf{e}_0$ is obtained using the grasp module [18] based on $p_0\in \mathbb{R}^2$ . The series of poses form the action to be executed. We categorize actions into two types: translation (e.g., move to, push, pull) and rotation (e.g., flip, knock-down, adjust knob). For translational tasks, we assume linear motion without rotation, ensuring stable and simplified planning for rigid object transport. At each time step $t$ , the robot performs: + +1. State Observation: Acquire the current end-effector pose $\mathbf{e}_t \in \mathrm{SE}(3)$ and target keypoint $p_i' \in \mathbb{R}^3$ from the RGB-D camera. +2. Cost Function Minimization: $\mathcal{L}_i(t)$ : Minimize the cost function by moving towards $p_i'$ leveraging motion planning and interpolation. +3. Keypoint Transition: If $\mathcal{L}_i(t) \leq \epsilon$ , mark $p_i'$ as reached and proceed to $p_{i+1}'$ . $i$ accumulates until $i = N$ , then end the current action step. + +The goal at each time step $t$ is to minimize $\mathcal{L}_i(t)$ : + +$$ +\arg \min \mathcal {L} _ {i} (t), \tag {3} +$$ + +$$ +\mathcal {L} _ {i} (t) = \alpha_ {i} \delta_ {\text {t r a n s}} (t) + (1 - \alpha_ {i}) \delta_ {\text {r o t}} (t), \tag {4} +$$ + +where $\alpha_{i}$ indicates the action type: $\alpha_{i} = 1$ for translation and $\alpha_{i} = 0$ for rotation. + +Translational Cost: $\delta_{\mathrm{trans}}(t) = \| \mathbf{e}_t - \mathbf{e}_i\|$ , where $\mathbf{e}_t$ is the current end-effector pose and $\mathbf{e}_i$ is the target pose, with $\| \cdot \|$ denoting the Euclidean norm. + +Rotational Cost: $\delta_{\mathrm{rot}}(t) = |\theta_t - \theta_i|$ , where $\theta_t$ is the current rotation angle, $\theta_i$ is computed as: + +$$ +\theta_ {i} = \arccos \left(\frac {\left(\mathbf {v} _ {i}\right) ^ {\top} \mathbf {v} _ {i + 1}}{\| \mathbf {v} _ {i} \| \| \mathbf {v} _ {i + 1} \|}\right), \tag {5} +$$ + +with $\mathbf{v}_i = p_i' - c$ and $\mathbf{v}_{i + 1} = p_{i + 1}' - c$ , where $c$ is the rotation center. + +# 6. Experiment + +Our experiments aim to conduct in-depth research on the following questions: + +1. How does RoVI perform in generalizing over unseen environments and tasks in the real world and simulation? (section 6.1 and 6.2) +2. How well do current VLMs understand RoVI? (section 6.3) +3. How do the components of RoVI and VIEW impact the overall performance of the whole pipeline? (section 6.4) + +Model Training. We select GPT-4o [1] and LLaVA-13B [37] as the VLMs in VIEW to control the robotic manipulation tasks. We also fine-tune the LLaVA-7B and 13B models [37] using the LoRA [25] on our RoVI Book dataset, with one training epoch and a learning rate of 2e-4. All experiments are conducted on an NVIDIA A40 GPU. + +Drawing Setting. In our experiments, RoVI is generated directly using drawing software on tablets or PCs, with green (RGB: 0, 255, 94) marking the first step of the manipulation task, blue (RGB: 0, 255, 247) marking the second step, and pink (RGB: 255, 106, 138) marking the third step. For more steps, extra color can be assigned flexibly. + +Implement Procedure. We train a YOLOv8 model [30] to extract starting points, waypoints, and endpoints from hand-drawn instructions, providing keypoint constraints. These constraints are used to filter the grasp poses generated by AnyGrasp [18] to obtain the closest one. The obtained 3D coordinates from RGB-D mapping and grasp poses are then input into VLM-generated Python functions for code-based low-level control. + +Manipulation Tasks. We meticulously design 11 tasks: 8 in real environments and 3 in simulated settings shown in Figure 5 and 6. For our method, all tasks and environments are previously unseen, with new objects introduced. Our design includes 7 single-step tasks. Some involve cluttered environments with disturbances, such as 'select a desired object' or 'move between objects', requiring precise spatial alignment and trajectory-following abilities. Additionally, there are 4 multi-stage (Task 6-8 in real environment, Task 3 in simulation) tasks to test further reasoning ability for spatio-temporal dependency. + +# 6.1. Generalization to In-the-Wild Manipulation + +Real World Setting & Baselines. For real-world experiments, we use two robotic arms with two-finger grippers: UFACTORY X-Arm 6 and UR5. Two calibrated RealSense D435 cameras are positioned for top-down and third-person views. Both robotic arms operated at a $20\mathrm{Hz}$ control frequency with an end-effector delta control mode. + +We compare our approach against two language-conditioned policy baselines, CoPa [26] and VoxPoser [27], both leveraging a GPT model for low-level policy control. + +
Robotic BaselineReal WorldAverageRobotic BaselineSimulatorAverage
12345678123
Voxposer [27]30808010030302043.8RT-1-X [7]4020020
CoPa [26]40908060040203045Octo-goal-image [43]1030013.3
VIEW-GPT4o [1]8010090906070908082.5Octo-language [43]10003
VIEW-LLaVA-13B [37] (RoVI Book)90901001007070909087.5VIEW*706010076.6
+ +Table 1. Success Rate in unseen environments and unseen tasks. The numbers correspond to tasks in Figure 5 and Figure 6. VIEW* denotes both VIEW-GPT4o and VIEW-LLaVA 13B (RoVI Book), as their test results are identical. Bold score means the best result. + +![](images/9fdf3d427eea8b51bfa268283564c4054c55e229b6b56ca5f15bc15b9974384e.jpg) +Figure 5. Robotic visual instruction is capable of generalizing to a variety of in-the-wild real-world situations, including multi-stage tasks that require precise spatial coordination, reasoning, and spatio-temporal dependencies, even in cluttered environments with disturbances. + +![](images/98d291ec5464a02212594702ea184756ff5877dbef58df61d95adb68aea5cfdc.jpg) + +![](images/86a5aa3b8acd0093efcdf5f61468ee4cb425a58a3bd1413876a2e5369cc8d45a.jpg) + +![](images/2824f9804f7e33fbc7596d43efcf07c404bce340051d8064943a7e117ced89bc.jpg) + +![](images/1fac03c0b636abf5cf31307fe0fb4f94cb9f9aea6726d531fad4f53e0b7fe34a.jpg) + +![](images/07b850224a7a89d39b5deebf6ae1231b27dc259d21fcae4d16d4a8df45f5f026.jpg) + +![](images/3cc4a885bd61897dbc15d6a1a7d6054ab59bcef9d1c15f0c6376f80321bf9078.jpg) + +![](images/5fae9f992aa44d2d897d8ab5929ad6c903fb734a663671c4754161cd8e6d3946.jpg) + +![](images/ae25216cde025d32ab145909c875ffff34ce7c5b7d54675595971d0c66aa916c.jpg) +Figure 6. Experiment tasks in the SIMPLER [35] environment for the comparative study of language instruction, goal image, and visual instruction. + +![](images/4c60f3a9c1a2af24fc3fc41471a7c5e126ecc9c0b340d6787c233d9d9efa9d1d.jpg) + +![](images/7baab2eae3905eae1dbe13acf9a85bfab3402e9661dd3ca9c4d64fdb4aec90e8.jpg) +Figure 7. Performance comparison of average spatiotemporal alignment across all methods. See supplementary materials for detailed statistics. + +CoPa [26] additionally utilizes Set-of-Mark (SoM) [49] for object tagging as a visual prompt. To ensure a fair comparison, all methods used GPT-4o [1] as the VLM. + +Evaluation Metrics for Action. We report two metrics for assessing manipulation execution: action success rate, measuring the percentage of tasks that meet defined goals, and spatiotemporal alignment, evaluating the consistency of movement trajectories and the alignment of an object's final spatial state with semantic goals. A 6-point Likert scale is used for assessment (details in the appendix). Each task is evaluated over 10 trials. + +Results. Table 1 shows that Voxposer [27] and CoPa [26] struggle with spatial precision tasks, such as 'move the lemon close to and below the potato' and the 'choose a snack' task with similar object disturbances. Both of these two methods also failed in Task 5, indicating the difficulty of the trajectory following. This is due to the inherent ambiguity of language-based instructions, which provide only object-level information, whereas RoVI en + +![](images/0e159499c3644d7c79ef42fd226c1fd6d8ae3f991dc5b75755d8da301d0ff07b.jpg) + +![](images/8015595f996ca8e8b05cf5a5be551cbaa99907954a70fefd21153afd23d2cff5.jpg) + +ables pixel-level precision. In contrast, VIEW performs well on these tasks, as its keypoint module provides spatial constraints and waypoints. Unlike VoxPoser [27] and CoPa [26], which use an open-vocabulary object detector, VIEW's keypoint module focuses on RoVI symbol parts, making it less susceptible to environmental variation or distractors. This enables VIEW's strong generalization and robustness in real-world manipulation tasks. Compared to other approaches that employ VLMs for temporal sequence reasoning in embodied planning, our method also achieves superior performance on long-horizon tasks (Task 6-8). By decomposing multi-step tasks into individual steps guided by color cues, we effectively reduce the complexity of temporal reasoning. + +# 6.2. Comparative Study in Simulation + +Simulation Setting & Baselines. This section compares the manipulation performance of three instruction methods—language instruction, goal-image, and RoVI—in a simulated environment. We use SAPIEN [47] as the simulator and SIMPLER [35] as the base environment. + +For the simulated experiments, we evaluate our approach + +
VLMs w/ RoVIReal WorldSimulator
12345678Average123Average
Small Models0000000000000
Claude 3.5-Sonnet [4]1009501009055506770301005060
Gemini-1.5 Pro [2]1010010010020956057680100033
GPT-4o [1]10010010040609010055811001009097
LLaVA-13B [37] (RoVI Book)94508207514823836827364
+ +Table 2. Task and Planning evaluation in language response. It showcases the capability of existing VLMs to comprehend RoVI. The numbers correspond to tasks in Figure 5 and Figure 6. + +![](images/ec5b219c885835c8f55f14143ddb052cec673771db49d7e36254c275106d5adc.jpg) +RoVI + +![](images/90ab43ac79a48d5e1cf3c719610ae9874d37bf0de3c9213844c4b5e7c8c59d74.jpg) +Octo-goal image + +![](images/e9681e5a9c5a62a8813ce7ed80d56eed48e024b3570c46b984e4678b4f60376b.jpg) +RT-1X +Figure 8. Visual comparison of trajectory between RoVI, natural language, and goal image policies. For each example, we sample six successful action trajectories from 50 trials and find that only RoVI's end state and path are more convergent and controllable. + +against RT-1-X [7] and Octo [43], both of which are end-to-end, language-conditioned Vision-Language-Action (VLA) models trained on the Open X-Embodiment dataset [13]. Octo [43] additionally supports goal-image input modalities. In our setup, we use the same robotic arms and background settings as in their training set and include new tasks in cluttered environments to test generalization. + +Quantitative Analysis. These three tasks are performed in cluttered environments, where both language and goal-image inputs face significant challenges. Long-horizon tasks, in particular, are nearly impossible to accomplish under such conditions. However, our approach performs exceptionally well. These results indicate that end-to-end vision-language-action (VLA) models struggle with generalization to new tasks, while our method demonstrates robust generalization, with performance in simulation closely aligning with real-world outcomes. + +Qualitative Study. To study the potential capability of RoVI, we delve into further qualitative comparison with nature language and goal-image conditioned policies. As shown in Figure 8, RoVI is the only instruction format that effectively conveys both path information and the end state. In contrast, the goal image policy performs well in terms of the end state but falls short in describing movement paths. For methods like RT-X [7] and Octo [43], the generated paths and end states lack consistency and exhibit limited spatial precision. In the evaluated examples, RoVI demonstrates a clear advantage in spatiotemporal alignment. + +![](images/b925147ff7b20c2c4e8756721f07c836f8326d66f449a1533c8abf0b79aef7eb.jpg) +Figure 9. Error breakdown of language responses. Training with the RoVI book significantly reduces errors in action decisions and temporal sequences (highlighted in the black box). + +# 6.3. RoVI Comprehension by Modern VLMs. + +We evaluate the capability of VLMs to extract semantic meaning from RoVI in novel tasks and environments, employing in-context learning and a zero-shot approach (see details in supplementary in-context learning). + +Metrics. We evaluate 'Task and Planning' success rates by assessing the accuracy of language responses using human feedback. This evaluation has two components: 'task', measuring the VLMs' comprehension of task definitions based on RoVI and observations (e.g. 'Open the bottom drawer, then place the clothes inside'); and 'planning', evaluating the reasoning capability of VLMs to decompose complex RoVI tasks into sequential sub-goals. Each task is evaluated over 10 trials. We compare our trained model with diverse VLMs, including large-scale models: GPT-4o [1], Gemini-1.5 Pro [2], Claude 3.5-Sonnet [4], as well as smaller models: InternLM-XComposer2-VL-7B [16], LLaVA-HF/LLaVA-v1.6-Mistral-7B [37], MiniGPT-4 [52], and VIP-LLaVA 7B [11]. + +Results. The Table 2 demonstrates that advanced large models (Gemini [2], GPT-4o [1], Claude [4]) exhibit a strong ability to understand RoVI-conditioned manipulation tasks through in-context learning, even without being trained on expert datasets. In contrast, models with fewer than 13 billion parameters fail to comprehend RoVI effectively. Combining both simulation and real-world performance, GPT-4o [1] exhibits the best overall results. Furthermore, advanced large models generalize better in terms of RoVI comprehension compared to smaller models trained + +![](images/2f577e09413285a987eeed4bfaa6c08f8926969114243e403cb7af0febf8f6a5.jpg) +Figure 10. Showcase of two drawing styles in modified Open X-Embodiment dataset [13]. + +
ModelTask Prediction + Subgoal Planning
MovePick up / ChooseRotateAverage
LGLGLGLG
GPT-4o [1]0.61.00.90.90.21.00.570.97
Gemini 1.5 pro [2]0.10.01.01.01.00.60.70.53
Claude 3.5 sonnet [4]1.00.81.01.00.90.90.970.9
Total Average0.570.60.970.970.70.830.740.8
+ +on the RoVI Book dataset, such as LLaVA-13B [37]. However, as the number of steps in the task increases, the large models' comprehension accuracy decreases. In contrast, LLaVA-13B [37], trained on the RoVI Book dataset, performs well on long-sequence task 8, indicating that the RoVI Book dataset is effective for learning multi-step tasks under RoVI conditions. + +Error Breakdown. It is worth noting that LLaVA-13B [37] (trained on the RoVI Book) shows a low success rate in task and planning predictions but performs exceptionally well in action execution. In conjunction with Figure 9, we can conclude that the execution function maps action and sequence errors, making it unaffected by perception errors. After training on the RoVI Book, errors related to the execution function were significantly reduced. + +# 6.4. Ablations Study + +Drawing. Analogous to how language prompts often require 'prompt engineering', free-form drawing can exhibit significant variability. And hand-drawn instruction raises another question: how can we optimize the drawing style to enhance model comprehension? In this section, we classify the drawing styles into two distinct categories for comparison to investigate their impact on VLMs' reasoning performance. The corresponding visualization and experiments are shown in Figure 10 and Table 3. Our findings indicate that the more structured geometric style yielded superior comprehension. Further experimental details are attached in the supplementary material. + +Table 3. Comparison of drawing styles in modified Open X-Embodiment. 'L' and 'G' denote Loose style and Geometric style respectively. On average, the more structured geometric style offers VLMs better task comprehension ability. + +
TaskMetricGDINO [38]OWL-ViT [40]OWL-V2 [41]YOLOv8 [30]
1MD482.71 ± 0.00N/A114.18 ± 92.656.83 ± 0.00
mAP0.00 ± 0.00N/A0.33 ± 0.471.00 ± 0.00
2MD507.35 ± 183.27N/A52.47 ± 61.4419.45 ± 8.92
mAP0.00 ± 0.00N/A0.57 ± 0.491.00 ± 0.00
3MD510.33 ± 183.25153.92 ± 0.00131.03 ± 33.4313.27 ± 5.81
mAP0.00 ± 0.000.00 ± 0.000.00 ± 0.001.00 ± 0.00
4MD751.44 ± 196.8557.51 ± 89.8563.28 ± 80.4711.64 ± 4.73
mAP0.00 ± 0.000.67 ± 0.470.64 ± 0.481.00 ± 0.00
+ +Table 4. Ablation of the proposed keypoint module. The tested tasks and RoVI are shown in the supplementary material. MD represents mean distance. + +Keypoint Module. We evaluate the proposed keypoint module, a trained YOLOv8 model [30], for spatial constraint generation across four different RoVI tasks. We compare it against three popular open-vocabulary detection models [38, 40, 41], using two strategies: (1) manually inputting the target's semantic information as the text prompt, and (2) identifying and localizing arrow components (arrowhead and tail). Two primary metrics are used for evaluation: Euclidean distance error (measured in pixels) to assess precision, and Mean Average Precision (mAP) at a 50-pixel threshold to measure accuracy. Results in Table 4 indicate that, despite its smaller parameter size, the keypoint module achieves more efficient task-relevant keypoint extraction directly from pixel space compared to transformer-based open-vocabulary detection models. Additional limitations and details can be found in the supplementary material. + +# 7. Conclusion and Future works + +In this paper, we propose Robotic Visual Instruction (RoVI), a user-friendly and spatially precise alternative to natural language for guiding robotic tasks. To implement RoVI, we develop a pipeline, Visual Instruction Embodied Workflow (VIEW), which demonstrates strong generalization and robustness across cluttered environments and long-horizon tasks. Additionally, we meticulously create a dataset to fine-tune VLMs for a better understanding of RoVI and potential future edge device deployment. Ablation studies also reveal the factors influencing the performance of RoVI-conditioned policies, including RoVI comprehension, drawing strategies, and grounding methods. + +Future works. Future research will focus on scaling up the RoVI Book dataset and collecting a wider variety of free-form drawn instruction. This expansion aims to equip the model with a broader understanding of the general principles by which humans employ visual symbols to convey dynamic movements. On the other hand, by scaling up the dataset, we can more efficiently train a smaller model like 7B, further enhancing its ability to interpret RoVI instructions and output code. This will facilitate the deployment of edge devices within our robotic system. + +# 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. arXiv preprint arXiv:2303.08774, 2023. 3, 4, 5, 6, 7, 8 +[2] Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, Katie Millican, et al. Gemini: A family of highly capable multimodal models. arXiv preprint arXiv:2312.11805, 1, 2023. 7, 8 +[3] Anonymous. Embodiedgpt: Vision-language pre-training via embodied chain of thought. Under Review, 2023. 3 +[4] AI Anthropic. The claude 3 model family: Opus, sonnet, haiku. Claude-3 Model Card, 2024. 7, 8 +[5] Suneel Belkhale, Tianli Ding, Ted Xiao, Pierre Sermanet, Quon Vuong, Jonathan Tompson, Yevgen Chebotar, Debidatta Dwibedi, and Dorsa Sadigh. Rt-h: Action hierarchies using language. In https://arxiv.org/abs/2403.01823, 2024.4 +[6] Andrea Bonarini. Communication in human-robot interaction. 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However, the scarcity of diverse, high-quality demonstration data and real-world-aligned evaluation benchmarks severely limits such development. To address this, we introduce RoboTwin, a generative digital twin framework that uses 3D generative foundation models and large language models to produce diverse expert datasets and provide a real-world-aligned evaluation platform for dual-arm robotic tasks. Specifically, RoboTwin creates varied digital twins of objects from single 2D images, generating realistic and interactive scenarios. It also introduces a spatial relation-aware code generation framework that combines object annotations with large language models to break down tasks, determine spatial constraints, and generate precise robotic movement code. Our framework offers a comprehensive benchmark with both simulated and real-world data, enabling standardized evaluation and better alignment between simulated training and real-world performance. We validated our approach using the opensource COBOT Magic Robot platform. Policies pre-trained on RoboTwin-generated data and fine-tuned with limited real-world samples demonstrate significant potential for enhancing dual-arm robotic manipulation systems by improving success rates by over $70\%$ for single-arm tasks and over $40\%$ for dual-arm tasks compared to models trained solely on real-world data. + +# 1. Introduction + +Robotic systems with intricate dual-arm coordination and precise dexterity are essential for complex object manipu + +![](images/5eae7f88450bcbe5003b96564baac3e5f96d2ade93b01b70b4ad235428740517.jpg) +Figure 1. RoboTwin Benchmark. A framework leveraging generative foundational models to generate realistic and interactive training scenarios and diverse expert demonstrations for benchmarking dual-arm robotic manipulation. + +lation to unlock advanced capabilities across domains such as healthcare, manufacturing, logistics, and domestic assistance. However, creating robust and versatile robotic systems that meet these demands remains a challenge, with a major bottleneck being the absence of diverse, high-quality training data and comprehensive evaluation benchmarks that are aligned with the real world. + +Traditional approaches to data collection, particularly human teleoperation [4, 12, 16, 18, 20, 31], yield high-quality demonstrations but face significant practical limitations. While these methods provide reliable training data, they are often prohibitively expensive, time-intensive, and struggle to cover the diverse range of scenarios robots encounter in real-world deployments. To address these limitations, researchers have turned to algorithmic trajectory generators in simulations [15, 23, 34]. These alternatives, however, frequently require task-specific design, hindering their generalizability and scalability. Recent advances such as MimicGen [54] and RoboCaca [59] have demonstrated significant progress in generating large-scale simulated expert data from limited human demonstrations. However, these approaches operate under fixed scenario settings and snug- + +gle to handle task variants beyond their predefined configurations, limiting their generalizability to novel scenarios. + +Another limitation of existing benchmarks is that they predominantly focus on single-arm tasks [23, 55] or bimanual tasks with two separated arms [22], which fail to capture the complexity and coordination requirements inherent in integrated dual-arm systems. While HumanoidBench [64] and BiGym [13] explore benchmarks for humanoid bimanual manipulation, their scalability is limited by fixed environments or reliance on VR teleoperation for demonstration collection. As a result, these gaps highlight the urgent need for a scalable and standardized dual-arm collaboration benchmark with an efficient data collection pipeline. + +To address these challenges, as shown in Fig. 1, we propose RoboTwin, a generative digital twin framework empowered by 3D generative foundation models and large language models (LLMs), aiming to produce diverse expert datasets and provide a real-world-aligned evaluation platform for dual-arm robotic tasks. Starting from a single 2D RGB image, we employ generative foundation models for 3D modeling and texture generation, enabling the efficient creation of varied object instances with different shapes, sizes, and appearances. Each object class is incorporated with spatial annotations, which define function axes, approach axes, lateral axes, and contact points and are applicable across various instances within an object class via feature point matching technology. Building upon these spatially-aware digital twins, RoboTwin leverages LLMs to interpret and decompose complex tasks into manageable sub-tasks. For each sub-task, we infer the constraints of the terminal state. For example, in a hammering task, the functional point of the hammer head needs to align with the surface of the target object. RoboTwin then generates executable code that calculates key poses based on these spatial constraints and object properties, interfacing with underlying planning modules to produce complete, feasible trajectories for execution. + +Within the above framework, our RoboTwin features diverse dual-arm manipulation tasks that combine simulated expert data with real-world teleoperated datasets under consistent environmental and hardware setups. We then benchmark and evaluate the ability of RoboTwin to improve policy generalization in real-world scenarios. Experimental results demonstrated that policies pre-trained on 300 RoboTwin-generated samples and fine-tuned with 20 real-world samples improve the success rate by $70\%$ in single-arm manipulation tasks like hammer beat, and over $40\%$ in dual-arm coordination tasks, such as ball sweep, compared to those trained exclusively on 20 real-world samples. + +We summarize our key contributions as: 1) we establish a convenient real-to-sim pipeline that requires only an RGB image from the real world to generate diverse 3D models of target objects, empowered by a 3D generative foundation + +model; 2) we create a spatial-aware code generation framework, which automatically creates expert-level demonstration data via a large language model and the spatial annotations of the target objects. 3) we develop a standard benchmark for dual-arm manipulation tasks including both real-world teleoperated data and high-fidelity synthetic data generated for corresponding scenarios. These advancements provide a robust framework for generating diverse, high-quality training data and policy evaluation for dual-arm manipulation tasks, significantly contributing to the development of more capable and versatile robotic systems. + +# 2. Related Work + +# 2.1. Datasets and Benchmarks for Robotics + +To collect effective demonstrations for robotic tasks, human teleoperation is the most common approach, where human manually guides a robot across various tasks [18, 31, 50, 51, 53, 57]. Recent advancements have extended this methodology by employing teams of human operators over prolonged periods to assemble substantial real-world datasets [2, 7, 18, 31]. An alternative method employs algorithmic trajectory generators within simulators [15, 23, 30, 34, 74]. Nevertheless, such approaches typically demand manual, task-specific design for individual tasks. Recent initiatives like MimicGen [54] and RoboCaca [59] generate simulated expert data by adapting actions to new object poses, but remain limited to fixed scenarios and predefined task configurations. Furthermore, their reliance on fixed 3D objects limits the diversity of interacting objects and shapes. Besides, Maniskill [23, 69] provides diverse simulation scenarios but lakes automated data collection mechanism. + +In contrast, RoboTwin leverages 3D generative foundation models and LLMs to autonomously create both task variations and corresponding expert demonstrations. From 3D assets, it generates task scenarios and executable code via spatial reasoning, minimizing human intervention and supporting diverse object appearances. + +# 2.2. Dual-arm Manipulation + +While significant advances have been made in single-arm manipulation, coordinated multi-arm manipulation remains largely unexplored. Peract2 [22] offers benchmarks for bimanual tasks with separated arms, but its setup lacks the complexity of integrated dual-arm systems. Humanoid-Bench [64] evaluates dexterous, whole-body manipulation with a humanoid robot in a fixed reinforcement learning benchmark, while BiGym [13] provides a bimanual benchmark but is constrained by VR teleoperation, limiting their scalability in data collection and evaluation. As a benchmark for dual-arm tasks, RoboTwin enables automatic and large-scale coordinated manipulation data generation with comprehensive policy evaluation. + +![](images/eba8465167bef71b9c52cad9a75383cbf5a5ac51696c22d11a17be700f61a488.jpg) +Figure 2. Real-to-simulation transfer and expert data generation. We first leverage a 3D generative foundation model to create diverse 3D assets from 2D images, complete with geometry, normals, and textures. This process is augmented by vision-language models to generate variations of object descriptions, enabling the creation of visually diverse yet functionally consistent 3D models. We then implement a spatial annotation framework that marks key functional and contact points, along with functional, approach, and lateral axes on these 3D assets. Finally, we employ LLMs to generate expert demonstrations by decomposing tasks into subtasks, inferring spatial constraints, and generating collision-free robot behavior executable code that satisfies kinematic requirements. + +# 2.3. Robot Manipulation Learning Methods + +The adoption of human demonstrations to instruct robots in manipulation skills is a prevalent method in Robot Manipulation Learning [5, 6, 11, 14, 19, 32, 48, 49, 66, 73]. Among the techniques, Behavioral Cloning stands out for learning policies offline from these demonstrations. It replicates observed actions from a curated dataset [7, 15, 18, 31, 34, 52, 61, 75]. Conversely, Offline Reinforcement Learning enhances policy learning by optimizing actions based on a predefined reward function and exploiting large datasets [8, 24, 36-39, 47]. The Action Chunking with Transformers (ACT) technique integrates a Transformer-based visuomotor policy with a conditional variational autoencoder to structure the learning of action sequences [67, 70, 76]. Diffusion models have been introduced into robot imitation learning and are gradually becoming a mainstream approach due to their excellent generative capabilities [3, 33, 43-45, 60]. Recently, the Diffusion Policy method has gained prominence. It employs a conditional denoising diffusion process for visuomotor policy representation, effectively reducing the accumulative error in trajectory generation that is often observed in Transformer-based visuomotor policies [14]. The 3D Diffusion Policy [73] uses point clouds for environmental observations, enhancing spatial information utilization and managing various robotic tasks in both simulated and real environments with only a small number of demonstrations. + +# 2.4. LLM for Robotic Code Generation. + +With their remarkable ability in natural language understanding and code generation, Large Language Models (LLMs) have revolutionized numerous domains in artificial intelligence. In robotics, these models have shown excep + +tional capabilities in bridging the gap between natural language commands and executable robot actions [9, 10, 17, 21, 25-29, 42, 46, 58, 65, 71]. Code as Policies [41] and RoboCodeX [10, 56] established that LLMs can effectively translate high-level task descriptions into functional robot control programs. While Rekep [29] advances spatial reasoning between key points, it has limitations in handling functional axis constraints and fails to account for spatial relationships between object functional axes and the table surface during code generation. Furthermore, existing code generation approaches predominantly focus on single-arm robots, overlooking crucial aspects of dual-arm collaboration and active collision avoidance strategies. + +# 3. Bridging Physical and Digital Worlds for Di-verse Robot Behavior Generation + +# 3.1. Generation of Diverse Digital Assets + +Our approach utilizes Deemos's Rodin platform $^{\S}$ to create 3D models from simple 2D RGB images. This method significantly reduces the need for expensive sensors while achieving realistic visual effects and supporting physical simulations. The process begins with capturing photographs of real-world objects. As shown in Fig. 2, we use GPT-4V [1] to analyze these images to generate corresponding descriptions, which are then autonomously modified via language model to create similar yet visually distinct object descriptions. We use these descriptions with SDXL-Turbo [63] to generate a diverse set of 2D images representing various appearances of the same object class. An image-conditioned 3D generation model then processes this + +![](images/e6a31f51ebee2888255826b196e0e3573e347bdf2c1a98b0e875c36e9fd8ca7a.jpg) +Figure 3. Examples of spatial annotations. Function and contact points with principal axes for functional parts and approach directions are extracted semi-automatically within RoboTwin for spatial- and geometry-aware manipulation and code generation. + +collection of images, producing a wide range of 3D models for a single object type. The final output transforms a 2D image into a comprehensive 3D model, featuring detailed geometry, surface normals, wireframes, and textures. We validate asset quality using two complementary approaches: quantitative evaluation via UCLIP-I [40] similarity metrics and qualitative assessment through GPT-4V visual validation. Assets falling below quality thresholds are automatically flagged for regeneration. This dual validation approach ensures both visual and geometry consistency for effective sim-to-real transfer. To ensure physical fidelity, our pipeline leverages GPT-4V to classify object materials and assign appropriate physics parameters with $\pm 5\%$ random variations to enhance robustness. + +# 3.2. Spatial Annotation Framework for 3D Assets + +To enhance the structural integrity and universal applicability of generated assets, we implement a systematic approach for annotating key points and axes on tools. This methodology aims to render the data more comprehensible and accessible to large language models for complex task code generation. As shown in Fig. 3, the annotation process focuses on two primary elements: key points and axes. + +Key Points. Key points represent specific locations on tools directly associated with their functional operations or user interaction points. We distinguish between these two types: (1) Point for Function: This key point designates the primary functional component of the tool, such as the striking surface of a hammer. It defines the tool's functional origin or point of action, directly correlating to the tool's primary purpose in a given task. (2) Point for Contact: This key point indicates the area of interaction between the tool and its user or other objects. It represents the gripping point or contact area, serving as a crucial human-machine interface point. Annotating this point facilitates understanding of tool's operational posture. + +Axes. Axes are used to describe the spatial directionality of tools during task execution, encompassing the direction of functional execution and the tool's approach towards objects. We identify three principal axes: (1) Function Axis: This axis represents the direction in which the tool executes its primary function. It typically aligns with the tool's main operational vector, guiding the understanding of the tool's intended use and movement during task performance. (2) Approach Axis: The approach axis delineates the direction + +in which the tool approaches or is applied to the target object. This axis is crucial for comprehending the spatial relationship between the tool and its subject of operation. (3) Lateral Axis: This axis is perpendicular to both the function and approach axes, completing a three-dimensional coordinate system for the tool. The lateral axis aids in defining the tool's orientation and potential rotational movements during use. + +By systematically annotating these key points and axes, we create a comprehensive spatial framework for each tool. This framework enables a more precise and context-aware understanding of tool functionalities, facilitating improved task planning and execution by large language models. We do not need to repeatedly annotate different 3D models from the same class. Instead, to streamline the annotation process for various 3D models of similar objects, we employ a feature point matching approach leveraging the Stable Diffusion [62] encoder. This method enables the transfer of key points across various 3D models within the same object class. Our approach utilizes feature point matching to determine the target point. Specifically, under the table top view, given a source image $I_{s}$ , a target image $I_{t}$ , and a source point $p_{s}$ , we aim to locate the corresponding point $p_{t}$ in the target image. Following the methodology outlined in [35, 68], we extract diffusion features from both $I_{s}$ and $I_{t}$ . Since these diffusion features correspond to individual pixels in the target image, we can identify the pixel in $I_{t}$ with the highest similarity to $p_{s}$ by analyzing the extracted features. This technique allows for efficient key point migration across different 3D models of similar objects, eliminating the need for redundant annotations and enhancing the overall efficiency of the 3D modeling process. + +# 3.3. Expert Data Generation + +Building upon our spatial annotation framework and expert data generation pipeline, we present a systematic approach to generating robot behaviors that satisfy spatial constraints while ensuring collision-free execution. At the core of our framework lies a comprehensive dual-arm manipulation system with three key capabilities. First, it enables synchronized arm movements through screw motion interpolation coupled with coordinated gripper actions, ensuring stable object handling. Second, it supports independent arm operations for scenarios requiring asymmetric movements. Third, it implements dynamic collision + +avoidance through continuous adjustment of safe intermediate positions between arms. Our motion generation implements a three-stage approach: (1) spatial constraint inference that analyzes object annotations to establish geometric relationships, (2) LLM-based code generation translating constraints into executable code using the MPlib trajectory optimization library, and (3) execution validation ensuring task completion. We incorporate a self-correction mechanism where execution errors are fed back to the language model, with minimal human oversight for complex cases. Leveraging these integrated capabilities, we employ large language models (LLMs) with predefined APIs to systematically generate expert demonstrations across diverse robotic tasks. The process consists of the following detailed steps: + +1. Scene Initialization: The task environment is set up with relevant objects and their initial poses. For instance, a hammering task would involve placing the hammer and target objects in their starting positions. +2. Task Decomposition: Based on human input describing the task, we use LLM to break it down into subtasks. For example, a "hammer a nail" task might be decomposed into: a) grasping the hammer, b) positioning the hammer over the nail, c) striking the nail, and d) returning the hammer to its original position. +3. Constraint Inference: For each sub-task, we use LLM to systematically infer spatial and temporal constraints through a hierarchical constraint analysis process. This analysis begins with identifying the functional relationships between objects' key points and axes. For grasping sub-tasks, we derive constraints between the end-effector's pose and the object's annotated contact points and approach axis, ensuring stable and effective grasps. For manipulation sub-tasks, we establish geometric constraints between the tool's functional points and the target object. These constraints encompass both positional alignments and directional requirements. +4. Robot Behavior Generation: Based on the derived spatial constraints, the LLM proceeds to generate corresponding behavioral code for each sub-task by calling relevant APIs (See prompts and examples in Appendix D). During execution, the system performs precise calculations of end-effector poses based on these spatial constraints. The process begins by identifying functional points on the object within the world coordinate system, which serves as the fundamental reference frame for all subsequent pose calculations. Building upon this foundation, our system implements a dual approach to determine optimal target poses. The first approach leverages pre-labeled contact points on the object to generate grasp poses. This method takes into account both the object's geometric properties and the robot's kinematic limitations. For more complex manipulation tasks, the second approach comes into play, comput + +ing target poses by aligning the object's functional point with a designated target point while adhering to specific directional constraints. To illustrate this, consider a hammering task: the system would align the hammer's head with the nail while calculating the proper orientation for an effective strike. The core of behavior generation for each sub-task is an optimization problem that seeks optimal joint trajectories $\theta(t)$ . Using a screw motion planner, the system minimizes a cost function $J(\theta(t))$ while satisfying all task-specific constraints. This optimization is formulated as: + +$$ +\begin{array}{l} \min _ {\theta (t)} \quad J (\theta (t)) \\ \begin{array}{l} \text {s . t .} \quad \left\{ \begin{array}{l l} \mathbf {T} _ {\mathrm {e e}} = f _ {\mathrm {F K}} (\theta (t)) & (\text {K i n e m a t i c c o n s t r a i n t}) \\ \mathbf {P} _ {\mathrm {e e}} = \mathbf {P} _ {o} - d \cdot \vec {a} _ {o} & (\text {P o s i t i o n a l i g n m e n t}) \\ \vec {n} _ {\mathrm {e e}} = \vec {a} _ {o} & (\text {O r i e n t a t i o n a l i g n m e n t}) \\ \theta (t) \in \mathcal {C}, \forall t \in [ t _ {0}, t _ {f} ] & (\text {C o l l i s i o n a v o i d a n c e}) \end{array} \right. \end{array} \\ \end{array} +$$ + +where, $J(\theta(t))$ represents a cost function that may incorporate factors such as energy efficiency, execution time, and motion smoothness. The constraints ensure that the robot's end-effector pose $\mathbf{T}_{\mathrm{ee}}$ matches the desired pose calculated through the forward kinematics function $f_{\mathrm{FK}}(\theta(t))$ , aligning with the object's contact point $\mathbf{P}_o$ and approach axis $\vec{a}_o$ (position and orientation alignment). Finally, the trajectory $\theta(t)$ must remain within the collision-free configuration space $\mathcal{C}$ throughout the time interval $[t_0, t_f]$ , ensuring collision avoidance. This comprehensive optimization framework enables the generation of robot behaviors that are efficient, satisfy spatial constraints, and guarantee safe, collision-free execution of complex tasks like hammering. + +5. Success Evaluation: We implement criteria to assess successful task completion. For the hammering task, this might include verifying that the nail has been driven to the correct depth. +6. Iterative Refinement: The system gathers error data from multiple sources: runtime error messages, failed trajectory planning steps, and deviations between the final object states and their target configurations. To regenerate improved code, the system takes a comprehensive set of inputs including the collected error information, original task description, object annotations, and the previous version of code. The newly generated code is then tested, and if issues persist, the cycle continues until the desired performance is achieved. + +# 4. Benchmark + +Based on the methods introduced in Sec. 3, we design a comprehensive benchmark called RoboTwin[57] to assess dual-arm robots, which includes 15 tasks in total. The underlying physics engine is ManiSkill3[69]. We employ the + +![](images/98669ed8c62d8831209776a69fcd2115f455e1263f249a1428a23c431936004c.jpg) +Figure 4. Illustration of our robot platform, with the capabilities for teleoperation and data acquisition. + +![](images/7c5d2d7e248d871951f12a3b82dcdadabe911ffbc2fce0b53c75f786e35cf15e.jpg) +Figure 5. Success rate of the generated code for RoboTwin benchmark. + +open-source Robot Magic platform as depicted in Fig. 4, which is equipped with four robot arms and four Intel RealSense D-435 RGBD cameras and is built on the Tracer chassis. These cameras are strategically positioned: one on the high part of the stand for an expansive field of view, two on the wrists of the robot's arms, and one on the low part of the stand which is optional for use. The front, left, and right cameras capture data simultaneously at a frequency of $30\mathrm{Hz}$ . We utilize ManiSkill [69], an open-source simulation platform with GPU-accelerated data collection built on SAPIEN [72]. The details of each task in RoboTwin can be found in Appendix A. + +In RoboTwin benchmark, the agent needs to choose the appropriate collaboration method to successfully complete the task according to the distance of the target object from the left arm and the right arm. It involves the handover of the two arms, such as the handover task and putting the cup on the coaster, and the avoidance of interference between the two arms, such as the shoe placement task, which requires the two arms to coordinate with each other to place a pair of shoes in the limited space of the shoe box. The initial position and posture of the target objects in all our tasks are random. Before the scene is loaded, the mechanical dynamics accessibility of the randomly initialized scene will be checked to ensure that it is feasible. The task also includes objects of different shapes and appearances. The dual bottle pick task includes different models such as Coke bottles, Sprite bottles, and mineral water bottles, all of which are generated from 2D real pictures. The size of the objects in the environment is also randomized within a certain threshold. For each task, we provide well-designed script files that generate expert data across diverse scenarios, including various object placements and environmental conditions. We also report the success rate of generated code using our proposed method in Fig. 5, as described in Sec. 3.3. + +For each task in our benchmark, we have pre-collected 100 sets of simulation data and 20 sets of real-world data. The hardware setup for the real-world experiments strictly matches that of the simulation environment. In both the simulation and real-world datasets, each captured frame consists of three images from the cameras, each provid + +ing an RGB and depth image. We also provide the point cloud data transformed from depth image, and colored point cloud data transformed from RGB and depth image for different types of algorithm evaluation. Additionally, the data includes the poses of the robotic arms' joints and end-effectors for both master and slave configurations, encompassing both left and right arms. + +# 5. Experiment on RoboTwin Benchmark + +# 5.1. Baselines and Experimental Setup + +Diffusion Policy is a generative model for robotic imitation learning that models the distribution of potential actions to create diverse and complex action sequences. The approach has evolved into two main variants based on input dimensionality: The 2D Diffusion Policy [14] processes two-dimensional visual information like images and video frames to predict actions for robotic manipulation tasks. While effective for many applications, this approach may have limitations in tasks requiring depth perception and spatial reasoning. The 3D Diffusion Policy (DP3)[73] addresses these limitations by incorporating three-dimensional visual representations through point clouds. By using efficient point encoders to create compact 3D representations, DP3 enhances spatial awareness and demonstrates improved performance in tasks requiring complex spatial understanding. + +We evaluated both 3D (DP3, w & w/o color) and 2D (DP) input imitation learning methods across 14 benchmark tasks, as shown in Fig. 6, tailoring our assessment approach to each model's characteristics using 20, 50, 100 expert demonstrations. The success rate is determined by satisfying the target pose constraints after execution completion and achieving collision-free trajectory execution throughout the task. + +# 5.2. Experimental Results + +As shown in Table 1, the experimental results reveal distinct performance patterns across different imitation learning methods. DP3 demonstrates superior few-shot learning capabilities, achieving remarkable performance with + +![](images/eb24a3fec5aad930b28dfa043670512d2f5c302e443085481c29773d488ba2f4.jpg) +Figure 6. Examples of task execution in the RoboTwin benchmark. + +
Number of Demonstrations20501002050100
Block Hammer BeatBlock Handover
DP3 (XYZ)55.7 ± 8.564.7 ± 10.155.7 ± 0.6DP3 (XYZ)89.0 ± 2.684.3 ± 9.177.3 ± 11.6
DP3 (XYZ+RGB)47.7 ± 4.079.3 ± 3.882.0 ± 6.6DP3 (XYZ+RGB)86.0 ± 1.094.0 ± 0.085.3 ± 14.5
DP0.0 ± 0.00.0 ± 0.00.0 ± 0.0DP0.0 ± 0.012.0 ± 5.076.0 ± 16.1
Bottle AdjustContainer Place
DP3 (XYZ)64.7 ± 10.871.7 ± 13.873.3 ± 12.5DP3 (XYZ)52.7 ± 5.077.7 ± 2.585.3 ± 3.2
DP3 (XYZ+RGB)25.0 ± 5.036.0 ± 8.542.0 ± 7.0DP3 (XYZ+RGB)37.3 ± 2.151.3 ± 7.162.3 ± 6.8
DP6.3 ± 5.933.7 ± 9.035.7 ± 2.9DP1.7 ± 0.68.0 ± 1.714.0 ± 6.9
Empty Cup PlaceMug Hanging (Easy)
DP3 (XYZ)33.7 ± 4.271.3 ± 4.061.7 ± 13.1DP3 (XYZ)7.3 ± 3.214.0 ± 3.615.3 ± 4.0
DP3 (XYZ+RGB)23.7 ± 5.568.0 ± 7.581.0 ± 2.6DP3 (XYZ+RGB)4.3 ± 3.11.7 ± 1.53.0 ± 1.0
DP0.0 ± 0.025.0 ± 2.687.7 ± 0.6DP0.0 ± 0.00.0 ± 0.00.0 ± 0.0
Mug Hanging (Hard)Pick Apple Messy
DP3 (XYZ)4.0 ± 1.710.7 ± 3.115.3 ± 5.5DP3 (XYZ)4.0 ± 1.712.7 ± 5.59.7 ± 2.1
DP3 (XYZ+RGB)0.0 ± 0.01.7 ± 1.22.3 ± 2.5DP3 (XYZ+RGB)6.0 ± 2.631.0 ± 7.554.0 ± 12.8
DP0.0 ± 0.00.0 ± 0.00.0 ± 0.0DP5.3 ± 2.516.7 ± 1.529.3 ± 5.0
Put Apple CabinetDual Bottles Pick (Easy)
DP3 (XYZ)50.0 ± 38.273.3 ± 9.266.3 ± 22.3DP3 (XYZ)40.3 ± 8.074.7 ± 2.955.3 ± 11.5
DP3 (XYZ+RGB)53.7 ± 14.254.3 ± 17.478.3 ± 3.8DP3 (XYZ+RGB)36.7 ± 5.974.7 ± 5.575.7 ± 17
DP0.0 ± 0.00.0 ± 0.08.0 ± 12.2DP1.7 ± 0.638.3 ± 6.785.7 ± 6.7
Dual Bottles Pick (Hard)Diverse Bottles Pick
DP3 (XYZ)31.7 ± 9.048.0 ± 7.958.0 ± 3.0DP3 (XYZ)11.3 ± 2.132.3 ± 10.137.0 ± 10.0
DP3 (XYZ+RGB)28.0 ± 4.447.3 ± 4.255.7 ± 4.9DP3 (XYZ+RGB)2.0 ± 1.07.7 ± 4.014.7 ± 4.7
DP8.0 ± 2.039.3 ± 4.059.3 ± 5.5DP0.7 ± 0.60.3 ± 0.612.0 ± 5.3
Shoe PlaceDual Shoes Place
DP3 (XYZ)38.0 ± 11.559.3 ± 7.454.3 ± 0.6DP3 (XYZ)4.0 ± 1.07.7 ± 2.112.0 ± 1.7
DP3 (XYZ+RGB)14.0 ± 2.644.3 ± 2.954.0 ± 11.5DP3 (XYZ+RGB)1.7 ± 1.53.3 ± 0.66.0 ± 1.0
DP3.0 ± 1.24.3 ± 3.233.0 ± 15.8DP0.0 ± 0.01.7 ± 1.23.0 ± 1.0
+ +Table 1. Benchmarking imitation learning algorithms for dual-arm manipulation under D435 camera setting. We tested on 14 tasks with 20, 50, and 100 expert demonstrations on DP3 (XYZ), DP3 (XYZ+RGB), and DP with 3 seeds and reported the success rate. + +![](images/58cc11342f89846d2dcf63b1caeff160f5a3ccc7982adc639c9221a572a721e4.jpg) +Figure 7. Comparison on scaling up real and simulation data. + +merely 20 demonstrations. However, its performance exhibits limited scalability, with minimal improvements or even decreases as training data expands to 100 samples. Conversely, the DP algorithm shows poor initial perfor + +mance with limited data, likely due to insufficient geometric priors, but demonstrates significant scalability as training samples increase. With 100 demonstrations, DP outperforms DP3 in several tasks, significantly improving from 1. $7\%$ to $85.7\%$ in the Dual Bottles Pick (Easy) task. This indicates superior learning capabilities with larger datasets. The integration of RGB data with point cloud representations yields inconsistent benefits, highlighting a fundamental limitation in current bimanual manipulation approaches. While DP3 $(XYZ + RGB)$ shows dramatic improvements in cluttered environments such as Pick Apple Messy, it simultaneously exhibits performance degradation in some other tasks like Container Place. This indicates that better fusion representations of RGB semantic information and point cloud 3D information need to be developed (see more results in Appendix Table 4). + +![](images/b9e596da80801bbebf51e606635a11b01ed6afaa70675c1941b8327bdfa3d856.jpg) +Figure 8. Visualization of Real Scene and Simulation Scene. More details can be found in Appendix Fig. 9. + +![](images/aec8ad113ea9321f833367f808fee06197832a92a32e04aeb84afcbe48240005.jpg) + +
Success Rates
Task20 real300Sim+20Real
Bottle Pick (Easy)0/5042/50
Bottle Pick (Hard)0/5016/50
Container Place0/5049/50
Cup Place1/5039/50
Hammer Beat2/5037/50
Average1.2%72%
+ +Experimental results show significant performance variation based on coordination complexity. Simple operations like Dual Bottles Pick achieved high success rates (85.7% with DP at 100 demonstrations), while tasks requiring complex bimanual coordination, such as Dual Shoes Place, performed poorly (below 15% success across all methods). Notably, tasks demanding complex dual-arm coordination significantly underperformed compared to those where robot arms could operate more independently, with arm selection based primarily on proximity to target objects. This highlights the current limitations in dual-arm coordination within imitation learning algorithms. + +# 5.3. Real World Experiment + +To validate the effectiveness of RoboTwin-generated training data in real-world policy deployment, we conducted comprehensive experiments on both single-arm and dual-arm manipulation tasks, as shown in Fig. 8. We conducted a comparative experiment between policies trained solely on 20 real-world datasets and those pre-trained on 300 simulation datasets before fine-tuning on 20 real-world datasets (see more details and results in Appendix B). + +The selection of 300 simulation datasets as our hyperparameter was based on empirical evidence shown in Fig. 7. Through progressive scaling of real-world data, we found that combining 300 simulation datasets with 20 real-world datasets yielded comparable performance than using 300 real-world datasets alone for both single-arm bottle pick and dual-arm cup placement tasks. + +To investigate the performance disparity between baseline algorithms in single-arm versus dual-arm tasks, we conducted sim-to-real transfer experiments for both task categories. Each task underwent 50 test trials with randomized initial configurations, including varying object positions and orientations, as well as robot arm placements + +Table 2. Real world evaluation with a single arm. + +
Success Rates
Task20 real300Sim+20Real
Dual bottle Pick (Easy)0/5031/50
Dual bottle Pick (Hard)0/5011/50
Container Place25/5044/50
Cup Place0/5026/50
Sweep Ball25/5043/50
Average20%62%
+ +Table 3. Real world evaluation with dual arms. + +within predetermined boundaries. As shown in Table 2 and Table 3, experimental results revealed that policies trained on the combined dataset achieved markedly superior performance in real-world testing scenarios. Specifically, the integration of simulation data yielded a $72\%$ improvement in success rates for single-arm tasks compared to policies trained exclusively on real-world data. For the more complex dual-arm tasks, we observed a significant improvement of over $40\%$ in success rates. Our findings validate the effectiveness of our benchmark and data generation approach in bridging the sim-to-real gap, suggesting a promising direction for developing more robust and generalizable policies for dual-arm robotic manipulation tasks. + +We observed significant disparities between single-arm and dual-arm scenarios. In the bottle rearrangement task, dual-arm operations presented substantially greater challenges, primarily due to the diverse initial states of target bottles (upright or lying down). While the incorporation of simulation data enabled the policy to achieve non-zero success rates, the overall performance remained suboptimal. This underscores the pressing need for developing more effective imitation learning algorithms specifically tailored to dual-arm coordination tasks. + +# 6. Conclusion + +This work introduces RoboTwin, a comprehensive benchmark integrating real-world and synthetic data for dual-arm robotic manipulation. Building upon the COBOT Magic Robot platform and leveraging 3D generative models for generative digital twins, our framework enables the efficient generation of diverse training data from single RGB images. Furthermore, our spatial-aware code generation framework automatically produces expert demonstrations by combining object annotations with LLMs to decompose complex tasks and generate precise movements. Experiments show that policies trained with RoboTwin-simulated data achieve higher success rates with less real data compared to those trained solely on real-world data. These results confirm our approach effectively bridges the sim-to-real gap while identifying limitations in dual-arm coordination tasks. Future work will focus on developing advanced algorithms for dual-arm coordination and expanding the framework to handle more complex manipulation tasks. + +# Acknowledgements + +We extend our profound gratitude to D-robotics for their invaluable support in supplying the necessary cloud computing resources that facilitated the execution of this research. Furthermore, we extend sincere appreciation to Deeoms for their contribution in providing essential model support, which was pivotal to the successful completion of this study. This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000 and the General Research Fund of Hong Kong No.17200622 and 17209324. + +# References + +[1] Gpt-4v(ision) system card. 2023. 3 +[2] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Keerthana Gopalakrishnan, Karol Hausman, Alex Herzog, et al. Do as i can, not as i say: Grounding language in robotic affordances. arXiv preprint arXiv:2204.01691, 2022. 2 +[3] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua B Tenenbaum, Tommi S Jaakkola, and Pulkit Agrawal. Is conditional generative modeling all you need for decision making? 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Phan, and Wei Xiang* La Trobe University + +{m.do, k.han, p.lai, k.phan, w.xiang}@latrobe.edu.au + +# Abstract + +Foundation models for remote sensing have garnered increasing attention for their strong performance across various observation tasks. However, current models lack robustness in managing diverse input types and handling incomplete data in downstream tasks. In this paper, we propose RobSense, a robust multi-modal foundation model for Multi-spectral and Synthetic Aperture Radar data. RobSense is designed with modular components and pre-trained by a combination of temporal multimodal alignment and masked autoencoder strategies on a huge-scale dataset. Therefore, it can effectively support diverse input types, from static to temporal, uni-modal to multi-modal. To further handle the incomplete data, we incorporate two uni-modal latent reconstructors that recover rich representations from incomplete inputs, addressing variability in spectral bands and temporal sequence irregularities. Extensive experiments demonstrate that RobSense consistently outperforms state-of-the-art baselines on complete datasets across four input types for segmentation, classification, and change detection. On incomplete datasets, RobSense outperforms the baselines by considerably larger margins when the missing rate increases. Project page: https://ikhado.github.io/robsense/ + +# 1. Introduction + +Remote sensing data play a crucial role in Earth observation, offering a rich array of information essential for understanding our planet. To analyze this data effectively across tasks such as land use and land cover mapping, scene classification, and more, deep learning models have become increasingly popular [23]. Typically, these models rely on supervised learning, which requires a substantial amount of annotated data to achieve high performance on specific tasks. However, collecting + +and labeling this data demands significant resources and considerable human effort [10], posing a major challenge. This challenge is especially pronounced in remote sensing, where annotation requires specialized expertise to accurately interpret the data [27]. + +Meanwhile, there is a large volume of unlabelled data collected from Sentinel missions. These missions mainly consist of Sentinel-2 acquiring Multi-spectral (MS) imagery and Sentinel-1 acquiring Synthetic Aperture Radar (SAR) data. MS imagery provides rich spatial information and enables the identification and analysis of the material composition of objects across multiple spectral bands [8]. SAR data offers all-weather, day-and-night radar, allowing complete monitoring of surface changes regardless of weather conditions [11]. Therefore, designing multi-modal foundation models that integrate both data types through self-supervised pre-training is crucial [7, 8, 21], as it significantly reduces the amount of annotated data required for downstream tasks. + +Foundation models have achieved remarkable success in diverse domains, including computer vision and language processing [13, 26]. However, their development for remote sensing remains underexplored. Recently, emerging models have begun to address this gap [4, 7]. These models can be classified as either uni-modal, which handles a single type of data, or multi-modal, which integrates multiple data types. Both typically employ a self-supervised learning approach. This approach leverages Masked Autoencoder strategy (MAE) [4, 20], which involves reconstructing masked portions of the input. For uni-modal models, the typical input consists of MS images. These images can be divided into patches across all bands [4] or 3D tube-shaped patches [9] spanning several adjacent bands. Meanwhile, multi-modal models integrate SAR data with MS images. To capture the latent representations between these two modalities, contrastive learning is commonly applied alongside MAE [7]. While these models demonstrate promising results on various downstream tasks, two key robustness challenges remain: supporting diverse input types and effectively handling incomplete data. + +The first challenge is designing a foundation model that supports diverse input types in downstream tasks. The current models only support limited input types. Tab. 1 illustrates the adaptability of recent representative models across four input types. SatMAE++ [18] mainly supports static MS inputs. While SatlasNet [1] and SpectralGPT [9] can process from static to temporal MS inputs, they are not capable of handling multi-modal input. In contrast, Croma [7] processes multi-modal data by integrating MS and SAR data with patch contrastive learning, applying contrastive loss to spatially aligned MS-SAR patch pairs as positives and non-aligned patches as negatives. However, it heavily relies on data augmentation, which can lead to information loss in latent representations from two heterogeneous modalities. This issue is especially evident when MS-SAR patches are misaligned or neighboring patches representing the same scene are mistakenly treated as negative pairs across modalities [7, 30]. Moreover, Croma is limited to static inputs and does not support temporal downstream datasets. + +The second challenge is to enhance model performance when handling incomplete downstream datasets. None of the existing models directly address the incomplete data in the downstream tasks. Two critical scenarios often cause this incompleteness: (i) varying the number of spectral bands and (ii) irregularities in temporal sequences. Firstly, existing models typically require downstream datasets to have a fixed number of spectral bands as in the pretraining datasets. However, the number of spectral bands can vary due to different capturing instruments in practice, e.g. Sentinel-2, Landsat-8, etc., [15] as well as factors such as extreme atmospheric conditions or physical degradation [17]. Therefore, this variation limits the adaptability of models in downstream datasets affected by such conditions. Secondly, in practice, capturing data frequently from the same location is challenging [15]. This infrequency leads to time point gaps in temporal sequences. These gaps lead to missing information about fluctuations in human activities or seasonal patterns. This issue could result in sparse representations in the latent space, causing information loss while fine-tuning models. + +To address the aforementioned challenges, we propose a robust multi-modal foundation model tailored for MS and SAR data, namely RobSense. We design two parallel Vision Transformer [6] (ViT)-based encoders for uni-modal inputs, called uni-modal encoders, along with a multi-modal encoder that integrates representations from these uni-modal encoders to produce multi-modal representations. To facilitate multi-modal learning and prevent information loss, we employ two pre-training phases, namely temporal multi-modal learning and latent reconstruction learning. The first phase focuses on enhancing latent representations between two modalities. In order to preserve specific + +Table 1. Supported input types in recent representative remote sensing foundation models. + +
ModelSupported input type
Static uni-modalStatic multi-modalTemporal uni-modalTemporal multi-modal
SatlasNet [1]✓✓
SpectralGPT [9]✓✓
SatMAE++ [18]✓
Croma [7]✓✓
RobSense (ours)✓✓✓✓
+ +information about seasonal changes, human activities, etc., in the representations for each time-point, we employ multivariate Kullback-Leibler (KL) divergence as temporal distribution alignment (TDA). This technique treats each time step of the MS-SAR sequences as a Gaussian distribution, constraining two uni-modal representations at the same time point to the same distribution. The second phase aims to bolster the performance with incomplete inputs. Specifically, we design two latent reconstructors following two uni-modal encoders to recover rich representations caused by variational spectral bands or gaps in temporal sequences. In summary, the main contributions of this paper are as follows: + +- We propose RobSense, a robust multi-modal foundation model for remote sensing that supports diverse input types, including static to temporal, uni-modal to multimodal, and incomplete data. +- We propose a temporal multi-modal learning for remote sensing, which leverages temporal multi-modal data through distribution alignment over time to preserve time-specific distributions. Therefore, our model produces consistent and rich representations. +- To address the data incompleteness, we design two unimodal latent reconstructors, enabling the recovery of rich representations from sparse ones caused by incomplete remote sensing data. +- Extensive experiments show that RobSense outperforms recent baselines on three key downstream tasks with the complete datasets. Furthermore, RobSense consistently surpasses baselines on incomplete downstream datasets across various missing rates, with a larger performance margin as the missing rate increases. + +# 2. Related Work + +Remote sensing foundation models have gained significant attention due to their ability to apply to various tasks. There are two primary approaches for training these models: multi-task learning and self-supervised learning. + +Multi-task learning offers generalization benefits by leveraging shared information across related tasks. Wang et al. [25] adopted an aerial scene recognition dataset for pre-training three backbones, i.e., CNN, ViT, and ViTAE. + +These models were subsequently evaluated across four downstream tasks to assess their performance. SatlasNet [1] was simultaneously pre-trained on seven label types with seven heads, leveraged by the incorporation of different common tasks. Although these models demonstrate the ability to handle diverse downstream tasks, they require a large amount of annotated data, making them resource-intensive and challenging to scale. + +Meanwhile, self-supervised learning has recently become more prevalent and provided an alternative by reducing dependency on annotated datasets [23]. A common strategy in self-supervised learning is MAE, which reconstructs the original input from randomly masked data portions. This strategy allows models to learn rich, generalized representations. SatMAE [4] is one of the pioneering models applying MAE to MS images, employing different masking strategies across spatial and temporal dimensions. Building on this, SatMAE++ [18] improves performance by utilizing multiscale reconstruction with multi-level convolutional-based blocks. Danfeng et al. [9] introduced a 3D spatial-spectral masking strategy to preserve spectral continuity. While these models have demonstrated promising results on various downstream tasks, they are limited to the MS modality. Other efforts [7, 12, 16] have explored multi-modal data integration by combining MAE with a contrastive learning objective. This approach faces challenges with information loss, particularly when positive pairs in the contrastive learning objective are not well-aligned spatially. Moreover, these models predominantly process static inputs and lack robustness in the temporal dimension. + +Unlike previous models, which are pre-trained on either static multi-modal data or static/temporal uni-modal data, the proposed model leverages temporal multi-modal data to capture rich representations across both multi-view and temporal dimensions. Therefore, it supports diverse input types and effectively addresses the critical issue of incomplete downstream datasets. + +# 3. Method + +In this section, we first detail the pre-training stage of RobSense, detailing each phase. We then demonstrate its downstream usage. + +# 3.1. Pre-training + +Fig. 1 illustrates the two phases of the pre-training stage: temporal multi-modal learning and latent reconstruction learning. The first phase focuses on training two uni-modal encoders, the multi-modal encoder, and the multi-modal decoder. This phase employs temporal distribution alignment to enable the encoders to generate rich representations from complete data. In the second + +phase, we train two uni-modal latent reconstructors to recover the rich representations from sparse ones caused by incomplete data. This phase ensures that the model is resilient to missing information. For both phases, the input is the temporal multi-modal pair, $pair = (ms, sar)$ , with sequence length $T$ . + +# 3.1.1 Temporal Multi-modal Learning + +The primary objective of this training phase is to train two uni-modal encoders ( $G_{MS}$ and $G_{SAR}$ for MS and SAR, respectively), multi-modal encoder ( $MG$ ), and multimodal decoder ( $MD$ ). The uni-modal encoders process the sequence of uni-modal time point $\mathbf{x} \in \mathbb{R}^{H \times W \times C}$ from the temporal pair ( $ms, sar$ ), where $H, W$ , and $C$ denote the height, width, and number of bands, respectively. The time point $\mathbf{x}$ is patchified into non-overlapping patches as the sequence $\mathbf{x} = \{\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_L\}$ , where $\mathbf{x}_i \in \mathbb{R}^{p \times p \times C}$ , $p$ is the patch size, $L = (H / p) \cdot (W / p)$ is the number of patches. As a result, the temporal dimension of $ms$ and $sar$ is $(T, L, p, p, C)$ . Then, each patch is passed into the patch embedding $f_p: \mathbb{R}^{p \times p \times C} \mapsto \mathbb{R}^d$ to create sequence $(T, L, d)$ with embedding vector $\mathbf{x}' \in \mathbb{R}^{L \times d}$ of each time point $\mathbf{x}$ . In order to enable efficient learning of rich representations, we employ the MAE [24] strategy, which randomly keeps a set $\mathbb{V}$ of visible patch embeddings and masks other invisible patch embeddings from each embedding vector $\mathbf{x}'$ . We apply consistent masking [21], which means that the masking regions are consistent across all time points $\mathbf{x}$ from $(ms, sar)$ . The masking ratio is chosen as $90\%$ to facilitate effective training [9]. The resulting masked embedding vector is denoted as $\tilde{\mathbf{x}}' \in \mathbb{R}^{|\mathbb{V}| \times d}$ . To incorporate temporal information from the temporal sequences, we employ the joined embedding of position and acquisition day of the year ( $DOY$ ) [31] corresponding to $\mathbf{x}$ . The $k^{th}$ element of the embedding vector $PE(DOY_x)$ is defined as Eq. (1). + +$$ +P E \left(D O Y _ {\mathbf {x}}\right) _ {k} = \left\{ \begin{array}{l l} \sin \left(\frac {D O Y _ {i}}{1 0 0 0 0 ^ {2 j / d}}\right), & \text {i f} k = 2 j, \\ \cos \left(\frac {D O Y _ {i}}{1 0 0 0 0 ^ {2 j / d}}\right), & \text {i f} k = 2 j + 1. \end{array} \right. \tag {1} +$$ + +The masked embedding vector with $PE(DOY_{\mathbf{x}})$ is passed into the uni-modal encoder. The time point representation of the time point $\mathbf{x}$ is computed as $z = G(\tilde{x}^{\prime} + PE(DOY_{\mathbf{x}}))$ . Therefore, the latent representations for $ms$ and $sar$ are presented as $\mathbf{z}_{ms}$ and $\mathbf{z}_{sar}$ , respectively. After passing the uni-modal encoders, the zero vectors are inserted into the output to form the complete set of latent representations $(\mathbf{z}_{ms},\mathbf{z}_{sar}) = \left(\{z_{ms}^{t}\}_{t = 1}^{T},\{z_{sar}^{t}\}_{t = 1}^{T}\right)$ . + +Temporal Distribution Alignment Loss (TDA). In multi-modal learning, effectively extracting the information from the heterogeneous between modalities is important. + +![](images/0173b459b1dedc6367128f6fe865d85011641fee3520a73eac1adb0d4f05015d.jpg) +Figure 1. Illustration of RobSense pre-training, which consists of two training phases: Temporal Multi-modal Learning for training MS/SAR encoder, multi-modal encoder and multi-modal decoder, and Latent Reconstruction Learning for training Latent MS/SAR reconstructor. TSD stands for Time-specific Distribution. + +The prior study [7] uses contrastive learning, which struggles to control positive and negative patch pairs, often causing information loss [4, 30]. To address this, we introduce temporal distribution alignment that leverages temporal multi-modal data to constrain latent representations from both modalities. This approach ensures that two uni-modal representations with similar timestamps follow a consistent distribution, preserving time-specific distribution at each time point. This enables the model to produce consistent, rich representations across both modal and temporal dimensions. + +Every time point representation $z$ within the temporal latent representations $(\mathbf{z}_{ms},\mathbf{z}_{sar})$ is presented under a single Gaussian distribution $\mathcal{N}(\mathbf{x};\mu ,\sigma^2)$ with the mean $\mu$ and the standard deviation $\sigma$ . Therefore, the whole temporal sequence is the multivariate Gaussian distribution. In particular, the modalities MS and SAR follow the continuous distributions $P_{ms}(\mathbf{z})\sim \mathcal{N}(\mathbf{z}_{ms};\boldsymbol{\mu}_{ms},\boldsymbol{\Sigma}_{ms}^{2})$ and $P_{sar}(\mathbf{z})\sim \mathcal{N}(\mathbf{z}_{sar};\boldsymbol{\mu}_{sar},\boldsymbol{\Sigma}_{sar}^{2})$ with the expectations $\pmb {\mu}\in \mathbb{R}^{T\times 1}$ and the diagonal matrix of standard deviation $\pmb {\Sigma}\in \mathbb{R}^{T\times T}$ . KL divergence aligns the distributions of two temporal sequences by quantifying the divergence between their corresponding multivariate Gaussian distributions. In particular, the KL divergence from $P_{ms}(\mathbf{z})$ distribution to $P_{sar}(\mathbf{z})$ is presented as Eq. (2), + +$$ +\operatorname {K L} _ {(m s, s a r)} = \int P _ {m s} (\mathbf {z}) \log \frac {P _ {m s} (\mathbf {z})}{P _ {s a r} (\mathbf {z})} d \mathbf {z}, \tag {2} +$$ + +and the KL divergence can be expressed by Gaussian + +process as Eq. (3), + +$$ +\begin{array}{l} \mathrm {K L} _ {(m s, s a r)} = \frac {1}{2} \left[ \log \frac {\left| \boldsymbol {\Sigma} _ {s a r} \right|}{\left| \boldsymbol {\Sigma} _ {m s} \right|} + \operatorname {T r} \left(\boldsymbol {\Sigma} _ {s a r} ^ {- 1} \boldsymbol {\Sigma} _ {m s}\right) \right. \tag {3} \\ \left. + \Delta_ {m s, s a r} ^ {\top} \Sigma_ {s a r} ^ {- 1} \Delta_ {m s, s a r} - T \right], \\ \end{array} +$$ + +where $\Delta_{ms,sar} = (\pmb{\mu}_{sar} - \pmb{\mu}_{ms})$ . Since KL divergence is not symmetric, the TDA loss for this phase is the mean between $\mathrm{KL}_{(ms,sar)}$ and $\mathrm{KL}_{(sar,ms)}$ as Eq. (4), + +$$ +\mathcal {L} _ {\mathrm {T D A}} = \frac {1}{2} \left(\mathrm {K L} _ {(m s, s a r)} + \mathrm {K L} _ {(s a r, m s)}\right). \tag {4} +$$ + +Autoencoder Loss. The temporal latent representations pair $\mathbf{z}_{ms},\mathbf{z}_{sar}$ are concatenated and forwarded through the multi-modal encoder and decoder to recover the original patches. The set of recovered patches for each time point $\mathbf{x}$ is denoted as $\hat{\mathbf{x}}$ . The autoencoder loss $(\mathcal{L}_{\mathrm{AE}})$ is computed as Eq. (5), + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {A E}} = \frac {1}{N _ {\mathbb {V}}} \sum_ {t = 1} ^ {T} \sum_ {j \notin \mathbb {V}} \left[ \left(\mathbf {x} _ {j, M S} ^ {t} - \hat {\mathbf {x}} _ {j, M S} ^ {t}\right) ^ {2} \right. \tag {5} \\ \left. + \left(\mathbf {x} _ {j, S A R} ^ {t} - \hat {\mathbf {x}} _ {j, S A R} ^ {t}\right) ^ {2} \right], \\ \end{array} +$$ + +where $N_{\mathbb{V}} = 2T(L - |\mathbb{V}|)$ is the total number of invisible patches. The objective is to train the encoders to learn rich + +representation by recovering the invisible patches. In the first pre-training phase, the objective function is formulated by combining the TDA loss and the Autoencoder loss, as $\mathcal{L} = \mathcal{L}_{\mathrm{TDA}} + \mathcal{L}_{\mathrm{AE}}$ + +# 3.1.2 Latent Reconstruction Learning + +This phase aims to enhance the performance of the model to data incompleteness. As shown in Fig. 1, two uni-modal latent reconstructors, i.e., latent MS reconstructor $(R_{MS})$ and latent SAR reconstructor $(R_{SAR})$ are trainable, and other modules are frozen. + +Satellite-based remote sensing data acquisition is often incomplete due to various operational and environmental factors [15]. Furthermore, the diversity of sensors leads to variations in the spectral bands. Consequently, there are two main scenarios: (i) variability in the number of spectral bands and (ii) irregularities in the temporal sequences. Therefore, this phase trains the model to be more resilient, creating two input scenarios by randomly removing (i) invisible spectral bands from MS images and (ii) time points from MS and SAR sequences. + +Band masking in MS images. This scenario simulates the potential absence of certain spectral bands in MS image that may occur in real-world situations. To simulate this, some spectral bands are randomly removed, and zero-valued bands are padded to maintain the total number of bands as $C$ . Let $\mathbf{x} = \{x^{(1)}, x^{(2)}, \ldots, x^{(C)}\}$ be a MS image with $C$ spectral bands. The first three bands (i.e., RGB) are not often absent in remote sensing acquisitions and provide valuable information for reconstructing other spectral bands [2, 14]. Therefore, these bands are kept, while the remaining invisible bands are randomly removed. The resultant image $\mathbf{x}_{\mathrm{drop}}$ is formed by padding the retained channels with a sequence of zero channels, ensuring the total number of channels is $C$ as shown in Eq. (6), + +$$ +\mathbf {x} _ {\text {d r o p}} = \left\{x ^ {(1)}, x ^ {(2)}, x ^ {(3)} \right\} \cup \left\{x ^ {(c)} \mid c \notin \mathcal {C} _ {\text {d r o p}} \right\} \cup \left\{0 ^ {c} \right\} ^ {\left| \mathcal {C} _ {\text {d r o p}} \right|}, \tag {6} +$$ + +where $\mathcal{C}_{\mathrm{drop}}$ is the set of indices corresponding to the dropped channels, and $0^{c} \in \mathcal{R}^{H \times W \times 1}$ is the zeros channel. All the images from the temporal sequence $ms$ are consistently removed with the same band indices to form the sequence $ms_{\mathrm{drop}}$ . + +Time point masking in sequences. The second scenario focuses on the temporal sequences, where time points from both temporal sequences of $ms_{\mathrm{drop}}$ and $sar$ are randomly omitted during training. The approach is similar to the band removal in MS image. A temporal sequence is removed with some time points $\mathbf{x}$ and padded with zero values to keep the total length as $T$ . As a result, the final incomplete pair is presented as $\tilde{pair} = (\tilde{m}s_{\mathrm{drop}},\tilde{s}\tilde{a}r)$ . + +Latent Reconstruction Loss. The main purpose of this loss is to minimize the distance between the reconstructed + +![](images/3b4c7b6d6fde83409510135e11d329587175ec10e1115337cb463a9f7a09f38f.jpg) +Figure 2. Downstream usage of RobSense. By combining different modules, the model can accept either static (sta) or sequential (seq) inputs. It supports both complete (solid line) and incomplete (dashed line) inputs. + +and the rich representations. Mathematically, the latent reconstruction loss $\mathcal{L}_{\mathrm{LatRes}}$ is formulated as Eq. (7) with MSE is the Mean Square Error function, + +$$ +\begin{array}{l} \mathcal {L} _ {\text {L a t R e s}} = \operatorname {M S E} \left(G _ {M S} (m s), R _ {M S} \left(G _ {M S} (\tilde {m} s _ {\text {d r o p}})\right)\right) \\ + \operatorname {M S E} \left(G _ {S A R} (s a r), R _ {S A R} \left(G _ {S A R} (s \tilde {a} r)\right)\right). \tag {7} \\ \end{array} +$$ + +# 3.2. Downstream Usage + +Fig. 2 illustrates different modules that can be flexibly combined to support diverse input types, from uni-modal to multi-modal, from static to temporal, and incomplete data. Specifically, the uni-modal encoders can process uni-modal inputs independently (Fig. 2a) or work alongside the multi-modal encoder to accommodate multi-modal inputs (Fig. 2b). These uni-modal encoders could be followed by the uni-modal latent reconstructors to recover the rich representations from incomplete inputs. + +# 4. Experiments + +# 4.1. Setting + +Pre-training. RobSense is pre-trained on SatlasPretrain dataset [1], which covers all continents except Antarctica. This huge-scale dataset provides both spatial and temporal contexts for multi-modal data, including 9-band MS imagery (B02-B08, B11, and B12) and 2-band SAR data + +(VH and VV). Following Favyen et al. [1], each sequence is limited to $T = 8$ time points, sorted by acquisition date. Temporal alignment is maintained by constraining the time gap between each pair $ms_{i}$ and $sar_{i}$ to a maximum of 30 days. A ViT-Base backbone with 12 layers is used for both the uni-modal and multi-modal encoders. Each uni-modal latent reconstructor has 4 ViT layers due to low-dimensional representations. The decoder, typically narrower than the encoder [9], has half as many layers, consisting of 6 ViT layers. The proposed model is pre-trained in two phases, processing temporal multi-modal MS-SAR data pairs. It operates at a spatial resolution (224, 224) with a patch size of 16. Each phase uses a batch size of 8, an initial learning rate of $1e - 4$ , and a half-cycle cosine decay over 30 epochs. Pre-training utilizes 8 NVIDIA A100 80GB GPUs, totaling about 4,500 GPU hours. + +Fine-tuning. We quantitatively assess the performance of the foundation models on three downstream tasks, i.e., semantic segmentation, classification, and change detection. For comparison, we employ recent models with publicly available pre-trained weights, as shown in Tab. 1. All models are fine-tuned by a single GPU. + +Semantic Segmentation. We use the labelled dataset from SatlasPretrain [1] for land use/land cover segmentation, containing around 53K temporal sequence pairs with MS and SAR modalities. The data is split into $80\%$ for training and $20\%$ for evaluation. Following Danfeng et al. [9], we utilize UperNet [29] as a segmentation head and apply a soft target cross-entropy loss function. We evaluate the fine-tuned models using the mean Intersection over Union (mIoU) metric across 11 categories. + +Classification. We employ BigEarthNet dataset [19], which consists of static pairs of MS and SAR modalities. The MS modality has 12 bands, though some are noninformative [4]; our model utilizes nine, consistent with the SatlasPretrain dataset. Following prior studies [9, 18], $10\%$ of the 360K samples are for fine-tuning, while about 119K remain for evaluation. A linear classifier head is added to the encoders, trained with a multi-label soft margin loss. Alongside the foundation models from Tab. 1, we incorporate ConvNeXtV2 [28], which was trained explicitly for this downstream dataset by Kai et al. [3]. The fine-tuned models are evaluated using the mean Average Precision (mAP) metric across 19 classes. + +Change Detection. The OSCD dataset [5] is employed, comprising 14 MS samples for training and 10 for evaluation. Each pair of images is simultaneously processed through a shared encoder, and their difference is then passed to UperNet. The models are fine-tuned for 60 epochs with a batch size of 32 and a learning rate of $1e - 3$ , and the final performance is measured using the F1 score. + +Complete & Incomplete Dataset. For each downstream task, we evaluate the fine-tuned models using two types + +Table 2. Segmentation results (mIoU↑) for models fine-tuned on datasets with varying missing rates and diverse input types, ranging from static uni-modal to temporal (T-) multi-modal data. Rand. indicates a random missing rate applied to each sequence. + +
ModelInputMissing rate
0%20%30%Rand.
SatlasNet [1]MS41.5740.8138.9739.09
T-MS43.5143.0241.3841.69
SAR36.22---
SpectralGPT [9]MS42.6742.2241.3141.21
T-MS45.6944.8543.1542.49
Satmae++ [18]MS42.9042.4341.9740.07
Croma [7]MS40.7739.5539.1438.59
SAR36.48---
MS-SAR44.0143.8042.9741.45
RobSense (Ours)MS43.9843.2942.8742.76
T-MS46.1145.1543.9343.88
SAR38.33---
MS-SAR44.9444.4343.6242.96
T-MS-SAR46.3645.8144.7244.26
+ +of datasets, i.e., complete dataset and incomplete dataset. For the complete dataset, we retain all data in its original form. For the incomplete dataset, which is not publicly available, we randomly remove values from the complete datasets [22]. To simulate sensor degradation or extreme atmospheric conditions [17, 22], we randomly remove invisible spectral bands and time points from the sequence of both MS and SAR data. The visible bands, i.e., RGB bands, are retained to preserve the essential information for model learning [2]. We implement three missing rates: $20\%$ , $30\%$ , and random (Rand.). The fixed rates remove $20\%$ and $30\%$ of invisible bands and time points, while the Rand. setting applies a variable rate for each spectral band sequence and temporal sequence. + +# 4.2. Performance on Downstream tasks + +Semantic Segmentation. Tab. 2 compares foundation models fine-tuned on datasets with missing rates from $0\%$ to a random rate (Rand.). Most models show declining performance as the missing rate increases. However, SatlasNet improves from a $30\%$ missing rate to Rand. + +In comparison, RobSense consistently outperforms baselines in terms of mIoU across both missing rates. On the complete dataset using uni-modal data, RobSense achieves the highest mIoU of 46.11, surpassing the second-best model, SpectralGPT with sequential MS input (T-MS), by $0.92\%$ . Fig. 3 illustrates that RobSense effectively captures seasonal changes in dynamic areas, such as shrublands and crop fields. In multi-modal settings, RobSense reaches a mIoU of 46.36, outperforming SpectralGPT by $1.47\%$ and Croma by $5.34\%$ . This highlights RobSense's ability to effectively capture time-specific distribution through the temporal distribution + +![](images/55633677a808090b12c26aa8172a912938fe378b798dc259ff19f644ddfa73b6.jpg) +Figure 3. Visual comparison of fine-tuned models on the segmentation dataset. RobSense (ours), SpectralGPT, and SatlasNet receive sequential MS images, while Croma and Satmae++ utilize the static MS image with the best result. + +alignment of multi-modal data utilizing multivariate KL divergence. At missing rates $20\%$ and $30\%$ , RobSense outperforms the two next best models, i.e., SpectralGPT and Croma by $0.96 - 1.57\%$ and $1.75\% - 2.01\%$ , respectively. Under random missing rate, RobSense maintains the highest mIoU at 44.26. Specifically, Fig. 4 illustrates each model's performance at varying missing rates in the Rand dataset. The proposed model consistently outperforms the others across all missing rates, with performance gaps widening as the missing rate increases. Notably, it demonstrates a significant advantage at a $70\%$ missing rate, where only the RGB bands remain. This demonstrates RobSense has strong performance across missing rates by effectively employing latent reconstructors to reconstruct the rich representations from RGB information. + +Classification. Tab. 3 compares foundation models finetuned on the BigEarthNet dataset at varying missing rates. Overall, all models show a performance decline as missing data increases across input types. The proposed model achieves the highest mAP across complete and incomplete datasets with multi-modal data. + +On the complete dataset, Croma's performance declines when incorporating MS-SAR data compared to using MS data alone. This is likely due to misalignment in the patch-level multi-modal pairs, resulting in information loss in the multi-modal representations. Tab. 4 demonstrates that Croma fails to predict the multi-modal input with large and complex regions such as mixed forest or complex cultivation patterns. In contrast, ConvNeXtV2 achieves better results by effectively stacking MS-SAR data pairs. Additionally, while RobSense lags behind SpectralGPT and Croma with uni-modal MS input, it outperforms both models when SAR data is incorporated, improving by + +![](images/f0ee43528583ddaba1841a9348d3660c19312bb89b420f1b23dabc5f23c4501f.jpg) +Figure 4. Performance comparison of foundation models finetuned on the segmentation dataset with static MS input under different missing rates. The performance gap relative to the second-best model, SpectralGPT, widens as the rate of missing data increases, underscoring the effectiveness of the proposed latent reconstructor in handling incomplete inputs. + +Table 3. Classification results (mAP ↑) for models fine-tuned on datasets with varying missing rates. Rand. indicates a random missing rate applied to each sequence. + +
ModelInputMissing rate
0%20%30%Rand.
SatlasNet [1]MS82.880.8379.7676.21
SAR74.21---
SpectralGPT [9]MS87.5084.6881.9081.21
Satmae++ [18]MS85.1183.6580.7978.91
Croma [7]MS87.5884.8682.9682.69
SAR76.06---
MS-SAR86.2883.7083.2782.33
ConvNeXtV2 [28]MS84.8980.6176.5673.12
SAR78.90---
MS-SAR85.1082.5577.7475.19
RobSense (Ours)MS86.3685.2884.3683.69
SAR81.11---
MS-SAR88.1787.2385.4684.87
+ +Table 4. Comparison of multi-label classification for RobSense and Croma, with multi-modal input. Correct predictions are marked with $\checkmark$ and incorrect predictions with strikethrough text. + +
MSSARGround truthRobSense (ours)Croma
Arable land✓ Arable land✓ Arable land
Broad-leaved forest✓ Broad-leaved forest✓ Broad-leaved forest
Coniferous forest✓ Coniferous forest✓ Coniferous forest
Mixed forest✓ Mixed forestPastures
Arable land✓ Arable land✓ Arable land
Complex cultivation patterns✓ Complex cultivation patternsUrban-labrie
Broad-leaved forest✓ Broad-leaved forest✓ Broad-leaved forest
Coniferous forest✓ Coniferous forest✓ Coniferous forest
Mixed forest✓ Mixed forest
+ +Table 5. Change detection results (F1↑) for foundation models fine-tuned on the MS-only dataset with varying missing rates. + +
ModelMissing rate
0%20%30%Rand.
SpectralGPT [9]54.2954.0452.2350.09
Satmae++ [18]56.2854.3454.1053.20
RobSense (Ours)58.2256.2656.2555.47
+ +Table 6. Impacts of Temporal Distribution Alignment (TDA) and Latent Reconstructors (Res) on model classification performance. +(a) Impact of TDA + +
Weights\( \mathbf{{mAP}} \uparrow \)
Rand. Init79.82
RobSenseAE81.11
RobSenseAE + Cons81.53
RobSenseAE + TDA84.19
+ +(b) Impact of Res + +
WeightsmAP↑
Rand. Init73.13
RobSensew/o Res78.67
RobSensew/ Res80.70
+ +0.77% and 0.67%, respectively. This suggests that the proposed model, pre-trained with multi-modal temporal distribution alignment, can effectively mitigate information loss and enrich multi-modal representations. On the incomplete dataset, as the missing rate increases to 20% and 30%, RobSense maintains its lead with mAPs of 87.23 and 85.46 in multi-modal settings, outperforming the second best models, i.e., Croma, by 2.37% and 2.5%, respectively. Under the random missing condition, RobSense achieves a strong mAP of 84.87, showing a margin of 2.54% over Croma and 3.66% over SpectralGPT. + +Change Detection. Tab. 5 presents the quantitative results of SOTA models, i.e. SpectralGPT, Satmae++ for this task. Unlike the baselines, which either lack input diversity or suffer from information loss when data are incomplete, our model leverages TDA-based temporal multi-modal pretraining and reconstructed representations for robustness. Consequently, on the complete dataset, our model achieves an F1 score of 58.22, outperforming SatMAE++ and SpectralGPT by roughly $2 - 4\%$ . Moreover, even under conditions of missing data (with $20 - 30\%$ or randomly missing), our model maintains the highest performance, underscoring its resilience and effectiveness. + +# 4.3. Ablation Study + +We examine the impact of two key factors: temporal distribution alignment and latent reconstructors. Due to computational constraints and these factors being less influenced by data scale, the model is pre-trained on $5\%$ of the dataset, with BigEarthNet used for fine-tuning on static multi-modal input. Tab. 6 presents the impact of the examined factors. + +Temporal Distribution Alignment. To evaluate TDA's effectiveness, the model is pre-trained with three strategies: (i) Autoencoder loss (AE), (ii) AE + contrastive loss (AE + ++ Cons), and (iii) AE + TDA. Meanwhile, other settings are kept the same. Starting from random initialization, the model's baseline mAP is 79.82. Pre-training with AE loss or AE + Cons loss leads to moderate improvements. Pre-training with AE or AE + Cons yields moderate improvements while incorporating TDA (AE + TDA) achieves the highest mAP of 84.19, indicating that TDA significantly enhances latent representations by aligning the distributions of both modalities consistently over time. + +Latent Reconstructors. To evaluate the effectiveness of uni-modal latent reconstructors, we pre-train the proposed model under two settings: (i) with latent reconstructors (w/ Res), and (ii) without latent reconstructors (w/o Res). In the second setting, we add four additional ViT layers to the uni-modal encoders, maintaining a fair total parameter count. Additionally, for this setting, we pre-train with only one phase, i.e., temporal multi-modal learning, and apply three masking strategies during pretraining: patch, invisible band masking in MS images, and time-point masking with only one phase. Results show that both configurations outperform random initialization on incomplete datasets, but the model with reconstructors pre-trained by two phases achieves the highest mAP. In contrast, pre-training with one phase and all three masking strategies can result in significant information loss, thereby diminishing performance. These findings demonstrate that training latent reconstructors separately can effectively handle missing data by preserving rich representations. + +# 5. Conclusion + +In conclusion, we propose RobSense, a robust multimodal foundation model for remote sensing that effectively integrates MS and SAR data. Our model addresses two key robustness challenges: supporting diverse input types and handling incomplete data. The model employs parallel uni-modal encoders and a multi-modal encoder to pretrain with temporal distribution alignment and a masked autoencoder strategy, enabling it to handle four input types flexibly. To manage incomplete data, RobSense includes two uni-modal latent reconstructors trained with masked spectral bands and time points, which effectively reconstruct rich representations even with missing data. Therefore, RobSense demonstrates strong performance on both complete and incomplete datasets. However, RobSense requires higher computational costs for pretraining due to its two pre-training phases. Future work will evaluate RobSense on a wider array of remote sensing tasks to assess its generalization in earth observation and to expand its capabilities to include language for tasks requiring both visual and linguistic understanding. + +# 6. Acknowledgement + +This work was supported in part by the Australian Government through the Australian Research Council's Discovery Projects Funding Scheme under Project DP220101634, and by the NVIDIA Academic Grant Program. + +# References + +[1] Favyen Bastani, Piper Wolters, Ritwik Gupta, Joe Ferdinando, and Aniruddha Kembhavi. Satlaspretrain: A large-scale dataset for remote sensing image understanding. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 16772-16782, 2023. 2, 3, 5, 6, 7 +[2] Yuanhao Cai, Jing Lin, Zudi Lin, Haoqian Wang, Yulun Zhang, Hanspeter Pfister, Radu Timofte, and Luc Van Gool. 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However, their effectiveness is significantly compromised in real-world conditions, due to imperfect object segmentation by off-the-shelf models and the prevalence of occlusions. To effectively address these issues, we propose a unified regression model that integrates segmentation and reconstruction, specifically designed for occlusion-aware 3D shape reconstruction. To facilitate its reconstruction in the wild, we also introduce a scalable data synthesis pipeline that simulates a wide range of variations in objects, occluders, and backgrounds. Training on our synthetic data enables the proposed model to achieve state-of-the-art zero-shot results on real-world images, using significantly fewer parameters than competing approaches. + +# 1. Introduction + +The abundance of large-scale 3D shapes [4, 7, 9, 10, 16, 33] has enabled the development of reconstruction models with strong generalization capabilities, even allowing for zero-shot monocular 3D shape reconstruction [25, 29, 41, 66, 68, 74]. However, these models are not deployable in real-world settings, as they assume object images that have no backgrounds and occlusions. Thus, they utilize off-the-shelf segmentation models [32, 60] to handle in-the-wild images. This dependency introduces two main challenges: (i) error accumulation by off-the-shelf models, and (ii) removal of occluded object parts by segmentation. Both issues hinder precise shape reconstruction, as shown in Figure 1. + +To tackle the challenges, we propose ZeroShape-W, an occlusion-aware 3D shape reconstruction model (Fig. 2a). Our model jointly regresses the silhouettes of a salient object and its occluders, along with a depth map and camera intrinsics to estimate the object's visible 3D shape. Then, its full 3D shape is reconstructed by using the visible 3D shape and the silhouette of occluders. This approach enables the reconstruction of occluded object parts, making it effective + +![](images/0e7ced35697692fec628900c5f59179f3cb5e5a3156ba05799ac5b67074d75e3.jpg) +Image + +![](images/2bacf4578080e3ce258312f359a602dcfa37217521dc8eb1b1160435c0703419.jpg) +$\mathrm{LRM}_{\mathrm{w / SAM}}$ + +![](images/292c2afe463f927415c624223415b93ee1529006e3f6e3f3b1d883bf22e670bd.jpg) +Figure 1. Single-view 3D shape reconstruction on real-world images [65]. Compared with LRM [25] that requires an off-the-shelf segmentation model (e.g., SAM [32]), our approach not only eliminates the need for such an additional model but also achieves greater robustness to occlusions. + +![](images/9921c7e73f469f5dcfb08206676a37799b43c7c88fd47231b394cf87aed49e3f.jpg) +Ours + +![](images/adf8297e88a9bdde513bf571da0d5a29ea56e616d366274c6f3d80d30543dda8.jpg) + +in real-world conditions. However, a significant challenge remains: how can we train our model for robust zero-shot reconstruction in the wild? To achieve this goal, we need large-scale diverse data that can cover various real environments. Unfortunately, the availability of real-world images annotated with precise 3D shapes is limited. An alternative approach is to generate realistic renderings from 3D object collections [4, 7, 9, 10, 16], but this is also limited by the availability of high-quality synthetic assets. + +In this paper, we introduce a scalable data synthesis pipeline (Fig. 2b) that simulates a wide range of variations using generative models, thereby removing the reliance on limited real-world data or high-quality synthetic assets. Our pipeline first synthesizes foreground object images using a conditional generative model [86], with spatial conditions obtained by rendering 3D shapes available from extensive object collections [4, 9, 10]. Then, their backgrounds are generated by an object-aware background outpainting model [13]. For these synthesized images, we apply Copy-Paste augmentation [19] to simulate occluders on-the-fly during model training. + +![](images/82d062806390475105e0cc844e29f11abc2a2c62ba2ab12cbcf5383ff5e0b9f3.jpg) +Occlusion-Aware 3D Shape Reconstruction +(a) Regression-based Model +Figure 2. Proposed approach for zero-shot monocular 3D shape reconstruction in the wild. (a) Our model reconstructs the full 3D shape of a salient object using its visible 3D shape and the silhouette of its occluders. The visible 3D shape is estimated from camera intrinsics, depth map, and visible region of the object. (b) We create our training dataset by synthesizing diverse data. We render 3D shapes and then simulate their appearances and backgrounds using generative models. Occluders are inserted on-the-fly during model training. + +![](images/011f670719c4eb0d1a5af0056a2f98bc4d98c061312225eafe2d3e7041497149.jpg) +Data Synthesis & Occlusion Augmentation +(b) Diverse Synthetic Data + +By training the proposed model on our diverse synthetic data, we expose it to a wide variety of foreground objects, their occluders, and backgrounds. This process enables our model to focus on learning to capture domain-invariant and object-centric geometric priors. In this way, we improve its generalization across various environments. + +To validate the effectiveness of our approach, we first create our training dataset by synthesizing diverse images using 3D shapes from Objaverse [10] and ShapeNet [4]. Then, we train our model on the data augmented with occlusions. We evaluate the model on the real-world benchmark, Pix3D [65], where it outperforms state-of-the-art models while using significantly fewer model parameters. In addition to the benchmark, we also qualitatively evaluate the proposed model on in-the-wild images from ObjectNet [2], OfficeHome [72], and PACS [35]. + +# 2. Related Work + +Single-view 3D shape reconstruction in the wild. This task aims to estimate the 3D shape of an object from a single image captured in a real-world environment. It is challenging because objects exhibit a variety of 3D shapes while their appearances are greatly altered by environmental factors. To handle such variations, 3D shape reconstruction models [1, 6, 18, 20-23, 25, 28-30, 38, 41, 48, 50, 53, 66, 68, 70, 73, 74, 76-78, 80, 81, 83, 85, 88] should generalize well across various environments. However, the scarcity of real-world 3D data poses a significant obstacle in pursuing this goal. In this paper, we address this issue by synthesizing large-scale data using generative models. + +Single-view reconstruction methods fall into two categories: generative model-based approaches [41, 66, 74, 81] and regression-based approaches [25, 29, 68]. The genera + +tive model-based approaches synthesize multi-view images using diffusion models such as Zero-1-to-3 [39], which are effective to estimate 3D shapes with textures but incur significant computational costs. In contrast, regression-based approaches such as ZeroShape [29] estimate 3D shapes in a single forward pass, offering much greater efficiency. + +Recent state-of-the-art methods in both approaches assume clean object-segmented images without occlusions, making them difficult to operate in real-world settings. In this work, we tackle this issue by introducing a unified regression model that both segments and reconstructs while accounting for occlusions. To the best of our knowledge, our work is the first regression-based approach for zero-shot single-view 3D shape reconstruction in the wild. + +Improving model robustness to distribution shifts. It is common to exploit multiple domains for learning domain-invariant features [3, 12, 31, 34, 36, 44, 45, 63, 90, 91] to enhance the model robustness. However, multiple domains from real-world environments might not be accessible. To effectively tackle this issue, domain randomization methods [8, 14, 26, 46, 56, 61, 67, 69, 84] synthesize multiple domains via a random simulation of diverse scenarios. By exposing a model to randomized variations, it learns to capture generalizable representations capable of handling a wide range of variations encountered in real-world settings. + +Following the paradigm of domain randomization, we simulate diverse variations in foreground objects, occluders, and backgrounds. However, this is not done completely randomly, as the background outpainting model [13] generates backgrounds while considering the foreground objects. By training the proposed model on our data, it could learn to capture domain-invariant and object-centric geometric priors, which are useful for handling diverse objects. + +![](images/ddae2563ed7ca038e222a78ceafc3ae69c2d1e4975e6fcd66831c1a44a4147ef.jpg) +Figure 3. Overall architecture of ZeroShape-W. Given an object-centric RGB image, our model leverages the backbone of Dense Prediction Transformer (DPT) [59] to regress camera intrinsics, a depth map, a visible mask of a salient object, and an occluder mask that represents the object's occluders. These components are used to derive the object's visible 3D shape, which is then combined with the occluder mask to regress occupancy values of 3D point queries through cross-attention layers [71]. This process recovers the object's full 3D shape, including occluded object parts. To alleviate difficulties of in-the-wild reconstruction, we optionally incorporate open-set category priors by estimating the object's category, "[object]" (e.g., "cup"), using an additional vision-language model (VLM) [37]. + +Synthetic data generation. To train 3D shape reconstruction models, we can synthesize data by rendering 3D objects from extensive object collections [4, 7, 9, 10, 16, 33] via computer graphics tools. As long as sufficient 3D shape and texture assets are available for objects and environments, this approach could also facilitate 3D shape reconstruction in the wild. However, it is expensive to collect a great variety of high-quality assets (e.g., 4K-resolution texture maps, HDR environment maps) needed to bridge the gap between synthetic and real environments. Moreover, the diversity of object appearances and backgrounds depicted by rendered images is determined by the combination of available assets. Compared with these computer graphics tools, our data synthesis pipeline could simulate more diverse object appearances and backgrounds without relying on such additional high-quality assets, by leveraging generative models pre-trained on large-scale datasets. + +Generative models with 3D assets. Recent works [17, 43, 87] use conditional generative models [49, 57, 86] to synthesize images with 3D assets for various tasks, e.g., object pose estimation. Compared with them, accurate preservation of silhouettes within spatial conditions is more crucial for 3D shape reconstruction. To better preserve silhouettes, our data synthesis pipeline employs a two-step generation process. We utilize an initial guidance for foreground object synthesis and exploit a background outpainting model [13] specifically designed for preserving silhouettes. In this way, each synthesized image is paired with its precise 3D shape. + +![](images/1fc9416e66fee0f64dbe6f43aed539c1fbefef454bc1b8cfe5445d3f66bbb355.jpg) +Image + +![](images/13f62f0db88bd50f96dc14c78270c7309aea55d7abcc6c3bf9b74782a06876d6.jpg) +w/o Occluder Mask + +![](images/e7399ba049d8e795a0ad7de9b21c93d0a3a707c50dd2bbeaacb08a7294a3af28.jpg) + +![](images/2808ad18f6ad64884872b0b8af909757f8352bafb3815b4479eadcdd27255978.jpg) +w/ Occluder Mask +Figure 4. Effect of using an occluder mask. It enables full 3D shape reconstruction, even for occluded object parts. Note that existing state-of-the-art methods [25, 29, 41, 66, 68, 74] struggle with occlusions, as they assume the salient visible object in the current view is unobstructed. + +# 3. Method + +The proposed ZeroShape-W (Fig. 3) aims to regress the full 3D shape of a salient object from a single image, including its visible and occluded parts (Fig. 4). Inspired by [29, 75], our model first regresses pixel-level information, which is used as condition to regress occupancy values of 3D point queries. These occupancy values represent the visible and hidden geometry of the salient object, while also accounting for occluded regions that were not addressed in [29, 75]. + +During pixel-level regression, our model regresses a depth map, a visible mask of the object, and an occluder mask that depicts the object's occluders. It also estimates camera intrinsic to convert depth values into the object's visible 3D shape in a viewer-centric coordinate system. + +During 3D point-wise regression, our model regresses occupancy values of 3D point queries through cross-attention layers [71], utilizing features from the visible 3D shape and occluder mask as keys and values. This approach + +can effectively reconstruct the object's hidden geometry, with the help of learned 3D shape priors. + +For in-the-wild images, identifying arbitrary salient objects is often challenging due to complex backgrounds or occlusions, which can result in noisy mask estimations. In such cases, visible 3D shapes may mistakenly include background geometries. To address these issues, we optionally incorporate category-specific priors by leveraging a vision-language model [37] and CLIP text encoder [58]. Specifically, the vision-language model generates a category-specific prompt "[object]" (e.g., "cup" in Fig. 3) that describes the salient object in the input image. For stable inference with unseen object categories, we use an averaged CLIP text embedding obtained from the category-specific prompt and a category-agnostic prompt "object". In cases where the category-specific priors are not used, our model relies solely on the category-agnostic prompt without estimating the object's category. + +# 3.1. Pixel-level Regression + +For an object-centric RGB image $I \in \mathbb{R}^{H \times W \times 3}$ , we first obtain image embeddings $\mathbf{E}_I \in \mathbb{R}^{(H/16) \times (W/16) \times D}$ using ResNet50 [24], as done in ViT-Hybrid [11]. Then, we feed the embeddings $\mathbf{E}_I$ into the backbone of Dense Prediction Transformer (DPT) [59]. From the backbone, we extract a global feature map $\mathbf{X}_G \in \mathbb{R}^{(H/32) \times (W/32) \times D}$ and a fine-grained feature map $\mathbf{X}_F \in \mathbb{R}^{(H/2) \times (W/2) \times C}$ . The global feature map $\mathbf{X}_G$ is the reassembled output from the last transformer layer in DPT, while the fine-grained feature map $\mathbf{X}_F$ is the output from the last fusion layer in DPT. + +Camera intrinsics. To regress the visible 3D shape of the salient object, we estimate camera intrinsics $K \in \mathbb{R}^{3 \times 3}$ from the global feature map $\mathbf{X}_G$ . Specifically, we obtain the camera intrinsics $K$ by predicting a focal length scaling factor and principal point shifts, as done in [29]. The scaling factor adjusts a base focal length according to the image resolution $H \times W$ , and the principal point shifts are also specified relative to the image resolution. These parameters are estimated from the global feature map $\mathbf{X}_G$ using shallow convolutional layers, a pooling layer, and a feed forward network (FFN). + +Depth map. To derive the visible 3D shape by unprojecting depth values using the estimated camera intrinsics $K$ , we regress a depth map $\mathbf{M}_D \in \mathbb{R}^{H \times W \times 1}$ from the fine-grained feature map $\mathbf{X}_F$ . For this regression, we use shallow convolutional layers with interpolation. + +Visible mask. To identify the visible region of the salient object, we regress a visible mask $\mathbf{M}_V\in \mathbb{R}^{H\times W\times 1}$ from the fine-grained feature map $\mathbf{X}_F$ . For precise regression, we adaptively adjust the fine-grained feature map $\mathbf{X}_F$ based on the object's category. Inspired by [25, 54, 55], we modulate the feature map using an affine transformation with a scaling factor $\gamma \in \mathbb{R}^C$ and a shift factor $\beta \in \mathbb{R}^C$ , estimated + +by an FFN with CLIP text encoder [58]. We modulate the feature map $\mathbf{X}_F$ at each spatial location $(i,j)$ as follows: + +$$ +\bar {\mathbf {X}} _ {F _ {i j}} = (1 + \gamma) \mathbf {X} _ {F _ {i j}} + \beta , \tag {1} +$$ + +where $\bar{\mathbf{X}}_F\in \mathbb{R}^{(H / 2)\times (W / 2)\times C}$ . From this modulated feature map, we regress the visible mask $\mathbf{M}_V$ using shallow convolutional layers with interpolation. + +Visible 3D shape. Using the estimated camera intrinsics $K$ , depth map $\mathbf{M}_D$ , and visible mask $\mathbf{M}_V$ , we derive the visible 3D shape $\mathbf{S}_V \in \mathbb{R}^{H \times W \times 3}$ that contains $(x, y, z)$ -coordinates of each pixel location $(i, j)$ as follows: + +$$ +\mathbf {S} _ {V _ {i j}} = \mathbb {1} _ {\left\{\mathbf {M} _ {V _ {i j}} \geq \eta \right\}} \cdot \left(\mathbf {M} _ {D _ {i j}} K ^ {- 1} [ i, j, 1 ] ^ {\top}\right), \tag {2} +$$ + +where $\mathbb{1}_{\{\cdot\}}$ is an indicator function, and $\eta$ denotes a threshold. We normalize $\mathbf{S}_V$ to have a zero mean and a unit scale. Occluder mask. To determine the object's occluded region, we regress an occluder mask $\mathbf{M}_O \in \mathbb{R}^{H \times W \times 1}$ using the fine-grained feature map $\mathbf{X}_F$ and visible mask $\mathbf{M}_V$ . Specifically, we resize the visible mask to the resolution of $H/2 \times W/2$ , and concatenate it with the feature map along the channel dimension. Then, we regress the occluder mask $\mathbf{M}_O$ using shallow convolutional layers with interpolation. + +# 3.2. 3D Point-wise Regression + +We regress occupancy values of 3D point queries using cross-attention layers to effectively consider local features from pixel-level estimations. We begin by concatenating the visible 3D shape $\mathbf{S}_V$ and the occluder mask $\mathbf{M}_O$ along the channel dimension, which is then fed into an encoder. It produces $Z$ -dimensional vectors that serve as keys and values in cross-attention layers. + +For each 3D point query, we construct a $Z$ -dimensional query vector by concatenating two $Z/2$ -dimensional embeddings: one from the point's $(x,y,z)$ -coordinates and the other from CLIP text encoder [58]. The query vectors are processed through $L$ cross-attention layers, where each query independently attends to its relevant spatial features. Then, to reconstruct the object's full 3D shape, we estimate the occupancy value of each query using an FFN. + +# 3.3. Loss + +We train our model using binary cross-entropy losses with the estimated visible mask $\mathbf{M}_V$ , occluder mask $\mathbf{M}_O$ , and occupancy values. For the estimated depth map $\mathbf{M}_D$ , we apply a scale- and shift-invariant MAE loss [15] over two regions: (i) the visible mask region with ground-truth depth and (ii) the entire region with pseudo depth estimated from a pre-trained model, referred to as the auxiliary depth loss. This auxiliary loss addresses the limitation of our data synthesis pipeline, which only provides depth for object areas. For the estimated camera intrinsics $K$ , we use an MSE loss by comparing the visible 3D shape $\mathbf{S}_V$ to the ground truth. + +![](images/89562cde4caca84ed09c82643e1e3e5d6c08657a433fd92c55da8c6d0a907357.jpg) +Figure 5. Overview of our data synthesis. Given a camera and 3D object, we render it to obtain an object mask, image, and depth map. We simulate object appearances via a conditional diffusion model [86] using the depth as its spatial condition and "a [color] [material] [object]" (e.g., "a red wood chair") as its textual condition. To alleviate shape distortion by the generative model, we use the rendered image as initial guidance. We simulate its background via an object-aware background outpainting model [13] using the mask and "a [object] in the [scene]" (e.g., "a chair in the canyon") as its textual condition. Then, we put occluders during data augmentation. + +# 3.4. Implementation Details + +We input an image of resolution $H \times W$ , where $H = W = 224$ . Using DPT-Hybrid [59], we extract the $D$ -dimensional feature $\mathbf{X}_G$ and $C$ -dimensional feature $\mathbf{X}_F$ , where $D = 768$ and $C = 256$ . In eq. (2), we set $\eta = 0.5$ . In $L$ cross-attention layers, we employ $Z$ -dimensional vectors, where $L = 2$ and $Z = 256$ . During training, we use Depth Anything V2 [82] for the auxiliary depth loss. At inference time, we optionally use LLaMA-VID [37] to identify the object's category. Further details can be found in the supplementary material. + +# 4. Data Synthesis + +Our scalable data synthesis pipeline (Fig. 5) produces diverse images, along with their corresponding 3D shapes, camera parameters, depth maps, and masks. We use CopyPaste [19] augmentation to insert occluders at each training iteration. Please see the supplementary material for details. + +# 4.1. Object Rendering + +A great variety of 3D shapes can be readily obtained from 3D object collections [4, 7, 9, 10, 16, 33] or generative models [5, 40, 64, 77]. In line with ZeroShape [29], we utilize the same set of 3D objects spanning over 1,000 categories, including 52K objects from ShapeNetCore.v2 [4] and 42K objects from Objaverse-LVIS [10]. + +Each 3D object is rendered by multiple cameras constructed with varying camera distances, elevation angles, focal lengths, and LookAt points. This rendering process produces over 1 million object images, and each output is paired with precise 3D shapes, camera parameters, depth maps, and masks. + +![](images/9d0cf127cc7947adf1e280a6201fb6ad224f782d764da2ddd0247abef2cf3768.jpg) +3D Shape + +![](images/d72a05d60054b90e2a6397a1a3fa0558151c57c2efdf668b189d0693d3d264c8.jpg) +Depth Map + +![](images/fbd082c92ba08e918d623aba9d292b5e944ae12df65cd04889adffde394d9ee5.jpg) +w/o Guidance +Figure 6. Effect of using an initial guidance. The guidance assists in preserving the object silhouette depicted in the spatial condition. + +![](images/b4ebcf59f759fb46145af29b8460d387a87d188bc32d22d048040624dd80affd.jpg) +w/ Guidance + +# 4.2. Object Appearance Diversification + +To simulate diverse visual variations in object appearances, we employ ControlNet [86] which is a conditional diffusion model capable of realistically synthesizing diverse images. In our data synthesis, the generative model simulates a wide range of variations by using a depth map as its spatial condition and "a [color] [material] [object]" as its textual condition. Here, the placeholders [color] and [material] are replaced by words selected from predefined color and material lists, while [object] denotes the category of the used 3D object. + +Initial guidance. The diffusion model [86] occasionally distorts the object silhouette depicted in the spatial condition. To alleviate this distortion, we utilize the rendered image as initial guidance. Motivated by SDEdit [47], we perturb the guidance with Gaussian noise and feed it to the model. Since the noisy guidance retains the original spatial structure, it effectively reduces silhouette distortion (Fig. 6). + +# 4.3. Background Diversification + +To simulate diverse backgrounds, we use an object-aware background outpainting model [13]. It adapts Stable Diffusion Inpainting 2.0 [62] by using modified ControlNet [86], allowing for background generation without extending the + +![](images/6f1beb4fe9c64532429c91dfd538dea2b8c7dac214dd298f7a1bada38fa00ff3.jpg) +Figure 7. Diverse synthetic data produced by our scalable data synthesis pipeline. Based on 3D shape renderings from ShapeNetCore.v2 [4] and Objaverse-LVIS [10], we synthesize diverse images using ControlNet [86] and object-aware background outpainting model [13]. + +object's silhouette. We generate various backgrounds using the object image, its mask, and the prompt "a [object] in the [scene]", where [scene] is selected from scene categories [79, 89]. Ideally, it synthesizes backgrounds that appear to be captured by cameras with focal lengths similar to those used for the object's rendering. + +# 4.4. Augmentation + +For images generated by our data synthesis (Fig. 7), we simulate occluders on-the-fly during model training via CopyPaste augmentation [19] using our synthesized foreground objects. To enable stable estimation of camera intrinsics, we put objects rendered by similar focal lengths. + +# 5. Experiments + +# 5.1. Evaluation Settings + +Protocol. To convert implicit 3D shape representation into explicit 3D meshes, we extract the isosurface from the implicit representation via the Marching Cubes [42] algorithm. Following [23, 50, 85], we align predicted and ground-truth meshes using the Iterative Closest Point algorithm. Then, we uniformly sample 10K points from each mesh. + +Metrics. Using 10K sampled points, we compute Chamfer Distance (CD) and F-Score (FS) for quantitative evaluation, as in [27-29]. Specifically, FS@ $\tau$ denotes the harmonic mean of precision@ $\tau$ and recall@ $\tau$ , which represents the concordance between predicted and ground-truth points within a distance threshold $\tau$ . + +Datasets. We evaluate our model on real-world object images from Pix3D [65], ObjectNet [2], OfficeHome [72], and PACS [35]. As Pix3D is the widely recognized benchmark for 3D shape reconstruction in the wild, we use it for comparison with other state-of-the-art models [25, 29]. + +# 5.2. Experimental Results + +Quantitative comparison. Currently, there is no zero-shot monocular 3D shape reconstruction model capable of directly processing in-the-wild images. Therefore, we compare our model with state-of-the-art reconstruction models, LRM $[25]^2$ and ZeroShape [29], which operate on object-segmented images without occlusions. For comprehensive comparisons with these baselines, we equip them with the off-the-shelf modal segmentation model, SAM [32], and amodal completion model, pix2gestalt [52]. + +In Table 1, we evaluate the baselines and our model on the Pix3D benchmark [65]. Although the proposed model does not utilize such off-the-shelf models, it substantially outperforms them. In terms of FS@ $\tau$ , our model outperforms the strongest baseline ZeroShape $_{\mathrm{w/SAM + pix2gestalt}}$ by a large margin of $13.7\%$ (38.2 vs. 33.6). With regard to CD, the proposed model also surpasses the strongest baseline by a large margin of $13.4\%$ (0.097 vs. 0.110); lower is better for CD evaluation metric. + +Our model requires significantly fewer parameters than the baselines, since it performs joint regression using the shared feature map $\mathbf{X}_F$ . For example, the number of parameters used by our model is less than $1/12$ of the parameters used by $\mathrm{LRM}_{\mathrm{w/SAM} + \mathrm{pix2gestalt}}$ , as shown in Table 1. + +Qualitative comparison. Figure 8 presents single-view 3D shape reconstruction results on real-world images from Pix3D [65]. When existing reconstruction models [25, 29] utilize an off-the-shelf modal segmentation model [32], they struggle to estimate the geometry for occluded object parts. To enable occlusion-aware 3D reconstruction, they should incorporate an amodal completion model [52]. However, + +
ModelOff-the-shelf ModelOverheadPix3D Evaluation
Modal SegmentationAmodal Completion#ParamsFS@τ↑FS@2τ↑FS@3τ↑FS@5τ↑CD↓
LRMSAM—>1100M31.054.569.987.10.121
SAMpix2gestalt>2400M31.154.970.687.70.119
ZeroShapeSAM—>800M32.156.872.188.00.116
SAMpix2gestalt>2100M33.659.074.289.20.110
Ours (category-agnostic)——193.7M38.265.379.992.50.097
+ +![](images/bf75f56d87adb60a79a9c9198eb4d3e181a7a8c6d94687de529badad99abdf50.jpg) +Figure 8. Comparison of single-view 3D shape reconstruction on Pix3D [65]. In this comparison, LRM [25] and ZeroShape [29] take modal segmentation results (from SAM [32]) or amodal completion results (from pix2gestalt [52]) as inputs. In contrast, our model directly takes original images as inputs, and performs occlusion-aware reconstruction by regressing visible 3D shapes and occluder silhouettes. + +this approach often leads to error accumulation. Even with well-completed amodal images, shape reconstruction errors may still occur (see $\mathrm{LRM_w / SAM + pix2gestalt}$ in the left column of Figure 8). This might be due to compatibility issues with off-the-shelf models, as they were trained on different datasets. In contrast, our model achieves promising results without the need to heavily pre-process input images using the off-the-shelf models. + +Evaluation on non-occluded or occluded images only. In Table 2, we compare evaluation results on non-occluded or occluded object images from the Pix3D dataset [65], which consists of $42.6\%$ non-occluded and $57.4\%$ occluded images. Under both scenarios, our end-to-end regression method substantially outperforms existing approaches [25, 29] that depend on an off-the-shelf model [32]. + +Optional category-specific priors. To evaluate the effect of incorporating such category priors, we compare results obtained using the category-agnostic prompt "object" and the category-specific prompt "[object]" (estimated by a VLM [37]). Table 3 shows that the priors improve our model's accuracy. Please see the supplementary material for more analyses. + +Table 1. Comparison of single-view 3D shape reconstruction on Pix3D [65]. Existing state-of-the-art reconstruction models, LRM [25] and ZeroShape [29], require an off-the-shelf modal segmentation model (e.g., SAM [32]), because they assume object-segmented images without any occlusions. For occlusion-aware reconstruction, they need an additional amodal completion model (e.g., pix2gestalt [52]). In this comparison, our model is evaluated using the category-agnostic prompt "object". + +
ModelNon-OccludedOccluded
FS@τ↑CD↓FS@τ↑CD↓
LRMw/SAM33.50.11129.10.128
ZeroShapew/SAM34.60.10630.20.123
Ours (category-agnostic)43.60.08234.20.107
+ +Table 2. Quantitative evaluation exclusively on non-occluded or occluded object images from the Pix3D dataset [65]. + +
PromptPix3D Evaluation
FS@7↑FS@57↑CD↓
Category Agnostic38.292.50.097
Category Specific (w/ VLM)39.192.60.095
+ +Table 3. Pix3D [65] evaluation according to category prompts. We incorporate category-specific priors by using a VLM [37]. + +Reconstruction of diverse objects. Figure 9 presents single-view 3D shape reconstruction results on real-world images from ObjectNet [2], OfficeHome [72], and PACS [35]. By leveraging learned priors, the proposed model can regress 3D shapes of various objects captured in real-world environments. + +![](images/2a45584e558f3e1f35e798433a60b02c29db2600c992099b4230289cd6b4db4d.jpg) +Figure 9. Single-view 3D shape reconstruction of diverse object shapes. We qualitatively evaluate our model on real-world object images from ObjectNet [2], OfficeHome [72], and PACS [35]. The proposed model achieves promising in-the-wild reconstruction results, which demonstrates that our regression-based model has effectively learned generalizable 3D shape priors. + +
ModelPix3D Evaluation
FS@τ↑FS@5τ↑CD↓
w/o auxiliary depth*35.990.70.105
w/o occluders*37.791.20.102
w/o text prompt38.091.50.101
Ours (category-specific)*39.692.80.094
+ +# 5.3. Ablation Study + +Effect of auxiliary depth loss. In the absence of this loss, we observe that predicted depth values for non-object regions are not precise, leading to worse results (see w/o auxiliary depth in Table 4). This depth loss helps to accurately regress depth values across the entire image, which aids in distinguishing the salient object from its occluders and backgrounds based on depth. Moreover, the auxiliary loss prevents our model from overfitting to the training data. + +Effect of simulating occluders. Without the Copy-Paste augmentation and the occluder mask estimation branch, our model struggles to reconstruct the full 3D shape when the salient object is occluded. Although this variant estimates visible 3D shapes fairly well in the absence of occlusions, its overall accuracy is degraded on in-the-wild images from the Pix3D dataset [65] (see w/o occluders in Table 4). + +Effect of text prompt. When we do not use text prompts, our model sometimes incorrectly splits a single object into visible and occluder regions based on depth. In addition, it struggles to handle noisy visible 3D shapes that contain background geometries by mistake. As a result, its accuracy is diminished (see w/o text prompt in Table 4). + +Table 4. Effects of key components. On Pix3D [65], we analyze the accuracy of our model by ablating each component. * denotes using ground-truth object names for category-specific prompts. + +
ModelTrain GPUsFeat. Res.Train Res.Inference Res.
LRM128 A10032×32128×128×128384×384×384
Ours4 RTX309014×1432×32×32128×128×128
+ +Table 5. Used resources and resolutions. Feat. Res. denotes image feature resolutions from DINOv2 [51] or ResNet50 [24], while Train/Inference Res. indicate spatial resolutions. + +# 6. Limitations + +Lack of training resources. As shown in Table 5, resolutions differ significantly due to limited resources (i.e., 4 RTX3090 vs. 128 A100). Consequently, our reconstructed 3D shapes appear smoother than the shapes from LRM [25]. + +Challenges with boundary-clipped objects. Our model can handle occlusions, but it may struggle to estimate the geometry of object parts clipped by image boundaries. + +Dataset ambiguity. Ambiguity in the dataset may hinder our model's ability to distinguish the salient object from its occluders. For example, some "bed" 3D objects only consist of bed frames, while others include pillows. + +Unrealistic occluders. Copy-Paste augmentations have proven effective [19], but they introduce a domain gap when compared to actual occluders in real-world environments. + +# 7. Conclusion + +To enable zero-shot single-view reconstruction in the wild, we presented (i) a unified regression model for occlusion-aware 3D shape reconstruction, and (ii) a scalable data synthesis pipeline for creating training dataset. Our approach achieved state-of-the-art accuracy on in-the-wild images. Unlike other existing methods, our method does not utilize off-the-shelf segmentation or amodal completion models, leading to significantly fewer model parameters. + +Acknowledgments. This work was supported by ADD grant funded by the Korean government. T.-H. Oh and K. 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Most previous methods emphasize spatial or temporal multi-modal modeling, yet overlook challenges from ambiguous audio-visual correspondences—such as nearby visually similar but acoustically different objects and frequent shifts in objects' sounding status. Consequently, they may struggle to reliably correlate audio and visual cues, leading to over- or under-segmentation. To address these limitations, we propose a novel framework with two primary components: an audio-guided modality alignment (AMA) module and an uncertainty estimation (UE) module. Instead of indiscriminately correlating audio-visual cues through a global attention mechanism, AMA performs audio-visual interactions within multiple groups and consolidates group features into compact representations based on their responsiveness to audio cues, effectively directing the model's attention to audio-relevant areas. Leveraging contrastive learning, AMA further distinguishes sounding regions from silent areas by treating features with strong audio responses as positive samples and weaker responses as negatives. Additionally, UE integrates spatial and temporal information to identify high-uncertainty regions caused by frequent changes in sound state, reducing prediction errors by lowering confidence in these areas. Experimental results demonstrate that our approach achieves superior accuracy compared to existing state-of-the-art methods, particularly in challenging scenarios where traditional approaches struggle to maintain reliable segmentation. + +# 1. Introduction + +Given an audio signal, Audio-Visual Segmentation (AVS) aims to identify and segment audible objects within a visual scene [49, 50]. Existing studies [9, 16, 18] focus on + +![](images/4ef356762b171e3b81594b73bf0830ac946e2d2460e30b6349ff4a73c426e063.jpg) +Figure 1. (a) Illustration of ambiguous spatio-temporal correspondences. Case (1): At time $t_1$ , #Dog1 and #Dog2 are positioned closely but have differing sounding states, challenging the model to identify the genuine sounding one. Case (2): Over frames $t_1$ , $t_2$ , and $t_3$ , #Dog1 switches between sounding and silent states, posing challenges for models to capture the object's sounding status variations over time reliably. (b) Distribution of Special Cases in AVSS Dataset. We conduct a sample analysis utilizing a random $33.3\%$ subset of AVSS-V2 [50], which reveals substantial occurrences of cases (1) and (2), indicating the frequent presence of challenging frames. + +modeling spatio-temporal audio-visual information to capture associations between audio and visual cues, such as dynamic sound properties and object motion. Although these methods demonstrate strong performance, they often overlook challenges arising from ambiguous audio-visual spatio-temporal correspondences in real-world scenarios, potentially resulting in suboptimal segmentation, i.e., over- or under-segmentation. + +As illustrated in Fig. 1, we analyze and categorize the challenging cases in the AVS dataset, identifying two primary difficulties that arise from the audio-visual ambiguous correspondence. Incorrect Audio-Visual Associations Due to Visually Similar Objects with Different Sound States (case 1). In such cases, typical attention-based audio + +visual alignment methods [16, 49, 50] rely on global context to weight information. However, for visually similar yet acoustically distinct objects, these methods struggle to adjust attention distribution adaptively based on their actual sounding states, causing both silent and audible objects to be mistakenly aligned with audio cues. To address this, some methods [5, 24] employ ground-truth masks to filter out silent regions or employ ground-truth masks as references to construct positive and negative samples for contrastive learning. Although these approaches can temporarily exclude interference from silent areas, the model cannot rely solely on the GT mask to learn each object's unique sound response, resulting in attention still being mistakenly allocated to silent areas. Learning Instability Due to Frequent Sounding Status Changes (case 2). As shown in Fig. 1, the sounding status of objects may frequently shift over short periods, complicating the learning of stable temporal audio-visual relationships. When sound states change quickly, existing methods [5, 9, 16, 24, 50] tend to smooth over variations based on the preceding continuous sounding state, leading over-segmentation results. In this paper, we propose a novel framework consisting of an audio-guided modality alignment (AMA) module aimed at addressing 1 and an uncertainty estimation (UE) module targeting 2. + +Considering that employing global attention-based methods may lead to dispersed attention, AMA first groups visual features based on their semantic density, thereby restricting audio-visual interaction to a group level. Then, the sound-guided semantic merging module performs audioguided weighted merging of group features. Each feature is assigned a weight based on its audio responsiveness, with features corresponding to sounding objects being amplified and those corresponding to silent objects being suppressed. This process introduces an audio-driven feature competition that effectively differentiates sounding and silent objects, generating compact representations. These representations are then reprojected onto the visual feature map. After performing the above process across multiple layers, the sounding regions are highlighted while the silent regions gradually weaken. To further strengthen the model's ability to differentiate between silent and sounding features, we treat compact representations with high audio responsiveness as positive samples and those with low responsiveness as negative samples. Contrastive learning is then employed to maximize the feature space distance between these positive and negative samples, ensuring better separation and discriminability [4, 10, 15, 33]. + +Furthermore, to enhance the model's reliability in handling frequent sound state changes, we introduce an uncertainty estimation (UE) module. When an object's sound state shifts rapidly, the model may experience high uncertainty in mask predictions on transition frames. To address this, we first apply temporal modeling through + +an attention-based layer to capture temporal dependencies across frames. The resulting features are then fed into two separate heads in UE: a mask prediction head and an uncertainty estimation head. By incorporating uncertainty estimation into the mask prediction, the model adaptively reduces prediction confidence in regions with high uncertainty, effectively mitigating the impact of unreliable predictions during transitions. + +In summary, our contributions are three-fold: + +- We introduce an audio-guided modality alignment module that adaptively identifies and highlights sounding regions through audio-driven feature competition and semantic grouping, improving the model's robustness against incorrect audio-visual associations. +- We develop an uncertainty estimation module to mitigate prediction errors caused by frequent changes in the sounding states of objects. +- Extensive experiments on benchmark datasets show that our framework outperforms previous state-of-the-art methods across all AVS datasets, with a $4.2\%$ gain in $\mathcal{J} \& \mathcal{F}_{\beta}$ on the AVS-Semantic dataset and an $11.5\%$ gain on the challenging VPO-MSMI dataset. + +# 2. Related Work + +# 2.1. Audio-Visual Alignment. + +Effective audio-visual alignment is crucial for achieving precise sound source segmentation. Many studies have shown that attention-based modules [9, 16, 18, 24, 50] and contrastive learning are powerful methods for modal alignment. For instance, TPAVI [49, 50] utilizes an attention mechanism to align audio and visual modalities in both spatial and temporal dimensions. To minimize interference from background noise and irrelevant regions, stepstone [24] introduces ground-truth masks to filter out the silent visual regions, enhancing audio-visual alignment. However, pre-filtering these silent regions prevents the model from learning to differentiate between silent and active objects, limiting its ability to fully explore multimodal integration. + +Contrastive learning is another popular approach for audio-visual alignment, particularly in audio-visual localization [25, 31, 32, 38]. Inspired by this, recent works [5, 6] adapt contrastive learning to AVS to enhance audio-visual correlation. Traditional AVL methods [2, 12, 14, 28, 30–32, 34, 35, 39, 42] treat audio-visual pairs from the same video as positive samples and pairs from different videos as negative. However, this approach neglects the potential semantic alignment between features from different videos, mistakenly treating them as negative pairs and disregarding cross-video consistency. To address this, Chen et al. [5] employ the ground truths to select positive samples, linking them with the corresponding audio signals, and treating background regions or mismatched audio-visual pairs + +as negative samples. While this method improves sample precision, it still overlooks semantic mismatches caused by visually similar but acoustically different objects in a frame. + +In this work, we employ audio as the guidance to construct positive and negative samples, facilitating the model to be distinguishable for sounding and silent regions. + +# 2.2. Audio Visual Segmentation. + +Audio-visual segmentation aims to correctly partition the regions and label them with specific sound types [49, 50]. Existing methods can be categorized by input granularity into two main types: frame-level input [5, 6, 20, 21] (i.e., a single frame paired with one-second of audio), and segment-level input [9, 11, 13, 16, 18, 23, 27, 37, 41, 44, 45, 49, 50] (i.e., multiple frames paired with an audio segment of matching length). For example, BAVS [21] utilizes frame-level input to mitigate the model's tendency to over-segment silent objects. In contrast, methods emphasizing temporal information, such as CATR [16], claim that incorporating temporal dynamics better captures sound source variations over time, employing temporal audio-visual interactions through cross-attention mechanisms. Moreover, with the emergence of query-based video segmentation models [7, 46], several approaches have developed AVS frameworks built upon this architecture, incorporating audio information into the queries to facilitate audio-visual alignment [18, 24, 37], thereby effectively modeling the temporal dynamics of the fused features. + +While these approaches have improved AVS performance, there are still limitations. Frame-level methods fail to fully utilize multimodal information across time, limiting segmentation accuracy. Meanwhile, temporal modeling may favor generating smooth prediction results and overlook abrupt sound changes, resulting in suboptimal segmentation performance at sound transition points. In this work, we address these issues by estimating the prediction uncertainty caused by sound transitions and adjusting the mask prediction confidence based on the uncertainty map. + +# 3. Proposed Method + +Fig. 2 depicts a diagram of our proposed framework. Before elaborating on our method, we first provide a preliminary in §3.1. Then we introduce the key components of our method: (i) Audio-Guided Modality Alignment (cf. §3.2), which details the progress of facilitating the model in learning to distinguish between sounding and silent objects. (ii) Uncertainty Estimation (cf. §3.3), which measures the model's confidence changes over time regarding sounding state transitions. The training objective is detailed in §3.4. + +# 3.1. Notation and Preliminaries + +Task Setup. Formally, given a video consisting of $T$ one-second clips, where each second's data is represented as + +![](images/9c0bf144af197494687d062bfd3121b2143d202e6c83d42ee70738461040f851.jpg) +Figure 2. Method Overview. Our framework takes video frames $\{I_t\}_{t=1}^T$ and audio signals $\{A_t\}_{t=1}^T$ as input to segment masks $\{\hat{Y}_t\}_{t=1}^T$ for audible objects. Visual and audio features extracted by the visual block $\mathcal{E}_{v_l}$ and audio encoder $\mathcal{E}_a$ are aligned through audio-guided modality alignment. The multi-scale features from each frame are then fed into the mask decoder to generate a fused feature map. Through temporal modeling, the feature maps are processed by the uncertainty estimation module to obtain the uncertainty map and mask confidence predictions. The final predicted results are generated by integrating the uncertainty map with mask confidence predictions. + +$\{I_t, A_t\}_{t=1}^T$ , with $I_t$ denoting the last video frame of the $t$ -th second and $A_t$ representing the corresponding one-second audio segment. A robust audio-visual segmentation model $f$ is designed to process the input pairs and generate pixelwise localization maps $\{\hat{Y}_t\}_{t=1}^T$ for audible regions: + +$$ +\left\{\hat {Y} _ {t} \right\} _ {t = 1} ^ {T} = f \left(\left\{I _ {t}, A _ {t} \right\} _ {t = 1} ^ {T}\right). \tag {1} +$$ + +The optimal solution $f^{*}$ is typically determined by minimizing a composite segmentation loss $\mathcal{L}_{SEG}$ across a dataset of $N$ videos $\{\mathcal{V}_n\}_{n=1}^N$ : + +$$ +f ^ {*} = \underset {f} {\operatorname {a r g m i n}} \frac {1}{N T} \sum_ {n} \sum_ {t} \mathcal {L} _ {\mathrm {s e g}} (\hat {Y} _ {t}, Y _ {t}), \tag {2} +$$ + +where $\mathcal{L}_{\mathrm{seg}}$ typically includes cross-entropy loss, Dice loss [17], and IoU loss [47]. + +Architecture Overview. Similar to other established audiovisual segmentation frameworks [5, 18, 50], our architecture consists of a visual encoder with $L$ blocks, an audio encoder, and a mask decoder, defined as follows: + +- Visual Encoder processes a single image $I_{t} \in \mathbb{R}^{H \times W \times 3}$ with resolution $H \times W$ . Each block $\mathcal{E}_{v_l}$ extracts a feature map $f_{V_l} \in \mathbb{R}^{D_l \times H_l \times W_l}$ , yielding a total of $L$ multi-scale feature maps, where $H_{l}$ and $W_{l}$ denote the spatial dimensions at level $l$ , and $D_{l}$ is the number of channels. +- Audio encoder $\mathcal{E}_a$ extracts an audio representation $f_{a}$ from the Mel spectrogram of the audio segment $A_{t} \in$ + +![](images/e461240193b84a9dc3a99cdf10e43f13c8e410561ae7b5b8cf35869611b3d9fe.jpg) +(a) The Process of Audio Guided Modality Alignment +Figure 3. (a) Image features are first grouped based on their semantic similarity. Audio and visual features interact at the group level, where features within each group are merged into compact representations guided by the audio signal. Through multiple layers of interaction, the sounding regions are progressively highlighted. The compact representations from the final layer are then used to perform contrastive learning with audio cues. (b) Guided by audio features, the features within each group merge into compact semantic representations. These grouped semantics are then remapped onto the feature map to perform the next level of alignment. + +![](images/af2acb5e01e6b7e1e0a5f789d8b56531f4495ad57f67e968e69e7f047c6b1152.jpg) +(b) Sound Guided Semantic Merging (SGSM) + +$\mathbb{R}^{T\times F}$ , where $T$ is the temporal duration and $F$ is the number of Mel filter banks. The output feature is $f_{a} = \mathcal{E}_{a}(A_{t})\in \mathbb{R}^{D}$ , with $D$ as the feature dimension. + +- Mask decoder $\mathcal{D}$ takes the multi-scale feature maps $\{f_l\}_{l=1}^L$ as input and produces a fused feature map $f_f \in \mathbb{R}^{D_f \times H_f \times W_f}$ . Here, $H_f$ and $W_f$ denote the spatial dimension, and $D_f$ is the number of channels. + +# 3.2. Audio Guided Modality Alignment + +To focus the model's attention on sound-relevant regions and prevent it from spreading to irrelevant areas, we first group visual features by semantic similarity, and then merge these groups based on their responsiveness to sound, thereby achieving compact representations. Contrastive learning is subsequently applied to reinforce the distinction between sounding and silent objects by treating sound-responsive compact representations as positive samples and less responsive ones as negatives. Fig. 3 (a) illustrates the process intuitively. + +Visual Feature Grouping. We employ a k-nearest neighbor variant of Density Peaks Clustering (DPC-KNN) as [8, 48] for visual feature grouping due to its ability to effectively capture complex data distributions through local density. Visual features are divided into $P$ groups, $\mathbf{G} = \{\mathbf{g}_1; \mathbf{g}_2; \dots; \mathbf{g}_P\}$ , where $\mathbf{g}_{\mathbf{p}} \in \mathbb{R}^{N_p \times D}$ . Here, $N_p$ denotes the token amount in group $p$ , which varies across groups. Principally, DPC-KNN works as follows: + +① For each visual token $f_{V_l}^i$ (where $i = 1,2,\dots ,H_lW_l$ ), DPC-KNN begins by calculating the local density $\rho_{i}$ based on its $k$ nearest neighbors $\mathcal{N}_k(i)$ : + +$$ +\rho_ {i} = \sum_ {j \in \mathcal {N} _ {k} (i)} \exp \left(- \left| \left| f _ {v _ {l}} ^ {i} - f _ {v _ {l}} ^ {j} \right| \right|\right). \tag {3} +$$ + +② Each token $f_{V_l}^i$ is then assigned to a cluster by identifying its nearest neighbor $h_i$ with a higher density: + +$$ +h _ {i} = \underset {j \in \mathcal {H} (i)} {\arg \min } \| f _ {v _ {l}} ^ {i} - f _ {v _ {l}} ^ {j} \|, c _ {i} = \left\{ \begin{array}{l l} i, & \text {i f} \rho_ {i} = \max (\rho) \\ c h _ {i}, & \text {o t h e r w i s e} \end{array} , \right. \tag {4} +$$ + +where $\mathcal{H}(i) = \{j|\rho_i > \rho_j\}$ is the set of tokens with higher density than token $i$ , and $c_{i}$ is the label assigned to token $i$ . + +With these assigned labels, we group the visual features, defining each group as $\mathbf{g}_{\mathbf{p}} = \{f_{v_l}^i |c_i = p\}$ , $\forall p\in$ $\{1,2,\ldots ,P\}$ . + +Sound Guided Semantic Merging. To prevent attention dispersion caused by global attention, we restrict the audio-visual attention calculation to local regions. We further merge visual features based on their responsiveness to audio signals, creating a compact representation that emphasizes features with high responsiveness to audio signals and more clearly reflects their association with audio cues, as depicted in Fig. 3 (b). + +To be specific, we first obtain the audio-visual interaction feature map $\hat{f}_{v_l}$ through a Multi-Head Cross-Attention (MCA) layer: + +$$ +\hat {f} _ {v _ {l}} = \operatorname {M C A} \left(f _ {v _ {l}}, f _ {a _ {l}}\right), \tag {5} +$$ + +where $f_{a_l} \in \mathbb{R}^{D_l}$ is the audio feature projected through a linear layer to ensure dimensional consistency with $f_{v_l}$ . Next, we estimate the relevance score $S \in \mathbb{R}^{H_lW_l}$ of $\hat{f}_{v_l}$ via a multi-perception layer and calculate the weight vector $w_{\mathbf{g_p}} \in \mathbb{R}^{N_p}$ for each group by applying an exponential function. This process is formulated as: + +$$ +w _ {x} = \frac {\exp \left(s _ {x}\right)}{\sum_ {j \in \mathbf {g} _ {\mathbf {p}}} \exp \left(s _ {j}\right)}, g _ {p} = \sum_ {x \in \mathbf {g} _ {\mathbf {p}}} w _ {x} \cdot x, \tag {6} +$$ + +where $\mathbf{g}_{\mathbf{p}}$ is the set of visual tokens assigned to the group $p$ , and $w_{x}$ is a scalar weight for $x \in \mathbb{R}^{D_l}$ in group $p$ . The compact representation of the input audio-visual pair is then defined as $G_{l} \in \mathbb{R}^{P \times D_{l}}$ , where $P$ is the group number. This operation enables the model to focus on the most relevant tokens within each group, enhancing the distinction of regions with high audio response. + +To highlight the sounding regions in the visual feature map, we enhance the compact representations using a query-based scheme and then project the updated representations back onto the visual feature map based on the token positions within each group. Specifically, the compact representations are updated by a stack of transformer decoders to converge high-level semantics: + +$$ +G _ {l} \leftarrow G _ {l} + \operatorname {s o f t m a x} \left(G _ {l} f _ {v _ {l}} ^ {T} / \sqrt {D _ {l}} + S\right) f _ {v _ {l}}. \tag {7} +$$ + +Here, the relevance score $S$ is added to the attention weights to ensure that visual tokens with high responsiveness to sound contribute more significantly to the output. The feature map obtained by remapping the compact representations is then passed into the next block. Specifically, we first retrieve the corresponding group feature from $G_{l}$ for each visual token $f_{v_l}^i$ based on its group index, and then add the retrieved feature to the visual token to enhance the representation of sounding regions. + +Contrastive-based Audio-visual Alignment. While the audio-guided feature merging yields compact visual representations that are more responsive to audio signals, it does not fully separate silent objects from sounding ones in the feature space. To address this, we employ InfoNCE contrastive loss [33] to align audio and visual features for sounding objects while repelling those of silent objects. + +Let $\hat{G} \in \mathbb{R}^{P \times D}$ represents the normalized compact features obtained in the final block, and $\hat{f}_a \in \mathbb{R}^D$ the normalized audio features. We compute similarity scores between audio and visual features via a dot product, followed by a sigmoid to derive alignment scores. These scores are then utilized to differentiate positive and negative samples based on their response to audio signals, as defined below: + +$$ +A = f _ {a} \hat {G} ^ {\top}, I = \operatorname {s i g m o i d} \left(A \cdot \sigma_ {p}\right), \tag {8} +$$ + +where $A$ represents the similarity scores, and $\sigma_{p}$ is a scaling parameter that controls the sharpness of alignment. The contrastive loss is then formulated as follows: + +$$ +\mathcal {L} _ {\mathrm {c s t}} = - \log \frac {\sum_ {i \in \mathcal {P}} \exp \left(A _ {i} / \tau\right)}{\sum_ {i \in \mathcal {P}} \exp \left(A _ {i} / \tau\right) + \sum_ {j \in \mathcal {N}} \exp \left(A _ {j} / \tau\right)}. \tag {9} +$$ + +Here, $\mathcal{P}$ is the set of indices for positive samples, defined by $I_{i} > \epsilon_{a},\mathcal{N}$ denotes the set of indices for negative samples, defined by $I_{j} < \epsilon_{a}$ , and $\tau$ is the temperature parameter. + +# 3.3. Uncertainty Estimation. + +When the sounding status of objects frequently changes in a video, the model may struggle to generate accurate and stable predictions during these transitions. To address this, we introduce uncertainty estimation to assess changes in the model's prediction confidence across all video frames. The final predictions are then refined by weighting uncertainty estimates alongside mask prediction probabilities. + +Generation of Uncertainty Map and Mask Probability Map. After passing the multi-scale feature maps from all audio-visual pairs in a video through the mask decoder $\mathcal{D}$ , we obtain fused feature maps. These fused maps are subsequently processed by a Multi-Head Attention layer to capture semantic dependencies across all time steps. The resulting feature maps, denoted as $F_{f} = \{f_{f}\}_{t = 1}^{T}\in$ $\mathbb{R}^{T\times C\times H\times W}$ , are input to the segmentation head, which generates the class logits $m\in \mathbb{R}^{T\times C\times H\times W}$ for each pixel. + +To quantify the model's prediction uncertainty, we adopt the Dirichlet distribution, as it provides granular, robust confidence information, enabling accurate uncertainty estimation and class competition [29, 36]. Specifically, $F_{f}$ is processed by the uncertainty head to obtain the uncertainty logits $\alpha \in \mathbb{R}^{T \times C \times H \times W}$ . We then apply a softplus activation to the logits to ensure non-negativity. These values serve as the parameters for the Dirichlet distribution, which allows us to compute pixel-wise uncertainty as follows: + +$$ +\delta = \frac {\alpha \left(\sum_ {c = 1} ^ {C} \alpha^ {c} - \alpha\right)}{\left(\sum_ {c = 1} ^ {C} \alpha^ {c}\right) ^ {2} \left(\sum_ {c = 1} ^ {C} \alpha^ {c} + 1\right)}, \tag {10} +$$ + +where $\delta \in \mathbb{R}^{T\times C\times H\times W}$ represents the prediction uncertainty across spatial locations. Higher values of $\delta$ indicate regions with greater uncertainty in predictions. + +Uncertainty-Weighted Prediction Adjustment. To ensure compatibility between uncertainty values and predicted probability distributions, we first normalize the spatial uncertainty by linearly scaling it to the [0, 1] range. The final predictions are then obtained via the following equation: + +$$ +\{\hat {Y} \} _ {t = 1} ^ {T} = \sigma (m) / (\delta + \epsilon), \tag {11} +$$ + +where $\sigma$ represents the softmax operation for semantic segmentation (or the sigmoid operation for binary segmentation), $m$ denotes the class logits from the segmentation head, and $\epsilon$ is set to $1\times 10^{-6}$ to ensure numerical stability. + +# 3.4. Loss function + +The final learning objective combines the typical segmentation loss $\mathcal{L}_{\mathrm{seg}}$ (cf. Eq. 2) and the contrastive loss (cf. Eq. 9): + +$$ +\mathcal {L} = \lambda_ {\mathrm {s e g}} \mathcal {L} _ {\mathrm {s e g}} + \lambda_ {\mathrm {c s t}} \mathcal {L} _ {\mathrm {c s t}}, \tag {12} +$$ + +where $\lambda_{cst} = 0.1$ and $\lambda_{seg} = 1$ are the weight parameters. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and Metrics. We conduct experiments on: AVS-Object [49], AVS-Semantic [50], and VPO [5]. + +- AVS-Objects comprises 5,356 audio-visual pairs, each with five frames extracted from a video and a corresponding 5-second audio segment. Among these pairs, 4,932 contain a single audio event, while 424 involve multiple audio events. Binary masks are provided as ground truth to identify regions as either sounding or silent. +- AVS-Semantic extends the AVS-Object dataset, consisting of 12,356 audio-visual pairs. This extended dataset includes ten frames paired with a 10-second audio segment. It provides semantic annotations that identify both the sounding regions and the specific audio type. + +Table 1. Quantitative results on AVS-Objects and AVS-Semantic (resized to $224 \times 224$ ). The best results are highlighted in bold, while the second-best results are underlined. Results are obtained using our complete design but with different backbones. See analysis in §4.2. + +
MethodsVisual BackboneAudio BackboneAVS-Objects-S4AVS-Objects-MS3AVS-Semantic
J&Fm↑J↑Fm↑J&Fm↑J↑Fm↑J&Fm↑J↑Fm↑
TPAVI [49] [ECCV22]PVT-V2-B5VGGish83.378.787.959.354.064.532.529.835.2
AVSC [20] [ACM-MM23]Swin-BaseVGGish85.081.388.662.659.565.8---
CATR [16] [ACM-MM23]PVT-V2-B5VGGish87.984.491.368.662.774.535.732.838.5
DiffusionAVS [26] [Arxiv23]PVT-V2-B5VGGish85.781.490.064.658.270.9---
ECMVAE [27] [ICCV23]PVT-V2-B5VGGish85.981.790.164.357.870.8---
AuTR [22] [Arxiv23]PVT-V2-B5VGGish82.177.686.572.066.277.7---
AQFormer [13] [IJCAI23]PVT-V2-B5VGGish85.581.689.467.562.272.7---
AVSegFormer [9] [AAAI24]PVT-V2-B5VGGish86.883.190.567.261.373.040.137.342.8
AVSBG [11] [AAAI24]PVT-V2-B5VGGish86.181.790.461.055.166.8---
GAVS [41] [AAAI24]ViT-BaseVGGish85.180.190.070.663.777.4---
BAVS [21] [TMM24]Swin-BaseBeats86.282.789.862.859.665.935.633.637.5
COMBO [45] [CVPR24]PVT-V2-B5VGGish88.384.791.965.259.271.244.142.146.1
QDFounder [18] [CVPR24]Swin-TinyVGGish83.979.588.264.061.966.1-53.4-
CAVP [5] [CVPR24]PVT-V2-B5VGGish90.587.393.672.767.378.155.348.662.0
AVSStone [24] [ECCV24]Swin-BaseVGGish87.383.291.372.567.377.661.556.866.2
BiasAVS [37] [ACM-MM24]Swin-BaseVGGish88.283.393.074.067.280.847.244.449.9
RAVS (OURS)PVT-V2-B5VGGish91.390.392.274.769.779.663.958.769.0
RAVS (OURS)MIT-B5VGGish92.291.692.874.268.380.165.459.871.0
RAVS (OURS)MIT-B5HTSAT93.593.193.876.470.682.165.760.870.6
+ +- VPO is a synthetic dataset that combines single-frame images from COCO [19] with 3-second audio clips from VGGSound [1]. It includes three subsets: VPO-SS (12,202 single-source samples), VPO-MS (9,817 multi-source samples), and VPO-MSMI (12,855 samples), where weighted single-source data represent spatial information for multi-source sounds. + +Following [5, 6, 18], we evaluate the performance of all methods using the mean Intersection over Union $\mathcal{J}$ and F-score $(\mathcal{F}_{\beta})$ , where $\beta$ is set as 0.3. Additionally, due to space constraints, we provide comparisons using the metrics from TPAVI [49, 50] in the supplementary material. + +Network Configuration. Our framework is end-to-end trainable, with all components parameterized by neural networks. The spatial dimensions of the three feature maps used for sound-guided semantic merging are 1/4, 1/8, and 1/16 of the input image size. The number of groups for each feature map is set to 14, 7, and 5. The threshold $\epsilon_{a}$ for selecting positive and negative samples is set to 0.5. + +# 4.2. Quantitative Performance + +Performance on AVS-Objects and AVS-Semantic. Table 1 presents a comparative analysis of our approach against 16 recent audio-visual segmentation (AVS) methods evaluated on AVS-Objects and AVS-Semantic. In addition to the commonly adopted PVT-V2-B5 [40] and VGGish [1], we leverage advanced visual and audio models, MIT-B5 [43] and HTSAT [3], to further enhance segmentation performance. Our approach achieves impressive results, with $\mathcal{J}\&\mathcal{F}_{\beta}$ scores of $93.0\%$ on S4 and $76.4\%$ on MS3 for AVS-Objects, demonstrating precise localization of audible objects. In particular, on the AVS-Semantic dataset, our method achieves a substantial $4.2\%$ improvement in $\mathcal{J}\&\mathcal{F}_{\beta}$ over the previous state-of-the-art, AVSStone. Notably, even + +with the standard backbones PVT-V2-B5 and VGGish, our model sets new benchmarks across all metrics. + +Performance on VPO. In Table 2, we report the performance comparison on VPO series datasets. Our approach greatly outperforms the second-best one AVSStone. Specifically, for the VPO-SS dataset, we achieve $\mathcal{J} \& \mathcal{F}_{\beta}$ scores of $74.97\%$ compared to $68.54\%$ , for VPO-MS: $73.48\%$ vs. $64.26\%$ , and for VPO-MSMI: $69.30\%$ vs. $58.76\%$ . Notably, VPO-MSMI includes many cases where objects from the same visual category appear in a frame but have different auditory states [5]. This substantial improvement over AVSStone— $\mathcal{J}$ on VPO-MSMI: $61.89\%$ vs. $50.11\%$ and $\mathcal{F}$ : $76.70\%$ vs. $67.40\%$ —demonstrates that our method effectively directs attention to the genuine sounding regions. + +# 4.3. Qualitative Performance + +Fig. 4 presents qualitative comparisons between our method and three competing approaches: TPAVI [50], CAVP [5], and AVSStone [24]. In scenario (a), two men are positioned closely but are in different sounding states. AVSStone, CAVP, and TPAVI all tend to over-segment the silent man's region while under-segmenting the audible man's, reflecting their difficulty in distinguishing between visually similar objects with differing sound states. In contrast, our method accurately localizes the speaking man, effectively avoiding these mis-segmentations. In the more complex scenario (b), the sound status of the bird switches between the second and third frames. TPAVI and AVSStone tend to assume the bird is sounding in all frames, leading to segmentation of the bird throughout, while CAVP assumes silence and barely segments the bird region. By contrast, our method robustly handles these rapid sound transitions, mitigating these challenges effectively. + +![](images/ed3bf7b4949ecc55fa110f3cf8b1e5d4d51c5a4390ed2ea8efc916ab372041f7.jpg) +Figure 4. Visual comparison of challenging cases (illustrated 1 and 2 in §1) in AVSBench-Semantic. Refer to §4.3 for detailed analysis. + +![](images/b18bdaa7d2b3a7c5ce28b05503a8852f4e279fce97df1f57cfa4458e1bf33f77.jpg) + +Table 2. Quantitative comparisons on VPO datasets (§4.2). 'CPM*' indicates that training and testing are performed on images with the original resolution, while other methods employ images resized to $224 \times 224$ pixels. The best results are highlighted in bold, and the second-best results are in underlined. Results are obtained using our complete design but with different audio-visual backbones. + +
MethodsVisual BackboneAudio BackboneTrainable ParamsVPO-SSVPO-MSVPO-MSMI
J&Fβ↑J↑Fβ↑J&Fβ↑J↑Fβ↑J&Fβ↑J↑Fβ↑
TPAVI [49] [ECCV22]PVT-V2-B5VGGish101.32M44.6341.6447.6245.6842.349.0643.1940.0346.34
AVSegFormer [9] [AAA124]PVT-V2-B5VGGish186.05M45.9443.8148.0643.7247.340.1449.9347.1952.67
CAVP [5] [CVPR24]ResNet50VGGish119.79M67.0258.8175.2361.3253.2469.3956.4848.1864.78
BiasAVS [37] [ECCV24]SwinBaseVGGish107.12M67.4659.1475.7863.4255.6171.2357.9449.666.27
AVSStone [24] [ACM-MM24]SwinBaseVGGish114.63M68.5459.7277.3564.2656.2372.2958.7650.1167.40
CPM* [6] [ECCV24]ResNet50VGGish-73.4967.0979.8872.9165.9179.968.0760.5575.58
RAVS (OURS)MIT-B5VGGish103.84M74.2767.5181.0272.9266.3379.5168.6961.3276.05
RAVS (OURS)MIT-B5HTSAT103.84M74.9768.0381.9073.4966.9780.0169.3061.8976.70
+ +# 4.4. Further Analysis + +Ablation Study. We carry out ablation studies on AVS-Object-MS3 and AVS-Semantic to evaluate the effectiveness of individual components and design choices in our framework. Our baseline model includes audio and visual encoders, cross-attention layers for fusion, and a mask decoder. Based on this baseline, we set up two configurations to examine the effectiveness of SGSM. The first configuration, shown in Row 2 (Baseline+GTF), utilizes ground truth masks to filter silent regions during modality alignment. The second configuration, shown in Row 3 (Baseline+SGSM), incorporates our proposed sound-guided semantic merger (SGSM). As results indicate, SGSM improves the baseline by $7.4\%$ in $\mathcal{J}\& \mathcal{F}_{\beta}$ on AVS-Semantic and achieves $3\%$ better performance than Baseline+GTF. This demonstrates that SGSM effectively directs the model's attention to audible regions, mitigating interference from silent areas. + +Building on SGSM, we introduce contrastive modality alignment (CST), shown in Row 4. Compared to SGSM alone, this alignment design improves $\mathcal{J} \& \mathcal{F}_{\beta}$ by $1.6\%$ on AVS-Semantic, indicating that aligning compact features with audio representations enhances audio-visual alignment. Additionally, we integrate our uncertainty estimation + +module (UE) on top of SGSM+CMA, yielding further performance gains. On AVS-Semantic, $\mathcal{I}$ and $\mathcal{F}_{\beta}$ increase by $1.7\%$ and $1.3\%$ , respectively, confirming that UE effectively mitigates errors caused by frequent changes in an object's audible state, resulting in more accurate segmentation. + +Effectiveness of Audio Guided Alignment. In Fig. 5, we map the compact representation identified as a positive or negative sample back onto the image based on the locations of their visual combinations and show their responsiveness to the audio cues. When two objects of the same visual category but different sound states appear in a video frame, our method effectively identifies the truly sounding object as a positive sample and the silent object as a negative sample. For example, in (a)-(c), in scenes with two women where only one is speaking, and in scenes with multiple adjacent cars where only one is making sounds, our method accurately associates the sound with the truly audible objects. + +When multiple objects of the same category are sounding simultaneously, our method consistently classifies all sounding objects as positive samples, as shown in (d)-(f). Additionally, by analyzing the sound responsiveness of all samples, we observe that regions around positive samples typically show lower sound responsiveness. This indicates that the audio-guided feature merging not only focuses ef + +![](images/4dd35496cc71cf1166e1af126d5c857f3973cc9e5555b1644527bb9b1d60cc52.jpg) +Figure 5. Visualization of positive (Pos.) and negative (Neg.) samples generated by the AMA module. Red indicates negative samples, while blue represents positive samples. Darker blue indicates regions with a higher responsiveness to audio cues, while darker red indicates lower responsiveness. See detailed analysis in §4.4. + +Table 3. Evaluation of component effectiveness (§4.4). GTF: Ground-Truth mask filtering; SGSM: sound-guided semantic merging; CST: contrastive-based alignment; AMA: audio-guided modality alignment; UE: uncertainty estimation. + +
SettingsAVS-Objects-MS3AVS-Semantic
J&Fβ↑J↑Fβ↑J&Fβ↑J↑Fβ↑
Baseline64.359.868.757.251.462.9
+GTF67.962.273.659.655.164.1
+SGSM70.965.376.462.657.767.5
+SGSM+CST (AMA)72.266.178.364.259.169.3
+AMA+UE (Ours)76.470.682.165.760.870.6
+ +fectively on relevant sounding regions but also assists in identifying hard samples around the sounding regions. + +Effectiveness of Uncertainty Estimation. Fig. 6 presents the visualizations of uncertainty maps generated by our uncertainty estimation (UE) module. In (a), where the sound state of all objects remains constant, the model shows consistently low uncertainty values across the entire image, indicating high confidence in its segmentation predictions. In contrast, in (b), where a 'leopard' undergoes a transition in the sound state between adjacent frames, the model exhibits higher uncertainty for both sound-emitting and silent frames, with even higher uncertainty values in the silent frames. This higher uncertainty effectively lowers the prediction probability in the 'leopard' region in the second frame, reducing over-segmentation in silent frames. These findings demonstrate that frequent sound state transitions significantly impact the model's confidence in its predictions, suggesting that uncertainty estimation is an effective way to mitigate mis-segmentation issues. + +Effects of Group Number. We conduct a study on the impact of different group numbers when conducting audioguided alignment. The grouping setting of [14, 7, 5] (approximately 1/4 of the feature map size) achieves the best + +![](images/d9f58c5ee99b6d2e88b918eea3b445365c7ca20b8936321c4a0a96b79328a5ff.jpg) +Figure 6. Visualizations of uncertainty maps, with colors ranging from red (high uncertainty) to blue (low uncertainty). + +Table 4. Comparison of different group numbers for three-scale feature maps. See analysis in §4.4. + +
GroupsAVS-Objects-MS3AVS-Semantic
J&Fβ↑J↑Fβ↑J&Fβ↑J↑Fβ↑
[28, 14, 5]73.768.678.863.457.868.9
[14, 7, 5]76.470.682.165.760.870.6
[10, 7, 5]75.169.380.864.458.870.0
[5,5,5]71.566.776.362.656.568.7
+ +performance, attaining the highest $\mathcal{I} \& \mathcal{F}_{\beta}$ scores on both datasets. In contrast, smaller grouping numbers like [5, 5, 5] led to decreased performance. This suggests that progressively reducing the group number supports more effective semantic merging of sound-emitting regions under audio guidance. Additionally, a larger group number, such as [28, 14, 5], divides the feature map into many small groups, dispersing attention across numerous small regions and thus leading to poorer results. + +# 5. Conclusion + +In this paper, we propose a novel framework to address modality misalignment caused by ambiguous spatiotemporal correspondences. Unlike previous methods that rely on global attention or employ masks to exclude silent regions, our approach first utilizes audio to guide the merging of sounding regions, followed by contrastive learning to align compact visual representations with audio cues. This design enhances the model's ability to distinguish between audible and silent objects, even when visually similar but acoustically different objects are in close proximity. Additionally, we introduce uncertainty estimation to mitigate predictive instability arising from frequent changes in an object's sound state. The two items enable our framework to prevent the over-segmentation of silent regions in complex scenarios. Extensive experiments demonstrate the effectiveness of our approach in handling challenging cases. + +Acknowledgements. This work is supported by ARC-Discovery (DP220100800 to XY), and ARC-DECRA (DE230100477 to XY). Chen Liu is funded by the China Scholarship Council and CSIRO top-up (50092128). + +# References + +[1] Honglie Chen, Weidi Xie, Andrea Vedaldi, and Andrew Zisserman. Vggsound: A large-scale audio-visual dataset. In ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 721-725. 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This technique has tremendous potential in scenarios like copyright protection and information retrospection. Some previous studies have proposed to enhance the robustness of the methods against image disturbances to increase their applicability. However, they generally cannot achieve a satisfying balance between the steganography quality and robustness. Instead of image-in-image steganography, we focus on the issue of message-in-image embedding that is robust to various real-world image distortions. This task aims to embed information into a natural image and the decoding result is required to be completely accurate, which increases the difficulty of data concealing and revealing. Inspired by the recent developments in transformer-based vision models, we discover that the tokenized representation of image is naturally suitable for steganography task. In this paper, we propose a novel message embedding framework, called Robust Message Steganography (RMSteg), which is competent to hide message via QR Code in a host image based on an normalizing flow-based model. The stego image derived by our method has imperceptible changes and the encoded message can be accurately restored even if the image is printed out and photographed. To our best knowledge, this is the first work that integrates the advantages of transformer models into normalizing flow. The code is available at https://github.com/huayuan4396/RMSteg. + +# 1. Introduction + +Steganography, the art of hiding secret information in a carrier, has long been a prominent research direction. This technique is competent to embed information like images and text into target containers, thus achieving copyright + +![](images/2b256ddd9b923408ecb273fd96eb334787bcf2883d0a6c7a4e4a507cc707de28.jpg) +Figure 1. Compared with previous methods that can only embed limited bit-level information, RMSteg can achieve a much higher embedding capacity and meanwhile has better steganography quality. Also, it can survive various real-world distortions. + +protection [10, 37] and information retrospection [48, 52]. Steganography aims to prevent people from discovering the existence of secret data instead of obscuring meaning of data, differentiating it from cryptography. Specifically, image steganography uses image to carry secret information. + +Traditional image steganography methods mainly modify the image in spatial domain [14, 17, 25, 28, 29] or transform domain [2, 36, 55]. This kind of method is easy to be detected by steganalysis techniques [9, 50], compromising security. Recently, with the developments of deep learning, some deep steganography methods have been proposed. Most of them are based on autoencoder [3, 44, 52, 54] and normalizing flow [5, 12, 16, 24, 47, 48]. + +Images can undergo various digital or real-world disturbances during dissemination. To enable the stego images to survive these distortions, some robust steganography methods have been proposed. They consider various distortion situations like light field messaging (LFM) [44], JPEG compression [47], etc. In the field of robust steganography, robust message embedding is very promising in many ap- + +plication scenarios like hyperlink hiding [37] and metadata embedding [13, 52]. However, this task requires high decoding accuracy, which poses a challenge to the balance of decoding performance and stego image quality, especially when facing real-world distortions. Although some studies [10, 37] have proposed to hide messages in host images and try to make them survive printing and photography, which is among the most demanding situations that require high steganography robustness, they cannot achieve enough steganography quality and capacity at the same time. + +As the most widely utilized method, normalizing flow-based model [6, 7, 18] has achieved impressive performance in various steganography tasks. Existing methods [5, 12, 16, 24, 47, 48] generally incorporate normalizing flow by utilizing a convolutional neural network (CNN) based backbone. However, according to our experiments, this kind of model design can lead to obvious artifacts in stego images when handling robust steganography tasks due to the lack of inner-channel feature fusion. Inspired by the transformer-based vision models, we discover that the tokenized representation of image is naturally suitable for robust steganography that requires highly abstract feature learning. As a result, we aim to take advantages of it to address the robust message-in-image steganography problem. + +In this paper, we propose a new framework for message embedding, called Robust Message Steganography (RMSteg), a simple demo is demonstrated in Figure 1. We use QR Code as the message carrier and encode it into the host image. Unlike previous methods that directly encode the secret image, we propose an invertible QR Code transition as a preprocessing step, which transforms the QR Code based on the features of the host image, lowering down the artifacts in stego images and meanwhile maintaining a high decoding accuracy. We outline a steganography model called AttnFlow, which integrates tokenized image representation into normalizing flow. We propose an attention affine coupling block (AACB) that leverages the attention mechanism [8, 41] instead of traditional CNN for invertible steganography function learning, thus significantly improving the stego image quality. Compared with previous methods, our method can overcome the aforementioned difficulties and achieve robust, high-quality and high-capacity message-in-image steganography. The main contributions of this paper include three aspects: + +- We use QR Code as the message carrier and propose a transition scheme to transform the QR Code before steganography. This process can improve the stego image quality while maintaining decoding accuracy. +- We propose an invertible token fusion module that can effectively improve the steganography quality by simply including a small learnable matrix. +- We propose a normalizing flow-based steganography network that integrates the tokenized image representation. + +Our network can generate stego images with significantly higher quality and can survive extreme distortions. We use the case of printing and photography to validate our method's effectiveness. + +# 2. Related Work + +# 2.1. Image Steganography + +Traditional Steganography Image steganography hides information in an image by performing imperceptible changes on a host image. Traditional methods modify the image in spatial or transform domain [3]. Spatial-domain steganography generally leverages least-significant-bit (LSB) replacement [25], bit plane complexity segmentation (BPCS) [17, 28] and palette reordering [14, 29] to conceal information. However, this kind of scheme may raise statistical anomalies that can be detected by steganalysis techniques [9, 50]. Some methods utilize high-dimensional features [30] and distortion constraints [20] to improve steganography security and quality. Transform-based steganography can hide data in a transformed domain using discrete cosine transform (DCT) [2] and discrete wavelet transform (DWT) [36, 55]. Due to the limited ability of feature representation and transformation, traditional methods generally cannot achieve a satisfying quality. + +Deep Steganography. Recently, various deep learning-based image steganography schemes have been proposed and have achieved impressive performance. HiDDeN [54] adopted the autoencoder (AE) to embed binary messages. Baluja [3] first utilized an end-to-end network to hide a color image in another. Some studies [10, 31, 34, 38, 39, 51] incorporated generative adversarial network (GAN) [11] to reduce the image artifacts and defend steganalysis. More recently, the invertible neural network (INN) [6, 7, 18] has been widely used for steganography. These methods successfully hide single [5, 16, 24] or multiple [12, 45, 48] images in a carrier image. There are also some studies focusing on coverless steganography [21, 23, 26, 49] that directly transforms the secret information into a cover image. These methods mainly focus on improving the embedding capacity instead of robustness, as a result, they generally cannot survive image distortions. + +Robust Steganography Robust steganography allows information decoding even if the images are interfered with by digital transmission or real-world distortions, which is meaningful for scenarios like copyright protection, secret communication, etc. VisCode [52] hides QR Codes in host images and can survive image brightness changes and slight tampering. LFM [44] is robust to light field messaging. RIIS [47] considers JPEG compression and various kinds of noise separately based on a conditional network. StegaS-tamp [37] and ChartStamp [10] take printing and photography into account but can only embed very little informa + +tion at a cost of visual quality loss. As far as we know, existing methods cannot achieve both high-quality and high-capacity message steganography that is robust to extreme image distortions. In this paper, we aim to take the advantages of transformer-based model to address this problem. + +# 2.2. Normalizing Flow-Based Models + +Normalizing flow model was first proposed as a generative model by Dinh et al. [6]. With further improvement by RealNVP [7] and GLOW [18], it is also known as the invertible neural network (INN). INN can learn an invertible function using a set of affine coupling layers with shared parameters to map the original data distribution to a simple distribution (e.g., Gaussian distribution). Chen et al. [4] proposed an unbiased estimation for normalizing flow model. i-RevNet [15] utilizes an explicit inversion to improve the invertible architecture. + +Recently, normalizing flow has been applied to various downstream tasks in computer vision, such as image [46] and video [56] super-resolution, image-to-image translation [40]. Especially, in the field of steganography, normalizing flow-based methods [5, 24, 48] have shown promising performance. HiNet [16] introduces the discrete wavelet transform to guide channel squeezing and improve the steganography quality. DeepMIH [12] hides single or multiple images with a saliency detection module. Mou et al. [27] incorporated a key-controllable network design to implement secure video steganography. Xu et al. [47] simulated distortions during model training to improve the robustness and security of their method. Although previous studies have leveraged various methods to improve the network architecture for better performance, they cannot attend to both image quality and steganography robustness simultaneously. + +# 3. Method + +# 3.1. Overview + +Given a secret message $T_{s}$ , we first encode it into a QR Code image $I_{q}$ . The concealing procedure aims to embed $I_{q}$ into a host image $I_{h}$ and derive a stego image $I_{s}$ that is perceptually similar to $I_{h}$ . Then, $I_{s}$ can suffer from various real-world image distortions, resulting in a distorted image $I_{s}'$ . After that, the revealing procedure aims to restore a QR Code $\hat{I}_{q}$ from $I_{s}'$ that can be successfully recognized to obtain the original message. + +To achieve the aforementioned targets, we first leverage a QR Code transition scheme (Sec. 3.3) to transform the original QR Code according to the host image, reducing the artifacts it causes in the subsequent steganography process. Then, we use an invertible token fusion (ITF) module (Sec. 3.4) to improve the stego image quality. After that, we propose an AttnFlow model (Sec. 3.5) to perform mes + +sage embedding. To make our method robust to real-world distortions, we incorporate a distortion simulation module during the training stage, which will be described in detail in Sec. 3.6. Fig. 2 demonstrates an overview of the pipeline of our RMSteg. + +# 3.2. Preliminary: Normalizing Flow + +Normalizing Flow [6, 7, 18], also called the invertible neural network (INN), is proposed to model a bijective projection from a complex distribution (e.g., images) to a tractable distribution (e.g. Gaussian distribution and Dirac distribution). This kind of model generally comprises several invertible affine coupling blocks (ACBs). The most basic ACB architecture is proposed by NICE [6], in which the input $u^{i}$ of the $i^{\text{th}}$ ACB is split into two parts, $u_{1}^{i}$ and $u_{2}^{i}$ , whose corresponding outputs are $u_{1}^{i+1}$ and $u_{2}^{i+1}$ , respectively. For the forward process, the following transformation is performed: + +$$ +u _ {1} ^ {i + 1} = u _ {1} ^ {i} + \sigma \left(u _ {2} ^ {i}\right), \quad u _ {2} ^ {i + 1} = u _ {2} ^ {i} + \delta \left(u _ {1} ^ {i + 1}\right), \tag {1} +$$ + +where $\sigma (\cdot)$ and $\delta (\cdot)$ are arbitrary functions. Obviously, the backward process can be formulated as: + +$$ +u _ {2} ^ {i} = u _ {2} ^ {i + 1} - \delta \left(u _ {1} ^ {i + 1}\right), u _ {1} ^ {i} = u _ {1} ^ {i + 1} - \sigma \left(u _ {2} ^ {i}\right). \tag {2} +$$ + +In the normalizing flow architecture, $\delta(\cdot)$ and $\sigma(\cdot)$ in Equation 1 and Equation 2 can be implemented by neural network modules with shared parameters and inverse calculation manner. By stacking multiple ACBs, the network can learn an invertible transformation between two distributions. Since this scheme is inherently suitable for steganography, many studies have utilized it for data hiding and proposed various improvements. In this paper, we further extend the ability of normalizing flow and propose a new network architecture for our robust message embedding task. + +# 3.3. Invertible QR Code Transition + +For the message embedding task in this paper, the hidden QR code needs to be restored with enough accuracy to be identified by common devices like cell phones, webcams, etc. To balance the trade-off between the stego image quality and decoding accuracy, VisCode [52] obtains a visual saliency map to guide the QR Code embedding while Chart-Stamp [10] utilizes the semantic segmentation result as the training loss guidance. Although this kind of rule-based strategy can improve the visual quality of the stego image, it does not consider the inherent relationship between QR Codes and the host image. + +In our method, we adopt a more direct approach, which is modifying the QR Code image according to the host image (shown in Figure 2 (a)). We call it invertible QR Code transition (IQRT). The key idea of IQRT is that, the QR Code used for steganography is not necessarily to be + +![](images/f9d3330aaa7cf9cdcfa2931293b817d21be4b1aacd7e01ccdcfe043bafe40115.jpg) +Figure 2. The pipeline of RMSteg. We first transform the QR Code encoded with the secret message to make it easier to hide through an invertible neural network (a). After that, we perform invertible token fusion (ITF) (b) on the tokenized QR Code. We then use a normalizing flow-based model with attention affine coupling blocks (AACBs) to implement data concealing and revealing (c). During training, we employ a distortion simulation module (d) to simulate real-world image disturbances. + +black-and-white to keep its information. Thus, a learnable transformation can be applied to the QR Code for a better steganography quality as long as the transformed code is still identifiable. Formally, given a host image $I_h$ and a QR Code $I_q$ with the same size, we use an off-the-shelf INN architecture (with only two invertible blocks) proposed by ISN [24] to learn an invertible function $f(\cdot)$ that derives the transformed QR Code $I_q^*$ by $I_q^* = f(I_q, I_h)$ . In the reverse process, the restored QR Code $\hat{I}_q$ can be obtained by $\hat{I}_q = f^{-1}(I_q^*, I_s')$ , where $f^{-1}(\cdot)$ is the inverse function of $f(\cdot)$ defined by normalizing flow and $I_s'$ is the distorted stego image. Here $I_s'$ is used instead of $I_h$ since the latter is unknown in the decoding procedure. + +During network training, the transition network is jointly trained with the subsequent steganography network. We employ the same constraint as ArtCoder [35] to the transformed QR Code to ensure that it is still identifiable. Specifically, a Gaussian convolution kernel is applied to each code module to simulate the QR Code scanning procedure. For more details, we suggest referring to the original paper [35]. We do not use extra constraint to the transition network so that it can learn the best transition strategy according to the overall optimization targets. Figure 3 shows some transition results, it can be observed that the transformed QR Codes have lower brightness. However, with the aforementioned constraint, the transformed QR Codes are still identifiable, guaranteeing almost no information loss. + +# 3.4. Invertible Token Fusion + +With the transformed QR Code, we first use a ViT [8] to obtain a tokenized representation $T_{q} \in \mathbb{R}^{N \times D}$ , in which $N$ + +![](images/60bd79a0c18e84abe15c26a818c2e66653c54999c60f1f172372f6df6c5e9cf3.jpg) +Figure 3. Some QR Code transition results, the transformed QR Codes are still identifiable. + +is the number of tokens and $D$ represents the token dimensionality. Inspired by the invertible $1 \times 1$ convolution proposed by GLOW [18], before feeding $T_{q}$ to the subsequent steganography network, we put forth an invertible token fusion (ITF) module (as shown in Figure 2 (b)) to transform the QR Code tokens for a better steganography quality. + +Formally, we use a learnable matrix $\mathcal{M} \in \mathbb{R}^{N \times N}$ , which is initialized as an orthogonal matrix using Cholesky decomposition [19], as a transform matrix for $T_{q}$ . In the steganography process, $T_{q}$ is transformed by performing a matrix multiplication: $T_{q}' = \mathcal{M} \cdot T_{q}$ . Obviously, in the decoding procedure, the restored tokens $\hat{T}_{q}$ can be obtained by: $\hat{T}_{q} = \mathcal{M}^{-1} \cdot \hat{T}_{q}'$ , where $\mathcal{M}^{-1}$ is the inverse matrix. + +Different from GLOW [18] that utilizes the invertible convolution to learn the channel-wise fusion strategy, our ITF module learns a patch-wise transformation that enables inner-channel feature interaction. Our experiments also prove that ITF can efficiently and effectively improve the steganography quality by simply introducing the aforementioned learnable matrix. + +# 3.5. Steganography with AttnFlow + +Previous steganography studies based on normalizing flow generally adopt a convolutional neural network (CNN) based backbone, mostly DenseNet [42], to construct the affine coupling blocks (ACBs). This kind of design only considers the channel-wise feature fusion and can lead to perceptible artifacts in stego images, especially in the robust steganography task. Motivated by the impressive performance achieved by the transformer-based [8, 41] vision models recently, we propose a model called AttnFlow that introduces attention mechanism to normalizing flow to implement robust steganography. + +As shown in Figure 2 (c), similar to ordinary normalizing flow, AttnFlow contains several attention affine coupling blocks (AACBs) for invertible function learning. Assume that the input of the $i^{\mathrm{th}}$ AACB is split into $T_{h}^{(i - 1)}$ and $T_{q}^{(i - 1)}$ , corresponding to the host image tokens and QR Code tokens, respectively. Specifically, $T_{h}^{(0)}$ is the tokenized host image obtained with a basic ViT [8] and $T_{q}^{(0)}$ represents the QR Code image tokens output by the ITF module. For the $i^{\mathrm{th}}$ AACB, we perform the following affine transformation: + +$$ +T _ {h} ^ {(i)} = T _ {h} ^ {(i - 1)} + \phi \left(T _ {q} ^ {(i - 1)}\right) + \mathcal {C} \left(T _ {q} ^ {(i - 1)}, T _ {h} ^ {(0)}\right) \times \alpha_ {i}, \tag {3} +$$ + +$$ +T _ {q} ^ {(i)} = \eta \left(T _ {h} ^ {(i)}\right) + T _ {q} ^ {(i - 1)} \odot e x p \left(\rho \left(T _ {h} ^ {(i)}\right)\right), +$$ + +in which $\phi (\cdot),\eta (\cdot),\rho (\cdot)$ are self-attention blocks [41] followed by a feedforward multilayer perceptron (MLP), $\mathcal{C}(q,kv)$ represents the cross-attention block [41], $exp(\cdot)$ is the exponential function, $\odot$ indicates the Hadamard product and $\alpha_{i}$ is a dependent trainable coefficient for each AACB. We calculate the attention value with: + +$$ +A t t n (Q, K, V) = M \cdot V, M = S o f t m a x \left(\frac {Q K ^ {T}}{\sqrt {d}}\right), (4) +$$ + +where $Q, K, V$ are derived from the learned projections and $d$ is the dimension of the projected tokens. As described in Equation 3, in addition to the self-attention value, we also calculate the cross-attention value of the initial host image tokens $T_{h}^{(0)}$ upon the QR code tokens $T_{q}^{(i - 1)}$ for each AACB. Then, we add these values to $T_{h}^{(i - 1)}$ to help AACBs gradually integrate the information from the QR code into the image. For the QR Code tokens, we choose to adopt a generally incorporated [5, 16, 24, 48] affine transformation and replace the original convolutional blocks with $\eta(\cdot)$ and $\rho(\cdot)$ . After $n$ AACBs, $T_{h}^{(n)}$ further goes through a detokenizer $^{1}$ , resulting in the final stego image. Although some methods further map $T_{h}^{(n)}$ and $T_{q}^{(n)}$ as a conditional distribution for better performance, here we choose to adopt + +the same assumption as HiNet [16], which is simply positing that $T_{q}^{(n)}$ obeys a Gaussian distribution. We follow this scheme since it would not increase calculation overload by including extra networks and we empirically find it would make almost no performance loss in our task. + +In the revealing process, we aim to restore the original QR Code from a distorted stego image $I_{s}^{\prime}$ , we first use a UNet [32] for feature enhancement and tokenize it to derive $\hat{T}_h^{(n)}$ . Then, we obtain $\hat{T}_q^{(n)}$ by sampling from a standard Gaussian distribution. After that, we perform the inverse AACB transformation by going through them with inverse calculation manner: + +$$ +\hat {T} _ {q} ^ {(i - 1)} = \left(\hat {T} _ {q} ^ {(i)} - \eta \left(\hat {T} _ {h} ^ {(i)}\right)\right) \odot e x p (- \rho \left(\hat {T} _ {h} ^ {(i)}\right)), \\ \hat {\alpha} (i, 1) = \hat {\alpha} (i) = \hat {\alpha} (i - 1) = \hat {\alpha} (i, 1) = \hat {\alpha} (i, 0) \tag {5} +$$ + +$$ +\hat {T} _ {h} ^ {(i - 1)} = \hat {T} _ {h} ^ {(i)} - \phi (\hat {T} _ {q} ^ {(i - 1)}) - \mathcal {C} (\hat {T} _ {q} ^ {(i - 1)}, \hat {T} _ {h} ^ {(0)}) \times \alpha_ {i}, +$$ + +in which $\hat{T}_h^{(0)}$ is obtained by tokenizing $I_s^\prime$ since $I_{h}$ is unknown in the decoding process. Then, $\hat{T}_q^{(0)}$ is detokenized and fed into the reversed QR Code transition (introduced in Sec. 3.3) with $I_s^\prime$ to get the final decoded QR Code image. + +# 3.6. Optimization Target and Training Strategy + +Distortion Simulation Module We use a module to simulate the distortions that the stego images may undergo during printing and photography. In this paper, we choose to use the same simulation module proposed by StegaS-tamp [37] that considers color shifting, blurring, noising, etc. We mainly modify the standard deviation of Gaussian noise from 0.02 to 0.07 and increase the JPEG compression quality from 25 to 60 for our task. During training, we perform random distortion combinations on stego images to simulate real-world image disturbances. + +Loss Function The aforementioned three networks (IQRT, ITF and AttnFlow) are trained jointly. We use the following loss functions to guide the training process: + +$$ +\mathcal {L} _ {s t e g} ^ {L 1} = \left\| I _ {h} - I _ {s} \right\| _ {1}, \tag {6} +$$ + +$$ +\mathcal {L} _ {s t e g} ^ {s s i m} = s s i m \left(I _ {h}, I _ {s}\right), \tag {7} +$$ + +$$ +\mathcal {L} _ {s t e g} ^ {l p i p s} = l p i p s \left(I _ {h}, I _ {s}\right), \tag {8} +$$ + +$$ +\mathcal {L} _ {q r} = \left\| I _ {q} - \hat {I} _ {q} \right\| _ {1}, \tag {9} +$$ + +in which $ssm(\cdot)$ represents the structural similarity index [43] and $lpips(\cdot)$ indicates the perception loss [53]. Besides, as introduced in Sec. 3.3, an additional QR Code transition loss $\mathcal{L}_t$ is incorporated. The overall loss function is the weighted sum of the above functions: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \mathcal {L} _ {\text {s t e g}} ^ {L 1} + \beta \mathcal {L} _ {\text {s t e g}} ^ {\text {s s i m}} + \gamma \mathcal {L} _ {\text {s t e g}} ^ {\text {l p i p s}} + \delta \mathcal {L} _ {\text {q r}} + \epsilon \mathcal {L} _ {t}, \tag {10} +$$ + +where $\alpha, \beta, \gamma, \delta, \epsilon$ are weight coefficients. + +Table 1. Steganography quality under different situations. Here $\sigma$ represents the standard deviation of Gaussian noise (given the image pixel values range in [0, 1]). The best and second-best results are marked in red and blue colors, respectively. + +
MethodStego Imageσ = 0.1σ = 0.15JPEG Q = 20JPEG Q = 40MixedPrinting
PSNR↑SSIM↑LPIPS↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓
ISN†32.1750.87650.32660.7281.5630.1785.0200.9910.7210.9990.1840.7133.1310.9601.125
HiNet†31.6290.86620.34230.8271.0770.1623.7240.9860.5730.9970.0990.6773.4260.9701.619
StegaStamp21.2150.70270.30550.0516.1520.00010.570.9511.2590.9770.7980.5573.8430.7503.214
StegaStamp†21.1730.69030.34180.4813.2980.0156.5000.9531.1040.9690.8330.6932.9750.9001.917
Ours32.8830.91090.07070.7941.2350.2163.3060.9950.1171.0000.0380.8590.8611.0000.606
+ +![](images/dee6d77cf38d601bf1d04b3e4156ebcd57b5fa25e649ce21ff9feea7e5a8264d.jpg) +Figure 4. Stego images and decoded QR Codes under different distortions. QR Codes with green borders can be recognized while those with red borders cannot. Zoom in for better observation. + +# 4. Experiment + +# 4.1. Experimental Settings + +Datasets Our training and testing datasets of host images are the train2017 (118K) and test2017 (41K) datasets of COCO [22], respectively. For QR Code images, we manually construct the training (50K) and testing (41K) datasets with random encoded messages. We generate the QR Code images by adopting the scheme of QR Code version 5 [1] with highest error correction (ECC) level of 'H'. We incorporate this code version for most of our experiments except the evaluation in Sec. 4.3. The image used for training and testing is $224 \times 224$ and the patch size of ViT [8] is 16. + +Metrics Our experiments focus on two aspects: stego image quality and decoding accuracy. For stego image quality, we use the peak signal-to-noise ratio (PSNR), SSIM [43] and LPIPS [53] to measure the difference between host images and stego images. For decoding accuracy, we adopt the text recovery accuracy (TRA) [48, 52], which is the ratio of the successfully decoded QR Codes. In addition, we calculate the error module rate (EMR), which represents the error rate (in percentage) of the modules in the QR Code. + +Baselines We compare our method with some state-of-the-art methods $^2$ , including ISN [24], HiNet [16] and StegaStamp [37]. Since these methods are not designed specif + +![](images/d957b1b72ffc91e75c705c9d9177a34d482ec7eaa912e57932f834a457e7a951.jpg) +Figure 5. Stego images generated by different methods. + +ically for our task, we train these models on our datasets for a fair comparison. Moreover, for ISN and HiNet, since they are not robust steganography methods, we incorporate the distortion simulation module when training them. The retrained models of these two methods are illustrated as $\mathrm{ISN}^{\dagger}$ and $\mathrm{HiNet}^{\dagger}$ , respectively. For StegaStamp, we also additionally train it by using the same distortion level as our method, represented as $\mathrm{StegaStamp}^{\dagger}$ . + +# 4.2. Steganography Quality + +Steganography quality indicates both stego image quality and decoding accuracy. To compare the robustness of different methods against image distortions, we first consider several manually created situations3: Gaussian noise, JPEG compression and random noise combinations. We generate random noise combinations (represented by Mixed) with the distortion simulation module introduced in Sec. 3.6. We then consider the printing and photography case to validate the methods' robustness against real-world distortions since it is one of the most extremely severe distortion situations and contains mixed disturbance factors. We randomly select 100 host images and embed random message in them. We then use a inkjet printer to print the encoded images out and take photos with a cell phone. To eliminate the potential errors caused by factors like print quality, we repeat the experiment for 5 times and choose the best result. + +Table 1 shows the experiment results, Figure 4 and Figure 5 demonstrate some qualitative results. It can be observed that our method can achieve higher stego image quality, especially for LPIPS that represents the perceptual sim + +![](images/96915d9b0c1c68b7a2ced7ea2dfbe53efc3c1a9197960281e41796f99f942d4f.jpg) +Figure 6. Photos of printed stego images and their decoding errors under different shooting situations. The actual image used for decoding is cropped out and resized from the photo. Photos shown in this figure are intended for an intuitive demonstration of the shooting results. QR Codes with green borders can be recognized while those with red borders cannot. Zoom in for better observation. + +![](images/d3822939f580aaad4be2f96c3a3b80f99fd5840047d608ffca03d7421e448a09.jpg) +Figure 7. TRA and EMR under different levels of distortions. + +ality. StegaStamp incorporates adversarial training [11] to make the generated stego image more realistic and it does work when facing low-level distortions. However, with the distortion used during training increases, $\text{StegaStamp}^\dagger$ fails to preserve a sound visual quality and instead lead to hue shifting and artifacts. In addition, adversarial training can sometimes bring severe artifacts in some regions, as shown in the 3rd and 4th row of Figure 4. For HiNet and ISN that both leverage normalizing flow, due to the lack of inner-channel interaction by using CNN-based affine block, the stego images they derive have obvious QR Code-like artifacts, making the existence of secret message easy to detect. In terms of decoding accuracy, although $\text{HiNet}^\dagger$ outperforms our method in some cases, we achieve the best performance in the mixed noise and printing tests, which are more close to the real-world application scenarios. + +Figure 7 shows the decoding accuracy under more levels of distortions, which are Gaussian Noise whose standard deviation ranges from 0.02 to 0.2 and JPEG compression + +with quality ranging from 10 to 90. It can be observed that our method demonstrates a stable and good performance under these situations. + +In practical application scenarios, the shooting condition may vary from time to time and a good message embedding method should keep its robustness in most cases. As a result, we further measure the decoding accuracy under different shooting situations. We mainly consider the shooting distance and angle (the offset relative to vertical shooting). Given the default printed image side length / shooting distance ratio and angle of this paper are $5.4\mathrm{cm} / 11\mathrm{cm}$ and $0^{\circ}$ , we gradually increase the distance and angle, the test results are shown in Table 2. It can be found that, with the shooting distance and angle grow, the EMRs exhibit a significant increase for all methods. However, for TRA that directly reflects the identifiability of QR Codes, our method maintains a fair performance. The comparison shown in Figure 6 also indicates that RMSteg can achieve high decoding accuracy under different shooting situations. + +# 4.3. Quality under Different Embedding Capacity + +To validate the generality of our method, we test it under different embedding capacity, i.e., using QR Codes with different versions for training. We demonstrate the model performance on code versions from v5 to v8 in Table 3. Although the steganography quality is getting worse with the embedding capacity increases, the artifacts in the stego images are still not perceptible, especially when the image is printed out, as shown in Figure 8. In addition, RMSteg keeps a TRA of more than 0.8 even for code v8 whose embedding capacity is two more times higher than v5. Compared with StegaStamp [37] that is also designed for robust message embedding, its PSNR is lower than 25 when en + +![](images/f7dbd2e92660d40e9fd126ae12b509739289f7e2f4515ae9027c77d0e5ef21c8.jpg) +Host Image + +![](images/e0d42a3a1fd0456df80a739af16cce6e46f04894cbaf474a0547a45c215a3f5e.jpg) +Stego Image (v5) + +![](images/012a6bbb71dd53cad6adfc130e0d0a478d5553196b2b0da09db43908da628fa4.jpg) +Print and Error +Figure 8. Stego images (the residual is shown in the upper right) and decoding results for printing situation with different code versions. + +![](images/1ca298125ac55fd9b0ccee184d6214082774d1fc14c77a98bb6bdd758f10ae5a.jpg) +Stego Image (v6) + +![](images/12c9de39b624a7661cc5b535eea22a173e9432c89d670d9eba13ea25f37c2c59.jpg) +Print and Error + +![](images/304d1683abb9bc6a5c6a3e86c9add4a55b8dc0c365c8bd536646625beb65f438.jpg) +Stego Image (v7) + +![](images/2444517d83c859fa949cedf7ef0a112d60c81734c6e348aec5d9c5fb7ea587d5.jpg) +Print and Error + +![](images/84ddc537afb8557666dfa094d0aab350126f7f62f0081adfd240dc928484b0e1.jpg) +Stego Image (v8) + +![](images/1a52c687391b700c28923292ec6d01d541f9c3fca9599a921d9885198c2d4196.jpg) +Print and Error + +Table 2. Decoding accuracy under different shooting situations. Here $d$ indicates the shooting distance (measured by cm) and $\alpha$ is the shooting angle offset (measured by degree). The best and second-best results are marked in red and blue colors, respectively. + +
Methodd=11,α=0d=13d=15α=10α=20α=30
TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓TRA↑EMR↓
ISN†0.9601.1250.9202.1730.7902.7800.9101.8590.8202.3940.5903.389
HiNet†0.9701.6190.8503.0330.6803.9090.8802.3960.8003.3620.6603.828
StegaStamp0.7503.2140.6104.1310.3505.3210.5403.7840.3604.2580.0405.916
StegaStamp†0.9001.9170.7902.4690.7102.9220.8602.2720.8402.4130.5703.978
Ours1.0000.6061.0000.8910.9801.2691.0000.9531.0001.1630.9601.680
+ +Table 3. Model performance under different QR Code versions. The numbers in parentheses indicate the encoding capacity in bit. + +
VersionStego ImageMixedPrinting
PSNR↑SSIM↑LPIPS↓TRA↑EMR↓TRA↑EMR↓
v5 (368)32.8830.91090.07070.8590.8611.0000.606
v6 (480)31.3630.89030.08920.8590.9341.0000.877
v7 (528)31.1670.88800.09020.7821.2160.8901.290
v8 (688)30.7650.87620.10200.7431.3700.8201.476
+ +coding 200 bits in a $400 \times 400$ image according to the original paper. In contrast, our method is able to keep a PSNR of around 30 when encoding more than 600 bits in a $224 \times 224$ image. Thus, RMSteg can achieve a higher steganography quality and meanwhile a much larger embedding capacity. + +# 4.4. Ablation Study + +We conduct an ablation study to validate the effectiveness of the IQRT procedure, the ITF module and the AttnFlow model. The results are shown in Table 4. + +IQRT The model without IQRT performs slightly better than the full model in decoding accuracy. This is because IQRT may sometimes cause information loss, e.g., some code module could be wrongly transformed during this procedure, although the QR Code is still identifiable. On the other hand, IQRT can largely improve stego image quality. + +ITF Module As discussed in Sec. 3.4, the ITF module can learn a transformation for image tokens and thus leading to better stego image quality. We also find that the ITF module can help derive a better distribution of artifacts brought by message embedding. As shown in Figure 9, the stego image generated using ITF has less distortion in homogenous regions (the sky), achieving a better visual quality. + +Tokenized Representation We replace the AttnFlow model with ISN and HiNet (two CNN-based normalizing flow model), respectively, to validate the effectiveness of introducing tokenized image representation (the IQRT module is retained). The result shows that, compared with CNN-based scheme, incorporating tokenized image representation makes normalizing flow more competent for robust steganography task. + +AACB Number We also train our model with different + +Table 4. Ablation study result. Here CAT indicates cross attention, TR represents tokenize representation. The best and second-best results are marked in red and blue colors, respectively. + +
MethodStego ImageMixed
PSNR↑SSIM↑LPIPS↓TRA↑EMR↓
w/o IQRT30.6620.86510.10590.8710.828
w/o ITF31.4220.87710.09190.8330.947
w/o TR + ISN32.4440.88560.32090.6923.698
w/o TR + HiNet31.5130.86740.33700.7143.321
1 AACB30.4260.87280.10760.7981.135
2 AACBs31.0830.89720.08310.8190.924
3 AACBs31.6490.90080.07960.8190.924
Ours Full Model32.8830.91090.07070.8560.861
+ +![](images/3a62439493e87a06d78168f814d5e034c29a711d096f7d03c0b6c694a261f3f3.jpg) +Host Image +Figure 9. The generated stego images using and not using ITF. + +![](images/fe187acaede377c94aed0816c8f341e7f9e8ad35c0d8be09286626bbfd59f43a.jpg) +w. ITF + +![](images/09938529a2f3ecbeead952888862ac171b68182599426e934b9b0f1cd7b0fa3f.jpg) +residual $\times 2$ + +![](images/029260e7dced7f77a15a9cbcb8652fbc6d427760dac6cff3f2074313b71ea543.jpg) +w/o ITF + +![](images/9563f990833a927f120b82b938153af94f51abdcc32d2536b7e5c76e05cfd93f.jpg) +residual $\times 2$ + +AACB numbers ranging from 1 to 4. The result shows that, with the increase of the block number, both the stago image quality and the recovery accuracy are gradually improved. + +# 5. Conclusion + +We propose a robust message embedding framework based on an attention flow-based model, called RMSteg. Our method is capable of generating stego images that can survive various real-world distortions, especially for printing and photography. 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However, the existing studies always hold the assumption that full modalities are available. As a matter of fact, the cost for collecting genomic data is high, which sometimes makes genomic data unavailable in testing samples. A common way of tackling such incompleteness is to generate the genomic representations from the pathology images. Nevertheless, such strategy still faces the following two challenges: (1) The gigapixel whole slide images (WSIs) are huge and thus hard for representation. (2) It is difficult to generate the genomic embeddings with diverse function categories in a unified generative framework. To address the above challenges, we propose a Conditional Latent Differentiation Variational AutoEncoder (LD-CVAE) for robust multimodal survival prediction, even with missing genomic data. Specifically, a Variational Information Bottleneck Transformer (VIB-Trans) module is proposed to learn compressed pathological representations from the gigapixel WSIs. To generate different functional genomic features, we develop a novel Latent Differentiation Variational AutoEncoder (LD-VAE) to learn the genomic and function-specific posteriors for the genomic embeddings with diverse functions. Finally, we use the product-of-experts technique to integrate the genomic posterior and image posterior for the joint latent distribution estimation in LD-CVAE. We test the effectiveness of our method on five different cancer datasets, and the experimental results demonstrate its superiority in both complete and missing modality scenarios. The code is released†. + +# 1. Introduction + +Survival analysis aims at estimating the survival time for an individual or a group of patients, which is a valid solu + +![](images/68550c437278017600e7d2f167d9aedae465117dcf0adc7bae83b7aba8947522.jpg) +Figure 1. Comparison between (a) traditional and (b) our proposed multimodal survival prediction methods, where the traditional methods require the complete multi-modal data while our method is still effective if the genomic data is missing. + +tion for cancer treatment and precision medicine [13, 29]. So far, diverse biomarkers are verified to be sensitive to the survival prediction of human cancers, and these biomarkers can be broadly classified into two categories, i.e., image biomarkers and genomic biomarkers [1, 33]. Among all image biomarkers, the histopathological images provide rich visual information for the assessment of histological features, cellular organization, and other phenotypic characteristics that are generally considered as the golden standard for cancer prognosis [21, 24]. Besides histopathological images, genomic data also offers insights into the underlying molecular mechanisms of cancer [9, 44], and thus many researchers leverage patients' molecular profiles such as genetic alterations and gene expression signatures to drive prognostic practice [28, 35]. + +In many clinical and research studies, it is common to acquire multiple biomarkers for a more accurate assessment of disease status and progression stages [10]. Recently, researches also explore to combine both pathological images and genomic markers for the prognosis of cancer [4-6]. For instance, the authors in [5, 46] have presented different integrative survival prediction models based on the co-attention transformer framework. Zuo et al. [48] explore the interactions among different tumor micro-environment components and propose an explainable multi-modal fusion frame + +work for prognosis predictions of breast cancer. All these studies suggest that the combination of genomic data and pathological images can better stratify cancer patients with distinct prognosis than using single biomarker. + +Although much progress has been achieved, the existing multimodal studies hold the assumption that both the imaging and genomic data are available. As a matter of fact, the cost for collecting genomic data is much higher than acquiring the pathology images [30], which sometimes makes genomic data unavailable in the testing samples and thus deteriorates the prediction performance for multimodal learning. A common way to address the issue of missing modality is to utilize one modality to reconstruct the features of another modality, and thus the reconstructed feature can fill in for the missing ones [7, 15, 22, 25, 26, 37, 40]. However, such strategy still faces the following two challenges for the generation of the missing genomic features from the whole-slide pathological images (WSIs): + +1. The representation of gigapixel whole slide images (WSIs): The WSIs are usually with huge size (e.g., 150,000 $\times$ 150,000 pixels) but only a small fraction of areas are closely associated with the genotype information [3, 47]. It is challenge to learn effective representation from the WSIs for the reconstruction of the genomic feature. +2. Generate the genomic embeddings with diverse function categories: Since different genes are usually with diverse biological functional impact (e.g., oncogenesis and cell differentiation), it is difficult to address such difference for the generation of genomic embeddings in an unified generative framework. + +To address the above challenges, we present a Conditional Latent Differentiation Variational AutoEncoder (LD-CVAE) that can reconstruct the genomic embeddings with diverse biological functions from WSIs for robust multimodal survival prediction, even with the missing genomic data (as shown in Fig. 1). The experimental results on five cancer cohorts derived from the The Cancer Genome Atlas (TCGA) clearly demonstrate its advantage for both complete and missing modality scenarios when comparing with the existing studies. We summarize the main contributions of this study as follows: + +- We introduce a robust multimodal survival prediction model that can handle the missing of the genomic data. +- We develop a Variational Information Bottleneck Transformer (VIB-Trans), which employs both the information bottleneck theory and Transformer to obtain useful pathological representation for genomic profile reconstruction. +- We propose a novel Latent Differentiation Variational AutoEncoder (LD-VAE) that can help generate different functional genomic embeddings by learning both the genomic and function-specific posteriors. +- We further learn the joint posterior in LD-CVAE by the product-of-experts technique that can integrate genomic + +posterior and pathological posterior. Additionally, an alignment loss is introduced to align pathological and genomic latent distributions for better estimating the joint distribution. + +# 2. Related Work + +# 2.1. Multimodal Survival Analysis + +By integrating pathological WSIs and genomic data, multimodal approaches [4-6, 18, 42, 45, 46] provide a more comprehensive perspective on patient stratification and prognosis. For instance, Chen et al. [4] use the Kronecker Product to model pairwise feature interactions across multimodal data. Chen et al. [5] present a multimodal coAttention transformer (MCAT) framework that learns an interpretable, dense co-attention mapping between WSIs and genomic features formulated in an embedding space. Furthermore, Xu et al. [42] propose an optimal transport based co-attention learning module that can match instances between histology and genomics to represent the gigapixel WSI. Zhang et al. [45] explore multimodal cancer survival prediction and propose a new framework called PIBD aimed at addressing both "intra-model redundancy" and "inter-model redundancy" challenges. However, the above multimodal studies usually require the completeness of all modalities for training and evaluation, limiting their applicability in real-world with missing-modality challenges. + +# 2.2. Missing Modality in Multimodal Learning + +To address the missing modality issues in multimodal learning. Ma et al. [25] propose a new method named SMIL that leverages Bayesian meta-learning for the generation of missing modality data. Wu et al. [40] introduce a multimodal variational autoencoder (MVAE) that uses a subsampled training paradigm to solve the missing modality problem. In addition, the study in [26] comprehensively examines the behavior of Transformers in the presence of modality-incomplete data and further improves the robustness of the Transformer via multi-task optimization. ShaSpec [37] is introduced to model and fuse shared and specific features to address the missing modality data. However, it is still challenge to recover the missing genomic profiles from WSIs since they are with high-resolution that are hard for representation. Additionally, the extracted genomic features have diverse biological functions, and it is not easy to reconstruct them in an unified framework. + +# 3. Method + +# 3.1. Overview + +The overall framework of the proposed robust multimodal survival prediction model is shown in Fig. 2. Specifically, after extracting the multimodal features from both WSI + +![](images/dca0646cfb38ab47a854f716a3abbb366c75d3b9da82699f90c51c5222973ca9.jpg) +Figure 2. The flowchart of the proposed robust multimodal survival prediction model is consisted of three steps. In the multimodal bag representation step, we extract multimodal features from both WSI and genomic data. Then, a conditional latent Differentiation Variational AutoEncoder (LD-CVAE) is proposed to reconstruct the genomic representation from the image data, and thus our method is still effective if the genomic data is missing in the testing stage. Finally, the co-attention module is applied to guide the selection of survival-associated instance, which is then combined with the reconstructed genomic features for survival prediction. + +and genomic data, a VIB-Trans block is proposed to learn compressed pathological representation from the gigapixel WSIs. To reconstruct the genomic features from WSIs, we introduce LD-VAE to learn the genomic posterior by which we can further learn function-specific posteriors for generating genomic features with diverse biological functions. Furthermore, we use a product-of-experts to obtain the joint latent distribution and introduce an alignment loss to improve modality consistency and enhance the estimation of the joint distribution. Finally, the co-attention module is applied to guide the selection of survival-associated instances, which is then combined with the reconstructed genomic features for survival prediction. + +# 3.2. Problem Formulation. + +We aim to predict time-to-event results for survival analysis, where the event outcome is not always observed (e.g. right-censored data); these predictions are obtained to estimate the probability of an event occurring before a specified time. For the $k$ -th patient, we can model the survival function $f_{surv}^{(k)}(T \geq t, I^{(k)})$ and hazard function $f_{hazard}^{(k)}(T = t | T \geq t, I^{(k)})$ given relative information $I^{(k)} = (P^{(k)}, G^{(k)}, c^{(k)}, t^{(k)})$ , where $P^{(k)}$ represents the set of WSIs, $G^{(k)}$ denotes the genomic profiles, $c^{(k)} \in \{0, 1\}$ indicates the right uncensorship status, and $t^{(k)} \in \mathbb{R}^+$ is the overall survival time (in months). We learn the representation $f(I^{(k)})$ for the computation of the survival loss $\mathcal{L}_{surv}(\{f(I^{(k)}), t^{(k)}, c^{(k)}\}_{k=1}^{N_D})$ , where $N_D$ is the number of samples in the training sets. Specifically, we adopt + +the negative log-likelihood (NLL) loss [43] as the objective function: + +$$ +\begin{array}{l} \mathcal {L} _ {s u r v} = - \sum_ {k = 1} ^ {N _ {D}} c ^ {(k)} \log (f _ {s u r v} ^ {(k)} (t | f (I ^ {(k)}))) \\ + \left(1 - c ^ {(k)}\right) \log \left(f _ {s u r v} ^ {(k)} (t - 1 | f (I ^ {(k)}))\right) \tag {1} \\ + \left(1 - c ^ {(k)}\right) \log \left(f _ {h a z a r d} ^ {(k)} (t | f (I ^ {(k)}))\right) \\ \end{array} +$$ + +# 3.3. Data Construction + +# 3.3.1 Pathological Features Preparation + +Given an input WSI $P^{(k)}$ for the $k$ -th patient, we first segment the tissue regions from it and then crop it into a set of non-overlapping patches at $10 \times$ magnification, which can be denoted as $\{p_j^{(k)}\}_{j=1}^M$ , where $M$ represents the total number of patches. Next, a pre-trained feature extractor $\varphi_p(\cdot)$ (we use CTransPath [38, 39] in this work) following with a fully connected layer is employed to extract the pathological features $Y^{(k)}$ as follows: + +$$ +Y ^ {(k)} = \{\varphi_ {p} (p _ {j} ^ {(k)}) \} _ {j = 1} ^ {M} = \{y _ {1} ^ {(k)}, y _ {2} ^ {(k)}, \dots , y _ {M} ^ {(k)} \} \tag {2} +$$ + +# 3.3.2 Genomic Features Preparation + +Genomic data are typically quantified as $1 \times 1$ measurements. Following previous works [5, 42], the genomic data can be grouped into $N = 6$ functional categories: 1) Tumor Suppression, 2) Oncogenesis, 3) Protein Kinases, 4) Cellular Differentiation, 5) Transcription, and 6) Cytokines and + +Growth. We denote the grouped genomic data for the $k$ -th patient as $\{g_i^{(k)}\}_{i=1}^N$ . Then, a fully connected layer $\varphi_g(\cdot)$ introduced in [5] is applied to extract the genomic features for the $k$ -th patient as: + +$$ +X ^ {(k)} = \{\varphi_ {g} (g _ {i} ^ {(k)}) \} _ {i = 1} ^ {N} = \{x _ {1} ^ {(k)}, x _ {2} ^ {(k)}, \dots , x _ {N} ^ {(k)} \} \quad (3) +$$ + +# 3.4. Conditional VAE + +The conditional variational autoencoder (CVAE) [32] performs the variational inference with condition from the prior latent distribution. In this study, our goal is to generate target genomic features $X$ with pathological features $Y$ . Mathematically, the objective function of the evidence lower bound (ELBO) in CVAE under our settings can be formulated as (more details can be found in the Supplementary Material): + +$$ +\begin{array}{l} \mathcal {L} _ {E L B O} = - \mathbb {E} _ {q _ {\phi} (z | X, Y)} \log p _ {\theta} (X | z, Y) \tag {4} \\ + \beta K L [ q _ {\phi} (z | X, Y), p (z) ] \\ \end{array} +$$ + +where the likelihood $p_{\theta}(X|z,Y)$ is parameterized by deep neural network (decoder) with $\theta$ , $q(z|X,Y)$ refers to the joint posterior of pathology and genomics, and $p(z)$ represents a prior distribution. + +# 3.5. Pathological VIB Transformer + +The CVAE is conditioned on pathological features, however, WSIs are consisted of huge number of instances that are hard for representation. Accordingly, we propose the Pathological Variational Information Bottleneck Transformer (VIB-Trans) that can effectively generate the bag-level representation. Specifically, following the goal of Information Bottleneck (IB) [34], we aim to learn $z_{Y}$ compressed from the pathological features $Y$ while maximally conserving useful information for the survival prediction target $T$ . Then, we use the Variational Information Bottleneck (VIB) [2] to approximate the computation of IB by using variational inference with the following objective function as (more details can be found in the Supplementary Material): + +$$ +\begin{array}{l} \mathcal {L} _ {V I B - T r a n s} = \mathbb {E} _ {z _ {Y} \sim p (z _ {Y} | Y)} [ \mathcal {L} _ {s u r v (z _ {Y}, t, c)} ] \tag {5} \\ + \beta K L (p (z _ {Y} | Y), r (z _ {Y})) \\ \end{array} +$$ + +where the $\mathcal{L}_{\text{surv}(z_Y, t, c)}$ is the survival prediction loss in Eq. (1). $r(z_Y)$ and $p(z_Y|Y)$ correspond to the variational approximation of $p(z_Y)$ and posterior distribution over $z_Y$ , respectively. + +In practice, the posterior $p(z|Y)$ can be approximated by an encoder in the form of $p(z_{Y}|Y) = \mathcal{N}(z_{Y}|f_{e}^{\mu_{Y}}(Y),f_{e}^{\Sigma_{Y}}(Y))$ , where $f_{e}$ is an MLP. However, the traditional MLP can not capture the special correlations among different instances. Consequently, we add the transformer encoder to VIB denoted as VIB-Trans (see Fig. 3(a)). + +![](images/7e2cf32266e65d9ed38082d96662b85405b9498db38a4cb39782e408fd6cb7af.jpg) +Figure 3. The architectures of (a) VIB-Trans and (b) LD-VAE. Both VIB-Trans and LD-VAE obtain posterior parameters by employing their respective transformer encoder with two learnable tokens, i.e., $\mu^{token}$ and $\Sigma^{token}$ . Additionally, LD-VAE further learns the function-specific posteriors from the genomic posterior $\mu$ and $\Sigma$ . + +![](images/6d0e97f921697309b42235e6aa4136f91a4dad80eeb113416f5e2f413fc3635f.jpg) + +for the architecture of VIB-Trans). Specifically, VIB-Trans takes the instance-level features $Y = \{y_{1}, y_{2}, \dots, y_{M}\}$ as input, and outputs the distribution parameters $\mu_{Y}$ and $\Sigma_{Y}$ in VIB. To embed arbitrary sizes of pathological features into a shared latent space, we apply the pooling operation to obtain the bag-level representation $\mu_{Y}$ and $\Sigma_{Y}$ . Inspired by the [class] token, which has been widely used in other domains for information aggregation [8], we also set two learnable tokens $\mu_{Y}^{token}$ and $\Sigma_{Y}^{token}$ to learn the global information of pathological features for the construction of the posterior distribution $p(z_{Y}|Y)$ . To tackle the computation burden in traditional self-attention [36], we employ the Nystrom attention [31, 41, 46] for approximation. In summary, VIB-Trans can describe the global information of WSIs with the compressed representation $z_{Y}$ . + +# 3.6. Conditional Latent Differentiation VAE + +# 3.6.1 Latent Differentiation VAE + +In general, genomic features extracted from different functional groups usually have diverse statistical properties [23], making it challenging to generate all genomic features in a unified generative model. Therefore, we propose the Latent Differentiation Variational AutoEncoder (LD-VAE) for the reconstruction of genomic features $X = \{x_{1}, x_{2}, \ldots, x_{N}\}$ with $N$ functional categories. Specifically, we assume that each genomic feature in $X$ is conditionally independent given a latent variable $z_{X}$ . Then, the objective of VAE can be optimized with the ELBO, and the loss function can be defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {E L B O} = - \mathbb {E} _ {q _ {\phi} (z _ {X} | X)} [ \sum_ {i = 1} ^ {N} \log p _ {\theta} \left(x _ {i} \mid z _ {X}\right) ] \tag {6} \\ + \beta K L \left[ q _ {\phi} \left(z _ {X} \mid X\right), p \left(z _ {X}\right) \right] \\ \end{array} +$$ + +However, it is difficult to generate different functional genomic features $x_{i}$ directly from the genomic posterior $p(z|x_1,x_2,\dots,x_N)$ as solely the genomic posterior will affect the diversity of the generated genomic features [40]. To address this, we introduce the function-specific posteriors $p(z_i|X)$ by applying a latent differentiation process that transforms the genomic posterior into function-specific posteriors. Therefore, we can establish a shared latent space on all genomic features as well as refining the function-specific posteriors for each genomic category. + +Specifically, we assign a unique latent variable $z_{i}$ to each $x_{i}$ and assume that $x_{i}, z_{i}$ and $z_{X}$ satisfy the Markov chain $x_{i} \leftrightarrow z_{i} \leftrightarrow z_{X}$ . Thus, we can reformulate $\log p(x_{i}|z_{X})$ in Eq. (6) as follows (more details are provided in the Supplementary Material): + +$$ +\log p \left(x _ {i} \mid z _ {X}\right) = \log p \left(x _ {i}, z _ {i} \mid z _ {X}\right) = \log p \left(x _ {i} \mid z _ {i}\right) p \left(z _ {i} \mid z _ {X}\right) \tag {7} +$$ + +Then the loss function of LD-VAE can be derived as: + +$$ +\begin{array}{l} \mathcal {L} _ {E L B O} = - \mathbb {E} _ {q _ {\phi} (z _ {X} | X)} [ \sum_ {i = 1} ^ {N} \log p _ {\theta} (x _ {i} | z _ {i}) p (z _ {i} | z _ {X}) ] \\ + \beta \left(\sum_ {i = 1} ^ {N} K L \left[ q _ {\phi} \left(z _ {i} \mid X\right), p \left(z _ {i}\right) \right] + K L \left[ q _ {\phi} \left(z _ {X} \mid X\right), p \left(z _ {X}\right) \right]\right) \tag {8} \\ \end{array} +$$ + +Here, $p(z_i|z_X)$ can be approximated in the form of $p(z_i|z_X) = \mathcal{N}(z_i|\psi_i^\mu (z_X),\psi_i^\Sigma (z_X))$ where $\psi_{i}$ serves as an MLP mapper. In practice, each function-specific posterior should also approximate prior distribution $r(z_{i})$ , which can be accomplished by minimizing the Kullback-Leibler divergence. The detailed architecture of LD-VAE has been shown in Fig. 3(b), and we provide more details in the Supplementary Material. + +# 3.6.2 Conditional Latent Differentiation VAE + +The Conditional Latent Differentiation VAE (LD-CVAE) adds the condition of pathological features $Y$ into LD-VAE for the reconstruction of different functional genomic features $X$ , and we can derive the loss function of ELBO in LD-CVAE by combining Eq. (4) and Eq. (8) as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {E L B O} = - \mathbb {E} _ {q _ {\phi} (z | X, Y)} [ \sum_ {i = 1} ^ {N} \log p _ {\theta} (x _ {i} | z _ {i}, Y) p (z _ {i} | z) ] \\ + \beta \left(\sum_ {i = 1} ^ {N} K L \left[ q _ {\phi} \left(z _ {i} \mid X, Y\right), p \left(z _ {i}\right) \right] + K L \left[ q _ {\phi} \left(z \mid X, Y\right), p (z) \right]\right) \tag {9} \\ \end{array} +$$ + +where $q_{\theta}(z|X,Y)$ represents the joint posterior of the pathological and genomic features. For the purpose of computing $\log p_{\theta}(x_i|z_i,Y)$ , we additionally incorporate the latent representation $z_{Y}$ into the reconstruction network $\theta_{i}$ . + +# 3.6.3 Joint Pathology-Genomics Distribution Learning + +One critical problem for optimizing Eq. (9) is to estimate the joint posterior $q(z|X,Y)$ . According to the previous work [40], a product-of-experts (PoE) can be applied to approximate the joint posterior $q(z|X,Y)$ by the combination of the marginal posteriors $\tilde{q}(z|X)$ and $\tilde{q}(z|Y)$ , with the following formulation (derivation can be found in the Supplementary Material): + +$$ +p (z | X, Y) \approx \tilde {q} (z | X) \tilde {q} (z | Y) p (z) \equiv q (z | X, Y) \tag {10} +$$ + +Here, we approximate $p(z|X) \equiv \tilde{q}(z|X)p(z)$ , $p(z|Y) \equiv \tilde{q}(z|Y)p(z)$ where $\tilde{q}(\cdot)$ is the underlying inference network. Specifically, $\tilde{q}(z|X)$ and $\tilde{q}(z|Y)$ can be represented as $\tilde{q}(z|X) = \mathcal{N}(z|\mu_X, \Sigma_X)$ and $\tilde{q}(z|Y) = \mathcal{N}(z|\mu_Y, \Sigma_Y)$ , which can be derived from the variational genomic posterior of genomic features (shown in Eq. (8)) and variational posterior of pathological features (shown in Eq. (5)). In practice, $p(z)$ is a spherical Gaussian distribution $\mathcal{N}(z|x_0, y_0)$ . Since the product of Gaussian still follows the Gaussian distribution, we can derive the joint posterior in the closed form as: $q(z|X,Y) = \mathcal{N}(\mu, \Sigma)$ , where $\Sigma = (\Sigma_0^{-1} + \sum_{i \in \{X,Y\}} \Sigma_i^{-1})^{-1}$ , $\mu = (\mu_0\Sigma_0^{-1} + \sum_{i \in \{X,Y\}} \mu_i\Sigma_i^{-1}\Sigma^{-1})$ . It worth noting that the employment of PoE allows us to learn the joint posterior using complete multimodal data during training and approximate the joint posterior distribution during testing, even in the absence of genomic data. + +To enhance the consistency between pathological features and genomic features, we propose an alignment loss that optimizes the Wasserstein distance [11] between the marginal distributions $\tilde{q} (z|X) = \mathcal{N}(z|\mu_X,\Sigma_X)$ and $\tilde{q} (z|Y) = \mathcal{N}(z|\mu_Y,\Sigma_Y)$ , which can be denoted as follows: + +$$ +\mathcal {L} _ {\text {A l i g n}} = \left\| \mu_ {X} - \mu_ {Y} \right\| ^ {2} + \operatorname {T r} \left(\Sigma_ {X} + \Sigma_ {Y} - 2 \left(\Sigma_ {Y} ^ {1 / 2} \Sigma_ {X} \Sigma_ {Y} ^ {1 / 2}\right) ^ {1 / 2}\right) \tag {11} +$$ + +Since the covariance matrices are diagonal, it can be further simplified to: + +$$ +\mathcal {L} _ {\text {A l i g n}} = \left\| \mu_ {X} - \mu_ {Y} \right\| ^ {2} + \left\| \Sigma_ {X} - \Sigma_ {Y} \right\| ^ {2} \tag {12} +$$ + +# 3.6.4 The Objective Function of LD-CVAE + +By the combination of Eq. (9) and Eq. (12), the final objective function of LD-CVAE can be formulated as follows: + +$$ +\mathcal {L} _ {L D - C V A E} = \mathcal {L} _ {E L B O} + \alpha \mathcal {L} _ {A l i g n} \tag {13} +$$ + +where $\alpha$ controls the impact of $\mathcal{L}_{Align}$ . + +# 3.7. Multimodal Fusion and Prediction + +After obtaining the pathological features $Y$ and the reconstruction genomic features $\bar{X}$ from the LD-CVAE, we combine them to obtain the fused representation. Specifically, + +we apply the Genomic-Guided Co-Attention Layer reported in [5] to model pairwise interactions between the instance-level pathological features $Y$ and their corresponding genomic features $\tilde{X}$ , which can be formulated as + +$$ +C o A t t n _ {\tilde {X} \rightarrow Y} (\tilde {X}, Y) = \operatorname {s o f t m a x} \left(\frac {\mathbf {W} _ {q} \tilde {X} \left(\mathbf {W} _ {k} Y\right) ^ {\top}}{\sqrt {d _ {k}}}\right) \mathbf {W} _ {v} Y \tag {14} +$$ + +We further apply two set-based MIL Transformers $\mathcal{T}_P, \mathcal{T}_G$ [5] with the global attention pooling function $\mathcal{F}_{\mathrm{attpool}(\cdot)}$ to construct the bag-level pathological and genomic features by aggregating feature embeddings of $\hat{Y}$ and $\tilde{X}$ . The two embeddings are concatenated and then fed into the fully connected layer to obtain the final feature embeddings for survival prediction. + +Overall Loss. The final loss consists of three terms: the survival loss $\mathcal{L}_{\text{surv}}$ , VIB-Trans loss $\mathcal{L}_{\text{VIB-Trans}}$ and LD-CVAE loss $\mathcal{L}_{\text{LD-CVAE}}$ , which can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s u r v}} + \mathcal {L} _ {\text {V I B - T r a n s}} + \mathcal {L} _ {\text {L D - C V A E}} \tag {15} +$$ + +# 4. Experiments + +# 4.1. Datasets and Settings + +Datasets and Evaluation. To validate the effectiveness of our proposed method, we use five different cancer datasets from The Cancer Genome Atlas (TCGA) $^{1}$ : Bladder Urothelial Carcinoma (BLCA), Breast Invasive Carcinoma (BRCA), Glioblastoma and Lower Grade Glioma (GBMLGG), Lung Adenocarcinoma (LUAD), and Uterine Corpus Endometrial Carcinoma (UCEC). We employ 5-fold cross-validation for each dataset. The performance of our model is assessed by concordance index (C-index) [14]. Additionally, we employ the Kaplan-Meier (KM) survival curves [19] and Log-rank test [27] to test the patient stratification performance among different methods. + +Implementation. For each WSI, we employ a pre-trained Swin Transformer encoder (CTransPath) [38, 39] as the pathological encoder $\varphi_{p}$ . For genomic data, we use the SNN [20] as the encoder $\varphi_{g}$ . During the training process, we empirically set the parameter $\alpha$ in Eq. (13) as 0.1. The hyperparameter $\beta$ for Kullback-Leibler divergence is annealed using a cosine schedule, and thus forming a valid lower bound on the evidence. More discussions for the parameter settings can be found in the Supplementary Material. We adopt Adam optimizer with the initial learning rate of $2\times 10^{-4}$ and weight decay of $1\times 10^{-5}$ . Following the setting of [5], we use the batch size of 1 for model training. + +# 4.2. Comparisons with State-of-the-Arts + +To demonstrate the effectiveness of our model on complete multimodal data, we compare it with state-of-the-art (SOTA) methods for both unimodal and multimodal survival analysis. For unimodal methods, we consider genomic-based approaches such as MLP [16], SNN [20] and SNNTrans [20, 31], along with histopathological baselines like ABMIL [17], CLAM [24], TransMIL [31]. For multimodal methods, we compare our model with Porpoise [6], MCAT [5], MOTCat [42], CMTA [46], SurvPath [18], and PIBD [45]. In addition, to further verify the effectiveness of our model with missing genomic data, we compare it with the following studies that can address missing modality data for multimodal learning: (a) VAEs [2] and GANs [12] are both generative models and we can use them to generate the missing genomic data; (b) MVAE [40] is a multimodal generative model that can tackle missing modality in the testing stage. (c) SMIL [25] is proposed to handle missing modality in multimodal learning by leveraging Bayesian meta-learning. (d) ShaSpec [37] fuses shared and specific features to address the missing modality data. (e) Robust Multimodal Transformer [26] is presented to improve the robustness of multimodal Transformer via multi-task learning. + +Compared with Unimodal Models. From the results in Tab. 1, we can observe that the multimodal methods consistently outperform unimodal approaches, demonstrating the advantage of the integrative analysis of genomics and histology for survival analysis. Note that our approach outperforms its unimodal counterparts across all datasets. Specifically, compared to the best model relying on genomic data, our method can improve the overall performance by $5.2\%$ . On the other hand, our method also surpasses the best existing studies based on pathology image data by $5.9\%$ . + +Compared with Multimodal Models. As can be seen from Tab. 1, compared with all multimodal approaches, the proposed method achieves the highest performance in 4 out of 5 cancer datasets with $1.0\% -3.9\%$ improvement. These results clearly demonstrate the advantage of our method that can better learn genomic representation and fuse multimodal data for survival prediction of human cancers. + +Compared with Baseline Models Addressing Missing Modality. For our method and its competitors, we use complete data for model training and test their performance with missing genomic data. The experimental results shown in Tab. 2 suggest that all the studies addressing missing modality can achieve higher C-index values in comparison with the studies solely relying on the pathology image data (shown in Tab. 1). On the other hand, the experimental results in Tab. 2 also indicate that our method can achieve higher C-index values than the comparing studies, high- + +Table 1. Comparisons of C-index (mean ± std) with SOTA methods over five cancer datasets. g. and h. refer to solely relies on image and genomic data, respectively. The best results and the second-best results are highlighted with bold and in underline, respectively. + +
ModelModalityBLCA +(N=373)BRCA +(N=957)GBMLGG +(N=571)LUAD +(N=452)UCEC +(N=480)Overall
MLPg.0.613 ± 0.0190.587 ± 0.0330.809 ± 0.0290.617 ± 0.0260.657 ± 0.0360.657
SNNg.0.619 ± 0.0230.596 ± 0.0270.805 ± 0.0300.625 ± 0.0190.651 ± 0.0180.659
SNNTransg.0.627 ± 0.0190.618 ± 0.0180.816 ± 0.0370.631 ± 0.0230.641 ± 0.0260.667
ABMILh.0.622 ± 0.0510.614 ± 0.0370.786 ± 0.0280.596 ± 0.0670.649 ± 0.0280.652
CLAM-SBh.0.613 ± 0.0580.607 ± 0.0160.792 ± 0.0320.590 ± 0.0760.650 ± 0.0660.650
CLAM-MBh.0.621 ± 0.0650.617 ± 0.0120.799 ± 0.0280.596 ± 0.0750.657 ± 0.0280.658
TransMILh.0.625 ± 0.0500.614 ± 0.0370.803 ± 0.0370.593 ± 0.0630.665 ± 0.0190.660
Porpoiseg.+h.0.661 ± 0.0340.644 ± 0.0100.829 ± 0.0330.646 ± 0.0250.660 ± 0.1060.694
MCATg.+h.0.660 ± 0.0460.652 ± 0.0190.833 ± 0.0290.642 ± 0.0540.686 ± 0.0420.695
MOTCatg.+h.0.667 ± 0.0380.659 ± 0.0340.835 ± 0.0370.656 ± 0.0210.683 ± 0.0600.700
CMTAg.+h.0.671 ± 0.0390.648 ± 0.0480.846 ± 0.0410.666 ± 0.0250.699 ± 0.0350.706
SurvPathg.+h.0.663 ± 0.0260.661 ± 0.0240.839 ± 0.0390.671 ± 0.0360.709 ± 0.0390.709
PIBDg.+h.0.634 ± 0.0290.636 ± 0.0280.817 ± 0.0380.628 ± 0.0630.687 ± 0.0720.680
Oursg.+h.0.686 ± 0.0350.680 ± 0.0300.849 ± 0.0170.676 ± 0.0150.703 ± 0.0690.719
+ +Table 2. Comparisons of C-index (mean ± std) with methods addressing missing modality over five cancer datasets. The best results and the second-best results are highlighted in bold and in underline, respectively + +
ModelBLCABRCAGBMLGGLUADUCECOverall
VAE0.622 ± 0.0100.629 ± 0.0200.805 ± 0.0320.598 ± 0.0290.660 ± 0.0290.663
GAN0.621 ± 0.0180.621 ± 0.0270.793 ± 0.0450.608 ± 0.0280.663 ± 0.0360.661
MVAE0.629 ± 0.0090.619 ± 0.0270.790 ± 0.0180.610 ± 0.0300.661 ± 0.0240.662
SMIL0.627 ± 0.0150.610 ± 0.0100.807 ± 0.0120.608 ± 0.0350.678 ± 0.0160.666
ShaSpec0.630 ± 0.0310.626 ± 0.0270.810 ± 0.0240.613 ± 0.0360.672 ± 0.0370.670
Transformer0.629 ± 0.0220.621 ± 0.0460.814 ± 0.0160.610 ± 0.0200.673 ± 0.0120.669
Ours0.649 ± 0.0400.641 ± 0.0120.821 ± 0.0210.628 ± 0.0080.681 ± 0.0440.684
+ +lighting the capability of our method in handling the missing modality of genomic data for survival prediction. + +# 4.3. Ablation Study + +Impact of VIB-Trans. For the variant of w/o VIB-Trans, we use TransMIL encoder as a baseline to represent WSI (additional results of other baselines are provided in the Supplementary Material). As shown in Tab. 3, compared with the TransMIL encoder, VIB-Trans improves the overall performance by $1.8\%$ on complete data and $1.9\%$ with missing genomic data, which implies that VIB-Trans can effectively obtain the representation of WSIs. + +Impact of LD-VAE. For the variant of w/o LD-VAE, we only use the VAE architecture for the genomic posterior estimation without considering the functional difference among diverse genomic features. As shown in Tab. 3, our method surpass w/o LD-VAE by $1.2\%$ and $0.9\%$ on complete multi-modal data and the scenario with missing genomic data, respectively. These results again validate the advantage of our method that can generate better genomic representations for survival prediction. + +Impact of Alignment Loss. Additionally, we evaluate the effect of the alignment loss (shown in Eq. (12) in our method. As can be seen from Tab. 3, our method achieves higher C-index values than its variant i.e., w/o Alignment loss. This is because the proposed alignment loss can improve the consistency for multi-modal integration, and thus can enhance the estimation of joint posterior with marginal pathological posterior. More discussions for the ablation study can be found in the Supplementary Material + +# 4.4. Patient Stratification + +Besides comparing the prognosis performance of different methods by the measurements of C-index, another important task for cancer prognosis is to stratify cancer patients into different groups with diverse clinical outcomes, by which we could develop personalized treatment for different cancer patients. In Fig. 4, we compare the patient stratification performance of our method under the settings of complete multi-modal data (top row of Fig. 4) and missing genomic data (bottom row of Fig. 4). As shown in Fig. 4, we derive similar stratification performance under these two settings across different cancer cohorts. These results further clearly demonstrate that the generated genomic feature + +Table 3. Ablation study under both complete modality and missing modality scenarios. + +
VariantsMissingBLCABRCAGBMLGGLUADUCECOverall
w/o VIB-Trans✓0.651 ± 0.0350.685 ± 0.0200.833 ± 0.0580.646 ± 0.0480.691 ± 0.0530.701
0.616 ± 0.0240.619 ± 0.0190.820 ± 0.0400.623 ± 0.0350.647 ± 0.0370.665
w/o LD-VAE✓0.674 ± 0.0170.671 ± 0.0240.835 ± 0.0270.668 ± 0.0240.688 ± 0.0250.707
0.641 ± 0.0350.634 ± 0.0480.814 ± 0.0190.616 ± 0.0120.672 ± 0.0560.675
w/o Alignment Loss✓0.663 ± 0.0240.676 ± 0.0400.828 ± 0.0330.659 ± 0.0170.689 ± 0.0240.703
0.643 ± 0.0310.629 ± 0.0260.783 ± 0.0190.621 ± 0.0210.670 ± 0.0360.669
Ours✓0.686 ± 0.0350.680 ± 0.0300.849 ± 0.0170.676 ± 0.0150.703 ± 0.0690.719
0.649 ± 0.0400.641 ± 0.0120.821 ± 0.0210.628 ± 0.0080.681 ± 0.0440.684
+ +![](images/26be8c48e7ba8610a304e90c4dd9080be9cb8ed3a9b13424727b695fc85ed591.jpg) + +![](images/163a29026f1d005bd82da6cfa738c7fb5743865036b6d1e3bbc97bd0960dcd4a.jpg) + +![](images/bd62f0292e4cda33266c9b7a87ee74a42ba6a8f7290b81f5aff230f306f933a6.jpg) + +![](images/3d094102ef467c1bbbe3282906ca608e76c5002dfa08b45e321d913622cf6d79.jpg) + +![](images/dda8ec02c850a05c2188368e21646f50e97890fbc5aa3ce34ad164ee1c6a4015.jpg) + +![](images/8da38c02451b0f4b322e3b06938ec07d615584d7c74b5a0172c358d6359c20e2.jpg) +Figure 4. Kaplan-Meier Analysis of predicted high-risk (red) and low-risk (green) groups on five cancer datasets under both complete modality (top) and missing modality (bottom) scenarios. Shaded areas refer to the confidence intervals. + +![](images/549beadf5e1df756a021b54aaf4f524e195135744e1ce3fd5c1fc75568e05555.jpg) + +![](images/26ccb2f13ffb43c3508a305530c93691cf1d7fa3d824d34abda4efa2979416ae.jpg) + +![](images/feeefa1eaa0be10da4c9fe1bd62938c0b37cf554844731f18edda72f437e79d9.jpg) + +![](images/e0eab38229751aa8805e06fafe129ff7554654664c1b80f8e8ed1eba3842c90b.jpg) + +![](images/8ac02fc300a392c30b130c7a68a12f5f001399d650de312e6b4422979af452cf.jpg) +Figure 5. Comparison of the co-attention weights calculated from the genuine (top) and generated (bottom) genomic features. + +by our method is also associated with the survival information, which in turn can help predict the clinical outcome of cancer patients. We also compare the prognosis performance of our method for patient stratification with other SOTA algorithms in the Supplementary Materials, and our method can still achieve superior prediction results. + +# 4.5. Visualization Results + +In this section, we further compare the co-attention weights that are calculated from the ground truth and generated genomic feature. In Fig. 5, we visualize the co-attention weights and show the patches with top-5 scores for the ge + +nomic features with the function of Tumor Suppression. As shown in Fig. 5, we could derive similar visualization results of co-attention score among genuine and reconstructed genomic features. In addition, their corresponding top-5 highly correlated patches also share similar visual appearance. These results again suggest the advantage of our method that can generate genomic features with close connection to the pathology images. More visualization results are provided in the Supplementary Material. + +# 5. Conclusion + +In this paper, we present a Conditional Latent Differentiation Variational AutoEncoder (LD-CVAE) that can reconstruct the genomic embeddings with diverse biological functions from WSIs for robust multimodal survival prediction. The experimental results on five different cancer datasets demonstrate the superiority of our method under both complete and missing modality scenarios. + +# Acknowledgments + +This work is supported by the National Natural Science Foundation of China (Nos.62136004, 62272226, 62402219) and the Key Research and Development Plan of Jiangsu Province (No.BE2022842). + +# References + +[1] Julián N Acosta, Guido J Falcone, Pranav Rajpurkar, and Eric J Topol. Multimodal biomedical ai. Nature Medicine, 28(9):1773-1784, 2022. 1 +[2] Alexander A Alemi, Ian Fischer, Joshua V Dillon, and Kevin Murphy. 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Springer, 2022. 1 \ No newline at end of file diff --git a/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/images.zip b/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..35246c6af66a15636db08ca2bf17f215c6277627 --- /dev/null +++ b/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c270cd5e0b3440a88c8e7d34f1e038f5428d90ad4b03b591eb8616068b8e2285 +size 646784 diff --git a/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/layout.json b/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c36cd2da588b85c621116d2e349fa5cc961e9d35 --- /dev/null +++ b/robustmultimodalsurvivalpredictionwithconditionallatentdifferentiationvariationalautoencoder/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2483f92b2f90fff6a7aba3732386eccfc3e3d1959b022b5282823cb49f7cda9f +size 421692 diff --git a/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_content_list.json b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ec04986deda8509eecd715208b3dac27f14a8d00 --- /dev/null +++ b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60a28198c4ce7106a51e3991994b54b84a786e9de78466e61c11ba4951223b66 +size 70307 diff --git a/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_model.json b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d93966e9cc24cbb422b5ee420a15ef1a5c49f2e4 --- /dev/null +++ b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a003dc551568ebe3bdcf04868b44eb454cc006d7a2bc2ba7b0ce990712ca339d +size 88564 diff --git a/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_origin.pdf b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0df00beae5e89860d8caab1c1f170013c13a7120 --- /dev/null +++ b/robustmultiobject4dgenerationforinthewildvideos/5608bb67-dff7-4952-a0b9-ba92a1ee0b94_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d72514649939164ad1601966f6b062b8ae3fe1e60d3aaa062b6e649a09da096 +size 7780272 diff --git a/robustmultiobject4dgenerationforinthewildvideos/full.md b/robustmultiobject4dgenerationforinthewildvideos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f66ba4d69d56c31db91d514e6dd64f315b884d78 --- /dev/null +++ b/robustmultiobject4dgenerationforinthewildvideos/full.md @@ -0,0 +1,248 @@ +# Robust Multi-Object 4D Generation for In-the-wild Videos + +Wen-Hsuan Chu $^{1*}$ Lei Ke $^{1*}$ Jianmeng Liu $^{1*}$ Mingxiao Huo $^{1}$ +Pavel Tokmakov $^{2}$ Katerina Fragkiadaki $^{1}$ $^{1}$ Carnegie Mellon University $^{2}$ Toyota Research Institute + +# Abstract + +We address the challenge of generating dynamic 4D scenes from monocular multi-object videos with heavy occlusions and introduce GenMOJO, a novel approach that integrates rendering-based deformable 3D Gaussian optimization with generative priors for view synthesis. While existing view-synthesis models excel at novel view generation for isolated objects, they struggle with full scenes due to their complexity and data demands. To overcome this, GenMOJO decomposes scenes into individual objects, optimizing a differentiable set of deformable Gaussians per object while capturing 2D occlusions from a 3D perspective through joint Gaussian splatting. Joint splatting ensures occlusion-aware rendering losses in observed frames, while explicit object decomposition allows the usage of object-centric diffusion models for object completion in unobserved viewpoints. To reconcile the differences between object-centric priors and the global frame-centric coordinate system of the video, GenMOJO employs differentiable transformations to unify the rendering and generative constraints within a single framework. The result is a model capable of generating 4D objects across space and time while producing 2D and 3D point tracks from monocular videos. To rigorously evaluate the quality of scene generation and the accuracy of the motion under multi-object occlusions, we introduce MOSE-PTS, a subset of the challenging MOSE benchmark, which we annotated with high-quality 2D point tracks. Quantitative evaluations and perceptual human studies confirm that GenMOJO generates more realistic novel views of scenes and produces more accurate point tracks compared to existing approaches. Project page: https://genmojo.github.io/. + +# 1. Introduction + +Humans effortlessly perceive complete, coherent objects and their motions from videos even though they only observe the pixels on the front surface of a dynamic scene, which constantly changes due to motion, occlusion, and + +reappearance. Recovering persistent and accurate 4D representations from monocular videos with multiple objects is a highly under-constrained problem. However, it is critical for fine-grained video understanding, visual imitation in robotics [12], and building causal world models of intuitive physics [50] that can simulate the consequences of actions. + +Recent view-predictive generative models [24, 40] provide powerful priors for novel view synthesis. However, existing video-to-4D generation works [5, 14, 55, 56] based on these generative models often struggle to maintain temporal coherence and accurate 3D geometry in complex multi-object scenes due to the intricate dynamics involved, such as heavy occlusions and fast motion. + +In this paper, we propose GenMOJO, a compositional method that enables Multi-Object JOint splatting for 4D scene GENeration from monocular videos by combining frame-centric test-time rendering error optimization with object-centric generative priors. GenMOJO decomposes a scene into individual foreground objects and background, representing each object with a differentiable and deformable set of 3D Gaussians. We optimize the parameters of these Gaussians by: (1) jointly splatting all Gaussians to compute rendering errors in the input video frames, accounting for occlusions; and (2) individually rendering each object's Gaussians from unobserved viewpoints to optimize a score distillation (SDS) objective. To bridge frame-centric and object-centric coordinate frames, GenMOJO employs differentiable affine transformations that align the object-centric Gaussians with the frame-centric Gaussians. + +The work most closely related to ours is DreamScene4D [5], which also leverages object-centric generative priors to produce 4D scene completions from monocular video. However, their approach inpaints and optimizes the 3D deformable Gaussians for each object independently and only combine them during a final rendering step to infer object depth ordering. This strategy struggles with cross-object occlusions, as rendering objects separately fails to account for occluders. As a result, their method often produces unnatural, inter-penetrating artifacts in scenes with multiple heavily occluded objects, as demonstrated in our experiments. In contrast, our approach unifies + +![](images/4f846cc18ade0a5767dbc9cafa626d4fd2254cc6d19fb14c5a0e8c969ef96f25.jpg) +Figure 1. GenMOJO extends video-to-4D generation to complex, real-world scenarios characterized by heavy multi-object occlusions and rapid motion, enabling the creation of complete 4D scene representations with $360^{\circ}$ novel view synthesis and accurate point motion tracking. We showcase rendered images from diverse viewpoints and motion trajectories (visualizing a single object for clarity) in the re-rendered images across different time steps. + +image-based and object-centric constraints within a single gradient-based optimization framework. By jointly splating all object Gaussians, we accurately model cross-object occlusions and interactions, while still imposing strong appearance priors by rendering each object independently. + +As shown in Figure 1, GenMOJO emphasizes addressing real-world complexity through the evaluation of challenging datasets with frequent object interactions. Unlike previous methods that focused on single-object [14, 37] or simple multi-object videos [5], GenMOJO is designed to handle scenes with heavy occlusions, crowded environments, and intricate dynamics. + +We evaluate GenMOJO on multi-object videos from DAVIS and a subset of MOSE [6], for which we manually annotated accurate point tracks. These videos feature complex multi-object interactions and frequent real-world occlusions. We compare against state-of-the-art NeRF- and Gaussian-based 4D generation methods [5, 14, 47]. Our results show substantial improvements in both 4D rendering quality and motion accuracy. In addition, we conducted human evaluations to assess the perceptual realism of our results, which further support our quantitative findings. + +# 2. Related work + +Dynamic Scene Reconstruction. Dynamic scene reconstruction aims to lift the visible parts of a video to a dynamic 3D representation for novel view synthesis. These + +methods often take videos where a large number of camera views exist as input [27, 49, 54], alleviating the issue of partial observability. As a result, many of these methods can not be readily applied to monocular videos, as no constraints exist in unobserved viewpoints. These methods fall into two large categories. Dynamic Neural Radiance Field (NeRF) based methods [3, 21, 25, 31, 34] extend NeRFs [29] to dynamic scenes and model a dynamic scene using grid-based, voxel-based representations [4, 23, 26] or through deformation networks [4, 8]. Recently, Gaussian Splatting [18, 27, 49] has gained great attention in the field of neural rendering. Compared to NeRF-based methods, Gaussian Splatting represents the scene as explicit Gaussians and uses efficient rasterization techniques for rendering, greatly improving the computation efficiency. There have also been efforts to model the visible parts of a video scene from monocular inputs, but they do not attempt to model the unobserved parts [20, 44, 47, 48]. Compared to these works, we adopt dynamic Gaussians to synthesize both the visible and unobserved parts of the video scene. + +Dynamic Scene Generation. In contrast to dynamic scene reconstruction, dynamic scene generation is concerned with modeling a complete video scene across both visible and unobserved viewpoints, often operating under monocular or sparse view settings. Existing text-to-4D [1, 2, 22, 43] or image-to-4D [37, 53, 59] works use dif + +fusion models [24] to condition on text or image inputs and generate synthetic videos, then use score distillation sampling (SDS) [33] losses to supply constraints in unobserved viewpoints to synthesize complete 4D representations using dynamic NeRFs or Gaussians. Many existing video-to-4D works simplify this problem by assuming that the input consists of a single object undergoing small movements [9, 14, 30, 37, 55, 56]. More recently, this line of work has been extended to multi-object video by first decomposing the video into multiple object tracks, optimizing them independently, and then using depth models [51] to recompose the optimized 4D objects to re-form the original video scene [5]. However, the late multi-object composition strategy in [5] is extremely reliant on the quality of the depth model, and the optimization process itself is unaware of the occlusions that occur in the observed video sequence. In comparison, we propose to compose early and optimize the deformations of the objects jointly, which naturally allows the optimization process to reason about the cross-object occlusions that occur in videos. + +Point Motion via 4D Generation / Reconstruction. 4D generation or reconstruction from monocular videos enables the extraction of point trajectories through test-time optimization by fitting dynamic radiance fields [5, 27, 41, 46, 47] to the observed video frames without the need for point annotations. In contrast, data-driven point trackers are trained on synthetic training data, yet outperform others in existing benchmarks by a noticeable margin [15]. While our dynamic Gaussian representation is not specifically designed for precise point tracking via Gaussian Splatting, it facilitates straightforward extraction of point trajectories for motion accuracy evaluation. In particular, we observe that the gap in tracking performance between our method and feedforward approaches decreases significantly in multi-object videos with heavy occlusions [6], since the reconstruction objective bounds the tracking error. + +# 3. Robust Multi-Object 4D Generation + +To generate dynamic 4D scenes from a monocular video with complex multi-object dynamics, we introduce GenMOJO, which utilizes Gaussian Splatting [18, 49] as the 4D scene representation and leverages diffusion-based generative models [24] for novel view synthesis. + +# 3.1. Background: Generative Gaussian Splatting + +Gaussian Splatting [18] represents a scene through a set of 3D Gaussians, each characterized by its position $\mu$ , scale $s$ , rotation $q$ , opacity $\alpha$ , and spherical harmonic (SH) coefficients $f$ to represent color. To extend 3D Gaussians for novel view synthesis, Score Distillation Sampling (SDS) [33] is commonly applied. For example, Dream-Gaussian [45] leverages Zero-1-to-3 [24] as the diffusion + +prior, which uses a reference view and a relative camera pose to generate plausible images given a target viewpoint, lifting a single frame from 2D to 3D. + +To model 3D scene dynamics, existing methods [5, 37] then deform these 3D Gaussians over time. Starting with a set of 3D Gaussians derived from the initial frame, each Gaussian is parameterized at each timestep by a set of learnable variables such as its 3D position $\mu_t$ , 3D rotation (a quaternion) $q_t$ , and 3D scale $s_t$ . The RGB (spherical harmonics) values and opacity remain constant across timesteps, inherited from the first-frame 3D Gaussians. DreamGaussian4D [37] models object dynamics by directly optimizing Gaussian deformations in an object-centric video through a K-plane [8] based deformation network with an RGB rendering loss and a SDS loss. DreamScene4D [5] extends this approach to multi-object scenes by introducing a "decompose-recompose" strategy that optimizes 4D Gaussians for each object track independently. However, these methods struggle with multi-object occlusions since they model objects separately, without considering the interactions and occlusions between them. + +# 3.2.GenMOJO + +We introduce GenMOJO, a framework for video-to-4D generation in complex multi-object scenes, specifically designed to accurately model object interactions and occlusions. GenMOJO employs an "early-composition" strategy by first composing 3D Gaussians in a global space with depth initialization, then optimizing for their temporal deformations. Furthermore, we render instance masks to preserve Gaussian instance identities during the joint splating process, effectively managing significant 2D mutual occlusions between objects by leveraging the compositional structure of the 3D scene. + +As illustrated in Figure 2, our method processes a monocular multi-object video by first isolating each object using state-of-the-art segmenters and trackers [17, 36, 38]. We then apply Score Distillation Sampling (SDS) [33] with diffusion priors to generate static 3D Gaussian representations for each object. Unlike DreamScene4D [5], which independently optimizes Gaussian deformations and later composes the objects, GenMOJO composes the entire 3D scene upfront using initial depth predictions. This enables a joint optimization of all Gaussian deformations, enhancing stability and overall generation quality. + +# 3.2.1. Multi-object Joint Splatting + +After independently optimizing 3D Gaussians for each object in the initial frame, we compose them within a unified coordinate frame to create a coherent 3D scene with initial depth ordering. This process involves determining the depth and scaling of each object along camera rays. Specifically, we employ a pre-trained consistent video depth estimator [13] to determine the relative depth of each object, + +![](images/3108e0e6574e530b5797b211c420aca416e22252f36978b5d2d8fb005add0ec4.jpg) +Figure 2. Method overview of GenMOJO. Starting with a monocular video, GenMOJO uses segmentation and tracking methods [36, 38] to isolate each object. Score Distillation Sampling (SDS) [33] is applied to generate static 3D Gaussian representations. The 3D Gaussians for each object are first composed in global space with depth-based initialization [13] and optimized using re-projection error from the video, along with individual object renders for score distillation. Differentiable affine transformations are employed to jointly optimize both image-centric reprojection and object-centric score distillation objectives within a unified framework. + +which then guides the composition of the scene. We randomly select a "reference" object $j$ and compute the relative depth scaling for every other object $i$ as $k_{i} = \frac{D_{i}}{D_{j}}$ in each frame, where $D_{i}$ and $D_{j}$ is the median depth for objects $i$ and $j$ . + +In the $t$ -th frame, the original 3D position $\mu_t^i$ and the scale $\mathbf{s}_t^i$ of the Gaussians for object $i$ are scaled along the camera rays using the scaling factor $k_i$ : $\mathbf{p}_t^i = \mathcal{C}^r - (\mathcal{C}^r - \mu_t^i) \times k_i$ and $\mathbf{s}_t^i = \mathbf{s}_t^i \times k_i$ , where $\mathbf{p}$ is the updated 3D position and $\mathcal{C}^r$ denotes the camera position. + +With these multi-object 3D scenes composed at each timestep, we jointly render and optimize Gaussians from all objects using the RGB rendering loss $\mathcal{L}_{rgb}$ [18] and flow rendering loss $\mathcal{L}_{flow}$ [5, 47]. + +# 3.2.2. Instance and Occlusion-aware Gaussian Splitting + +Jointly optimizing deformations can introduce a failure mode where Gaussians from different objects "jump" to another during close interactions or occlusions. To mitigate this, we assign a one-hot encoding instance label to each Gaussian as a fixed Gaussian attribute and incorporate an instance mask rendering loss. + +We extend the differentiable 3D Gaussian renderer from [18] to render these instance labels, giving us an instance segmentation map for each frame. We then compare the rendered instance segmentation map $\hat{y}_k$ against the masks obtained from the pre-trained object mask trackers $y_k$ (Section 3.2) using a standard negative log-likelihood loss $\mathcal{L}_{\mathrm{class}} = -\sum_{k} y_k \log \hat{y}_k$ . + +During optimization, the one-hot class labels remain fixed, so any adjustments to the rendered instance segmentation map $\hat{y}_k$ can only result from Gaussian movements in the 3D space. This approach ensures that the deformed Gaussians do not undergo identity switches (i.e. "jump" to another object), allowing us to model complex multi-object + +occlusions accurately. + +# 3.2.3. Robust Scene Modeling for In-the-Wild Videos + +Long videos captured in natural environments often exhibit shadow and illumination changes as objects move, leading to variations in observed RGB values. To model this behavior, we draw on techniques from 3D scene reconstruction with unconstrained multiview image sets [19, 28] and diverge from previous dynamic Gaussian splatting works [27, 47], which keep Gaussian colors fixed over time. Instead, we allow Gaussian colors to change smoothly over time by introducing an additional MLP head on top of the deformation K-plane [4] to predict time-dependent adjustments to spherical harmonic (SH) coefficients in response to these observed color changes. The K-plane provides an inductive bias where Gaussians nearby in space and time should have similar color changes. An additional L1 regularization term $\mathcal{L}_{\mathrm{reg}}$ is introduced on the magnitude of SH changes to prevent Gaussians from abusing this relaxation to explain all visual changes in the video. + +# 3.2.4. Object-centric SDS Optimization in Global Scene + +In monocular videos, unobserved views of the scene lack constraints, so we rely on view-conditioned generative models for regularization [33]. However, these view-conditioned generative models work best in object-centric settings, while GenMOJO directly represents all objects within a global coordinate frame. To bridge this gap, we employ affine transformations to transform object Gaussians from the world coordinate frame to object-centric coordinate frames and back, combining object-centric SDS and rendering losses in a unified framework. + +Specifically, we fit bounding boxes to each object segmentation mask to obtain $\mathbf{B}\mathbf{B}\mathbf{o}\mathbf{x}_t$ in frame $t$ . We then solve for the 2D affine warps $\{W_t\}$ that transforms $\mathbf{B}\mathbf{B}\mathbf{o}\mathbf{x}_t$ to + +![](images/3f2a736b2e7f51ff7ea3f0e1eb7fe88e2e31ca01f2541a8d3f49fa720f3b1ab0.jpg) +Figure 3. Sample annotation from MOSE-PTS. We visualize annotated points that are not occluded, with corresponding point tracks displayed in matching colors. + +bounding boxes that correspond to that of an object-centric video. Geometrically, each warp $W_{t}$ can be interpreted as a translation to reposition the object at the center of a sphere on which virtual cameras are sampled, and a scaling factor to resize it to the desired dimensions. $W_{t}$ is then unprojected to 3D using the camera projection matrix and applied to object Gaussians to transform and render them in an object-centric frame. In this way, we can jointly optimize the object Gaussians using the SDS loss by rendering in the object-centric frame, and rendering losses on the observed video frames $I_{t}$ under the reference camera pose. + +# 3.2.5. Optimization Objective + +Our optimization objective is described by a combination of $\mathcal{L}_{rgb}$ and $\mathcal{L}_{flow}$ (Section 3.2.1), the SDS loss, $\mathcal{L}_{class}$ (Section 3.2.2), and $\mathcal{L}_{reg}$ (Section 3.2.3). We also include the local rigidity loss [27] as an additional regularization term. Please refer to the supplementary materials for the weighting coefficients for each loss term. + +# 4. MOSE-PTS Dataset and Analysis + +The proposed MOSE-PTS dataset includes 20 videos selected from MOSE [6], a dataset designed for complex video object segmentation with substantial real-world occlusions. We filter the videos using 2D visible object masks to exclude low-interaction scenes, ensuring meaningful object interactions and tracking challenges. Compared to contemporary datasets like TAP-Vid-DAVIS[7], which often feature salient and isolated objects, MOSE-PTS presents more complex, cluttered scenes. Annotators labeled up to five objects per video, with five key points per object, and all annotations were conducted at a high resolution of 1080p to ensure precision and detail. Some annotation samples are visualized in Figure 3. Further annotation details can be found in the supplementary material. + +Point Trajectory Analysis. In Figure 4, we compare MOSE-PTS with TAP-Vid-DAVIS [7] based on four metrics: average number of points, occlusion rate per trajectory, + +![](images/8dadca30b85bbfcd47fabcb195ae1fbd1c5ee35681ffe494663787600fcb1905.jpg) +Figure 4. Statistical comparison between MOSE-PTS and TapVid-DAVIS [7]. Avg. number of points: the labeled points in each dataset. Avg. OCC. Rate (Traj / Video): the mean occlusion rate across individual trajectories, capturing the frequency of occlusions within distinct trajectories or videos. Avg. Motion Movement: the mean displacement of points between frames. These metrics show that MOSE-PTS contains more complex point tracks that have varied motion and undergo large occlusions. + +motion range, and occlusion rate per video. MOSE-PTS has a higher average number of points, requiring more simultaneous tracking and increasing the complexity of the dataset. Additionally, MOSE-PTS has more complex multi-object occlusions and a wider motion range than TAP-Vid-DAVIS. + +# 5. Experiments + +We evaluate GenMOJO for its ability to generate novel views of scenes and to track points in videos through occlusions. Our experiments aim to address these questions: (1) How does GenMOJO compare to other methods [5, 14, 37] in terms of novel view synthesis? (2) How does GenMOJO perform in tracking points through occlusions compared to existing state-of-the-art supervised point trackers [15, 16] and test-time optimization [5, 37, 47] methods? (3) To what extent do generative priors and object-based video decomposition contribute to improved view synthesis and point tracking? (4) Do object-centric generative priors [24] in GenMOJO outperform priors obtained from scene-level view-conditioned generative models [39, 40]? + +Datasets. To evaluate GenMOJO on complex, real-world scenarios and provide a strong basis for comparison with existing baselines, we select a challenging subset of 15 multi-object videos from DAVIS [7, 32] and incorporate the 30 videos from our newly proposed MOSE-PTS dataset. This combined evaluation set spans a wide range of difficult scenes with diverse object motions and interactions, enabling a rigorous assessment of GenMOJO's ability to generate coherent 4D scenes that handle object interactions and accurately track points across occlusions. + +Implementation Details. We conduct experiments on a 48GB A6000 GPU. We crop and scale the individual objects to around $65\%$ of the image size for object lifting. For static 3D Gaussian optimization, we optimize for 1000 iterations with a batch size of 16, similar to previous works [5, 37]. To optimize the deformations, we optimize for 40 times the number of frames with a batch size of 8 and accumulate gradients for 2 steps. Details are provided in the appendix. + +![](images/88d047e1e11445c99cdfb7c201ec95061516ac9ad9718d4d96022b94bf198707.jpg) +Figure 5. Video to 4D Scene Generation Comparisons. We render Shape of Motion [47], DreamScene4D [5], and GenMOJO on a DAVIS video (left) and a MOSE video (right) from the reference view (top three rows) and a novel view (bottom two rows). We can see that the baselines produce artifacts or incorrectly model spatial relationships between objects, while our method does not exhibit such errors. We also render novel views for DreamScene4D and our method, where we can similarly observe improvements. + +# 5.1. Video to 4D Scene Generation + +Baselines. We consider the following baselines for evaluating 4D scene generation: (1) Consistent4D [14], a method for video-to-4D generation from monocular videos that fits dynamic NeRFs per video using rendering losses and score distillation. (2) DreamGaussian4D [37], a 4D video generation method that, like our approach, uses dynamic Gaussian Splatting but does not employ object priors and thus lacks video decomposition. (3) DreamScene4D [5], a recent SOTA approach for 4D generation from multi-object monocular videos using dynamic Gaussian Splatting, making it the most directly comparable to our method. However, unlike GenMOJO, it optimizes each object's motion independently, whereas GenMOJO jointly optimizes motion across all objects to capture object interactions. + +Evaluation Metrics. The quality of 4D generation can be assessed in two key aspects: the view rendering qual + +ity of the generated 3D geometry and the accuracy of the 3D motion. This section focuses on view rendering quality. Following previous works [14, 37], we report CLIP [35] and LPIPS [57] scores between four novel-view rendered frames and the input video frames, and calculate the average score per video. These metrics evaluate the semantic similarity between rendered and input video frames. Furthermore, we conducted a user study on MOSE videos, using a two-way voting method to compare GenMOJO with the state-of-the-art method DreamScene4D. Finally, we measure PSNR by comparing the rendered frame from the reference camera view to the input video sequence, providing a metric for the faithfulness of the 4D generation results. + +4D Generation Results. The 4D generation results on MOSE and DAVIS videos are presented in Table 1. Since GenMOJO directly models objects in world space, it achieves the most faithful scene representation, as indicated + +Table 1. Video to 4D Scene Generation Comparisons. We report the PSNR score for the re-rendered video under the reference camera pose, and the CLIP and LPIPS scores in novel views for MOSE [10] and DAVIS [32]. For user preference, we report the preference between DreamScene4D and GenMOJO in a two-way voting. GenMOJO outperforms existing methods for both novel view synthesis and produces faithful re-renderings in the reference camera view. + +
MethodMOSEDAVIS
CLIP ↑PSNR ↑LPIPS ↓User Pref.CLIP ↑PSNR ↑LPIPS ↓
Consistent4D [14]77.7822.590.172-77.1722.310.146
DreamGaussian4D [37]81.9617.820.195-81.6217.680.183
DreamScene4D [5]85.1622.980.16936.8%84.1321.730.163
GenMOJO (Ours)85.4125.560.16863.2%84.1723.510.163
+ +by its high PSNR scores on both MOSE and DAVIS. Gen-MOJO also produces high-quality novel views, supported by its CLIP and LPIPS scores, which measure semantic similarity with the reference view, and by the user preference study. Consistent4D and DreamGaussian4D, originally designed for object-centric inputs, struggle with multi-object scenes like those in MOSE and DAVIS. This limitation often leads to distorted 3D geometry or artifacts due to ineffective motion optimization. While DreamScene4D can handle multi-object videos, it optimizes each object independently, which limits its ability to model inter-object occlusions or interactions in more complex videos. + +We show qualitative comparisons on MOSE and DAVIS videos between in Figure 5, highlighting instances where DreamScene4D fails to capture accurate relationships between interacting objects, leading to clipping problems. Additionally, we display reference view renderings from Shape of Motion, a recent Gaussian splatting-based method for point tracking. Since Shape of Motion only models visible parts of the scene, we exclude its results for novel views, and observe noisy renderings even in the reference view. These results demonstrate the robustness of GenMOJO in handling complex real-world videos with frequent occlusions and object interactions. + +# 5.2. 4D Gaussian Motion Accuracy + +Baselines. For evaluating Gaussian motion accuracy, we compare GenMOJO with DreamGaussian4D [37] and DreamScene4D [5], as in the previous section. Consistent4D [14] is not included since extracting accurate point motion from implicit NeRF representations is highly nontrivial and beyond our scope. We also include Shape of Motion [47], a recent optimization-based point-tracking method that employs 4D Gaussian Splatting. However, unlike GenMOJO, Shape of Motion does not leverage object or generative priors in optimizing dynamic Gaussians. + +Evaluation Metrics. To evaluate motion accuracy, we use both Average Trajectory Error (ATE) and Median Trajectory Error (MTE) [58], which measure the L2 distance between the estimated tracks and the ground truth tracks in all timesteps. MTE is included because it is less sensi + +tive to extreme failure cases, providing a robust assessment of typical tracking accuracy. We also report the Average End Point Error (A-EPE) and Median End Point Error (M-EPE) [5, 11], which calculate the L2 distance specifically at the final timestep. This provides specific insights into the tracking accuracy over long time horizons. For consistency, the predicted point tracks of all the methods are normalized to a resolution of $256 \times 256$ during the evaluation [7, 15]. + +Point Tracking Results. Table 2 presents the point tracking results on MOSE and DAVIS video datasets, including comparisons with SOTA supervised methods [15, 16] trained on point annotations serving as an upper bound for performance. Supervised trackers like CoTrackerV2 and CoTrackerV3 show significantly lower accuracy on MOSE compared to DAVIS, highlighting the greater challenge posed by MOSE videos due to frequent, prolonged occlusions and larger object and point displacements. GenMOJO achieves the lowest tracking error in all semi-supervised and optimization-based methods, excelling in each evaluation metric. It also performs competitively on the simpler DAVIS dataset. + +Both DreamScene4D [5] and GenMOJO benefit from object priors that help the Gaussians stay anchored to the same object throughout the video, enhancing tracking accuracy over other baselines, where tracked points often drift and get lost on different objects. This drift is a common issue for GMRW [42], Shape-of-Motion [47], and CoTracker [15], especially during occlusions. However, DreamScene4D, unlike GenMOJO, lacks cross-object interaction modeling, which hinders its performance during occlusions. Without joint motion optimization, DreamScene4D's Gaussian motion tracks in separate objects struggle to account for observed interactions in the video, causing tracks to drift or flicker within objects during occlusions, ultimately reducing tracking accuracy. + +# 5.3. Ablation Experiments + +We perform ablation studies to assess the impact of various components in GenMOJO on the generation quality and the motion accuracy, as shown in Table 3 using MOSE videos. First, we evaluate the effect of removing joint splatting + +Table 2. Point tracking comparison between 4D generation / reconstruction methods. We report the Average Trajectory Error (ATE), Median Trajectory Error (MTE) [58], Average End Point Error (A-EPE), and Median End Point Error (M-EPE) [5] in MOSE [10] and DAVIS [7, 32]. GenMOJO outperforms existing methods that were not trained on point tracks in MOSE, and achieves competitive performance when compared against learning-based methods. + +
MethodMOSEDAVIS
ATE ↓MTE ↓A-EPE↓M-EPE↓ATE ↓MTE ↓A-EPE↓M-EPE↓
(a) Not trained on point tracking data
GMRW [42]24.8520.8742.5936.9942.1726.7375.6160.14
DreamGaussian4D [37]27.7325.7146.1843.5530.2728.1861.555.69
Shape of Motion [47]18.3910.4028.2518.308.913.9318.946.08
DreamScene4D [5]13.4710.4922.4816.979.596.5017.4710.29
GenMOJO (Ours)9.918.4715.4611.118.166.3214.149.36
(b) Trained on point tracking data
CoTrackerv2 [15]15.7412.1527.9620.3521.902.0826.223.49
CoTrackerv3 [16]11.548.3322.1616.1121.241.7424.03.11
+ +Table 3. Ablation experiments. We report motion accuracy and view synthesis metrics in MOSE [10] by removing different proposed components in GenMOJO. We additionally replace object-centric SDS with scene-level SDS [40], and replace DepthCrafter with DepthAnything-V2 [52] for depth initialization. + +
MethodMOSE
A-EPE ↓M-EPE ↓CLIP ↑PSNR ↑
Full Model15.4611.1185.4125.56
w/o Multi-object Joint Splitting23.4816.9785.1822.88
w/o Transformed Obj-centric rendering19.4414.5081.4425.30
w/o Instance Masks Rendering16.7712.4984.8825.19
Scene-Level SDS [40]20.0315.4983.0525.17
DepthAnything-V2 [52]17.3212.8485.2925.33
+ +optimization and instead use a method similar to DreamScene4D, where objects are optimized independently. This change leads to a marked drop in motion accuracy and PSNR, confirming that joint splatting is crucial for accurately modeling object occlusions and interactions. + +Next, we investigate the role of unseen object modeling by testing the integration of SDS during motion optimization. As expected, omitting this results in a substantial decrease in the quality of novel view synthesis. The motion accuracy also suffers, which we hypothesize is due to Gaussians in unobserved views becoming underconstrained without SDS and can move unpredictably. We further ablate with a scene-level SDS model [40] rather than object-centric SDS ones [24], which also led to performance drops. This may be due to object-centric NVS diffusion models outperforming scene-level ones, and leading to lower quality SDS gradients. + +To examine GenMOJO's robustness to different depth models, we replace DepthCrafter [13] with DepthAnythingV2 [52], which generates less consistent depth across frames. We observe a minor performance impact, likely due to occasional depth inaccuracies. Lastly, we remove the instance mask rendering loss and find a reduction in motion accuracy, though the novel view synthesis quality remains + +largely unchanged. We observed that this is due to some Gaussians drifting between objects without this loss, leading to less accurate motion tracking. + +# 5.4. Limitations + +Despite the progress demonstrated in this paper, GenMOJO has several limitations: (1) Similar to previous methods [5, 37], our approach relies on the generalization capabilities of the view-conditioned generative model, which struggles with videos featuring unconventional camera poses. (2) Although our joint motion optimization procedure can correctly determine the depth ordering of objects, jittery depth estimations can still cause objects to "jump" along the depth axis. (3) Due to the reliance on test-time optimization, our method is not suitable for online applications. We hope to develop novel feedforward models that can enable both real-time inference and provide stronger priors for test-time optimization in future work. + +# 6. Conclusion + +In this work, we introduce GenMOJO, a novel approach for generating complete 4D scenes from complex monocular videos containing multiple objects, prolonged occlusions, and intricate inter-object interactions. GenMOJO leverages state-of-the-art pre-trained models to decompose scenes into individual object trajectories while employing a joint motion optimization strategy to capture inter-object dynamics accurately. Experimental results in in-the-wild video datasets, such as DAVIS and MOSE, highlight the superiority of our method in view-synthesis tasks, outperforming existing baselines. Furthermore, we annotated the point tracks in MOSE videos to assess the accuracy of Gaussian motion, revealing that the Gaussian tracks generated by GenMOJO outperform previous methods in challenging scenarios characterized by large movements and extended occlusions. + +# References + +[1] Sherwin Bahmani, Ivan Skorokhodov, Victor Rong, Gordon Wetzstein, Leonidas Guibas, Peter Wonka, Sergey Tulyakov, Jeong Joon Park, Andrea Tagliasacchi, and David B Lindell. 4d-fy: Text-to-4d generation using hybrid score distillation sampling. arXiv preprint arXiv:2311.17984, 2023. 2 +[2] Sherwin Bahmani, Xian Liu, Yifan Wang, Ivan Skorokhodov, Victor Rong, Ziwei Liu, Xihui Liu, Jeong Joon Park, Sergey Tulyakov, Gordon Wetzstein, et al. 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Explanar results of Robust-MVTON. We propose a robust multi-view try-on solution that takes both front- and back-view garments as input and allows garments to be tried on people in any view. + +# Abstract + +This paper tackles the emerging challenge of multi-view virtual try-on, utilizing both front- and back-view clothing images as inputs. Extending frontal try-on methods to a multi-view context is not straightforward. Simply concatenating the two input views or encoding their features for a generative model, such as a diffusion model, often fails to produce satisfactory results. The main challenge lies in effectively extracting and fusing meaningful clothing fea + +tures from these input views. Existing explicit warping-based methods, which establish direct correspondence between input and target views, tend to introduce artifacts, particularly when there is a significant disparity between the input and target views. Conversely, implicit encoding-based methods often lose spatial information about clothing, resulting in outputs that lack detail. To overcome these challenges, we propose Robust-MVTON, an end-to-end method for robust and high-quality multi-view try-ons. Our approach introduces a novel cross-pose feature alignment technique to guide the fusion of clothing features and incorporates a newly designed loss function for training. + +With the fused multi-scale clothing features, we employ a coarse-to-fine diffusion model to generate realistic and detailed results. Extensive experiments conducted on the Deepfashion and MPV datasets affirm the superiority of our method, achieving state-of-the-art performance. + +# 1. Introduction + +Virtual Try-On (VTON) is a classical task that aims to generate plausible images of individuals wearing specified clothing while maintaining the integrity of the person's identity and the clothing's details. It can greatly enhance user experiences in virtual applications, such as online shopping [13]. In the past decade, VTON has seen rapid advancements [60], especially the recent diffusion-based methods [8, 62], which significantly enhance its realism and yield impressive results. However, most existing approaches concentrate solely on frontal VTON, overlooking multi-view VTON (i.e. any-view try-ons including side and back ones). Considering the latter is also essential in practical applications, this paper is dedicated to tackling this emerging task. Unfortunately, extending from frontal to multi-view virtual try-on (MVTON) is not straightforward. We have to provide clothing information from other views, since a single frontal view cannot contain sufficient information, such as the shape of the back collar, how the straps cross at the back, whether the top has a hat, and the details of the coat waist as shown in Fig. 2. + +In this study, we simultaneously use the front-view and back-view clothing images as inputs to try the garment on any view pose, as these two perspectives nearly encompass all the information about the garment from various angles. Although more views of input can provide a richer perspective of the clothing, it unavoidably introduces redundant visual features, thus increasing the difficulty for models like the stable diffusion [45] to align reference features containing redundant view information to the target perspective. + +To transfer the two input clothing images onto a specific person image, traditional warping-based methods (such as thin-plate spline methods [52] and the flow-based methods [14, 18, 21]) explicitly calculate the correspondence between the input and the target views and integrate multiview clothing information. However, studies based on explicit warping suggest that try-on results are significantly influenced by the target pose, especially when warping clothing onto poses with occlusions [6, 29, 57], such as side-view poses. Moreover, previous warping-based methods have mainly focused on warping flat in-shop clothing onto target poses. In our MVTON setting, the input clothing is not flat or aligned but rather comes from a clothed person's image. These garments have already been distorted or occluded by human poses, further increasing the difficulty of achieving MVTON using warping-based methods [55, 56]. + +![](images/08134ce048be8e86e7eee8f643a099a259bbabc3f75fc59fcea031b0ab7b9ebb.jpg) +Figure 2. Clothing samples in the front and back views. + +Recently, MV-VTON [53] proposed a pose-based clothing feature fusion method to align the two input clothing images with the target view. However, MV-VTON aligns the front-view and back-view features to the target pose separately by calculating the similarity between each input pose and the target pose. Then, these aligned features are concatenated to form the reference feature for a generative model. One significant drawback of this fusion strategy is that the alignment will be ineffective when the target view is far from the inputs. For example, when the target pose corresponds to the back view, the reference feature inputted to the generative model should not contain any front-view cloth features. However, MV-VTON still fuses the front-view clothing to obtain the final features. To address this issue, MV-VTON introduced a hard selection by determining which input pose (i.e. front-view or back-view) is closer to the target pose. However, this rough determination cannot effectively and adaptively eliminate the interference caused by view features that are different from the target. + +Our key insight is that the clothing on the individual and the individual's pose skeleton have a complete spatial alignment relationship. We can supervise the alignment and fusion of input clothing features to the target view using the pose aligning and fusing process. Unlike MV-VTON, what sets us apart is our ability to adaptively fuse input view features and significantly eliminate interference from view information that is very different from the target view. We achieve this by setting multi-scale supervisory constraints in pose feature fusion, instead of crudely calculating the similarity between each input-view and target-view pose. + +In this paper, we present Robust-MVTON, an end-to-end method designed for robust and high-quality multi-view virtual try-ons. Our approach features two main components: a cross-pose feature alignment module for clothing feature fusion and a coarse-to-fine diffusion model for generating multi-view try-ons. To achieve effective pose alignment, we employ two projectors that implicitly map front- and back-view features into the target view space. We intro + +duce a novel loss function to supervise this alignment by measuring the error between the fused pose feature and the target feature. Once trained, these projectors can be seamlessly integrated into our clothing feature fusion process. Next, we apply a coarse-to-fine diffusion model to utilize the fused clothing features, generating the desired try-on effects. This model calculates multi-scale features, capturing both high-level semantic details and fine-grained appearance features, to deliver high-quality results. We conducted extensive experiments using the Deepfashion [32] and MPV [11] datasets. Both quantitative and qualitative results demonstrate that our method significantly outperforms existing approaches in the multi-view virtual try-on task. Additionally, an ablation study confirms the effectiveness of the main components of our method. + +In summary, our main contributions are as follows: + +- We tackle the emerging and challenging task of Multiview VTON, and propose a novel framework which is the first one that enables robust and high-quality outputs. +- We introduce an innovative method for cross-pose feature alignment and fusion, utilizing a newly developed loss function for training. This approach efficiently extracts multi-scale clothing features from multi-view inputs and contributes to a versatile coarse-to-fine diffusion model. +- We conduct extensive experiments to show the superiority of Robust-MVTON and the effectiveness of each component. Robust-MVTON achieves state-of-the-art MVTON results on the DeepFashion and MPV datasets. + +# 2. Related Work + +Multi-View Human Generation Multi-view human generation primarily utilizes human pose information in conjunction with other conditions to generate human images from various perspectives. These tasks focus on creating realistic images under different poses, appearances, and viewpoints. One of the most widely explored areas within this field is pose transfer, initially introduced by [36], which uses adversarial refinement to enhance the generated images. MUST-GAN [37] proposed a multi-level statistics transfer model for self-supervised human image synthesis, while TransMoMo [63] introduced an unsupervised motion retargeting network for human motion transfer. With the advent of diffusion models, PIDM [2] developed a texture diffusion module integrated with a backbone denoising network, enabling close alignment between the appearance of the source image and the target pose. PoCoLD [19] introduced a Pose-constrained Attention module, refining the cross-attention mechanism by feature dimension reduction to decrease spatial and temporal complexity. At the same time, CFLD [35] adopted a coarse-to-fine latent diffusion approach using fine-grained attention. With advancements in text-to-image models, some methods have extended their application to multi-view image generation. For instance, + +Text2Human [25] employs DensePose [17] to predict parsing maps as guidance for generating humans from text descriptions, and HumanSD [26] uses skeleton-based guidance to fine-tune pre-trained models for text-to-human synthesis. In the domain of skeleton-sequence and reference-image-guided human video generation,AnimateAnyone [24] introduced ReferenceNet, a custom-designed symmetric UNet architecture that captures spatial details from reference images. MagicAnimate [61] combines motion signals with an appearance encoder to transform static portraits into low-dimensional vectors, capturing the portrait's appearance features such as style, pose, and expression. + +Image-Based Virtual Try-on Image-based virtual try-on (VTON) methods aim to synthesize realistic images of individuals wearing specified garments while preserving identity and garment details. Early methods often adopted a two-stage warping-based approach: garment warping and try-on generation. For garment warping, some methods [7, 38, 51] used affine transformations for geometric matching, while others [1, 10, 15, 20, 58] predicted garment flows using neural networks. However, warping-based methods often struggle with achieving high realism due to the loss of structural information and subtle garment features. To address these issues, recent advancements in VTON have focused on leveraging the generative power of pre-trained diffusion models [43, 45] to overcome the limitations of explicit warping. Some approaches [16, 31, 40, 50, 53] use diffusion models to refine the try-on results after warping. Currently, a popular method involves using trainable garment encoders; some methods [27, 48, 59] replicate the backbone network to encode garment features, while others utilize pre-trained image encoders like DINOv2 [42] and CLIP [44]. There are also innovative approaches such as MMTryOn [66], IMAGDressing [47], MagicClothing [5], and Wear-Any-Way [4], which incorporate additional multimodal control capabilities on top of the try-on task. CatVTON [9] explores the efficiency of virtual try-on models. However, current mainstream image-based VTON methods still focus on single-view try-ons. For back or side poses, these methods often fail to produce realistic results. Using multi-view garment information for arbitrary viewpoint try-ons remains an area that requires further exploration. + +# 3. Method + +To tackle the emerging and challenging task of MV-TON, we propose an end-to-end method, named Robust-MVTON, which mainly consists of a cross-posed alignment and fusion module for effective feature extraction and a coarse-to-fine feature-conditioned stable diffusion model for high-quality try-on generation. As shown in Fig. 3, given two views (i.e. the front and back view) of clothing and an arbitrary view of the target person, we first ex + +![](images/ff92a8ca2fcaed8feb2c300084ff045377698d79fe76b7bc8d647f417297b108.jpg) +Figure 3. Overview of our proposed Robust-MVTON. Given the front- and back-view images of clothing, we first utilize a cross-pose feature alignment and fusion method to obtain multi-scale clothing features, then feed these features to a coarse-to-fine latent diffusion model to generate high-quality try-on results for any target views. + +tract their corresponding skeletons and utilize a multi-view pose alignment learning method to guide the feature transformation from the input view to target view, followed by an adaptive multi-view feature fusion. Wherein, we calculate multi-scale features to acquire high-level semantic and fine-grained appearance features. To further enhance the performance of view alignment and fusion, we define spatial labels and input them to provide additional clothing and view information. Then, we adopt a coarse-to-fine diffusion model using the fused multi-scale features as conditions to generate the try-on results on the target view. Our easy cross-pose alignment and fusion strategy reduces the burden on the stable diffusion model to learn alignment between the input and target views, significantly improving the performance of MVTON. + +# 3.1. Cross-Pose Feature Alignment and Fusion + +Given two input and one target views of clothed people, we first calculate their pose skeleton images using [3], then learn the pose alignment from input views to the target. Our key insight is that the clothing on the individual is spatially in line with the pose skeleton. We can directly apply the learned pose alignment to the clothing feature fusion. + +Cross-View Pose Feature Alignment For each input pose image, we use the same Swin Transformer [33] as the pose encoder $\varepsilon_{p}$ to extract a stacked multi-scale feature maps (total 4-scale feature maps, including coarse semantic feature and fine-grained appearance feature as in [34]), then map the input features to the target view space, implicitly aligning cross-pose features. Concretely, we adopt two linear layers (i.e., the projector illustrated in Fig. 3) to project the front- and back-view pose features into two new pose representations in spatial channels, respectively. Then, we fuse the two new pose representations by simply adding them to approximate the target-view pose feature, i.e., + +$$ +P _ {f u s e} ^ {i} = \operatorname {L i n e a r} _ {f} ^ {i} (P _ {f} ^ {i}) + \operatorname {L i n e a r} _ {b} ^ {i} (P _ {b} ^ {i}), \tag {1} +$$ + +where $P_{fuse}^{i}, P_{f}^{i}$ and $P_{b}^{i}$ are the $i$ -th fused, front- and back-view pose features, respectively, and $i = 1,2,3,4$ . The Linear $f$ and Linear $b$ correspond to the two projectors for front and back views. + +To make the dedicated linear layers devoted to spatially aligning the input and target pose features, we design a novel pose alignment loss to supervise it in our network training, i.e., + +$$ +L o s s _ {p o s e} = \sum_ {i = 1} ^ {4} \left| P _ {f u s e} ^ {i} - P _ {t a r g e t} ^ {i} \right|, \qquad (2) +$$ + +where $P_{target}^{i}$ is the $i$ -th target feature maps, $i = 1,2,3,4$ . + +Pose-Guided Clothing Feature Fusion With the aligned cross-view pose, we can apply the pose feature transformations (i.e. the two linear layers) to the alignment and fusion of clothing features since we find the clothing on the individual and the individual's pose skeleton have a complete spatial alignment relationship. Concretely, we first calculate the clothing image using a parsing method [30], then adopt another Swin Transformer [33] as clothing encoder $\varepsilon_{i}$ to extract 4 stacked feature maps. Then, we adopt the same spatial linear layer in the pose alignment to map the front- and back-view clothing features to the target view and add them as the final fused clothing features, i.e., + +$$ +C _ {f u s e} ^ {i} = \operatorname {L i n e a r} _ {f} ^ {i} \left(C _ {f} ^ {i}\right) + \operatorname {L i n e a r} _ {b} ^ {i} \left(C _ {b} ^ {i}\right), \tag {3} +$$ + +where $C_{fuse}^{i}, C_{f}^{i}$ and $C_b^i$ are the $i$ -th fused, front- and back-view clothing features, respectively, and $i = 1,2,3,4$ . With the multi-scale fused clothing features, we can feed them into a coarse-to-fine diffusion model to generate try-ons. + +Spatial Label Assistance To enhance the pose skeleton with additional human body view information, we introduce a pixel-wise spatial label map for each given image and learn the label feature alignment to improve the robustness of our cross-posed alignment. To be specific, we adopt the standard OpenPose map and the annotation order as in OpenPose [3], then extract 3 essential feature points containing the Neck, Left Shoulder and Right Shoulder, that can represent the main view of a human body. Lastly, we use two different colors to label the front view and back view on the input front-, back-, and target-view clothing mask, denoted as $L_{f}$ , $L_{b}$ , and $L_{target}$ , respectively. For cases where the body is facing left or right (determined by the Neck, Left Shoulder, and Right Shoulder in OpenPose), such as the target view in Fig. 3, we label the directions in the horizontal direction from the Neck to the Left Shoulder and from the Neck to the Right Shoulder using the colors corresponding to the front- and back views, respectively. In addition, we calculate the spatial label on the clothing-agnostic mask of the target view, denoted to as $L_{agnostic}$ . The spatial label and pose skeleton images possess the same sizes. We apply the label encoder $\varepsilon_{l}$ (which shares the same network structure as $\varepsilon_{p}$ ) and projectors (i.e., $Linear_{f}$ and $Linear_{b}$ ) to obtain 4-scale spatial label features and supervise their cross-view alignment as the pose process, i.e., + +$$ +L _ {f u s e} ^ {i} = \operatorname {L i n e a r} _ {f} ^ {i} \left(L _ {f} ^ {i}\right) + \operatorname {L i n e a r} _ {b} ^ {i} \left(L _ {b} ^ {i}\right), \tag {4} +$$ + +$$ +L o s s _ {l a b l e} = \sum_ {i = 1} ^ {4} \left| L _ {f u s e} ^ {i} - L _ {t a r g e t} ^ {i} \right|, \tag {5} +$$ + +where $L_{\text{fuse}}^i$ and $L_{\text{target}}^i$ are the $i$ -th fused and target spatial label features, and $i = 1,2,3,4$ . + +# 3.2. Coarse-to-Fine Latent Diffusion Model + +After the cross-posed feature alignment and fusion, we adopt a similar architecture of the coarse-to-fine latent diffusion model [34] to generate high-quality MVTON results. As illustrated in Fig. 3, we input a random noise map, the target clothing-agnostic image as well as its corresponding pose skeleton and spatial label features to the model, then feed our multi-scale fused clothing features to its perception-refined decoder and hybrid-granularity attention module for learning. Finally, we optimize the reconstructed noise error $Loss_{diffusion}$ to fine-tune the model. For more implementation details, please refer to [34]. + +Pose and View Control For effective pose and view control, we concatenate the target pose features and clothing-agnostic label features along the channel dimension and match the concatenated channel to the channel dimension of each down-sampling block in stable diffusion [45] by using $1 \times 1$ ConvNets. The concatenated feature maps are added directly to the end of each down-sampling block, similar to injecting pose control information into the stable diffusion method in [41]. + +Person Identity Preservation To efficiently preserve the identity of the target person, such as pose, face, hair, and unchanged clothing parts, we feed the clothing-agnostic image and mask into the latent diffusion model with VAE encoder [12]. For concise illustration, we omit the VAE encoder and decoder model in Fig. 3. + +Training Loss We train our end-to-end pipeline with the following loss + +$$ +L o s s = L o s s _ {d i f f u s i o n} + \lambda L o s s _ {p o s e} + \mu L o s s _ {l a b l e}, \tag {6} +$$ + +where $\lambda$ and $\mu$ are the weight for balancing the $Loss_{\text{pose}}$ and $Loss_{\text{table}}$ . During the training process, we set $\lambda$ and $\mu$ to 0.01 respectively. + +# 4. Experiments and Results + +# 4.1. Datasets and Baselines + +We conduct experiments on two public datasets, DeepFashion [32] and MPV [11]. To meet the requirements of MV-TON, each data sample should possess both front-view and back-view images. For the DeepFashion dataset, there are a total of 14,120 pairs of data available for the multi-view try-on task. These pairs from DeepFashion generally contain at least 3 views: the front, back, and side views, providing us with rich variations in perspectives for our multiview try-on task. However, most pairs in the MPV dataset only consist of one or two views (i.e., the front and back views), so we had to select some garments with only two views for our data. In the MPV dataset, there are a total of 12,032 pairs available. We designate $20\%$ of pairs from + +![](images/26d111a1eb468d241617084eedf661137b54f073857bd54d1253d2439bb5ee61.jpg) +Figure 4. Qualitative comparisons on the DeepFashion dataset [32]. + +![](images/33bc8a18fbcae8095d6a677b441b26ce2eb0504e9d83faac95954c7a17bd0167.jpg) + +![](images/5d8428f2bfdce2e7691285e95aa53a8170cb0bc3e0139d8ff672fee38d76cc96.jpg) +Figure 5. Qualitative comparisons on the DeepFashion dataset [32] for more views. + +each dataset as the test set, with the remainder used for the training set. All experiments in this paper are conducted using the same training and test sets. We use three different metrics to evaluate the generated images quantitatively, including FID [22], LPIPS [65], SSIM [54]. + +We compare our pipeline with four state-of-the-art methods, including frontal view VTON methods CATDM [64] and StableVITON [27], and multi-view try-on MV-VTON [53]. For CAT-DM and StableVITON, we utilize the pre-trained models on the VITION-HD dataset [6], while for MV-VTON, we employ the pre-trained models on the MVP dataset [53]. Considering that currently, MVVTON is the only research on MVTON, we apply the CFLD model [34] used for pose-guided image transfer tasks to the MVTON task by spatially concatenating the frontview and back-view clothing as inputs. We define the CFLD model used for the MVTON task as CFLD* in our experiments. For a fair comparison, we retrained CFLD* on DeepFashion and MPV datasets respectively. + +# 4.2. Qualitative Comparison + +We provide qualitative results of Robust-MVTON on the DeepFashion and MPV in Figure 4 and Figure 6. The results demonstrate that our method showcases superior performance in preserving the clothing shape, retaining texture details, and the design elements of the clothing across various views. CAT-DM and StableVITON fail to preserve the original texture information of the clothing. Furthermore, in Figure 4b and Figure 6b, the features corresponding to the back-view perspective are generated as features for the front-view perspective. Compared to Robust-MVTON, which incorporates view feature selection and fusion strategies, the try-on results generated by CFLD* lack realism and naturalness, as shown in Figure 6a. Visual comparative experiments between CFLD* and Robust-MVTON demonstrate the effectiveness of our proposed pose-supervised cloth feature fusion in feature fusion and alignment. For MV-VTON, we strictly follow the implementation process of MV-VTON, including the preprocessing step of warp + +![](images/e086061191782bde2b3cce392a5326761c105a19998d23012e5d7683c26fd0bb.jpg) +Figure 6. Qualitative comparisons on the MPV dataset [11]. + +![](images/09a5f0dcb256dccb6cc1b4d014114daccd578b9475e94ba52e2bd44e418dd18e.jpg) + +![](images/9d77e3c1610baac38fc921e9c291198ad0b652b4974a046ec695529e45e7360f.jpg) +Figure 7. Qualitative comparisons on the MPV dataset [11]. + +ing [21, 39]. In practice, we found it difficult to accurately align input cloth that carries source pose information, such as being occluded or having its shape altered by the source pose, to the target pose, especially in side poses. The above analysis based on warp is one of the reasons for the poor performance of MV-VTON. In addition, experimental results also indicate that the hard-selection and soft-selection proposed in MV-VTON are not effective cloth feature and fusion strategies. + +# 4.3. Quantitative Comparison + +We conduct experiments under both paired and unpaired settings. In the paired setting, we place the garment with front-view and back-view on the same person, with either the same or different view poses. In contrast, in the unpaired setting, the input garments are worn by another person, who has varying views. We conducted experiments at a resolution of $512 \times 384$ . FID was obtained in the un + +
MethodDeepFashion
FID ↓LPIPS ↓SSIM ↑User Study ↑
CAT-DM16.470.1910.7595.2%
StableVITON15.700.2050.7643.9%
CFLD*14.310.1810.78212.6%
MV-VTON21.130.2550.7033.0%
w/o Spatial Label11.420.1600.817-
w/o Pose Loss12.450.1780.810-
Ours11.400.1580.82075.2%
+ +Table 1. Quantitative comparison on the DeepFashion dataset [32]. + +paired setting, while LPIPS and SSIM were obtained in the paired setting. The experimental results show that our pipeline significantly outperforms other methods. In practice, for StableVITON and CAT-DM, we only input front-view clothing, while for MV-VTON and CFLD*, we input both front-view and back-view clothing simultaneously. Table 1 and Table 2 present that our Robust-MVTON shows state-of-the-art performance for all the evaluation metrics with a large margin. The experimental results of CFLD* indicate that directly concatenating front-view and back-view and inputting them into the diffusion model is not an effective approach to embedding multi-view reference features. During the experiment, we found that MV-VTON heavily relies on the preprocessing step of warping garments to the target view. In fact, in our multi-view try-on task, there is no ground truth to train a specific warp model. However, aligning front-view and back-view garments to the target view using the currently available pre-trained models based on in-shop garments is extremely challenging. + +# 4.4. Ablation Study + +Pose Loss Constraint To evaluate the effectiveness of pose loss constraints in cross-pose feature fusion, we conducted + +
MethodMPV
FID ↓LPIPS ↓SSIM ↑User Study ↑
CAT-DM17.810.1870.7512.9%
StableVITON16.700.2040.7665.1%
CFLD*14.360.1850.7796.5%
MV-VTON19.200.2370.7072.2%
Ours12.510.1740.81883.3%
+ +Table 2. Quantitative comparison on the MPV dataset [11]. + +![](images/7fb00f39ee4f8d570b28e5e999ca1064653c2a471521d29765db393a0c7441b0.jpg) +Figure 8. Visual comparisons under the training condition with and without the pose loss constraint. + +ablation experiments based on pose constraint loss. The results from Fig. 8 and Table 1 demonstrate that the training condition using loss contain could better align the input cloth features to the target view, thus improving the quality of try-on generation. With the pose loss constraints at different scales, the fusion strategy effectively functions as an information bottleneck that feeds the most useful information regarding the target pose to the stable diffusion model while removing irrelevant garment visual information. + +Spatial Label Assistance Color Label can effectively assist the fusion module in providing the overall perspectives information, such as front-view and back-view. As shown in Fig. 9, some details of the clothing's back design are also well aligned with the target view. This achievement is completely unattainable using only the front-view try-on method. + +# 5. Conclusion + +In this paper, we introduce Robust-MVTON, an end-to-end method for robust and high-quality multi-view virtual try-ons using front- and back-view clothing inputs. To effectively integrate information from multiple views, we pro + +![](images/6599f9d85800bc1dbf454e9849384371ab5f5fb6514f061cae51ccfc8862ecc7.jpg) +Figure 9. Visual comparisons with or without the spatial label assistance in cross-pose feature fusion. + +pose a novel cross-posed feature alignment and fusion strategy, complemented by a newly designed loss function to enhance learning. Additionally, we extract multi-scale clothing features and utilize a coarse-to-fine model to produce high-quality try-on results with fantastic details. Experiments conducted on the Deepfashion and MPV datasets demonstrate the superiority of Robust-MVTON, achieving state-of-the-art performance. + +**Limitations** Our proposed Robust-MVTON is mainly limited by the availability of suitable multi-view try-on datasets. At present, there is a scarcity of datasets that are truly appropriate for the 2D multi-view try-on task. For instance, the MPV dataset [11] we utilize predominantly contains only front and back view pairs. There is a pressing need for a large-scale 2D dataset that encompasses a broader range of multi-view perspectives. In the future, we would like to collect more multi-view clothing data to enhance the performance of Robust-MVTON. + +# Acknowledgements + +The work was supported in part by the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone, by Guangdong Provincial Outstanding Youth Fund (No.2023B1515020055), by Shenzhen Science and Technology Program No. JCYJ20220530143604010, and No.NSFC61931024. It is also partly supported by the National Key R&D Program of China with grant No.2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No.2017ZT07X152 and No.2019CX01X104, by Key Area R&D Program of Guangdong Province (Grant No.2018B030338001), by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No.2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No.ZDSYS201707251409055). + +# References + +[1] Shuai Bai, Huiling Zhou, Zhikang Li, Chang Zhou, and Hongxia Yang. Single stage virtual try-on via deformable attention flows, 2022. 3 +[2] Ankan Kumar Bhunia, Salman Khan, Hisham Cholakkal, Rao Muhammad Anwer, Jorma Laaksonen, Mubarak Shah, and Fahad Shahbaz Khan. Person image synthesis via denoising diffusion model, 2023. 3 +[3] Zhe Cao, Tomas Simon, Shih-En Wei, and Yaser Sheikh. Realtime multi-person 2d pose estimation using part affinity fields. 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High-fidelity human novel view synthesis. Given very sparse-view input images (e.g., 4 views) that do not enable accurate human template estimation due to the limited overlappings, our method can robustly synthesize high-fidelity novel views in a generalizable manner, without requiring any further fine-tuning or subject-specific optimization. Compared to both NeRF-based method, e.g., TransHuman [55], and 3D Gaussian Splatting (3DGS) based methods, e.g., vanilla 3DGS [30] and GPS-Gaussian [90], our approach produces better result. + +# Abstract + +This paper presents RoGSplat, a novel approach for synthesizing high-fidelity novel views of unseen human from sparse multi-view images, while requiring no cumbersome per-subject optimization. Unlike previous methods that typically struggle with sparse views with few overlappings and are less effective in reconstructing complex human geometry, the proposed method enables robust reconstruction in such challenging conditions. Our key idea is to lift SMPL vertices to dense and reliable 3D prior points representing accurate human body geometry, and then regress human Gaussian parameters based on the points. To account for possible misalignment between SMPL model and images, we propose to predict image-aligned 3D prior points by leveraging both pixel-level features and voxel-level features, from which we regress the coarse Gaussians. To enhance the ability + +to capture high-frequency details, we further render depth maps from the coarse 3D Gaussians to help regress fine-grained pixel-wise Gaussians. Experiments on several benchmark datasets demonstrate that our method outperforms state-of-the-art methods in novel view synthesis and cross-dataset generalization. Our code is available at https://github.com/iSEE-Laboratory/RoGSplat. + +# 1. Introduction + +Novel view synthesis is a widely discussed topic with various applications in video games, telepresence, sports broadcasting, and the metaverse [59]. The past few years have witnessed remarkable progress in this domain, primarily due to the emergence of neural radiance fields (NeRF) [49] and 3D Gaussian Splatting (3DGS) [30]. However, human novel view synthesis still faces many challenges. First, a tedious per-subject optimization is typically required by + +existing methods to adapt to unseen human subjects, which significantly lowers their overall efficiency and practicability. Second, previous methods usually require dense input views or precise proxy geometry as input, thus their performance may degrade severely when only sparse views with limited overlappings are available. Third, the inherent intricate textures and self-occlusion in human characters introduce extra difficulty for high-fidelity free-view human rendering. + +To address these challenges, various NeRF-based methods are proposed to learn generalizable novel view synthesis for unseen human by leveraging pixel-aligned image features from multi-view images and human parametric template model (e.g., SMPL [46]) as structural prior [17, 23, 33, 34, 55]. However, their performance is sensitive to the quality of the estimated template model, which is mostly unreliable for sparse multi-view images even ignoring the possible self-occlusion and depth ambiguities arising from varying human poses (see Figure 1). Moreover, these methods introduce extra computational overhead in addition to the costly MLP-based queries in NeRF, gaining generalizability at the expense of further degrading the rendering speed. While there are numerous works speeding up NeRF by adopting explicit representation such as voxels [16, 43, 52], tri-planes [6, 62], and point clouds [24, 29, 78], developing generalizable NeRF that enables high-fidelity and efficient novel view synthesis remains an open problem. + +3DGS-based methods have recently become mainstream for generalizable novel view synthesis because of the advantage of 3DGS in real-time rendering at high visual quality. Several pioneering works propose to achieve generalizability by incorporating depth estimation [4, 11, 45, 90], but these methods are less effective for sparse multi-view images that can contain limited overlappings or depth ambiguity derived from self-occlusions of human body (see Figure 1). Although a recent work [54] proposes to learn generalizable human 3DGS from a single-view image by utilizing a 2D multi-view diffusion model. However, it fails to offer high-fidelity novel view synthesis, especially when intricate garments and accessories involved. + +In this paper, we present RoGSplat, a new generalizable human Gaussian Splitting approach that can robustly render high-fidelity novel views of unseen human subjects from sparse multi-view images. The core idea of our method lies in lifting SMPL vectics to more dense and accurate 3D points that accurately represent human body geometry for fine-grained 3D Gaussian regression. To enhance the robustness to the misalignment between SMPL model and multiview images, we propose to leverage both the pixel-level features and voxel-level features for adaptive misalignment compensation, by which we are able to obtain 3D prior points well aligned with images. Based on the 3D prior points, we further introduce a coarse-to-fine pixel-wise Gaussian prediction strategy to regress fine-grained Gaussians that can + +effectively model high-frequency details. + +In summary, the main contributions of our work are: + +- We present a novel generalizable human Gaussian Splatting method that enables robust high-fidelity novel view synthesis from sparse multi-view images. +- We propose a method to effectively lift SMPL vertices to dense image-aligned 3D points, and introduce a coarse-to-fine pixel-wise Gaussian prediction strategy to enhance the effectiveness in modeling finer details. +- Experiments on benchmark datasets demonstrate that our method outperforms state-of-the-art methods in novel view synthesis and cross-dataset generalization. + +# 2. Related Work + +Neural implicit human reconstruction. Early methods [61, 77, 92] focus primarily on leveraging pixel-aligned image features to regress the signed distance field (SDF) under the supervision of ground-truth 3D models. Later, the emerging of neural radiance field (NeRF) [49] opens up a new paradigm to render high-fidelity human based only on sparse multi-view images [57, 63, 89] or even a monocular image/video [20, 23, 26, 71]. Although NeRF-based methods have demonstrated impressive results in animating [37, 38, 44, 69] and editing [10, 12, 13, 76, 79, 81] human avatars, these methods typically fail to generalize to unseen subjects because of requiring per-subject optimization, and their rendering efficiency is low due to the inherent high computation to render each pixel. To achieve generalizable NeRF, a common solution is to construct feed-forward scene modeling conditioned on image-based features [5, 40, 68, 86], but it is shown to be highly sensitive to large variation in pose and clothing. To address the issue, human priors such as SMPL [46] and 3D skeleton keypoints are widely employed in recent works [18, 23, 33, 48, 55, 89]. On the other hand, there are various works for accelerating scene-specific NeRF [6, 16, 52, 62]. However, developing efficient yet generalizable NeRF remains a challenge. + +Point-based rendering. As a discrete and unstructured representation that can represent geometry with arbitrary topology, point element has been widely used in multi-view 3D reconstruction [3, 32, 36, 41, 60, 72, 78, 91]. Recently, 3D Gaussian Splatting [30], a novel scene representation allowing real-time and high-fidelity rendering by formulating point clouds as 3D Gaussians with learnable properties such as position, color, opacity and anisotropic covariance. Due to its superior performance in rendering quality and efficiency, a large number of works have been proposed to extend 3D Gaussian representation for widespread applications including dynamic scene modeling [25, 47, 73, 84, 85], human reconstruction [15, 21, 22, 27, 28, 31, 39, 50, 51, 67, 80], and autonomous driving [14, 82, 93, 94]. However, these + +![](images/38979845401c6e246cd1e17a1b3179973d867b4e66bc244adb99d0889befbf87.jpg) +Figure 2. Overview of RoGSplat. We first fit the SMPL model from input sparse views, and then feed the SMPL depth into a depth refiner to get refined depth, from which we obtain voxel-level features. These features are then aggregated with pixel-level features extracted from source images, followed by the SPD network [74, 75] to generate dense image-aligned prior points for coarse Gaussian rasterization. To help model finer details, the image-aligned depth maps from coarse Gaussians are unprojected to yield finer pixel-wise points. These points are then refined by an offset estimator, and finally employed to regress fine-grained Gaussians. + +methods, although enable real-time inference, typically require either per-scene or per-frame optimization, preventing them from generalizing to unseen scenes. Recent attempts towards generalizable 3D Gaussian Splitting are basically built upon feed-forward regression of Gaussian parameters [4, 7, 8, 11, 35, 45, 54, 58, 65, 90]. In particular, GPS-Gaussian [90] achieves generalizable novel view synthesis of unseen humans by jointly learning an iterative stereo-matching based depth estimation along with a Gaussian parameter regression, while GHG [35] regresses the 3D Gaussian parameters on the 2D UV space of a human template. However, these methods are usually less effective in handling sparse views with limited overlappings, from which depth can not be effectively estimated. + +# 3. Method + +Figure 2 presents the overview of our method. As shown, given sparse views of a subject, our goal is to estimate prior points that well represent the human body geometry, and then regress 3D Gaussians in a feed-forward manner to gain generalizability and eliminate the need for per-subject optimization. Specifically, our method is comprised of two components, i.e., image-aligned human points prediction and coarse-to-fine pixel-wise Gaussian regression, with the former for prior points estimation and the latter for Gaussian regression. Below we describe our method in detail. + +# 3.1. Image-aligned Human Points Prediction + +As shown in Figures 1 and 5, the SMPL model fitted from sparse views is typically unreliable due to limited overlappings. To get reliable yet dense prior points for Gaussian + +regression, we develop image-aligned human points prediction. Considering that SMPL model contains only sparse points, we employ the Snowflake Point Deconvolution (SPD) network [74, 75] that is suitable for refining and densifying the estimated SMPL points $\mathbf{P}$ due to the ability to learn local geometric characteristics. Akin to [74, 75], we employ two SPD steps. To enhance its effectiveness and robustness, we integrate it with both pixel-level and voxel-level features to get the output human points by: + +$$ +\mathbf {P} ^ {o} = \mathcal {F} _ {S P D} (\mathbf {P}, f _ {p}, f _ {v}), \tag {1} +$$ + +where $\mathbf{P}^o$ denotes the output points. $f_{p}$ and $f_{v}$ represent the utilized pixel-level and voxel-level features, respectively. + +Pixel-level features. To obtain projection-aware encoding that captures fine-grained local human details, while promoting the learning of spatial relationships between points and also the semantic information, we choose to adopt pixel-level features. To get the features, we first feed source multi-view images $\{I_m|m = 1,2,\dots,M\}$ into a U-Net based feature extractor $\mathcal{F}_{img}$ to obtain the corresponding feature maps $f_{m} = \mathcal{F}_{img}(I_{m})$ . Next, we conduct feature projection for these features, which consists of point projection and multiview feature aggregation. Specifically, we first project the SMPL points $\mathbf{P}$ onto the multi-view feature maps to fetch points' feature embeddings $z_{m} = \Pi (f_{m},\mathbf{P})$ , where $\Pi$ denotes projection. We then employ a visibility-aware aggregation strategy [35, 66, 89] to obtain pixel-level features $f_{p}$ by: + +$$ +f _ {p} = \sum_ {m = 1} ^ {M} w _ {m} \cdot z _ {m}, \tag {2} +$$ + +where $w_{m}$ denotes normalized visibility. + +Voxel-level features. While pixel-level features provide projection-aware local details for human subject, they fail to represent accurate human geometry due to the lack of 3D geometric information. Therefore, we propose to adopt voxel-level features to complement the limitation of pixel-level features. We first feed the SMPL depth under the $m$ -th view, denoted as $D_{m}$ , and the related image $I_{m}$ into a U-Net based depth refiner network $\mathcal{F}_d$ to obtain the refined depth map $\hat{D}_{m}$ and corresponding depth features $H_{m}$ : + +$$ +\left(\hat {D} _ {m}, H _ {m}\right) = \mathcal {F} _ {d} \left(D _ {m}, I _ {m}\right). \tag {3} +$$ + +Considering that directly unprojecting depth maps to 3D points is often too noisy to get reliable geometric information. We propose to voxelize them for producing a coarser but cleaner voxel feature volume that provides spatially aligned information. Specifically, we unproject the depth maps together with the corresponding features to 3D space, and then aggregate them to yield 3D points and per-point features. Next, we employ a sparse 3D convolution network [19, 42] to fuse nearby features. The final voxel-level features $f_{v}$ are obtained via tri-linear interpolation as follows: + +$$ +f _ {v} = \mathbf {T} (\mathbf {V}, \mathbf {P}), \tag {4} +$$ + +where $\mathbf{T}$ denotes tri-linear interpolation. $\mathbf{V}$ is the feature volume generated by the sparse convolution network. By integrating both pixel-level and voxel-level features, we can obtain image-aligned prior points that capture both fine-grained local 2D details and 3D-aware geometric information, which benefits generating high-fidelity human renderings, as demonstrated in Figure 6. + +3D Gaussian regression. In the absence of available 3D information for supervision, we instead regress a set of coarse Gaussians. These can be rendered into images using differentiable rasterization, thereby providing effective supervision for SPD network. Each Gaussian point in 3D space is defined by attributes $\{\mu, \mathbf{R}, \mathbf{S}, \alpha, \mathbf{c}\}$ , representing position, rotation, scaling, opacity, and color, respectively. We utilize the prior points $\mathbf{P}^o$ as the positions of the 3D Gaussians, and then regress the remaining four properties based on both point features $\mathbf{q}$ from the last layer of SPD network and the pixel-level image features $f_p^o$ of prior points $\mathbf{P}^o$ : + +$$ +\mathcal {G} = \mathcal {F} _ {g s} (\mathbf {q}, f _ {p} ^ {o}), \tag {5} +$$ + +where $\mathcal{G}$ represents the estimated Gaussian properties. Note, although our utilized 3D prior points are significantly denser compared to the SMPL vertices, they are still insufficient to regress fine-grained Gaussians that allow for high-fidelity novel view synthesis, as demonstrated in Figure 6. However, the coarse Gaussians offer a rough yet image-aligned representation of geometric information, which is a basis of our subsequent coarse-to-fine pixel-wise Gaussian regression. + +# 3.2. Coarse-to-fine Pixel-wise Gaussian Regression + +As described above, the predicted coarse Gaussians are insufficient for rendering high-fidelity novel views. To render high-fidelity images with fine-grained details, existing methods usually regress pixel-wise Gaussians based on depth information [90]. However, these methods basically fail to deal with sparse views that do not allow reliable depth estimation. Unlike previous methods, we find that our coarse Gaussians derived from prior points can help produce robust depth maps, which inspires us to develop an effective coarse-to-fine pixel-wise Gaussian regression. + +With the coarse Gaussians derived from the prior points, we first rasterize them to generate per-view depth maps, which are then similarly refined via Eq. (3) to produce image-aligned depth maps. Then, we unproject these depth maps into 3D space to obtain pixel-wise points $\mathbf{P}^{\prime}$ that capture high-frequency details and more accurate human geometry. To further enhance the robustness of these points, we follow previous methods [56, 57, 64] to utilize the prior points and the corresponding point features $\mathbf{q}$ to generate a latent feature volume $\mathbf{V}^{\prime}$ via sparse convolution network, and then interpolate the voxel-level features $f_{v}^{\prime}$ for pixel-wise points: + +$$ +f _ {v} ^ {\prime} = \mathbf {T} \left(\mathbf {V} ^ {\prime}, \mathbf {P} ^ {\prime}\right), \tag {6} +$$ + +where $\mathbf{T}$ denotes tri-linear interpolation and $\mathbf{V}^{\prime}$ represents the feature volume generated by sparse convolution network. This interpolated feature is then fed into a tiny MLP to predict offset $\delta$ of each point: + +$$ +\delta = \mathcal {F} _ {\delta} \left(f _ {v} ^ {\prime}\right). \tag {7} +$$ + +The final points $\mathbf{P}^g$ are computed as $\mathbf{P}^g = \mathbf{P}' + \delta$ . Once the final points are obtained, we employ additional MLPs to predict pixel-wise 3D Gaussians: + +$$ +\mathcal {G} ^ {\prime} = \mathcal {F} _ {g s} ^ {\prime} \left(\hat {f} _ {p} ^ {g}, f _ {p} ^ {g}\right), \tag {8} +$$ + +where $\hat{f}_p^g$ and $f_{p}^{g}$ represent the pixel-level depth and image features of final points $\mathbf{P}^g$ , respectively. + +# 3.3. Training Details + +To stabilize the training while obtaining better performance, we train our method in two stages. We first train the image-aligned human points prediction module to obtain stable coarse Gaussians. Then, we freeze this module and proceed to train the coarse-to-fine pixel-wise Gaussian regression. + +Loss function for stage 1. We follow [30, 90] to use L1 loss and SSIM loss [70] respectively indicated by $\mathcal{L}_{mae}$ and $\mathcal{L}_{SSIM}$ , to measure the difference between the rendered output and the ground truth. Besides, we apply a mask loss [22] to provide supervision for geometry learning: + +$$ +\mathcal {L} _ {m} = \left| \left| \mathbf {M} _ {g t} - \mathbf {M} \right| \right| _ {2}, \tag {9} +$$ + +![](images/8478abc195defb285495d8de5851c68f69310756704d926335e34e15cd8e32a7.jpg) +Figure 3. Qualitative comparison of in-domain generalization on THuman2.0 [87] dataset. + +![](images/3e0acddcac0aaa82f450e75f9b2565af5577168e68719a972cf888e8b70623b3.jpg) + +![](images/2ee9ec7780591dd3534f3bb95d950562177d518ddd9cd4ef45b743d571651f46.jpg) + +![](images/03c090570c4484e3b06c86ffa1213c46277e1d584ffcb59e3f1351a40ec57d2e.jpg) + +Table 1. Quantitative comparison of in-domain generalization with NeRF-based methods on THuman2.0 [87], RenderPeople [1], and ZJU-MoCap [57]. Note, except for SHERF [23] which is evaluated on single view input, all other methods are evaluated on 4-view inputs. + +
MethodTHuman2.0RenderPeopleZJU-MoCapParam.
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
SHERF [23]19.250.89420.112123.380.93790.076727.810.95820.052656.4M
NHP [33]25.740.93560.074826.010.93840.072630.960.96440.045716.2M
GP-NeRF [9]23.280.93250.079825.330.93260.079229.640.95630.05339.5M
TransHuman [55]27.360.94870.050526.370.94510.057931.410.96560.037021.9M
Ours28.940.96150.043327.000.95300.051931.890.96230.035312.2M
+ +where $\mathbf{M}$ denotes the predicted target-view mask. $\mathbf{M}_{gt}$ indicates ground-truth mask. To constrain the depth refiner to produce meaningful estimations, we enforce its output $\hat{D}_m$ to be close to the input depth $D_m$ in valid areas: + +$$ +\mathcal {L} _ {d} = \left| \left| D _ {m} [ \mathcal {M} ] - \hat {D} _ {m} [ \mathcal {M} ] \right| \right| _ {1}, \tag {10} +$$ + +where $\mathcal{M}$ means valid mask of depth map. Furthermore, inspired by [83], we similarly define a semantic alignment loss to constrain the DINOv2 [53] semantic features of the refined depth to be close to those of the input images: + +$$ +\mathcal {L} _ {s} = \left\| h _ {\text {i m g}} - h _ {\text {d e p t h}} \right\| _ {1}, \tag {11} +$$ + +where $h_{img}$ and $h_{depth}$ represent the semantic features of input images and refined depth. + +The overall loss function for stage 1 is formulated as: + +$$ +\mathcal {L} _ {1} = \lambda_ {1} \mathcal {L} _ {m a e} + \lambda_ {2} \mathcal {L} _ {S S I M} + \lambda_ {3} \mathcal {L} _ {m} + \lambda_ {4} \mathcal {L} _ {d} + \lambda_ {5} \mathcal {L} _ {s}, \tag {12} +$$ + +where we empirically set $\lambda_1 = 0.8$ , $\lambda_2 = 0.2$ , $\lambda_3 = 1.0$ , $\lambda_4 = 0.1$ and $\lambda_5 = 0.1$ . + +Loss function for stage 2. Since the coarse Gaussians are already approximately aligned with the images, we employ only the two photometric losses (i.e., $\mathcal{L}_{mae}$ and $\mathcal{L}_{SSIM}$ ) and the depth refinement loss $\mathcal{L}_d$ for training: + +$$ +\mathcal {L} _ {2} = \lambda_ {6} \mathcal {L} _ {\text {m a e}} + \lambda_ {7} \mathcal {L} _ {\text {S S I M}} + \lambda_ {8} \mathcal {L} _ {d}, \tag {13} +$$ + +where we set $\lambda_6 = 0.8$ , $\lambda_7 = 0.2$ and $\lambda_8 = 0.1$ . + +# 3.4. Implementation details + +We first train the depth refiner for $20k$ iterations and then jointly train all modules for $200k$ iterations using a minibatch size of 1 on an NVIDIA RTX 4090 GPU. The entire network is optimized using the AdamW optimizer with a learning rate of $1 \times 10^{-4}$ . We set the voxel size for sparse + +![](images/5f9047aade4c52914b46049ae1b803f0937e08132ddbd7e834a44c1945ffad5c.jpg) + +![](images/20152a2b466dbce3b325bd7079d654c1871f47dc58568ef9568cee96edd7cfdc.jpg) + +![](images/3a59f28c6516c72f3bdbfbd91f0e4e9a9f3875eada477b4988d41f7729c3e4d3.jpg) +Input + +![](images/b687f2c2eb295732e32dab94171b57e820aebbba6eb2666742f77e520e9da494.jpg) + +![](images/d83940e3478d58653e8f785cd5cf3f7960974a9349e059be2fa600ad98e52996.jpg) +NHP + +![](images/2d55dcd3c3cd48d2d0b03e031a7216a1eb4fb2eaa6edae2d7a291fd9649c2943.jpg) + +![](images/e010abb3df5b3e20da691e32051843438af3fb580a7856cb0bcc061e43676863.jpg) +GP-NeRF + +![](images/35bd7be674a26f415b94726a9774193baa50f62f25dc7375e5574146532bae96.jpg) + +![](images/fc4897c45f2331e5144de4f2ed6ba7d1186a5b9ada2df9e859e1579e7f234db4.jpg) +TransHuman + +![](images/48a79187035f8a29e271cf427f76757ddf8442e36dae9a163b0019f2039efc90.jpg) + +![](images/31f7f9ec66f0483de8d10547e756a0189f041b68c1c2d01983a92ec7c60212e8.jpg) +GPS-Gaussian + +![](images/8b7eaf9275c03fd8ac960c818e509d51e3e2326c78e1201af21886053e834b15.jpg) + +![](images/b29e48d457f28d912278d7bcdc443401cb1a8836533369f8405707b95c209e78.jpg) +Ours +Figure 4. Qualitative comparison of cross-domain generalization. The results of each method here are produced by their models trained on the THuman2.0 dataset [87]. + +![](images/e8215ee4ee72bde5954a00cdfce8b1006b1bcd39439f9dc16032059203cc5103.jpg) + +![](images/89d957d3c40755b21a22af790351cfa4d92a516df99ff93a47508ac6308736b7.jpg) +GT + +Table 2. Quantitative comparison of cross-domain generalization on RenderPeople [1], ZJU-MoCap [57], and the real-world dataset collected by[90]. Note, the results of each method here are produced by their models trained on the THuman2.0 dataset [87]. + +
MethodViewRenderPeopleZJU-MoCapReal-world data
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
NHP [33]423.830.92760.076529.460.94670.061423.510.91820.0947
GP-NeRF [9]423.130.92280.085226.780.93980.069320.090.89860.1130
TransHuman [55]424.850.93470.064029.570.94730.058324.600.92570.0744
GPS-Gaussian [90]625.110.93250.068229.060.95270.046421.550.92310.0847
Ours425.120.93800.066130.800.95960.043525.990.94520.0572
+ +convolution as $5mm \times 5mm \times 5mm$ , and produce output feature volumes with downsampling factors of $2\times, 4\times, 8\times$ , and $16\times$ . Our method takes about 20 hours to train on the THuman2.0 dataset and 180ms for inference on $512 \times 512$ images. + +# 4. Experiments + +# 4.1. Datasets and Metrics + +We evaluate our method on three benchmark human datasets including THuman2.0 [87], RenderPeople [1], and + +ZJU-MoCap [57]. For THuman2.0, we select 400 subjects for training while the remaining 125 subjects for testing. As for RenderPeople, we utilize the version processed by [23], which consists of 482 subjects. We use 340 subjects for training and the others for testing. For ZJU-MoCap, we select 7 subjects for training and the other 3 subjects for testing. We also employ one real-world dataset collected by [90]. Note, we adopt [2] to estimate SMPL model parameters using fixed four-view (i.e., front, back, left, and right) images for all datasets. Similar to [90], we employ PSNR, SSIM [70], and LPIPS [88] as metrics to quantitatively evaluate + +Table 3. Quantitative comparison of in-domain generalization with Gaussian Splatting based methods on THuman2.0 [87]. + +
MethodPSNR↑SSIM ↑LPIPS ↓Param.
3DGS [30]22.070.90680.0846/
GPS-Gaussian [90]27.790.96030.03975.1M
GHG [35]24.980.94180.052217.8M
Ours28.940.96150.043312.2M
+ +![](images/1a8ab63911ff6cc8377c7b513c96565843f5674354838474173ac87dc9293665.jpg) +Figure 5. Robustness to inaccurate SMPL. Our method, unlike previous methods, can produce visually similar high-fidelity renderings from either inaccurate fitted SMPL or the GT SMPL. + +the rendering quality on the entire image. + +# 4.2. Comparison with State-of-the-art Methods + +Baselines. We compare our method against four NeRF-based generalizable human rendering methods, including NHP [33], GP-NeRF [9], TransHuman [55] and SHERF [23], on THuman2.0 [87], RenderPeople [1], and ZJU-MoCap [57] datasets, and two generalizable human Gaussian Splatting methods including GPS-Gaussian [90] and GHG [35] only on THuman2.0 dataset due to following reasons: (i) GPS-Gaussian relies on RGB-D data rendered from 3D model for training while we only have available 3D models in THuman2.0. (ii) The training code of GHG [35] has not been released, we instead use their publicly-available pre-trained model trained on THuman2.0 dataset. For fair comparison, we retrain all baselines (except GHG) under the same training setting with 4 sparse input views, except GPS-Gaussian because it requires at least 6 views to train. + +In-domain generalization comparison. Tables 1 and 3 quantitatively compare our method with others on in-domain generalization. As shown, our approach clearly outperforms NeRF-based methods on THuman2.0, RenderPeople, ZJUMoCap datasets, and exhibits superiority over other Gaussian Splitting based methods on THuman2.0 dataset. Figure 3 further qualitatively demonstrates that our method is able + +Table 4. Ablation studies on THuman2.0 [87] dataset. Note, "baseline" here indicates we directly feed originally fitted SMPL points into the SPD network for coarse Gaussian regression. + +
MethodPSNR↑SSIM ↑LPIPS ↓
baseline23.280.93010.0975
w/o pixel & voxel-level features27.410.94670.0629
w/o pixel-level features28.450.96030.0460
w/o voxel-level features28.280.95850.0459
w/o coarse-to-fine Gaussian regress.28.000.95630.0602
w/o offset estimator28.560.96110.0439
full method28.940.96150.0433
+ +to generate high-fidelity human novel view renderings with well-preserved geometry and texture details. Note, although GHG also utilizes human template to serve as geometry prior like us, it does not consider the possible misalignment between template model and sparse-view images, and thus may induce results with inaccurate geometry. As for GPS-Gaussian, due to the difficulty to infer reliable depth from sparse views with limited overlapping, this method tends to produce incomplete human renderings. + +Cross-domain generalization comparison. To evaluate the cross-domain generalizability of our method, we train our method and the compared methods on THuman2.0 dataset and then perform comparison on three challenging datasets including RenderPeople [1], ZJU-MoCap [57], and a real-world dataset collected by [90], without any test-time optimization. As shown in Table 2, our method achieves the best performance on all the three metrics, manifesting its advantage in cross-domain generalization. In addition, by comparing the visual results in Figure 4, it is clear that our method is able to produce renderings with more accurate geometry and finer details. + +# 4.3. More Analysis + +Ablation studies. Here we conduct ablation studies to validate the effectiveness of our pixel/voxel-level features, coarse-to-fine pixel-wise Gaussian regression, and offset estimator. Table 4 presents the numerical results of ablation studies on THuman2.0 dataset, where we can see that each of the four components has a clear contribution to the success of our method. Figure 6 further presents visual demonstration. As shown, the adoption of the pixel- and voxel-level features benefits more accurate geometry estimation, while the coarse-to-fine pixel-wise Gaussian regression enables our method to capture finer details. The offset estimator helps obtain clearer rendering by avoiding incorrect Gaussian positioning. + +Robustness to inaccurate SMPL. We also validate the robustness of our method to inaccurate SMPL models in Figure 5, where the top row gives the results of different methods produced with the SMPL model fitted from sparse + +![](images/7b58bcb6bbe09c1bbb5d76528a208567f0e4ae689320422e11d10d036b555991.jpg) + +![](images/c51e1a3d6d77413a1842ccedfd91436dd4189cb31613dde8fafcf931755dcf84.jpg) +w/o pix. & vox. feat. + +![](images/6373cb6cefd6ca5c89b8a681204d915b9625e693e7233dca13835684c47fee6d.jpg) + +![](images/c43f4acb750658b883235b6b82e6b4f1c3219dc863735545d8bbed368a099852.jpg) +w/o pixel. feat. + +![](images/a151507646be30d65643323ce99f88b945cfbbe701adc03d13c4747591f8df9b.jpg) + +![](images/c9bacde67cadd98ac0b20e156a4830660ca28ce9f2cc01ff54c49bb62a794108.jpg) +w/o voxel. feat. +Figure 6. Ablation studies on THuman2.0 dataset. "w/o pix. & voxel. feat." refers to omitting both pixel-level and voxel-level features, while "w/o pixel. feat." and "w/o voxel. feat." correspond to ignoring pixel-level features and voxel-level features, respectively. "w/o coarse-to-fine" means we directly use coarse Gaussians for novel view synthesis, and "w/o offset" indicates removing the offset estimator. + +![](images/c9ac43d8475f4d23d12db82de83daeb143b0ce90e34db6f4064a5ca74d24484e.jpg) + +![](images/e70a089006662ce7c06503f032f30182a176e7d647d310d11f8d2310b3edf386.jpg) +w/o coarse-to-fine + +![](images/282bc1fdd2224d2530468ae4b561c8f22ed35cda9f777e93a2ad9948de6f76b8.jpg) + +![](images/b6c1bd148aab6f0f71d8f276c2e592f9612efa4bef423807f3b7d5755fa7be46.jpg) +w/o offset + +![](images/ba2758e5af6b65a59ef1b6f977d353a043518ffd69fd6a5a1ad4c547159de5c9.jpg) + +![](images/7b27dd8c8e6b24e70b206f20fb703c7f33882ee26a38981845246d4cd7cd3438.jpg) +full method + +![](images/c14c0890d8f059e98d739a88f9debd3d60fb0c0527947f052dd55654ecb7af4b.jpg) + +![](images/6aa51b669886262a54708f55525c07b75011a931512e6b716f0e20c5145cf6aa.jpg) +ground truth + +![](images/8962ff8d65a6f3e5c4b8715958720d5729680711c9c8e034c24cece0853e3fec.jpg) +Fitted SMPL pcd + +![](images/2fe4da831ef3863624286a852f746ddb5ff5da181824c186e9b0a2a8ab6311ba.jpg) +Our refined pcd +Figure 7. Comparison of our estimated prior points and GT SMPL points. Here we project estimated SMPL points, our predicted prior points as well as the GT SMPL points provided in dataset onto image for comparison. + +![](images/fd2afdc6417fe67a3b5dab57bfb53df18cb0fa2d80e3c5cd5241c01402eca8b8.jpg) +GT SMPL pcd + +views, while results on the bottom are produced from GT SMPL model provided in dataset. As shown, despite that the fitted SMPL model on the top is clearly inaccurate, our method still produces high-fidelity result close to the one produced with GT SMPL. In contrast, the use of GT SMPL leads to significant performance increase in results of other compared methods. Figure 7 further compares our estimated prior points and the GT SMPL points. As shown, our prior points are denser and capture accurate human geometry conformed with the GT SMPL points, effectively eliminating the misalignment between fitted SMPL points and the images. + +Limitations. As shown in Figure 8, our method may fail to handle loose clothing, from which it is very difficult to get a sufficient number of prior points. Besides, it may also struggle to recover high-frequency finer details for face and hands. Additionally, our method cannot animate or edit the reconstructed human models, and is designed to receive only fixed-view images as input. + +![](images/3eeb4f55a08db69367f9da0704f15b818e6ccb70c2c1fb2f3d96dee89b0ba3b6.jpg) +NHP +Figure 8. Failure case. Our method fails to handle loose clothing. + +![](images/23903fd670d120ebec9690ab22d34bc7ea68de5898fce48120b7d97b17b3bffc.jpg) +TransHuman + +![](images/bb8e1caaa22a711c4a66fbae021fb3dc79c0c3079eb0ea11b0aad48ef4700103.jpg) +Ours + +![](images/ae01ce2a5ddcafe353edd0c43f73a9b2a53fa3c5b6b98caf42530be986b24135.jpg) +GT + +# 5. Conclusion + +We have presented RoGSplat, a robust generalizable human Gaussian Splatting that enables high-fidelity novel views from very sparse views. The key idea lies in lifting SMPL vertices to dense image-aligned 3D points representing human body geometry, and then performing point-based Gaussian regression. To this end, we present image-aligned human points prediction that integrates both pixel-level and voxel-level features to adaptively compensate the misalignment between the SMPL model and the multi-view images. With the obtained image-aligned points, we then introduce a coarse-to-fine pixel-wise Gaussian regression strategy to enhance the ability to model finer details. Experiments show that our method outperforms state-of-the-arts in photorealistic novel view synthesis and cross-dataset generalization. + +Acknowledgement. This work was supported by the National Natural Science Foundation of China (62471499), the Guangdong Basic and Applied Basic Research Foundation (2023A1515030002). + +# References + +[1] Renderpeople. https://renderpeople.com/.5,6,7 +[2] Easymocap - make human motion capture easier. 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