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referencebased3dawareimageeditingwithtriplanes/full.md

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+# Reference-Based 3D-Aware Image Editing with Triplanes
+
+Bahri Batuhan Bilecen<sup>1</sup> Yigit Yalin<sup>1</sup> Ning Yu<sup>2</sup> Aysegul Dundar<sup>1</sup>  
+Bilkent University<sup>1</sup> Netflix Eyeline Studios<sup>2</sup>
+
+{batuhan.bilecen@, yigit.yalin@ug., adundar@cs.}bilkent.edu.tr, ning.yu@scanlinevfx.com
+
+Our unified, 3D-aware reference-based editing method on triplanes only requires a single source  $\sharp$  reference image as inputs, and can perform...
+
+![](images/a0a36b7e116959eb3e19a25b96ecb8c2742059ccb9d88c4a58da3c9a3c42288c.jpg)
+
+![](images/7442c3a84b2579d80144c196668f96fc766e2262142dc6e44247d972be7fee95.jpg)
+
+![](images/6168e27a3336f8aab04f9a8400ac4f29da5b67e6cd7bdf59e6685ed032215449.jpg)
+
+![](images/fd6989f040ee76daf32e44c6ca84b2ca01c719a26fed30f3798581ee69893e6b.jpg)  
+Figure 1. 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.  
+
+<table><tr><td rowspan="2"></td><td colspan="3">Eyeglasses</td><td colspan="3">Hair</td><td>Time</td></tr><tr><td>FID ↓</td><td>MSIM↑</td><td>ML2↓</td><td>FID ↓</td><td>MSIM↑</td><td>ML2↓</td><td>(s)</td></tr><tr><td>HiSD [40]</td><td>77.56</td><td>0.9471</td><td>0.0090</td><td>94.53</td><td>0.9743</td><td>0.0036</td><td>1.1</td></tr><tr><td>VecGAN++ [14]</td><td>71.47</td><td>0.7483</td><td>0.0630</td><td>80.47</td><td>0.9296</td><td>0.0090</td><td>2.2</td></tr><tr><td>Barbershop [85]</td><td>X</td><td>X</td><td>X</td><td>62.80</td><td>0.8756</td><td>0.0182</td><td>125</td></tr><tr><td>HairCLIPv2 [63]</td><td>X</td><td>X</td><td>X</td><td>85.75</td><td>0.8769</td><td>0.0173</td><td>180</td></tr><tr><td>StyleFusion [33]</td><td>X</td><td>X</td><td>X</td><td>84.67</td><td>0.8435</td><td>0.0198</td><td>2.4</td></tr><tr><td>InterfaceGAN [59]</td><td>88.13</td><td>0.9398</td><td>0.0104</td><td>80.93</td><td>0.7888</td><td>0.0387</td><td>0.6</td></tr><tr><td>StyleCLIP [53]</td><td>80.13</td><td>0.8421</td><td>0.0476</td><td>92.60</td><td>0.8716</td><td>0.0196</td><td>0.6</td></tr><tr><td>SFE [7]</td><td>106.1</td><td>0.9341</td><td>0.0099</td><td>89.49</td><td>0.9355</td><td>0.0050</td><td>5.1</td></tr><tr><td>E3DGE [36]</td><td>X</td><td>X</td><td>X</td><td>77.86</td><td>0.8083</td><td>0.0257</td><td>1.2</td></tr><tr><td>NoiseCLR [13]</td><td>107.1</td><td>0.7958</td><td>0.0440</td><td>X</td><td>X</td><td>X</td><td>17.2</td></tr><tr><td>LEDSIIS++[8]</td><td>115.2</td><td>0.9645</td><td>0.0047</td><td>96.56</td><td>0.9717</td><td>0.0025</td><td>25.9</td></tr><tr><td>InfEdit [69]</td><td>90.33</td><td>0.8338</td><td>0.1042</td><td>105.4</td><td>0.7425</td><td>0.0613</td><td>9.1</td></tr><tr><td>Paint by ex. [70]</td><td>74.18</td><td>0.8828</td><td>0.0252</td><td>82.38</td><td>0.9229</td><td>0.0155</td><td>9.6</td></tr><tr><td>Ours</td><td>66.68</td><td>0.9818</td><td>0.0021</td><td>64.59</td><td>0.9720</td><td>0.0029</td><td>6.0</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td colspan="4">FFHQ</td><td colspan="3">AFHQ</td></tr><tr><td></td><td>Eyes</td><td>Nose</td><td>Mouth</td><td>Overall</td><td>Eyes</td><td>Nose+Mouth</td><td>Overall</td></tr><tr><td>Original</td><td>40%</td><td>29%</td><td>34%</td><td>34%</td><td>40%</td><td>42%</td><td>41%</td></tr><tr><td>Ours (edited)</td><td>49%</td><td>59%</td><td>40%</td><td>49%</td><td>49%</td><td>43%</td><td>46%</td></tr><tr><td>Undecided</td><td>11%</td><td>13%</td><td>26%</td><td>16%</td><td>11%</td><td>15%</td><td>13%</td></tr></table>
+
+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.  
+
+<table><tr><td colspan="5">Eyeglasses</td><td colspan="3">Hair</td></tr><tr><td>V1</td><td>V2</td><td>V3</td><td>FID ↓</td><td>MSSIM ↑</td><td>ML2 ↓</td><td>FID ↓</td><td>MSSIM ↑</td></tr><tr><td>X</td><td>X</td><td>X</td><td>79.50</td><td>0.8451</td><td>0.0323</td><td>82.42</td><td>0.8177</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>74.46</td><td>0.9814</td><td>0.0022</td><td>77.30</td><td>0.9674</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>68.19</td><td>0.9822</td><td>0.0020</td><td>67.04</td><td>0.9691</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>66.68</td><td>0.9818</td><td>0.0021</td><td>64.59</td><td>0.9720</td></tr></table>
+
+![](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. Restyle: A residual-based stylegan encoder via iterative refinement. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6711–6720, 2021. 1  
+[4] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y. Ogras, and Linjie Luo. Panohed: Geometry-aware 3d fullhead synthesis in 360deg. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 20950-20959, 2023. 2, 8  
+[5] Qingyan Bai, Zifan Shi, Yinghao Xu, Hao Ouyang, Qiuyu Wang, Ceyuan Yang, Xuan Wang, Gordon Wetzstein, Yujun Shen, and Qifeng Chen. Real-time 3d-aware portrait editing from a single image. In European Conference on Computer Vision, 2024. 3  
+[6] Ananta R. Bhattarai, Matthias Nießner, and Artem Sevastopolsky. Triplanenet: An encoder for eg3d inversion. In IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 2024. 3, 4  
+[7] Denis Bobkov, Vadim Titov, Aibek Alanov, and Dmitry Vetrov. The devil is in the details: Stylefeatureeditor for detail-rich stylegan inversion and high quality image editing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9337-9346, 2024. 2, 5  
+[8] Manuel Brack, Felix Friedrich, Katharia Kornmeier, Linoy Tsaban, Patrick Schramowski, Kristian Kersting, and Apolinario Passos. Ledits++: Limitless image editing using text-to-image models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8861-8870, 2024. 2, 3, 5  
+[9] Eric R Chan, Marco Monteiro, Petr Kellnhofer, Jiajun Wu, and Gordon Wetzstein. pi-gan: Periodic implicit generative adversarial networks for 3d-aware image synthesis. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5799-5809, 2021. 1  
+[10] Eric R Chan, Connor Z Lin, Matthew A Chan, Koki Nagano, Boxiao Pan, Shalini De Mello, Orazio Gallo, Leonidas J Guibas, Jonathan Tremblay, Sameh Khamis, et al. Efficient geometry-aware 3d generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16123-16133, 2022. 1, 2, 3, 8  
+[11] Zhaoxi Chen, Jiaxiang Tang, Yuhao Dong, Ziang Cao, Fangzhou Hong, Yushi Lan, Tengfei Wang, Haozhe Xie, Tong Wu, Shunsuke Saito, Liang Pan, Dahua Lin, and Ziwei Liu. 3dtopia-xl: Scaling high-quality 3d asset generation via primitive diffusion. In CVPR, 2025. 8
+
+[12] Yunjey Choi, Youngjung Uh, Jaejun Yoo, and Jung-Woo Ha. Stargan v2: Diverse image synthesis for multiple domains. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2020. 2  
+[13] Yusuf Dalva and Pinar Yanardag. Noiseclar: A contrastive learning approach for unsupervised discovery of interpretable directions in diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 24209-24218, 2024. 2, 3, 5  
+[14] Yusuf Dalva, Said Fahri Altindis, and Aysegul Dundar. Vecgan: Image-to-image translation with interpretable latent directions. Proceedings of the European conference on computer vision (ECCV), 2022. 2, 5  
+[15] Yusuf Dalva, Hamza Pehlivan, Oyku Irmak Hatipoglu, Cansu Moran, and Aysegul Dundar. Image-to-image translation with disentangled latent vectors for face editing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023. 2  
+[16] Matt Deitke, Dustin Schwenk, Jordi Salvador, Luca Weihs, Oscar Michel, Eli VanderBilt, Ludwig Schmidt, Kiana Ehsani, Aniruddha Kembhavi, and Ali Farhadi. Objav- verse: A universe of annotated 3d objects. arXiv preprint arXiv:2212.08051, 2022. 3  
+[17] Matt Deitke, Ruoshi Liu, Matthew Wallingford, Huong Ngo, Oscar Michel, Aditya Kusupati, Alan Fan, Christian Laforte, Vikram Voleti, Samir Yitzhak Gadre, Eli VanderBilt, Aniruddha Kembhavi, Carl Vondrick, Georgia Gkioxari, Kiana Ehsani, Ludwig Schmidt, and Ali Farhadi. Objverse-xl: A universe of  $10\mathrm{m} + 3\mathrm{d}$  objects. arXiv preprint arXiv:2307.05663, 2023. 3  
+[18] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4690-4699, 2019. 4  
+[19] Zheng Ding, Cecilia Zheng, Zhihao Xia, Lars Jebe, Zhuowen Tu, and Xiuming Zhang. Diffusionrig: Learning personalized priors for facial appearance editing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023. 3  
+[20] Zijian Dong, Xu Chen, Jinlong Yang, Michael J Black, Otmar Hilliges, and Andreas Geiger. AG3D: Learning to Generate 3D Avatars from 2D Image Collections. In International Conference on Computer Vision (ICCV), 2023. 2, 8  
+[21] Aysegul Dundar, Karan Sapra, Guilin Liu, Andrew Tao, and Bryan Catanzaro. Panoptic-based image synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8070-8079, 2020. 2  
+[22] Ziya Erkoç, Can Gümeli, Chaoyang Wang, Matthias Nießner, Angela Dai, Peter Wonka, Hsin-Ying Lee, and Peiye Zhuang. Preditor3d: Fast and precise 3d shape editing. In CVPR, 2025. 3  
+[23] Anna Frihstuck, Nikolaos Sarafianos, Yuanlu Xu, Peter Wonka, and Tony Tung. VIVE3D: Viewpoint-independent video editing using 3D-aware GANs. In Proceedings of the IEEE/CVF International Conference on Computer Vision and Pattern Recognition (CVPR), 2023. 2
+
+[24] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. Advances in neural information processing systems, 27, 2014. 1  
+[25] Jiatao Gu, Lingjie Liu, Peng Wang, and Christian Theobalt. Stylererf: A style-based 3d-aware generator for high-resolution image synthesis. arXiv preprint arXiv:2110.08985, 2021. 1  
+[26] Yuming Gu, Hongyi Xu, You Xie, Guoxian Song, Yichun Shi, Di Chang, Jing Yang, and Linjie Luo. Diffportrait3d: Controllable diffusion for zero-shot portrait view synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10456-10465, 2024. 3  
+[27] Erik Härkönen, Aaron Hertzmann, Jaakko Lehtinen, and Sylvain Paris. Ganspace: Discovering interpretable gan controls. Advances in Neural Information Processing Systems, 33, 2020. 2  
+[28] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems, 30, 2017. 4  
+[29] Yicong Hong, Kai Zhang, Jiumiang Gu, Sai Bi, Yang Zhou, Difan Liu, Feng Liu, Kalyan Sunkavalli, Trung Bui, and Hao Tan. LRM: Large reconstruction model for single image to 3d. In The Twelfth International Conference on Learning Representations, 2024. 2, 8  
+[30] Xianxu Hou, Xiaokang Zhang, Hanbang Liang, Linlin Shen, Zhihui Lai, and Jun Wan. Guided style: Attribute knowledge guided style manipulation for semantic face editing. Neural Networks, 145:209-220, 2022. 2  
+[31] Xun Huang, Ming-Yu Liu, Serge Belongie, and Jan Kautz. Multimodal unsupervised image-to-image translation. ECCV, 2018. 2  
+[32] Heewoo Jun and Alex Nichol. Shap-e: Generating conditional 3d implicit functions, 2023. 8  
+[33] Omer Kafri, Or Patashnik, Yuval Alaluf, and Daniel Cohen-Or. Stylefusion: A generative model for disentangling spatial segments, 2021. 2, 5  
+[34] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4401-4410, 2019. 1  
+[35] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8110-8119, 2020. 1, 2  
+[36] Yushi Lan, Xuyi Meng, Shuai Yang, Chen Change Loy, and Bo Dai. Self-supervised geometry-aware encoder for style-based 3d gan inversion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 20940-20949, 2023. 2, 5  
+[37] Yushi Lan, Fangzhou Hong, Shuai Yang, Shangchen Zhou, Xuyi Meng, Bo Dai, Xingang Pan, and Chen Change Loy. Ln3diff: Scalable latent neural fields diffusion for speedy 3d generation. In ECCV, 2024. 2, 8
+
+[38] Yushi Lan, Shangchen Zhou, Zhaoyang Lyu, Fangzhou Hong, Shuai Yang, Bo Dai, Xingang Pan, and Chen Change Loy. Gaussiananything: Interactive point cloud latent diffusion for 3d generation. In ICLR, 2025. 8  
+[39] Biwen Lei, Kai Yu, Mengyang Feng, Miaomiao Cui, and Xuansong Xie. Diffusiongan3d: Boosting text-guided 3d generation and domain adaption by combining 3d gans and diffusion priors. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 2, 3  
+[40] Xinyang Li, Shengchuan Zhang, Jie Hu, Liujuan Cao, Xiaopeng Hong, Xudong Mao, Feiyue Huang, Yongjian Wu, and Rongrong Ji. Image-to-image translation via hierarchical style disentanglement. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8639-8648, 2021. 2, 5  
+[41] Guilin Liu, Aysegul Dundar, Kevin J Shih, Ting-Chun Wang, Fitsum A Reda, Karan Sapra, Zhiding Yu, Xiaodong Yang, Andrew Tao, and Bryan Catanzaro. Partial convolution for padding, inpainting, and image synthesis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. 2  
+[42] Liyuan Liu, Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and Jiawei Han. On the variance of the adaptive learning rate and beyond. In Proceedings of the Eighth International Conference on Learning Representations (ICLR 2020), 2020. 4  
+[43] Ruoshi Liu, Rundi Wu, Basile Van Hoorick, Pavel Tokmakov, Sergey Zakharov, and Carl Vondrick. Zero-1-to-3: Zero-shot one image to 3d object. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 9298–9309, 2023. 3  
+[44] Yuan Liu, Cheng Lin, Zijiao Zeng, Xiaoxiao Long, Lingjie Liu, Taku Komura, and Wenping Wang. Syncdreamer: Generating multiview-consistent images from a single-view image. In The Twelfth International Conference on Learning Representations, 2024. 3  
+[45] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaou Tang. Deep learning face attributes in the wild. In Proceedings of the IEEE international conference on computer vision, pages 3730-3738, 2015. 2, 4  
+[46] Ziwei Liu, Ping Luo, Shi Qiu, Xiaogang Wang, and Xiaou Tang. Deepfashion: Powering robust clothes recognition and retrieval with rich annotations. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016. 8  
+[47] Yueming Lyu, Jing Dong, Bo Peng, Wei Wang, and Tieniu Tan. Sogan: 3d-aware shadow and occlusion robust gan for makeup transfer. In Proceedings of the 29th ACM International conference on multimedia, pages 3601-3609, 2021. 2  
+[48] Yueming Lyu, Peibin Chen, Jingna Sun, Bo Peng, Xu Wang, and Jing Dong. Dran: detailed region-adaptive normalization for conditional image synthesis. IEEE Transactions on Multimedia, 2023. 2  
+[49] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021. 1
+
+[50] Chong Mou, Xintao Wang, Liangbin Xie, Yanze Wu, Jian Zhang, Zhongang Qi, Ying Shan, and Xiaohu Qie. T2i-adapter: Learning adapters to dig out more controllable ability for text-to-image diffusion models. arXiv preprint arXiv:2302.08453, 2023. 3  
+[51] Roy Or-El, Xuan Luo, Mengyi Shan, Eli Shechtman, Jeong Joon Park, and Ira Kemelmacher-Shlizerman. Stylesdf: High-resolution 3d-consistent image and geometry generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13503–13513, 2022. 1  
+[52] Karran Pandey, Paul Guerrero, Metheus Gadelha, Yannick Hold-Geoffroy, Karan Singh, and Niloy J. Mitra. Diffusion handles: Enabling 3d edits for diffusion models by lifting activations to 3d. CVPR, 2024. 3  
+[53] Or Patashnik, Zongze Wu, Eli Shechtman, Daniel Cohen-Or, and Dani Lischinski. Styleclip: Text-driven manipulation of stylegan imagery. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2085–2094, 2021. 2, 5  
+[54] Hamza Pehlivan, Yusuf Dalva, and Aysegul Dundar. Styleres: Transforming the residuals for real image editing with stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1828-1837, 2023. 2  
+[55] Ben Poole, Ajay Jain, Jonathan T. Barron, and Ben Mildenhall. Dreamfusion: Text-to-3d using 2d diffusion. In The Eleventh International Conference on Learning Representations, 2023. 8  
+[56] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel Cohen-Or. Encoding in style: a stylegan encoder for image-to-image translation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2287–2296, 2021. 2  
+[57] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10684-10695, 2022. 3  
+[58] Wei Shen and Rujie Liu. Learning residual images for face attribute manipulation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4030-4038, 2017. 2  
+[59] Yujun Shen, Jinjin Gu, Xiaou Tang, and Bolei Zhou. Interpreting the latent space of gans for semantic face editing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9243-9252, 2020. 2, 3, 5  
+[60] Kunpeng Song, Ligong Han, Bingchen Liu, Dimitris Metaxas, and Ahmed Elgammal. Diffusion guided domain adaptation of image generators. arXiv preprint https://arxiv.org/abs/2212.04473, 2022. 2, 3, 8  
+[61] Yizhi Song, Zhifei Zhang, Zhe Lin, Scott Cohen, Brian Price, Jianming Zhang, Soo Ye Kim, and Daniel Aliaga. Object-stitch: Object compositing with diffusion model. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 18310-18319, 2023. 3
+
+[62] Omer Tov, Yuval Alaluf, Yotam Nitzan, Or Patashnik, and Daniel Cohen-Or. Designing an encoder for stylegan image manipulation. ACM Transactions on Graphics (TOG), 40(4): 1-14, 2021. 2  
+[63] Tianyi Wei, Dongdong Chen, Wenbo Zhou, Jing Liao, Weiming Zhang, Gang Hua, and Nenghai Yu. Hairclipv2: Unifying hair editing via proxy feature blending. Proceedings of the IEEE/CVF International Conference on Computer Vision, 2023. 2, 5  
+[64] Zongze Wu, Dani Lischinski, and Eli Shechtman. Stylespace analysis: Disentangled controls for stylegan image generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12863-12872, 2021. 2  
+[65] Jianfeng Xiang, Zelong Lv, Sicheng Xu, Yu Deng, Ruicheng Wang, Bowen Zhang, Dong Chen, Xin Tong, and Jiaolong Yang. Structured 3d latents for scalable and versatile 3d generation. arXiv preprint arXiv:2412.01506, 2024. 8  
+[66] Taihong Xiao, Jiapeng Hong, and Jinwen Ma. Elegant: Exchanging latent encodings with gan for transferring multiple face attributes. In Proceedings of the European conference on computer vision (ECCV), pages 168-184, 2018. 2  
+[67] Jiaxin Xie, Hao Ouyang, Jingtan Piao, Chenyang Lei, and Qifeng Chen. High-fidelity 3d gan inversion by pseudomulti-view optimization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 321-331, 2023. 2  
+[68] Jiale Xu, Weihao Cheng, Yiming Gao, Xintao Wang, Shenghua Gao, and Ying Shan. Instantmesh: Efficient 3d mesh generation from a single image with sparse-view large reconstruction models. arXiv preprint arXiv:2404.07191, 2024. 2, 8  
+[69] Sihan Xu, Yidong Huang, Jiayi Pan, Ziqiao Ma, and Joyce Chai. Inversion-free image editing with natural language. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 2, 3, 5  
+[70] Binxin Yang, Shuyang Gu, Bo Zhang, Ting Zhang, Xuejin Chen, Xiaoyan Sun, Dong Chen, and Fang Wen. Paint by example: Exemplar-based image editing with diffusion models. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023. 2, 3, 5  
+[71] Guoxing Yang, Nanyi Fei, Mingyu Ding, Guangzhen Liu, Zhiwu Lu, and Tao Xiang. L2m-gan: Learning to manipulate latent space semantics for facial attribute editing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2951-2960, 2021. 2  
+[72] Yunhan Yang, Yukun Huang, Xiaoyang Wu, Yuan-Chen Guo, Song-Hai Zhang, Hengshuang Zhao, Tong He, and Xihui Liu. Dreamcomposer: Controllable 3d object generation via multi-view conditions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8111-8120, 2024. 3  
+[73] Hu Ye, Jun Zhang, Sibo Liu, Xiao Han, and Wei Yang. Ip-adapter: Text compatible image prompt adapter for text-to-image diffusion models. In arXiv preprint arxiv:2308.06721, 2023. 3  
+[74] Ahmet Burak Yildirim, Hamza Pehlivan, Bahri Batuhan Bilecen, and Aysegul Dundar. Diverse inpainting and editing
+
+with gan inversion. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 23120-23130, 2023. 2  
+[75] Fei Yin, Yong Zhang, Xuan Wang, Tengfei Wang, Xiaoyu Li, Yuan Gong, Yanbo Fan, Xiaodong Cun, Ying Shan, Cengiz Oztireli, et al. 3d gan inversion with facial symmetry prior. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 342-351, 2023. 2  
+[76] Ziyang Yuan, Yiming Zhu, Yu Li, Hongyu Liu, and Chun Yuan. Make encoder great again in 3d gan inversion through geometry and occlusion-aware encoding. arXiv preprint arXiv:2303.12326, 2023. 2, 3, 4  
+[77] Gang Zhang, Meina Kan, Shiguang Shan, and Xilin Chen. Generative adversarial network with spatial attention for face attribute editing. In Proceedings of the European conference on computer vision (ECCV), pages 417-432, 2018. 2  
+[78] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 3836-3847, 2023. 3  
+[79] Longwen Zhang, Ziyu Wang, Qixuan Zhang, Qiwei Qiu, Anqi Pang, Haoran Jiang, Wei Yang, Lan Xu, and Jingyi Yu. Clay: A controllable large-scale generative model for creating high-quality 3d assets. TOG, 2024. 8  
+[80] Michael Zhang, James Lucas, Jimmy Ba, and Geoffrey E Hinton. Lookahead optimizer: k steps forward, 1 step back. In Advances in Neural Information Processing Systems. Curran Associates, Inc., 2019. 4  
+[81] Qihang Zhang, Yinghao Xu, Chaoyang Wang, Hsin-Ying Lee, Gordon Wetzstein, Bolei Zhou, and Ceyuan Yang. 3ditscene: Editing any scene via language-guided disentangled gaussian splatting. In The Thirteenth International Conference on Learning Representations, 2025. 3  
+[82] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 4  
+[83] Jun-Yan Zhu, Richard Zhang, Deepak Pathak, Trevor Darrell, Alexei A Efros, Oliver Wang, and Eli Shechtman. Multimodal image-to-image translation by enforcing bi-cycle consistency. In Advances in neural information processing systems, pages 465-476, 2017. 2  
+[84] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. Sean: Image synthesis with semantic region-adaptive normalization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5104-5113, 2020. 2  
+[85] Peihao Zhu, Rameen Abdal, John Femiani, and Peter Wonka. Barbershop: Gan-based image compositing using segmentation masks. ACM Trans. Graph., 40(6), 2021. 2, 5

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+# Ref-GS: Directional Factorization for 2D Gaussian Splatting
+
+Youjia Zhang<sup>1</sup> Anpei Chen<sup>2,3,\dagger</sup> Yumin Wan<sup>1</sup> Zikai Song<sup>1</sup> Junqing Yu<sup>1</sup> Yawei Luo<sup>4</sup> Wei Yang<sup>1,\dagger</sup>
+
+<sup>1</sup> Huazhong University of Science and Technology
+
+<sup>3</sup> Westlake University
+
+$^{2}$  University of Tübingen, Tübingen AI Center
+
+4 Zhejiang University
+
+![](images/244fbec147dde44c5019d81880b97723a66855ead07064e2523dbee1f679317e.jpg)  
+GaussianShader
+
+![](images/db3b296543e36b8331d96f932b61e0d7b81f7be403afb6430796a2ef65732408.jpg)  
+3DGS-DR
+
+![](images/c8d891a8076c0fcc537f901607ea540ffd2bb830a6de2ecb846a07b1c1dc6e6e.jpg)  
+Ours
+
+![](images/64ae7eca188055fbc2e3091008826af609235dc7c7705c924d2992b58a09df52.jpg)  
+Mesh
+
+![](images/152ab2cd726bfa36c3cdf57fa3b2684782936d727f1a49f4755180eed0c1ff69.jpg)
+
+![](images/eed8c907eed483447175d65e90c12cbd067176eff59c1f4cafac704d0fbad151.jpg)
+
+![](images/a89a732458fab7d5190824d556d9f7bde29126224745c43591297886a7acebb3.jpg)  
+Rendering  
+Figure 1. 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
+
+<table><tr><td rowspan="2"></td><td colspan="7">Shiny Blender</td><td colspan="4">Shiny Real</td></tr><tr><td>Car</td><td>Ball</td><td>Helmet</td><td>Teapot</td><td>Toaster</td><td>Coffee</td><td>Avg.</td><td>Garden</td><td>Sedan</td><td>Toycar</td><td>Avg.</td></tr><tr><td colspan="12">PSNR†</td></tr><tr><td>Ref-NeRF [29]</td><td>30.41</td><td>29.14</td><td>29.92</td><td>45.19</td><td>25.29</td><td>33.99</td><td>32.32</td><td>22.01</td><td>25.21</td><td>23.65</td><td>23.62</td></tr><tr><td>NeRO [17]</td><td>25.53</td><td>30.26</td><td>29.20</td><td>38.70</td><td>26.46</td><td>28.89</td><td>29.84</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>ENVIDR [16]</td><td>28.46</td><td>38.89</td><td>32.73</td><td>41.59</td><td>26.11</td><td>29.48</td><td>32.88</td><td>21.47</td><td>24.61</td><td>22.92</td><td>23.00</td></tr><tr><td>3DGS [11]</td><td>27.24</td><td>27.69</td><td>28.32</td><td>45.68</td><td>20.99</td><td>32.32</td><td>30.37</td><td>21.75</td><td>26.03</td><td>23.78</td><td>23.85</td></tr><tr><td>3GiS [28]</td><td>27.52</td><td>26.82</td><td>28.08</td><td>46.05</td><td>22.71</td><td>32.64</td><td>30.64</td><td>21.96</td><td>26.59</td><td>23.75</td><td>24.10</td></tr><tr><td>3DGS-DR [40]</td><td>30.43</td><td>33.44</td><td>31.49</td><td>47.00</td><td>26.69</td><td>34.61</td><td>33.94</td><td>21.52</td><td>26.32</td><td>23.57</td><td>23.80</td></tr><tr><td>Ours</td><td>30.94</td><td>36.10</td><td>33.40</td><td>46.69</td><td>27.28</td><td>34.38</td><td>34.80</td><td>22.48</td><td>26.63</td><td>24.20</td><td>24.44</td></tr><tr><td colspan="12">SSIM†</td></tr><tr><td>Ref-NeRF [29]</td><td>0.949</td><td>0.956</td><td>0.955</td><td>0.995</td><td>0.910</td><td>0.972</td><td>0.956</td><td>0.584</td><td>0.720</td><td>0.633</td><td>0.646</td></tr><tr><td>NeRO [17]</td><td>0.949</td><td>0.974</td><td>0.971</td><td>0.995</td><td>0.929</td><td>0.956</td><td>0.962</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>ENVIDR [16]</td><td>0.961</td><td>0.991</td><td>0.980</td><td>0.996</td><td>0.939</td><td>0.949</td><td>0.969</td><td>0.561</td><td>0.707</td><td>0.549</td><td>0.606</td></tr><tr><td>3DGS [11]</td><td>0.930</td><td>0.937</td><td>0.951</td><td>0.996</td><td>0.895</td><td>0.971</td><td>0.947</td><td>0.571</td><td>0.771</td><td>0.637</td><td>0.660</td></tr><tr><td>GaussianShader [9]</td><td>0.930</td><td>0.954</td><td>0.955</td><td>0.995</td><td>0.900</td><td>0.969</td><td>0.951</td><td>0.576</td><td>0.728</td><td>0.637</td><td>0.647</td></tr><tr><td>3GiS [28]</td><td>0.930</td><td>0.933</td><td>0.951</td><td>0.996</td><td>0.909</td><td>0.972</td><td>0.948</td><td>0.557</td><td>0.789</td><td>0.626</td><td>0.657</td></tr><tr><td>3DGS-DR [40]</td><td>0.962</td><td>0.979</td><td>0.971</td><td>0.997</td><td>0.942</td><td>0.976</td><td>0.971</td><td>0.570</td><td>0.773</td><td>0.635</td><td>0.659</td></tr><tr><td>Ours</td><td>0.961</td><td>0.981</td><td>0.975</td><td>0.997</td><td>0.950</td><td>0.973</td><td>0.973</td><td>0.607</td><td>0.783</td><td>0.656</td><td>0.682</td></tr><tr><td colspan="12">LPIPS↓</td></tr><tr><td>Ref-NeRF [29]</td><td>0.051</td><td>0.307</td><td>0.087</td><td>0.013</td><td>0.118</td><td>0.082</td><td>0.110</td><td>0.251</td><td>0.234</td><td>0.231</td><td>0.239</td></tr><tr><td>NeRO [17]</td><td>0.074</td><td>0.094</td><td>0.050</td><td>0.012</td><td>0.089</td><td>0.110</td><td>0.072</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>ENVIDR [16]</td><td>0.049</td><td>0.067</td><td>0.051</td><td>0.011</td><td>0.116</td><td>0.139</td><td>0.072</td><td>0.263</td><td>0.387</td><td>0.345</td><td>0.332</td></tr><tr><td>3DGS [11]</td><td>0.047</td><td>0.161</td><td>0.079</td><td>0.007</td><td>0.126</td><td>0.078</td><td>0.083</td><td>0.248</td><td>0.206</td><td>0.237</td><td>0.230</td></tr><tr><td>GaussianShader [9]</td><td>0.045</td><td>0.148</td><td>0.088</td><td>0.012</td><td>0.111</td><td>0.085</td><td>0.082</td><td>0.274</td><td>0.259</td><td>0.239</td><td>0.257</td></tr><tr><td>3GiS [28]</td><td>0.045</td><td>0.166</td><td>0.073</td><td>0.006</td><td>0.098</td><td>0.077</td><td>0.077</td><td>0.252</td><td>0.190</td><td>0.251</td><td>0.231</td></tr><tr><td>3DGS-DR [40]</td><td>0.034</td><td>0.104</td><td>0.050</td><td>0.006</td><td>0.083</td><td>0.076</td><td>0.059</td><td>0.251</td><td>0.208</td><td>0.249</td><td>0.236</td></tr><tr><td>Ours</td><td>0.034</td><td>0.098</td><td>0.045</td><td>0.006</td><td>0.070</td><td>0.082</td><td>0.056</td><td>0.242</td><td>0.196</td><td>0.236</td><td>0.224</td></tr></table>
+
+![](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'.  
+
+<table><tr><td rowspan="2"></td><td colspan="3">NeRF Synthetic</td><td colspan="3">Glossy Synthetic</td><td>ShinyB</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>MAE°↓</td></tr><tr><td>Ref-NeRF [29]</td><td>31.29</td><td>0.947</td><td>0.058</td><td>27.50</td><td>0.927</td><td>0.100</td><td>18.38</td></tr><tr><td>ENVIDR [16]</td><td>28.13</td><td>0.953</td><td>0.068</td><td>29.58</td><td>0.952</td><td>0.057</td><td>4.61</td></tr><tr><td>3DGS [11]</td><td>33.30</td><td>0.969</td><td>0.030</td><td>26.50</td><td>0.917</td><td>0.092</td><td>—</td></tr><tr><td>GShader [9]</td><td>31.48</td><td>0.960</td><td>0.042</td><td>27.54</td><td>0.922</td><td>0.087</td><td>10.93</td></tr><tr><td>3iGS [28]</td><td>33.60</td><td>0.970</td><td>0.029</td><td>26.39</td><td>0.913</td><td>0.089</td><td>15.47</td></tr><tr><td>3DGS-DR [40]</td><td>31.02</td><td>0.962</td><td>0.047</td><td>29.78</td><td>0.954</td><td>0.057</td><td>2.43</td></tr><tr><td>GS-ROR [47]</td><td>—</td><td>—</td><td>—</td><td>29.70</td><td>0.956</td><td>—</td><td>7.23</td></tr><tr><td>Ours</td><td>33.20</td><td>0.966</td><td>0.036</td><td>30.59</td><td>0.957</td><td>0.058</td><td>2.21</td></tr></table>
+
+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.
+
+<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>MAE°↓</td></tr><tr><td>w/o Sph-Mip</td><td>29.95</td><td>0.943</td><td>0.090</td><td>3.61</td></tr><tr><td>w/o mipmap</td><td>30.12</td><td>0.945</td><td>0.091</td><td>5.12</td></tr><tr><td>w/o DS</td><td>31.79</td><td>0.957</td><td>0.062</td><td>2.57</td></tr><tr><td>w/o K⊗S</td><td>33.37</td><td>0.966</td><td>0.051</td><td>2.38</td></tr><tr><td>Ours</td><td>34.00</td><td>0.969</td><td>0.046</td><td>2.21</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td>Rendering Speed</td><td>Train Time</td></tr><tr><td>3DGS [11]</td><td>1.00×</td><td>1.00×</td></tr><tr><td>GaussianShader [9]</td><td>0.17×</td><td>11.05×</td></tr><tr><td>3iGS [28]</td><td>0.44×</td><td>2.07×</td></tr><tr><td>3DGS-DR [40]</td><td>0.93×</td><td>3.25×</td></tr><tr><td>Ours</td><td>0.37×</td><td>2.63×</td></tr></table>
+
+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. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5470-5479, 2022. 1, 2, 6  
+[3] Mojtaba Bemana, Karol Myszkowski, Jeppe Revall Frisvad, Hans-Peter Seidel, and Tobias Ritschel. Eikonal fields for refractive novel-view synthesis. In ACM SIGGRAPH 2022 Conference Proceedings, pages 1-9, 2022. 6, 7  
+[4] Anpei Chen, Minye Wu, Yingliang Zhang, Nianyi Li, Jie Lu, Shenghua Gao, and Jingyi Yu. Deep surface light fields. Proceedings of the ACM on Computer Graphics and Interactive Techniques, 1(1):1-17, 2018. 2  
+[5] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In European conference on computer vision, pages 333-350. Springer, 2022. 2, 3, 5  
+[6] Michael Deering, Stephanie Winner, Bic Schediwy, Chris Duffy, and Neil Hunt. The triangle processor and normal vector Shader: a vsli system for high performance graphics. Acm siggraph computer graphics, 22(4):21-30, 1988. 4  
+[7] Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5501-5510, 2022. 2  
+[8] Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields. In SIGGRAPH 2024 Conference Papers. Association for Computing Machinery, 2024. 1, 2, 3, 4, 7  
+[9] Yingwenqi Jiang, Jiadong Tu, Yuan Liu, Xifeng Gao, Xiaoxiao Long, Wenping Wang, and Yuexin Ma. Gaussian-shader: 3d gaussian splatting with shading functions for reflective surfaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5322-5332, 2024. 3, 4, 5, 7, 8  
+[10] Haian Jin, Isabella Liu, Peijia Xu, Xiaoshuai Zhang, Songfang Han, Sai Bi, Xiaowei Zhou, Zexiang Xu, and Hao Su. Tensoir: Tensorial inverse rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 165-174, 2023. 3
+
+[11] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkuhler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics, 42 (4), 2023. 2, 3, 4, 7, 8  
+[12] Diederik P Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 7  
+[13] Arno Knapitsch, Jaesik Park, Qian-Yi Zhou, and Vladlen Koltun. Tanks and temples: Benchmarking large-scale scene reconstruction. ACM Transactions on Graphics (ToG), 36 (4):1-13, 2017. 1, 6  
+[14] Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. Modular primitives for high-performance differentiable rendering. ACM Transactions on Graphics (ToG), 39(6):1-14, 2020. 7  
+[15] Jia Li, Lu Wang, Lei Zhang, and Beibei Wang. Tensosdf: Roughness-aware tensorial representation for robust geometry and material reconstruction. ACM Transactions on Graphics (TOG), 43(4):1-13, 2024. 3  
+[16] Ruofan Liang, Huiting Chen, Chunlin Li, Fan Chen, Selvakumar Panneer, and Nandita Vijaykumar. Envidr: Implicit differentiable renderer with neural environment lighting. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 79-89, 2023. 3, 4, 7  
+[17] Yuan Liu, Peng Wang, Cheng Lin, Xiaoxiao Long, Jiepeng Wang, Lingjie Liu, Taku Komura, and Wenping Wang. Nano: Neural geometry and brdf reconstruction of reflective objects from multiview images. 2023. 3, 4, 5, 6, 7  
+[18] Li Ma, Vasu Agrawal, Haithem Turki, Changil Kim, Chen Gao, Pedro Sander, Michael Zollhöfer, and Christian Richardt. Specnerf: Gaussian directional encoding for specular reflections. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21188-21198, 2024. 2  
+[19] Ricardo Martin-Brualla, Noha Radwan, Mehdi SM Sajjadi, Jonathan T Barron, Alexey Dosovitskiy, and Daniel Duckworth. Nerf in the wild: Neural radiance fields for unconstrained photo collections. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 7210–7219, 2021. 2  
+[20] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In European Conference on Computer Vision, pages 405-421. Springer, 2020. 2, 6, 7  
+[21] Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM transactions on graphics (TOG), 41(4):1-15, 2022. 2  
+[22] Jacob Munkberg, Jon Hasselgren, Tianchang Shen, Jun Gao, Wenzheng Chen, Alex Evans, Thomas Müller, and Sanja Fidler. Extracting Triangular 3D Models, Materials, and Lighting From Images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8280-8290, 2022. 5  
+[23] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. 2019. 7
+
+[24] Hanspeter Pfister, Matthias Zwicker, Jeroen Van Baar, and Markus Gross. Surfels: Surface elements as rendering primitives. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 335-342, 2000. 3  
+[25] Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5459-5469, 2022. 2  
+[26] Jia-Mu Sun, Tong Wu, Ling qI Yan, and Lin Gao. Nu-nerf: Neural reconstruction of nested transparent objects with uncontrolled capture environment. In ACM Transactions on Graphics(ACM SIGGRAPH Asia 2024), 2024. 3  
+[27] Matthew Tancik, Vincent Casser, Xinchen Yan, Sabeek Pradhan, Ben Mildenhall, Pratul P Srinivasan, Jonathan T Barron, and Henrik Kretzschmar. Block-nerf: Scalable large scene neural view synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8248–8258, 2022. 2  
+[28] Zhe Jun Tang and Tat-Jen Cham. 3igs: Factorised tensorial illumination for 3d gaussian splatting. In European Conference on Computer Vision, pages 143-159. Springer, 2024. 3, 5, 7, 8  
+[29] Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. Ref-nerf: Structured view-dependent appearance for neural radiance fields. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5481-5490. IEEE, 2022. 2, 4, 5, 6, 7, 8  
+[30] Bruce Walter, Stephen R Marschner, Hongsong Li, and Kenneth E Torrance. Microfacet models for refraction through rough surfaces. Rendering techniques, 2007:18th, 2007. 2  
+[31] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Advances in Neural Information Processing Systems, 34:27171-27183, 2021. 2  
+[32] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600-612, 2004. 7  
+[33] Zhiru Wang, Shiyun Xie, Chengwei Pan, and Guoping Wang. Specgaussian with latent features: A high-quality modeling of the view-dependent appearance for 3d gaussian splatting. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 6270-6278, 2024. 2  
+[34] Daniel N. Wood, Daniel I. Azuma, Ken Aldinger, Brian Curless, Tom Duchamp, David Salesin, and Werner Stuetzle. Surface light fields for 3d photography. In Computer Graphics and Interactive Techniques, 2000. 2  
+[35] Liwen Wu, Sai Bi, Zexiang Xu, Fujun Luan, Kai Zhang, Iliyan Georgiev, Kalyan Sunkavalli, and Ravi Ramamoorthi. Neural directional encoding for efficient and accurate view-dependent appearance modeling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21157-21166, 2024. 2
+
+[36] Tong Wu, Jia-Mu Sun, Yu-Kun Lai, Yuewen Ma, Leif Kobbelt, and Lin Gao. Deferreds: Decoupled and editable gaussian splatting with deferred shading. arXiv preprint arXiv:2404.09412, 2024. 3  
+[37] Ziyi Yang, Xinyu Gao, Yang-Tian Sun, Yihua Huang, Xiaoyang Lyu, Wen Zhou, Shaohui Jiao, Xiaojuan Qi, and Xiaogang Jin. Spec-gaussian: Anisotropic view-dependent appearance for 3d gaussian splatting. Advances in Neural Information Processing Systems, 37:61192-61216, 2024. 2  
+[38] Yao Yao, Jingyang Zhang, Jingbo Liu, Yihang Qu, Tian Fang, David McKinnon, Yanghai Tsin, and Long Quan. Neilf: Neural incident light field for physically-based material estimation. In European Conference on Computer Vision, pages 700-716. Springer, 2022. 2, 3  
+[39] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Advances in Neural Information Processing Systems, 34:4805-4815, 2021. 2  
+[40] Keyang Ye, Qiming Hou, and Kun Zhou. 3d gaussian splatting with deferred reflection. In ACM SIGGRAPH 2024 Conference Papers, pages 1-10, 2024. 2, 3, 5, 7, 8  
+[41] Wang Yifan, Felice Serena, Shihao Wu, Cengiz Öztireli, and Olga Sorkine-Hornung. Differentiable surface splatting for point-based geometry processing. ACM Transactions on Graphics (TOG), 38(6):1-14, 2019. 3  
+[42] Jingyang Zhang, Yao Yao, Shiwei Li, Jingbo Liu, Tian Fang, David McKinnon, Yanghai Tsin, and Long Quan. Neilf++: Inter-reflectable light fields for geometry and material estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3601-3610, 2023. 3  
+[43] Kai Zhang, Gernot Riegler, Noah Snavely, and Vladlen Koltun. Nerf++: Analyzing and improving neural radiance fields. arXiv:2010.07492, 2020. 2  
+[44] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 7  
+[45] Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul Debevec, William T Freeman, and Jonathan T Barron. Ner-factor: Neural factorization of shape and reflectance under an unknown illumination. ACM Transactions on Graphics (ToG), 40(6):1-18, 2021. 2  
+[46] Youjia Zhang, Teng Xu, Junqing Yu, Yuteng Ye, Yanqing Jing, Junle Wang, Jingyi Yu, and Wei Yang. Nemf: Inverse volume rendering with neural microflake field. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 22919-22929, 2023. 2  
+[47] Zuo-Liang Zhu, Beibei Wang, and Jian Yang. Gs-ror: 3d gaussian splatting for reflective object relighting via sdf priors. arXiv preprint arXiv:2406.18544, 2024. 3, 7  
+[48] Matthias Zwicker, Hanspeter Pfister, Jeroen Van Baar, and Markus Gross. Ewa volume splatting. In Proceedings Visualization, 2001. VIS'01., pages 29-538. IEEE, 2001. 3

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+# RefPose: Leveraging Reference Geometric Correspondences for Accurate 6D Pose Estimation of Unseen Objects
+
+Jaeguk Kim $^{1}$  Jaewoo Park $^{1}$  Keuntek Lee $^{1}$  Nam Ik Cho $^{1,2}$
+
+$^{1}$ Department of ECE, INMC, Seoul National University, Korea  $^{2}$ IPAI, Seoul National University, Korea
+
+{jaeguk, bjw0611, leekt000, nicho}@snu.ac.kr
+
+# Abstract
+
+Estimating the 6D pose of unseen objects from monocular RGB images remains a challenging problem, especially due to the lack of prior object-specific knowledge. 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.  
+
+<table><tr><td>Method</td><td>Refinement</td><td>YCB-V</td><td>LM-O</td><td>T-LESS</td><td>TUD-L</td><td>IC-BIN</td><td>ITODD</td><td>HB</td><td>Mean</td><td>Run-time</td></tr><tr><td>OSOP [41]</td><td>-</td><td>29.6</td><td>27.4</td><td>40.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZS6D [1]</td><td>-</td><td>32.4</td><td>29.8</td><td>21.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MegaPose [15]</td><td>-</td><td>28.1</td><td>22.9</td><td>17.7</td><td>25.8</td><td>15.2</td><td>10.8</td><td>25.1</td><td>20.8</td><td>15.5s</td></tr><tr><td>GenFlow [28]</td><td>-</td><td>27.7</td><td>25.0</td><td>21.5</td><td>30.0</td><td>16.8</td><td>15.4</td><td>28.3</td><td>23.</td><td>3.8s</td></tr><tr><td>GigaPose [30]</td><td>-</td><td>27.8</td><td>29.6</td><td>26.4</td><td>30.0</td><td>22.3</td><td>17.5</td><td>34.1</td><td>26.8</td><td>0.4s</td></tr><tr><td>FoundPose [32]</td><td>-</td><td>45.2</td><td>39.6</td><td>33.8</td><td>46.7</td><td>23.9</td><td>20.4</td><td>50.8</td><td>37.2</td><td>1.7s</td></tr><tr><td>RefPose (Ours)</td><td>-</td><td>50.0</td><td>35.8</td><td>38.1</td><td>48.5</td><td>23.1</td><td>21.5</td><td>49.8</td><td>38.1</td><td>3.1s</td></tr><tr><td>MegaPose [15]</td><td>MegaPose</td><td>60.1</td><td>49.9</td><td>47.7</td><td>65.3</td><td>36.7</td><td>31.5</td><td>65.4</td><td>50.9</td><td>17.0s</td></tr><tr><td>MegaPose [15]</td><td>MegaPose, MH</td><td>62.1</td><td>56.0</td><td>50.7</td><td>68.4</td><td>41.4</td><td>33.8</td><td>70.4</td><td>54.7</td><td>21.9s</td></tr><tr><td>MegaPose [15]</td><td>RefPose (Ours)</td><td>65.3</td><td>56.0</td><td>52.8</td><td>66.4</td><td>45.3</td><td>41.1</td><td>73.6</td><td>57.2</td><td>16.4s</td></tr><tr><td>GenFlow [28]</td><td>GenFlow, MH</td><td>63.3</td><td>56.3</td><td>52.3</td><td>68.4</td><td>45.3</td><td>39.5</td><td>73.9</td><td>57.0</td><td>20.8s</td></tr><tr><td>GigaPose [30]</td><td>MegaPose</td><td>63.2</td><td>55.7</td><td>54.1</td><td>58.0</td><td>45.0</td><td>37.6</td><td>69.3</td><td>54.7</td><td>2.3s</td></tr><tr><td>GigaPose [30]</td><td>GenFlow, MH</td><td>65.2</td><td>63.1</td><td>58.2</td><td>66.4</td><td>49.8</td><td>45.3</td><td>75.6</td><td>60.5</td><td>10.6s</td></tr><tr><td>FoundPose [32]</td><td>MegaPose, MH + Featuremetric</td><td>69.0</td><td>61.0</td><td>57.0</td><td>69.4</td><td>47.9</td><td>40.7</td><td>72.3</td><td>59.6</td><td>20.5s</td></tr><tr><td>RefPose (Ours)</td><td>MegaPose</td><td>63.7</td><td>56.3</td><td>51.1</td><td>65.8</td><td>43.7</td><td>41.4</td><td>71.8</td><td>56.3</td><td>4.6s</td></tr><tr><td>RefPose (Ours)</td><td>RefPose (Ours)</td><td>72.7</td><td>59.6</td><td>57.8</td><td>69.7</td><td>51.2</td><td>43.8</td><td>76.2</td><td>61.4</td><td>3.9s</td></tr></table>
+
+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.  
+
+<table><tr><td>N</td><td>YCB-V</td><td>LM-O</td><td>T-LESS</td><td>TUD-L</td><td>IC-BIN</td><td>ITODD</td><td>HB</td><td>Mean</td></tr><tr><td>64</td><td>45.2</td><td>29.8</td><td>36.5</td><td>43.7</td><td>20.1</td><td>18.8</td><td>43.5</td><td>33.9</td></tr><tr><td>128</td><td>50.0</td><td>35.8</td><td>38.1</td><td>48.5</td><td>23.1</td><td>21.5</td><td>49.8</td><td>38.1</td></tr><tr><td>256</td><td>48.8</td><td>37.2</td><td>39.5</td><td>45.8</td><td>24.3</td><td>23.1</td><td>49.8</td><td>38.3</td></tr></table>
+
+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.  
+
+<table><tr><td>k</td><td>YCB-V</td><td>LM-O</td><td>T-LESS</td><td>TUD-L</td><td>IC-BIN</td><td>ITODD</td><td>HB</td><td>Mean</td></tr><tr><td>1</td><td>42.6</td><td>31.0</td><td>28.8</td><td>40.1</td><td>18.8</td><td>18.1</td><td>40.8</td><td>31.5</td></tr><tr><td>2</td><td>46.8</td><td>37.2</td><td>34.0</td><td>43.1</td><td>19.8</td><td>18.8</td><td>46.5</td><td>35.2</td></tr><tr><td>4</td><td>50.0</td><td>35.8</td><td>38.1</td><td>48.5</td><td>23.1</td><td>21.5</td><td>49.8</td><td>38.1</td></tr><tr><td>8</td><td>50.0</td><td>29.8</td><td>36.4</td><td>44.5</td><td>21.7</td><td>19.9</td><td>51.0</td><td>36.2</td></tr></table>
+
+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.  
+
+<table><tr><td>Setting</td><td>YCB-V</td><td>LM-O</td><td>T-LESS</td><td>TUD-L</td><td>IC-BIN</td><td>ITODD</td><td>HB</td><td>Mean</td></tr><tr><td>w/o Flow features</td><td>46.8</td><td>34.2</td><td>33.2</td><td>47.1</td><td>22.3</td><td>20.9</td><td>45.8</td><td>35.8</td></tr><tr><td>w/o Medoid</td><td>49.6</td><td>29.6</td><td>36.8</td><td>45.9</td><td>21.3</td><td>18.8</td><td>50.2</td><td>36.0</td></tr><tr><td>Ours</td><td>50.0</td><td>35.8</td><td>38.1</td><td>48.5</td><td>23.1</td><td>21.5</td><td>49.8</td><td>38.1</td></tr></table>
+
+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.  
+
+<table><tr><td>Setting</td><td>YCB-V</td><td>LM-O</td><td>T-LESS</td><td>TUD-L</td><td>IC-BIN</td><td>ITODD</td><td>HB</td><td>Mean</td></tr><tr><td>w/o P.E.</td><td>69.3</td><td>57.1</td><td>57.0</td><td>68.4</td><td>48.3</td><td>39.5</td><td>73.9</td><td>59.1</td></tr><tr><td>w/o Convex.</td><td>70.0</td><td>56.8</td><td>58.2</td><td>68.4</td><td>47.9</td><td>43.1</td><td>75.6</td><td>60.0</td></tr><tr><td>w/o C.G. atm.</td><td>68.8</td><td>61.0</td><td>52.8</td><td>66.0</td><td>47.3</td><td>41.9</td><td>74.8</td><td>58.9</td></tr><tr><td>Ours</td><td>72.7</td><td>59.6</td><td>57.8</td><td>69.7</td><td>51.2</td><td>43.8</td><td>76.2</td><td>61.4</td></tr></table>
+
+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. Zs6d: Zero-shot 6d object pose estimation using vision transformers. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 463-469. IEEE, 2024.  
+[2] Benjamin Busam, Marco Esposito, Simon Che'Rose, Nassir Navab, and Benjamin Frisch. A stereo vision approach for cooperative robotic movement therapy. In Proceedings of the IEEE international conference on computer vision workshops, pages 127-135, 2015.  
+[3] Ming Cai and Ian Reid. Reconstruct locally, localize globally: A model free method for object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3153-3163, 2020.  
+[4] Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015.  
+[5] Xiaozhi Chen, Huimin Ma, Ji Wan, Bo Li, and Tian Xia. Multi-view 3d object detection network for autonomous driving. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 1907-1915, 2017.  
+[6] Xu Chen, Zijian Dong, Jie Song, Andreas Geiger, and Otmar Hilliges. Category level object pose estimation via neural analysis-by-synthesis. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXVI 16, pages 139-156. Springer, 2020.  
+[7] Yan Di, Fabian Manhardt, Gu Wang, Xiangyang Ji, Nassir Navab, and Federico Tombari. So-posed: Exploiting self-occlusion for direct 6d pose estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12396–12405, 2021.  
+[8] Alexey Dosovitskiy, Philipp Fischer, Eddy Ilg, Philip Hausser, Caner Hazirbas, Vladimir Golkov, Patrick Van Der Smagt, Daniel Cremers, and Thomas Brox. Flownet: Learning optical flow with convolutional networks. In Proceedings of the IEEE international conference on computer vision, pages 2758-2766, 2015.  
+[9] Laura Downs, Anthony Francis, Nate Koenig, Brandon Kinman, Ryan Hickman, Krista Reymann, Thomas B McHugh, and Vincent Vanhoucke. Google scanned objects: A high-quality dataset of 3d scanned household items. In 2022 International Conference on Robotics and Automation (ICRA), pages 2553-2560. IEEE, 2022.
+
+[10] Yang Hai, Rui Song, Jiaojiao Li, and Yinlin Hu. Shape-constraint recurrent flow for 6d object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4831-4840, 2023.  
+[11] Tomas Hodan, Daniel Barath, and Jiri Matas. Epos: Estimating 6d pose of objects with symmetries. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11703-11712, 2020.  
+[12] Tomas Hodan, Martin Sundermeyer, Yann Labbe, Van Nguyen Nguyen, Gu Wang, Eric Brachmann, Bertram Drost, Vincent Lepetit, Carsten Rother, and Jiri Matas. Bop challenge 2023 on detection segmentation and pose estimation of seen and unseen rigid objects. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5610-5619, 2024.  
+[13] Yinlin Hu, Pascal Fua, and Mathieu Salzmann. Perspective flow aggregation for data-limited 6d object pose estimation. In European Conference on Computer Vision, pages 89-106. Springer, 2022.  
+[14] Yann Labbe, Justin Carpentier, Mathieu Aubry, and Josef Sivic. Cosypose: Consistent multi-view multi-object 6d pose estimation. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XVII 16, pages 574-591. Springer, 2020.  
+[15] Yann Labbe, Lucas Manuelli, Arsalan Mousavian, Stephen Tyree, Stan Birchfield, Jonathan Tremblay, Justin Carpentier, Mathieu Aubry, Dieter Fox, and Josef Sivic. Megapose: 6d pose estimation of novel objects via render & compare. arXiv preprint arXiv:2212.06870, 2022.  
+[16] Vincent Lepetit, Francesc Moreno-Noguer, and Pascal Fua. Ep n p: An accurate o (n) solution to the p n p problem. International journal of computer vision, 81:155-166, 2009.  
+[17] Fu Li, Ivan Shugurov, Benjamin Busam, Minglong Li, Shaowu Yang, and Slobodan Ilic. Polarmesh: A star-convex 3d shape approximation for object pose estimation. IEEE Robotics and Automation Letters, 7(2):4416-4423, 2022.  
+[18] Yi Li, Gu Wang, Xiangyang Ji, Yu Xiang, and Dieter Fox. Deepim: Deep iterative matching for 6d pose estimation. In Proceedings of the European Conference on Computer Vision (ECCV), pages 683-698, 2018.  
+[19] Zhigang Li, Gu Wang, and Xiangyang Ji. Cdpn: Coordinates-based disentangled pose network for real-time rgb-based 6-dof object pose estimation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 7678-7687, 2019.  
+[20] Ruyi Lian and Haibin Ling. Checkerpose: Progressive dense keypoint localization for object pose estimation with graph neural network. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14022-14033, 2023.  
+[21] I Loshchilov. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.  
+[22] Ilya Loshchilov and Frank Hutter. Sgdr: Stochastic gradient descent with warm restarts. arXiv preprint arXiv:1608.03983, 2016.  
+[23] Fabian Manhardt, Wadim Kehl, and Adrien Gaidon. Roi10d: Monocular lifting of 2d detection to 6d pose and metric shape. In Proceedings of the IEEE/CVF Conference
+
+on Computer Vision and Pattern Recognition, pages 2069-2078, 2019.  
+[24] Fabian Manhardt, Gu Wang, Benjamin Busam, Manuel Nickel, Sven Meier, Luca Minciullo, Xiangyang Ji, and Nassir Navab. Cps++: Improving class-level 6d pose and shape estimation from monocular images with self-supervised learning. arXiv preprint arXiv:2003.05848, 2020.  
+[25] Eric Marchand, Hideaki Uchiyama, and Fabien Spindler. Pose estimation for augmented reality: a hands-on survey. IEEE transactions on visualization and computer graphics, 22(12):2633-2651, 2015.  
+[26] Nikolaus Mayer, Eddy Ilg, Philip Hausser, Philipp Fischer, Daniel Cremers, Alexey Dosovitskiy, and Thomas Brox. A large dataset to train convolutional networks for disparity, optical flow, and scene flow estimation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4040-4048, 2016.  
+[27] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021.  
+[28] Sungphill Moon, Hyeontae Son, Dongcheol Hur, and Sangwook Kim. Genflow: Generalizable recurrent flow for 6d pose refinement of novel objects. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10039-10049, 2024.  
+[29] Van Nguyen Nguyen, Thibault Groueix, Georgy Ponimatkin, Vincent Lepetit, and Tomas Hodan. Cnos: A strong baseline for cad-based novel object segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2134-2140, 2023.  
+[30] Van Nguyen Nguyen, Thibault Groueix, Mathieu Salzmann, and Vincent Lepetit. Gigapose: Fast and robust novel object pose estimation via one correspondence. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9903-9913, 2024.  
+[31] Maxime Oquab, Timothee Darcet, Theo Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, et al. Dinov2: Learning robust visual features without supervision. arXiv preprint arXiv:2304.07193, 2023.  
+[32] Evin Pinar Örnek, Yann Labbe, Bugra Tekin, Lingni Ma, Cem Keskin, Christian Forster, and Tomas Hodan. Found- pose: Unseen object pose estimation with foundation features. In European Conference on Computer Vision, pages 163-182. Springer, 2025.  
+[33] Jaewoo Park and Nam Ik Cho. Dprost: Dynamic projective spatial transformer network for 6d pose estimation. In European Conference on Computer Vision, pages 363-379. Springer, 2022.  
+[34] Jaewoo Park, Jaeguk Kim, and Nam Ik Cho. Leveraging positional encoding for robust multi-reference-based object 6d pose estimation. arXiv preprint arXiv:2401.16284, 2024.  
+[35] Kiru Park, Timothy Patten, and Markus Vincze. Pix2pose: Pixel-wise coordinate regression of objects for 6d pose estimation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 7668-7677, 2019.
+
+[36] Luis Pérez, Ínigo Rodríguez, Nuria Rodríguez, Rubén Usamentiaga, and Daniel F García. Robot guidance using machine vision techniques in industrial environments: A comparative review. Sensors, 16(3):335, 2016.  
+[37] Mahdi Rad and Vincent Lepetit. Bb8: A scalable, accurate, robust to partial occlusion method for predicting the 3d poses of challenging objects without using depth. In Proceedings of the IEEE international conference on computer vision, pages 3828-3836, 2017.  
+[38] Jason Rambach, Alain Pagani, Michael Schneider, Oleksandr Artemenko, and Didier Stricker. 6dof object tracking based on 3d scans for augmented reality remote live support. Computers, 7(1):6, 2018.  
+[39] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention-MICCAI 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, pages 234-241. Springer, 2015.  
+[40] Usha Ruby and Vamsidhar Yendapalli. Binary cross entropy with deep learning technique for image classification. Int. J. Adv. Trends Comput. Sci. Eng, 9(10), 2020.  
+[41] Ivan Shugurov, Fu Li, Benjamin Busam, and Slobodan Ilic. Osop: A multi-stage one shot object pose estimation framework. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6835-6844, 2022.  
+[42] Yongzhi Su, Mahdi Saleh, Torben Fetzer, Jason Rambach, Nassir Navab, Benjamin Busam, Didier Stricker, and Federico Tombari. Zebrapose: Coarse to fine surface encoding for 6 dof object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6738-6748, 2022.  
+[43] Zachary Teed and Jia Deng. Raft: Recurrent all-pairs field transforms for optical flow. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part II 16, pages 402-419. Springer, 2020.  
+[44] Bugra Tekin, Sudipta N Sinha, and Pascal Fua. Real-time seamless single shot 6d object pose prediction. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 292-301, 2018.  
+[45] Gu Wang, Fabian Manhardt, Federico Tombari, and Xi-angyang Ji. Gdr-net: Geometry-guided direct regression network for monocular 6d object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16611-16621, 2021.  
+[46] He Wang, Srinath Sridhar, Jingwei Huang, Julien Valentin, Shuran Song, and Leonidas J Guibas. Normalized object coordinate space for category-level 6d object pose and size estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2642-2651, 2019.  
+[47] Sergey Zakharov, Ivan Shugurov, and Slobodan Ilic. Dpod: 6d pose object detector and refiner. In Proceedings of the IEEE/CVF international conference on computer vision, pages 1941-1950, 2019.

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+# Relation3D: Enhancing Relation Modeling for Point Cloud Instance Segmentation
+
+Jiahao Lu  
+University of Science and Technology of China
+
+Jiacheng Deng*  
+University of Science and Technology of China
+
+# Abstract
+
+3D instance segmentation aims to predict a set of object instances in a scene, representing them as binary foreground masks with corresponding semantic labels. 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)
+
+<table><tr><td colspan="3">Point feature variation (Maft)</td><td colspan="2">1.8603 (Excessive)</td></tr><tr><td>Setting</td><td>Maft</td><td>Ours (Stage 1)</td><td>Ours (Stage 2)</td><td>Ours (Stage 3)</td></tr><tr><td>Lcont</td><td>1.057</td><td>0.7255</td><td>0.5841</td><td>0.5739</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">ScanNetV2 validation</td><td colspan="3">ScanNetV2 test</td></tr><tr><td>mAP</td><td>AP@50</td><td>AP@25</td><td>Box</td><td>AP@50</td><td>Box</td><td>AP@25</td><td>mAP</td></tr><tr><td>3D-SIS [14]</td><td>/</td><td>18.7</td><td>35.7</td><td>22.5</td><td>40.2</td><td>16.1</td><td>38.2</td><td>55.8</td></tr><tr><td>3D-MPA [16]</td><td>35.3</td><td>51.9</td><td>72.4</td><td>49.2</td><td>64.2</td><td>35.5</td><td>61.1</td><td>73.7</td></tr><tr><td>DyCo3D [49]</td><td>40.6</td><td>61.0</td><td>/</td><td>45.3</td><td>58.9</td><td>39.5</td><td>64.1</td><td>76.1</td></tr><tr><td>PointGroup [40]</td><td>34.8</td><td>56.9</td><td>71.3</td><td>48.9</td><td>61.5</td><td>40.7</td><td>63.6</td><td>77.8</td></tr><tr><td>MaskGroup [50]</td><td>42.0</td><td>63.3</td><td>74.0</td><td>/</td><td>/</td><td>43.4</td><td>66.4</td><td>79.2</td></tr><tr><td>OccuSeg [51]</td><td>44.2</td><td>60.7</td><td>/</td><td>/</td><td>/</td><td>48.6</td><td>67.2</td><td>74.2</td></tr><tr><td>HAIS [52]</td><td>43.5</td><td>64.4</td><td>75.6</td><td>53.1</td><td>64.3</td><td>45.7</td><td>69.9</td><td>80.3</td></tr><tr><td>SSTNet [17]</td><td>49.4</td><td>64.3</td><td>74</td><td>52.7</td><td>62.5</td><td>50.6</td><td>69.8</td><td>78.9</td></tr><tr><td>SoftGroup [18]</td><td>45.8</td><td>67.6</td><td>78.9</td><td>59.4</td><td>71.6</td><td>50.4</td><td>76.1</td><td>86.5</td></tr><tr><td>DKNet [53]</td><td>50.8</td><td>66.9</td><td>76.9</td><td>59.0</td><td>67.4</td><td>53.2</td><td>71.8</td><td>81.5</td></tr><tr><td>ISBNet [41]</td><td>54.5</td><td>73.1</td><td>82.5</td><td>62.0</td><td>78.1</td><td>55.9</td><td>75.7</td><td>83.5</td></tr><tr><td>Spherical Mask [42]</td><td>62.3</td><td>79.9</td><td>88.2</td><td>/</td><td>/</td><td>61.6</td><td>81.2</td><td>87.5</td></tr><tr><td>Mask3D [19]</td><td>55.2</td><td>73.7</td><td>82.9</td><td>56.6</td><td>71.0</td><td>56.6</td><td>78.0</td><td>87.0</td></tr><tr><td>QueryFormer [21]</td><td>56.5</td><td>74.2</td><td>83.3</td><td>61.7</td><td>73.4</td><td>58.3</td><td>78.7</td><td>87.4</td></tr><tr><td>SPFormer [20]</td><td>56.3</td><td>73.9</td><td>82.9</td><td>/</td><td>/</td><td>54.9</td><td>77.0</td><td>85.1</td></tr><tr><td>Maft [22]</td><td>58.4</td><td>75.9</td><td>84.5</td><td>63.9</td><td>73.5</td><td>57.8</td><td>77.4</td><td>/</td></tr><tr><td>Maft‡ [22]</td><td>59.9</td><td>76.5</td><td>/</td><td>/</td><td>/</td><td>59.6</td><td>78.6</td><td>86.0</td></tr><tr><td>Ours</td><td>62.5</td><td>80.2</td><td>87.0</td><td>66.7</td><td>75.3</td><td>62.2</td><td>81.6</td><td>90.1</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">ScanNet++ validation</td><td colspan="3">ScanNet++ test</td></tr><tr><td>mAP</td><td>AP@50</td><td>AP@25</td><td>mAP</td><td>AP@50</td><td>AP@25</td></tr><tr><td>PointGroup [40]</td><td>/</td><td>/</td><td>/</td><td>8.9</td><td>14.6</td><td>21.0</td></tr><tr><td>HAIS [52]</td><td>/</td><td>/</td><td>/</td><td>12.1</td><td>19.9</td><td>29.5</td></tr><tr><td>SoftGroup [18]</td><td>/</td><td>/</td><td>/</td><td>16.7</td><td>29.7</td><td>38.9</td></tr><tr><td>Maft [22]</td><td>23.1</td><td>32.6</td><td>39.7</td><td>20.9</td><td>31.3</td><td>40.4</td></tr><tr><td>Ours</td><td>28.2</td><td>39.3</td><td>46.1</td><td>24.2</td><td>35.5</td><td>44.0</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">ScanNet200 validation</td></tr><tr><td>mAP</td><td>AP@50</td><td>AP@25</td></tr><tr><td>SPFormer [20]</td><td>25.2</td><td>33.8</td><td>39.6</td></tr><tr><td>Mask3D [19]</td><td>27.4</td><td>37.0</td><td>42.3</td></tr><tr><td>QueryFormer [21]</td><td>28.1</td><td>37.1</td><td>43.4</td></tr><tr><td>Maft [22]</td><td>29.2</td><td>38.2</td><td>43.3</td></tr><tr><td>Ours</td><td>31.6</td><td>41.2</td><td>45.6</td></tr></table>
+
+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.  
+
+<table><tr><td>Method</td><td>AP@50</td><td>AP@25</td></tr><tr><td>PointGroup [40]</td><td>57.8</td><td>/</td></tr><tr><td>MaskGroup [50]</td><td>65.0</td><td>/</td></tr><tr><td>SoftGroup [18]</td><td>66.1</td><td>/</td></tr><tr><td>SSTNet [17]</td><td>59.3</td><td>/</td></tr><tr><td>SPFormer [20]</td><td>66.8</td><td>/</td></tr><tr><td>Mask3D [19]</td><td>68.4</td><td>75.2</td></tr><tr><td>QueryFormer [21]</td><td>69.9</td><td>/</td></tr><tr><td>Maft [22]</td><td>69.1</td><td>75.7</td></tr><tr><td>Spherical Mask [42]</td><td>72.3</td><td>/</td></tr><tr><td>Ours</td><td>72.5</td><td>78.5</td></tr></table>
+
+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.
+
+<table><tr><td></td><td>ASAM</td><td>CLSR</td><td>RSA</td><td>mAP</td><td>AP@50</td><td>AP@25</td></tr><tr><td>[A]</td><td>X</td><td>X</td><td>X</td><td>59.8</td><td>77.4</td><td>85.4</td></tr><tr><td>[B]</td><td>✓</td><td>X</td><td>X</td><td>60.1</td><td>77.9</td><td>85.6</td></tr><tr><td>[C]</td><td>X</td><td>✓</td><td>X</td><td>60.9</td><td>78.7</td><td>86.2</td></tr><tr><td>[D]</td><td>✓</td><td>✓</td><td>X</td><td>61.5</td><td>78.8</td><td>86.3</td></tr><tr><td>[E]</td><td>X</td><td>X</td><td>✓</td><td>61.0</td><td>78.5</td><td>86.0</td></tr><tr><td>[F]</td><td>✓</td><td>✓</td><td>✓</td><td>62.5</td><td>80.2</td><td>87.0</td></tr></table>
+
+# 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.  
+
+<table><tr><td>Setting</td><td>mAP</td><td>AP@50</td><td>AP@25</td></tr><tr><td>W/o contrastive loss</td><td>60.1</td><td>77.9</td><td>85.6</td></tr><tr><td>W contrastive loss</td><td>60.5</td><td>78.4</td><td>85.9</td></tr></table>
+
+Table 7. Effectiveness of contrastive loss to ASAM.  
+
+<table><tr><td>Setting</td><td>mAP</td><td>AP@50</td><td>AP@25</td></tr><tr><td>W max-pooling</td><td>62.2</td><td>79.9</td><td>86.7</td></tr><tr><td>W mean-pooling</td><td>62.3</td><td>79.7</td><td>86.7</td></tr><tr><td>W max-pooling &amp; mean-pooling</td><td>62.5</td><td>80.2</td><td>87.0</td></tr></table>
+
+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. Robotics and Computer-Integrated Manufacturing, 82:102541, 2023.  
+[2] Kyeong-Beom Park, Minseok Kim, Sung Ho Choi, and Jae Yeol Lee. Deep learning-based smart task assistance in wearable augmented reality. Robotics and ComputerIntegrated Manufacturing, 63:101887, 2020.  
+[3] Alessandro Manni, Damiano Oriti, Andrea Sanna, Francesco De Pace, and Federico Manuri. Snap2cad: 3d indoor environment reconstruction for ar/vr applications using a smartphone device. Computers & Graphics, 100:116-124, 2021.  
+[4] Guanjun Wu, Taoran Yi, Jiemin Fang, Lingxi Xie, Xiaopeng Zhang, Wei Wei, Wenyu Liu, Qi Tian, and Xinggang Wang. 4d gaussian splatting for real-time dynamic scene rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20310-20320, 2024.  
+[5] Ruijie Zhu, Yanzhe Liang, Hanzhi Chang, Jiacheng Deng, Jiahao Lu, Wenfei Yang, Tianzhu Zhang, and Yongdong Zhang. Motiongs: Exploring explicit motion guidance for deformable 3d gaussian splatting. arXiv preprint arXiv:2410.07707, 2024.  
+[6] Jiahao Lu, Tianyu Huang, Peng Li, Zhiyang Dou, Cheng Lin, Zhiming Cui, Zhen Dong, Sai-Kit Yeung, Wenping Wang, and Yuan Liu. Align3r: Aligned monocular depth estimation for dynamic videos. arXiv preprint arXiv:2412.03079, 2024.  
+[7] Jiahao Lu, Jiacheng Deng, Ruijie Zhu, Yanzhe Liang, Wenfei Yang, Tianzhu Zhang, and Xu Zhou. Dn-4dgs: Denoised deformable network with temporal-spatial aggregation for dynamic scene rendering. arXiv preprint arXiv:2410.13607, 2024.  
+[8] Jonathon Luiten, Georgios Kopanas, Bastian Leibe, and Deva Ramanan. Dynamic 3d gaussians: Tracking by persistent dynamic view synthesis. arXiv preprint arXiv:2308.09713, 2023.  
+[9] Davy Neven, Bert De Brabandere, Stamatios Georgoulis, Marc Proesmans, and Luc Van Gool. Towards end-to-end lane detection: an instance segmentation approach. In 2018 IEEE intelligent vehicles symposium (IV), pages 286-291. IEEE, 2018.  
+[10] Ekim Yurtsever, Jacob Lambert, Alexander Carballo, and Kazuya Takeda. A survey of autonomous driving: Common practices and emerging technologies. IEEE access, 8:58443-58469, 2020.  
+[11] Ville V Lehtola, Harri Kaartinen, Andreas Nüchter, Risto Kaijaluoto, Antero Kukko, Paula Litkey, Eija Honkavaara, Tomi Rosnell, Matti T Vaaja, Juho-Pekka Virtanen, et al. Comparison of the selected state-of-the-art 3d indoor scanning and point cloud generation methods. Remote sensing, 9(8):796, 2017.  
+[12] Maciej Halber, Yifei Shi, Kai Xu, and Thomas Funkhouser. Rescan: Inductive instance segmentation for indoor rgbd
+
+scans. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2541-2550, 2019.  
+[13] Li Yi, Wang Zhao, He Wang, Minhyuk Sung, and Leonidas J Guibas. Gspn: Generative shape proposal network for 3d instance segmentation in point cloud. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3947-3956, 2019.  
+[14] Ji Hou, Angela Dai, and Matthias Nießner. 3d-sis: 3d semantic instance segmentation of rgb-d scans. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4421-4430, 2019.  
+[15] Bo Yang, Jianan Wang, Ronald Clark, Qingyong Hu, Sen Wang, Andrew Markham, and Niki Trigoni. Learning object bounding boxes for 3d instance segmentation on point clouds. Advances in neural information processing systems, 32, 2019.  
+[16] Francis Engelmann, Martin Bokeloh, Alireza Fathi, Bastian Leibe, and Matthias Nießner. 3d-mpa: Multi-proposal aggregation for 3d semantic instance segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9031-9040, 2020.  
+[17] Zhihao Liang, Zhihao Li, Songcen Xu, Mingkui Tan, and Kui Jia. Instance segmentation in 3d scenes using semantic superpoint tree networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2783-2792, 2021.  
+[18] Thang Vu, Kookhoi Kim, Tung M Luu, Thanh Nguyen, and Chang D Yoo. Softgroup for 3d instance segmentation on point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2708-2717, 2022.  
+[19] Jonas Schult, Francis Engelmann, Alexander Hermans, Or Litany, Siyu Tang, and Bastian Leibe. Mask3d for 3d semantic instance segmentation. arXiv preprint arXiv:2210.03105, 2022.  
+[20] Jiahao Sun, Chunmei Qing, Junpeng Tan, and Xiangmin Xu. Superpoint transformer for 3d scene instance segmentation. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 2393-2401, 2023.  
+[21] Jiahao Lu, Jiacheng Deng, Chuxin Wang, Jianfeng He, and Tianzhu Zhang. Query refinement transformer for 3d instance segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 18516-18526, 2023.  
+[22] Xin Lai, Yuhui Yuan, Ruihang Chu, Yukang Chen, Han Hu, and Jiaya Jia. Mask-attention-free transformer for 3d instance segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3693-3703, 2023.  
+[23] Jiahao Lu, Jiacheng Deng, and Tianzhu Zhang. Beyond the final layer: Hierarchical query fusion transformer with agent-interpolation initialization for 3d instance segmentation. arXiv preprint arXiv:2502.04139, 2025.  
+[24] Bowen Cheng, Alex Schwing, and Alexander Kirillov. Per-pixel classification is not all you need for semantic segmentation. Advances in Neural Information Processing Systems, 34:17864-17875, 2021.  
+[25] Bowen Cheng, Ishan Misra, Alexander G Schwing, Alexander Kirillov, and Rohit Girdhar. Masked-attention mask transformer for universal image segmentation. In Proceedings of
+
+the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1290-1299, 2022.  
+[26] Jingyang Lin, Yingwei Pan, Rongfeng Lai, Xuehang Yang, Hongyang Chao, and Ting Yao. Core-text: Improving scene text detection with contrastive relational reasoning. In 2021 IEEE International Conference on Multimedia and Expo (ICME), pages 1-6. IEEE, 2021.  
+[27] Xiuquan Hou, Meiqin Liu, Senlin Zhang, Ping Wei, Badong Chen, and Xuguang Lan. Relation detr: Exploring explicit position relation prior for object detection. arXiv preprint arXiv:2407.11699, 2024.  
+[28] Xixuan Hao, Danqing Huang, Jieru Lin, and Chin-Yew Lin. Relation-enhanced detr for component detection in graphic design reverse engineering. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 4785–4793, 2023.  
+[29] Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan. Supervised contrastive learning. Advances in neural information processing systems, 33:18661-18673, 2020.  
+[30] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International conference on machine learning, pages 1597-1607. PMLR, 2020.  
+[31] Jiahao Lu, Jiacheng Deng, and Tianzhu Zhang. Bsnet: Box-supervised simulation-assisted mean teacher for 3d instance segmentation. arXiv preprint arXiv:2403.15019, 2024.  
+[32] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5828-5839, 2017.  
+[33] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12-22, 2023.  
+[34] David Rozenberszki, Or Litany, and Angela Dai. Language-grounded indoor 3d semantic segmentation in the wild. In European Conference on Computer Vision, pages 125-141. Springer, 2022.  
+[35] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1534-1543, 2016.  
+[36] Kaiming He, Georgia Gkioxari, Piotr Dólár, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961-2969, 2017.  
+[37] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652-660, 2017.  
+[38] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Advances in neural information processing systems, 30, 2017.
+
+[39] Harold W Kuhn. The hungarian method for the assignment problem. Naval research logistics quarterly, 2(1-2):83-97, 1955.  
+[40] Li Jiang, Hengshuang Zhao, Shaoshuai Shi, Shu Liu, Chi-Wing Fu, and Jiaya Jia. Pointgroup: Dual-set point grouping for 3d instance segmentation. In Proceedings of the IEEE/CVF conference on computer vision and Pattern recognition, pages 4867-4876, 2020.  
+[41] Tuan Duc Ngo, Binh-Son Hua, and Khoi Nguyen. Isbnet: a 3d point cloud instance segmentation network with instance-aware sampling and box-aware dynamic convolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13550-13559, 2023.  
+[42] Sangyun Shin, Kaichen Zhou, Madhu Vankadari, Andrew Markham, and Niki Trigoni. Spherical mask: Coarse-to-fine 3d point cloud instance segmentation with spherical representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4060-4069, 2024.  
+[43] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu, Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao Xi-ang, Philip HS Torr, et al. Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 6881-6890, 2021.  
+[44] Feng Li, Hao Zhang, Huaizhe Xu, Shilong Liu, Lei Zhang, Lionel M Ni, and Heung-Yeung Shum. Mask dino: Towards a unified transformer-based framework for object detection and segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3041-3050, 2023.  
+[45] Spconv Contributors. Spconv: Spatially sparse convolution library. https://github.com/traveller59/spconv, 2022.  
+[46] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems, 32, 2019.  
+[47] Alexander Neubeck and Luc Van Gool. Efficient nonmaximum suppression. In 18th international conference on pattern recognition (ICPR'06), volume 3, pages 850-855. IEEE, 2006.  
+[48] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.  
+[49] Tong He, Chunhua Shen, and Anton Van Den Hengel. Dyco3d: Robust instance segmentation of 3d point clouds through dynamic convolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 354-363, 2021.  
+[50] Min Zhong, Xinghao Chen, Xiaokang Chen, Gang Zeng, and Yunhe Wang. Maskgroup: Hierarchical point grouping and masking for 3d instance segmentation. In 2022 IEEE International Conference on Multimedia and Expo (ICME), pages 1-6. IEEE, 2022.  
+[51] Lei Han, Tian Zheng, Lan Xu, and Lu Fang. Occuseg: Occupancy-aware 3d instance segmentation. In Proceedings
+
+of the IEEE/CVF conference on computer vision and pattern recognition, pages 2940-2949, 2020.  
+[52] Shaoyu Chen, Jiemin Fang, Qian Zhang, Wenyu Liu, and Xinggang Wang. Hierarchical aggregation for 3d instance segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15467-15476, 2021.  
+[53] Yizheng Wu, Min Shi, Shuaiyuan Du, Hao Lu, Zhiguo Cao, and Weicai Zhong. 3d instances as 1d kernels. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXIX, pages 235-252. Springer, 2022.

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+# RelationField: Relate Anything in Radiance Fields
+
+Sebastian Koch<sup>1,2</sup> Johanna Wald<sup>3</sup> Mirco Colosi<sup>2</sup> Narunas Vaskevicius<sup>2</sup> Pedro Hermosilla<sup>4</sup> Federico Tombari<sup>3,5</sup> Timo Ropinski<sup>1</sup>
+
+<sup>1</sup>University Ulm <sup>2</sup>Bosch Center for AI <sup>3</sup>Google <sup>4</sup>TU Vienna <sup>5</sup>TU Munich
+
+![](images/48de3d62bd9c2d6e0f28bb965f6a0dfa160669f8bbed547a0b2eb0955ae5b737.jpg)
+
+![](images/8c80f9f0a0ba1ac454bca391bed65529029d91d7b99cb4657e2fe497c257a0b5.jpg)
+
+![](images/c130b7e631198257660082b7ff0aaec53d4a8c584fde5006747f9783949c6849.jpg)
+
+![](images/50b97d82efb5a18d69d38418c362cbca703611142b7a682b033fb247a9c0bcfb.jpg)
+
+![](images/fb528f4a2564bbb5aecd95b497092195b5089705ae4c2d5b95b3d59abbffb3d6.jpg)
+
+![](images/6d82ab5a11b7c7922d75e712a7f1aa12afc183cc8e1af6078eaf2ecab8fb0e7a.jpg)  
+Figure 1. 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
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Object</td><td colspan="2">Predicate</td><td colspan="2">Relationship</td></tr><tr><td>R@5</td><td>R@10</td><td>R@3</td><td>R@5</td><td>R@50</td><td>R@100</td></tr><tr><td>GPT-4 [1] (2D+depth)</td><td>0.34</td><td>0.42</td><td>0.55</td><td>0.58</td><td>0.52</td><td>0.54</td></tr><tr><td>Llama 3.2 [12] (2D+depth)</td><td>0.40</td><td>0.52</td><td>0.46</td><td>0.48</td><td>0.45</td><td>0.51</td></tr><tr><td>Open3DSG [27]</td><td>0.56</td><td>0.61</td><td>0.58</td><td>0.65</td><td>0.55</td><td>0.56</td></tr><tr><td>ConceptGraphs [15]</td><td>0.37</td><td>0.46</td><td>0.74</td><td>0.79</td><td>0.69</td><td>0.71</td></tr><tr><td>RelationField</td><td>0.69</td><td>0.80</td><td>0.76</td><td>0.82</td><td>0.73</td><td>0.74</td></tr></table>
+
+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
+
+<table><tr><td>Method</td><td>IoU</td><td>Acc</td></tr><tr><td>LERF [22]</td><td>0.25</td><td>0.50</td></tr><tr><td>OpenNeRF [13]</td><td>0.45</td><td>0.83</td></tr><tr><td>LangSplat [38]</td><td>0.49</td><td>0.87</td></tr><tr><td>RelationField</td><td>0.53</td><td>0.96</td></tr></table>
+
+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. This work was partly supported by the EU Horizon 2020 research and innovation program under grant agreement No. 101017274 (DARKO).
+
+# 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. 1, 5, 7  
+[2] Christopher Agia, Krishna Murthy Jatavallabhula, Mohamed Khodeir, Ondrej Miksik, Vibhav Vineet, Mustafa Mukadam, Liam Paull, and Florian Shkurti. Taskgraphy: Evaluating robot task planning over large 3d scene graphs. In Proceedings of the 5th Conference on Robot Learning, pages 46-58. PMLR, 2022. 2  
+[3] Iro Armeni, Zhi-Yang He, JunYoung Gwak, Amir R. Zamir, Martin Fischer, Jitendra Malik, and Silvio Savarese. 3d scene graph: A structure for unified semantics, 3d space, and camera. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 2  
+[4] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the International Conference on Computer Vision (ICCV), 2021. dino. 1, 2  
+[5] Lianggangxu Chen, Xuejiao Wang, Jiale Lu, Shaohui Lin, Changbo Wang, and Gaoqi He. Clip-driven open-vocabulary 3d scene graph generation via cross-modality contrastive learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 27863-27873, 2024. 3  
+[6] An-Chieh Cheng, Hongxu Yin, Yang Fu, Qiushan Guo, Ruihan Yang, Jan Kautz, Xiaolong Wang, and Sifei Liu. Spatial-rgpt: Grounded spatial reasoning in vision-language models. In NeurIPS, 2024. 3  
+[7] Seokhun Choi, Hyeonseop Song, Jaechul Kim, Taehyeong Kim, and Hoseok Do. Click-gaussian: Interactive segmentation to any 3d gaussians. arXiv preprint arXiv:2407.11793, 2024. 3  
+[8] Christopher Choy, JunYoung Gwak, and Silvio Savarese. 4d spatio-temporal convnets: Minkowski convolutional neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3075-3084, 2019. 1, 2  
+[9] Wenliang Dai, Junnan Li, Dongxu Li, Anthony Meng Huat Tiong, Junqi Zhao, Weisheng Wang, Boyang Li, Pascale Fung, and Steven Hoi. Instructblip: Towards general-purpose vision-language models with instruction tuning. arXiv preprint arXiv:2305.06500, 2023. 2, 7  
+[10] Alexandros Delitzas, Ayca Takmaz, Federico Tombari, Robert Sumner, Marc Pollefeys, and Francis Engelmann.
+
+Scenefun3d: Fine-grained functionality and affordance understanding in 3d scenes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 14531-14542, 2024. 2  
+[11] Dingsheng Deng. Dbscan clustering algorithm based on density. In 2020 7th International Forum on Electrical Engineering and Automation (IFEEA), pages 949-953, 2020. 6  
+[12] Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024. 1, 7  
+[13] Francis Engelmann, Fabian Manhardt, Michael Niemeyer, Keisuke Tateno, Marc Pollefeys, and Federico Tombari. OpenNerf: Open Set 3D Neural Scene Segmentation with Pixel-Wise Features and Rendered Novel Views. In International Conference on Learning Representations, 2024. 2, 3, 4, 8  
+[14] Golnaz Ghiasi, Xiuye Gu, Yin Cui, and Tsung-Yi Lin. Scaling open-vocabulary image segmentation with image-level labels. In European Conference on Computer Vision (ECCV), pages 540-557, 2022. 5  
+[15] Qiao Gu, Ali Kuwajerwala, Sacha Morin, Krishna Murthy Jatavallabhula, Bipasha Sen, Aditya Agarwal, Corban Rivera, William Paul, Kirsty Ellis, Rama Chellappa, Chuang Gan, Celso Miguel de Melo, Joshua B. Tenenbaum, Antonio Torralba, Florian Shkurti, and Liam Paull. Conceptgraphs: Open-vocabulary 3d scene graphs for perception and planning. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 5021-5028, 2024. 3, 7  
+[16] Huy Ha and Shuran Song. Semantic abstraction: Open-world 3D scene understanding from 2D vision-language models. In Proceedings of the 2022 Conference on Robot Learning, 2022. 1, 2  
+[17] Benran Hu, Junkai Huang, Yichen Liu, Yu-Wing Tai, and Chi-Keung Tang. Nerf-rpn: A general framework for object detection in nerfs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 23528-23538, 2023. 3  
+[18] Zhening Huang, Xiaoyang Wu, Xi Chen, Hengshuang Zhao, Lei Zhu, and Joan Lasenby. Openins3d: Snap and lookup for 3d open-vocabulary instance segmentation. In European Conference on Computer Vision (ECCV), 2024. 2  
+[19] N. Hughes, Y. Chang, and L. Carlone. Hydra: A real-time spatial perception system for 3D scene graph construction and optimization. In Robotics: Science and Systems (RSS), 2022. 2  
+[20] Jacob Devlin Ming-Wei Chang Kenton and Lee Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of naacL-HLT, page 2. Minneapolis, Minnesota, 2019. 4  
+[21] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkuhler, and George Drettakis. 3d gaussian splattering for real-time radiance field rendering. ACM Transactions on Graphics, 42(4), 2023. 2, 3  
+[22] Justin Kerr, Chung Min Kim, Ken Goldberg, Angjoo Kanazawa, and Matthew Tancik. Lef: Language embed
+
+ded radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 19729-19739, 2023. 2, 3, 4, 5, 8  
+[23] Chung Min Kim, Mingxuan Wu, Justin Kerr, Ken Goldberg, Matthew Tancik, and Angjoo Kanazawa. Garfield: Group anything with radiance fields. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 21530-21539, 2024. 2, 3, 4  
+[24] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C. Berg, Wan-Yen Lo, Piotr Dollar, and Ross Girshick. Segment anything. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 4015-4026, 2023. 1, 2, 3, 4  
+[25] Sebastian Koch, Pedro Hermosilla, Narunas Vaskevicius, Mirco Colosi, and Timo Ropinski. Sgrec3d: Self-supervised 3d scene graph learning via object-level scene reconstruction. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 3404-3414, 2024. 2, 3  
+[26] Sebastian Koch, Pedro Hermosilla, Narunas Vaskevicius, Mirco Colosi, and Timo Ropinski. Lang3dsg: Language-based contrastive pre-training for 3d scene graph prediction. In 2024 International Conference on 3D Vision (3DV), pages 1037-1047. IEEE, 2024. 3  
+[27] Sebastian Koch, Narunas Vaskevicius, Mirco Colosi, Pedro Hermosilla, and Timo Ropinski. Open3dsg: Open-vocabulary 3d scene graphs from point clouds with queryable objects and open-set relationships. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 14183-14193, 2024. 2, 3, 7  
+[28] Nilesh Kulkarni, Ishan Misra, Shubham Tulsiani, and Abhinav Gupta. 3d-relnet: Joint object and relational network for 3d prediction. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 2  
+[29] Yuchen Liu, Luigi Palmieri, Sebastian Koch, Ilche Georgievski, and Marco Aiello. Delta: Decomposed efficient long-term robot task planning using large language models. arXiv preprint arXiv:2404.03275, 2024. 2  
+[30] Samuel Looper, Javier Rodriguez-Puigvert, Roland Siegwart, Cesar Cadena, and Lukas Schmid. 3d vsg: Long-term semantic scene change prediction through 3d variable scene graphs. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 8179-8186. IEEE, 2023. 2  
+[31] Cewu Lu, Ranjay Krishna, Michael Bernstein, and Li Fei-Fei. Visual relationship detection with language priors. In Computer Vision-ECCV 2016: 14th European Conference, Proceedings, Part I 14, pages 852–869. Springer, 2016. 7  
+[32] Dominic Maggio, Yun Chang, Nathan Hughes, Matthew Trang, Dan Griffith, Carlyn Dougherty, Eric Cristofalo, Lukas Schmid, and Luca Carlone. Clio: Real-time task-driven open-set 3d scene graphs. IEEE Robotics and Automation Letters, 9(10):8921-8928, 2024. 3  
+[33] Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In European Conference on Computer Vision (ECCV),
+
+pages 405-421. Springer International Publishing, 2020. 2, 3, 4  
+[34] Ishan Misra, Rohit Girdhar, and Armand Joulin. An End-to-End Transformer Model for 3D Object Detection. In ICCV, 2021. 1, 2  
+[35] Phuc Nguyen, Tuan Duc Ngo, Evangelos Kalogerakis, Chuang Gan, Anh Tran, Cuong Pham, and Khoi Nguyen. Open3dis: Open-vocabulary 3d instance segmentation with 2d mask guidance. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 4018-4028, 2024. 2  
+[36] Songyou Peng, Kyle Genova, Chiyu "Max" Jiang, Andrea Tagliasacchi, Marc Pollefeys, and Thomas Funkhouser. Openscene: 3d scene understanding with open vocabularies. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 815-824, 2023. 1, 2  
+[37] Charles R Qi, Or Lityan, Kaiming He, and Leonidas J Guibas. Deep hough voting for 3d object detection in point clouds. In Proceedings of the IEEE International Conference on Computer Vision, 2019. 1, 2  
+[38] Minghan Qin, Wanhua Li, Jiawei Zhou, Haoqian Wang, and Hanspeter Pfister. Langsplat: 3d language gaussian splatting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 20051-20060, 2024. 2, 3, 8  
+[39] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. Learning transferable visual models from natural language supervision. In Proceedings of the 38th International Conference on Machine Learning, pages 8748-8763. PMLR, 2021. CLIP. 1, 2, 3, 4, 5, 6, 7, 8  
+[40] Krishan Rana, Jesse Haviland, Sourav Garg, Jad Abou-Chakra, Ian Reid, and Niko Suenderhauf. Sayplan: Grounding large language models using 3d scene graphs for scalable task planning. In 7th Annual Conference on Robot Learning, 2023. 2  
+[41] Antoni Rosinol, Arjun Gupta, Marcus Abate, Jingnan Shi, and Luca Carlone. 3d dynamic scene graphs: Actionable spatial perception with places, objects, and humans. In Robotics: Science and Systems (RSS), 2020. 2  
+[42] Antoni Rosinol, Andrew Violette, Marcus Abate, Nathan Hughes, Yun Chang, Jingnan Shi, Arjun Gupta, and Luca Carlone. Kimera: From slam to spatial perception with 3d dynamic scene graphs. The International Journal of Robotics Research, 40(12-14):1510-1546, 2021. 2  
+[43] Sayan Deb Sarkar, Ondrej Miksik, Marc Pollefeys, Daniel Barath, and Iro Armeni. Sgaligner: 3d scene alignment with scene graphs. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 21927-21937, 2023. 2  
+[44] Jonas Schult, Francis Engelmann, Alexander Hermans, Or Litany, Siyu Tang, and Bastian Leibe. Mask3D: Mask Transformer for 3D Semantic Instance Segmentation. In International Conference on Robotics and Automation (ICRA), 2023. 1, 2
+
+[45] Yawar Siddiqui, Lorenzo Porzi, Samuel Rota Bulò, Norman Müller, Matthias Nießner, Angela Dai, and Peter Kontschieder. Panoptic lifting for 3d scene understanding with neural fields. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9043-9052, 2023. 2, 3  
+[46] Julian Straub, Thomas Whelan, Lingni Ma, Yufan Chen, Erik Wijmans, Simon Green, Jakob J Engel, Raul Mur-Artal, Carl Ren, Shobhit Verma, et al. The replica dataset: A digital replica of indoor spaces. arXiv preprint arXiv:1906.05797, 2019. 5  
+[47] Saba Sturua, Isabelle Mohr, Mohammad Kalim Akram, Michael Günther, Bo Wang, Markus Krimmel, Feng Wang, Georgios Mastrapas, Andreas Koukounas, Andreas Koukounas, Nan Wang, and Han Xiao. jina-embeddings-v3: Multilingual embeddings with task lora, 2023. 5, 6  
+[48] Ayca Takmaz, Elisabetta Fedele, Robert W. Sumner, Marc Pollefeys, Federico Tombari, and Francis Engelmann. OpenMask3D: Open-Vocabulary 3D Instance Segmentation. In Advances in Neural Information Processing Systems (NeurIPS), 2023. 1, 2  
+[49] Matthew Tancik, Ethan Weber, Evonne Ng, Ruilong Li, Brent Yi, Terrance Wang, Alexander Kristoffersen, Jake Austin, Kamyar Salahi, Abhik Ahuja, et al. Nerfstudio: A modular framework for neural radiance field development. In ACM SIGGRAPH 2023 Conference Proceedings, pages 1-12, 2023. 5  
+[50] Johanna Wald, Helisa Dhamo, Nassir Navab, and Federico Tombari. Learning 3d semantic scene graphs from 3d indoor reconstructions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 2, 3, 7  
+[51] Ziqin Wang, Bowen Cheng, Lichen Zhao, Dong Xu, Yang Tang, and Lu Sheng. Vl-sat: Visual-linguistic semantics assisted training for 3d semantic scene graph prediction in point cloud. arXiv preprint arXiv:2303.14408, 2023. 2  
+[52] Abdelrhman Werby, Chenguang Huang, Martin Büchner, Abhinav Valada, and Wolfram Burgard. Hierarchical Open-Vocabulary 3D Scene Graphs for Language-Grounded Robot Navigation. In Proceedings of Robotics: Science and Systems, Delft, Netherlands, 2024. 2  
+[53] Shun-Cheng Wu, Johanna Wald, Keisuke Tateno, Nassir Navab, and Federico Tombari. Scenegraphfusion: Incremental 3d scene graph prediction from rgb-d sequences. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 7515-7525, 2021. 2, 3  
+[54] Shun-Cheng Wu, Keisuke Tateno, Nassir Navab, and Federico Tombari. Incremental 3d semantic scene graph prediction from rgb sequences. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5064-5074, 2023. 3  
+[55] Chenfeng Xu, Bichen Wu, Ji Hou, Sam Tsai, Ruilong Li, Jialiang Wang, Wei Zhan, Zijian He, Peter Vajda, Kurt Keutzer, and Masayoshi Tomizuka. Nerf-det: Learning geometry-aware volumetric representation for multi-view 3d object detection. In Proceedings of the IEEE/CVF Interna
+
+tional Conference on Computer Vision (ICCV), pages 23320-23330, 2023. 3  
+[56] Jianwei Yang, Jiasen Lu, Stefan Lee, Dhruv Batra, and Devi Parikh. Graph r-cnn for scene graph generation. In Proceedings of the European conference on computer vision (ECCV), pages 670-685, 2018. 7  
+[57] Jianwei Yang, Hao Zhang, Feng Li, Xueyan Zou, Chunyuan Li, and Jianfeng Gao. Set-of-mark prompting unleashes extraordinary visual grounding in gpt-4v. arXiv preprint arXiv:2310.11441, 2023. 3, 5  
+[58] Jianwei Yang, Hao Zhang, Feng Li, Xueyan Zou, Chunyuan Li, and Jianfeng Gao. Set-of-mark prompting unleashes extraordinary visual grounding in gpt-4v. arXiv preprint arXiv:2310.11441, 2023. 4  
+[59] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 12-22, 2023. 2, 5, 8  
+[60] Mert Yuksekgonul, Federico Bianchi, Pratyusha Kalluri, Dan Jurafsky, and James Zou. When and why vision-language models behave like bags-of-words, and what to do about it? arXiv preprint arXiv:2210.01936, 2022. 4  
+[61] Shoulong Zhang, Shuai Li, Aimin Hao, and Hong Qin. Knowledge-inspired 3d scene graph prediction in point cloud. In Advances in Neural Information Processing Systems, pages 18620-18632. Curran Associates, Inc., 2021. 3  
+[62] Shuaifeng Zhi, Tristan Laidlow, Stefan Leutenegger, and Andrew J. Davison. In-place scene labelling and understanding with implicit scene representation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 3

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+# 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.
+
+<table><tr><td colspan="3">Open-set</td><td colspan="5">Closed-set</td></tr><tr><td>Dataset</td><td>FUNSD [20]</td><td>XFUND [48]</td><td>CORD [35]</td><td>EPHOIE [43]</td><td>POIE [26]</td><td>SROIE [17]</td><td>DocILE [39]</td></tr><tr><td>#Img.</td><td>199</td><td>199 per lang.</td><td>1000</td><td>1494</td><td>3000</td><td>1000</td><td>real: 6680 syn:100K*</td></tr><tr><td>#Keys</td><td>Free</td><td>Free</td><td>30</td><td>10</td><td>21</td><td>4</td><td>55</td></tr></table>
+
+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 <content> tags after the document title, (2) paragraphs are organized using header tags (<h1>, <h2>, 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":["<FILL_1>]},..., {"text":tN,"box":["<FILL_N>]}]
+```
+
+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
+\[
+\begin{array}{l}
+\{\text{"<FILL_1>}": \text{"xleft_1, ytop_1, xright_1, ybottom_1", ..., }\} \\
+\text{"<FILL_N>}": \text{"xleft_N, ytop_N, xright_N, ybottom_N"}
+\end{array}
+\]
+```
+
+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.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Open-set</td><td colspan="6">Closed-set</td></tr><tr><td>FUNSD F1 %</td><td>XFUND-ZH F1 %</td><td>CORD F1 %</td><td>CORD- ANLS %</td><td>EPHOIE Acc %</td><td>ANOLES %</td><td>POIE Acc %</td><td>SROIE- ANLS%</td></tr><tr><td>LayoutLLM [33] (CVPR&#x27;24)</td><td>-</td><td>-</td><td>-</td><td>63.10</td><td>-</td><td>-</td><td>-</td><td>72.12</td></tr><tr><td>Monkey [29] (CVPR&#x27;24)</td><td>34.27</td><td>28.02</td><td>54.54</td><td>69.48</td><td>22.44</td><td>30.96</td><td>30.64</td><td>43.95</td></tr><tr><td>DocOwl-1.5-Chat [14] (EMNLP&#x27;24)</td><td>50.88</td><td>10.14</td><td>64.01</td><td>63.15</td><td>4.85</td><td>8.25</td><td>51.57</td><td>61.35</td></tr><tr><td>LLaVA-NeXT-Mistral-7B [32]</td><td>31.18</td><td>6.02</td><td>46.58</td><td>63.81</td><td>4.31</td><td>8.02</td><td>49.88</td><td>60.05</td></tr><tr><td>LLaVA-NeXT-Mistral-7B+</td><td>33.41</td><td>10.33</td><td>52.32</td><td>63.93</td><td>5.39</td><td>12.07</td><td>51.46</td><td>62.13</td></tr><tr><td>Δ↑</td><td>2.23</td><td>4.31</td><td>5.74</td><td>0.12</td><td>1.08</td><td>4.05</td><td>1.58</td><td>2.08</td></tr><tr><td>Qwen2-VL-7B [44]</td><td>59.89</td><td>62.08</td><td>82.71</td><td>80.40</td><td>76.91</td><td>86.52</td><td>93.51</td><td>96.01</td></tr><tr><td>Qwen2-VL-7B+</td><td>66.48</td><td>69.84</td><td>84.47</td><td>85.53</td><td>77.89</td><td>87.79</td><td>94.04</td><td>96.71</td></tr><tr><td>Δ↑</td><td>6.59</td><td>7.76</td><td>1.76</td><td>5.13</td><td>0.98</td><td>1.27</td><td>0.53</td><td>0.70</td></tr></table>
+
+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.
+
+<table><tr><td rowspan="2">Dataset Combinations</td><td rowspan="2">FUNSD F1 %</td><td rowspan="2">CORD F1 %</td><td rowspan="2">CORD- ANLS %</td><td colspan="2">POIE</td><td rowspan="2">SROIE- ANLS %</td></tr><tr><td>Acc %</td><td>ANLS %</td></tr><tr><td>Qwen2-VL-7B [44]</td><td>59.89</td><td>82.71</td><td>80.40</td><td>93.51</td><td>96.01</td><td>97.50</td></tr><tr><td>+RIDGE</td><td>65.72 (+5.83)</td><td>84.20 (+1.49)</td><td>83.71 (+3.31)</td><td>94.45 (+0.94)</td><td>96.71 (+0.70)</td><td>97.64 (+0.14)</td></tr><tr><td>+RIDGE+DocVQA</td><td>66.21 (+6.32)</td><td>84.06 (+1.35)</td><td>85.66 (+5.26)</td><td>94.08 (+0.57)</td><td>96.67 (+0.66)</td><td>97.72 (+0.22)</td></tr><tr><td>+RIDGE+DocVQA+FUNSD</td><td>67.54 (+7.65)</td><td>84.25 (+1.54)</td><td>85.57 (+5.17)</td><td>94.11 (+0.60)</td><td>96.72 (+0.71)</td><td>97.71 (+0.21)</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">SROIE-ANLS%</td><td colspan="2">EPHOIE</td></tr><tr><td>Acc%</td><td>ANLS%</td></tr><tr><td>Qwen2-VL-7B [44]</td><td>97.50</td><td>76.91</td><td>86.52</td></tr><tr><td>+RIDGE</td><td>97.74 (+0.24)</td><td>77.89 (+0.98)</td><td>87.79 (+1.27)</td></tr><tr><td>+RIDGE+RIDGE-DS</td><td>98.05 (+0.55)</td><td>80.91 (+4.00)</td><td>89.82 (+3.30)</td></tr></table>
+
+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
+
+<table><tr><td>Pre-training Data</td><td>Fine-tuning Data</td><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>10-shot</td></tr><tr><td>-</td><td rowspan="2">FUNSD</td><td>-</td><td>45.42</td><td>72.45</td><td>71.03</td></tr><tr><td>RIDGE</td><td>62.77</td><td>71.07</td><td>73.25</td><td>74.79</td></tr><tr><td>-</td><td rowspan="2">XFUND-ZH</td><td>-</td><td>52.02</td><td>76.39</td><td>81.18</td></tr><tr><td>RIDGE</td><td>69.75</td><td>70.91</td><td>78.57</td><td>83.02</td></tr></table>
+
+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 LayoutLMv3<sub>BASE</sub> [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.  
+
+<table><tr><td></td><td>Hierarchical Structure Learning</td><td>FUNSD</td><td>XFUND-ZH</td><td>CORD</td></tr><tr><td>r1</td><td>Qwen2-VL-7B [44]</td><td>59.89</td><td>62.08</td><td>82.71</td></tr><tr><td>r2</td><td></td><td>64.87</td><td>67.32</td><td>83.77</td></tr><tr><td>r3</td><td>✓</td><td>66.48</td><td>69.84</td><td>84.47</td></tr></table>
+
+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.  
+
+<table><tr><td>(a)</td><td colspan="2">MLM response:
+&lt;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
+&lt;hz&gt;</td></tr><tr><td>(b)</td><td colspan="2">MLM response:
+&lt;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
+&lt;hz&gt;</td></tr><tr><td>(c)</td><td colspan="2">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</td></tr><tr><td>(d)</td><td colspan="2">###Answer: 14</td></tr></table>
+
+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. We thank to National Center for High-performance Computing (NCHC) of National Applied Research Laboratories (NARLabs) in Taiwan for providing computational and storage resources.
+
+# References
+
+[1] Diego Martin Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In CVPR, pages 13642-13652, 2021. 2  
+[2] Sanket Biswas, Pau Riba, Josep Lladós, and Umapada Pal. Docsynth: A layout guided approach for controllable document image synthesis. In International Conference on Document Analysis and Recognition (ICDAR), 2021. 2  
+[3] Manuel Carbonell, Pau Riba, Mauricio Villegas, Alicia Fornés, and Josep Lladós. Named entity recognition and relation extraction with graph neural networks in semi structured documents. In 2020 25th International Conference on Pattern Recognition (ICPR), pages 9622-9627, 2021. 3  
+[4] Jingye Chen, Yupan Huang, Tengchao Lv, Lei Cui, Qifeng Chen, and Furu Wei. Textdiffuser-2: Unleashing thenbsp;power ofnbsp;language models fornbsp;text rendering. In Computer Vision - ECCV 2024: 18th European Conference, Milan, Italy, September 29–October 4, 2024, Proceedings, Part V, page 386–402, Berlin, Heidelberg, 2024. Springer-Verlag. 2  
+[5] Zhe Chen, Weiyun Wang, Hao Tian, Shenglong Ye, Zhang-wei Gao, Erfei Cui, Wenwen Tong, Kongzhi Hu, Jiapeng Luo, Zheng Ma, et al. How far are we to gpt-4v? closing the gap to commercial multimodal models with open-source suites. Science China Information Sciences, 67(12):220101, 2024. 3  
+[6] Jaemin Cho, Abhay Zala, and Mohit Bansal. Visual programming for step-by-step text-to-image generation and evaluation. NeurIPS, 36, 2024. 2  
+[7] Brian Davis, Bryan Morse, Brian Price, Chris Tensmeyer, Curtis Wigington, and Vlad Morariu. End-to-end document recognition and understanding with dessurt. In Computer Vision - ECCV 2022 Workshops: Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part IV, page 280-296, Berlin, Heidelberg, 2022. Springer-Verlag. 3  
+[8] Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024. 6, 1  
+[9] Weixi Feng, Wanrong Zhu, Tsu-Jui Fu, Varun Jampani, Arjun Reddy Akula, Xuehai He, S Basu, Xin Eric Wang, and William Yang Wang. LayoutGPT: Compositional visual planning and generation with large language models. In NeurIPS, 2023. 2, 3, 4
+
+[10] Andrea Gemelli, Sanket Biswas, Enrico Civitelli, Josep Lladós, and Simone Marinai. Doc2graph: A task agnostic document understanding framework based on onnbsp;graph neural networks. In Computer Vision - ECCV 2022 Workshops: Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part IV, page 329-344, Berlin, Heidelberg, 2022. Springer-Verlag. 3  
+[11] Adam W Harley, Alex Ufkes, and Konstantinos G Derpanis. Evaluation of deep convolutional nets for document image classification and retrieval. In 2015 13th International Conference on Document Analysis and Recognition (ICDAR), pages 991-995. IEEE, 2015. 6  
+[12] Liu He, Yijuan Lu, John Corring, Dinei Florencio, and Cha Zhang. Diffusion-based document layout generation. In Document Analysis and Recognition - ICDAR 2023, pages 361-378. Springer Nature Switzerland, 2023. 2  
+[13] Teakgyu Hong, Dongyun Kim, Mingi Ji, Wonseok Hwang, Daehyun Nam, and Sungrae Park. Bros: A pre-trained language model focusing on text and layout for better key information extraction from documents. In AAAI, pages 10767-10775, 2022. 1, 3  
+[14] Anwen Hu, Haiyang Xu, Jiabo Ye, Ming Yan, Liang Zhang, Bo Zhang, Ji Zhang, Qin Jin, Fei Huang, and Jingren Zhou. mPLUG-DocOwl 1.5: Unified structure learning for OCR-free document understanding. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 3096-3120, Miami, Florida, USA, 2024. Association for Computational Linguistics. 5, 6, 7, 3  
+[15] Edward J Hu, yelong shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. LoRA: Low-rank adaptation of large language models. In ICLR, 2022. 6, 1  
+[16] Yupan Huang, Tengchao Lv, Lei Cui, Yutong Lu, and Furu Wei. Layoutlmv3: Pre-training for document ai with unified text and image masking. In ACM MM, pages 4083-4091, 2022. 1, 6, 8, 3  
+[17] Zheng Huang, Kai Chen, Jianhua He, Xiang Bai, Dimosthenis Karatzas, Shijian Lu, and CV Jawahar. Icdar2019 competition on scanned receiptOCR and information extraction. In 2019 International Conference on Document Analysis and Recognition (ICDAR), pages 1516-1520. IEEE, 2019. 2, 1  
+[18] Mude Hui, Zhizheng Zhang, Xiaoyi Zhang, Wenxuan Xie, Yuwang Wang, and Yan Lu. Unifying layout generation with a decoupled diffusion model. In CVPR, pages 1942-1951, 2023. 2  
+[19] Naoto Inoue, Kotaro Kikuchi, Edgar Simo-Serra, Mayu Otani, and Kota Yamaguchi. LayoutDM: Discrete Diffusion Model for Controllable Layout Generation. In CVPR, pages 10167-10176, 2023. 1, 2, 3, 6  
+[20] Guillaume Jaume, Hazim Kemal Ekenel, and Jean-Philippe Thiran. Funsd: A dataset for form understanding in noisy scanned documents. In 2019 International Conference on Document Analysis and Recognition Workshops (ICDARW). IEEE, 2019. 2, 6  
+[21] Peidong Jia, Chenxuan Li, Yuhui Yuan, Zeyu Liu, Yichao Shen, Bohan Chen, Xingru Chen, Yinglin Zheng, Dong Chen, Ji Li, Xiaodong Xie, Shanghang Zhang, and Baining
+
+Guo. Cole: A hierarchical generation framework for multilayered and editable graphic design, 2024. 2  
+[22] Zhaoyun Jiang, Shizhao Sun, Jihua Zhu, Jian-Guang Lou, and Dongmei Zhang. Coarse-to-fine generative modeling for graphic layouts. In AAAI, pages 1096-1103, 2022. 2  
+[23] Zhaoyun Jiang, Jiaqi Guo, Shizhao Sun, Huayu Deng, Zhongkai Wu, Vuksan Mijovic, Zijiang James Yang, JianGuang Lou, and Dongmei Zhang. Layoutformer++: Conditional graphic layout generation via constraint serialization and decoding space restriction. In CVPR, pages 18403- 18412, 2023. 1, 2, 6  
+[24] Akash Abdu Jyothi, Thibaut Durand, Jiawei He, Leonid Sigal, and Greg Mori. Layoutvae: Stochastic scene layout generation from a label set. In ICCV, pages 9895-9904, 2019. 2  
+[25] Geewook Kim, Teakgyu Hong, Moonbin Yim, JeongYeon Nam, Jinyoung Park, Jinyeong Yim, Wonseok Hwang, Sangdoo Yun, Dongyoon Han, and Seunghyun Park. Ocr-free document understanding transformer. In ECCV, 2022. 2, 3  
+[26] Jianfeng Kuang, Wei Hua, Dingkang Liang, Mingkun Yang, Deqiang Jiang, Bo Ren, and Xiang Bai. Visual information extraction in the wild: practical dataset and end-to-end solution. In International Conference on Document Analysis and Recognition, pages 36-53. Springer, 2023. 2  
+[27] Fengheng Li, An Liu, Wei Feng, Honghe Zhu, Yaoyu Li, Zheng Zhang, Jingjing Lv, Xin Zhu, Junjie Shen, Zhangang Lin, and Jingping Shao. Relation-aware diffusion model for controllable poster layout generation. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, page 1249-1258, 2023. 2  
+[28] Jianan Li, Tingfa Xu, Jianming Zhang, Aaron Hertzmann, and Jimei Yang. LayoutGAN: Generating graphic layouts with wireframe discriminator. In ICLR, 2019. 1, 2  
+[29] Zhang Li, Biao Yang, Qiang Liu, Zhiyin Ma, Shuo Zhang, Jingxu Yang, Yabo Sun, Yuliang Liu, and Xiang Bai. Monkey: Image resolution and text label are important things for large multi-modal models. In CVPR, pages 26763-26773, 2024. 6  
+[30] Long Lian, Boyi Li, Adam Yala, and Trevor Darrell. LLM-grounded diffusion: Enhancing prompt understanding of text-to-image diffusion models with large language models. Transactions on Machine Learning Research, 2024. Featured Certification. 2  
+[31] Jiawei Lin, Jiaqi Guo, Shizhao Sun, Zijiang James Yang, Jian-Guang Lou, and Dongmei Zhang. Layoutprompter: Awaken the design ability of large language models. In NeurIPS, 2023. 2, 3, 4  
+[32] Haotian Liu, Chunyuan Li, Yuheng Li, Bo Li, Yuanhan Zhang, Sheng Shen, and Yong Jae Lee. Llava next: Improved reasoning,OCR, and world knowledge, 2024.5,6, 1,3  
+[33] Chuwei Luo, Yufan Shen, Zhaoqing Zhu, Qi Zheng, Zhi Yu, and Cong Yao. Layoutllm: Layout instruction tuning with large language models for document understanding. In CVPR, pages 15630-15640, 2024. 5, 6, 1, 3  
+[34] Minesh Mathew, Dimosthenis Karatzas, and CV Jawahar. Docvqa: A dataset for vqa on document images. In WACV, 2021. 1
+
+[35] Seunghyun Park, Seung Shin, Bado Lee, Junyeop Lee, Jaeheung Surh, Minjoon Seo, and Hwalsuk Lee. Cord: a consolidated receipt dataset for post-ocr parsing. In Workshop on Document Intelligence at NeurIPS 2019, 2019. 2  
+[36] Akshay Gadi Patil, Omri Ben-Eliezer, Or Perel, and Hadar Averbuch-Elor. Read: Recursive autoencoders for document layout generation. In CVPRW, pages 544–545, 2020. 2  
+[37] Qiming Peng, Yinxu Pan, Wenjin Wang, Bin Luo, Zhenyu Zhang, Zhengjie Huang, Yuhui Cao, Weichong Yin, Yongfeng Chen, Yin Zhang, Shikun Feng, Yu Sun, Hao Tian, Hua Wu, and Haifeng Wang. ERNIE.layout: Layout knowledge enhanced pre-training for visually-rich document understanding. In Findings of the Association for Computational Linguistics: EMNLP 2022, pages 3744-3756, Abu Dhabi, United Arab Emirates, 2022. Association for Computational Linguistics. 1, 3  
+[38] Partha Pratim Ray. Chatgpt: A comprehensive review on background, applications, key challenges, bias, ethics, limitations and future scope. _Internet of Things and CyberPhysical Systems_, 3:121-154, 2023. 1, 6, 7  
+[39] Štepan Šimsa, Milan Šulc, Michal Uřicář, Yash Patel, Ahmed Hamdi, Matej Kocián, Matyáš Skalický, Jíří Matas, Antoine Doucet, Mickaël Coustaty, et al. Docile benchmark for document information localization and extraction. In International Conference on Document Analysis and Recognition, pages 147-166. Springer, 2023. 2  
+[40] Zecheng Tang, Chenfei Wu, Juntao Li, and Nan Duan. LayoutNUWA: Revealing the hidden layout expertise of large language models. In ICLR, 2024. 1, 2, 3, 4, 6  
+[41] Yi Tu, Ya Guo, Huan Chen, and Jinyang Tang. LayoutMask: Enhance text-Layout interaction in multi-modal pre-training for document understanding. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 15200–15212, Toronto, Canada, 2023. Association for Computational Linguistics. 1, 3  
+[42] Dongsheng Wang, Natraj Raman, Mathieu Sibue, Zhiqiang Ma, Petr Babkin, Simerjot Kaur, Yulong Pei, Armineh Nourbakhsh, and Xiaomo Liu. DocLLM: A layout-aware generative language model for multimodal document understanding. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 8529-8548, Bangkok, Thailand, 2024. Association for Computational Linguistics. 3  
+[43] Jiapeng Wang, Chongyu Liu, Lianwen Jin, Guozhi Tang, Jiaxin Zhang, Shuai tao Zhang, Qianying Wang, Yaqiang Wu, and Mingxiang Cai. Towards robust visual information extraction in real world: new dataset and novel solution. In AAAI, pages 2738-2745, 2021. 2, 1  
+[44] Peng Wang, Shuai Bai, Sinan Tan, Shijie Wang, Zhihao Fan, Jinze Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Yang Fan, Kai Dang, Mengfei Du, Xuancheng Ren, Rui Men, Dayiheng Liu, Chang Zhou, Jingren Zhou, and Junyang Lin. Qwen2-vl: Enhancing vision-language model's perception of the world at any resolution. arXiv preprint arXiv:2409.12191, 2024. 1, 5, 6, 7, 8, 3  
+[45] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian richter, Fei Xia, Ed Chi, Quoc V Le, and Denny
+
+Zhou. Chain-of-thought prompting elicits reasoning in large language models. In NeurIPS, pages 24824-24837. Curran Associates, Inc., 2022. 5  
+[46] Yiheng Xu, Minghao Li, Lei Cui, Shaohan Huang, Furu Wei, and Ming Zhou. Layoutm: Pre-training of text and layout for document image understanding. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pages 1192-1200, 2020. 1, 3  
+[47] Yang Xu, Yiheng Xu, Tengchao Lv, Lei Cui, Furu Wei, Guoxin Wang, Yijuan Lu, Dinei Florencio, Cha Zhang, Wanxiang Che, Min Zhang, and Lidong Zhou. LayoutLMv2: Multi-modal pre-training for visually-rich document understanding. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 2579-2591, Online, 2021. Association for Computational Linguistics. 1, 3  
+[48] Yiheng Xu, Tengchao Lv, Lei Cui, Guoxin Wang, Yijuan Lu, Dinei Florencio, Cha Zhang, and Furu Wei. XFUND: A benchmark dataset for multilingual visually rich form understanding. In Findings of the Association for Computational Linguistics: ACL 2022, Dublin, Ireland, 2022. Association for Computational Linguistics. 2, 6  
+[49] Jiabo Ye, Anwen Hu, Haiyang Xu, Qinghao Ye, Ming Yan, Guohai Xu, Chenliang Li, Junfeng Tian, Qi Qian, Ji Zhang, Qin Jin, Liang He, Xin Lin, and Fei Huang. UReader: Universal OCR-free visually-situated language understanding with multimodal large language model. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 2841-2858, Singapore, 2023. Association for Computational Linguistics. 3  
+[50] Wenwen Yu, Chengquan Zhang, Haoyu Cao, Wei Hua, Bohan Li, Huang Chen, Mingyu Liu, Mingrui Chen, Jianfeng Kuang, Mengjun Cheng, et al. Icdar 2023 competition on structured text extraction from visually-rich document images. In International Conference on Document Analysis and Recognition, pages 536-552. Springer, 2023. 6

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+# Relative Pose Estimation through Affine Corrections of Monocular Depth Priors
+
+Yifan Yu $^{1,2*}$  Shaohui Liu $^{1}$  Rémi Pautrat $^{3}$  Marc Pollefeys $^{1,3}$  Viktor Larsson $^{4}$ $^{1}$ ETH Zurich  $^{2}$ PICO  $^{3}$ Microsoft Spatial AI Lab  $^{4}$ Lund University
+
+# Abstract
+
+Monocular depth estimation (MDE) models have undergone significant advancements over recent years. 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 scenes<sup>1</sup> 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
+
+<table><tr><td rowspan="2">Matches</td><td rowspan="2">Method</td><td rowspan="2">MD Model</td><td colspan="2">Med. Err. ↓</td><td colspan="3">Pose Error AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td rowspan="7">SP+LG</td><td>PoseLib-5pt</td><td>-</td><td>1.86</td><td>5.53</td><td>21.55</td><td>39.11</td><td>55.60</td></tr><tr><td>PoseLib-PnP</td><td>DA-met.</td><td>2.03</td><td>6.44</td><td>15.05</td><td>34.16</td><td>53.97</td></tr><tr><td>PoseLib-PnP</td><td>MoGe</td><td>1.72</td><td>5.37</td><td>19.69</td><td>40.21</td><td>58.73</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>DA-met.</td><td>1.90</td><td>5.67</td><td>20.62</td><td>38.45</td><td>54.94</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>MoGe</td><td>1.88</td><td>5.66</td><td>20.74</td><td>38.53</td><td>54.98</td></tr><tr><td>Ours-calib</td><td>DA-met.</td><td>1.68</td><td>4.97</td><td>22.41</td><td>42.18</td><td>59.96</td></tr><tr><td>Ours-calib</td><td>MoGe</td><td>1.57</td><td>4.77</td><td>23.36</td><td>43.39</td><td>61.08</td></tr><tr><td rowspan="7">RoMa</td><td>PoseLib-5pt</td><td>-</td><td>1.29</td><td>3.18</td><td>33.40</td><td>55.34</td><td>72.41</td></tr><tr><td>PoseLib-PnP</td><td>DA-met.</td><td>1.63</td><td>4.46</td><td>22.83</td><td>47.04</td><td>68.12</td></tr><tr><td>PoseLib-PnP</td><td>MoGe</td><td>1.38</td><td>3.75</td><td>28.38</td><td>52.62</td><td>71.61</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>DA-met.</td><td>1.32</td><td>3.27</td><td>32.27</td><td>54.34</td><td>71.72</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>MoGe</td><td>1.33</td><td>3.29</td><td>32.21</td><td>54.29</td><td>71.62</td></tr><tr><td>Ours-calib</td><td>DA-met.</td><td>1.26</td><td>3.14</td><td>34.21</td><td>56.55</td><td>73.55</td></tr><tr><td>Ours-calib</td><td>MoGe</td><td>1.24</td><td>3.12</td><td>34.26</td><td>56.77</td><td>73.67</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Matches</td><td rowspan="2">Method</td><td rowspan="2">MD Model</td><td colspan="2">Med. Err. ↓</td><td colspan="3">Pose Error AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td rowspan="7">SP+LG</td><td>PoseLib-5pt</td><td>-</td><td>0.46</td><td>1.23</td><td>60.16</td><td>74.25</td><td>84.34</td></tr><tr><td>PoseLib-PnP</td><td>DA-met.</td><td>0.99</td><td>3.29</td><td>34.79</td><td>54.55</td><td>72.32</td></tr><tr><td>PoseLib-PnP</td><td>MoGe</td><td>0.56</td><td>1.80</td><td>52.46</td><td>71.05</td><td>83.80</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>DA-met.</td><td>0.52</td><td>1.37</td><td>57.83</td><td>72.85</td><td>83.73</td></tr><tr><td>2PT+D&amp;5pt [4]</td><td>MoGe</td><td>0.54</td><td>1.44</td><td>55.86</td><td>70.97</td><td>82.20</td></tr><tr><td>Ours-calib</td><td>DA-met.</td><td>0.47</td><td>1.26</td><td>59.80</td><td>74.77</td><td>85.47</td></tr><tr><td>Ours-calib</td><td>MoGe</td><td>0.41</td><td>1.16</td><td>63.48</td><td>77.79</td><td>87.18</td></tr></table>
+
+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].  
+
+<table><tr><td rowspan="2">Matches</td><td rowspan="2">Method</td><td rowspan="2">MD Model</td><td colspan="3">Med. Err. ↓</td><td colspan="3">Pose Err. AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>εf(%)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td rowspan="3">SP+LG</td><td>PoseLib-6pt</td><td>-</td><td>2.71</td><td>8.05</td><td>10.94</td><td>14.19</td><td>29.49</td><td>45.47</td></tr><tr><td>3p3d [17]</td><td>DAv2</td><td>3.27</td><td>9.37</td><td>13.66</td><td>12.09</td><td>26.09</td><td>41.88</td></tr><tr><td>Ours-sf</td><td>DA-met.</td><td>1.93</td><td>5.78</td><td>6.99</td><td>17.74</td><td>36.71</td><td>55.12</td></tr><tr><td rowspan="3">RoMa</td><td>PoseLib-6pt</td><td>-</td><td>1.52</td><td>3.85</td><td>4.49</td><td>27.17</td><td>49.24</td><td>67.42</td></tr><tr><td>3p3d [17]</td><td>DAv2</td><td>1.64</td><td>4.15</td><td>5.30</td><td>25.46</td><td>47.17</td><td>65.47</td></tr><tr><td>Ours-sf</td><td>DA-met.</td><td>1.37</td><td>3.54</td><td>3.71</td><td>29.81</td><td>53.11</td><td>71.15</td></tr><tr><td rowspan="4">MASt3R</td><td>PoseLib-6pt</td><td>-</td><td>1.44</td><td>3.31</td><td>4.18</td><td>30.28</td><td>54.16</td><td>72.87</td></tr><tr><td>3p3d [17]</td><td>DAv2</td><td>1.51</td><td>3.40</td><td>4.54</td><td>29.17</td><td>52.28</td><td>71.08</td></tr><tr><td>Ours-sf</td><td>DA-met.</td><td>1.35</td><td>3.09</td><td>3.73</td><td>31.87</td><td>56.20</td><td>74.51</td></tr><tr><td></td><td>MASt3R</td><td>1.32</td><td>3.06</td><td>3.79</td><td>32.58</td><td>56.99</td><td>74.91</td></tr><tr><td colspan="3">Reference entry - DUSt3R</td><td>1.29</td><td>4.02</td><td>3.80</td><td>25.90</td><td>48.45</td><td>68.03</td></tr><tr><td colspan="3">Reference entry - MAST3R</td><td>1.53</td><td>4.22</td><td>5.72</td><td>23.94</td><td>46.44</td><td>66.18</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Matches</td><td rowspan="2">Method</td><td rowspan="2">MD Model</td><td colspan="3">Med. Err. ↓</td><td colspan="4">Pose Err. AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>εf(%)</td><td>@2°</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td rowspan="3">SP+LG</td><td>PoseLib-7pt</td><td>-</td><td>16.83</td><td>21.57</td><td>59.88</td><td>5.85</td><td>13.95</td><td>21.94</td><td>30.71</td></tr><tr><td>4p4d [17]</td><td>DAv2</td><td>19.27</td><td>21.64</td><td>66.57</td><td>5.31</td><td>13.66</td><td>21.78</td><td>30.22</td></tr><tr><td>Ours-tf</td><td>DAv2-met.</td><td>5.66</td><td>9.26</td><td>29.06</td><td>9.15</td><td>22.22</td><td>32.80</td><td>43.26</td></tr><tr><td rowspan="3">RoMa</td><td>PoseLib-7pt</td><td>-</td><td>7.99</td><td>8.77</td><td>37.72</td><td>8.73</td><td>20.31</td><td>30.45</td><td>41.48</td></tr><tr><td>4p4d [17]</td><td>DAv2</td><td>10.94</td><td>11.35</td><td>44.94</td><td>7.23</td><td>16.50</td><td>25.31</td><td>36.26</td></tr><tr><td>Ours-tf</td><td>DAv2-met.</td><td>3.33</td><td>4.32</td><td>17.29</td><td>13.50</td><td>29.19</td><td>42.18</td><td>54.42</td></tr><tr><td rowspan="4">MASt3R</td><td>PoseLib-7pt</td><td>-</td><td>3.21</td><td>3.34</td><td>19.95</td><td>12.58</td><td>30.27</td><td>45.57</td><td>59.85</td></tr><tr><td>4p4d [17]</td><td>DAv2</td><td>3.21</td><td>3.28</td><td>20.07</td><td>12.13</td><td>29.82</td><td>45.30</td><td>60.05</td></tr><tr><td>Ours-tf</td><td>DAv2-met.</td><td>1.98</td><td>2.22</td><td>11.27</td><td>18.05</td><td>39.92</td><td>56.64</td><td>70.86</td></tr><tr><td></td><td>MASt3R</td><td>1.33</td><td>1.66</td><td>7.93</td><td>22.44</td><td>48.02</td><td>64.79</td><td>76.55</td></tr><tr><td colspan="3">Reference entry - DUS3R</td><td>2.65</td><td>4.65</td><td>7.41</td><td>6.43</td><td>24.47</td><td>42.39</td><td>58.36</td></tr><tr><td colspan="3">Reference entry - MAST3R</td><td>1.71</td><td>2.49</td><td>2.91</td><td>13.39</td><td>38.41</td><td>57.92</td><td>71.91</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">MD Model</td><td colspan="3">Med. Err. ↓</td><td colspan="3">Pose Err. AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>εf(%)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td>PoseLib-7pt</td><td>-</td><td>1.97</td><td>5.72</td><td>23.64</td><td>21.23</td><td>36.80</td><td>54.89</td></tr><tr><td>4p4d [17]</td><td>DAv2</td><td>3.48</td><td>8.70</td><td>39.92</td><td>14.04</td><td>26.70</td><td>44.08</td></tr><tr><td>Ours-tf</td><td>DA-met.</td><td>1.25</td><td>4.81</td><td>15.99</td><td>25.70</td><td>42.90</td><td>61.79</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">MD Model</td><td rowspan="2">Hybrid</td><td rowspan="2">Shift</td><td colspan="2">Med. ER↓</td><td colspan="3">Pose Error AUC (%)↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td rowspan="8">ScanNet -1500</td><td rowspan="4">DA-met.</td><td>✓</td><td>✓</td><td>1.74</td><td>4.73</td><td>23.12</td><td>43.37</td><td>62.26</td></tr><tr><td>✓</td><td></td><td>1.80</td><td>5.09</td><td>19.96</td><td>41.45</td><td>61.58</td></tr><tr><td></td><td>✓</td><td>1.88</td><td>5.33</td><td>19.13</td><td>40.21</td><td>60.65</td></tr><tr><td></td><td></td><td>2.00</td><td>5.85</td><td>16.63</td><td>37.24</td><td>59.37</td></tr><tr><td rowspan="4">Marigold</td><td>✓</td><td>✓</td><td>1.87</td><td>5.05</td><td>20.68</td><td>40.71</td><td>59.92</td></tr><tr><td>✓</td><td></td><td>2.85</td><td>9.17</td><td>12.34</td><td>26.64</td><td>44.53</td></tr><tr><td></td><td>✓</td><td>2.19</td><td>6.41</td><td>14.70</td><td>33.73</td><td>54.75</td></tr><tr><td></td><td></td><td>6.24</td><td>20.44</td><td>1.09</td><td>4.84</td><td>17.15</td></tr><tr><td rowspan="4">MegaDepth -1500</td><td rowspan="4">MoGe</td><td>✓</td><td>✓</td><td>0.42</td><td>1.16</td><td>63.48</td><td>77.44</td><td>86.85</td></tr><tr><td>✓</td><td></td><td>0.63</td><td>1.90</td><td>51.32</td><td>70.09</td><td>83.02</td></tr><tr><td></td><td>✓</td><td>0.55</td><td>1.56</td><td>56.87</td><td>73.80</td><td>85.11</td></tr><tr><td></td><td></td><td>0.74</td><td>2.45</td><td>44.15</td><td>64.90</td><td>79.84</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Solver</td><td rowspan="2">LO</td><td rowspan="2">Score</td><td colspan="3">Med. Err. ↓</td><td colspan="3">Pose Error AUC (%) ↑</td></tr><tr><td>εR(°)</td><td>εt(°)</td><td>εf(%)</td><td>@5°</td><td>@10°</td><td>@20°</td></tr><tr><td>H</td><td>H</td><td>H</td><td>2.00</td><td>5.70</td><td>6.84</td><td>18.35</td><td>37.54</td><td>57.58</td></tr><tr><td>D</td><td>H</td><td>H</td><td>2.20</td><td>5.89</td><td>7.42</td><td>17.17</td><td>36.17</td><td>56.03</td></tr><tr><td>P</td><td>H</td><td>H</td><td>2.20</td><td>6.10</td><td>7.36</td><td>16.60</td><td>35.33</td><td>55.26</td></tr><tr><td>D</td><td>D</td><td>H</td><td>2.22</td><td>6.33</td><td>7.95</td><td>15.42</td><td>34.39</td><td>55.14</td></tr><tr><td>P</td><td>P</td><td>H</td><td>2.42</td><td>6.68</td><td>9.09</td><td>15.06</td><td>32.32</td><td>51.00</td></tr><tr><td>D</td><td>D</td><td>D</td><td>2.21</td><td>6.83</td><td>8.18</td><td>13.85</td><td>32.11</td><td>53.50</td></tr><tr><td>P</td><td>P</td><td>P</td><td>2.84</td><td>7.45</td><td>11.30</td><td>14.06</td><td>29.86</td><td>48.13</td></tr></table>
+
+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. In ECCV, 2024. 2  
+[6] Axel Barroso-Laguna, Eric Brachmann, Victor Adrian Prisacariu, Gabriel J Brostow, and Daniyar Turmukhambetov. Two-view geometry scoring without correspondences. In CVPR, 2023. 2  
+[7] Shariq Farooq Bhat, Ibraheem Alhashim, and Peter Wonka. Adabins: Depth estimation using adaptive bins. In CVPR, 2021. 2  
+[8] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. Zoedepth: Zero-shot transfer by combining relative and metric depth. arXiv:2302.12288, 2023. 1, 2  
+[9] Reiner Birkl, Diana Wofk, and Matthias Muller. Midas v3.1 - a model zoo for robust monocular relative depth estimation. arXiv:2307.14460, 2023. 1, 3  
+[10] Aleksei Bochkovskii, Amaël Delaunoy, Hugo Germain, Marcel Santos, Yichao Zhou, Stephan R Richter, and Vladlen Koltun. Depth pro: Sharp monocular metric depth in less than a second. arXiv:2410.02073, 2024. 2  
+[11] Sylvain Bougnoux. From projective to euclidean space under any practical situation, a criticism of self-calibration. In ICCV, 1998. 5  
+[12] Federico Camposeco, Andrea Cohen, Marc Pollefeys, and Torsten Sattler. Hybrid Camera Pose Estimation. In CVPR, 2018. 3, 5  
+[13] Ondrej Chum, Jiří Matas, and Josef Kittler. Locally optimized ransac. In Pattern Recognition: 25th DAGM Symposium, Magdeburg, Germany, September 10-12, 2003. Proceedings 25, 2003. 2  
+[14] Jan Czarnowski, Tristan Laidlow, Ronald Clark, and Andrew J Davison. Deepfactors: Real-time probabilistic dense monocular slam. IEEE Robotics and Automation Letters, 5 (2):721-728, 2020. 1, 2  
+[15] Angela Dai, Angel X. Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In CVPR, 2017. 5, 6, 8, 12, 13, 16  
+[16] Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superpoint: Self-supervised interest point detection and description. In CVPR Deep Learning for Visual SLAM Workshop, 2018. 2, 3, 5  
+[17] Yaqing Ding, Václav Várvá, Snehal Bhayani, Qianliang Wu, Jian Yang, and Zuzana Kukelova. Fundamental matrix estimation using relative depths. In ECCV, 2024. 1, 2, 5, 6, 7, 12
+
+[18] Mihai Dusmanu, Ignacio Rocco, Tomas Pajdla, Marc Pollefeys, Josef Sivic, Akihiko Torii, and Torsten Sattler. D2-net: A trainable cnn for joint detection and description of local features. arXiv:1905.03561, 2019. 2  
+[19] Johan Edstedt, Ioannis Athanasiadis, Mårten Wadenback, and Michael Felsberg. Dkm: Dense kernelized feature matching for geometry estimation. In CVPR, 2023. 2  
+[20] Johan Edstedt, Qiyu Sun, Georg Bokman, Marten Wadenback, and Michael Felsberg. Roma: Robust dense feature matching. In CVPR, 2024. 2, 3, 6  
+[21] Ainaz Eftekhar, Alexander Sax, Jitendra Malik, and Amir Zamir. Omnidata: A scalable pipeline for making multi-task mid-level vision datasets from 3d scans. In CVPR, 2021. 3  
+[22] Ivan Eichhardt and Daniel Barath. Relative pose from deep learned depth and a single affine correspondence. In ECCV, 2020. 2  
+[23] David Eigen, Christian Puhrsch, and Rob Fergus. Depth map prediction from a single image using a multi-scale deep network. In NeurIPS, 2014. 2  
+[24] Martin A. Fischler and Robert C. Bolles. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM, 1981. 5  
+[25] Huan Fu, Mingming Gong, Chaohui Wang, Kayhan Bat-manghelich, and Dacheng Tao. Deep ordinal regression network for monocular depth estimation. In CVPR, 2018. 2  
+[26] Xiao Fu, Wei Yin, Mu Hu, Kaixuan Wang, Yuexin Ma, Ping Tan, Shaojie Shen, Dahua Lin, and Xiaoxiao Long. Geowizard: Unleashing the diffusion priors for 3d geometry estimation from a single image. In ECCV, 2024. 2  
+[27] Clément Godard, Oisin Mac Aodha, Michael Firman, and Gabriel J Brostow. Digging into self-supervised monocular depth estimation. In CVPR, 2019. 2  
+[28] Vitor Guizilini, Rares Ambrus, Sudeep Pillai, Allan Raventos, and Adrien Gaidon. 3d packing for self-supervised monocular depth estimation. In CVPR, 2020. 1  
+[29] Richard Hartley and Andrew Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2004. 2, 3, 5  
+[30] Wenzel Jakob, Jason Rhinelander, and Dean Moldovan. pybind11 - seamless operability between c++11 and python, 2017. https://github.com/pybind/pybind11.6  
+[31] Oğuzhan Fatih Kar, Teresa Yeo, Andrei Atanov, and Amir Zamir. 3d common corruptions and data augmentation. In CVPR, 2022. 1, 6, 12  
+[32] Bingxin Ke, Anton Obukhov, Shengyu Huang, Nando Metzger, Rodrigo Caye Daudt, and Konrad Schindler. Repurposing diffusion-based image generators for monocular depth estimation. In CVPR, 2024. 1, 2, 3, 6, 7, 8, 12, 15  
+[33] Viktor Larsson and contributors. PoseLib - Minimal Solvers for Camera Pose Estimation, 2020. 2, 5, 12, 15  
+[34] Viktor Larsson, Kalle Astrom, and Magnus Oskarsson. Efficient solvers for minimal problems by syzygy-based reduction. In CVPR, 2017. 4, 13  
+[35] Karel Lebeda, Jiri Matas, and Ondrej Chum. Fixing the Locally Optimized RANSAC. In BMVC, 2012. 3, 5
+
+[36] Karel Lebeda, Jiri Matas, and Ondrej Chum. Fixing the locally optimized ransac-full experimental evaluation. In BMVC, 2012. 2  
+[37] Vincent Leroy, Yohann Cabon, and Jérôme Revaud. Grounding image matching in 3d with mast3r. In ECCV, 2024. 2, 5, 6, 7  
+[38] Zhengqi Li and Noah Snavely. Megadepth: Learning single-view depth prediction from internet photos. In CVPR, 2018, 2, 5, 6, 7, 8, 12  
+[39] Zhenyu Li, Xuyang Wang, Xianming Liu, and Junjun Jiang. Binsformer: Revisiting adaptive bins for monocular depth estimation. IEEE Transactions on Image Processing, 2024. 2  
+[40] Philipp Lindenberger, Paul-Edouard Sarlin, and Marc Pollefeys. LightGlue: Local Feature Matching at Light Speed. In ICCV, 2023. 2, 3, 5  
+[41] Sheng Liu, Xiaohan Nie, and Raffay Hamid. Depth-guided sparse structure-from-motion for movies and tv shows. In CVPR, 2022. 1, 2, 5  
+[42] Shing Yan Loo, Syamsiah Mashohor, Sai Hong Tang, and Hong Zhang. Deeprelativefusion: Dense monocular slam using single-image relative depth prediction. In IROS, 2021. 2  
+[43] David G Lowe. Distinctive image features from scale-invariant keypoints. IJCV, 60:91-110, 2004. 2  
+[44] Xuan Luo, Jia-Bin Huang, Richard Szeliski, Kevin Matzen, and Johannes Kopf. Consistent video depth estimation. ACM TOG, 39(4):71-1, 2020. 2  
+[45] Quang-Tuan Luong and Olivier D. Faugeras. The fundamental matrix: Theory, algorithms, and stability analysis. IJCV, 1996. 5  
+[46] David Nister. An efficient solution to the five-point relative pose problem. In CVPR, 2003. 2, 3, 5  
+[47] Suraj Patni, Aradhye Agarwal, and Chetan Arora. Ecodepth: Effective conditioning of diffusion models for monocular depth estimation. In CVPR, 2024. 2  
+[48] Luigi Piccinelli, Yung-Hsu Yang, Christos Sakaridis, Mattia Segu, Siyuan Li, Luc Van Gool, and Fisher Yu. Unidepth: Universal monocular metric depth estimation. In CVPR, 2024. 1, 2  
+[49] Matia Pizzoli, Christian Forster, and Davide Scaramuzza. Remode: Probabilistic, monocular dense reconstruction in real time. In ICRA, 2014. 2  
+[50] René Ranftl and Vladlen Koltun. Deep fundamental matrix estimation. In ECCV, 2018. 2  
+[51] René Ranftl, Katrin Lasinger, David Hafner, Konrad Schindler, and Vladlen Koltun. Towards robust monocular depth estimation: Mixing datasets for zero-shot cross-dataset transfer. IEEE TPAMI, 44(3), 2022. 2, 3  
+[52] Anirban Roy and Sinisa Todorovic. Monocular depth estimation using neural regression forest. In CVPR, 2016. 2  
+[53] Paul D. Sampson. Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm. Comput. Graph. Image Process., 1982. 2, 5  
+[54] Paul-Edouard Sarlin, Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. SuperGlue: Learning feature matching with graph neural networks. In CVPR, 2020. 2
+
+[55] Torsten Sattler et al. RansacLib - A Template-based *SAC Implementation, 2019. 6  
+[56] Ashutosh Saxena, Sung Chung, and Andrew Ng. Learning depth from single monocular images. In NeurIPS, 2005. 2  
+[57] Ashutosh Saxena, Min Sun, and Andrew Y Ng. Make3d: Learning 3d scene structure from a single still image. IEEE TPAMI, 31(5):824-840, 2008. 2  
+[58] Saurabh Saxena, Charles Herrmann, Junhwa Hur, Abhishek Kar, Mohammad Norouzi, Deqing Sun, and David J Fleet. The surprising effectiveness of diffusion models for optical flow and monocular depth estimation. In NeurIPS, 2024. 2  
+[59] Thomas Schöps, Johannes L. Schonberger, Silvano Galliani, Torsten Sattler, Konrad Schindler, Marc Pollefeys, and Andreas Geiger. A multi-view stereo benchmark with high-resolution images and multi-camera videos. In CVPR, 2017. 5, 7, 12, 13, 15  
+[60] Peter H Schonemann. A generalized solution of the orthogonal procrustes problem. In Psychometrika, 1966. 4  
+[61] Mengyi Shan, Brian Curless, Ira Kemelmacher-Shlizerman, and Steve Seitz. Animating street view. In SIGGRAPH Asia 2023 Conference Papers, pages 1-12, 2023. 1  
+[62] Jiuhn Song, Seonghoon Park, Honggyu An, Seokju Cho, Min-Seop Kwak, Sungjin Cho, and Seungryong Kim. Därf: boosting radiance fields from sparse inputs with monocular depth adaptation. In NeurIPS, 2023. 2  
+[63] Henrik Stewénius, David Nister, Fredrik Kahl, and Frederik Schaffalitzky. A minimal solution for relative pose with unknown focal length. Image and Vision Computing, 2008. 2, 3, 5  
+[64] Jiaming Sun, Zehong Shen, Yuang Wang, Hujun Bao, and Xiaowei Zhou. Loftr: Detector-free local feature matching with transformers. In CVPR, 2021. 2  
+[65] Keisuke Tateno, Federico Tombari, Iro Laina, and Nassir Navab. Cnn-slam: Real-time dense monocular slam with learned depth prediction. In CVPR, pages 6243-6252, 2017. 2  
+[66] Prune Truong, Martin Danelljan, Radu Timofte, and Luc Van Gool. Pdc-net+: Enhanced probabilistic dense correspondence network. IEEE TPAMI, 45(8):10247-10266, 2023. 2  
+[67] Michal Tyszkiiewicz, Pascal Fua, and Eduard Trulls. Disk: Learning local features with policy gradient. In NeurIPS, 2020. 2  
+[68] Qing Wang, Jiaming Zhang, Kailun Yang, Kunyu Peng, and Rainer Stiefelhagen. Matchformer: Interleaving attention in transformers for feature matching. In ACCV, 2022. 2  
+[69] Ruicheng Wang, Sicheng Xu, Cassie Dai, Jianfeng Xiang, Yu Deng, Xin Tong, and Jiaolong Yang. Moge: Unlocking accurate monocular geometry estimation for open-domain images with optimal training supervision. In CVPR, 2025. 1, 2, 6, 7, 12  
+[70] Shuzhe Wang, Vincent Leroy, Yohann Cabon, Boris Chidlovskii, and Jerome Revaud. Dust3r: Geometric 3d vision made easy. In CVPR, 2024. 2, 5, 6  
+[71] Tong Wei, Yash Patel, Alexander Shekhotsov, Jiri Matas, and Daniel Barath. Generalized differentiable ransac. In ICCV, 2023. 2
+
+[72] Yi Wei, Shaohui Liu, Yongming Rao, Wang Zhao, Jiwen Lu, and Jie Zhou. Nerfingmvs: Guided optimization of neural radiance fields for indoor multi-view stereo. In ICCV, 2021. 2  
+[73] Haofei Xu, Songyou Peng, Fangjinhua Wang, Hermann Blum, Daniel Barath, Andreas Geiger, and Marc Pollefeys. Depthsplat: Connecting gaussian splatting and depth. In CVPR, 2025. 2  
+[74] Lihe Yang, Bingyi Kang, Zilong Huang, Xiaogang Xu, Jiashi Feng, and Hengshuang Zhao. Depth anything: Unleashing the power of large-scale unlabeled data. In CVPR, 2024. 1, 2, 6, 8, 12  
+[75] Lihe Yang, Bingyi Kang, Zilong Huang, Zhen Zhao, Xiaogang Xu, Jiashi Feng, and Hengshuang Zhao. Depth anything v2. In NeurIPS, 2024. 1, 2, 3, 6, 7, 12, 13  
+[76] Wei Yin, Chi Zhang, Hao Chen, Zhipeng Cai, Gang Yu, Kaixuan Wang, Xiaozhi Chen, and Chunhua Shen. Metric3d: Towards zero-shot metric 3d prediction from a single image. In ICCV, 2023. 1, 2  
+[77] Zehao Yu, Songyou Peng, Michael Niemeyer, Torsten Sattler, and Andreas Geiger. Monosdf: Exploring monocular geometric cues for neural implicit surface reconstruction. In NeurIPS, 2022. 2  
+[78] Ziyao Zeng, Daniel Wang, Fengyu Yang, Hyoungseob Park, Stefano Soatto, Dong Lao, and Alex Wong. Wordepth: Variational language prior for monocular depth estimation. In CVPR, 2024. 2  
+[79] Xinyue Zhang, Jiaqi Yang, Xiangting Meng, Abdelrahman Mohamed, and Laurent Kneip. fcop: Focal length estimation from category-level object priors. arXiv:2409.19641, 2024. 2  
+[80] Wang Zhao, Shaohui Liu, Yezhi Shu, and Yong-Jin Liu. Towards better generalization: Joint depth-posed learning without posenet. In CVPR, 2020. 2  
+[81] Xiaoming Zhao, Xingming Wu, Weihai Chen, Peter CY Chen, Qingsong Xu, and Zhengguo Li. Aliked: A lighter keypoint and descriptor extraction network via deformable transformation. IEEE Transactions on Instrumentation and Measurement, 72:1-16, 2023. 2  
+[82] Qunjie Zhou, Torsten Sattler, Marc Pollefeys, and Laura Leal-Taixe. To learn or not to learn: Visual localization from essential matrices. In ICRA, 2020. 2

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+# Reloc3r: Large-Scale Training of Relative Camera Pose Regression for Generalizable, Fast, and Accurate Visual Localization
+
+Siyan Dong $^{1*}$  Shuzhe Wang $^{2*}$  Shaohui Liu $^{3}$  Lulu Cai $^{1}$
+
+Qingnan Fan $^{4}$  Juho Kannala $^{2,5\dagger}$  Yanchao Yang $^{1\dagger}$
+
+$^{1}$ The University of Hong Kong  $^{2}$ Aalto University  $^{3}$ ETH Zurich  $^{4}$ VIVO  $^{5}$ University of Oulu
+
+# Abstract
+
+Visual localization aims to determine the camera pose of a query image relative to a database of posed images. 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.
+
+<table><tr><td>Datasets</td><td>Scene type</td><td>Number of image pairs</td></tr><tr><td>CO3Dv2 [75]</td><td>Object-centric</td><td>~1M</td></tr><tr><td>ScanNet++ [123]</td><td>Indoor</td><td>~850K</td></tr><tr><td>ARKitScenes [12]</td><td>Indoor</td><td>~2.1M</td></tr><tr><td>BlendedMVS [121]</td><td>Outdoor</td><td>~1M</td></tr><tr><td>MegaDepth [56]</td><td>Outdoor</td><td>~1.8M</td></tr><tr><td>DL3DV [61]</td><td>Indoor &amp; outdoor</td><td>~1.1M</td></tr><tr><td>RealEstate10K [130]</td><td>Indoor &amp; outdoor</td><td>~100K</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td>Methods</td><td>RRA@15</td><td>RTA@15</td><td>mAA@30</td></tr><tr><td rowspan="8">Non-PR</td><td>PixSfM [59]</td><td>33.7</td><td>32.9</td><td>30.1</td></tr><tr><td>RelPose [127]</td><td>57.1</td><td>-</td><td>-</td></tr><tr><td>PoseDiffusion [106]</td><td>80.5</td><td>79.8</td><td>66.5</td></tr><tr><td>RelPose++ [57]</td><td>82.3</td><td>77.2</td><td>65.1</td></tr><tr><td>RayDiffusion* [128]</td><td>93.3</td><td>-</td><td>-</td></tr><tr><td>VGGSfM [107]</td><td>92.1</td><td>88.3</td><td>74.0</td></tr><tr><td>DUSt3R (w/ PnP) [111]</td><td>94.3</td><td>88.4</td><td>77.2</td></tr><tr><td>MASt3R [51]</td><td>94.6</td><td>91.9</td><td>81.1</td></tr><tr><td rowspan="4">PR</td><td>PoseReg [106]</td><td>53.2</td><td>49.1</td><td>45.0</td></tr><tr><td>RayReg* [128]</td><td>89.2</td><td>-</td><td>-</td></tr><tr><td>Reloc3r-224 (Ours)</td><td>93.6</td><td>91.9</td><td>79.1</td></tr><tr><td>Reloc3r-512 (Ours)</td><td>95.8</td><td>93.7</td><td>82.9</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Methods</td><td colspan="3">ScanNet1500</td><td colspan="3">RealEstate10K</td><td colspan="3">ACID</td><td rowspan="2">Inference time</td></tr><tr><td>AUC@5</td><td>AUC@10</td><td>AUC@20</td><td>AUC@5</td><td>AUC@10</td><td>AUC@20</td><td>AUC@5</td><td>AUC@10</td><td>AUC@20</td></tr><tr><td rowspan="5">Non-PR</td><td>Efficient LoFTR [112]</td><td>19.20</td><td>37.00</td><td>53.60</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>40 ms</td></tr><tr><td>ROMA [34]</td><td>28.90</td><td>50.40</td><td>68.30</td><td>54.60</td><td>69.80</td><td>79.70</td><td>46.30</td><td>58.80</td><td>68.90</td><td>300 ms</td></tr><tr><td>DUSt3R [111]</td><td>23.81</td><td>45.91</td><td>65.57</td><td>39.70</td><td>56.88</td><td>70.43</td><td>21.50</td><td>35.95</td><td>49.70</td><td>441 ms</td></tr><tr><td>MASt3R [51]</td><td>28.01</td><td>50.24</td><td>68.83</td><td>63.54</td><td>76.39</td><td>84.50</td><td>52.12</td><td>64.54</td><td>73.61</td><td>294 ms</td></tr><tr><td>NoPoSplat [122]</td><td>31.80</td><td>53.80</td><td>71.70</td><td>69.10</td><td>80.60</td><td>87.70</td><td>48.60</td><td>61.70</td><td>72.80</td><td>&gt;2000 ms</td></tr><tr><td rowspan="6">PR</td><td>Map-free (Regress-SN) [4]</td><td>1.84</td><td>8.75</td><td>25.33</td><td>0.83</td><td>4.06</td><td>13.97</td><td>1.32</td><td>5.82</td><td>16.28</td><td>10 ms</td></tr><tr><td>Map-free (Regress-MF) [4]</td><td>0.50</td><td>3.48</td><td>13.15</td><td>1.61</td><td>6.74</td><td>18.38</td><td>2.57</td><td>9.96</td><td>24.50</td><td>10 ms</td></tr><tr><td>ExReNet (SN) [116]</td><td>2.30</td><td>10.71</td><td>26.13</td><td>2.17</td><td>7.94</td><td>20.43</td><td>1.90</td><td>7.53</td><td>18.69</td><td>17 ms</td></tr><tr><td>ExReNet (SUNCG) [116]</td><td>1.61</td><td>7.00</td><td>18.03</td><td>3.27</td><td>12.06</td><td>27.85</td><td>4.14</td><td>13.43</td><td>27.70</td><td>17 ms</td></tr><tr><td>Reloc3r-224 (Ours)</td><td>28.34</td><td>52.60</td><td>71.56</td><td>59.70</td><td>75.05</td><td>84.71</td><td>28.25</td><td>47.34</td><td>62.54</td><td>15 ms</td></tr><tr><td>Reloc3r-512 (Ours)</td><td>34.79</td><td>58.37</td><td>75.56</td><td>66.70</td><td>80.20</td><td>88.39</td><td>38.18</td><td>56.39</td><td>70.34</td><td>25 ms</td></tr></table>
+
+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.  
+
+<table><tr><td></td><td>Methods</td><td>Chess</td><td>Fire</td><td>Heads</td><td>Office</td><td>Pumpkin</td><td>RedKitchen</td><td>Stairs</td><td>Average</td><td>Dataset-specific training time</td></tr><tr><td rowspan="4">APR</td><td>LENS [69]</td><td>0.03 / 1.30</td><td>0.10 / 3.70</td><td>0.07 / 5.80</td><td>0.07 / 1.90</td><td>0.08 / 2.20</td><td>0.09 / 2.20</td><td>0.14 / 3.60</td><td>0.08 / 3.00</td><td>Days / scene</td></tr><tr><td>PMNet [58]</td><td>0.03 / 1.26</td><td>0.04 / 1.76</td><td>0.02 / 1.68</td><td>0.06 / 1.69</td><td>0.07 / 1.96</td><td>0.08 / 2.23</td><td>0.11 / 2.97</td><td>0.06 / 1.93</td><td>Days / scene</td></tr><tr><td>DFNet [21]+NeFeS [22]</td><td>0.02 / 0.57</td><td>0.02 / 0.74</td><td>0.02 / 1.28</td><td>0.02 / 0.56</td><td>0.02 / 0.55</td><td>0.02 / 0.57</td><td>0.05 / 1.28</td><td>0.02 / 0.79</td><td>Days / scene</td></tr><tr><td>Marepo [23]</td><td>0.02 / 1.24</td><td>0.02 / 1.39</td><td>0.02 / 2.03</td><td>0.03 / 1.26</td><td>0.04 / 1.48</td><td>0.04 / 1.71</td><td>0.06 / 1.67</td><td>0.03 / 1.54</td><td>15min / scene</td></tr><tr><td rowspan="7">RPR (Seen)</td><td>EssNet (7S) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22 / 8.03</td><td>Hours</td></tr><tr><td>Relative PN (7S) [49]</td><td>0.13 / 6.46</td><td>0.26 / 12.72</td><td>0.14 / 12.34</td><td>0.21 / 7.35</td><td>0.24 / 6.35</td><td>0.24 / 8.03</td><td>0.27 / 11.82</td><td>0.21 / 9.30</td><td>Hours</td></tr><tr><td>NC-EssNet (7S) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.21 / 7.50</td><td>Hours</td></tr><tr><td>RelocNet (7S) [7]</td><td>0.12 / 4.14</td><td>0.26 / 10.4</td><td>0.14 / 10.5</td><td>0.18 / 5.32</td><td>0.26 / 4.17</td><td>0.23 / 5.08</td><td>0.28 / 7.53</td><td>0.21 / 6.73</td><td>Hours</td></tr><tr><td>Relpose-GNN [101]</td><td>0.08 / 2.70</td><td>0.21 / 7.50</td><td>0.13 / 8.70</td><td>0.15 / 4.10</td><td>0.15 / 3.50</td><td>0.19 / 3.70</td><td>0.22 / 6.50</td><td>0.16 / 5.20</td><td>Hours</td></tr><tr><td>AnchorNet [78]</td><td>0.06 / 3.89</td><td>0.15 / 10.3</td><td>0.08 / 10.9</td><td>0.09 / 5.15</td><td>0.10 / 2.97</td><td>0.08 / 4.68</td><td>0.10 / 9.26</td><td>0.09 / 6.74</td><td>Hours</td></tr><tr><td>CamNet [29]</td><td>0.04 / 1.73</td><td>0.03 / 1.74</td><td>0.05 / 1.98</td><td>0.04 / 1.62</td><td>0.04 / 1.64</td><td>0.04 / 1.63</td><td>0.04 / 1.51</td><td>0.04 / 1.69</td><td>Hours</td></tr><tr><td rowspan="11">RPR (Unseen)</td><td>EssNet (CL) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.57 / 80.06</td><td>None</td></tr><tr><td>NC-EssNet (CL) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.48 / 32.97</td><td>None</td></tr><tr><td>Relative PN (U) [49]</td><td>0.31 / 15.05</td><td>0.40 / 19.00</td><td>0.24 / 22.15</td><td>0.38 / 14.14</td><td>0.44 / 18.24</td><td>0.41 / 16.51</td><td>0.35 / 23.55</td><td>0.36 / 18.38</td><td>None</td></tr><tr><td>RelocNet (SN) [7]</td><td>0.21 / 10.9</td><td>0.32 / 11.8</td><td>0.15 / 13.4</td><td>0.31 / 10.3</td><td>0.40 / 10.9</td><td>0.33 / 10.3</td><td>0.33 / 11.4</td><td>0.29 / 11.3</td><td>None</td></tr><tr><td>ImageNet+NCM [129]†</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.19 / 4.30</td><td>None</td></tr><tr><td>Map-free (Match) [4]†</td><td>0.10 / 2.93</td><td>0.12 / 4.95</td><td>0.11 / 5.40</td><td>0.12 / 3.01</td><td>0.16 / 3.19</td><td>0.14 / 3.45</td><td>0.21 / 4.50</td><td>0.14 / 3.92</td><td>None</td></tr><tr><td>Map-free (Regress) [4]</td><td>0.09 / 2.66</td><td>0.13 / 4.54</td><td>0.11 / 4.81</td><td>0.11 / 2.77</td><td>0.16 / 3.11</td><td>0.14 / 3.48</td><td>0.18 / 4.70</td><td>0.13 / 3.72</td><td>None</td></tr><tr><td>ExReNet (SN) [116]</td><td>0.06 / 2.15</td><td>0.09 / 3.20</td><td>0.04 / 3.30</td><td>0.07 / 2.17</td><td>0.11 / 2.65</td><td>0.09 / 2.57</td><td>0.33 / 7.34</td><td>0.11 / 3.34</td><td>None</td></tr><tr><td>ExReNet (SUNCG) [116]</td><td>0.05 / 1.63</td><td>0.07 / 2.54</td><td>0.03 / 2.71</td><td>0.06 / 1.75</td><td>0.07 / 2.04</td><td>0.07 / 2.10</td><td>0.19 / 4.87</td><td>0.08 / 2.52</td><td>None</td></tr><tr><td>Reloc3r-224 (Ours)</td><td>0.03 / 0.99</td><td>0.04 / 1.13</td><td>0.02 / 1.23</td><td>0.05 / 0.88</td><td>0.07 / 1.14</td><td>0.05 / 1.23</td><td>0.12 / 2.25</td><td>0.05 / 1.26</td><td>None</td></tr><tr><td>Reloc3r-512 (Ours)</td><td>0.03 / 0.88</td><td>0.03 / 0.81</td><td>0.01 / 0.95</td><td>0.04 / 0.88</td><td>0.06 / 1.10</td><td>0.04 / 1.26</td><td>0.07 / 1.26</td><td>0.04 / 1.02</td><td>None</td></tr></table>
+
+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.
+
+<table><tr><td></td><td>Methods</td><td>GreatCourt</td><td>KingsCollege</td><td>OldHospital</td><td>ShopFacade</td><td>StMarysChurch</td><td>Average (4)</td><td>Average</td><td>Dataset-specific training time</td></tr><tr><td rowspan="3">APR</td><td>LENS [69]</td><td>-</td><td>0.33 / 0.50</td><td>0.44 / 0.90</td><td>0.27 / 1.60</td><td>0.53 / 1.60</td><td>0.39 / 1.20</td><td>-</td><td>Days / scene</td></tr><tr><td>PMNet [58]</td><td>-</td><td>0.31 / 0.55</td><td>0.44 / 0.79</td><td>0.17 / 0.86</td><td>0.31 / 0.96</td><td>0.31 / 0.79</td><td>-</td><td>Days / scene</td></tr><tr><td>DFNet [21]+NeFeS [22]</td><td>-</td><td>0.37 / 0.54</td><td>0.52 / 0.88</td><td>0.15 / 0.53</td><td>0.37 / 1.14</td><td>0.35 / 0.77</td><td>-</td><td>Days / scene</td></tr><tr><td rowspan="4">RPR (Seen)</td><td>EssNet (CL) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.08 / 3.41</td><td>-</td><td>Hours</td></tr><tr><td>Relpose-GNN [101]</td><td>3.20 / 2.20</td><td>0.48 / 1.00</td><td>1.14 / 2.50</td><td>0.48 / 2.50</td><td>1.52 / 3.20</td><td>0.91 / 2.30</td><td>1.37 / 2.30</td><td>Hours</td></tr><tr><td>NC-EssNet (CL) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.85 / 2.82</td><td>-</td><td>Hours</td></tr><tr><td>AnchorNet [78]</td><td>-</td><td>0.57 / 0.88</td><td>1.21 / 2.55</td><td>0.52 / 2.27</td><td>1.04 / 2.69</td><td>0.84 / 2.10</td><td>-</td><td>Hours</td></tr><tr><td rowspan="9">RPR (Unseen)</td><td>EssNet (7S) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>10.36 / 85.75</td><td>-</td><td>None</td></tr><tr><td>NC-EssNet (7S) [129]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>7.98 / 24.35</td><td>-</td><td>None</td></tr><tr><td>Map-free (Match) [4]†</td><td>9.09 / 5.33</td><td>2.51 / 3.11</td><td>3.89 / 6.44</td><td>1.04 / 3.61</td><td>3.00 / 6.14</td><td>2.61 / 4.83</td><td>3.90 / 4.93</td><td>None</td></tr><tr><td>Map-free (Regress) [4]</td><td>8.40 / 4.56</td><td>2.44 / 2.54</td><td>3.73 / 5.23</td><td>0.97 / 3.17</td><td>2.91 / 5.10</td><td>2.51 / 4.01</td><td>3.69 / 4.12</td><td>None</td></tr><tr><td>ExReNet (SN) [116]</td><td>10.97 / 6.52</td><td>2.48 / 2.92</td><td>3.47 / 3.90</td><td>0.90 / 3.27</td><td>2.60 / 4.98</td><td>2.36 / 3.77</td><td>4.08 / 4.32</td><td>None</td></tr><tr><td>ExReNet (SUNCG) [116]</td><td>9.79 / 4.46</td><td>2.33 / 2.48</td><td>3.54 / 3.49</td><td>0.72 / 2.41</td><td>2.30 / 3.72</td><td>2.22 / 3.03</td><td>3.74 / 3.31</td><td>None</td></tr><tr><td>ImageNet+NCM [129]†</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.83 / 1.36</td><td>-</td><td>None</td></tr><tr><td>Reloc3r-224 (Ours)</td><td>1.71 / 0.94</td><td>0.47 / 0.41</td><td>0.87 / 0.66</td><td>0.18 / 0.53</td><td>0.41 / 0.73</td><td>0.48 / 0.58</td><td>0.73 / 0.65</td><td>None</td></tr><tr><td>Reloc3r-512 (Ours)</td><td>1.22 / 0.73</td><td>0.42 / 0.36</td><td>0.62 / 0.55</td><td>0.13 / 0.58</td><td>0.34 / 0.58</td><td>0.38 / 0.52</td><td>0.55 / 0.56</td><td>None</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">ScanNet1500</td></tr><tr><td>AUC@5</td><td>AUC@10</td><td>AUC@20</td></tr><tr><td>Reloc3r-512 asymmetric</td><td>32.71</td><td>56.84</td><td>74.63</td></tr><tr><td>Reloc3r-512 metric pose</td><td>25.70</td><td>50.20</td><td>70.07</td></tr><tr><td>Reloc3r-512 (default)</td><td>34.79</td><td>58.37</td><td>75.56</td></tr></table>
+
+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. Siyan Dong would like to thank the support from HKU School of Computing and Data Science.
+
+# References
+
+[1] Yehya Abouelnaga, Mai Bui, and Slobodan Ilic. Distillpose: Lightweight camera localization using auxiliary learning. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 7919-7924. IEEE, 2021. 2  
+[2] Relja Arandjelovic and Andrew Zisserman. Three things everyone should know to improve object retrieval. In 2012 IEEE conference on computer vision and pattern recognition, pages 2911-2918. IEEE, 2012. 2  
+[3] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomas Pajdla, and Josef Sivic. Netvlad: Cnn architecture for weakly supervised place recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5297-5307, 2016. 3, 5  
+[4] Eduardo Arnold, Jamie Wynn, Sara Vicente, Guillermo Garcia-Hernando, Aron Monszpart, Victor Prisacariu, Daniyar Turmukhambetov, and Eric Brachmann. Map-free visual relocalization: Metric pose relative to a single image. In European Conference on Computer Vision, pages 690-708. Springer, 2022. 2, 3, 4, 5, 6, 7  
+[5] 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. 3  
+[6] Yutong Bai, Xinyang Geng, Karttikeya Mangalam, Amir Bar, Alan L Yuille, Trevor Darrell, Jitendra Malik, and Alexei A Efros. Sequential modeling enables scalable learning for large vision models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22861-22872, 2024. 2, 3  
+[7] Vassileios Balntas, Shuda Li, and Victor Prisacariu. Relocnet: Continuous metric learning relocalisation using neural nets. In Proceedings of the European conference on computer vision (ECCV), pages 751-767, 2018. 2, 6, 8  
+[8] Daniel Barath and Jiri Matas. Graph-cut ransac. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6733-6741, 2018. 2  
+[9] Daniel Barath and Jiri Matas. Graph-cut ransac: Local optimization on spatially coherent structures. IEEE transactions on pattern analysis and machine intelligence, 44(9): 4961-4974, 2021.  
+[10] Daniel Barath, Jiri Matas, and Jana Noskova. Magsac: marginalizing sample consensus. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10197-10205, 2019.  
+[11] Daniel Barath, Jana Noskova, Maksym Ivashechkin, and Jiri Matas. Magsac++, a fast, reliable and accurate robust estimator. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1304-1312, 2020. 2  
+[12] Gilad Baruch, Zhuoyuan Chen, Afshin Dehghan, Tal Dimry, Yuri Feigin, Peter Fu, Thomas Gebauer, Brandon Joffe, Daniel Kurz, Arik Schwartz, et al. Arkitsscenes: A diverse real-world dataset for 3d indoor scene understanding using mobile rgb-d data. arXiv preprint arXiv:2111.08897, 2021. 5
+
+[13] Eric Brachmann and Carsten Rother. Learning less is more-6d camera localization via 3d surface regression. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4654–4662, 2018. 1, 2  
+[14] Eric Brachmann and Carsten Rother. Visual camera relocalization from rgb and rgb-d images using dsac. IEEE transactions on pattern analysis and machine intelligence, 44(9):5847-5865, 2021.  
+[15] Eric Brachmann, Alexander Krull, Sebastian Nowozin, Jamie Shotton, Frank Michel, Stefan Gumhold, and Carsten Rother. Dsac-differentiable ransac for camera localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6684-6692, 2017. 7  
+[16] Eric Brachmann, Tommaso Cavallari, and Victor Adrian Prisacariu. Accelerated coordinate encoding: Learning to relocalize in minutes using rgb and poses. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5044-5053, 2023. 1, 2  
+[17] G Bradski. The opencv library. Dr. Dobb's Journal of Software Tools, 2000. 5  
+[18] Samarth Brahmbhatt, Jinwei Gu, Kihwan Kim, James Hays, and Jan Kautz. Geometry-aware learning of maps for camera localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2616-2625, 2018. 1, 2  
+[19] Avishek Chatterjee and Venu Madhav Govindu. Efficient and robust large-scale rotation averaging. In Proceedings of the IEEE international conference on computer vision, pages 521-528, 2013. 4  
+[20] Shuai Chen, Zirui Wang, and Victor Prisacariu. Directposenet: Absolute pose regression with photometric consistency. In 2021 International Conference on 3D Vision (3DV), pages 1175-1185. IEEE, 2021. 1, 2  
+[21] Shuai Chen, Xinghui Li, Zirui Wang, and Victor A Prisacariu. Dfnet: Enhance absolute pose regression with direct feature matching. In European Conference on Computer Vision, pages 1-17. Springer, 2022. 2, 6, 7  
+[22] Shuai Chen, Yash Bhalgat, Xinghui Li, Jia-Wang Bian, Kejie Li, Zirui Wang, and Victor Adrian Prisacariu. Neural refinement for absolute pose regression with feature synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20987-20996, 2024. 1, 2, 6, 7  
+[23] Shuai Chen, Tommaso Cavallari, Victor Adrian Prisacariu, and Eric Brachmann. Map-relative pose regression for visual re-localization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20665-20674, 2024. 2, 3, 6  
+[24] Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al. Palm: Scaling language modeling with pathways. Journal of Machine Learning Research, 24(240): 1-113, 2023. 3  
+[25] Ondrej Chum, Jiri Matas, and Josef Kittler. Locally optimized ransac. In Pattern Recognition: 25th DAGM Symposium, Magdeburg, Germany, September 10-12, 2003. Proceedings 25, pages 236-243. Springer, 2003. 2
+
+[26] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5828-5839, 2017. 1, 5, 6  
+[27] Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superpoint: Self-supervised interest point detection and description. In Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pages 224-236, 2018. 1, 2  
+[28] Jacob Devlin. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.3  
+[29] Mingyu Ding, Zhe Wang, Jiankai Sun, Jianping Shi, and Ping Luo. Camnet: Coarse-to-fine retrieval for camera relocalization. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2871-2880, 2019. 2, 6  
+[30] Siyan Dong, Shuzhe Wang, Yixin Zhuang, Juho Kannala, Marc Pollefeys, and Baoquan Chen. Visual localization via few-shot scene region classification. In 2022 International Conference on 3D Vision (3DV), pages 393-402. IEEE, 2022. 1, 2  
+[31] Siyan Dong, Shaohui Liu, Hengkai Guo, Baoquan Chen, and Marc Pollefeys. Lazy visual localization via motion averaging. arXiv preprint arXiv:2307.09981, 2023. 2, 4  
+[32] Alexey Dosovitskiy. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020. 2, 3  
+[33] Mihai Dusmanu, Ignacio Rocco, Tomas Pajdla, Marc Pollefeys, Josef Sivic, Akihiko Torii, and Torsten Sattler. D2-net: A trainable cnn for joint description and detection of local features. In Proceedings of the IEEE/cvf conference on computer vision and pattern recognition, pages 8092-8101, 2019. 1, 2  
+[34] Johan Edstedt, Qiyu Sun, Georg Bokman, Marten Wadenback, and Michael Felsberg. Roma: Robust dense feature matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19790-19800, 2024. 1, 2, 6, 7  
+[35] Sovann En, Alexis Lechervy, and Frédéric Jurie. Rpnet: An end-to-end network for relative camera pose estimation. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 2  
+[36] Martin A Fischler and Robert C Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395, 1981. 1, 2, 4  
+[37] Khang Truong Giang, Soohwan Song, and Sungho Jo. Learning to produce semi-dense correspondences for visual localization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19468-19478, 2024. 1, 2  
+[38] Richard Hartley and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. 1, 2
+
+[39] Richard I Hartley and Peter Sturm. Triangulation. Computer vision and image understanding, 68(2):146-157, 1997. 4  
+[40] Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, and Ross Girshick. Masked autoencoders are scalable vision learners. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 16000-16009, 2022. 2  
+[41] Martin Humenberger, Yohann Cabon, Nicolas Guerin, Julien Morat, Vincent Leroy, Jérôme Revaud, Philippe Rerole, Noé Pion, Cesar de Souza, and Gabriela Csurka. Robust image retrieval-based visual localization using kapture. arXiv preprint arXiv:2007.13867, 2020. 2  
+[42] Alex Kendall and Roberto Cipolla. Modelling uncertainty in deep learning for camera relocalization. In 2016 IEEE international conference on Robotics and Automation (ICRA), pages 4762-4769. IEEE, 2016. 1, 2  
+[43] Alex Kendall and Roberto Cipolla. Geometric loss functions for camera pose regression with deep learning. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5974-5983, 2017. 1  
+[44] Alex Kendall, Matthew Grimes, and Roberto Cipolla. Posenet: A convolutional network for real-time 6-dof camera relocalization. In Proceedings of the IEEE international conference on computer vision, pages 2938-2946, 2015. 2, 6, 7, 8  
+[45] Fadi Khatib, Yuval Margalit, Meirav Galun, and Rosen Basri. Leveraging image matching toward end-to-end relative camera pose regression. arXiv preprint arXiv:2211.14950, 2022. 2  
+[46] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al. Segment anything. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4015-4026, 2023. 2, 3  
+[47] Laurent Kneip, Davide Scaramuzza, and Roland Siegwart. A novel parametrization of the perspective-three-point problem for a direct computation of absolute camera position and orientation. In CVPR 2011, pages 2969-2976. IEEE, 2011. 1  
+[48] Viktor Larsson and contributors. PoseLib - Minimal Solvers for Camera Pose Estimation, 2020. 2  
+[49] Zakaria Laskar, Iaroslav Melekhov, Surya Kalia, and Juho Kannala. Camera relocalization by computing pairwise relative poses using convolutional neural network. In Proceedings of the IEEE International Conference on Computer Vision Workshops, pages 929-938, 2017. 2, 3, 6, 8  
+[50] Karel Lebeda, Jiri Matas, and Ondrej Chum. Fixing the locally optimized ransac-full experimental evaluation. In British machine vision conference. Citeseer Princeton, NJ, USA, 2012. 2  
+[51] Vincent Leroy, Yohann Cabon, and Jérôme Revaud. Grounding image matching in 3d with mast3r. arXiv preprint arXiv:2406.09756, 2024. 2, 3, 5, 6, 7  
+[52] Jake Levinson, Carlos Esteves, Kefan Chen, Noah Snavely, Angjoo Kanazawa, Afshin Rostamizadeh, and Ameesh
+
+Makadia. An analysis of svd for deep rotation estimation. Advances in Neural Information Processing Systems, 33: 22554-22565, 2020. 4  
+[53] Xiaotian Li, Juha Ylioinas, and Juho Kannala. Full-frame scene coordinate regression for image-based localization. arXiv preprint arXiv:1802.03237, 2018. 1, 2  
+[54] Xiaotian Li, Shuzhe Wang, Yi Zhao, Jakob Verbeek, and Juho Kannala. Hierarchical scene coordinate classification and regression for visual localization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11983-11992, 2020. 1, 2, 7  
+[55] Yunpeng Li, Noah Snavely, and Daniel P Huttenlocher. Location recognition using prioritized feature matching. In Computer Vision-ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part II 11, pages 791-804. Springer, 2010. 2  
+[56] Zhengqi Li and Noah Snavely. Megadepth: Learning single-view depth prediction from internet photos. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2041-2050, 2018. 5  
+[57] Amy Lin, Jason Y Zhang, Deva Ramanan, and Shubham Tulsiani. Relpose++: Recovering 6d poses from sparse-view observations. In 2024 International Conference on 3D Vision (3DV), pages 106-115. IEEE, 2024. 3, 5, 7  
+[58] Jingyu Lin, Jiaqi Gu, Bojian Wu, Lubin Fan, Renjie Chen, Ligang Liu, and Jieping Ye. Learning neural volumetric pose features for camera localization. arXiv preprint arXiv:2403.12800, 2024. 1, 2, 6, 7  
+[59] Philipp Lindenberger, Paul-Edouard Sarlin, Viktor Larsson, and Marc Pollefeys. Pixel-perfect structure-from-motion with featuremetric refinement. In Proceedings of the IEEE/CVF international conference on computer vision, pages 5987-5997, 2021. 5, 7  
+[60] Philipp Lindenberger, Paul-Edouard Sarlin, and Marc Pollefeys. Lightglue: Local feature matching at light speed. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 17627-17638, 2023. 1, 2  
+[61] Lu Ling, Yichen Sheng, Zhi Tu, Wentian Zhao, Cheng Xin, Kun Wan, Lantao Yu, Qianyu Guo, Zixun Yu, Yawen Lu, et al. DL3dv-10k: A large-scale scene dataset for deep learning-based 3d vision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22160–22169, 2024. 5  
+[62] Andrew Liu, Richard Tucker, Varun Jampani, Ameesh Makadia, Noah Snavely, and Angjoo Kanazawa. Infinite nature: Perpetual view generation of natural scenes from a single image. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14458-14467, 2021. 5, 6  
+[63] Haotian Liu, Chunyuan Li, Qingyang Wu, and Yong Jae Lee. Visual instruction tuning. Advances in neural information processing systems, 36, 2024. 2, 3  
+[64] Shaohui Liu, Yidan Gao, Tianyi Zhang, Rémi Pautrat, Johannes L Schonberger, Viktor Larsson, and Marc Pollefeys. Robust incremental structure-from-motion with hybrid features. In European Conference on Computer Vision, pages 249-269. Springer, 2025. 2
+
+[65] David G Lowe. Object recognition from local scale-invariant features. In Proceedings of the seventh IEEE international conference on computer vision, pages 1150-1157. IEEE, 1999. 2  
+[66] Iaroslav Melekhov, Juha Ylioinas, Juho Kannala, and Esa Rahtu. Image-based localization using hourglass networks. In Proceedings of the IEEE international conference on computer vision workshops, pages 879-886, 2017. 1, 2  
+[67] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021. 2  
+[68] Shervin Minaee, Tomas Mikolov, Narjes Nikzad, Meysam Chenaghlu, Richard Socher, Xavier Amatriain, and Jianfeng Gao. Large language models: A survey. arXiv preprint arXiv:2402.06196, 2024. 3  
+[69] Arthur Moreau, Nathan Piasco, Dzmitry Tsishkou, Bogdan Stanciulescu, and Arnaud de La Fortelle. Lens: Localization enhanced by nerf synthesis. In Conference on Robot Learning, pages 1347-1356. PMLR, 2022. 1, 2, 6, 7  
+[70] Tayyab Naseer and Wolfram Burgard. Deep regression for monocular camera-based 6-dof global localization in outdoor environments. In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 1525-1530. IEEE, 2017. 1, 2  
+[71] Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Advances in neural information processing systems, 35: 27730-27744, 2022. 3  
+[72] Vojtech Panek, Zuzana Kukelova, and Torsten Sattler. Meshloc: Mesh-based visual localization. In European Conference on Computer Vision, pages 589-609. Springer, 2022. 1, 2  
+[73] William Peebles and Saining Xie. Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4195-4205, 2023. 2, 3  
+[74] Nikhila Ravi, Valentin Gabeur, Yuan-Ting Hu, Ronghang Hu, Chaitanya Ryali, Tengyu Ma, Haitham Khedr, Roman Radle, Chloe Rolland, Laura Gustafson, et al. Sam 2: Segment anything in images and videos. arXiv preprint arXiv:2408.00714, 2024.3  
+[75] Jeremy Reizenstein, Roman Shapovalov, Philipp Henzler, Luca Sbordone, Patrick Labatut, and David Novotny. Common objects in 3d: Large-scale learning and evaluation of real-life 3d category reconstruction. In Proceedings of the IEEE/CVF international conference on computer vision, pages 10901-10911, 2021. 5, 7  
+[76] Jerome Revaud, Cesar De Souza, Martin Humenberger, and Philippe Weinzaepfel. R2d2: Reliable and repeatable detector and descriptor. Advances in neural information processing systems, 32, 2019. 1, 2  
+[77] Chris Rockwell, Nilesh Kulkarni, Linyi Jin, Jeong Joon Park, Justin Johnson, and David F Fouhey. Far: Flexible
+
+accurate and robust 6 dof relative camera pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19854-19864, 2024. 3  
+[78] Soham Saha, Girish Varma, and CV Jawahar. Improved visual relocalization by discovering anchor points. arXiv preprint arXiv:1811.04370, 2018. 2, 6, 7  
+[79] Paul-Edouard Sarlin, Cesar Cadena, Roland Siegwart, and Marcin Dymczyk. From coarse to fine: Robust hierarchical localization at large scale. In CVPR, 2019. 1, 5  
+[80] Paul-Edouard Sarlin, Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superglue: Learning feature matching with graph neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4938–4947, 2020. 1, 2, 5, 6  
+[81] Paul-Edouard Sarlin, Ajaykumar Unagar, Mans Larsson, Hugo Germain, Carl Toft, Viktor Larsson, Marc Pollefeys, Vincent Lepetit, Lars Hammarstrand, Fredrik Kahl, et al. Back to the feature: Learning robust camera localization from pixels to pose. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3247–3257, 2021. 1, 2  
+[82] Torsten Sattler, Bastian Leibe, and Leif Kobbelt. Fast image-based localization using direct 2d-to-3d matching. In 2011 International Conference on Computer Vision, pages 667–674. IEEE, 2011.  
+[83] Torsten Sattler, Bastian Leibe, and Leif Kobbelt. Improving image-based localization by active correspondence search. In Computer Vision-ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part I 12, pages 752-765. Springer, 2012.  
+[84] Torsten Sattler, Bastian Leibe, and Leif Kobbelt. Efficient & effective prioritized matching for large-scale image-based localization. IEEE transactions on pattern analysis and machine intelligence, 39(9):1744-1756, 2016. 1  
+[85] Torsten Sattler, Akihiko Torii, Josef Sivic, Marc Pollefeys, Hajime Taira, Masatoshi Okutomi, and Tomas Pajdla. Are large-scale 3d models really necessary for accurate visual localization? In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1637-1646, 2017.  
+[86] Torsten Sattler, Will Maddern, Carl Toft, Akihiko Torii, Lars Hammarstrand, Erik Stenberg, Daniel Safari, Masatoshi Okutomi, Marc Pollefeys, Josef Sivic, et al. Benchmarking 6dof outdoor visual localization in changing conditions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8601-8610, 2018. 2  
+[87] Torsten Sattler, Qunjie Zhou, Marc Pollefeys, and Laura Leal-Taixe. Understanding the limitations of cnn-based absolute camera pose regression. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3302-3312, 2019. 2  
+[88] Johannes L Schonberger and Jan-Michael Frahm. Structure-from-motion revisited. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4104-4113, 2016. 1
+
+[89] Yoli Shavit, Ron Ferens, and Yoshi Keller. Learning multiscene absolute pose regression with transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2733-2742, 2021. 1, 2  
+[90] Yoli Shavit, Ron Ferens, and Yoshi Keller. Coarse-to-fine multi-scene pose regression with transformers. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023. 1, 2  
+[91] Jamie Shotton, Ben Glocker, Christopher Zach, Shahram Izadi, Antonio Criminisi, and Andrew Fitzgibbon. Scene coordinate regression forests for camera relocalization in rgb-d images. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2930-2937, 2013. 6, 7  
+[92] Brandon Smart, Chuanxia Zheng, Iro Laina, and Victor Adrian Prisacariu. Splatt3r: Zero-shot gaussian splatting from uncalibrated image pairs. arXiv preprint arXiv:2408.13912, 2024. 3  
+[93] Shuran Song, Fisher Yu, Andy Zeng, Angel X Chang, Manolis Savva, and Thomas Funkhouser. Semantic scene completion from a single depth image. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1746-1754, 2017. 5  
+[94] Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, and Yunfeng Liu. Roformer: Enhanced transformer with rotary position embedding. Neurocomputing, 568: 127063, 2024. 3  
+[95] Jiaming Sun, Zehong Shen, Yuang Wang, Hujun Bao, and Xiaowei Zhou. Loftr: Detector-free local feature matching with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8922-8931, 2021. 1, 2, 5  
+[96] Hajime Taira, Masatoshi Okutomi, Torsten Sattler, Mircea Cimpoi, Marc Pollefeys, Josef Sivic, Tomas Pajdla, and Akihiko Torii. Inloc: Indoor visual localization with dense matching and view synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7199-7209, 2018. 2  
+[97] Shitao Tang, Chengzhou Tang, Rui Huang, Siyu Zhu, and Ping Tan. Learning camera localization via dense scene matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1831-1841, 2021. 2  
+[98] Shengbang Tong, Ellis Brown, Penghao Wu, Sanghyun Woo, Manoj Middepogu, Sai Charitha Akula, Jihan Yang, Shusheng Yang, Adithya Iyer, Xichen Pan, et al. Cambrian1: A fully open, vision-centric exploration of multimodal llms. arXiv preprint arXiv:2406.16860, 2024. 2, 3  
+[99] Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023. 3  
+[100] Diantao Tu, Hainan Cui, Xianwei Zheng, and Shuhan Shen. Panopose: Self-supervised relative pose estimation for panoramic images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20009-20018, 2024. 3
+
+[101] Mehmet Ozgur Turkoglu, Eric Brachmann, Konrad Schindler, Gabriel J Brostow, and Aron Monszpart. Visual camera re-localization using graph neural networks and relative pose supervision. In 2021 International Conference on 3D Vision (3DV), pages 145-155. IEEE, 2021. 2, 3, 5, 6, 7  
+[102] A Vaswani. Attention is all you need. Advances in Neural Information Processing Systems, 2017. 3  
+[103] Florian Walch, Caner Hazirbas, Laura Leal-Taixe, Torsten Sattler, Sebastian Hilsenbeck, and Daniel Cremers. Image-based localization using lstms for structured feature correlation. In Proceedings of the IEEE international conference on computer vision, pages 627-637, 2017. 1, 2  
+[104] Bing Wang, Changhao Chen, Chris Xiaoxuan Lu, Peijun Zhao, Niki Trigoni, and Andrew Markham. Atloc: Attention guided camera localization. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 10393-10401, 2020. 1, 2  
+[105] Hengyi Wang and Lourdes Agapito. 3d reconstruction with spatial memory. arXiv preprint arXiv:2408.16061, 2024. 3  
+[106] Jianyuan Wang, Christian Rupprecht, and David Novotny. Posediffusion: Solving pose estimation via diffusion-aided bundle adjustment. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9773–9783, 2023. 3, 5, 7  
+[107] Jianyuan Wang, Nikita Karaev, Christian Rupprecht, and David Novotny. Vggsfm: Visual geometry grounded deep structure from motion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21686-21697, 2024. 5, 7  
+[108] Ruicheng Wang, Sicheng Xu, Cassie Dai, Jianfeng Xiang, Yu Deng, Xin Tong, and Jiaolong Yang. Moge: Unlocking accurate monocular geometry estimation for open-domain images with optimal training supervision. arXiv preprint arXiv:2410.19115, 2024. 2  
+[109] Shuzhe Wang, Juho Kannala, and Daniel Barath. Dgc-gnn: Leveraging geometry and color cues for visual descriptor-free 2d-3d matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20881-20891, 2024. 1, 2  
+[110] Shuzhe Wang, Zakaria Laskar, Iaroslav Melekhov, Xiaotian Li, Yi Zhao, Giorgos Tolias, and Juho Kannala. Hscnet++: Hierarchical scene coordinate classification and regression for visual localization with transformer. International Journal of Computer Vision, pages 1-21, 2024. 2  
+[111] Shuzhe Wang, Vincent Leroy, Yohann Cabon, Boris Chidlovskii, and Jerome Revaud. Dust3r: Geometric 3d vision made easy. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20697-20709, 2024. 2, 3, 5, 6, 7, 8  
+[112] Yifan Wang, Xingyi He, Sida Peng, Dongli Tan, and Xiaowei Zhou. Efficient loftr: Semi-dense local feature matching with sparse-like speed. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21666-21675, 2024. 1, 2, 5, 6  
+[113] Philippe Weinzaepfel, Vincent Leroy, Thomas Lucas, Romain Brégier, Yohann Cabon, Vaibhav Arora, Leonid Ants
+
+feld, Boris Chidlovskii, Gabriela Csurka, and Jérôme Revaud. Croco: Self-supervised pre-training for 3d vision tasks by cross-view completion. Advances in Neural Information Processing Systems, 35:3502-3516, 2022. 3  
+[114] Philippe Weinzaepfel, Thomas Lucas, Vincent Leroy, Yohann Cabon, Vaibhav Arora, Romain Brégier, Gabriela Csurka, Leonid Antsfeld, Boris Chidlovskii, and Jérôme Revaud. Croco v2: Improved cross-view completion pretraining for stereo matching and optical flow. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 17969-17980, 2023. 3  
+[115] Kyle Wilson and Noah Snavely. Robust global translations with 1dsfm. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part III 13, pages 61-75. Springer, 2014. 4  
+[116] Dominik Winkelbauer, Maximilian Denninger, and Rudolph Triebel. Learning to localize in new environments from synthetic training data. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 5840-5846. IEEE, 2021. 2, 4, 5, 6, 7  
+[117] Jian Wu, Liwei Ma, and Xiaolin Hu. Delving deeper into convolutional neural networks for camera relocalization. In 2017 IEEE International Conference on Robotics and Automation (ICRA), pages 5644-5651. IEEE, 2017. 1, 2  
+[118] Fei Xue, Xin Wu, Shaojun Cai, and Junqiu Wang. Learning multi-view camera relocalization with graph neural networks. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11372-11381. IEEE, 2020. 3  
+[119] Luwei Yang, Ziqian Bai, Chengzhou Tang, Honghua Li, Yasutaka Furukawa, and Ping Tan. Sanet: Scene agnostic network for camera localization. In Proceedings of the IEEE/CVF international conference on computer vision, pages 42-51, 2019. 2  
+[120] Luwei Yang, Rakesh Shrestha, Wenbo Li, Shuaicheng Liu, Guofeng Zhang, Zhaopeng Cui, and Ping Tan. Scenesqueeze: Learning to compress scene for camera localization. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8259-8268, 2022. 2  
+[121] Yao Yao, Zixin Luo, Shiwei Li, Jingyang Zhang, Yufan Ren, Lei Zhou, Tian Fang, and Long Quan. Blendedmvs: A large-scale dataset for generalized multi-view stereo networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1790-1799, 2020. 5  
+[122] Botao Ye, Sifei Liu, Haofei Xu, Xueting Li, Marc Pollefeys, Ming-Hsuan Yang, and Songyou Peng. No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images. arXiv preprint arXiv:2410.24207, 2024. 3, 5, 6, 7  
+[123] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12-22, 2023. 5
+
+[124] Yingda Yin, Yang Wang, He Wang, and Baoquan Chen. A laplace-inspired distribution on so(3) for probabilistic rotation estimation. In International Conference on Learning Representations (ICLR), 2023. 1, 2  
+[125] Bernhard Zeisl, Torsten Sattler, and Marc Pollefeys. Camera pose voting for large-scale image-based localization. In Proceedings of the IEEE International Conference on Computer Vision, pages 2704-2712, 2015. 2  
+[126] Junyi Zhang, Charles Herrmann, Junhwa Hur, Varun Jampani, Trevor Darrell, Forrester Cole, Deqing Sun, and Ming-Hsuan Yang. Monst3r: A simple approach for estimating geometry in the presence of motion. arXiv preprint arXiv:2410.03825, 2024. 3  
+[127] Jason Y. Zhang, Deva Ramanan, and Shubham Tulsiani. RelPose: Predicting probabilistic relative rotation for single objects in the wild. In European Conference on Computer Vision, 2022. 3, 5, 7  
+[128] Jason Y Zhang, Amy Lin, Moneish Kumar, Tzu-Hsuan Yang, Deva Ramanan, and Shubham Tulsiani. Cameras as rays: Pose estimation via ray diffusion. arXiv preprint arXiv:2402.14817, 2024. 3, 5, 7  
+[129] Qunjie Zhou, Torsten Sattler, Marc Pollefeys, and Laura Leal-Taixe. To learn or not to learn: Visual localization from essential matrices. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 3319-3326. IEEE, 2020. 2, 3, 4, 6, 7, 8  
+[130] Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018. 5, 6  
+[131] Bingbing Zhuang, Loong-Fah Cheong, and Gim Hee Lee. Baseline desensitizing in translation averaging. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4539-4547, 2018. 4

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