We sincerely appreciate your valuable suggestions. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We earnestly look forward to the subsequent discussions with you.

1. Motivation of Using MLP for SDF

Thank you for the insightful comments. The main motivation of using an 8-layer MLP is to map any spatial position $x\in \mathbb{R}^{3}$ to its corresponding SDF value. This mapping is crucial for the unbiased SDF regularization, as shown in Eq. 8. We can obtain $f(o +t^* r)$ through the MLP and further encourage it approaches zero. Conversely, if the SDF is treated as an property of each Gaussian primitive, it is difficult to achieve point-level mapping because 3D Gaussian primitive is essentially a local probability representation. For example, if the SDF value at the center of a Gaussian primitive is taken as its SDF, the SDF value at $x = o + t^* r$ cannot be directly obtained.

2. Explanation of $x\_{i+1}$

Thank you for your valuable comments. In fact, $x\_{i+1}$ in this paper refers to the next sampled point along the ray. We calculate $f(x\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\_{i+1}) =f(x\_{i})+{f}'(x\_{i}) \Delta x$, where $\Delta x = \frac{z\_{\text{far}}-z\_{\text{near}}}{l}$. $f(x\_{i})$ is the SDF value of the center of the $i$-th Gaussian primitive. $z\_{\text{far}}$ and $z\_{\text{near}}$ are the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. Note that we use the annealing $(1-\frac{n}{N})(\Theta (\frac{1-r\cdot f' (x\_{i})}{2} ) )-\frac{n}{N} (\Theta (-r\cdot {f}' (x\_{i}) )$ to replace ${f}'(x\_{i})$ in actual computation for adaptive transformation of view-normal angle, where $n$ and $N$ denote the current iteration and total iterations respectively. $r$ is the normalized ray direction. $\Theta$ is the ReLU activation Function.

3. More Details of Mesh Generation and Deformable Field

Thank you for the helpful insights. We have already described the details of the deformable field in Section 3.2. Following your suggestion, we provide a more detailed elaboration on deformable field and mesh generation below. Once we finish the estimation of the joint type, we design different learnable parameters based on the joint type. For rotation joints, we define the pivot point $\mathbf{o}_{r}\in \mathbb{R}^{3}$ of the rotation axis and the normalized quaternion $\mathbf{q} \in \mathbb{R}^{4}$ as learnable parameters. For translation joints, the unit vector $\mathbf{d}\in \mathbb{R}^{3}$ of translation direction and translation distance $m$ are used as learnable parameters. Note that the deformable network in Fig. 2 is composed of these learnable parameters. We sincerely apologize for any misunderstanding we may have caused. Through Eq.10 and Eq.11, we can derive the center position $x\_{s}$ of the Gaussian primitives at any state $s$ through these learnable parameters. Therefore, the deformable field $\mathcal{g}$ can be represented as $\mathcal{g}(x)=x\_{s}$. Given any state $s$, we first obtain the deformed Gaussian primitives through the deformable field, and then render them into depth, opacity and RGB renderings. Finally we integrate these renderings into a voxel block grid and use TSDF Fusion to extract the surface mesh at state $s$. The mesh extration pipeline is described in Section 3.3.

4. Clarification on the Section 3.2

Thank you for your feedback. Although the process of mesh extraction is not directly described in Section 3.2, we elaborate on the key of mesh generation, i.e., generating accurate 3D Gaussian primitives. The dynamic texture mesh can be easily obtained by TSDF Fusion when the 3D Gaussian primitives learn the accurate motion, and the TSDF Fusion is illustrated in Section 3.3.

5. Clarification on Initialization

Thank you for your feedback. In fact, we have elaborated in detail on the initialization of Gaussian primitives of the generation state in Section 3.2. The initialization inherits the Gaussian primitives from the reconstruction stage. We define the canonical state $s^{*}=0.5$ to constrain the rotation $\theta$ within the interval $\left [ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$, preventing the singularity in exponential coordinates when $\theta > \pi$.

In the warm-up stage, we use the image supervisions from stage $s=1$ mainly for the initial part segmentation. Note that this does not affect the learning of Gaussian primitives, since the rendering loss is calculated through the deformed Gaussian primitives, which are obtained from the deformable field. Taking the rotation joint as an example, although the initialization of 3D Gaussians is used from stage $s=0$ and we define the canonical state $s^{*}=0.5$, we employ Eq. 9 and Eq. 10 to derive the deformed Gaussians and then back-propagate the rendering loss. As the rendering loss converges, the Gaussian primitives adjust to the spatial positions at state $s = 0.5$. Besides, the ablation experiments in Table. 9 also demonstrate the superiority of setting the canonical state of rotation joints to 0.5.

6. Results of More Reconstruction Datasets

Thank you for the valuable suggestions. Although our method is designed for articulated object reconstruction, it can also be generalized to common reconstruction datasets. According to your suggestion, we compared the performance on the general reconstruction datasets Tanks and Temples, DTU with the existing SOTA reconstruction methods 2DGS (Huang, 2024) and GOF. We present the following quantitative results below.

F1-score $\uparrow$ results on Tanks and Temples dataset:

CD $\downarrow$ results on DTU dataset:

7. The Significance of Introducing SDF

Opacity constitutes a fundamental attribute for the $\alpha$-blending in 3DGS. However, since the opacity cannot explicitly define the scene surface, opacity-based 3DGS methods typically yield surface mesh results with artifacts. For example, GOF extracts surface mesh through an opacity level set, but the Gaussian opacity field poses non-strict linearity, leading to mesh extraction with holes. In contrast, SDF has strong linearity and explicitly defines the scene surface. We hence aim to introduce the SDF to regularize the Gaussian opacity field. Concretely, we propose the unbiased regularization, which encourages Gaussians near the surface to exhibit a high opacity value, eliminating artifacts distant from the surface.

On the other hand, due to the irregular nature of 3D Gaussians, it is difficult to estimate their normal directions. Existing methods, such as 2DGS and PGSR, attempt to facilitate the normal estimation by compressing 3D Gaussian primitives to 2D shapes. This geometric constraint is not reasonable as the restriction on the shape of Gaussian primitives leads to degraded performance in capturing detailed structures. In contrast, our method introduces SDF in 3D Gaussian primitives and leverages the gradients of SDF to accurately define the normals, instead of restricting the shapes of Gaussian primitives.

Thank you for your timely reply. Our method is trained for 30,000 iterations on both Tanks and Temples and DTU datasets. Specifically, we only conduct the reconstrucion stage since neither Tanks and Temples dataset nor DTU dataset imposes any generation requirements for articulated objects. We omit the additional 3,000 warm-up iterations for SDF learning as we observe that they yield slight improvement on actual performance. We perform the densification and pruning of 3D Gaussians from 500 to 15,000 iterations and apply SDF-normal regularization and Eikonal regularization from 500 to 30,000 iterations, the unbiased SDF regularization is employed from 500 to 15,000 iterations.

The average training time on the Tanks and Temples and DTU dataset is 40 minutes and 30 minutes respectively. Note that we have conduct engineering optimizations to our method, which can be summarized as following. (1) We calculate $f(x\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\_{i+1}) =f(x\_{i})+{f}'(x\_{i}) \Delta x$. In previous experiments, we define $\Delta x = RS\cdot r$, where $R\in \mathbb{R}^{3\times3}$ is the R is the rotation matrix derived from Gaussian’s quaternion, and $S\in \mathbb{R}^{3}$ represents Gaussian's scaling. $r$ is the normalized ray direction. However, we observe that this calculation consumes a lot of time and it is difficult to obtain $\Delta x$ when the object size is extremely small. Therefore, we have refined the calculation to $\Delta x = \frac{z\_{\text{far}}-z\_{\text{near}}}{l}$, where $z\_{\text{near}}$, $z\_{\text{far}}$ are the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. This approach not only remarkably enhances the computational efficiency, but also demonstrates better robustness against extremely small objects. The average cd(ws) $\downarrow$ reduces -0.008 compared with previous results. (2) Inspired by PARIS, we also employ the Tiny-cuda-nn to accelerate our SDF network, achieving a significant time reduction. Besides, this acceleration have almost no impact on the mesh results.

Moreover, our approach still maintains SOTA results with the acceleration on the PartNet-Mobility dataset. Please refer to the response to reviewer BVdL for details.

We sincerely appreciate your recognition of our method. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.

1. Motivation of Using 3DGS

Thanks for the insightful opinions. NeRF and NeuS represent 3D scenes through neural implicit radiance fields, posing four major limitations. (1) The implicit representation tends to yield entangled neural representations, leading to the shape-radiance ambiguity. (2) Their ray marching sampling may skip over thin structures, resulting in unsatisfactory reconstruction of details. (3) When extracting surface meshes from NeRF-based methods, post-processing algorithms like Marching Cubes are typically required. However, using Marching Cubes from the neural representations often introduces unconsidered errors, producing noisy surface mesh results. (4) The texture is strongly coupled with the implicit representation, and high-frequency textures rely on positional encoding, which is prone to causing over smoothing.

In contrast, our motivation for adopting 3DGS is based on the following benefits. (1) 3DGS is an explicit point-based representation, which is inherently more consistent to surface mesh reconstruction. Through the anisotropic Gaussian primitives, 3DGS can precisely recover detailed structures. (2) The Spherical Harmonics (SH) of 3D Gaussian primitives support direct texture baking for texture extraction. For a detailed discussion on SH, please refer to Point 5. (3) In terms of training time, 3DGS uses the rasterization instead of volume rendering, significantly improving the training speed. For example, NeuS, which also introduces SDF, requires more than 12 hours. Please refer to Point 3 for details. (4) Leveraging the explicit nature of 3DGS, we can explicitly obtain the deformed Gaussian primitives through deformable fields. In contrast, Nerf-based methods like PAIRS require composite neural radiance fields for the two-stage inputs. Since spatial overlap exists between the composite density fields of the start and end states, the volume rendering with neural implicit representation produces noisy surface reconstruction results. As shown in Fig. 5, PARIS yields unsmooth surface mesh results while our method achieves high-quality detailed reconstruction. Therefore, the degraded mesh results stems from the limitations of the neural implicit radiance field and cannot be resolved merely by using NeuS.

2. Input View Setting

We follow the same input settings as PARIS and ArtGS, using 64 multi-view images and 50 test images per stage. We have also supplemented an ablation study on the number of input images from each stage below. We report the average surface mesh generation results on PartNet-Mobility dataset.

The experimental results demonstrate that even if the number of input images per stage is decreased to 16, our method still exhibits robust surface generation results.

3. Comparison of Training Time

We sincerely appreciate your invaluable comments. In the early experiments, the training process takes 65 minutes for reconstruction and 30 minutes for generation. Nevertheless, we have now implemented engineering optimizations in our approach, which significantly reduce the training time to approximately 30 minutes for reconstruction and approximately 10 minutes for generation. Moreover, Our approach still maintains SOTA results with the acceleration. Specifically, our main engineering optimizations can be summarized as following. (1) We calculate $f(x\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\_{i+1}) =f(x\_{i})+{f}'(x\_{i}) \Delta x$. In previous experiments, we define $\Delta x = RS\cdot r$, where $R\in \mathbb{R}^{3\times3}$ is the rotation matrix derived from Gaussian’s quaternion, and $S\in \mathbb{R}^{3}$ represents Gaussian's scaling. $r$ is the normalized ray direction. However, we observe that this calculation consumes a lot of time and it is difficult to obtain $\Delta x$ when the object size is extremely small. Therefore, we have refined the calculation to $\Delta x = \frac{z\_{\text{far}}-z\_{\text{near}}}{l}$, where $z\_{\text{far}}$ and $z\_{\text{near}}$ are the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. This approach not only remarkably enhances the computational efficiency, but also demonstrates better robustness against extremely small objects. For PartNet-Mobility data in the paper, the average cd(ws) $\downarrow$ reduces -0.008 compared with previous results. (2) Inspired by PARIS, we also employ the Tiny-cuda-nn to accelerate our SDF network, achieving a significant time reduction. Besides, this acceleration have almost no impact on the mesh results. (3) We observe that our method can stop early at 20,000 iterations during the generation stage, and the mesh quality only suffers a slight degradation (approximately +0.1 at average cd(ws) $\downarrow$).

Following your suggestion, we present a quantitative comparison for the average training time and the average CD(ws) results on PartNet-Mobility dataset, shown as following. “acc” denotes the aforementioned acceleration, and “Recon.” and “Gen.” are reconstruction and generation respectively.

4. Two-stage Joint Optimization

We sincerely appreciate your professional review comments. Although we adopt a two-stage optimization strategy, the data of each stage is not isolated. In fact, the two-stage image supervision can mutually compensate for each other's unseen regions. Since initialization of the generation stage inherits the Gaussian primitives from the reconstruction stage, the incomplete observation regions in the reconstruction stage can be effectively optimized by the image supervisions of the generation stage. Note that since the deformable field acts solely on movable parts, the rendering loss during the generation stage can be mapped to reasonable pixel coordinates.

Moreover, if the viewpoints in the generation stage do not completely cover the object, the reconstruction stage enables to provide a high-quality initialization for generation. To further validate the analysis, we have conducted ablation experiments with different input views for the two stages, shown as following. “View-1” and “View-2” denote the views of reconstruction and generation stage respectively.

The experimental results demonstrate that when one stage utilizes incomplete observation data (16 random sampled views) and the other stage offers more supervisions (64 views), the mesh results exhibit improvement compared to the case where both stages employ incomplete observations, demonstrating our analysis.

5. The SH coefficient in texture extraction

Thank you for your professional technical review. This is an interesting question. In fact, we first use all the Spherical Harmonics (SH) to obtain view-dependent rendered images when extracting textured meshes. However, The TSDF fusion only bakes the static RGB renderings, which is equivalent to SH0. This design aligns with two core objectives: (1) Higher-order SH coefficients with view-dependent effects are challenging to bake into fixed textures. (2) The view-dependent effects encoded by higher-order SH terms are spatially variant and non-transferable to novel lighting conditions. Retaining them in the static texture maps would introduce artifacts when relighting the mesh.

6. Questions on Table and Figure

Since Deformable-3DGS (D-3DGS) is a dynamic generation method, we only compare the mesh generation results with it. The qualitative results are shown in Fig 5 and 10, corresponding to the quantitative data in Table 2. ArtGS is essentially an RGBD image-based method. In the main draft, we have already compared its surface mesh reconstruction and generation results without depth inputs with our method to demonstrate our superiority on the core topic of this paper. In the supplementary material, we aim to further demonstrate the completeness of our method REArtGS, including part segmentation and joint estimation. Thus we mainly present the visualization results of our method in the supplementary material. Following your suggestions, we have finished additional qualitative comparisons with ArtGS in part segmentation and joint estimation and will supplement them after acceptance, due to the limitations on images and external links in this rebuttal. Meanwhile, please refer to the response to Reviewer E8MT for more quantitative comparison results with ArtGS, due to character limitations.

7. Qualitative Results of Multi-Part Articulated Objects

Thank you for your feedback. We have already presented the high-quality reconstruction and generation results of an articulated object with three movable parts at the fourth row of Figure 6 in the main draft. More qualitative results of multi-part articulated objects will be presented after acceptance, due to the limitation of uploading images and external links.

We sincerely appreciate your valuable comments. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.

1. Question on $x\_{i+1}$ and Undefined Symbols

Thank you for your insightful opinions. In fact, $x\_{i+1}$ in this paper refers to the next sampled point along the ray. We calculate $f(x\_{i+1})$ through Taylor's first-order expansion, i,e, $f(x\_{i+1}) =f(x\_{i})+{f}'(x\_{i}) \Delta x$, where $\Delta x = \frac{z\_{\text{far}}-z\_{\text{near}}}{l}$. $z\_{\text{far}}$ and $z\_{\text{near}}$ are the distances from the near and far cutting surfaces along the Z-negative axis to the viewpoint respectively. $l$ is set to 64. Note that we use the annealing $(1-\frac{n}{N})(\Theta (\frac{1-r\cdot f' (x\_{i})}{2} ) )-\frac{n}{N} (\Theta (-r\cdot {f}' (x\_{i}) )$ to replace ${f}'(x\_{i})$ in actual computation for adaptive transformation of view-normal angle, where $n$ and $N$ denote the current iteration and total iterations respectively. $r$ is the normalized ray direction. $\Theta$ is the ReLU activation Function. We also apologize for the undefined symbols. $x\_{L}$ and $t$ represent the spatial position of Gaussians local coordinate system and ray depth respectively.

2. Input View Setting

We follow the same input settings as PARIS and ArtGS, using 64 multi-view images and 50 test images per stage. We have also supplemented an ablation study on the number of input images. Due to character limitations, please refer to the rebuttal provided to Reviewer BVdL for details.

3. Question on the Geometry Constraints of GOF, 2DGS and PGSR

Thank you for your feedback. 2DGS, PGSR, and GOF are all essentially based on the Gaussian opacity fields. Among them, 2DGS and PGSR attempt to facilitate the normal estimation by compressing 3D Gaussian primitives to 2D shapes. This geometric constraint is not reasonable as the restriction on the shape of Gaussian primitives leads to degraded performance in capturing detailed structures. On the other hand, GOF attempts to optimize the rendering process of 3DGS and approximates the Gaussian’s normal as the normal of the ray-Gaussian intersection plane. The approximation typically introduces normal estimation errors. Moreover, since Gaussian opacity field cannot explicitly define the scene surface, the opacity-based methods often extracts surface meshes with artifacts distant from the surface. Therefore, they still lack more reasonable geometric constraints.

In contrast, our method introduces SDF in 3D Gaussian primitives and leverages the gradients of SDF to accurately define the normals, instead of restricting the shapes of Gaussian primitives or using approximation strategy. And the unbiased regularization encourages Gaussians near the surface to exhibit a high opacity value, achieving more reasonable geometric constraints.

4. Clarification on Originality

We sincerely appreciate your dedicated efforts in the research of the relevant works. We first clarify that this paper does not merely reuse the concepts from Neus, GOF, and 3DGSR. Instead, our REArtGS is the first framework that innovatively introduces SDF to regularize the Gaussian opacity field, which plays a core attribute in 3DGS rendering pipelne.

Among the existing methods, GOF is an opacity-based 3DGS method. The Eq. 3 and Eq. 5 in this paper fundamentally differ from GOF. Specifically, GOF solely determines the $\alpha$-blending weight by the rendering contribution $\varepsilon$, which fails to explicitly define the relationship between Gaussian primitives and the scene surface, leading to results with artifacts. In contrast, our method computes the $\alpha$-blending weight based on both SDF $\sigma(f(x))$ and the rendering contribution $\varepsilon$ (see Eq. 2, Eq. 3, and Eq. 5). The points with the maximum rendering contribution are aligned with the scene surface through the unbiased SDF regularization, enhancing surface reconstruction quality. Note that we quote Eq.4 for the detailed elaboration of the unbiased SDF regularization.

Although 3DGSR also incorporates SDF with 3DGS, its $\alpha$-blending weights purely depend on the SDF-derived opacity, which only utilizes Gaussians’ center as input and ignores their local features. In contrast, our REArtGS integrates both local and global information through Eq. 2 and Eq. 3. Conretely, Eq. 3 combines the rendering contribution derived from local properties of Gaussian primitives with the SDF encoding global spatial position information.

Besides, Neus is built upon a neural implicit continuous representation, allowing the continuous SDF to be seamlessly incorporated into its rendering pipeline. In contrast, 3DGS is a discrete point-based rendering method, making direct adoption of SDF infeasible. This constitutes the fundamental distinction between our method and Neus.

In summary, Our REArtGS has essential differences from these methods at the theoretical level and has achieved substantial improvements rather than simple reuse or combination.

5. Flawed Qualitative Results

Thank you for your insightful comments on our paper. In fact, the reconstruction of self-luminous screens and flat surfaces lacking texture features is a non-trivial task for current surface reconstruction technique. These two cases impose strict requirements on the geometric flatness of the reconstruction results and pose significant challenge for existing methods. In future work, we will introduce illumination decomposition to address self-luminous materials and enhance the planar constraints of 3DGS through RANSAC to enhance the reconstruction of flat surfaces lacking features

However, our method still achieves the best CD(rs) and EMD scores on washer and laptop, and accurately recovers the global structure as shown in Fig. 4. We also observe that key parts such as the keyboard and the washing machine lid are all reconstructed with high quality. Therefore, these local imperfections in the reconstructions do not affect the actual manipulation of articulated objects.

6. Missing Qualitative Comparison

We sincerely appreciate your invaluable feedback. Following your suggestions, we have already finished the qualitative comparisons with other methods on AKB-48 datasets, the qualitative comparison with Ditto, as well as the qualitative ablation results of geometric constraints.

Unfortunately, given the limitation that images and external links cannot be uploaded during this rebuttal, we sincerely apologize for not being able to share these qualitative results with you at the first time, and we formally promise to add these results in this paper after accepted.

Moreover, the content already presented in this paper is sufficient to illustrate the aforementioned issues. Firstly, we conduct extensive comparisons on synthetic datasets, comprehensive demonstrating the superiority of our method. For real-world experiments, our qualitative results aim to fully showcase the generalization ability of the method on real-world data, and the quantitative results in Table. 5 further confirm our performance advantages. Even though the qualitative results of Ditto are not presented, we present the qualitative comparisons with A-SDF, which also uses 3D supervision. And we have conductd a quantitative comparison with Ditto in Table. 1, which already indicates our superiority. Finally, we have presented the qualitative ablation results of unbiased SDF regularization at distribution level in Fig. 3, and the quantitative ablation results of geometric constraints in Table. 3, validating the effectiveness of proposed geometric constraints.

7. Comparison with 3DGSR

We appreciate the time you devoted to the related works. Although 3DGSR also uses SDF and a similar bell-shaped function as ours, we are sorry that we cannot provide a comparison with it because its codes are not available and its official experimental results on articulated objects are not provided. Based on your valuable suggestions, to further demonstrate the effectiveness of our unbiased SDF regularization, we have conducted a quantitative comparison with GSDF (Yu, 2024), which also introduces SDF in 3DGS, shown as following:

We sincerely thank you for your recognition and encouragement of our method. The following is a point-to-point response to the questions you raised. If you have any other questions, please let us know at the first time. We sincerely look forward to the subsequent discussion with you.

1. The Effect of The Diversity of The Two-Stage Views

We sincerely appreciate your professional review comments. Our approach exhibits remarkable robustness to the diversity of two-state views. Specifically, our method enable realistic surface mesh generation unless an articulated object undergoes extremely minimal rotation or translation.

To validate the robustness of our method on the diversity of two-state views, we have conducted ablation experiments on the rotation angles and translation distances in the second state for USB and storage of the PartNet-Mobility dataset. Concretely, we adjust the rotation angle and translation distance of articulated object at the second state to different values, and then generates the surface mesh at $s=0$ from the canonical state. We report the CD (ws) results below.

We observe that the diversity of two-state viewpoints does not lead to a significant influence on the mesh generation results of our method. For the storage, even a smaller translation distance yields superior surface mesh generation. This demonstrates the robustness of our method against the diversity of two-state views.

2. Question on Taking More State Inputs

Thank you for your valuable comment. This is an interesting question. During the generation stage, our method use the deformed Gaussians obtained from the deformable field to calculate the rendering loss with the image supervisions at corresponding state. Therefore, incorporating view inputs from additional states is equivalent to adding more image supervisions, which can naturally enhance the surface mesh generation quality.

We also validate this analysis on the USB of PartNet-Mobility dataset. Specifically, we introduce additional view inputs at the state $s = 0.1$. As a result, the CD (ws) result of surface mesh generation improves significantly from 1.68 to 0.85. This proves that our method can improve the mesh generation quality through additional state view inputs.

Moreover, we have demonstrated that views from different states mutually compensate for each other's unseen regions. For more details, kindly refer to our response to Reviewer BVdL.

3. Reliance on Camera Poses

Thank you for your valuable feedback. In fact, camera pose estimation is now a ready-to-use technology. For multi-view images, our method can directly use Colmap to estimate the corresponding camera poses. The camera poses estimated by Colmap are sufficient for our method to achieve high-quality surface reconstruction and generation. In recent years, many excellent camera pose estimation methods have also been able to meet our requirements for camera poses, such as Reloc3r (Dong, 2024). Therefore, we believe that the reliance on camera poses does not constitute an intractable shortcoming, and we aim to introduce Reloc3r into our framework for camera pose estimation in the future work.

4. Rendering of Objects with Transparent Materials and Non-Lambertian Surfaces

Thank you for the insightful comments. Transparent materials and non-Lambertian surfaces undoubtedly pose challenges in current 3D reconstruction due to their complex requirements for light modeling. However, several works attempt to address the reconstruction of transparent materials and non-Lambertian surfaces recently, and we are inspired by them. In the future works, we aim to introduce the Gaussian light field probes to encode both ambient light and specular refraction for transparent object reconstruction, following TransparentGS (Huang, 2025). Moreover, we consider the spectrum of a non-lambertian surface as a linear combination of the diffuse and specular components, and try to introduce the Dichromatic model in our framework for its reconstruction.

Dear reviewer, thank you so much for your thoughtful feedback and support of our work. We have carefully provided point-by-point responses for each of your comments. If you have any further questions or concerns, please don’t hesitate to let us know. We are willing to provide additional theoretical analysis and experimental results to address your questions. Your support means a lot to us, and we truly appreciate your continued kindness and encouragement.

We sincerely appreciate your valuable comments. The following is a point-by-point response to your questions. If you have any other questions, please let us know at the first time. We earnestly look forward to the subsequent discussions with you.

1. Question on Insufficient Evaluation

Thank you for your insightful opinions. We also recognize the significance of joint parameters and part-level meshes for articulated objects. However, as the main topic of this paper is the surface reconstruction and generation of articulated objects, we moved the evaluation results of joint parameter and part-level mesh results to the Appendix taking the page limitation into consideration. Additionally, the surface generation results presented in the main draft are essentially high-dimensional mappings of part-level meshes. Realistic surface generation already indicates accurate part-level mesh extraction.

As for not comparing the joint parameter and part-level mesh evaluation results of ArtGS, it is because ArtGS is essentially a method based on RGBD image inputs, while our method uses RGB images. We have already demonstrated in the main draft that our method outperforms ArtGS in surface reconstruction and generation when using the same RGB image inputs on both synthetic and real-world data. In kinematic parameter evaluation results of the supplementary material, we are more concerned with the comparison to PARIS, which also only uses RGB image inputs. Following your valuable suggestions, we have added quantitative comparisons of joint parameter estimation and part-level mesh reconstruction between our method and ArtGS. To ensure a fair comparison, we train ArtGS using the same RGB image inputs as our approach. The results are presented below. The experimental results demonstrate that our method outperforms ArtGS in joint estimation and part-level mesh reconstruction.

Quantitative comparison of joint parameter estimation:

Quantitative comparison of part-level mesh reconstruction:

2. Clarification on Technical Novelty

We sincerely appreciate your dedicated efforts in the research of the relevant works. To our best knowledge, our method first innovatively introduce the unbiased SDF regularization, establishing a connection between SDF and the Gaussian opacity field.

It is important to clarify that GOF is an opacity-based 3DGS method. SDF is not incorporated throughout its entire process and its mesh extraction solely relies on an opacity level set. Given that opacity cannot explicitly represent the relationship between 3D Gaussian primitives and the scene surface, the opacity-based method typically yields surface mesh results with artifacts distant from the surface.

Besidse, integrating SDF into 3DGS poses a significant challenge. This is because 3DGS is fundamentally a discrete point-based rendering pipeline, while SDF is a continuous implicit function representation. Existing works, such as GSDF and 3DGSR, merely utilize SDF guidance for normal constraint and the pruning of Gaussian primitives and fall short of futher regularizing the opacity of 3D Gaussians, which serves as the core attribute in $\alpha$-blending.

In contrast, our unbiased SDF regularization encourages the alignment of the Gaussian opacity field with SDF. Specifically, when the opacity reaches its maximum value, it drives the SDF value at the corresponding position to approach zero. This ensures that Gaussians near the surface exhibit high opacity values, eliminating artifacts away from the surface. Therefore, the unbiased SDF regularization effectively addresses the limitations of the opacity field in geometric representation and forms the core innovation of our method.

Note the TSDF fusion method mentioned in GOF's paper is distinct from the neural SDF representation and is designed for mesh extraction with discrete volume representations. Its SDF values are simply constructed through multi-view depth image fusion when extracting the mesh, rather than a continuous representation learned from the network.

3. Clarification on Single-Part Limitation

We sincerely appreciate your thorough consideration of our method. Our method is capable of effectively dealing with articulated objects exhibiting multiple movable parts. We have already presented the high-quality reconstruction and generation results of an articulated object with three movable parts at the fourth row of Figure 6 in the main draft. Moreover, we have elaborated in detail on the generation pipeline for articulated objects with multiple movable parts in Appendix C.4. We have put the details with italics below for your quick reference.

Mesh generation of multi-part articulated objects can be treated as a straightforward extension of the two-part task for our approach. We can generate meshes for multi-part objects in unseen states through a sequential learning strategy. Specifically, given an articulated object with $k$ dynamic parts $\omega\_{d_k}$ , we start by fixing all dynamic parts $\omega\_{d\_{2}}, ..., \omega\_{d\_{k}}$ except $\omega\_{d\_1}$ . The object is then decomposed into two parts: a dynamic part $\omega\_{d\_1}$ and a static part $\omega_s$ (comprising all remaining points). After learning the motion and segmentation mask for $\omega\_{d\_1}$ , we sequentially process the next dynamic part $\omega\_{d\_2}$—with the static part updated as: $\omega\_s = \hat{\omega}\_{d\_2} - \omega\_{d\_1}$ , where $\hat{\omega}\_{d\_2}$ denotes the remaining points excluding $\omega\_{d\_2}$ . By parity of reasoning, we extend this process to learn the motions and segmentation masks for all $k$ dynamic parts. Finally, mesh generation for any unseen state of the multi-part object is achieved using the pipeline proposed in Sec. 3.2.

Regarding the occlusion among multiple parts, the two-stage multi-view image inputs can mutually complement their respective unseen regions. Specifically, since the Gaussian primitives in the reconstruction stage undergo further optimization in the generation stage, the images from each viewpoint in both stages can act as valid rendering supervisions for 3D Gaussian primitives. This allows our method to make full use of the multi-viewpoint images from the two stages to refine the Gaussian primitives. Please refer to the response to Reviewer BVdL for details. Consequently, in most scenes, the two-stage multi-view image inputs are adequate to effectively mitigate the occlusion problem among multiple parts.