We thank the reviewer for recognizing the high efficiency of our GeoSplatting approach and the quality of our paper’s presentation. We also greatly appreciate the detailed suggestions provided. Below, we address the concerns point by point. For complex issues, please refer to the appendix in our revised submission for a more detailed explanation, if necessary.

1. Inadequate Discussion

We thank the reviewer for listing many valuable related works. For the carefully suggested works, we will provide a brief discussion as follows and will reference them in our paper.

• 3DGSR.

  It maintains the stochastic nature of 3DGS geometry, using the SDF-to-opacity transformation to align Gaussians with a deterministic surface defined by the SDF field. During training, the stochastic geometry converges to this surface, achieving excellent geometry reconstruction.

  GeoSplatting, on the other hand, prioritizes precise modeling of light-geometry interactions. It uses an explicit isosurface to represent deterministic geometry, enabling accurate normal modeling for complex lighting effects. Additionally, it extends 3DGS with PBR attributes for efficient, high-quality differentiable rendering, offering robust inverse rendering capabilities, especially for specular scenes.

• Isosurface-based inverse rendering.

  Isosurface-based methods (e.g. NVdiffrec, NVdiffrecmc) employ differential mesh-based rendering processes, which are prone to falling into local minima due to the deterministic visibility of isosurfaces.

  In contrast, our GeoSplatting employs Gaussian splatting as a more powerful differentiable PBR rendering technique.

• Neural-field-based inverse rendering.

  Several neural-field-based methods have been proposed for inverse rendering, integrating neural fields with PBR rendering, such as NeRFactor, PhySG, InvRender, TensoIR, and NeRO.

  While these methods offer varied solutions, they are much less efficient than 3DGS-based approaches in FPS and training time, and their rendering quality, lighting modeling, and relighting capabilities are limited by the sampling-intensive nature of neural fields.

  In contrast, our GeoSplatting is efficient and is able to model high-frequency light-material interaction by integrating 3DGS with isosurfaces.

2. Dataset Choice

We appreciate the reviewer’s suggestion that the Synthetic4Relight dataset may not be challenging enough to evaluate shadow modeling. However, we would like to respectfully point out that the suggested Hotdog scene from the NeRF Synthetic dataset can be too challenging for most of the existing inverse rendering methods to achieve effective material-shadow decoupling, as shown in Fig. 18 (Appendix D.2).

Therefore, to follow the reviewer’s constructive suggestion and to provide more results to evaluate shadow and BRDF decoupling, we performed additional experiments using the TensoIR Synthetic dataset. Results are shown in Fig. 32 (Appendix H.4), with quantitative data provided in Table 12 (Appendix H.4), which demonstrate GeoSplatting’s best relighting performance and its comparable albedo quality to state-of-the-art baselines including the 3DGS-based R3DG and the neural-field-based TensoIR.

3. NVS Comparison

Thanks for the reviewer’s constructive concerns that novel view synthesis (NVS) quality may not be critical for inverse rendering. This issue is very valuable and worth further discussion. We would respectfully argue that the importance of NVS quality in the context of inverse rendering depends on the dataset, and will carefully clarify as follows:

NVS quality is not important for diffuse scenes (in Fig. 6): NVS quality is unable to reflect ability in modeling complex light interactions, such as inter-reflections and shadows.

NVS quality is important for highly specular scenes (e.g., Materials): NVS quality provides strong evidence of the ability to model high-frequency lighting-material effects, like those on shiny surfaces. Additionally, many works, including Ref-NeRF, GaussianShader, and NeRO, use NVS experiments on the Shiny Blender dataset, where the scenes are highly specular, to demonstrate their ability to model high-frequency lighting-material effects.

As a result, while Table 1 and Fig. 6 offer limited insights into inverse rendering performance, we also conducted NVS comparisons on the Shiny Blender dataset that features highly specular scenes, following Ref-NeRF and GaussianShader, to validate our ability to model high-frequency lighting-material effects. Please see Appendix H.3 for more details.

4. Decomposition Quality

The reviewer's concern about GeoSplatting's limitations in shadow modeling is very valuable in the context of inverse rendering. However, while shadow and inter-reflection effects are important in inverse rendering, we respectfully highlight that modeling high-frequency lighting-material effects is equally crucial. Given the “impossible trinity” explained in our general response, we would also clarify that none of the existing works can address reflective surface, shadow, and efficiency at the same time.

In this context, we claim our GeoSplatting achieves state-of-the-art inverse rendering performance for the following reasons: (1) For specular objects, GeoSplatting surpasses all baselines in rendering and normal quality, delivering superior decomposition results, which is evidenced by experiments in Appendix H.3. (2) For general inverse rendering tasks including occluded cases, GeoSplatting leads in rendering quality, training efficiency, relighting performance, and normal quality, with decomposition results on par with the state-of-the-art methods, which is evidenced by Table 2 and additional experiments in Appendix H.4.

Additionally, we highlight that GeoSplatting can model shadow effects by introducing a learnable occlusion term (Appendix D.2) in the PBR pipeline. The qualitative results show that the occlusion term brings significant improvements in material-shadow decoupling, compared to those in the previously submitted version, as shown in Fig. 28-29 of the revised submission (e.g., Hotdog, Chair from Synthetic4Relight), with quantitative evidence provided in Table 2 (Sec. 4.2).

Again, we thank the reviewer for the insightful and constructive suggestions of the reviewer and agree that good work should focus on the long-standing issues in the field, to contribute to the community. We provide more discussions in Appendix D, sincerely hoping to find common ground with the reviewer on the advanced aspects of inverse rendering, while kindly requesting reconsideration of GeoSplatting's strengths and weaknesses.

5. Baseline Metrics and Training Times

Thanks for the kind suggestions. We apologize for the discrepancies in the reported metrics.

1. 3DGS. The training time for 3D-GS is based on our reimplementation using the gsplat repo on Github, which impacts performance. After using the original codebase, we confirmed a training time of approximately 5.4 minutes, with no errors in the SSIM metric upon re-evaluation.
2. 2DGS. The 2D-GS metrics are directly from the original codebase, so we believe there is no error.
3. Mip-NeRF. The reported 2.5 hours was cited from the original paper, but we missed that its experiments are conducted on TPU. On a single RTX 4090 GPU, our reimplementation shows a training time of ~48 hours (1152 minutes). We’ve updated these metrics in the revised version.

Q1. Typos in the Title

As the reviewer carefully pointed out, there are typos in the title and we’ve fixed them in our revised submission.

We sincerely thank the reviewer for the invaluable discussion, time, and effort. As mentioned, this discussion has certainly strengthened our paper. While the reviewer may think the decomposition results are poor, we respectfully clarify that these results are quantitatively competitive with TensoIR and R3DG, and the claims should be confined to the context of diffuse cases. Following the reviewer's suggestion, We've already de-emphasized decomposition performance for diffuse objects.

Additionally, we would like to highlight that our current contributions focus on:

1. Achieving the best efficiency (Table 1),
2. Providing the highest normal quality (Table 1 & 12),
3. Achieving the best specular surface decomposition performance (Table 1), and
4. Delivering competitive diffuse surface decomposition performance (Table 2 & Table 12).

We believe that (1), (2), and (3) are equally as important as (4) in the context of inverse rendering, which makes GeoSplatting ”a good paper”, as praised by the reviewer. We fully acknowledge that decomposition is a critical aspect and understand that this might be the primary concern of the reviewer. However, we respectfully suggest that a single point of evaluation should not be the sole basis for rejecting the paper. Once again, we sincerely thank the reviewer for the thoughtful feedback!

We sincerely thank the reviewer for the constructive suggestions and valuable reviews. We will address the concerns point by point in the responses below. For complicated issues, please refer to the appendix in our revised submission for a detailed explanation, if necessary.

1. Typos

Thanks for the kind suggestions. In our revised submission, we’ve fixed most typos.

2. Novelty

We greatly thank the reviewer for the constructive concern about the novelty of our work, but would respectfully hold a different opinion from the reviewer. We would like to emphasize our novelty as follows:

• Our MGAdapter is a novel Mesh-to-Gaussian module that explores the key problems in mesh-Gaussian alignment, including (1) The shape of the Gaussians does not align well with the triangle mesh in tangential directions, particularly near edges. (2) Strict alignment in normal directions reduces appearance quality (see Appendix B.4). (3) Standard 3DGS uses a fixed number of Gaussian points, but the Mesh-to-Gaussian module needs optimization for a variable number of points.

  Our MGAdapter effectively addresses all of these challenges, providing accurate geometric guidance while preserving the rendering quality as well as the efficiency of the standard 3DGS.

• Our integration of isosurface geometry guidance with Gaussian-based PBR rendering is a novel methodology in the field of inverse rendering, which bridges isosurface and Gaussian together, naturally resulting in more accurate local geometry and normal directions, therefore bringing better inverse rendering performance.

  Extensive experiments demonstrate the effectiveness of such an integration. Specifically, GeoSplatting achieves the best relighting performance, best normal quality, and state-of-the-art decomposition performance on multiple datasets including Synthetic4Relight, TensoIR Synthetic, and Shiny Blender.

3.1 Geometry Quality Comparison in Table 3

We appreciate the reviewer’s valuable concerns about the geometry quality of GeoSplatting and would like to clarify about geometry quality of GeoSplatting. Specifically,

• Our comparison in Table 3 is not “unfair”, as we only claim comparable performance in geometry reconstruction quality, not the best.

  The original statement, "Overall, our approach achieves the best average geometry performance" (L454-L455), is misleading. We do not claim superiority in geometry reconstruction quality, as GeoSplatting is designed for inverse rendering tasks.

  Instead, the results in Table 3 show that our method achieves comparable geometry recovery performance to state-of-the-art surface reconstruction techniques, demonstrating the effectiveness of our intermediate mesh guidance strategy.

  Considering the reviewer’s valuable concern, we remove the misleading Avg. column of Table 3 in our revised submission for a clearer representation.

• To further support our claim about normal quality, we conduct additional experiments to demonstrate GeoSplatting’s accurate normal estimation: (1) On TensoIR Dataset: Our method achieves the best average normal quality (mean angle error, MAE) among relightable baselines (see Table 12 in Appendix H.4, Line 1521-1540). (2) On Shiny Blender Dataset: Our approach significantly outperforms all listed inverse rendering methods in MAE (see Table 11 in Appendix H.3, Line 1426-1435).

3.2 Spot

While the best-performing scene (Spot) features relatively simple geometry, we respectfully disagree with the reviewer’s characterization of it as "too simple.” We hope the reviewer provides more context of the meaning of “simple,” and will carefully provide further explanation as follows:

• If "simple" means simple to reconstruct, we would like to highlight that the Spot scene remains challenging for reconstruction. This is evidenced by the failure of several powerful geometry reconstruction baselines, such as 2DGS and NeuS2. It would be contradictory to describe the case as "simple" when the leading reconstruction methods struggle with it. 2DGS and NeuS2 fail to capture specular surfaces in Spot, mainly due to their inability to model complicated light-material interactions.
• If "simple" means the Spot has a simple geometry and lacks challenge, we would like to emphasize that our discussion is in the context of inverse rendering, not purely geometric reconstruction. We want to emphasize that GeoSplatting is designed to address inverse rendering challenges, with a particular focus on capturing complex material-light interactions. For specular surfaces in Spot, GeoSplatting successfully models complicated light-material interaction, leading to state-of-the-art geometry quality in this case.

3.3 Lego

The reviewer concerns that GeoSplatting’s geometry on the Lego scene is “not good at all”. However, we would respectfully disagree with it and would like to provide convincing evidence. Therefore, we include a comparison of normal quality on the TensoIR dataset (Appendix H.4 in our revised submission), where GeoSplatting on the Lego scene achieves comparable normal quality to the best method, TenosIR, despite its $300^3$ grids over our $96^3$ ones.

Additionally, although the geometry quality of the Lego scene is constrained by the resolution of the FlexiCubes, we examine the effect of FlexiCubes resolution on GeoSplatting's performance in Appendix E. While higher-resolution FlexiCubes provide more precise normal guidance, the associated increase in computational cost and training time may outweigh the benefits.

Q1. Normal Map

Since each Gaussian point has a normal attribute, the normal map can be generated by directly splatting the normal attributes onto the screen, similar to how RGB colors are rendered. Most 3DGS-based inverse rendering methods produce normal maps in this way.

Dear Reviewer DXwn,

We greatly thank for your time and effort in the rebuttal period, and would greatly appreciate it if you could provide feedback on our replies. We would like to discuss further if there are any remaining concerns.

We would like to provide a brief quantitative comparison here, to address your earlier concern regarding potentially inadequent experimental results. We would like to highlight that our GeoSplating method achieves the best PSNR and normal quality (MAE) among all NeRF-based and 3DGS-based inverse rendering methods, demonstrating our approach as a state-of-the-art inverse rendering method for reflective scenes and validating GeoSplatting's excellent ability in capturing high-frequency lighting-material interactions.

Note that the "diffuse cases" denote scenes from the TensoIR Synthetic dataset and the "specular cases" denote scenes from the Shiny Blender dataset.

In light of these results, we sincerely hope that you could reconsider our contributions as we believe that GeoSplatting proposes a novel framwork, employing geometry guidance to both efficienctly and effectively enhance inverse rendering ability, which we see valuable to the community. We will also release all the code to facilitate future research. We are more than happy to address any additional feedback you may have.

Best regards,

Authors

Dear Reviewer DXWn,

We sincerely thank the reviewer for the time and effort in evaluating our work. We are happy that most concerns have been addressed. The reviewer raises new concerns as listed:

1. "... agree with Reviewer f2Bn ... should focus more on reflective scenes."
2. "... for datasets like TensoIR and Synthetic4Relight, Geo-Splatting's performance in normal quality is less competitive, and it does not account for visibility modeling..."
3. "... Geo-Splatting still requires a second stage ... which undermines the effectiveness of its differentiable isosurface extraction method"
4. "... methods like 3DGS-DR can handle reflective objects well ... could be used for geometry initialization instead of FlexiCube, as the latter is limited by its resolution"

We would like to provide further clarification as follows, to address the reviewer's concerns:

1. The reviewer kindly suggests focusing more on reflective scenes. Thanks for the suggestions. We have already revised our paper, restating our contribution (L98-L107, Sec. 1) and providing experimental results on reflective scenes (L324-L377, Sec. 4.1).

2. The reviewer may think GeoSplatting's normal quality is less competitive for datasets like TensoIR and Synthetic4Relight. We would like to highlight our performance in normal MAE is already the best for the TensoIR dataset (L1521-L1540, Table 12 in Appendix H.4). As for the Synthetic4Relight dataset, since this dataset does not provide normal, we cannot compare normal quality assessments on this dataset. As for visibility, we fully agree with the reviewer that it is important. We model it with occlusion map. While raytracing or neural visibility modeling would be a better solution, they typically take much longer time. Instead, Geosplatting applies occlusion map and achieves the best efficiency compared to all the inverse-rendering methods. As for the relighting performance, we want to emphasize that we have achieved the best relighting performance in both the TensoIR and Synthetic4Relight datasets (Table 2 & Table 12).

3. The reviewer may question the effectiveness of the differentiable isosurface extraction method in our first stage. We thank the reviewer for pointing this out. We have already conducted a quantitative comparison to demonstrate our method's effectiveness in enhancing geometry:

   Method	Normal MAE (TensoIR dataset)	Normal MAE (Shiny Blender dataset)
   3DGS*	~10	~15
   2DGS	4.17	13.65
   Ours	3.87	2.28

   The vanilla 3DGS/2DGS optimization alone leads to suboptimal geometry, validating that our first stage is crucial, as it brings accurate geometry and precise normals that are critical for inverse rendering tasks. It is further demonstrated that our method achieves the best inverse rendering performance on reflective datasets, primarily due to the best normal brought from the first stage.

4. The reviewer may think the 3DGS-DR method achieves better performance for reflective objects. We thank the reviewer for bringing this related work but want to point out that 3DGS-DR is not an inverse rendering method. Nevertheless, GeoSplatting still outperforms 3DGS-DR in both rendering quality and normal estimation accuracy. We will add it to the related work.

   Method (on Shiny Blender dataset)	Normal MAE	NVS PSNR
   3DGS-DR	4.87	34.09
   Ours	2.28	35.05

5. The reviewer may think GeoSplatting's geometry quality is limited by resolution. We acknowledge the resolution limitation but would like to highlight that even so, we still achieve the best normal quality among all the baselines.

Summary

We sincerely hope our explanation addresses the reviewer's concerns and will incorporate the above discussion into our revised paper. We would be happy to provide additional clarification if the reviewer has any further questions. Once again, we deeply thank you for the reviewer's hard work and would appreciate it if the reviewer could kindly reconsider our contribution.

Q1. Second Stage

The second stage of GeoSplatting is similar to the training stage of vanilla 3DGS but without any densification or pruning. Moreover, we also optimize the normals. Though it is totally free, in stage 1 it provides good initialization and in stage 2 the meaningful normal is still preserved.

Q2.1 Why can jointly training 3DGS and isosurface improve the quality of inverse rendering?

• 3DGS. For an intuitive understanding, vanilla 3DGS is highly effective in capturing multi-view-consistent appearances of 3D objects, not relying on normal information from light-surface interaction to guide the reconstruction. As evidenced by Fig. 30 (Appendix H.3), when 3DGS-based methods like R3DG fail on highly specular cases, they still obtain a coarse geometry and produce a reasonable appearance.

• NVdiffrec. In contrast, isosurface-based methods like NVdiffrec rely heavily on mesh-based differentiable PBR rendering processes, which heavily depend on normal information from light-surface interaction to guide the reconstruction. While this empowers NVdiffrec to reconstruct detailed lighting efficiently, the deterministic nature of isosurfaces makes it difficult to capture high-frequency light-material interactions. As a result, NVdiffrec’s failure cases on specular objects are frequently accompanied by completely noisy geometry, as illustrated in Fig. 30 (Appendix H.3).

• GeoSplatting. Returning to our GeoSplatting approach, the Gaussian points and the mesh mutually benefit the reconstruction process. Gaussian splatting provides strong gradient properties for capturing multi-view-consistent appearances, while the mesh offers guidance for more accurate light-surface interaction estimation. A supporting example is that GaussianShader also employs a split-sum approximation, which excels in capturing environmental lighting. However, our method achieves significantly better lighting reconstruction quality, likely due to improved normal estimation, as illustrated in Fig. 31 (Appendix H.3).

Q2.2: Does the CD scores in Table 3 mean that joint training affects the reconstruction quality of the geometry?

The CD scores do not indicate a geometry quality degradation from the joint training, and we would like to clarify that the CD scores in Table 3 have been scaled by 1e-4. We sincerely appreciate the reviewer's careful review and apologize for the lack of clarity in the original submission.

Q3. Inter-Reflection during Relighting

Currently, indirect lighting cannot be constructed during relighting in GeoSplatting, as our proposed residual terms are highly related to the current illumination and become invalid under a different illumination.

However, we believe by performing ray tracing for Monte Carlo sampling under the changed environmental lighting, the inter-reflection effects can be baked into our residual terms. While this simple technique could help improve relighting performance, we do not employ it primarily due to the inefficiency of such an extensive Monte Carlo sampling, but it raises a promising future direction and we will discuss it in the revision. Thanks for the reviewer's valuable suggestions.

We thank the reviewer for the recognition of our method as an innovative technique for geometry enhancement. We also greatly appreciate the reviewer’s detailed suggestions. Below, we address all the concerns point by point.

1. Object-Level Reconstruction vs. Scene-Level Reconstruction

The reviewer is constructively concerned that employing the FlexiCubes and the object mask loss may limit the method to object-level tasks. We acknowledge this and provide a detailed analysis of the impact of object mask in Appendix F.1. Specifically, GeoSplatting utilizes FlexiCubes to enable precise geometry and normals, while also inheriting the limitation from FlexiCubes that can be applied to the object level for its current version.

We agree that further extension to scene level is important and propose two promising directions. (1) For the object mask loss contributed to enhancing geometric stability in the optimization process (evidenced in Appendix F.1), a normal regularization technique, such as depth-normal consistency in 2DGS, can be a better alternative for scene-level extensions. (2) For the limited grid resolution in FlexiCubes, implementing FlexiCubes with adaptive resolution and incorporating scene contraction techniques, as seen in MipNeRF360, could be effective.

2 & 3. Ambient Occlusion & Roughness Reconstruction

We greatly thank the reviewer for the valuable concern about GeoSplatting's challenges in handling ambient occlusion. However, as pointed out in the general response, reflective surface modeling, shadows (which also includes inter-reflection and ambient occlusion), and efficiency can be the impossible trinity.

While we acknowledge that the quality of roughness reconstruction of GeoSplatting can be significantly affected by occlusion, Geosplatting manages to model shadow effects by introducing a learnable occlusion term (Appendix D.2) in the PBR pipeline. The qualitative results show that the occlusion term brings significant improvements in material-shadow decoupling, compared to those in the previously submitted version, as shown in Fig. 28-29 of the revised submission (e.g., Hotdog, Chair from Synthetic4Relight), with quantitative evidence provided in Table 2 (Sec. 4.2). More discussions are provided in Appendix D.2.

Among the compared split-sum approaches (e.g., NVdiffrec, GS-Shader), GeoSplatting achieves the best albedo & roughness reconstruction. Moreover, GeoSplatting excels in reflective surface modeling, achieving excellent roughness quality where all baselines fail. This strength is evidenced in Fig. 31 (Appendix H.3), where GeoSplatting significantly outperforms other methods.

Additionally, while GeoSplatting's split-sum approach struggles with roughness-shadow decoupling (Fig. 7 and Fig. 27-29), SG-based methods like TensoIR and R3DG also face significant limitations in handling specular surfaces, as illustrated in Fig. 16 (Appendix D) and Fig. 31 (Appendix H.3). We provide more discussions in Appendix D.1.

4. Language

Thanks for the reviewer’s kind suggestion. We’ve checked the grammar and fixed a lot in our revised submission.

Dear Reviewer T5mu,

We greatly thank for your valuable insights and helpful feedback on our work. We would like to provide a brief new quantitative comparison here, where our GeoSplating method achieves the best PSNR and normal quality (MAE) among all NeRF-based and 3DGS-based inverse rendering methods, demonstrating the effectiveness of our MGadapter as geometry guidance and highlighting our GeoSplatting's superior performance.

Note that the "diffuse cases" denote scenes from the TensoIR Synthetic dataset and the "specular cases" denote scenes from the Shiny Blender dataset.

We sincerely thank you for recognizing and appreciating our work. We will release all the code to the community to facilitate future research. Once again, we greatly thank for your time and effort during the rebuttal phase.

Best regards,

Authors

We thank the reviewer for the valuable suggestions. We address the concerns point by point in the responses below.

1. Suggested References

We thank the reviews for pointing out the missing reference works. Below we provide a brief discussion about them and will add them in the revision.

[1] and [2] both introduce a Mesh-to-Gaussian conversion module. However, compared to our MGadapter, their modules are non-differentiable and mainly aim to enable deformation through mesh-Gaussian alignment. In contrast, our pipeline is fully differentiable and mainly focuses on providing geometry guidance to enhance inverse rendering. [3] is similar to 2DGS which focuses on geometry reconstruction tasks, while ours targets inverse rendering challenges.

[4] also includes a Mesh-to-Gaussian module like ours. However, its basic Mesh-to-Gaussian module does not focus on geometry quality and ignores two important geometric issues: (1) The shape of the Gaussians does not align well with the triangle mesh in tangential directions, particularly near edges. (2) Strict alignment in normal directions reduces appearance quality (see discussion in Appendix B.4, L798-859). In contrast, our approach overcomes both issues with an efficient and effective Mesh-to-Gaussian module.

2. Insufficient Geometric Comparison

We appreciate the reviewer’s valuable suggestion and conduct additional experiments to support our claim (Line 084) about accurate normal estimation, where GeoSplatting achieves the best normal quality over baselines:

1. On TensoIR Dataset: Our method achieves the best average normal quality (mean angle error, MAE) among relightable baselines (see Table 12 in Appendix H.4, Line 1521-1540).
2. On Shiny Blender Dataset: Our approach significantly outperforms all listed inverse rendering methods in MAE (see Table 11 in Appendix H.3, Line 1426-1435).

3. Resolution Impact Survey

Thanks for the reviewer's suggestion. We conduct comparison experiments to analyze the impact of FlexiCubes resolution on both the results and speed, which is worth discussing.

Specifically, we conduct experiments on the Lego dataset using three different grid resolutions: 64, 96, and 128. We observe that when resolution increases, the normal MAE as well as NVS PSNR improves a little (~0.5 in MAE and ~0.4 in NVS). However, the training time increases (e.g., by a factor of 4x from 96 to 128), which may not justify the potential benefits. Therefore, it indicates the trade-off between performance vs. resolution, which justifies the choice of grid size as 96. We provide details results and discussions in Appendix E.

4. Writing Issues

We thank the reviewer for the kind suggestion about the incorrect citation format and have fixed it in our revised submission.

Q1. Efficiency

The reviewer valuably questions the efficiency of our method since our training time is 20 minutes, compared to 15 minutes for vanilla 3DGS with the same CUDA implementation, which we explain as follows:

• We use the HashGrid from Instant-NGP (implemented with tiny-cuda-nn) instead of a simple MLP, enabling very fast attribute querying. Details of the network configuration are provided in Appendix B.5.
• We employ FlexiCubes (scalar field) instead of an SDF field. (1) Unlike the SDF field, the scalar field does not require maintaining SDF properties (e.g., no need for an eikonal loss), making optimization more efficient. (2) Moreover, unlike neural field methods like NeuS that represent the SDF field by an MLP, our scalar field uses a 96x96x96 grid with iso-values stored at grid vertices. Directly optimizing these iso-values is much faster than training an SDF MLP.

Q2. Heuristic Function

We apologize for the lack of clarity in the submitted version and make a detailed explanation as follows:

• Specifically, for a given value of $\mu$, a set of barycentric factors is uniquely determined.
• From these factors, $S$ and $R$ are computed based on the shape of each triangle.
• A more detailed formulation can be found in Appendix B.2.

Q3. Second Stage

The second stage is similar to the training process of vanilla 3DGS, with key differences being that: (1) No densification or pruning is involved. (2) Gaussian points with normal attributes are optimized under PBR constraints, leading to limited movement.

While vanilla 3DGS’s free optimization enhances NVS quality, the light-material-interaction-aware geometry guidance in GeoSplatting’s first stage is essential for handling non-Lambertian surfaces. As evidenced by Table 10 (Appendix H.3), Vanilla 3DGS, with its free optimization and densification strategy, struggles to estimate glossy surfaces, whereas GeoSplatting’s geometry guidance can avoid these issues.

[1] Li, et al. "DreamMesh4D: Video-to-4D Generation with Sparse-Controlled Gaussian-Mesh Hybrid Representation." arXiv (2024).

[2] Gao, Lin, et al. "Mesh-based Gaussian Splatting for Real-time Large-scale Deformation." arXiv (2024).

[3] Dai, Pinxuan, et al. "High-quality Surface Reconstruction using Gaussian Surfels." SIGGRAPH (2024).

[4] Lin, et al. "Direct Learning of Mesh and Appearance via 3D Gaussian Splatting." arXiv (2024).

Dear Reviewer X2HQ,

We sincerely thank you for your time and effort during the rebuttal period and would greatly appreciate it if you could provide feedback on our responses. We would also welcome the opportunity to discuss any remaining concerns.

We would like to provide a brief quantitative comparison here, to address your earlier concern regarding potentially inadequent experimental results. We would like to highlight that our GeoSplating method achieves the best PSNR and normal quality (MAE) among all NeRF-based and 3DGS-based inverse rendering methods, demonstrating our approach as a state-of-the-art inverse rendering method for reflective scenes and validating GeoSplatting's excellent ability in capturing high-frequency lighting-material interactions.

Note that the "diffuse cases" denote scenes from the TensoIR Synthetic dataset and the "specular cases" denote scenes from the Shiny Blender dataset.

In light of these results, we sincerely hope that you could reconsider our contributions as we believe that GeoSplatting proposes a novel framwork, employing geometry guidance to both efficienctly and effectively enhance inverse rendering ability, which we see valuable to the community. We will also release all the code to facilitate future research. We are more than happy to address any additional feedback you may have.

Best regards,

Authors

Rebuttal: Contribution Claims

We sincerely thank the reviewer for the thoughtful suggestion and would like to make a fair and precise claim as follows:

GeoSplatting is a novel inverse rendering method that leverages a hybrid representation of 3DGS and isosurfaces. By inheriting the excellent efficiency of 3DGS and incorporating accurate isosurface geometry guidance, GeoSplatting achieves state-of-the-art inverse rendering performance in reflective scenes, which demonstrates its impressive ability in modeling high-frequency light-material interaction. Additionally, for general cases, GeoSplatting delivers decomposition results that are comparable to those of state-of-the-art inverse rendering baselines. Extensive quantitative and qualitative results are provided to support our claims.

Rebuttal: NeRO

As NeRO requires approximately 25 hours to train a single case on an RTX 2080Ti (as reported in the original paper), we will include its geometry results in Table 11 and Figure 30 in the revised version of our paper. Regarding excessive smoothing in the Helmet scene, the limited resolution may prevent GeoSplatting from reconstructing the detailed geometry near the seam.

Rebuttal: Results in Figure 32

We acknowledge that despite of higher PSNR, the hue inconsistency in GeoSplatting's qualitative results can be noticeable. It is still primarily due to GeoSplatting's subpar ability in shadow modeling.

The Armadillo scene shows the strongest shadow effects among the eight scenes in the Synthetic4Relight and TensoIR datasets. The hue inconsistency in relighting, which is constructively noted by the reviewer, is due to these shadow effects. Specifically, the ground-truth environment map for the training view features a strong blue hue. Underestimating the shadow effects results in the environment map being baked into the albedo, leading to less red-toned outputs. We will include additional discussion in the revised manuscript to present this as a failure case (as further supported by the quantitative results in Table 12). Further, we add the relighting results of TensoIR to Fig. 32. As illustrated, the TensoIR achieves better decomposition under such strong shadow effects.

Thanks

Thanks for all the valuable suggestions and we hope the discussion can help with a more clear understanding.

I appreciate the authors' explanation of shadow modeling and agree with some of their statements. However, I respectfully disagree with certain points.

Firstly, while I commend the authors for correctly categorizing current inverse rendering methods, I believe that the three approximations to the rendering equation they discuss do not fundamentally lead to significant differences. For instance, NeRO uses a split-sum approach in the first stage to obtain a geometry prior for reflective objects. Yet, the actual contribution to geometry comes from the combination of NeuS and Ref-NeRF's IDE encoding. In the second stage, NeRO employs MC but does not address the issue of shadow baking in the albedo.

Furthermore, I think the representative method for the split-sum approach is Neural-PIL and NeRO; and for SG, it is PhySG and InvRender. Their ability to model indirect illumination is not due to SG themselves but to the methods proposed by InvRender. Moreover, SG-based methods cannot achieve shadow removal; it was the subsequent method, RobIR, that achieved high-quality visibility modeling.

Regarding Geo-Splatting, the authors emphasized during the rebuttal phase that their method performs well not only in general scenes but also has significant advantages in reflective scenes. Based on this premise, I see issues with the contributions they claim.

• GeoSplatting is not the state-of-the-art for reflective scenes. Methods like NeRF-Casting, UniSDF, ENVIDR, GIR (https://arxiv.org/abs/2312.05133) and even GS-DR (based on 3D-GS) achieve better results than GeoSplatting in both visual quality and quantitative metrics. I am more inclined to agree that Geo-Splatting is the SOTA for reflective scenes based on inverse rendering. Additionally, in Table 11 and Figure 30, Geo-Splatting exhibits excessive smoothing in the helmet scene, making it inferior to NeRO (it could be better to add the geometry of NeRO in the corresponding figures and tables).

• While I agree with the authors' perspective if we consider only quantitative metrics, inverse rendering is not a field where a single metric can explain everything. In Figure 32, there is a noticeable hue inconsistency in relighting, which makes it difficult to consider this a better result than other methods. Furthermore, Figure 32 does not include a comparison with TensoIR.

We sincerely thank Reviewer f2Bn for the insightful discussion on shadow modeling. The reviewer mentioned many approaches that make a great effort in shadow modeling. To further address the reviewer's concern, we would like to rephrase and clarify some potentially misleading points in our previous explanations.

Discussion: Relationship between PBR Approximations with Shadow Modeling

As our previous explanation may have been overly brief and therefore misleading, we first clarify the relationship between the different approximations and the challenges in shadow modeling.

While highly appreciating the great effort made by the existing works (e.g., Neural-PIL, NeRO, PhySG, InvRender), we also strongly agree with Reviewer f2Bn that, it is not the approximations themselves that fundamentally enable certain outcomes. Rather, we believe it is the approximations that fundamentally limit what can be achieved.

For instance, as the reviewer noted, one of the most prominent SG-based methods, InvRender, introduces a crucial component to model visibility (Sec. 3.2 in InvRender). In our opinion, the same technique—or even methodology—cannot be straightforwardly adapted to split-sum-based methods. This limitation arises primarily from the non-decomposability inherent in split-sum-based lighting. We refer to this challenge as our “impossible trinity”, highlighting how split-sum-based methods face significant difficulties in modeling visibility effectively.

When discussing shadow modeling, the fundamental distinction between split-sum and SG lies in the decomposability of light. In SG approximations, the lighting representation is decomposable (as shown in Eq. 2 of InvRender), making it possible to perform an approximation that leads to Eq. 3 in InvRender.

$L_\text{SG}(\boldsymbol{\omega_i})=\sum_{k=1}^SG(\boldsymbol{\omega_i};\boldsymbol{\xi_k},\lambda_k,\boldsymbol{\mu_k})\quad\text{(w/o visibility term)}$

$L_\text{SG}(\boldsymbol{x_i},\boldsymbol{\omega_i})=V(\boldsymbol{x_i},\boldsymbol{\omega_i})\sum_{k=1}^SG(\boldsymbol{\omega_i};\boldsymbol{\xi_k},\lambda_k,\boldsymbol{\mu_k})\quad\text{(w/ visibility term)}$

In contrast, the split-sum approximation is non-decomposable (as indicated by Eq. 7 in NeRO). This non-decomposability means that exchanging the order of the visibility term and the integral introduces significant errors.

$L_\text{split-sum}(\boldsymbol{\omega_i})=\int_{\Omega(\boldsymbol{\omega_i})} I_\text{cubemap}(\boldsymbol{\omega})D_\text{GGX}(\rho,\text{reflect}(\boldsymbol{\omega}))\text{d}\boldsymbol{\omega} \quad\text{(w/o visibility term)}$

Although NeRO, which employs a neural light integral approximation similar to split-sum (Eq. 10 in NeRO), uses Monte Carlo (MC) sampling in its second stage, its shadow modeling capabilities are still inferior to those of state-of-the-art SG-based methods, RobIR, as the reviewer pointed out. We believe this is likely due to the inherent limitations of split-sum. Eq. 10 will introduce noticeable errors for high-frequency lighting, making it impossible to adopt similar visibility modeling techniques from SG-based methods to split-sum-based NeRO. Similarly, while RobIR demonstrates impressive shadow modeling performance, the reconstructed environment map remains highly blurred (Fig. 10), which stems from the low-frequency nature of SG and represents SG's fundamental limitation.

While we would emphasize the challenges of shadow modeling in our split-sum-based GeoSplatting by analyzing the “impossible trinity”, we also want to highlight the significant contributions and inspiring advancements made by NeRO and RobIR. Despite the limitations of split-sum, the techniques employed in NeRO offer promising directions for modeling visibility by utilizing different approximations across multiple stages, highlighting a potential avenue for future exploration in our work.