We’re thankful for your time and the valuable insights you’ve shared. Your input has significantly advanced our project. In response to your feedback, we proposed a brand new modeling for opacity in 3DGS-based inverse rendering based on the Bouguer-Beer-Lambert law and validated its effectiveness . We’ll address your concerns below.

1. Minor improvements have been observed compared to the baseline.

Thank you for your comment! We’d like to argue that the improvements are not minor. Our method outperformed baseline methods by ~0.4 PSNR, ~0.3 PSNR, ~0.4PSNR and ~0.5 PSNR on Synthetic4Relight, ShinyBlender, GlossySynthetic and Mip-NeRF 360 datasets respectively. Since PSNR is the log of MSE with base 10, our method is actually 2-3 times better than the baseline in terms of MSE. This is a common improvement scale in the relevant literatures[1, 2, 3]

2. A comparison with NeRF-based inverse rendering is missing.

Thank you for pointing this out! Since the baselines we build upon have already been compared with NeRF-based inverse rendering methods and generally outperform them, and our method is designed to be a plug-in module for 3DGS-based approaches, we focus on comparing our method against these baselines. While our approach could be integrated into NeRF-based inverse rendering, doing so would require significant effort to adapt and redesign the pipeline. We therefore consider this an exciting direction for future work.

3. The claim "The emergence of 3D Gaussian Splatting has boosted it to the next level" in Line 15 is not convincing.

Thank you for your comment! We’ve modified the manuscript in Ln. 15 to make it less ambitious. The intuition behind this sentence is that 3DGS-based methods introduce faster rendering speed, showing more potential than NeRF-based methods in terms of real-time rendering.

4. Maybe experiments on transparent or translucent objects can support the theory.

Thank you for carefully investigating our manuscript! We’ve conducted experiments on translucent objects and showcased the results here. Since there are no existing baselines that do inverse rendering for translucent objects, we run the baseline that we use, namely GaussianShader, on the Dex-NeRF dataset as well as GaussianShader + our method. Since Dex-NeRF dataset doesn't provide train-test split, we splited the image set and used $\frac{2}{3}$ for training and rest for testing. We also run the original 3DGS on this dataset to showcase the upper bound for an inverse rendering method. The discovery is that our method still makes the baseline superior compared to the original version despite that both methods couldn't provide convicing results. The reason is that albedo, roughness and metalness are not the parameters for describing translucent objects. We argue that developing such a method is out of the scope of this work.

Another aspect we want to mention is that, we are NOT trying to directly model the translucent objects themselves, but to perceive the Gaussian blobs that 3DGS-based methods use as absorbing bodies. Therefore the model, i.e. each Gaussian blob, should follow the Bouguer-Beer-Lambert law.

[1] Attal, Benjamin, et al. "Flash Cache: Reducing Bias in Radiance Cache Based Inverse Rendering." European Conference on Computer Vision. Springer, Cham, 2025.

[2] Liang, Zhihao, et al. "Gs-ir: 3d gaussian splatting for inverse rendering." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

[3] Jiang, Yingwenqi, et al. "Gaussianshader: 3d gaussian splatting with shading functions for reflective surfaces." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

Dear Reviewer RDFN,

We sincerely appreciate the time and effort you have devoted to reviewing our manuscript and providing valuable feedback. As the deadline for uploading visualizations and revising the manuscript is November 27th, we kindly ask if there are any remaining questions or if further clarifications are needed. We would be more than happy to provide any additional information or address any concerns.

Thank you once again for your thorough review and constructive input.

Best Regards,

Authors

Thank you for dedicating your time and providing such perceptive feedback. Your recommendations have considerably enhanced our work. Based on your comments, we proposed a plug-and-play module that perceives the alpha-blending in 3DGS as absorbing bodies. Our method archives superior performances compared to existing approaches. We will address your concerns below.

1. Relevant citations

Thank you for your suggestion. We’ve already added these relevant literatures (Section 2) into our work to make it more comprehensive.

2. Subtle improvement in Fig. 4

Thank you for carefully reading our manuscript and point this out! We agree that Fig.4 may not be the best representative of the qualitative experiments with R3DG on Synthetic4Relight dataset, therefore we added a new set of images in the appendix in Fig. C4. Please let us know if you have further suggestions!

3. Needs more geomentry comparison. ... I think the paper should include more quantitative comparisons on the reconstructed geometry, including normal accuaracy, and the extracted mesh if possible.

Thank you for your insightful comments. We carefully investigated the ground truth provided by the four datasets that we followed the baselines to conduct experiments on. We found that when synthesizing the ground truth images in simulated environments (i.e. Blender), the normal of the object is decided by the normal of the triangle on the mesh, therefore a ground truth normal map is not needed for providing ground truth images for the datasets. In that sense, the quantitative results on normal accuracy are not accessible. As for extracting mesh, we found a paper called SuGar[1] which aims to provide an algorithm for extracting mesh from 3DGS-based methods and is far beyond the scope of this paper. We agree that more understanding on the reconstructed geometry is beneficial, therefore we add more qualitative results in Fig. C5 in the Appendix.

4. Lack of interpretability in the cross section modeling.

Thank you for noticing the novelty of our approach! To the best of our knowledge, there is no closed-loop form for cross section in physics. And also there is no explicit equation for mapping the types of particles to macro appearances. These are the reasons why we use a general function approximator, i.e. an MLP, for cross section modeling.

5. It will be better to use vector graphics

Thank you for carefully investigating our manuscript! We’ve already changed the figures in the paper to SVG format per your suggestions!

6. Notation for Guassian covariance matrix.

Thank you for your question! The notation means the projection based on camera parameters applied on the covariance matrix. The expression follows 3DGS-MCMC [2] and we’ve added some clarification in Ln 185-186 in the text to make it clear.

7. The explanation on why the path length $s$ can be simply set to constant 1 is not clear and convincing. The authors should provide a more detailed explanation on it.

Thank you for pointing this out! We modified the manuscript in Ln. 265 - Ln. 269 to add an explanation to this design choice. In general, since all the 3D Gaussians are projected to the 2D plane, the blending algorithm omits the depth of the Gaussians into the formulation of the opacity value at the pixel location. We therefore observed that we can treat this opacity value as the density and since there is no concept of depth on the 2D plane, each Gaussian is then treated equally from this perspective, therefore it is reasonable to treat the path length to constant 1.

8. Implementation details of the MLP. Does it use positional encoding for the material properties, or just directly feed the properties into the MLP?

Thank you for noticing this! We added the implementation details of the MLP in the Appendix from Ln. 768 - Ln. 770. In one word, we directly feed the material properties into the MLP without any positional encoding.

9. Will the proposed method work better on surface-based Gaussian Splatting methods, e.g. 2D Gaussian Splatting, which has a more well-defined normal and surface geometry representation?

Thank you for providing this insightful comment! Nonetheless, as no existing approach employs 2D Gaussian Splatting for inverse rendering, and our method is specifically designed for inverse rendering, directly applying it to 2D Gaussian Splatting is not straightforward. That said, based on the observed improvements in normal estimation in our experiments, we hypothesize that our method could enhance the accuracy of normal estimation in 2DGS if applied to inverse rendering. Since it requires significant effort to design a pipeline utilizing 2DGS for inverse rendering, we’d like to retain this as an interesting future research direction.

[1] Guédon, Antoine, and Vincent Lepetit. "Sugar: Surface-aligned gaussian splatting for efficient 3d mesh reconstruction and high-quality mesh rendering." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

[2] Kheradmand, Shakiba, et al. "3D Gaussian Splatting as Markov Chain Monte Carlo." arXiv preprint arXiv:2404.09591 (2024).

Thanks for your reply! Most of my concerns have been addressed, but I have a few suggestions below:

Geometry comparison

We found that when synthesizing the ground truth images in simulated environments (i.e. Blender), the normal of the object is decided by the normal of the triangle on the mesh, therefore a ground truth normal map is not needed for providing ground truth images for the datasets.

I believe that the ground truth normal map can be obtained by a simple rasterization / ray casting process from the mesh in the rendering pipeline, also known as a G-buffer (geometry buffer). I personally think this is an important comparison and strongly encourage the authors to include this.

Cross section modeling

I acknowledge that cross section modeling does not have closed-form physical formula, but I think it will be interesting to qualitatively illustrate the $\sigma_\nu$ value learned from the MLP to see if the result is consistent with the human intuition.

Subtle improvements

It will be nice if the authors can highlight the areas in the results figures that demonstrate improvements over baselines (in Fig 4 and Fig C4), maybe using arrows or insets. I have to zoom in to carefully find out the difference by now. And it will also be nice to include quantitative metrics next to the figure to further emphasize the differences.

We are grateful for your time and insightful comments. Your valuable suggestions have significantly elevated our work. In light of your comments, we introduce a simple yet effective plug-and-play approach for inverse rendering using Gaussian Splatting and demonstrate its usefulness through various analyses and experiments. We will address your concerns below.

1. Additional results or visualizations could be provided to better illustrate the quality difference.

Thanks for your comment. We also notice that the visualization result of Synthetic4Religiht dataset does not make the effectiveness of our method clear. Therefore we chose another set of images and updated the manuscript in Appendix Fig. C4. For the other 2 visualization results, MIP-NeRF 360 is made clear with the zoom-in window (artifacts on the bicycle and on the tablecloth) while for the glossy datasets, the main intuition is to showcase the superior performance of our method in terms of better normal estimation. Please let us know if you find any of them unsatisfactory.

2. As mentioned by the authors, the impact of lighting frequency/spectrum is not considered, which could be an interesting future direction to model more complex materials.

Thank you for pointing this out. Since the purpose of this work is to introduce the concept of the Bouguer-Beer-Lambert law into the field, we plan to introduce lighting frequency as future work, i.e. designing a more sophisticated and accurate model for the relation between opacity and materials. This is also mentioned in the Limitations section in our manuscript.

Dear authors,

Thanks for your reply! Most of my concerns are addressed. My remaining question is about the visual comparison. As pointed by other reviewers (Reviewer rqsv), both Figure 4 and Figure C4 include visuals with subtal differences, which are hard to distinguish. Maybe a color visualizaion of MSE or zoomed-in insets could be provided to highlight the difference between the proposed method and baselines.

3. I am not fully convinced that the cross section network is really learning cross section from albedo, metalness, and roughness. ... Consider a translucent material that has some cross section parameter for the network to learn. This material may not have well-defined albedo, metalness, or roughness, which are properties in opaque appearance BRDFs. ... Why would albedo inform cross section?

Thank you for pointing this out. We’d like to argue that based on our experimental results that show no parameter increasement, we found that the performance improvements didn’t come from more parameters. Therefore, our cross-section network effectively captures meaningful dynamics, enabled by the thoughtful modeling we introduce.

On the other hand, as you mentioned in your statement, there doesn’t exist any methods that do inverse rendering for translucent objects and it’s also not the focus of our work, such a topic is beyond the scope of this paper.

The reason albedo can inform cross section can be intuitively understood as follows: in an absorbing body, the cross section is influenced by the type of the particles it contains, making the modeling of particle types the key challenge. On the other hand, the type of the particles can be represented by the albedo, roughness and metalness of the body because on the macro level different types of particles appear differently and can be described by different appearances.

4. Figure 1b is misleading

Thank you for pointing this out. We agree that Figure 1 is a little misleading. The point of using these figures is that we want to demonstrate that no matter how the light changes, different materials would react differently. We’d like to point out again that our motivation comes from the observation that each Gaussian blob is an absorbing, translucent body, instead of directly modeling translucent objects themselves. We’ve changed Figure 1 per your suggestion. Please let us know if you find it still inappropriate.

We’re thankful for your time and the valuable insights you’ve shared. Your input has significantly advanced our project. In response to your feedback, we proposed to model opacity based on the Bouguer-Beer-Lambert law by introducing a cross-section term and it achieved superior performance across various datasets. We’ll address your concerns below.

1. No result of transparent/translucent objects.

Per your comments, we conducted experiments on the Dex-NeRF dataset, the existing translucent object dataset for 3D reconstruction. Notice that there does not exist any inverse rendering baseline for translucent objects. To make a comparison, we run experiments using the GaussianShader as baseline and ours + GaussianShader as the demonstration of the effectiveness of our method. As can be seen from the results, our method still outperformed the baseline method. However, since albedo, roughness and metalness are not the parameters for describing translucent objects, we argue that developing such a method is out of the scope of this work.

On the other hand, we’d like to point out that our motivation is NOT based on modeling translucent objects, but on each Gaussian point is itself a translucent body that has density and cross section to describe its absorption coefficient, namely opacity. So the whole Gaussian Splatting pipeline is to use a set of translucent bodies to model objects, no matter if it's translucent or opaque. Therefore, the modeling itself, i.e. each Gaussian blob, should follow the Bouguer-Beer-Lambert law per our design.

2. Current improvements reported in the paper on opaque objects may simply be due to a bigger model with more parameters we can optimize

Thanks for your valuable suggestion. Parameters of a 3DGS model mainly come from the large number of points and each point has 24 parameters in the inverse rendering setting (take GaussianShader here as an example). We observe that our model on average (for GaussianShader on GlossySynthetic dataset) only has 3.29E+5 points and the original has 3.44E+5 points. Consider the MLP we have (Added in the Appendix on the architecture), which in total only contains 17,665 parameters (approximately 0.2% of the total number of parameters), our model’s parameters are even less than the baseline model. As for different datasets, the number of points is reported in the table. We therefore argue that the performance improvement does not come from increasing parameters but from our design.

Dear Reviewer G4SH,

Thank you for the time and effort you have dedicated to reviewing our manuscript and providing valuable feedback. As the deadline for submitting visualizations and revised manuscripts approaches on November 27th, we wanted to check if there are any outstanding questions or if further clarification is needed. We would be glad to provide any additional information as required. We deeply appreciate your insights and look forward to your guidance.

Best regards,

Authors