5. Concerns about the novelty and quality

We thank the reviewer for raising this important question. Below, we explain the differences between our method and the baselines.

The previous methods do take into account occlusion and indirect lighting, because global illumination is an important source of realism in the rendering results and is an important part of PBR. However, we claim that they obtain occlusion and indirect lighting in a very different way from our method.

To obtain occlusion, we need to determine whether the ray intersects the surface. However, for volume rendering, this is very difficult due to the lack of an explicit definition of the surface. For NeRF-based methods, such as InvRender and TensoIR, they use an MLP to estimate the visibility. This paradigm is relatively simple to implement, but lacks clear geometric meanings. Among the 3DGS-based methods, GS-IR first renders the depth cube-map of a point in the 3D space from 3DGS, obtains the occlusion at that point from it, and then bakes the occlusion information into the grid for subsequent use. Although GS-IR also obtains occlusion from the depth, it does not calculate the intersection of light and the surface. Instead, it determines the occlusion relationship by comparing the depth value with a predetermined threshold, which can lead to inaccurate occlusion estimation. Moreover, the subsequent baking process uses spherical harmonics for further approximation, which introduces more errors. As for Relightable 3DGS (R3DG), it uses point-based ray tracing accelerated by the Bounding Volume Hierarchy (BVH) to obtain the occlusion and also bakes the occlusion in each Gaussian. However, as analyzed in our abstract, the distribution of 3D Gaussian primitives does not necessarily conform to the geometry of objects (especially at the scene level), which limits the quality of point-based ray tracing and makes it difficult to extend to the scene level.

For indirect lighting calculation, NeRF-based methods often obtain it from the outgoing radiance fields parameterized by an MLP. As for 3DGS-based methods, such as GShader and R3DG, they model the indirect lighting as a learnable attribute for each Gaussian. Besides, GS-IR also uses a learnable volume to store the indirect lighting. However, these approaches do not model the multi-bounce of light and therefore cannot construct indirect illumination during relighting.

Unlike previous methods, our method performs path tracing in the screen space, so it can more accurately determine the intersection of light and surfaces. It also reuses the information stored in the G-buffer, which reduces the amount of calculations. Moreover, our indirect illumination is obtained from the result of direct lighting, so it can be constructed during relighting. In addition, by changing the path-tracing settings, our method can obtain global illumination with different effects to adapt to different scenes and requirements, which is impossible for the baselines. (See Fig.19 in Appendix F.4)

Q5. Relighting evaluation

We thank the reviewer for this insightful question. As shown in Figure 4, our method demonstrates a closer alignment to the ground truth in terms of overall color tone for the Lego example compared to GS-IR. This improvement is largely due to our method's effective handling of indirect illumination, which enhances color accuracy and realism. For the Hotdog example, our method produces a notably smoother appearance with fewer artifacts, particularly in shadowed regions, such as the lower part of the plate and the middle sections of the hotdog and sauce.

In addition, we have provided additional relighting evaluation on the Synthetic4Relight and Stanford-ORB datasets in Appendix I, which demonstrates the improvement of our method compared to baselines.

We sincerely thank the reviewer for the detailed assessment of our submitted paper. The review comments are very insightful and have provided us with valuable guidance for further improving our work. We hope the following responses well address the concerns.

1. Evaluation of diffuse and specular components

We appreciate the reviewer for raising this concern. There are two primary reasons why the decomposed diffuse and specular components were not evaluated in our study.

First, there is no ground truth in existing datasets to quantitatively evaluate these components. Notably, widely used datasets such as TensoIR Synthetic, DTU, and Shiny Blender do not include ground truth data for diffuse and specular components. This limitation prevents us from performing quantitative evaluations of these specific components. In addition, prior inverse rendering studies, including the **seven baselines we compare against, similarly lack evaluations of these components.

Second, conducting qualitative comparisons of the visualization results poses significant challenges. Our ability to assess rendering quality relies heavily on real-world observations. Generally, superior rendering results are those that closely approximate the appearance of real-world objects. However, diffuse and specular components cannot be decomposed in the real world, which means that we lack understanding and prior knowledge of them. Consequently, it is difficult to measure the quality of these results through human perception.

In response to the reviewer’s request, we have included visualization results of the decomposed diffuse and specular components in Fig. 21 in Appendix G for further reference.

2. Material evaluation

We thank the reviewer for this comment. In Table 1 and Fig. 4, we provide both quantitative and qualitative comparisons of the recovered albedo on the TensoIR dataset. The results show that the albedo recovered by our method outperforms all baselines on the TensoIR dataset.

It is important to note that the TensoIR dataset only provides ground truth of albedo, which limits our ability to assess other material properties such as specular and roughness. To address this limitation, we supplement the comparison results of material estimation on the Synthetic4Relight and Stanford-ORB datasets in Appendix I, which demonstrates the improvement of our method compared to baselines.

3. Occlusion evaluation

We thank the reviewer for this comment. In Fig. 6, we present a comprehensive evaluation of the estimated occlusion using our method compared to GS-IR. The results demonstrate that our approach significantly outperforms the baseline at both scene and object levels. Specifically, our method captures fine details of occlusion, particularly in scene-level scenarios, where it effectively recovers the occlusion of distant objects. In addition, the insightful feedback from Reviewer zyyD further supports the effectiveness of our method. To strengthen our claim, we have included additional occlusion comparison results with further baseline methods in Appendix F.1.

4. About indirect lighting

We appreciate the insightful comment and the opportunity to clarify our perspective on this issue. Indirect lighting is a fundamental concept in computer graphics and vision, and it should not be regarded as merely a residual term in the lighting optimization process. Even with precise ground truth information of light sources and material properties, indirect light persists due to the inherent nature of light's multiple reflections within an environment.

In some existing methods, including our baseline GShader, indirect lighting is treated as a residual term within the lighting optimization process. This simplification is primarily driven by the aim of reducing computational complexity, as accurately modeling multiple light reflections is highly challenging. However, this approach limits the representation of indirect lighting to the specific lighting conditions present in the training data. Consequently, it fails to generalize effectively during relighting. In contrast, our proposed method constructs indirect lighting based on the first-pass rendering results. This approach is equivalent to calculating indirect light from the outgoing radiance of the objects themselves, thereby enabling the computation of indirect lighting under any given lighting conditions. By doing so, our method does not rely on the residual term approximation and maintains the intrinsic characteristics of indirect illumination inherent to the environment.

While the quality of indirect lighting cannot be directly measured due to the absence of ground truth data, we employ indirect evaluation methods to assess its effectiveness. Specifically, we evaluate the performance of material estimation and relighting tasks. Our method outperforms all baseline approaches in material estimation and surpasses other 3DGS-based methods in relighting, ranking second only to TensoIR. This performance indicates the effectiveness and accuracy of our indirect lighting model.

It is important to note that our method's performance relative to TensoIR in relighting does not imply inferior quality in our material estimation or indirect lighting. The observed differences are primarily due to the different rendering equation calculation processes employed by each method. TensoIR achieves superior relighting results because it avoids the split-sum approximation for precomputing the environment map. Instead, it leverages Monte Carlo integration to accurately solve the rendering equation. For each surface point $x$, a set of rays is generated in various directions to sample the environment map, with visibility for each ray calculated separately using a visibility MLP. This approach allows TensoIR to compute the rendering equation with greater accuracy, leading to enhanced relighting results. However, this comes at the cost of increased training and rendering times.

Dear Reviewer uXjo,

We sincerely appreciate your time and effort in evaluating our work. We would greatly value the opportunity to engage in further discussion to see if our response solves the concerns. We have carefully addressed all of your insightful questions and hope that our responses help to better highlight the impact and results of our work. We kindly request you to review our responses and share any additional feedback or concerns, if any. We would be more than happy to address them further. Thank you!

Best wishes,

Authors

Thank you for providing the detailed explanation regarding the evaluation of diffuse and specular components, material decomposition, and relighting.

However, I believe there are issues in the separation of diffuse and specular components, as shown in Figure 21. Specifically, the specular reflection seems incorrectly modeled. Specular reflection, primarily originating from light sources, should not exhibit significant color baked-in. The results in Figure 21 suggest that your rendering equation fails to correctly represent specular reflection, resembling indirect illumination rather than specular reflection.

Similarly, the material decomposition results in Figures 24 through 28 show limitations in evaluation. These figures focus primarily on diffuse albedo, which has already been validated in your main paper. The roughness evaluation does not sufficiently demonstrate the effectiveness of your method, and there is no specular evaluation presented in these figures at all. Additionally, the relighting results in Figures 27 and 28 are absent, making it difficult to properly assess the relighting capabilities of your method. Another question arises regarding Figure 27: the decomposed diffuse albedo contains strong blue tones, yet in Relighting 1, which features white light sources and a blue ambient, these blue tones are noticeably absent in the relighting results.

As previously mentioned, my main concern lies in the unclear evaluation of material components, particularly diffuse and specular reflections, which are the primary reflections we perceive. Unfortunately, the supplementary results do not address this concern adequately.

The issue with specular reflection is particularly critical because it represents high-frequency components, whereas diffuse reflection corresponds to low-frequency components. Existing baseline methods have already demonstrated successful inverse rendering for low-frequency recovery. If diffuse and specular separation is not conducted accurately, evaluating indirect illumination becomes valid only for predominantly diffuse scenes. However, your results include objects with strong specular components, such as the reflective bowls and onions on the desk in Figure 10, which further highlights the importance of correctly modeling specular reflection.

Thanks to the reviewer for the detailed review and the valuable insights the reviewer has provided.

Response to Question 1

For the incomplete separation of diffuse and specular components, we believe that the main reason is inadequate normal estimation. Accurate normal estimation is very important for achieving high-quality specular reflections. Since our method does not use any geometric regularization, priors, or 3D representations with stronger geometric reconstruction capabilities like 2DGS, the estimated normals may not be very accurate. This inaccuracy can negatively affect the quality of the specular reflections observed in our results. To address this issue, we have provided a thorough analysis and a potential solution in our response to Reviewer zyyD. In addition, it is important to note that our method only considers diffuse indirect illumination, which may further affect the quality of specular reflection. However, this design choice primarily serves to improve efficiency, and we have included a detailed explanation in Response to Reviewer SvCz - 3.

Response to Question 2

We would like to clarify several points regarding the evaluation of our material decomposition.

First, our roughness estimation results outperform those of GS-IR, which is the previous SOTA method based on 3DGS for inverse rendering. Furthermore, while our roughness estimation is second only to InvRender, it offers a significant advantage in efficiency, with a training speed that is 30 times faster than InvRender.

Regarding the evaluation of specular, if the reviewer is referring to metallic, we did not conduct an evaluation due to a lack of ground truth data in the dataset. If the concern relates to general specular reflection, we have explained the reason in our previous responses. Specifically, commonly used inverse rendering datasets such as TensoIR, Synthetic4Relight, ShinyBlender, GlossyBlender, and Stanford-ORB do not provide ground truth for specular reflections. Moreover, upon reviewing the representative inverse rendering research in recent years, including Neural Reflectance Fields, Nerv, Nerd, Nerfactor, Neilf, Physg, NVdiffrec, GS-IR, and R3DG, we found that none of these studies have evaluated specular reflection. This suggests that evaluating specular reflection remains a challenging task in the current state of the art. If the reviewer is aware of any prior work that has successfully evaluated specular reflection, we would appreciate the information. We would also be grateful for any guidance on methodologies for evaluating specular reflection.

Regarding the relighting results shown in Figures 27 and 28, the absence of ground truth is due to the fact that the dataset does not provide relighting results for the specific environment map used. To address the reviewer's concern, we have included relighting results using the ground truth albedo provided in the dataset in our revised version. It is important to note, however, that the albedo provided by Stanford-ORB serves only as a pseudo-albedo representation of the actual object, which may affect the quality of the relighting results.

Despite using the albedo from the dataset for relighting, blue tones do not appear in Relighting1. This is because the environment map corresponding to Relighting1 has a yellow light source in the lower part, while the ambient light, although blue, is relatively dim. As a result, the relighting output is dominated by yellow tones. In contrast, when using an environment map with a strong white light source and more prominent blue ambient light in Relighting3, the relighting results showcase clear blue tones. To avoid potential confusion, we have provided further analysis in Fig. 31 in Appendix K. According to the ground truth relighting results in the TensoIR dataset, it can be observed that for the environment map in Relighting1, the ground truth relighting results for both the Hotdog and Lego show an obvious yellow color, which further confirms our statement.

We sincerely thank the reviewer for the detailed assessment of our submitted paper. The review comments are very insightful and have provided us with valuable guidance for further improving our work. We hope the following responses well address the concerns.

1.Sampling Strategy

We sincerely thank the reviewer for this insightful and constructive suggestion. As utilized by NeILF, Fibonacci sampling has good properties, and we will incorporate this method in our future improvements. We have provided a discussion of this method in the revised paper and cited NeILF as a reference. (See Appendix B, Lines 767-769)

2. Specular term and sharp shadows

We thank the reviewer for raising these critical points. Below, we provide detailed explanations to clarify our approach.

Why don't we consider specular terms? The main reason is efficiency. Different from the diffuse component, accurately modeling the specular component of indirect lighting typically requires Monte Carlo sampling based on the GGX distribution. This process significantly increases computational complexity and reduces rendering speed. Moreover, in most cases, the contribution of the specular component to indirect lighting is minimal and often imperceptible. Therefore, omitting the specular component is a reasonable trade-off that maintains efficiency without substantially compromising visual fidelity.

We acknowledge that the use of split-sum approximation in Eq. (7) leads to a certain limitation in modeling sharp shadows. This approximation necessitates pre-integrating the environment map, which prevents per-ray sampling of the original environment map. As a result, visibility cannot be accurately computed for each individual ray direction, thereby preventing the accurate rendering of sharp shadows. One potential solution is to abandon the split-sum approximation and use Monte Carlo sampling to calculate the rendering equation. This would allow us to calculate visibility for each sampled ray, enabling the modeling of sharp shadows. However, this approach would also lead to a significant increase in computational demands.

Alternatively, our method remains effective for relighting scenarios under natural light sources, such as point light sources or area light sources. In these cases, we can employ shadow map, a widely used technique in computer graphics, to achieve precise shadows. Specifically, we can first generate a depth map from the light source's perspective. By comparing the depth of each shaded point with the corresponding value in the depth map, we can effectively ascertain visibility. We illustrate the rendering results under point light sources in Fig. 20 in Appendix F.5, where the shadows cast by the shapes are clearly visible.

3&4. Path tracing and visibility calculation

We appreciate the reviewer for highlighting the need for a clearer explanation of our path-tracing procedure. In response, we have revised Equation 12 to enhance clarity regarding the visibility determination process, which may have previously led to some confusion. The reviewer's guess is basically consistent with our approach. However, we would like to clarify that the conditions for terminating the path-tracing process are somewhat different. Specifically, for each sampling point, we not only compare its depth $z$ with the rendered depth $z_d$, but also compare its depth with $z_d+\delta$, where $\delta$ represents the thickness of the surface and can be adjusted according to the scene. A ray is determined to have intersected the surface if and only if the sampled point satisfies $z_d < z < z_d+\delta$. This approach ensures a more precise detection of surface intersections by accounting for variations in surface thickness, thereby improving the robustness and accuracy of the path-tracing process.

We hope this clarification addresses the reviewer’s concerns and enhances the understanding of our path-tracing methodology.

Regarding the fourth question raised by the reviewer, we believe that the path-tracing strategy just explained can also address this concern. We have provided a detailed explanation in the Appendix F.3, Lines 1140-1161.

5. Indirect lighting calculation

We appreciate the reviewer for raising this important question, which is similar to the third comment from Reviewer tAkv. Below, we provide detailed explanations to clarify our approach.

In our first-pass rendering, the RGB values prior to tone mapping can be decomposed into diffuse and specular components as $I(\hat{u},\hat{v}) = L_o(\hat{x}, \omega_1) = L_d(\hat{x}) + L_s(\hat{x}, \omega_1)$, where the diffuse component $L_d(\hat{x})$ is isotropic and thus lacks directionality. The difference between $I(\hat{u},\hat{v})$ and the outgoing radiance $L_o(\hat{x}, -\omega)$ from $\hat{x}$ to $x$ is given by the specular component difference $\Delta L_s = L_s(\hat{x}, -\omega) - L_s(\hat{x}, \omega_1)$. In most practical scenarios, the specular component $\Delta L_s$ is relatively negligible compared to the diffuse component. Therefore, we believe that substituting $I(\hat{u}, \hat{v})$ to replace $L_o(\hat{x}, -\omega)$ serves as a practical approximation that avoids the need for additional calculations (See Appendix F.2 for more details). In addition, we have attempted to use only the diffuse component to calculate indirect lighting, but the experimental results are underperformed compared to our proposed strategy presented in the paper.

Since our method is based on screen space, it cannot take into account indirect lighting outside the camera frustum. However, in most cases, the information available in screen space is sufficient for accurately constructing global illumination. Moreover, our method demonstrates a significant advantage in rendering speed compared with existing approaches. It is worth noting that most current game engines leverage similar techniques, utilizing information stored in the G-buffer to construct global illumination, which also aligns with our methodology.

Moreover, we sincerely apologize for the confusion caused. We have modified the notations in Eq. (13) and the main text to better distinguish the formulas related to $x$ and $\hat{x}$.

We sincerely thank the reviewer for the detailed assessment of our method. The review comments are very insightful and have provided us with valuable guidance for further improving our work. We hope the following responses well address the concerns.

1. Differences from InvRender

The indirect incoming radiance $L_i(x,\omega)$ of a surface point $x$ in direction $\omega$ is from the outgoing radiance $L_o(\hat{x},-\omega)$ at the ray intersection point $\hat{x}$ in the opposite direction $-\omega$.

In InvRender, the outgoing radiance $L_o$ is modeled using an MLP. This approach inherently ties the outgoing radiance to the lighting conditions present in the training dataset, resulting in a fixed representation of outgoing radiance. Consequently, InvRender is limited in its ability to accurately reconstruct indirect illumination for novel lighting scenarios during relighting tasks, as the MLP cannot adapt the outgoing radiance beyond the training illumination conditions.

In contrast, our method derives the outgoing radiance from the rendering result of the first pass, rather than relying on a fixed MLP model. This allows the outgoing radiance to dynamically reflect lighting conditions beyond those seen during training, facilitating more accurate and adaptable indirect illumination calculations during relighting. In addition, compared with the MLP-based method, our approach achieves superior computational efficiency and reduced storage requirements.

2. Relighting Evaluation

We thank the reviewer for raising this concern. Below, we provide a detailed analysis of the relighting performance of TensoIR, GS-IR, and our proposed method.

Why TensoIR achieves high-quality relighting results

TensoIR achieves superior performance in relighting because it does not use the split-sum approximation typically used to precompute the environment map. Instead, TensoIR employs Monte Carlo integration to calculate the rendering equation during both the training and relighting phases. Specifically, for each surface point $x$, TensoIR generates a set of rays in various directions based on a distribution that samples the environment map. Visibility is then determined for each individual ray using a visibility MLP. This approach is similarly applied to compute indirect lighting from outgoing radiance. In this way, TensoIR can more accurately calculate the rendering equation, resulting in superior relighting quality. However, this high precision comes at the cost of increased training and rendering times, making TensoIR more computationally intensive.

Why the proposed method shows similar relighting results to GS-IR

GS-IR relies on caching occlusion and indirect illumination data under specific training lighting conditions within volumetric data. Consequently, these cached components become less effective during relighting under new lighting scenarios. However, in scenes with a single object, indirect lighting only originates from the object itself, which limits its impact on the final rendering results. For instance, in the case of a ball, there is no indirect lighting coming from itself. Therefore, relying solely on direct lighting does not significantly degrade the final rendering quality of GS-IR.

Despite the similarities with GS-IR in single-object scenes, our method offers additional advantages. As shown in Figure 4, our method demonstrates a closer alignment to the ground truth in terms of overall color tone for the Lego example compared to GS-IR. This improvement is largely due to our method's effective handling of indirect illumination, which enhances color accuracy and realism. For the Hotdog example, our method produces a notably smoother appearance with fewer artifacts, particularly in shadowed regions, such as the lower part of the plate and the middle sections of the hotdog and sauce. In addition, we have also provided comparison with GS-IR on the Stanford-ORB and Synthetic4Relight datasets in Appendix I, which demonstrates the improvement of our method compared to GS-IR.

3. Indirect illumination calculation

We appreciate the reviewer for raising this insightful point. Below, we provide a detailed clarification for the use of $I_{dir}(\hat{x}, \hat{v})$ in Eq. (13).

In our first-pass rendering, the RGB values prior to tone mapping can be decomposed into diffuse and specular components as $I(\hat{u},\hat{v}) = L_o(\hat{x}, \omega_1) = L_d(\hat{x}) + L_s(\hat{x}, \omega_1)$, where the diffuse component $L_d(\hat{x})$ is isotropic and thus lacks directionality. The difference between $I(\hat{u},\hat{v})$ and the outgoing radiance $L_o(\hat{x}, -\omega)$ from $\hat{x}$ to $x$ is given by the specular component difference $\Delta L_s = L_s(\hat{x}, -\omega) - L_s(\hat{x}, \omega_1)$. In most practical scenarios, the specular component $\Delta L_s$ is relatively negligible compared to the diffuse component. Therefore, we believe that substituting $I(\hat{u}, \hat{v})$ to replace $L_o(\hat{x}, -\omega)$ serves as a practical approximation that avoids the need for additional calculations (See Appendix F.2 for more details). In addition, we have attempted to use only the diffuse component to calculate indirect lighting, but the experimental results are underperformed compared to our proposed strategy presented in the paper.

Besides, re-applying the first rendering pass with a new look-at direction may significantly increase the computational load, as the normal directions for different surface points vary, necessitating separate rendering passes for each distinct view direction. Such a process would not only be computationally intensive but also impractical for real-time applications or complex scenes.

An alternative approach is to use Truncated Signed Distance Fields (TSDF) to rapidly reconstruct a mesh from 3DGS and subsequently perform path tracing to yield more accurate indirect lighting. However, constructing an accurate mesh at the scene level poses considerable challenges and introduces additional computational overhead.

4. Real-world Benchmark

We appreciate the reviewer for this important aspect. We acknowledge that demonstrating the effectiveness of our method in realistic and complex scenarios is crucial. To address this, we have conducted experiments using the Stanford-ORB dataset.As shown in Table 11, Fig. 27, and Fig. 28 in Appendix I.2, our method achieves better albedo estimation and relighting than GS-IR. Specifically, our method estimates the albedo with fewer shadows and highlights and achieves usable relighting results. However, GS-IR still bakes lighting into albedo and performs poorly in relighting.

Due to the lack of ground truth for relighting in the Stanford-ORB dataset, we have also conducted experiments on the Synthetic4Relight dataset. As shown in Table 10, Fig. 24, Fig. 25, and Fig. 26 in Appendix I.1, our method is also better than GS-IR in material estimation and relighting. In addition, it can be observed that the roughness estimated by our method has improved significantly compared with GS-IR, which is mainly due to the better occlusion estimation.

5. Other minor issues

1. Indeed, our adaptive path tracing operates within screen space, which inherently restricts its consideration to areas within the camera's frustum. Consequently, it does not account for objects that are completely occluded. However, in most cases, the information available in screen space is sufficient for accurately constructing global illumination. Moreover, our method demonstrates a significant advantage in rendering speed compared with existing approaches. It is worth noting that most current game engines leverage similar techniques, utilizing information stored in the G-buffer to construct global illumination, which also aligns with our methodology.
2. We thank the reviewer for pointing out this concern. We have modified Eq. (8) in the main text to avoid potential confusion.
3. To provide a more comprehensive evaluation, we have included the results of 3DGS in Table 8 in Appendix D. It is important to note that 3DGS was originally proposed for NVS. Besides, in most cases, the use of PRB in inverse rendering methods will negatively affect the quality of NVS. Therefore, for fairness, we only consider the inverse rendering methods when quantitatively comparing the NVS performance and use the results of 3DGS as a reference.

Q.1 Shadow in the albedo

We thank the reviewer for raising this important question. Below, we provide a detailed explanation of the presence of shadows in albedo, as well as potential solutions.

The shadows observed in the albedo come from the way we construct global illumination using screen space information and the use of split-sum approximation. Since the information is derived from the camera’s perspective, any indirect light or occlusion originating from areas outside the camera frustum may not be accurately represented. This limitation contrasts with the path-tracing method applied directly on the mesh, which typically yields more precise results. We choose this screen space approach primarily to enhance computational efficiency and to accommodate scenarios where mesh data may be unavailable or incomplete.

Furthermore, since we use split-sum approximation to calculate render equation, which assumes that the intensity of incident radiance in different directions is consistent. Under this assumption, occlusion obtained by integrating visibility represents the degree to which the point is occluded. Consider an example where there is a point light source in the center of an empty room. In this case, the points at the corners are not occluded in the direction of the light source, but the occlusion obtained by integration is 0.75. This shows that when the light source is anisotropic or has significant directionality, this estimation is often inaccurate. Using Monte Carlo sampling for the sampling ray in each direction and calculating the visibility separately can obtain a more accurate shadow, but it will significantly sacrifice the computational efficiency.

Q.2 Direct lighting visualization

We fully agree with the reviewer's point of view that direct lighting has a significant impact on rendering results. To illustrate this, we have visualized the direct lighting of indoor scenes from the Mip-NeRF dataset during relighting under conditions with and without normal supervision (See Figure 22 in Appendix G, Lines 1258-1277). It can be seen that incorrect direct lighting can severely compromise the quality of relighting results. This degradation is mainly caused by inaccurate normal estimation.

We sincerely thank the reviewer for the detailed assessment and recognition of our method. The review comments are very insightful and have provided us with valuable guidance for further improving our work. We hope the following responses well address the concerns.

1. Ablation study on albedo and relighting

We appreciate the reviewer's insightful suggestion and have conducted additional ablation studies on albedo estimation and relighting to demonstrate the effectiveness of occlusion and indirect illumination in our method.

Our experiments show that incorporating occlusion and indirect illumination enhances the decoupling of lighting and materials. The quantitative results demonstrate that both occlusion and indirect illumination have a significant impact on albedo estimation and relighting quality. Specifically, the lack of occlusion leads to more pronounced shadows in the albedo, while overlooking indirect illumination results in noticeable over-bright areas in the albedo. (See Table 9 and Fig. 23 in Appendix H)

2. Inadequate normal estimation

We sincerely thank the reviewer for the constructive comments regarding the normal estimation quality. Below, we provide the reasons for inadequate normal estimation and a discussion on how to improve its quality.

It is important to note that our method does not rely on additional geometric priors or regularization. As a result, the reconstructed normals are not perfectly accurate, which subsequently affects the overall performance of our method. In addition, our 3DGS-based baseline GS-IR also does not incorporate additional regularization terms or priors to supervise the normals. Therefore, the experimental results under the same setting ensure a fair comparison of occlusion and indirect illumination qualities between the methods.

To demonstrate that the inadequate normal estimation negatively affects the relighting results, we use a pre-trained Omnidata model for normal supervision. Experimental results show that incorporating additional priors to obtain more accurate normals significantly enhances the relighting quality of our method. (See Figures 14 and 15 in Appendix E, Lines 1029-1079)

In order to improve the quality of normal estimation, a straightforward approach is to use the shortest axis of the 3D Gaussian as the normal direction and apply additional regularization to make the Gaussian shape close to a disk. However, we observe that the introduction of regularization limits the representation capability of the 3DGS and results in the loss of details in complex geometric areas when reconstructing real-world scenes. Notably, some recent works [1] [2] have pointed out that optimizing BRDF and normal together can significantly improve the normal quality without sacrificing the representation capability of 3DGS. We believe that this paradigm offers a more effective means of supervising normals, and we plan to incorporate it in our future work.

[1] Wei M, Wu Q, Zheng J, et al. Normal-GS: 3D Gaussian Splatting with Normal-Involved Rendering[J]. arXiv preprint arXiv:2410.20593, 2024.

[2] Liang Z, Li H, Jia K, et al. GUS-IR: Gaussian Splatting with Unified Shading for Inverse Rendering[J]. arXiv preprint arXiv:2411.07478, 2024.

We are very grateful to the reviewers zyyD and tAKv for their comments and suggestions. As a result, we have revised some of the contents of the paper. Specifically, we have revised the following parts in the paper:

• Abstract, Lines 26 - 29.
• Contribution of our method, Lines 92 - 102.
• Add training time in Table 1, Lines 378 - 400.
• Experiment results, Lines 414 - 415
• Conclusion, Lines 533 - 534.

Moreover, we have provided further analysis of the relighting performance in Appendix J and additional relighting results of Stanford-ORB dataset in Table 11 and Fig. 29.

Thanks again to all the reviewers for their comments, which contributed to the further improvement of our work.