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# System prepended metadata

title: Responses to NIPS reviewers

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# Responses to NIPS reviewers Backup

[toc]

## repost
Dear Reviewer bpE7,

We just noticed that our previous comments posted under your Acknowledgement thread (titled “Author Rebuttal Acknowledgement by Paper1398 Reviewer bpE7”) are invisible to you and other reviewers. We therefore attach our comments again under this original thread for your reference. Sorry for the inconvenience caused. Thanks!

--------

Thank you very much for your previous comments that helped us improve this
manuscript. We have revised the paper as suggested (highlighted in blue font). The following summarizes the modifications.
- We have included the discussion for the demands of our setup and the challenges might occur in a more complicated scene in limitations in Sec. 5.
- We have added the nearest input image in Fig. 4 of the main paper. 
- We have included experiments on the real data in the main paper in Sec. 4.3.
- We have added other experiments to the supplementary materials.
- Implementation details are moved to the supplementary materials (Sec. C) due to page limitation.

We would like to emphasize again that our method tackles the problem of photometric stereo [A], and the setup we proposed is already more practical than existing photometric stereo methods [B,C]. Thus, it might be **unfair** to simply consider our work "The task can be unnecessarily challenging and ambiguous".

We have released the data of all real scenes and one synthetic scene, as well as the demo evaluation code in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance. 

We hope that our response has addressed your concerns and turned you to be positive about the paper. Please feel free to let us know if you have any further concerns or comments. Thanks!
<!-- Thanks again for your previous comments that helped us improve this manuscript.  -->

[A] A Benchmark Dataset and Evaluation for Non-Lambertian and Uncalibrated Photometric Stereo, TPAMI 2019
[B] GPS-Net: Graph-based Photometric Stereo Network, NeurIPS 2020
[C] Neural Reflectance for Shape Recovery with Shadow Handling, CVPR 2022
<!--Sorry for the inconvenience caused. We just noticed that our comments posted under your Acknowledgement (named “Author Rebuttal Acknowledgement by Paper1398 Reviewer bpE7 ”) are not available to you and other reviewers. We therefore post our comments again under this original thread for all your reference. Thanks!-->




## To AC
Dear ACs,

We sincerely appreciate your time and efforts in reviewing our paper. In this paper, we propose a new method for photometric stereo, which is a long-standing classic problem in computer vision [A,B,C]. Photometric stereo is particularly suitable for reconstructing the textureless surfaces and non-Lambertian objects, and it is **complementary** to multi-view stereo instead of **substitution**. 

<!-- However, Reviewer bpE7 keeps challenging our task setup with:
- “It makes the reconstruction task unnecessarily challenging and impractical” 
- “The reconstructed geometry of single-view setup is not on par with multi-view settings”
-  “The setup of single-view is more demanding than multi-view”. -->

However,  Reviewer bpE7 keeps challenging our task setup with “it makes the reconstruction task unnecessarily challenging and impractical” based on the reasons of "The setup is demanding" and "The reconstructed geometry is not on par with multi-view settings".

In fact, **such task setup has been widely used in the whole photometric stereo community**. Compared with existing methods, our method is capable of reconstructing the **full shape** of the object and the background of a real scene under a casual capturing setup (i.e., a fixed camera and a handheld cellphone flashlight without light calibrated. See https://sites.google.com/view/ps3d (Sec. A) for more details). We hope we can bring this to your attention. Thanks!

[A] Photometric method for determining surface orientation from multiple images, 1980
[B] A Benchmark Dataset and Evaluation for Non-Lambertian and Uncalibrated Photometric Stereo, TPAMI 2019
[C] Neural Reflectance for Shape Recovery with Shadow Handling, CVPR 2022


<!--In fact, **such task setup has been widely used in the whole photometric stereo community [A,B,C]** and show their values in ==**==, ==**== and ==**==. -->
## Response to R3


<!--
**Look forward for your further feedback**

Thanks again for your previous comments that helped us improve this manuscript. 

We notice that you haven't changed the rating yet. In our previous responses, we have addressed all your concerns. We would like to emphasize again that our method is based on near-field photometric stereo and its setup is already more complicated than most of existing PS works.

As the deadline for discussion is approaching, we sincerely look forward to your further feedback. Please feel free to let us know if you have any further concerns or comments. Thanks!
-->
<!--
**Look forward for your further feedback**

Thanks again for your previous comments that helped us improve this manuscript. 

In our previous responses, we have been trying to address all of your concerns. We would like to emphasize again that our method is based on near-field photometric stereo and its setup is already more complicated than most of existing PS works that ==constructs objects' shapes from a constraint single review and multi lighting== (e.g. [ref1], [ref2]). Thus, it might be unfair to simply consider our work "The task can be unnecessarily challenging and ambiguous".

As the deadline for discussion is approaching, we sincerely look forward to your further feedback. Please feel free to let us know if you have any further concerns or comments. Thanks!
Thanks again for your previous comments that helped us improve this manuscript. 
which is a classic and important problem in computer vision. In fact, our method can reconstruct both the background and the full shape of the objects, which is not possible by existing photometric stereo methods.  (i.e., including background and foreground)
-->
**Look forward for your further feedback**

Thanks again for your previous comments that helped us improve this manuscript. 

In our previous responses, we have been trying to address all of your concerns. We would like to emphasize again that our method tackles the problem of photometric stereo [A], and the setup we proposed is already more practical than existing photometric stereo methods [B,C]. Thus, it might be **unfair** to simply consider our work "The task can be unnecessarily challenging and ambiguous".

As the deadline for discussion is approaching, we sincerely look forward to your further feedback. Please feel free to let us know if you have any further concerns or comments. Thanks!

[A] A Benchmark Dataset and Evaluation for Non-Lambertian and Uncalibrated Photometric Stereo, TPAMI 2019
[B] GPS-Net: Graph-based Photometric Stereo Network, NeurIPS 2020
[C] Neural Reflectance for Shape Recovery with Shadow Handling, CVPR 2022

## General Response (Update): Release of Code and Data

### To R1
Thanks for your positive feedback, which has lead to a substantial improvement of our paper's quality! According to your comments and suggestions, we have added the additional results in the revised paper (highlighted in blue font). The following summarizes the modifications.
- We have updated the Fig. 2 and its caption and clarify the $C_v$ in Sec. 3.4. 
- We have included the experiments on real data to the main paper in Sec. 4.3. 
- We have added other additional experiments in the supplementary materials.
- Due to page limit, we moved the implementation details to supplementary materials (Sec. C). 

As promised in the abstract of our paper, we will release the code and dataset upon acceptance. In this stage, to help the reviewers better understand our method, we release the data of all real scenes and one synthetic scene, as well as the demo evaluation code in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance. Please kindly note that all the reviews and discussions on the OpenReview system will be made **public** after the paper gets accepted. We will keep our commitment.

Please feel free to let us know if you have any further concerns or comments. Thanks!


### To R3
Thank you very much for your previous comments that helped us improve this
manuscript. We have revised the paper as suggested (highlighted in blue font). The following summarizes the modifications.
- We have included the discussion for the demands of our setup and the challenges might occur in a more complicated scene in limitations in Sec. 5.
- We have added the nearest input image in Fig. 4 of the main paper. 
- We have included experiments on the real data in the main paper in Sec. 4.3.
- We have added other experiments to the supplementary materials.
- Implementation details are moved to the supplementary materials (Sec. C) due to page limitation.


We also release the data of all real scenes and one synthetic scene, as well as the demo evaluation code in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance. 

We hope that our response has addressed your concerns and turned you to be positive about the paper. Please feel free to let us know if you have any further concerns or comments. Thanks!


### To R2

Thanks again for the overall positive comments and insightful suggestions.

We have added the analysis of complicated background (Sec. E.2) and effect of light distribution on invisible regions (Sec. E.6) to the supplementary materials. Besides, we also included the experiments on the real data in the main paper in Sec. 4.3.

We also release the data of all real scenes and one synthetic scene, as well as the demo evaluation code in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance.

We sincerely look forward to your further feedback. Thanks!



### To R4

Thanks again for the positive comments and insightful suggestions.

We have added the analysis of normal smoothness loss to the supplementary materials (Sec. G). Besides, we also included the experiments on the real data in the main paper in Sec. 4.3.

We also release the data of all real scenes and one synthetic scene, as well as the demo evaluation code in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance.

We sincerely look forward to your further feedback. Thanks!



### To All

Thanks again for all reviewers' constructive comments. We have modified our paper according to reviewers' suggestions in the revised version, such as 
- update Fig. 2 and its caption [13bh] and Fig. 4 [bpE7],
- clarify $C_v$ in Sec. 3.4 [13bh],
- include experiments on real data in main paper in Sec. 4.3 [13bh,H2aV,bpE7],
- included the discussion for the demands of our setup and the challenges might occur in a more complicated scene in limitations in Sec. 5 [bpE7],
- add other experiments and move the implementation details to supplementary materials,
    - analysis on complicated background (Sec. E.2) [13bh,H2aV,bpE7],
    - analysis on shadow modeling in foreground and background regions (Sec. E.3) [13bh],
    - compare with MLP regression for shadow computation (Sec. E.4) [bpE7],
    - effect of area light (Sec. E.5) [bpE7],
    - effect of light distribution for invisible shape reconstruction (Sec. E.6) [H2aV],
    - effect of normal smoothness loss (Sec. E.7) [nudb],
    - more details of real dataset (Sec. G) [13bh,H2aV,bpE7].


We also release the data of all real scenes and one synthetic scene, as well as the **demo evaluation code** in https://github.com/neuralps3d/neuralps3d. The full code and datasets will be released upon acceptance. We hope our code and dataset can benefit future research in this direction. 

Please feel free to let us know if you have any further concerns or comments. Thanks!

<!-- ## Release of the Code and Data
Thanks for your positive feedback! We will include these additional results in the main paper in the revision.

As promised in the abstract of our paper, we will release the code and dataset upon acceptance. In this stage, to help the reviewers better understand our method, we release the data of all real scenes and one synthetic scene, as well as the demo evaluation code in ==add link==. The full code and datasets will be released upon acceptance. Please kindly note that all the reviews and discussions on the OpenReview system will be made **public** after the paper gets accepted. We will keep our commitment.

Please feel free to let us know if you have any further concerns or comments. Thanks!
<!--What's more, the discussion of rebuttal period on OpenReview will be **public** after the paper gets accepted. We will keep our commitment.-->
<!-- We provide a simple demo in ==link==. We also provide the data of one synthetic scene and three real scenes. --> -->


## Reminder

### Thanks for all your comments and look forward to post-rebuttal feedbacks!

Dear AC and all reviewers:

Thanks again for all of your constructive suggestions, which have helped us improved the quality and clarity of the paper!

Since the discussion phase has started for over three days, we have not heard any post-rebuttal response yet.

Please don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer, as we would love to convince you of the merits of the paper. We appreciate your suggestions. Thanks!


### To R1 `13bh`
**Looking forward to your post-rebuttal feedback**

Thanks again for your constructive suggestions and comments. As the deadline for discussion is approaching, we are glad to provide any additional clarifications that you may need.

In our previous response, we have carefully studied your comments and added a lot more experiments and analysis to complement your suggestions. We summarize our responses with regard to the following aspects:

- **We clarify and emphasize our main idea/contribution**  
We clarify that our method is an improvement over near-field photometric stereo (2.5D -> 3D) and our target is not to substitute multi-view stereo. Instead, we propose to utilize both shading and shadow information to infer the shape in both visible and invisible regions. 

- **We provide detailed explanations for some confusions** including sampling strategy for ray marching, intuitive explanation for the role of shadow modeling, depth estimation not satisfactory for LUCES dataset, comparison with NeRF/UNISURF, accurate background reconstruction.

- **We conduct new experiments and provide results as suggested**  
We conduct experiments to analyze the contribution of shadow modeling on foreground/background and study the capability on more complicated background cases.

- **We test on casually captured real data to demonstrate the practicality of our method**  
We utilize fixed camera and flashlight of a casually hand-held cellphone to capture the real data without any calibration. However, our method still gets satisfactory results which shows its scope in real-world applications.

We hope that the provided new experiments and additional explanations have convinced you of the merits of our work. Please do not hesitate to contact us if there are other clarifications or experiments we can offer.

Thank you for your time again!

Best, Authors

### To R2 `H2aV`
**Looking forward to your post-rebuttal feedback**

Thanks again for your positive comments and insightful suggestions. As the deadline for discussion is approaching, we are glad to provide any additional clarifications that you may need.

In our previous response, we have carefully studied your comments and added a lot more experiments and analysis to complement your suggestions. We summarize our responses with regard to the following aspects:

- **We emphasize our main idea/contribution**  
We clarify that our main contribution is that we propose to utilize both shading and shadow information to infer the shape in both visible and invisible regions and reconstruct the full 3D shape of the scene instead of 2.5D for existing near-field photometric stereo methds. 

- **We conduct new experiments and provide results as suggested**  
We conduct experiments to study the capability on more challenging synthetic dataset with complicated background and analyze the effect of light numbers by calculating the charmfer distance error for reconstructed shapes.

- **We test on casually captured real data to demonstrate the practicality of our method**  
We utilize fixed camera and flashlight of a casually hand-held cellphone to capture the real data without any calibration. However, our method still gets satisfactory results which shows its scope in real-world applications.

We hope that the provided new experiments and additional explanations have convinced you of the merits of our work. Please do not hesitate to contact us if there are other clarifications or experiments we can offer.

Thank you for your time again!

Best, Authors



### To R3 `bpE7`
**Looking forward to your post-rebuttal feedback**

Thanks again for your constructive suggestions and comments. As the deadline for discussion is approaching, we are glad to provide any additional clarifications that you may need.

In our previous response, we have carefully studied your comments and added a lot more experiments and analysis to complement your suggestions. We summarize our responses with regard to the following aspects:

- **We emphasize our main idea/contribution**  
We clarify that our main contribution is that we propose to utilize both shading and shadow information to infer the shape in both visible and invisible regions and reconstruct the full 3D shape of the scene instead of 2.5D for existing near-field photometric stereo methds. 

- **We provide detailed explanations for some confusions** including demanding setup, ambiguity caused by cast-shadow between background surface and object, discussion on potential applications.

- **We conduct new experiments and provide results as suggested**  to analyze the capability under larger light sources, and replace the shadow modeling with direct regression using MLP to show the necessity of explicit shadow modeling. We also show the nearest training samples for Fig. 4.

- **We test on casually captured real data to demonstrate the practicality of our method**  
We utilize fixed camera and flashlight of a casually hand-held cellphone to capture the real data without any calibration. However, our method still gets satisfactory results which shows its scope in real-world applications.

We hope that the provided new experiments and additional explanations have convinced you of the merits of our work. Please do not hesitate to contact us if there are other clarifications or experiments we can offer.

Thank you for your time again!

Best, Authors



 
### To R4 `nudb`
**Looking forward to your post-rebuttal feedback**

Thanks again for your positive comments and insightful suggestions. As the deadline for discussion is approaching, we are glad to provide any additional clarifications that you may need.

In our previous response, we have carefully studied your comments and added a lot more experiments and analysis to complement your suggestions. We summarize our responses with regard to the following aspects:

- **We conduct new experiments**   to  analyze the effect of normal smoothness loss and explain the possible reasons of the lack of details for LEGO object.

- **We test on casually captured real data to demonstrate the practicality of our method**  
We utilize fixed camera and flashlight of a casually hand-held cellphone to capture the real data without any calibration. However, our method still gets satisfactory results which shows its scope in real-world applications.

We hope that the provided new experiments and additional explanations have convinced you of the merits of our work. Please do not hesitate to contact us if there are other clarifications or experiments we can offer.

Thank you for your time again!

Best, Authors




## General Response: Contributions and New Experiments 
<!--
We sincerely appreciate all reviewers’ and ACs’ time and efforts in reviewing our paper. We thank all the reviewers for their recognization of our work, such as *"a promising framework for near-field photometric stereo"* [13bh], *"shows the originality"* [13bh], *"interesting setup"* [H2aV,bpE7], *"state-of-the-art performance"* [13bh,H2aV,nudb], *"well-written paper"* [H2aV,nudb].
-->
We sincerely appreciate all reviewers’ and ACs’ time and efforts in reviewing our paper. We thank all the reviewers for their recognization of our work on the following aspects.
* **Problem Setup.** *"interesting setup"* [H2aV,bpE7];
* **Model.** *"a promising framework for near-field photometric stereo"* [13bh], *"shows the originality"* [13bh];
* **Experiments.** *"state-of-the-art performance"* [13bh,H2aV,nudb], 
* **Wrting.** *"well-written paper"* [H2aV,nudb].


And we also thank all reviewers for their insightful and constructive suggestions, which help a lot in further improving our paper. In addition to the pointwise responses below, we clarify our idea and contribution, and summarize the new experiments suggested by the reviewers. 



**Idea and Contribution**

In this work, we propose a NeRF-based method for near-field photometric stereo (PS). By explicitly utilizing single-view shading and shadow cues, our method is able to reconstruct **the full 3D shape** of the object, including the **visible** and **invisible** regions. It is not possible by existing PS methods as they can only recover a **2.5D scene** representation (i.e., normal or depth map) to describe the **visible** surface. 
Note that our method is based on PS settings, where multi-view information is not available. And the goal of our method is not to substitute the multi-view stereo methods. Instead, we propose to utilize both shading and shadow information in the scene to improve the current PS methods (from 2.5D to 3D shape reconstruction). <font color="#E24A0F">Our work is complementary to existing multi-view methods while only single-view images are required. </font>Moreover, our idea of jointly modeling shading and shadow cues are also potentially beneficial for multi-view reconstruction.


**New Experiments**

To address the reviewers' questions and support our responses, we conduct the following experiments and put the results in the link: https://sites.google.com/view/ps3d. 
- Results on real data with casual imaging setup [13bh,H2aV,bpE7].
- Results on more complicated synthetic data [13bh,H2aV,bpE7].
- Effects of shadow modeling in foreground and background [13bh]. 
- Results on scenes illuminated by area light [bpE7].
- Replacing ray-marching shadow computation with direct MLP regression [bpE7].
- Effects of the surface normal smoothness loss [nudb].

**Details for the Experiment on Real Data**
- Casual capturing setting
We captured a real dataset using a fixed camera (the focal length is 28mm) and a handheld cellphone flashlight (see Sec. A in https://sites.google.com/view/ps3d). The object is put on the table and close to the wall. We turned off all the environmental light sources and only kept the flashlight on, which was randomly moved around to capture images illuminated under different light conditions. The captured dataset consists of 3 objects (around 70 images for each object).
- Lighting calibration
Our setup **does not** require mannual calibration of lights. Instead, we applied the state-of-the-art self-calibrated photometric stereo network (SDPS-Net [7]) for light direction initialization, and roughly measured the camera-object distance as initialization of light-object distance. After initialization, the position and direction of lights are jointly optimized with the shape and BRDF during training.
- Results
We tested our method on three objects and show their rerendered results as well as shape reconstruciton results in https://sites.google.com/view/ps3d (Sec. A). Even with this **casual capturing** setup and **uncalibrated** lights, our method achieves satisfactory results in full 3D shape reconstruction.

<!--==Note that the goal of this work is not to substitute the multi-view stereo methods. Instead, we propose an alternative 3D reconstruction method that only requires single-view images, which helps in dealing with cases where the camera cannot be moved (e.g., the surveillance camera). Our method is complementary to existing multi-view methods. Moreover, our idea of jointly modeling shading and shadow cues are also potentially beneficial for multi-view reconstruction.==-->
<!--<font color="#E24A0F">[wq: We test our method on three objects and show their rerendered results as well as shape reconstruciton results in ==ref==. Even with this **casual capturing** setup and **uncalibrated** lights, our method achieves satisfactory results in both material and shape reconstruction.]</font>-->

<!-- For practical Since we don't have the ground-truth light calibration, we roughly estimated the light position as an initialization. Specifically, we applied the state-of-the-art self-calibrated photometric stereo network (SDPS-Net [7]) for light direction estimation, and initialized the light-object distances as the camera-object distance. The camera-object distance is roughly measured. -->
<!-- - Optimization
Since the light positions were estimated and were not accurate enough for shape reconstruction, we jointly optimized the shape, BRDF, and lights during training. -->

<br><br>
## To R1 `13bh`
Thank you for the constructive comments.

**_Q1: No formula illustrates how $C_v$ in Eq.8 is calculated._**  
**A1:** Sorry for the confusion. The $C_v$ mentioned in Eq.8 is actually the $C(r)$ in Eq.7. We first derive volume rendering and later introduce surface rendering in Eq.10. We will clarify it in Sec. 3.4 in the revised version.

**_Q2: In Figure 2, the same "MLP" block is shown in two separate branches._**  
**A2:** Thanks for the good suggestion. We will redraw Figure 2 in the revised version.

**_Q3: "How the points along the rays are sampled is unclear to me"_**  
**A3:** Sorry for the confusion. The points along the camera ray are sampled following the manner of UNISURF [38]. For each ray, we first apply root-finding to locate the surface point, and then define an interval around the surface point to sample points. We use a relatively large interval for point sampling to make sure the full scene is well sampled. The term "around the surface" does not mean "close to the surface". We will update the caption in Figure 2 to avoid confusion.


**_Q4: "It is still unclear to me why the shadow becomes a strong constraint on the model that can substitute the constraint from multi-view photo-consistency"_**  
**A4:** This paper tackles **the problem of near-field photometric stereo**, which is a longstanding and important problem in computer vision [46]. Our goal is **not to substitute** the multi-view photo-consistency with shadow constraints. Instead, considering a scenario where single-view images are captured under different point lights, we target utilizing both shading and shadow information for full 3D shape reconstruction. Note that the shadow cues can also be incorporated with the multi-view photo-consistency to improve the shape reconstruction.

**_Q5: Analyze the contributions of cast shadows modeling in foreground and background separately._**  
**A5:** Thanks for the insightful comment. We have conducted extra experiments to analyze the effect of cast shadow modeling in both regions. Specifically, we trained two variant models, one without foreground shadow modeling and the other without background modeling. Results in https://sites.google.com/view/ps3d (Sec. C) show that modeling cast shadow in both regions is important, as disabling either one of them leads to decreased accuracy.

**_Q6: "Even the background is well reconstructed with little artifacts. However, the author didn't directly explain why their method is not sensitive to the background (it is almost perfect) and can reconstruct an accurate background simultaneously."_**  
**A6:** We do **not** claim that our method is better at reconstructing the background than other methods. There are possible two reasons why we got clean background results in the paper. First, the background in our synthetic dataset has a uniform texture with a regular shape, which is easier to recover. Second, our method makes use of the rich shading information that exists in images illuminated by multiple lights, providing strong regularization for the planar background.


**_Q7: "There is no intuitive explanation for the role of modeling shadow for shape estimation. What is the problem aiming to solve by considering the shadow, the ambiguity, additional clue of global shape information, useful clue for depth estimation, or even light refinement"_**  
**A7**: Our method explicitly makes use of this additional shadow cue for full shape reconstruction. Note that our method considers the classic problem of near-field photometric stereo, where the shading and shadow are two dominant cues for shape recovery. The shadows can provide strong information for the invisible region, which is analogy to shape from silhouette. Consider the light source as the camera viewpoint, shadow is formed when light rays are blocked by objects. If we view from light source, the contour of shadow is the same as the silhouette of the object on the image plane (light projects the contour of objects onto the scene, while objects are projected back onto the image plane).

**_Q8: "The evaluation is mainly conducted on the synthetic dataset built by the authors, which is less convincing. Although the paper shows the result of the LUCES dataset in the supplementary material, the depth estimation is not satisfactory (4.39 vs. 3.17 for the state-of-the-art). "_**  
**A8:** Note that the experiment on LUCES does not aim to achieve state-of-the-art depth estimation performance but shows that our method is able to work on the **real data** for completeness. In fact, when testing on the LUCES dataset, our method degenerates to the *"Ours w/o shadow"* baseline, which is much worse than the full model (see Table 3 and Figure 6 of the paper). As mentioned in Line 47 of the supplementary material, the LUCES dataset is **not** suitable to evaluate the full potential of our method, as the shadow and shading information of the background regions cannot be observed.  
To further evaluate our method, we evaluate our method on a real dataset captured by ourselves. Results in https://sites.google.com/view/ps3d (Sec. A) show that our method achieves **good normal** and **shape reconstruction** results on the **real** dataset given only roughly calibrated lightings, clearly demonstrating the effectiveness of our method.

**_Q9: "The compared methods, NeRF and UNISURF, are implemented in a naive way. It is unclear whether the authors have also sampled points along the light ray in those methods. If not, it can be expected that the reconstruction results are not good because NeRF and UNISURF are mainly applied in multi-view stereo..."_**  
**A9**: We are not about to show the superiority over NeRF/UNISURF on single view reconstruction. Instead, we would like to demonstrate that directly applying these nerual rendering methods or naively conditioning light on the radiance field does not work for single view reconstruciton. Note that we compared three types of methods in the experiments, including the single-image depth estimation, near-field photometric stereo methods, and NeRF-based methods. We did not include the explicit shadow computation (mentioned as "sample points along the light ray") for the NeRF-Based methods, as the shadow modeling is one of our main technical contributions. In fact, the "UNISURF+shadow" method is similar to the baseline method "Ours w/o shading" in the ablation study (see Line 228 of the paper). Table 3 of the paper shows that simply integrating UNISURF and shadow modeling cannot produce good results, e.g., MAE comparison for the CHAIR object is "Ours w/o shading" (32.49) vs. "Ours" (1.93).


**_Q10: This work has lots of pre-setting to the environment (the background color and the background complexity), which will limit the application scope of this method._**  
**_Q11: How well the proposed method can perform under a more complicated background._**  
**A10-11**: To further evaluate the robustness of our method on more complicated backgrounds, we evaluated it on four scenes rendered with different backgrounds, including two uniform color backgrounds with different lightness (denoted as 'Light' and 'Dark') and two textured backgrounds. Results in https://sites.google.com/view/ps3d (Sec. B) show that our method is robust to backgrounds with different lightness and textures. Moreover, our new real-world experiments show that the capturing setup can be very simple.

<!--<font color="#E24A0F">[wq:should we also mention the complexity of the background in real data?]</font>-->
<!--==For multi-view reconstruction, the cues are from the visible contour of the object, while for shadow, it provide silhlouette clues for invisible regions.==-->

<!-- We hypothesize that there are two reasons why our method reconstructs a clean background.  --> 
<!--Despite the shadows can provide strong information for the invisible region, existing methods often ignore them due to the difficulty of explicit shadow modeling, and can only estimate a depth or normal map for the visible surface.-->
<!--<font color="#E24A0F">[wq:Kenneth mentioned that this is the same as shape from silhouette. Consider the light source as the camera viewpoint, shadow is formed when light rays are blocked by objects. If we view from light source, the contour of shadow is the same as the silhouette of the object on the image plane. (light projects the contour of objects onto the scene, while objects are projected back onto the image plane) For multi-view reconstruction, the cues are from the visible contour of the object, while for shadow, it provide silhlouette clues for invisible regions.]</font>-->

<!--<font color="#E24A0F">[wq:Kenneth mentioned that We are not saying we are better than nerf/unisurf. However, it demonstrates that directly apply these nerual rendering methods or naively conditioning light on the radiance field does not work for single view reconstruciton.]</font>-->



<br><br>

## To R2 `H2aV`
Thank you for the positive comments and insightful suggestions.

**_Q1: "Each part of the proposed method is not novel. The method consists of three major parts: neural reflectance field representation follows [38]...the color and BRDF modeling follow [15,24]...the shadow computation is slightly different to [48], but it is similar to [24] where they both check the visibility of the surface point._**  
**A1:** The main contribution of our method is a NeRF-based framework for near-field photometric stereo which can reconstruct the *full* 3D shape of the object by jointly utilizing shading and shadow cues. To the best of our knowledge, we are the first near-field photometric stereo method that can reconstruct the invisible part of the scene. The technical novelty includes "an online shadow modeling strategy for efficient shadow modeling" and "combining volume and surface rendering loss for better shape regularization". We agree that the first two major parts are not very novel. However, our shadow modeling is largely different from [24], as [24] assumes a directional light and uses a depth map for shadow computation. In contrast, we assume a near-field point light and use occupancy field shadow computation.

**_Q2: "It is suggested to evaluate this method in more challenging real and synthetic datasets."_**  
**A2:** Thanks for the good suggestion. To further evaluate the robustness of our method, we additionally tested our method on a synthetic dataset with more complicated backgrounds, and a challenging real dataset captured by ourselves (see Sec. A & B in https://sites.google.com/view/ps3d). The results show that our method is robust to backgrounds with different lightness and textures, and our method can achieve good results on real data even in a weakly calibrated setup (i.e., the lights are initialized as the prediction of a lighting estimation method SDPS-Net [7] and then jointly optimized with the model). 

**_Q3: "I am curious to see how the number of lights affects the accuracy of the geometry in the invisible part of the scene...If lights fail to illuminate the invisible regions from different angles, how will the accuracy be affected?_**  
**A3:** We have discussed the effect of how the number of lights and the range of light distributions on the shape reconstruction in the paper. The normal MAE, depth L1, and side-view shape can be found in Table 4, Table 5, and Figure 9 of the paper. As it is not easy to isolate the invisible part given different objects have different shapes, we instead report the chamfer distance between the reconstructed and ground-truth meshes, which can quantify the full shape reconstruction. Results in https://sites.google.com/view/ps3d (Sec. F) show that the shape accuracy will improve given more lights, and our method is able to achieve robust results given 8 input lights. When the light distribution becomes narrow (small), the shape accuracy will decrease.

<!--**_Q4: Suggestions: It will be great to isolate the invisible region of the scene and show quantitatively how the proposed shadow rendering improve the accuracy in these regions._**  
**A4:** Thanks for the good suggestion. As it is not easy to isolate the invisible part given different objects have different shapes, we instead report the chamfer distance between the reconstructed and ground-truth mesh, which can quantify the full shape reconstruction. ==ref to results== We can see that the proposed shadow rendering can significantly improve the full shape reconstruction. Also from Figure 6 (last row) of the paper, we can see clearly that without shadow rendering, the invisible regions are severely distorted despite having a reasonable front view normal.
-->


<br><br>
## To R3 `bpE7`
Thank you for the constructive comments.

**_Q1: The scope of the paper is quite limited, in terms of the problem setup and the practicality. The setup is demanding -- real directional light plus known lighting direction. This highly controlled lighting setup seems to only be feasible in a laboratory or a light stage setting._**  
**A1:** Note that our method assumes a near-point light, instead of directional light. It is true that the setup of photometric stereo is demanding in the past. However, recent deep lighting calibration methods can achieve robust calibration results simply using the captured images of the target scene without any calibration tools [A,B], which significantly reduces the complexity of the capturing setup.
In our experiments on real data (see Sec. A in https://sites.google.com/view/ps3d), we simply use a fixed camera and a handheld cellphone flashlight as the light source. We use SDPS-Net [A] for initial lighting calibration, which is then jointly optimized with the model. Given only weakly calibrated lightings, our method achieves good reconstruction results for normal and shape on this challenging real dataset, clearly demonstrating the practicality of our method.
[A] Self-calibrating deep photometric stereo networks, CVPR 2019
[B] Self-calibrating Photometric Stereo by Neural Inverse Rendering, ECCV 2022

**_Q2: "Cast shadow depends on the object geometry, the lighting, and also the surface the shadow is cast on. The geometry of the surface and the geometry of the object can be entangled to cause ambiguity. This is more severe in real-world examples."_**  
**A2:** We agree that the appearance of cast shadow also depends on the surface that shadow is cast on (denoted as background for simplicity). But note that the background geometry itself is also constrained by the shading cues that exist in the multi-light images, which will not introduce ambiguity to the problem. In fact, our results on scenes with multiple objects provide strong evidence for this argument (Figure 7 of the paper). We can treat one of the objects as the foreground, and the rest as the background, resulting in a highly-irregular "background". The results show that our method can faithfully reconstruct the object as well as the "background".

**_Q3: The reconstructed geometry is not on par with multi-view settings, and degrades drastically as the number of lights decreases. My biggest concern about this paper is it makes the reconstruction task unnecessarily challenging and impractical._**  
**A3:** Note that the goal of this work is not to substitute the multi-view stereo methods. Instead, we propose an alternative 3D reconstruction method that only requires single-view images, which helps deal with cases where the camera cannot be moved (e.g., the surveillance camera). It is obvious that the performance of our method will decrease as the number of lights decreases, but a similar phenomenon also happens in multi-view methods when the number of views decreases. Our new experiments on real data show that the full shape of an object can be reconstructed from single-view images captured by a fixed camera and a moving handheld cellphone flashlight, clearly demonstrating the practicality of our method.

<font color="#E24A0F">Note that the goal of this work is not to substitute the multi-view stereo methods. Instead, as a PS-based method, our work greatly advance the near-field photometric stereo methods (from 2.5D to 3D reconstruction). This is complementary to existing multi-view methods while only single-view images are required.
It is obvious that the performance of our method will decrease as the number of lights decreases, but a similar phenomenon also happens in multi-view methods when the number of views decreases. And according to our analysis on light numbers  (Table 4 and Fig. 9 in main paper), our method can achieve comparable results even when only 8 lights are given. 
Our new experiments on real data show that the full shape of an object can be reconstructed from single-view images captured by a fixed camera and a moving handheld cellphone flashlight under a **casual** capturing setup, clearly demonstrating the practicality of our method.</font>

**_Q4: "to make the setup slightly more practical, how well does the method perform when shadow is softer, i.e., slightly larger light source, or small area lights?"_**  
**A4:** Thanks for the insightful comment. To analyze the effect of soft shadow caused by a larger light source, we tested our method on data rendered using light sources with different scales (i.e., a sphere with a radius of 1/50, 1/25, or 1/10 of the object size). Results in https://sites.google.com/view/ps3d (Sec. D) show that our method is robust to larger light sources (e.g., 1/50 and 1/25). We also observe that when the light source size is considerably large (e.g., 1/10), the results in the object boundary will decrease because of the heavy soft shadow. Note that this is not a problem in practice as it is very easy to find a point light source whose size is smaller than 1/25 of the object size (e.g., the cellphone flashlight). 

**_Q5: "line 149: has the proposed shadow generation method been validated over direct regression method using an MLP?"_**  
**A5:** Thanks for the suggestion. We trained a variant model replacing the ray-marching visibility computation with a direct visibility MLP. Results in https://sites.google.com/view/ps3d (Sec. E) show that simply regressing the visibility produce worse results, as this MLP cannot regularize the occupancy field. In contrast, our method performs ray-marching in the occupancy field to render shadow, providing strong constraints for the occupancy field.

**_Q6: "fig 4: should also show the nearest neighbor training samples"_**  
**A6:** Thanks for the suggestion. Results in https://sites.google.com/view/ps3d (Sec. G) show the nearest training samples, and error maps of the nearest sample and our results. We can see that our method can accurately render cast shadows under novel lights. We will include the nearest training samples in Figure 4 in the revised version. 



**_Q7: "The calibrated lighting is more demanding than calibrated camera pose... The lighting needs to be real directional light source, which is difficult to acquire in real-world scenarios."_**  
**A7:** Please kindly refer to the first response.


**_Q8: It would be also valuable to discuss potential applications for the proposed setup and algorithm._**  
**A8:** First, as a photometric stereo method, our method can be applied to any applications that require photometric stereo technique. Second, our method can reconstruct the full shape and BRDFs of the object from single-view images captured under different lightings, and supports novel-view rendering and relighting. It is particularly helpful in scenarios where the camera cannot be moved (e.g., the surveillance camera). Last, the proposed algorithm (e.g., the efficient shadow modeling strategy) can potentially be integrated with multi-view methods for better shape reconstruction. 






<br><br>
## To R4 `nudb`
Thank you for the positive comments and insightful suggestions.

**_Q1"The authors studied the contribution of different components (shading and shadow) of their method. But the impact of different loss terms was not included. Specially, at L171, how the value of  for normal smoothness loss is found is not illustrated."_**  
**A1:** Following UNISURF, we apply the normal smoothness loss to promote the surface smoothness. We adopt the same loss weight as in UNISURF [38].


**_Q2: "How’s the normal smoothness loss affect your method? Is that similar to UNISURF? From your result, especially on LEGO, the loss of detail of studs and track seems very serious. Is that caused by normal smoothness loss or by more complicated light reflection at those areas?"_**  
**A2:** Thanks for the insightful comment. The adopted normal smoothness loss is similar to UNISURF. Remember that the surfaces in the invisible region are primarily constrained by the shadow information, which is less constrained than the visible surface due to the lack of shading information. To further study the impact of the normal smoothness loss, we did an ablation study on the loss term. Results in https://sites.google.com/view/ps3d (Sec. H) show that imposing the normal smoothness loss is helpful to reduce the artifacts in the invisible regions.

We experimentally verified that the loss of details in LEGO is not caused by normal smoothness loss. We think it might be caused by two reasons. First, LEGO contains many complicated thin strutures and the object region is relatively small in our data (in a region of about 200X200 pixels). Second, our method only observes the object from a single view, making thin structures less distinguishable. We will consider improving our method for thin structure modeling in the future.






## Example rebuttals
- Volume Rendering of Neural Implicit Surfaces: https://openreview.net/forum?id=GlEWs-V9boR
- Dynamic Visual Reasoning by Learning Differentiable Physics Models from Video and Language: https://openreview.net/forum?id=lk1ORT35tbi



<!--We would like to emphasize again our main idea/novelty and address some common concerns as follows.
We provide analysis on complicated background textures and showcase the practical experiments on real data.
To make the responses clearer and easy to follow, we put the extra results in the link ==insert link==. Please kindly check the figures/tables on this site.-->
<!--Our method is a photometric-stereo-based method that aims at solving **3D** shape reconstruction with images illuminated by different **point lights** under a **fixed viewpoint**. Different from multi-view stereo (MVS) which takes multi-view texture/contour consistency as clues to solve shape reconstruction problem, photometric stereo (PS) targets at recovering surfaces with finer details according to shading information from multi-light images.
However, existing PS methods only recover 2.5D shape and ignore the invisible regions. 
In our paper, we leverage the fruitful shading and shadow information to infer both the shape of visible and invisible regions, and recover the full 3D shape of the scene. We are not about to substitute the multi-view stereo methods as the problem setting is totally different.-->


<!--
**Results on more complicated synthetic data**
To further elaborate the capability of our method on complicated background textures, we did some experiments on background 


**Results on real data**

In our main paper, we only evaluated our method on synthetic data. Since there is no suitable real data for evaluating our method, we then test on a near-field PS dataset with only object regions taken into account. To further explore its robustness and practicality, we manually captured some real data under a **flexible** setup and evaluated our method **without any calibration**.
<font color="#E24A0F">[wq: except for K matrix calibration]</font>

- Results
Please refer to the Author Response site for more information about the captured data and the results.
The results demonstrate the capability of our method in more practical applications.


We also separately address reviewers' questions according to their comments. We hope our responses could clarify all reviewers’ confusion and alleviate all concerns. We thank all reviewers’ time again.


- Experiment setting
Following our pipeline, we assume near-field point light and near-field camera. We therefore chose a lens with short focal (28cm) and use a smartphone flashlight as light source. We put the objects on the table and close to the wall so that the shadow can be projected onto the wall. We turned off all the environmental light sources and only kept the flashlight on. We randomly posed the light to capture the images under different light conditions. For easier initialization, we roughly estimate the distance between the object center and the light source and make them close to the camera-object distance (about $\pm 20\%$ error).
- Preliminary
We take the advantage of recent state-of-the-art self-calibrated photometric stereo work (SDPS-Net [7]) to estimate the light directions from the captured images. And set the light-object distance the same as camera-object distance.
- Training
Since the light position was estimated and may not be accurate enough for shape reconstruction, we jointly optimize the light position with other parameters in the training phase.
-->

<!--To further evaluate the robustness of our method, we additionally tested our method on a synethetic dataset with more complicated backgrounds and a challenging real dataset captured by ourselves. Please kindly read the following responses for more details.-->
<!--As there is no existing NeRF-based method designed for single-view photometric stereo, we compared with two straightforward baseline (i.e., NeRF and UNISURF).-->


<!--
**_Q: Evaluation on more challenging synthetic datasets._**

**_Q: Evaluation on more challenging real datasets._**
**_Q: How the number of lights affects the accuracy of the geometry in the invisible regions_**
**_Q: Show quantitatively how the proposed shadow rendering improve the accuracy in the invisible regions._**
-->
<!--Since we adopt 3D neural volume space for scene representation, the normal smoothness loss is adopted for smoother surface with less noises. Although the normal in visible surface is constrained by shading information, the surface in invisible regions are less constrained excepted for shadow information. -->
