A Non-parametric Factor Representation and Editing for Measured Anisotropic Spectral BRDFs
Letter Of Changes: We thank all the reviewers for their valuable comments and suggestions.
We have revised our paper according to the reviewer's comments as much as possible, and the revised sentences are highlighted in red.
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Area Chair eGoH:
1) addressing the writing issues in Section 3 and Section 4.1.
A1. We have clarified several unclear points about implementation details in Sections 3 and 4.1 raised by the reviewer 74HV.
We have described them in Sections 3.3 and 3.5. Please see the details for the responses to reviewer 74HV below.
2) providing more discussion for the comparison with NBRDF in Section 4.2.
A2. According to Reviewer sZZi, we have conducted an equal-memory comparison and added the discussion in the last paragraph of Section 4.2.
Please see the details in A21 below.
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Reviewer 74HV:
Q11. Does each parameter get updated during each iteration as [2]?
A11. Yes, each parameter is updated during each iteration.
Q12. The order of parameter fitting is not enforced from the main text. Though, it is clear in Section 2 of the supplementary (i.e., in order: D, F, G, $\rho_d$, $\rho_s$).
However, there is no argument on why that order is chosen. Does the order matter? Why G is optimized after F? It feels that the opposite would be more natural.
A12. We follow Bagher's order of parameter fitting. We have replaced the fitting order, i.e., fitting G before F.
Then, the average PSNR in this order (D,G,F,$\rho_d$, $\rho_s$) is 45.38 dB, which is slightly better but almost the same (45.08 dB).
The order may not have a significant impact on the fitting performance, but finding an optimal order would be an interesting problem.
We will leave it as future work.
Q13. In this paper, G is optimized the same way as other factors, whereas it was deduced from D in [2].
A13. Bagher's method [2] proposes two calculation methods for G (Sec. 4.3 in [2]), G-from-D and Independent-G.
G-from-D deduces G from D, while Independent-G optimizes G the same way as other factors.
According to Bagher's experiments (Fig.9 in [2]), Independent-G offers better results than G-from-D. Thus, Independent-G is employed in our method.
We have described this in the last sentence of Sec. 3.3.
Q14. Could the constant factor $rho_d$ be the cause of these errors?
A14. The fitted constant factors (diffuse coefficients) $rho_d$ are zero for most of the metallic materials (e.g., aniso_copper_sheet, aniso_metallic_paper_gold, aniso_miro_7).
Thus, the diffuse coefficients would not cause errors even for points viewed at grazing angles.
Q15. Have you tried optimizing a model with only the specular lobe for metallic-looking materials?
A15. We have not tried optimizing a model with only the specular lobe for metallic materials. We have optimized a model with the diffuse and specular coefficients,
and as a result of the optimization, the diffuse coefficients are almost zero for most metallic materials.
Q16. The timings in section 4.2 for importance sampling the model are not very useful without the implementations.
A16. As the reviewer suggested, our method employs the alias method proposed by Walker for importance sampling. We have described this in the last sentence of Sec. 3.5.
For the implementation of NBRDF, we re-implement the author's code using LibTorch, a C++ variant of Pytorch (the author's code is written using PyTorch).
We have described this in the seventh sentence of Sec. 4.3.
Q17. Will a public implementation be available at some point?
A17. We are planning to publicize our code and data.
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Reviewer sZZi:
Q21. One concern of this reviewer is the fairness of the comparison. When comparing the quality of compression methods, it is natural to show equal-memory comparisons.
For example, when comparing this new work with NBRDF, the memory overhead of the work is much larger than NBRDF.
It seems obvious to have higher quality by adding more memory.
A21. We have added the number of hidden layers and nodes for NBRDF with a 6x128x256x256x195 neural network.
The data size for this neural network is 660KB, which is comparable to ours (730KB with 95% PCA of D and G).
Using this network, the average PSNR is 53.44 dB, which is 9.61 dB higher than ours.
However, using the deeper network also increases the computational time.
The computational time for BRDF evaluation is 78.14 us, 41 times larger than that of our method.
Therefore, our method seems suitable for applications that require fast evaluation speeds with moderate data size.
We have added this in the last paragraph of Sec. 4.2.
Q22. I wonder about the memory size used for Table 1, which needs to be done with the same memory size.
A22. The data size used for rendering Bagher's method is the same as ours.
We just used Bagher's weight in the fitting optimization process, and the size of the fitted data using Bagher's weight is the same as ours.
Q23. Typos. "Table.2." in Sec. 4.1
A23. We have fixed them.
Keywords: anisotropic spectral BRDF, non-parametric factor representation, editing
TL;DR: This paper proposes a simple but efficient, easy to edit representation for measured anisotropic spectral BRDFs using non-parametric factorization.
Abstract: Measured bidirectional reflectance distribution functions (BRDFs) can accurately represent the measured material appearance but suffer from high storage costs and lack editability due to their high dimensionality. Recent advances in efficient acquisition techniques extend the dimensionality of measured BRDFs from 3D (isotropic) to 4D (anisotropic) and from RGB to spectra. This, however, further compounds the issues of measured BRDFs and limits their practical use. This paper proposes a non-parametric factor representation for measured anisotropic spectral BRDFs. Based on microfacet theory, our method decomposes 4D measured anisotropic BRDF per spectrum into low-dimensional, editable factors. We further compress the spectral domain of decomposed factors using principal component analysis. Experimental results show that our method can compress measured anisotropic spectral BRDFs 1/40 on average and up to 1/333. Our method also provides several editing tools for each factor to enhance the editability of measured anisotropic spectral BRDFs.
Supplementary Material: pdf
Submission Number: 12
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