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You have addressed the issues raised by the reviewers.
Most of the issues raised in the first review phase have been address. The authors have improved the manuscript to a level that could be useful for readers of PeerJ Computer Science.
Please address the issues raised by the reviewers.
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The paper is generally well written and clear, however the emphasis on the novelty using compared to the authors' previous work is missing in some parts including the abstract.
The importance of the work can be better shown if the authors explain in more details the advantages of having the objective function in the logarithmic domain which seems to be the main contribution of this work.
The results presented are promising, however they lack more discussions. For example, the Specularity can be seen on the apple and pepper reflectance images of the authors' proposed method and previous method, and this point is not discussed.
Moreover, the computation time of the proposed method compared to state of the art approaches is not specified.
The paper is clear with interesting results. However, I suggest to give more emphasis on the originality of
the paper compared to your previous work regarding the logarithmic objective function. Moreover, more details and discussions on the results especially on the errors in estimation is essential in my point of view for a better understanding and impact of this work.
A few typos are still present. I notice numerous errors in section 4.1. “Fig. 1 presents shading images g resulting from all methods on five examples”: where the fixe examples are in figure 1 ? “The next rows are respectively the results given by LS, KL, Barron, Yang…” it’s certainly columns ?
The authors cite a previous work. To my opinion, more information of this previous method must be given to understand this part.
It would be advisable to add a table with the computing time.
The paper deals with reflectance, shading and specularity estimation form multispectral image. The process has been evaluated in MIT and CAVE datasets. The authors provide an interesting method and seems to be very efficient. Unfortunately, a few typos are still present.
Major issues (not in priority order):
1°) “3 Method”: this part starts with a citation of a previous work on this topic. To my opinion, more information of this previous method must be given to understand this part.
2°) “4.1 Qualitative results”: I notice numerous errors in this section. “Fig. 1 presents shading images g resulting from all methods on five examples”: where the fixe examples are in figure 1 ? “The next rows are respectively the results given by LS, KL, Barron, Yang…” it’s certainly columns ?
3°) “4.2 Quantitative results”: it would be advisable to add a table with the computing time.
1°) Equation 1 is the Lambertian BDRF and the reference of 2012 is not appropriate.
2°) Page 2, line 28: “… a special case of the Bidirectional Reflectance Distribution Function (BRDF)…” the BRDF do not include the cos(theta).
3°) page 8, line 216: why “now” ? Only one method is proposed in the paper ?
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