Accelerated Phase Deviation Elimination for Measuring Moving Object Shape with Phase-Shifting-Profilometry

Round 1

Reviewer 1 Report

The manuscript proposes an accelerated method to solve the phase deviation caused by movement. By calculating the difference in image level and introducing the optimization algorithm of SGD, the experimental results prove that it brings faster speed and larger motion tolerance. Some questions need to be declared further:

• One of the advantages of the article is the larger motion tolerance. From my point of view, describing the movement speed of the method when citing references will highlight the advantages of this manuscript.
• In addition, the team of Refs.[18] has some recent work, which should also be incorporated in the reference for comparative analysis. The text content for comparison with the same technical route should be appropriately increased.
• It should be noted that the contents of the four experiments are to discuss the effect of different variables. If the authors add more advanced content descriptions or subtitles here, the manuscript will be more readable. Experiment 2 introduces θ to represent the phase deviation for simulation calculation. And experiment 3 discusses the impact of different speed.
• In the experiment, the order and the relationship between the subsections should be given more textual explanations, such as showing the simulation results firstly, and then verifying it through actual experiments.
• There are some writing problems in the manuscript, such as the citation of Table. 1. The authors need to double check.
• In addition, the captions of the figures need further discretion, especially the use of punctuation and spaces, which the authors need to check further.

Author Response

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Reviewer 2 Report

I think the manuscript deals with an interesting and promising topic. Also, it is clear that the authors have done a wealth of experiments to demonstrate that the proposed algorithm effectively eliminated the phase deviation caused by motion. However, I think there are a few things that need to be addressed in this paper:

1. I think the authors' citation format is not appropriate: For example, it is Eq or Figure should be specified and should not be a separate number. This may be caused by the improper use of latex, but I think this issue is very important.

2. Some parts of the writing could be improved. e.g. the first paragraph on page 9, “X and Y are the length and width of reconstruction result.” This sentence suffers from a lack of clarity. For 3D reconstruction, how the length and width of the results were obtained for irregular targets?

3. In Section 3.3 Iteration process, the corresponding text of Equation 11 is not very clear and the relationship between variables s’ and s_n’ needs to be further explained.

4. In Experiment 1 of Section 4 , the authors introduce the MSE calculation at the beginning and then compare the calculation time of the two methods. Of course, the authors made an additional explanation that the MSE of these two methods was controlled within 1°. But this result, I think, should be reflected in the Table 1, as the main supporting result of Experiment 1.

5. I do not agree with the layout of the authors' experimental section. Obviously the authors have considered many dimensions in designing the experimental validation, the computational cost, the simulation of the limiting case, and the 3D reconstruction of static and dynamic scenarios, and theexperiments at different motion step lengths. However, the relationship between the layers of the experiments needs further consideration. For example, in Experiment 4, the reconstruction results at different motion steps should be given first, and in order to further measure this result a comparison of the calculation of APDs values. 

Author Response

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Reviewer 3 Report

Authors proposed a speed up method for motion artifacts removal in fringe pattern profilometry. I have several remarks.

1. Authors considered several velocities, hwoever did not consider the cane where within a set of fringe pattern velocity changes (e.g., first two images are taken with X velocity and next ones are taken with 1.2X). How this type of scenatio would affect the outcomes of the proposed method?
2. Figure 6 is not informative as the images look the same.
3. Please provide evident shape error evaluation (in mm).
4. Why only method reported in [16] has been selected as reference technique? How about including other methods, e.g., Hilbert transform based technique, to make the analysis more valuable and impactful?

Author Response

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Round 2

Reviewer 3 Report

I recommend publication