Multifractal Detrended Fluctuation Analysis Combined with Allen–Cahn Equation for Image Segmentation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• The abstract is unclear and too brief. It should be expanded to highlight the key findings and provide a concise summary of the study.

• The introduction is overly long and could be made more concise. Nevertheless, it offers a comprehensive review of previous literature, effectively identifying the research gap and problem statement.

• "Currently, there are relatively few studies combining the MF-DFA method with the
  AC equation for power transmission tower image segmentation." Please provide the reference.

• Why Allen–Cahn Equation? Please provide the comparison with the other relevant equation.

• The final paragraph of the introduction should be removed.

• The use of the pronoun “we” should be avoided throughout the article.

• Each term in Equation 1 should be clearly explained.

• The methodology contains excessive detail and should be rewritten in a simpler and more accessible manner.

• How did the author develop the MF-AC-DFA methodology based on MF-DFA? Please also provide the reference for MF-DFA.

• The methodology and results/discussion sections are currently mixed; they need to be clearly separated.

• In the discussion section, the analysis should be more directly linked to the study’s objectives. The discussion should be made more coherent and focused.

• The conclusion should be revised to directly address the study’s objectives.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presented a new method, which combines both MF-DFA and Allen-Cahn equations in determining segmentation from images. This paper was organized well, and the method is interesting. However, several issues should be improved in the revised versions:

- The most important question is that the paper should include a method to evaluate the quality of the errors from methods in determining the segmentation for the geometric image as well as others. It means that for the geometric image, the positions of the segmentation are clear, and there should be a parameter to evaluate the accuracy of the method in determining the segmentation, not just shown by the segmented image. Parameters affecting to the results, such as background color (not just yellow color), and the resolutions of the image should be evaluated. How does changing the size and curve of the geometric model affect the result of the segmented image? Additionally, comparison with traditional methods, such as the gradient method in determining the segmented line should be included.

- Why were only electric wire segmentation experiments conducted? I recommend the authors to include more image cases to confirm the advantage of the method in determining the segmented lines.

- The introduction should be shortened and focus on the objective of the study.

- In section 2, the definition of all parameters in equations, such as u, t, and others should be included.

- The conclusion should add more detail about the novelty, significance, contribution of the paper, as well as limitations and quantitative uncertainty of the method.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is well-written and the subject matter is very interesting. In my opinion, the manuscript could be published, but there are a few issues that have to be addressed prior to publication.

 

**Major issues**

Perhaps, the main question to the methodology here would be the following: what if the background behind the wires in Fig. 7 and Fig. 8 is not so homogeneous and smooth? What would be the efficiency of the image segmentation of the proposed algorithm?

The similar, but more important question is about results in Fig. 9 and Fig. 10. The background of the wires (from Fig. 7 and 8) could actually be smooth - the user can control it. But you can not predict the state of the background behind the real transmission towers. It could be haze, fog, rain, snow, strong clouds behind. What would be the efficiency of the algorithm in those cases?
The impact of the different weather conditions, light scattering, atmospheric turbulence on the light propagation and image degradation is of great importance and could be found in literature (i.e., https://doi.org/10.1103/PhysRevLett.104.100601, https://doi.org/10.3390/photonics9050296, https://doi.org/10.1364/OE.23.012189). 

it is also interesting for me, does the image capture from UAV made from below the wires in order to have the more or less homogeneous background? 
And what if this image capture angle would be impractical in some cases? Is it possible to make the photo from above the wires? In this case the background would be strongly inhomogeneous and again - what would be the efficiency of the image segmentation algorithm.

In the lines 317-321 the authors state that "we predict the possible aging and corrosion problems of the transmission tower and develop a maintenance plan accordingly". It is not clear, how were all those predictions made from the segmented images provided? The single wire is reconstructed as a thin line, how should the operator find the corrosion or aging here? Please, explain this point more clearly.

**Minor issues**
- Line 54 - the space after the end of the sentence is missed, please correct.
- Line 87-88 - "outperforms the other methods in performance" - I would suggest to reorganize the sentence in order to get rid of duplicate words
- Line 270 - please, replace "Figure 4b - e" with "Figure 4b-4e"
- While describing the eq. 1 the authors say that u represents the state variable of the system. The label on the Y axis of the Fig. 1 is "Concentration u". What is concentration here? Please, explain it more clearly.
- I would suggest to make the color of the u0 curve the same for both Fig. 1 and Fig. 2 (either violet or blue, but same) for clarity reasons.
- Please, provide the explanation of parameters used in eq. 2 right after the eq. 2.
  The same is for eq. 3.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors,

Thank you for your interesting and important research in the field of increasing the accuracy and reliability of transmission tower image segmentation. In general, I agree with your presentation and evidence base. I will have just a couple of additional questions, which I hope will help your future Readers to understand the research in more detail:

1. Introduction. In the Review, you quite often refer to certain publications and say, for example, "friction dampers were particularly effective and robust in minimizing wind-induced vibrations in transmission towers" or "The study explored in detail the structural response, ultimate load-carrying capacity, and failure modes of the transmission tower by implementing full-scale tests". Can you clarify these statements about the advantages using specific parametric indicators or their range, so that Readers can understand what quantities are being discussed?

2. Section 2.2. Why is the image built from 16 * 16 pixels? What are the conditions for pixel breakdown initially? What is the source of these requirements?

I wish you success in all your future research!

Reviewer

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has been substantially improved and is now ready for acceptance.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper was revised accordingly my comments and it can be considered to publish.

Reviewer 3 Report

Comments and Suggestions for Authors

I thank the authors for very carefully addressing all the issues and conducting the additional experiments. In my opinion, the manuscript is ready to be published.