A Robust Skeletonization Method for High-Density Fringe Patterns in Holographic Interferometry Based on Parametric Modeling and Strip Integration
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsReview of the manuscript entitled ‘A Robust Skeletonization Method for High-Density Fringe Patterns in Holographic Interferometry Based on Parametric Modeling and Strip Integration’
Fringe identification in holography is a general technique and for patterns with moderate noise, edge detection algorithms different techniques can be used. However, for high-density patterns corrupted by strong speckle noise, the problem is more difficult. Authors proposes a genuinely original skeletonization strategy, combining physics-informed parametric modeling with a strip-integration functional.
The method is well motivated physically and the study is very interesting and can help a lot of people studying holography. The treatment of speckle noise is presented as an unavoidable, signal-dependent phenomenon rather than something to be filtered away.
The manuscript is very thorough technically: interpolation, quadrature, rasterization, and optimization are all described in depth.
Validation on both synthetic data with controlled noise and a real interferogram with > 100 fringes is convincing.
The approach clearly goes beyond classical edge detection or snake-based methods. The results would be significant for researchers who deals with fringe analysis.
The paper is very long and dense. Some sections are over-detailed at the algorithmic level, while other aspects (comparison to modern alternatives, limitations, generalization) are not enough discussed. The novelty is real, but it is not always highlighted clearly enough, especially relative to existing variational/active contour/phase-based approaches.
Here are some comments in order to improve the quality of the manuscript:
- Explicitly contrast your method with: phase-shifting / phase-unwrapping based approaches, Ridge detection + orientation field methods, Recent learning-based or hybrid approaches (even if only to justify why you do not use them)
- Clarify what problem your method solves that others fundamentally cannot: Is it topology preservation? Noise robustness at extreme fringe density? Sub-pixel accuracy without phase extraction?
There are points to address:
- What happens if the true fringe family deviates moderately from the assumed topology?
- How sensitive is the method to: incorrect center estimation?
- Is there a risk of model bias producing visually good but physically wrong fringes?
It could be suggested to add even a limited comparison with: a standard snake implementation, a ridge/edge-based skeletonization, or at least report why such comparisons are omitted (e.g. failure to converge at high noise)
- The synthetic interferogram generator is excellent, but the relationship between the simplified stochastic model and real speckle statistics could be clearer. Could authors briefly discuss whether the algorithm’s success depends on the exact noise statistics?
Consider: scale bars on images. Add additional informations in the figure captions for example for the figure 5: ‘Geometric correction example’ could be detailed.
- Consider the case of people who analyze patterns as winkle patterns, photoinduced patterns observed with atomic force microscopy.
Author Response
We sincerely thank all three reviewers for their thorough and constructive feedback on our manuscript.
The comments have helped us significantly improve the clarity, rigor, and presentation of our work.
Below (in pdf file) we provide a consolidated point-by-point response addressing all raised issues.
Where similar points were made by multiple reviewers, we provide a unified response with cross-references.
All changes in the revised manuscript are highlighted in red color for easy reference.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper presents a robust method for skeletonizing fringe patterns in holographic interferometry, particularly for high-density fringe patterns under heavy speckle noise. This allows reliable full-field deformation measurement in challenging real laboratory conditions. The paper is well-structured, including theoretical analysis, numerical implementation, and validationof the effectiveness of real interference fringes. It is written clearly, with fluent language and accurate scientific terminology. In addition, the limitations and applicable conditions of the methods discussed in the conclusion section are also included.
Suggest the author to further briefly analyze the fringe density limit at which the proposed method can be accurately applied under certain speckle noise level.
The relationship between the algorithm steps in the upper-right of Figure 6 and the other components is not clearly conveyed and could be further improved.
Author Response
We sincerely thank all three reviewers for their thorough and constructive feedback on our manuscript.
The comments have helped us significantly improve the clarity, rigor, and presentation of our work.
Below (in pdf file) we provide a consolidated point-by-point response addressing all raised issues.
Where similar points were made by multiple reviewers, we provide a unified response with cross-references.
All changes in the revised manuscript are highlighted in red color for easy reference.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors
- In the synthetic experiments, the manuscript uses noise levels of 10%/50%/80%/95% to demonstrate the superiority of strip integration under severe noise. However, the current text does not provide a computable definition that maps these percentage noise levels to the parameters of the adopted noise model. As a result, readers cannot reproduce the experiments, nor can they interpret what “95%” means in physical terms, e.g., the corresponding speckle contrast, correlation length, or an equivalent SNR.
- The applicability boundaries and failure modes of the proposed framework should be stated more explicitly. The core strategy is to constrain the fringe family to a physically motivated finite-dimensional parameter subspace, and it explicitly assumes that, for (near) axisymmetric plate/membrane bending, the fringes are closed, nested, quasi-concentric curves, which motivates the use of perturbed-circle or perturbed-ellipse parameterizations. The conclusion also acknowledges that the method relies on selecting an appropriate parametric model in advance and that performance may degrade for fringe patterns with bifurcations, interruptions, or multiple disconnected fringe families. It is therefore recommended to add a concise statement (in the abstract or at the beginning of the method section) specifying the fringe topologies where the method is most effective and those where it is not applicable, and to include at least one representative boundary/failure case, together with an explanation of why it fails and what kind of modifications would be required to address it.
- The completeness and fairness of baseline comparisons should be strengthened; otherwise, the claim of being “significantly better than baselines” is not sufficiently supported. The manuscript should clearly specify which baseline methods are included, along with their parameter settings and initialization strategies. In addition, all compared methods should share the same preprocessing pipeline (in particular, local intensity equalization, geometric correction, and the optional Fourier-domain filtering), so that the observed performance gain cannot be attributed primarily to preprocessing choices or implementation details, but can be more convincingly attributed to the strip-integration objective and the parametric-constraint framework itself.
- The rationale for selecting key parameters and the corresponding sensitivity evidence should be completed to form a transferable default configuration. The strip-integration functional introduces the strip half-width ω and the Gaussian scale σ, and argues that regional averaging improves robustness against speckle noise. However, the manuscript currently lacks a systematic analysis of how ω and σ affect localization bias, error statistics, and convergence behavior.
- The manuscript should more transparently report the convergence reliability of the optimization and recursive strategy, together with risk-control mechanisms. Constructing a smooth intensity field via bicubic interpolation to enable gradient-based optimization is a reasonable and important engineering choice; however, readers still need the concrete optimization details, including the optimizer used, step-size/line-search strategy, stopping criteria, and fallback mechanisms when the optimization fails or becomes trapped in poor local minima.
- The validation on real data should be broadened and made more quantitative by including additional real interferograms. While the current real-data demonstration is valuable, adding multiple real datasets (under different loading conditions and imaging/noise conditions) and reporting quantitative error statistics would provide stronger evidence of robustness and generalizability, beyond a single representative case.
Author Response
We sincerely thank all three reviewers for their thorough and constructive feedback on our manuscript.
The comments have helped us significantly improve the clarity, rigor, and presentation of our work.
Below (in pdf file) we provide a consolidated point-by-point response addressing all raised issues.
Where similar points were made by multiple reviewers, we provide a unified response with cross-references.
All changes in the revised manuscript are highlighted in red color for easy reference.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript can now be accepted. All the reviewer's comments have been considered.
Author Response
We are grateful for the opportunity to improve our work and hope that the manuscript is now suitable for publication.
Reviewer 3 Report
Comments and Suggestions for Authors- Although the revised manuscript better explains the meaning of the percentage noise level (via α), it would be stronger to add a small “nominal α vs measured statistics” table/plot (e.g., speckle contrast, correlation length, equivalent SNR), and to clarify whether the linearization assumption remains valid at extreme values such as α = 0.95 or should be explicitly bounded in scope.
- Please describe the calibration procedure that maps Eq.(9)’s parameter k to an “equivalent” α in a reproducible way (which statistic is matched, and how the mapping is searched/fitted). Without this, the alignment between the two noise models is still not reproducible.
- For spatially correlated speckle, consider adding a brief consistency check between the theoretical correlation function and the “Gaussian-kernel convolution” generation method (e.g., an autocorrelation curve comparison or the conditions under which they are approximately equivalent), to avoid the impression that theory and implementation are mismatched.
- The baseline discussion is improved, but adding 1-2 stronger, more relevant baselines for fringe centerline/ridge extraction (under the same preprocessing and evaluation protocol) would make the “better-than-baseline” claim more review-robust.
- The manuscript reports “>98% convergence”. Please provide the sample size, the covered ranges of noise level/fringe density, the success criterion, and one representative failure-case figure. This would make the reliability claim auditable and easier to reproduce.
Author Response
We believe that the revised manuscript, with the clarifications and additional explanations provided in pdf file, now addresses all concerns raised by the reviewers. We are grateful for the opportunity to improve our work and hope that the manuscript is now suitable for publication.
Author Response File: Author Response.pdf
Round 3
Reviewer 3 Report
Comments and Suggestions for AuthorsThe proposed issues have been revised, and the manuscript is recommended for acceptance
