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Summary of the research’s main findings and contribution

The manuscript proposes a locally adaptive modification of the Chan–Vese model intended to improve segmentation under intensity inhomogeneity and weak boundaries. The proposed method combines global region fitting with local Gaussian-window-based intensity information and reports substantially better performance than the traditional Chan–Vese model and a purely local comparison method. On the reported simulated liver image, the method achieves perfect Dice and specificity values of 1.000.

However, the claimed contribution is not convincingly established. Combining global and local information is already a well-developed direction in the level-set segmentation literature, and the manuscript does not provide sufficient evidence that its particular formulation represents a substantial methodological advance. More importantly, the empirical evaluation is far too limited to support the strong claims of accuracy, robustness, and superiority.

Major issues

• The experimental evaluation is fundamentally inadequate for the strength of the conclusions. The method appears to be evaluated on a single simulated image. A single synthetic example cannot establish robustness, generalizability, or superiority over existing segmentation approaches.

• The perfect results are not convincing without substantially stronger validation. Reporting Dice = 1.000 and specificity = 1.000 on one synthetic image is not sufficient evidence of algorithmic excellence. Such results may reflect favorable initialization, parameter tuning, a simple test case, or evaluation bias. The manuscript does not demonstrate that comparable performance persists across independent images or perturbations.

• The novelty of the method is insufficiently demonstrated. The central idea of combining global region information with local intensity fitting is not obviously new. The manuscript needs a precise mathematical comparison with existing local fitting, region-scalable, and hybrid global–local Chan–Vese-type models. At present, it is difficult to determine whether the work introduces a genuinely new model or mainly a relatively minor reformulation of existing approaches.

• The comparison strategy is too weak. Comparing the proposed method primarily against the classical Chan–Vese model and a single local model creates a weak benchmark. The classical C–V model is known to struggle with intensity inhomogeneity, so outperforming it does not by itself demonstrate a meaningful advance. The method should be compared with stronger and more recent models designed specifically for the same problem.

• The fairness of the comparison is unclear. The manuscript should specify whether all methods were optimized to a comparable degree. Without transparent reporting of initialization, parameter selection, stopping criteria, numerical implementation, and iteration limits, the reported superiority cannot be independently assessed.

• The robustness claim is unsupported. Robustness requires systematic testing under different noise levels, bias fields, contrast conditions, object geometries, and initial contours. A single successful segmentation does not justify describing the method as robust.

• Parameter dependence is not adequately addressed. The proposed method introduces local Gaussian information and additional model parameters. If performance depends strongly on these choices, the method may be difficult to use in practice. A sensitivity analysis is essential but appears to be missing.

• There is no convincing evidence of practical relevance to medical imaging. A simulated liver image is not equivalent to clinical data. Real medical images contain noise, artifacts, anatomical variability, acquisition-dependent intensity variation, partial-volume effects, and potentially ambiguous boundaries. The manuscript therefore overstates the medical significance of its results.

• The claim of “significantly higher” performance is inappropriate without statistical evidence. If only one image or one experimental run is used, statistical significance cannot be established. The wording should be removed or replaced unless repeated experiments and appropriate statistical tests are provided.

• The computational analysis is incomplete from a practical perspective. Theoretical complexity analysis is not enough. The manuscript should provide actual runtime measurements and compare computational cost against competing methods. An improved segmentation score may be less meaningful if obtained at a substantially higher computational cost.

Minor issues

• The mathematical novelty of the energy functional should be explained more clearly and distinguished explicitly from existing local and hybrid fitting energies.

• The definition of the Gaussian local window and its normalization should be fully specified.

• Boundary handling in the local neighborhood computation should be described.

• All parameter values should be reported in a dedicated table.

• The parameter-selection procedure should be explained. It should be clear whether parameters were tuned using the evaluation image.

• The initialization of the level-set function requires precise description, since segmentation results can depend strongly on initialization.

• The numerical approximations of the Heaviside and Dirac delta functions should be specified.

• The stopping criterion and convergence criterion should be reported.

• Metric values should not be presented only as ideal single numbers. Repeated experiments should include variability measures.

• The manuscript would benefit from failure cases. Showing only a successful example gives an incomplete picture of the method's limitations.

• The language throughout should be more cautious. Terms such as “significantly higher accuracy,” “good robustness,” and strong claims of effectiveness are currently not supported by the scale of the experiments.

Overall assessment: Major Revision. In its current form, the manuscript does not provide sufficient theoretical novelty or experimental evidence to justify its stronger claims. The main issue is not necessarily that the proposed model is incorrect, but that the paper does not demonstrate convincingly that the model is meaningfully new, robust, generalizable, or superior to existing methods.

Competing interests

The authors declare that they have no competing interests.

Use of Artificial Intelligence (AI)

The authors declare that they used generative AI to come up with new ideas for their review.