Terminology: Introduction l. 24-26 "pixels near the peripheral of the object of interest can generally be challenging, but not relevant to topology." I think this statement is problematic. When considering the inverse e.g. in the case of a surface or vessel, that a foreground pixel changes to background. Such a scenario would immediately lead to a topology mismatch (Betti error 1).
Terminology: "topologically critical location" --> I find this terminology to be not optimally chosen. I agree that the warping concept appears to help with identifying pixels which may close loops or fill holes. However, considering the warping I do not see a guarantee that such "locations" (as in the exact location) which I understand to refer to individual or groups of pixels are indeed part of the real foreground, nor are these locations unique. A slightly varying warping may propose a set of different pixels.
The identified locations are more likely to be relevant to topological errors. --> this statement should be statistically supported. Compared to what exactly? Does this rely on the point estimate for any pixel? Or given a particularly trained network?
Theorem 1: The presentation of a well known definition from Kong et al. is trivial and could be presented in a different way.
Experimentation, lack of implementation details: In Table 2 and a dedicated section, the authors show an ablation study on the influence of lamda on the results. Lamda is a linear parameter, weighting the contribution of the new loss to the overall loss. Similarly, the studied baseline methods, e.g. TopoNet [24], DMT [25], and clDice [42] have a loss weighting parameter. It would be important to understand how and if the parameters of the baselines were chosen and experimented with. (I understand that the authors cannot train ablation studies for all baselines etc.) However, it is an important information to understand the results in Table 1.
Terminology: l. 34 "to force the neural network to memorize them" --> I would tone down this statement, in my understanding, the neural network does not memorize an exact "critical point" as such in TopoNet [24]. Minor:
I find the method section to be a bit wordy, it could be compressed on the essential definitions.
There exist several grammatical errors, please double-check these with a focus on plurals and articles. E.g. l. 271 "This lemma is naturally generalized to 3D case."
l. 52 "language of topology" I find this to be an imprecise definition or formulation. Note:
After rebuttal and discussion I increased the rating to 5.
34 "to force the neural network to memorize them" --> I would tone down this statement, in my understanding, the neural network does not memorize an exact "critical point" as such in TopoNet [24]. Minor: I find the method section to be a bit wordy, it could be compressed on the essential definitions. There exist several grammatical errors, please double-check these with a focus on plurals and articles. E.g. l.