Review November 2022

Text review of 2022-11-24 after paper rejection by SIAM commitee.

Line 228: x is a point of C(0) and not C(1)

Sell the point that our model is flexible. We should show that we are capable to model a elastica energy with any type of energy. We are flexible. It would be nice to show another exanmples, and not obly graph cut and chan cese and not to compare with CNN or other things.

To show the difference flows that we have given the radius. We can show how the models stops after some iterations with certain raidus.

Higher the radius, higher the precision.

Think about a figure like 6.2 with mor einitializations to show that our model converges to the global optimum. Maybe a table. Remplacer la graphe in the bottom right by some analytic measure such as the haussdorf distance from the optimal shape.

We can put the Neighborhood of Shapes (figure 6.1) in the experimental section. It is not nice to show that as the first result.

Time complexity relations with the optimization band (higher n, higher the chances of find a better solution).

Pour le k max, on ne se interesse pas pour les courbures trop grandes.

Pour la figure 3.1, utiliser des figures discrets, avec pixels, where we see the differences between the columns. It will be maybe nice to also put real values. Then we can see an evolution and we reenforce that we work with discrete data.

Reviewer 2:

Expliquer meilleur dou vient les capacites du graph flow. Essayer de expliquer pourquoi on faire ça, peut etre en disant que on utilise des modeles classiques ; expliquer l'origine bayesienne du modeles, peut etre en ajoutant des references.

Commencer avec Chan-Vese because we have a mathematical formulation that is well known which the translation to a discrete equation is straightforward. I thinkg it will be easier to argue starting with chan vese. easier to convince

We need some figures to explain how graph-cut works. Maybe saying that our capacity functions translates the problem into finding a subset of edges that solve the problem.

The reviewer suggests a reference that we need to use.

Point 6: The reviewer did not understand graph-cut. By choosing the right edge weights we can find the perimeter (Boykov)