
Séminaire Image : « Mathematical foundations of a level-set-based shape convex hull identification algorithm », Carole Le Guyader
6 février / 14:15 - 15:15
Nous aurons le plaisir d’écouter Carole Le Guyader, Laboratoire LMI, INSA Rouen.
Elle donnera un séminaire IMAGE le jeudi 6 février 2025 à 14h15 en salle de séminaire F-200.
Titre : « Mathematical foundations of a level-set-based shape convex hull identification algorithm »
Résumé :
In this work, we introduce a proper mathematical framework to analyse a novel object convex hull extraction algorithm phrased in a level-set framework. The convex shape to be identified is modelled as the zero level-line of an unknown signed-distance function viewed as a minimiser of a suitably designed functional. This latter is stated in a subspace of the Special Bounded Hessian function space, whilst a non-negativity criterion satisfied by the absolutely continuous part of the Laplacian of the unknown on the whole domain expresses the convexity constraint.
A result of existence of minimisers is established for this preliminary problem. Then, to implement this optimisation problem, we provide a counterpart elliptic approximation, complemented by a Γ-convergence result and a splitting-strategy-based algorithm involving subproblems with closed-form solutions. Numerical experiments showing that the proposed approach is an appropriate compromise between mathematical thoroughness and algorithmic relevancy conclude the presentation.