Date/heure
4 mars 2022
11:00 - 12:00
Oratrice ou orateur
Carole Le Guyader
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
Motivated by Tadmor’s work dedicated to multiscale image representation using hierarchical (BV,L^2) decompositions, we propose transposing their approach to the case of registration, task which consists in determining a smooth deformation aligning the salient constituents visible in an image into their counterpart in another. The underlying goal is to obtain a hierarchical decomposition of the deformation in the form of a composition of intermediate deformations: the coarser one, computed from versions of the two images capturing the essential features, encodes the main structural/geometrical deformation, while iterating the procedure and refining the versions of the two images yields more accurate deformations that map faithfully small-scale features. The proposed model falls within the framework of variational methods and hyperelasticity by viewing the shapes to be matched as Ogden materials. The material behaviour is described by means of a specifically tailored strain energy density function, complemented by L^∞ penalisations ensuring that the computed deformation is a bi-Lipschitz homeomorphism. Theoretical results emphasising the mathematical soundness of the model are provided, among which the existence of minimisers, a Γ-convergence result and an analysis of a suitable numerical algorithm, along with numerical simulations demonstrating the ability of the model to produce accurate hierarchical representations of deformations.