Matching deformable objects
Mise en correspondance d’objets déformables
OPEN ACCESS
Moving away from constrained parametric to unconstrained flexible non parametric models is a deep trend in image processing that constant increase of computing resources makes each day more possible. Besides linear structure, more complex and often more natural geometrical structure graphs, trees, groups or manifolds come onto the stage. Deformable models offer a good illustration: from rigid parametric transformation to non parametric diffeomorphic matching, we show how the matching problem can be seen as search of optimal deformation paths between two objects, or equivalently determination of a minimal geodesic in a shape manifold.
Résumé
Nous présentons dans ce papier une illustration d'une tendance forte du traitement d'image actuel, qui, comptetenu des puissances de calculs disponibles, tend d'une part à privilégier les approches non-paramétriques sur les approches paramétriques, pour proposer des modèles moins contraints, plus souples, plus expressifs et, d'autre part, s'éloignant des descriptions linéarisées, essaie de replacer les objets d'études dans leurs structures géométriques naturelles. Dans le contexte des modèles déformables, cette tendance a amené à s'affranchir progressivement de l'estimation de déformations rigides paramétriques pour aller vers celle d'appariements dense quelconques sous la forme de champs de déplacements et plus encore vers celle de l'objet naturel qui est un difféomorphisme. Nous montrons comment la géométrisation du problème de l'appariement comme recherche d'un chemin optimal de déformation d'un objet source vers un objet but, permet de lier le problème de l'estimation d'un appariement à celui d'une géodésique dans un espace de formes.
Matching, deformations, diffeomorphismes, Riemannian geometry
Mots clés
Mise en correspondance, déformations, difféomorphismes, géométrie riemannienne
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