Piecewise rigid curve deformation via a Finsler steepest descent

Guillaume Charpiat 1, 2 Giacomo Nardi 3 Gabriel Peyré 4, 3 François-Xavier Vialard 3, 4
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
2 STARS - Spatio-Temporal Activity Recognition Systems
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima. We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves.
Type de document :
Article dans une revue
Interfaces and Free Boundaries, European Mathematical Society, 2015
Liste complète des métadonnées

Littérature citée [49 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00849885
Contributeur : Gabriel Peyré <>
Soumis le : vendredi 26 décembre 2014 - 16:32:35
Dernière modification le : vendredi 17 février 2017 - 16:10:25
Document(s) archivé(s) le : samedi 15 avril 2017 - 11:48:19

Fichiers

PiecewiseRigidityGradient.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00849885, version 2
  • ARXIV : 1308.0224

Citation

Guillaume Charpiat, Giacomo Nardi, Gabriel Peyré, François-Xavier Vialard. Piecewise rigid curve deformation via a Finsler steepest descent. Interfaces and Free Boundaries, European Mathematical Society, 2015. 〈hal-00849885v2〉

Partager

Métriques

Consultations de
la notice

516

Téléchargements du document

197