LE BRIGANT, Alice

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

LE BRIGANT, Alice
Institut de Mathématiques de Bordeaux [IMB]
Thales Research and Technology [Palaiseau]

Langue

Article de revue

Ce document a été publié dans

Journal of Mathematical Imaging and Vision. 2019, vol. 61, n° 1, p. 40–70

Springer Verlag

Date de soutenance

2019

Résumé en anglais

The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an optimal matching between two curves by computing the geodesic of the infinite-dimensional manifold of curves that is at all time horizontal to the fibers of the shape bundle. We focus on the elastic metric studied in the so-called square root velocity framework. The quotient structure of the shape bundle is examined, and in particular horizontality with respect to the fibers. These results are more generally given for any elastic metric. We then introduce a comprehensive discrete framework which correctly approximates the smooth setting when the base manifold has constant sectional curvature. It is itself a Riemannian structure on the product manifold of "discrete curves" given by a finite number of points, and we show its convergence to the continuous model as the size of the discretization goes to infinity. Illustrations of optimal matching between discrete curves are given in the hyperbolic plane, the plane and the sphere, for synthetic and real data, and comparison with dynamic programming is established.< Réduire

Métadonnées

Partager cette publication !

Licence d’utilisation du document

A discrete framework to find the optimal matching between manifold-valued curves

Langue

Ce document a été publié dans

Date de soutenance

Résumé en anglais

URI

Origine

Unités de recherche