Gauge Invariant Framework for Shape Analysis of Surfaces

Tumpach, Alice Barbara; Drira, Hassen; Daoudi, Mohamed; Srivastava, Anuj

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1109/TPAMI.2015.2430319

URL permanente :

http://hdl.handle.net/20.500.12210/121553

Titre :

Gauge Invariant Framework for Shape Analysis of Surfaces

Auteur(s) :

Tumpach, Alice Barbara [Auteur]

Institut CNRS-PAULI [ICP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Drira, Hassen [Auteur]

Daoudi, Mohamed [Auteur]
Srivastava, Anuj [Auteur]

Titre de la revue :

IEEE Transactions on Pattern Analysis and Machine Intelligence

Pagination :

46-59

Éditeur :

Institute of Electrical and Electronics Engineers

Date de publication :

2016-01-01

ISSN :

0162-8828

Discipline(s) HAL :

Informatique [cs]

Résumé en anglais : [en]

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient ...
Lire la suite >This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energy that measures only the normal components of velocities along the path. In other words, this paper defines and solves for geodesics directly on the shape space and avoids complications resulting from the quotient operation. This comprehensive framework is invariant to arbitrary parameterizations of surfaces along paths, a phenomenon termed as gauge invariance. Additionally, this paper makes a link between different elastic metrics used in the computer science literature on one hand, and the mathematical literature on the other hand, and provides a geometrical interpretation of the terms involved. Examples using real and simulated 3D objects are provided to help illustrate the main ideas.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :