Transport of relational structures in groups of diffeomorphisms

Laurent Younes, Anqi Qiu, Raimond Winslow, Michael I. Miller

Research output: Contribution to journalArticle

Abstract

This paper focuses on the issue of translating the relative variation of one shape with respect to another in a template centered representation. The context is the theory of Diffeomorphic Pattern Matching which provides a representation of the space of shapes of objects, including images and point sets, as an infinite dimensional Riemannian manifold which is acted upon by groups of diffeomorphisms. We discuss two main options for achieving our goal; the first one is the parallel translation, based on the Riemannian metric; the second one, based on the group action, is the coadjoint transport. These methods are illustrated with 3D experiments.

Original languageEnglish (US)
Pages (from-to)41-56
Number of pages16
JournalJournal of Mathematical Imaging and Vision
Volume32
Issue number1
DOIs
StatePublished - Sep 2008

Fingerprint

Group of Diffeomorphisms
Pattern matching
translating
Pattern Matching
Riemannian Metric
Group Action
Point Sets
Riemannian Manifold
Template
templates
Experiments
Experiment
Object
Context

Keywords

  • Deformable templates
  • Groups of diffeomorphisms
  • Image registration
  • Jacobi fields
  • Shape analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Artificial Intelligence
  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Transport of relational structures in groups of diffeomorphisms. / Younes, Laurent; Qiu, Anqi; Winslow, Raimond; Miller, Michael I.

In: Journal of Mathematical Imaging and Vision, Vol. 32, No. 1, 09.2008, p. 41-56.

Research output: Contribution to journalArticle

Younes, Laurent ; Qiu, Anqi ; Winslow, Raimond ; Miller, Michael I. / Transport of relational structures in groups of diffeomorphisms. In: Journal of Mathematical Imaging and Vision. 2008 ; Vol. 32, No. 1. pp. 41-56.
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