Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Jacobi fields in groups of diffeomorphisms and applications

Author: Laurent Younes
Journal: Quart. Appl. Math. 65 (2007), 113-134
MSC (2000): Primary 58E50; Secondary 53C22
DOI: https://doi.org/10.1090/S0033-569X-07-01027-5
Published electronically: February 15, 2007
MathSciNet review: 2313151
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper presents a series of applications of the Jacobi evolution equations along geodesics in groups of diffeomorphisms. We describe, in particular, how they can be used to perform implementable gradient descent algorithms for image matching, in several situations, and illustrate this with 2D and 3D experiments. We also discuss parallel translation in the group, and its projection on shape manifolds, and focus in particular on an implementation of these equations using iterated Jacobi fields.

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Additional Information

Laurent Younes
Affiliation: Department of Applied Mathematics and Statistics and Center for Imaging Science, Johns Hopkins University, 3400 N. Charles St., Baltimore MD 21218
Email: laurent.younes@jhu.edu

DOI: https://doi.org/10.1090/S0033-569X-07-01027-5
Keywords: Groups of diffeomorphisms, Jacobi fields, image registration, shape analysis, deformable templates
Received by editor(s): March 20, 2006
Published electronically: February 15, 2007
Additional Notes: This work is partially supported by NSF DMS-0456253
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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