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JACOBI FIELDS IN GROUPS OF DIFFEOMORPHISMS AND APPLICATIONS

LAURENT YOUNES
Quarterly of Applied Mathematics
Vol. 65, No. 1 (March 2007), pp. 113-134
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43638762
Page Count: 22
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JACOBI FIELDS IN GROUPS OF DIFFEOMORPHISMS AND APPLICATIONS
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Abstract

This paper presents a series of applications of the Jacobi evolution equations along geodesies 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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