A Riemannian Approach for Computing Geodesics in Elastic Shape Analysis

Authors

Yaqing You, Wen Huang, Kyle A. Gallivan, P.-A. Absil

Abstract

In the framework of elastic shape analysis, a shape is invariant to scaling, translation, rotation and reparameterization. Since this framework does not yield a closed form geodesic between two shapes, iterative methods are used. In particular, path straightening methods have been proposed and used for computing a geodesic that is invariant to curve scaling and translation. Path straightening can then be exploited within a coordinate-descent algorithm that computes the best rotation and reparameterization of the end point curves. In this paper, we propose a Riemannian quasi-Newton method to compute a geodesic invariant to scaling, translation, rotation and reparameterization and show that it is more efficient than the coordinate-descent/path-straightening approach.

Status

In Proceeding of the 3rd IEEE Global Conference on Signal & Information Processing

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BibTex entry

GlobalSIP
@inproceedings{YHGA2015,
author = "Yaqing You and Wen Huang and Kyle A. Gallivan and P.-A. Absil",
title = "A Riemannian Approach for Computing Geodesics in Elastic Shape Analysis",
booktitle = "Proceedings of the 3rd IEEE Global Conference on Signal & Information Processing",
year = 2015,
}