Karcher Mean in Elastic Shape Analysis
Authors
Wen Huang, Yaqing You, 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 of geodesic between two shapes, iterative methods have been proposed. 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. A Riemannian quasi-Newton method to compute a geodesic invariant to scaling, translation, rotation and reparameterization has been given and shown to be more efficient than the coordinate-descent/path-straightening approach. This paper extends previous results by showing that using the new approach to the geodesic when computing the Karcher mean yields a faster algorithm.
Status
In Proceeding of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV 2015)
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BibTex entry
- BMVA
@inproceedings{HYGA2015,
author = "Wen Huang and Yaqing You and Kyle A. Gallivan and P.-A. Absil",
title = "Karcher Mean in Elastic Shape Analysis",
booktitle = "Proceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV 2015)",
pages = "pp 2.1 - 2.11",
year = 2015,
}