Karcher Mean in Elastic Shape Analysis

Wen Huang, Yaqing You, Kyle Gallivan and Pierre-Antoine 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 the previous work by showing that using the new approach to the geodesic when computing the Karcher mean yields a faster algorithm.

Session

Workshop: 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV)

Files

Paper (PDF, 487K)

DOI

10.5244/C.29.DIFFCV.2
https://dx.doi.org/10.5244/C.29.DIFFCV.2

Citation

Bibtex

@inproceedings{DIFFCV2015_2,
	title={Karcher Mean in Elastic Shape Analysis},
	author={Wen Huang and Yaqing You and Kyle Gallivan and Pierre-Antoine Absil},
	year={2015},
	month={September},
	pages={2.1-2.11},
	articleno={2},
	numpages={11},
	booktitle={Proceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV 2015)},
	publisher={BMVA Press},
	editor={H. Drira, S. Kurtek, and P. Turaga},
	doi={10.5244/C.29.DIFFCV.2},
	isbn={1-901725-56-1},
	url={https://dx.doi.org/10.5244/C.29.DIFFCV.2}
}