-
The Square Root Velocity Framework for Curves in a Homogeneous Space
AbstractIn this paper we study the shape space of curves with values in a homogeneous space M = G/K, where G is a Lie group and K is a compact Lie subgroup. We generalize the square root velocity framework to obtain a reparametrization invariant metric on the space of curves in M. By identifying curves in M with their horizontal lifts in G, geodesics then can be computed. We can also mod out by reparametrizations and by rigid motions of M. In each of these quotient spaces, we can compute Karcher means, geodesics, and perform principal component analysis. We present numerical examples including the analysis of a set of hurricane paths.
Related Material
[pdf] [arXiv][bibtex]@InProceedings{Su_2017_CVPR_Workshops,
author = {Su, Zhe and Klassen, Eric and Bauer, Martin},
title = {The Square Root Velocity Framework for Curves in a Homogeneous Space},
booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
month = {July},
year = {2017}
}
These CVPR 2017 workshop papers are the Open Access versions, provided by the Computer Vision Foundation.
Except for the watermark, they are identical to the accepted versions; the final published version of the proceedings is available on IEEE Xplore.
Except for the watermark, they are identical to the accepted versions; the final published version of the proceedings is available on IEEE Xplore.
This material is presented to ensure timely dissemination of scholarly and technical work.
Copyright and all rights therein are retained by authors or by other copyright holders.
All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright.