ML Anthology

A Novel Representation for Riemannian Analysis of Elastic Curves in Rn

Shantanu H. Joshi, Eric Klassen, Anuj Srivastava, Ian Jermyn
CVPR 2007
doi:10.1109/CVPR.2007.383185 /cvpr/2007/joshi2007cvpr-novel/

Abstract

We propose a novel representation of continuous, closed curves in ℝ(n) that is quite efficient for analyzing their shapes. We combine the strengths of two important ideas - elastic shape metric and path-straightening methods -in shape analysis and present a fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesics between curves. Efficiency results from the fact that the elastic metric becomes the simple (2) metric in the proposed representation. We present step-by-step algorithms for computing geodesics in this framework, and demonstrate them with 2-D as well as 3-D examples.

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Text

Joshi et al. "A Novel Representation for Riemannian Analysis of Elastic Curves in Rn." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007. doi:10.1109/CVPR.2007.383185

Markdown

[Joshi et al. "A Novel Representation for Riemannian Analysis of Elastic Curves in Rn." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007.](https://mlanthology.org/cvpr/2007/joshi2007cvpr-novel/) doi:10.1109/CVPR.2007.383185

BibTeX

@inproceedings{joshi2007cvpr-novel,
  title     = {{A Novel Representation for Riemannian Analysis of Elastic Curves in Rn}},
  author    = {Joshi, Shantanu H. and Klassen, Eric and Srivastava, Anuj and Jermyn, Ian},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2007},
  doi       = {10.1109/CVPR.2007.383185},
  url       = {https://mlanthology.org/cvpr/2007/joshi2007cvpr-novel/}
}