A Novel Representation for Riemannian Analysis of Elastic Curves in R^{n}

Joshi, S.; Klassen, E.; Srivastava, A.; Jermyn, I.H.

Abstract

We propose a novel representation of continuous, closed curves in Rn 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 geodesies in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesies between curves. Efficiency results from the fact that the elastic metric becomes the simple L2 metric in the proposed representation. We present step-by-step algorithms for computing geodesies in this framework, and demonstrate them with 2-D as well as 3-D examples.

Citation

Joshi, S., Klassen, E., Srivastava, A., & Jermyn, I. (2007). A Novel Representation for Riemannian Analysis of Elastic Curves in R^{n}. In 2007 IEEE Conference on Computer Vision and Pattern Recognition (1-7). https://doi.org/10.1109/cvpr.2007.383185

• Conference Name: 2007 IEEE Conference on Computer Vision and Pattern Recognition
• Conference Location: Minneapolis
• Publication Date: Jun 1, 2007
• Deposit Date: Aug 12, 2011
• Publicly Available Date: May 24, 2016
• Publisher: Institute of Electrical and Electronics Engineers
• Pages: 1-7
• Book Title: 2007 IEEE Conference on Computer Vision and Pattern Recognition
• DOI: https://doi.org/10.1109/cvpr.2007.383185