Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves

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

Abstract

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves.

Citation

Joshi, S., Klassen, E., Srivastava, A., & Jermyn, I. (2007). Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves. In A. L. Yuille, S. C. Zhu, D. Cremers, & Y. T. Wang (Eds.), Energy minimization methods in computer vision and pattern recognition (387-398). https://doi.org/10.1007/978-3-540-74198-5_30

• Conference Name: 6th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
• Conference Location: Ezhou
• Publication Date: Aug 1, 2007
• Deposit Date: Aug 12, 2011
• Publicly Available Date: Apr 20, 2016
• Volume: 4679
• Pages: 387-398
• Series Title: Lecture notes in computer science
• Series Number: 4679
• Series ISSN: 0302-9743
• Book Title: Energy minimization methods in computer vision and pattern recognition.
• DOI: https://doi.org/10.1007/978-3-540-74198-5_30
• Public URL: https://durham-repository.worktribe.com/output/1158650