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.
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Joshi, S.H., Klassen, E., Srivastava, A., Jermyn, I. (2007). Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves. In: Yuille, A.L., Zhu, SC., Cremers, D., Wang, Y. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2007. Lecture Notes in Computer Science, vol 4679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74198-5_30
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DOI: https://doi.org/10.1007/978-3-540-74198-5_30
Publisher Name: Springer, Berlin, Heidelberg
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