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