Energy Minimization Methods in Computer Vision and Pattern Recognition

Volume 4679 of the series Lecture Notes in Computer Science pp 387-398

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

  • Shantanu H. JoshiAffiliated withDept. of Electrical Engineering, Florida State University, Tallahassee, FL 32310
  • , Eric KlassenAffiliated withDept. of Mathematics, Florida State University, Tallahassee, FL 32306
  • , Anuj SrivastavaAffiliated withDept. of Statistics, Florida State University, Tallahassee, FL 32306
  • , Ian JermynAffiliated withINRIA Sophia Antipolis, B.P. 93, 06902, Cedex

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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.