Shape Analysis of Elastic Curves in Euclidean Spaces

—This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in Euclidean spaces under an elastic metric. Due to this SRV representation the elastic metric simplifies to the L2 metric, the re-parameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is quotient space of (a submanifold of) the unit sphere, modulo rotation and re-parameterization groups, and we find geodesics in that space using a path-straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming and comparing shapes. These ideas are demonstrated using: (i) Shape analysis of cylindrical helices for studying protein backbones, (ii) Shape analysis of facial curves for recognizing faces, (iii) A wrapped probability distribution for capturing shapes of planar closed curves, and (iv) Parallel transport of deformations for predicting shapes from novel pos...

• Type: Journal
• Year: 2011
• Where: PAMI
• Authors: Anuj Srivastava, Eric Klassen, Shantanu H. Joshi, Ian H. Jermyn
• Keywords: Computer Networks, PAMI 2011, Quotient Space, Shape Analysis, Unit Sphere