Shape analysis on homogeneous spaces: a generalised SRVT framework

Abstract

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform (SRVT). In this paper we propose a generalised SRVT framework for shapes on homogeneous manifolds. The method opens up for a variety of possibilities based on different choices of Lie group action and giving rise to different Riemannian metrics.

28 pages; 4 figures, 30 subfigures; notes for proceedings of the Abel Symposium 2016: "Computation and Combinatorics in Dynamics, Stochastics and Control". v3: amended the text to improve readability and clarify some points; updated and added some references; added pseudocode for the dynamic programming algorithm used. The main results remain unchanged

References in corpus (4)

• Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance
• Shape Analysis on Lie Groups with Applications in Computer Animation
• Computing distances and geodesics between manifold-valued curves in the SRV framework
• Fundamentals of submersions and immersions between infinite-dimensional manifolds

Cited by in corpus (2)

• An introduction to infinite-dimensional differential geometry
• Fractional Sobolev metrics on spaces of immersions