Shape analysis on homogeneous spaces: a generalised SRVT framework
This work provides a theoretical extension of the SRVT to homogeneous spaces, offering new flexibility for shape analysis in pattern recognition, though it is an incremental methodological contribution.
The paper proposes a generalised Square Root Velocity Transform (SRVT) framework for shape analysis on homogeneous manifolds, enabling comparison of curves independent of parametrisation with various Lie group actions and Riemannian metrics.
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.