Shape analysis on Lie groups and homogeneous spaces

TL;DR

This paper extends the Square Root Velocity Transform (SRVT) for shape analysis from Euclidean spaces to curves on Lie groups and homogeneous manifolds, leveraging the geometry of Lie group actions.

Contribution

It introduces a generalized SRVT framework for shape spaces on Lie groups and homogeneous manifolds, enhancing shape analysis techniques with geometric insights.

Findings

Generalized SRVT applicable to Lie groups and homogeneous spaces

Preserves geometric properties of shape spaces

Facilitates analysis of curves on complex manifolds

Abstract

In this paper we are concerned with the approach to shape analysis based on the so called Square Root Velocity Transform (SRVT). We propose a generalisation of the SRVT from Euclidean spaces to shape spaces of curves on Lie groups and on homogeneous manifolds. The main idea behind our approach is to exploit the geometry of the natural Lie group actions on these spaces.