# Shape analysis on homogeneous spaces: a generalised SRVT framework

## TL;DR

This paper introduces a generalized SRVT framework for shape analysis on homogeneous spaces, enabling flexible shape comparison on manifolds with various Lie group actions and Riemannian metrics.

## Contribution

It extends the SRVT method to homogeneous manifolds, allowing for diverse applications with different Lie group actions and metrics.

## Key findings

- Framework accommodates various Lie group actions
- Enables computation of shape distances on manifolds
- Flexible choice of Riemannian metrics

## 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.