Shape analysis on Lie groups and homogeneous spaces
arXiv:1710.005395 citationsh-index: 26
AI Analysis
This provides a theoretical extension of a known method to new geometric domains, which is incremental for shape analysis researchers.
The paper generalizes the Square Root Velocity Transform (SRVT) from Euclidean spaces to shape spaces of curves on Lie groups and homogeneous manifolds, enabling elastic shape analysis in these settings.
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.