Shape spaces: From geometry to biological plausibility

TL;DR

This paper reviews Riemannian metrics in shape analysis, focusing on large deformation algorithms, elastic metrics, and introduces a new growth tensor-based metric with studied properties.

Contribution

It introduces a novel class of metrics involving growth tensor optimization, expanding the theoretical framework of shape space analysis.

Findings

Analysis of various Riemannian metrics for shape spaces

Introduction of a new growth tensor-based metric

Properties of the new metric are studied

Abstract

This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm, the attention is turned to elastic metrics, and to growth models that can be derived from it. In the latter context, a new class of metrics, involving the optimization of a growth tensor, is introduced and some of its properties are studied.