Parallel Transport on Kendall Shape Spaces

TL;DR

This paper introduces an implementation of the pole ladder algorithm for parallel transport on Kendall shape spaces, comparing it to differential equation integration methods for improved shape data analysis.

Contribution

It provides a novel implementation of the pole ladder algorithm for parallel transport on Kendall shape spaces and compares its performance with existing differential equation methods.

Findings

Pole ladder algorithm effectively computes parallel transport.

Comparison shows advantages over differential equation integration.

Enhances statistical analysis of shape data.

Abstract

Kendall shape spaces are a widely used framework for the statistical analysis of shape data arising from many domains, often requiring the parallel transport as a tool to normalise time series data or transport gradient in optimisation procedures. We present an implementation of the pole ladder, an algorithm to compute parallel transport based on geodesic parallelograms and compare it to methods by integration of the parallel transport ordinary differential equation.