Regression-Based Elastic Metric Learning on Shape Spaces of Cell Curves

Adele Myers, Nina Miolane

Keywords: metric learning, cell shape analysis, manifold of discrete curves, elastic metric, geodesic regression

TL;DR: We use metric learning on the manifold of discrete curves to optimize the elastic metric for geodesic regression of cell shape trajectories.

Abstract: We propose a metric learning paradigm, Regression-based Elastic Metric Learning (REML), which optimizes the elastic metric for geodesic regression on the manifold of discrete curves. Geodesic regression is most accurate when the chosen metric models the data trajectory close to a geodesic on the discrete curve manifold. When tested on cell shape trajectories, regression with REML’s learned metric has better predictive power than with the conventionally used square-root-velocity (SRV) metric. The code is publicly available here: https://github.com/bioshape-lab/dyn.