Regression-Based Elastic Metric Learning on Shape Spaces of Elastic Curves
This work addresses the problem of enhancing shape analysis for applications like cell biology by offering an incremental improvement in metric learning for geodesic regression.
The authors tackled the problem of improving geodesic regression accuracy on shape spaces of elastic curves by proposing REML, a metric learning paradigm that optimizes the elastic metric, and found that it provides better predictive power than the conventional SRV metric when tested on cell shape trajectories.
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.