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We propose a metric learning paradigm, Regression-based Elastic MetricLearning (REML), which optimizes the elastic metric for geodesic regression onthe manifold of discrete curves. Geodesic regression is most accurate when thechosen metric models the data trajectory close to a geodesic on the discretecurve manifold. When tested on cell shape trajectories, regression with REML'slearned metric has better predictive power than with the conventionally usedsquare-root-velocity (SRV) metric.

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