Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing
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Determining the mean shape of a collection of curves is not a trivial task, in particular when curves are only irregularly/sparsely sampled at discrete points. We propose an elastic full Procrustes mean of shapes of (oriented) plane curves, which are considered equivalence classes of parameterized curves with respect to translation, rotation, scale, and re-parameterization (warping), based on the square-root-velocity framework. Identifying the real plane with the complex numbers, we establish a connection to covariance estimation in irregular/sparse functional data analysis and propose Hermitian covariance smoothing for (in)elastic full Procrustes mean estimation. We demonstrate the performance of the approach in a phonetic study on tongue shapes and in different realistic simulation settings, inter alia based on handwriting data.
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