A0353
Title: Elastic full Procrustes analysis of plane curves via Hermitian covariance smoothing
Authors: Sonja Greven - Humboldt University of Berlin (Germany)
Lisa Steyer - Humboldt University of Berlin (Germany)
Manuel Pfeuffer - Humboldt-Universitaet zu Berlin (Germany)
Almond Stoecker - Ecole polytechnique federale de Lausanne (Switzerland) [presenting]
Abstract: Estimating the mean shape of a collection of curves is a challenging task, particularly when curves are only irregularly/sparsely sampled at discrete points, and so is testing group difference when, due to the sparse sampling, exact distances between curves cannot be computed. An elastic full Procrustes mean of shapes of (oriented) plane curves is newly proposed, which are considered equivalence classes of parameterized curves with respect to the shape invariances translation, rotation and scale, as well as re-parameterization (warping) based on the square-root-velocity (SRV) framework. Identifying the real plane with the complex numbers, a connection to covariance estimation in irregular/sparse functional data analysis is established, and Hermitian covariance smoothing is introduced to employ for (in)elastic full Procrustes mean estimation. Building on this new mean concept and estimator, one- and two-way analysis of variance (ANOVA) is also developed for sparsely sampled curve shape data. The performance of the approach is demonstrated in different realistic simulation settings and is used for an ANOVA of tongue shapes during speech production, taking into account variability in the subject's positioning and size, as well as the elasticity of the tongue.
