English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Determining the mean shape of a collection of curves is not a trivial task,in particular when curves are only irregularly/sparsely sampled at discretepoints. We newly propose an elastic full Procrustes mean of shapes of(oriented) plane curves, which are considered equivalence classes ofparameterized curves with respect to translation, rotation, scale, andre-parameterization (warping), based on the square-root-velocity (SRV)framework. Identifying the real plane with the complex numbers, we establish aconnection to covariance estimation in irregular/sparse functional dataanalysis. We introduce Hermitian covariance smoothing and show how to employthis extension of existing covariance estimation methods for obtaining anestimator of the (in)elastic full Procrustes mean, also in the sparse case notyet covered by existing (intrinsic) elastic shape means. For this, we providedifferent groundwork results which are also of independent interest: wecharacterize (the decomposition of) the covariance structure ofrotation-invariant bivariate stochastic processes using complexrepresentations, and we identify sampling schemes that allow for exactobservation of derivatives / SRV transforms of sparsely sampled curves. Wedemonstrate the performance of the approach in a phonetic study on tongueshapes and in different realistic simulation settings, inter alia based onhandwriting data.

Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing