Title: Small-sphere distributions for directional data with application to rotationally deformed objects
Authors: Joern Schulz - University of Stavanger (Norway) [presenting]
Byungwon Kim - University of Pittsburgh (United States)
Stephan Huckemann - University of Goettingen (Germany)
Sungkyu Jung - Seoul National University (Korea, South)
Abstract: Rotational deformations of 3D objects such as bending or twisting have been observed as the major variations in various medical applications. To provide a better surgery or treatment planning, it is crucial to model such deformations that can be described by the movements of multivariate directional vectors on $(S^2)^K$ for $K\geq1$. Such multivariate directional vectors are available in a number of different object representations. The proposed small-sphere distribution families enable to model these directions and their dependence structure. In addition, they facilitate random data generation and hypotheses testing of the directional data. A Likelihood-based estimation procedure is suggested for the estimation of the corresponding parameters. The proposed models will be compared to a non-parametric approach where estimates of the rotation axis of small-circle-concentrated data are obtained by fitting small circles applying sample Frechet means and least-square estimators. The performance of the proposed multivariate small-sphere distributions is demonstrated: i.) in a simulation study, ii.) on deformed ellipsoids and iii.) on knee motions during gait.