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Title: Analysis of rotational deformations from directional data using a parametric and non-parametric approach Authors:  Joern Schulz - University of Stavanger (Norway) [presenting]
Byung-Won Kim - University of Pittsburgh (United States)
Stephan Huckemann - University of Goettingen (Germany)
Steve Marron - University of North Carolina at Chapel Hill (United States)
Stephen Pizer - University of North Carolina at Chapel Hill (United States)
Sungkyu Jung - Seoul National University (Korea, South)
Abstract: Rotational deformations such as bending or twisting have been observed as the major variation in various medical applications. To provide a better surgery or treatment planning, it is crucial to model such deformations of 3D objects that can be described by the movements of directional vectors on the unit sphere. Such multivariate directional vectors are available in a number of different object representations and the rotation of each vector follows a small circle on the unit sphere. Thus, the proposed parametric and non-parametric estimation procedures are based on small circles on the unit sphere. The parametric approach is a likelihood-based estimation procedure using two novels small circle distributions called the Bingham-Mardia Fisher distribution and Bingham-Mardia-von Mises distribution. The proposed estimation procedures can model dependence structure between directions and facilitate hypotheses testing. In the non-parametric approach, estimates of the rotation axis and angles are obtained by fitting small circles applying sample Frechet means and least-square estimators. The performance of the proposed estimators are demonstrated i) in a simulation study, ii) on deformed ellipsoids and iii) on knee motions during gait.