Semiparametric skew distributions in shape representation

In this paper, we address the problem of shape modeling and template learning from a novel viewpoint - using a new class of semiparametric skew-symmetric distributions. The proposed method, called "semi-parametric skew-symmetric shape model" (SSSM) learns the template from several observed realizations of a shape and models them as a joint distribution of angle and distance from the centroid of all points on the boundary. To be specific, we are interested in learning templates for simple shapes, which may, however, have arbitrary and irregular boundary. The method entails sampling an aggregate of realizations and identifying scattered data points of the available boundary realizations that lie within some neighborhood of a given angle. From the clusters of data points, we learn a bimodal distribution of the radii distances for given angles and subsequently synthesize the overall joint distributions according to some prior on the angles. Finally, we substantiate our proposed methodology with a number of examples.