Morphological exploration of shape spaces

Abstract

The aim of this paper is to propose efficient tools for analysing shape families using morphological operators. The developments include the definition of shape statistics (mean and variance of shapes, modes of shape variation) and the interpolation/extrapolation in shape geodesic paths. The main required ingredients for the operators and the algorithms here introduced are well known in mathematical morphology such as the median set, the watershed on distance functions or the interpolation function. In addition, the projection of shapes in spaces with reduced dimensions using PCA or ISOMAP techniques permits to apply morphological interpolation techniques in shape manifolds. © 2009 Springer Berlin Heidelberg.