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Morphological Exploration of Shape Spaces Jess Angulo and Fernand Meyer

Summary: Morphological Exploration of Shape Spaces
Jesús Angulo and Fernand Meyer
CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES
Paristech; 35, rue Saint Honoré, 77305 Fontainebleau Cedex, France
jesus.angulo@ensmp.fr, fernand.meyer@ensmp.fr
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 func-
tion. In addition, the projection of shapes in spaces with reduced dimen-
sions using PCA or ISOMAP techniques permits to apply morphological
interpolation techniques in shape manifolds.
1 Introduction
Let X = {X1, X2, · · · , XN } = {Xi}
i=1 be a family (or collection) of N shapes,
where Xi P(E) represents the set (or binary image) of the shape i, and the


Source: Angulo,Jesús - Centre de Morphologie Mathématique, Ecole des Mines de Paris


Collections: Computer Technologies and Information Sciences