Morphological Exploration of Shape Spaces

Authors:
Jesús Angulo;Fernand Meyer
Affiliations:
CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES Paristech, Fontainebleau Cedex, France 77305;CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES Paristech, Fontainebleau Cedex, France 77305
Venue:
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Year:
2009

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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.