Morphological exploration of shape spaces

Jesus Angulo (1) , Fernand Meyer (1)

1 CMM - Centre de Morphologie Mathématique

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.

Mots clés: Mathematical morphology; Distance functions; Interpolation function; Interpolation techniques; Median set; Morphological operator; Shape geodesics; Shape manifold; Shape space; Shape statistics; Shape variations; Functions; Image processing; Imaging systems; Mathematical operators

Domaines: Traitement des images [eess.IV]

Jesus Angulo, Fernand Meyer. Morphological exploration of shape spaces. 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2009, Aug 2009, Groningen, Netherlands. pp.226-237, ⟨10.1007/978-3-642-03613-2_21⟩. ⟨hal-00834033⟩