.NTE1NA.MjYyMzk1

Fig » 3 - Tvvo homotopic figures and their tree. A transformation is homotopic when it préserves the homotopic tree of K. ïlote that homotopy is more severe than connectivity : a disk and an ring are both connected sets, "but they are not homotopic. These four properties are the corner stones for a ty- pology of the morphologica.1 criteria, giving them particular "characters". The reader must alv/ays keep them in mlnd if he ;?ants to mas ter the method. However, they are far from beiug the only ones : one may also wish to treat figure and background symmetrically, to perform isotropic analyses, to preserve con¬ nectivity, to be monotonie at each pixel, etc.. Fig. 4 lists the status of the four properties for a few basic geometrical transformations (displacements, convex hulls, etc..) plus for the basic Fuclidean morphological crite¬ ria •