Adaptive morphology applied to gray level object transformation

In this paper, we introduce a new approach to compute a directional transformation of gray-tone objects. The method is based on the definition of elementary forces exerted between the pixels. The dilation and the erosion are then obtained respectively by increasing and decreasing the membership function of the pixel according to the resultant force intensity. In order to emphasize the anisotropic effect of this force, we introduce a penalization function depending on the angular dispersion of the resultants. The effects of adaptive dilation and erosion are illustrated on both synthesized and real objects.