Segmentation into fuzzy regions using topographic distance

This paper exposes an algorithm which leads to a fuzzy segmentation. This algorithm performs, as in the watershed method, a progressive flood of the gradient image from pixels of lowest gradients. It uses a new distance, called topographic distance. Any local minimum of the gradient norm image constitutes a seed for the region growing, avoiding the use of a marker image. These seeds constitute the cores of the initial fuzzy regions. Then the sites are gradually agglomerated to the region, while their membership degrees to the region decrease, according to the distance to the core and to the gradient norms, by the way of the topographic distance. The numerous fuzzy regions are then merged and the membership degrees of pixels to final regions are computed. Applications concern crisp segmentation of colour or gray scale images and pattern recognition from fuzzy regions