Les distances de chanfrein en analyse d'images : fondements et applications
Édouard Thiel · HAL (Le Centre pour la Communication Scientifique Directe) · 1994
Chamfer distances are defined in the discrete space; they rely on the definition and the application of weighted masks, and they provide good approximations of the real Euclidean distance. They are often used in image analysis, for quantification and to describe the regions constituting the shape. In particular they allow the computation of weighted skeletons, with efficient algorithms. Our goal is to complete the knowledge above each level of these distances, and to generalise notions and algorithms. After some recalls, we study arithmetical and geometrical properties of chamfer disks, in such a way that we are able to determine the exact constraints, so as to induce a distance. These properties give also direct computation formulas. The mask optimization is then accomplished. The aim is to minimize the error relative to the Euclidean distance. Our method is validated with new optimal masks obtaining. We provide a universal medial axis computation algorithm, which generates look-up tables in a very fast way. A unified distance-driven scheme is proposed to extract the weighted skeleton of a digital pattern, which runs whichever distance is selected among the most common ones. Finally we present a shape description method, where the skeleton is suitably decomposed by a polygonal approximation. Any digital shape is reduced to a vectorial representation, which keeps some degree of reversibility.