Chamfer distances are discrete distances based on the propagation of local distances, or weights defined in a mask. The medial axis, i.e. the centers of the maximal disks (disks which are not contained in any other disk), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case with comparison tests involving look-up tables representing the covering relation of disks in a local neighborhood. Although look-up table values can be computed efficiently, the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced.