Medial Axis LUT Computation for Chamfer Norms Using $\mathcal{H}$ -Polytopes

Abstract

Abstract. 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 [1], the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope [2] descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced.

Visible Vectors and Discrete Euclidean Medial Axis

“…The computation of the LUT is linear in N for each vector in M n R . A fast algorithm to compute the test neighbourhood in the case of 2-dimensional chamfer norms, using the polytope description of discs, is proposed in [10]. The computation of M n R is time consuming in the case of the Euclidean distance, but M n R can be calculated once for all bounded size images and stored at low memory cost (while LUTs can be huge and might be recomputed each time).…”

Sparse Object Representations by Digital Distance Functions

“…One approach to overcome this problem is to relabel the distance values, see [1,14]. Relabeling is not enough for all distance functions and another approach is to use look-up tables to extract the set of CMBs, see, e.g., [14,4,12,11]. Another issue is that the set of local maxima and the points that do not propagate distance information when computing the DT are not always equal.…”

Appearance Radii in Medial Axis Test Mask for Small Planar Chamfer Norms

“…Algorithms to compute both LUT and T (R) are given by Rémy and Thiel in arbitrary dimension for chamfer norms and SED [9,10], with code available in dimensions 2 to 6 in [11]. In recent papers, Normand andÉvenou have proposed a faster method for chamfer norms in 2D and 3D based on a polytope representation of chamfer balls [12,13].…”