Medial axis for chamfer distances: computing look-up tables and neighbourhoods in 2D or 3D

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].…”

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

“…It produces output in the same format as the reference algorithm [16] so that outputs can be compared character-to-character. Tests were done on various chamfer masks and different maximal radii.…”

“…Speed gains from the reference algorithm [1] are attributable to the representation of chamfer balls as H-polytopes. This description allows to avoid the use of weight propagation in the image domain and permits a constant time covering test by the direct computation of covering radii.…”

“…The algorithm starts with an empty mask and balls with increasing radii are tested for direct covering relations as in [1]. However, in our case, the covering relations are seen from the perspective of the covered balls (in the covering function) whereas in [1], they are considered from the point of view of the covering balls (in the distance map).…”

“…However, in our case, the covering relations are seen from the perspective of the covered balls (in the covering function) whereas in [1], they are considered from the point of view of the covering balls (in the distance map). Another difference lies in the computation of covering radii which does not require the propagation of weights thanks to a direct formula (16). In order to remove useless points, all known LUT neighborhoods are checked for an indirect covering by the procedure visitPoint.…”