3-D chamfer distances and norms in anisotropic grids

Chamfer distances are widely used in image analysis and many authors have investigated the computation of optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: calculations have to be conducted manually for every mask size or image anisotropy. Since image acquisition (e.g. medical imaging) can lead to discrete anisotropic grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for efficient distance map computations. This article presents an automatic construction for chamfer masks of arbitrary sizes. This allows, first, to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice, and second, to compute optimal chamfer coefficients. In addition, the resulting chamfer map verifies discrete norm conditions.