Integer approximation of 3D chamfer mask coefficients using a scaling factor in anisotropic grids

For discrete data represented by three variable scalar functions, the sampling step may be different according to the axes, leading to parallelepipedic sampling grids. This is the case for instance with medical or industrial computed tomography and confocal microscopy, as well as in grey level image analysis if images are modelized by means of their set representation (mathematical morphology). In this paper, 3D non-cubic chamfer masks are introduced. The problem of coefficient optimization is addressed for arbitrary mask size. Thank to this, first, the maximal normalized error with respect to Euclidean distance can be derived analytically, in any 3D anisotropic lattice, and second, optimal chamfer mask coefficients can be computed. We propose a method to calculate lower and upper bounds for integer scaling factors in order to obtain integer approximations for the coefficients. This approach helps the algorithm perform in scenarios where memory is limited.

Research highlights
► The problem of coefficient optimization is addressed for arbitrary mask size.
► We proposed a method to calculate lower and upper bounds for scaling factors.
► Integer scaling factors are used to obtain integer chamfer mask coefficients.
► 3D cubic or non-cubic operators are concerned with this method.