Approximating non-metrical Minkowski distances in 2D

In this paper we discuss a possible discrete approximation of non-metrical Minkowski distances. The existing approaches for Minkowski metrics considering distance functions based on local neighborhoods are not suitable for this task in their present form. We can overcome this difficulty with considering the minimum of such distance functions. In this way we can take full advantage of the former theoretical and applied results. We consider several possibilities to measure the error of approximation and propose corresponding distance functions for optimal approximation. A fast chamfering algorithm is also provided to generate the approximate distance values for applications in digital domains.