Weighted distances based on neighbourhood sequences

By combining weighted distances and distances based on neighbourhood sequences, a new family of distance functions with potentially low rotational dependency is obtained. The basic theory for these distance functions, including functional form of the distance between two points, is presented. By minimizing an error function, the weights and neighbourhood sequence that give the distance function with the lowest rotational dependency are derived. To verify that the low rotational dependency of the proposed distance function is valid also in applications, the constrained distance transform on a binary image is computed and compared with some traditionally used distance functions.