Contents 1. Introduction
The digital geometry is an important part of image processing. In digital geometry the spaces we work in consist of discrete points with integer coordinates. In [9] Rosenfeld and Pfaltz defined two basic neighbourhood relations in the square grid. They gave two types of motions in the two dimensional square grid, namely the cityblock and the chessboard ones. Two points are neighbours if their coordinate difference values are at most 1. Generally, in the dimensional square (cubic) grid there are kinds of neighbourhood relations according to the number of differences. One can find more about this digital topology in [6], [10]. We define the distance of two points as the number of steps in a shortest path (it is possible several shortest paths of the same path-length exist), where by a step we mean a movement from a point to one of its neighbour points. This distance function depends not only on the points, but also the given neighbourhood criterion. Varying the neighbourhood relations in a path, we get the concept of neighbourhood sequences. After Rosenfeld and Pfaltz the theory of periodic neighbourhood sequences developed by Yamashita, Das and their co-authors in several papers. These distances obtain better approximations for the Euclidean distance than the ones using only one kind of steps. There is a very flexible family of distances. In [11] the concept and name of neighbourhood sequence was introduced. In [1] the authors presented a complex method to calculate the distance of any two points based on a neighbourhood sequence.
