Metric and non-metric distances on Zn by generalized neighbourhood sequences

The neighbourhood sequences have got a very important role in the digital image processing. In this paper we give some new results from this area. Using neighbourhood sequences on the n dimensional digital spaces, we give a formula to compute distances of any pairs of points. By practical reasons we underline the special cases of 2 and 3 dimensional digital spaces. It is known that there are non-metrical distances defined by neighbourhood sequences. Furthermore, in this paper we are answering the question what the necessary and sufficient condition is to have metrical distances.