DISTANCE FUNCTIONS DEFINED BY VARIABLE NEIGHBORHOOD SEQUENCES.

In the field of pattern recognition, many researchers adopt the definition that distance between two points x and y on digitized space is the length of the shortest path from x to y determined by a specific sequence of neighborhood forms. The diamond distance, and various octagonal distances are typical examples of these kinds of distances. However, not necessarily every sequence of neighborhood forms defines a distance function. Thus, this paper presents a necessary and sufficient condition for a sequence of neighborhood form to define a distance function.