Calculating distance with neighborhood sequences in the hexagonal grid

Abstract

The theory of neighborhood sequences is applicable in many image-processing algorithms. The theory is well examined for the square and the cubic grids. In this paper we consider another regular grid, the hexagonal one, and the distances based on neighborhood sequences are investigated. The points of the hexagonal grid can be embedded into the cubic grid. With this injection we modify the formula which calculates the distances between points in the cubic space to the hexagonal plane. Our result is a theoretical one, which is very helpful. It makes the distances based on neighborhood sequences in the hexagonal grid applicable. Some interesting properties of these distances are presented, such as the non-symmetric distances. It is possible that the distance depends on the ordering of the elements of the initial part of the neighborhood sequence. We show that these two properties are dependent. © Springer-Verlag 2004.