Nonmetrical distances on the hexagonal grid using neighborhood sequences
Benedek Nagy · Pattern Recognition and Image Analysis · 2007
the theory of neighborhood sequences is applicable in many image-processing algorithms. The theory is well known and has been analyzed for square and cubic grids. In this paper we consider a hexagonal grid. We use three kinds of neighbors; therefore, the neighborhood sequences allow more flexibility in the hexagonal plane than in the square one. Some interesting properties of these distances are presented, such as nonsymmetrical distances and that some of the distances do not meet the triangular inequality. In this paper we present sufficient and necessary conditions for neighborhood sequences define symmetric and/or triangular distance functions. Both metrical and nonmetrical distances are described on the hexagonal grid.