Optimal Neighborhood Sequences on the Hexagonal Grid

The neighborhood sequences have got a very important role in the digital image processing. In this paper we give some new results from this area on the hexagonal grid. Digital distances are used to approximate the Euclidean one. The approximation can be done through digital discs (circles). We obtain optimal neighborhood sequences defining digital circles the most close to the Euclidean circle. It is known that there are non-metrical distances defined by neighborhood sequences, moreover there is a neighborhood relation which is useless respecting the digital Jordan property of curves. Optimal neighborhood sequences and digital circles are presented with metric properties and/or with only that types of neighborhood relations which play at Jordan curves.