Lattice of generalized neighbourhood sequences in nD

The neighbourhood sequences have got a very important role in the digital picture processing. In this paper we give some new results from this area. We describe an ordering relation on the set of generalized nD-neighbourhood sequences. As this ordering does not have nice properties, we introduce another relation and prove that a complete distributive lattice can be obtained in this wax. Our investigations generalize the previous results of Das (1990) and Fazekas (1999) in 2D and 3D, respectively.