Metrical neighborhood sequences in Z
نویسندگان
چکیده
Digital metrics on the digital space play an important role in several branches of discrete mathematics, e.g. in discrete geometry or digital image processing. We perform an overall analysis on some properties of neighborhood sequences which induce metrics on Z.
منابع مشابه
General neighborhood sequences in Z
Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretica...
متن کاملGeneral neighborhood sequences in Zn
Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Zn only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretic...
متن کاملSkeletonization Based on Metrical Neighborhood Sequences
Skeleton is a shape descriptor which summarizes the general form of objects. It can be expressed in terms of the fundamental morphological operations. The limitation of that characterization is that its construction based on digital disks such that cannot provide good approximation to the Euclidean disks. In this paper we define a new type of skeleton based on neighborhood sequences that is muc...
متن کاملMetric and non-metric distances on Z by generalized neighbourhood sequences
The neighbourhood sequences have got a very important role in the digital image processing. In this paper we give some new results from this area. Using neighbourhood sequences on the n dimensional digital spaces, we give a formula to compute distances of any pairs of points. By practical reasons we underline the special cases of 2 and 3 dimensional digital spaces. It is known that there are no...
متن کاملNeighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids
The two-dimensional hexagonal grid and the three-dimensional face-centered cubic grid can be described by intersecting Z and Z with a (hyper)plane. Corresponding grids in higher dimensions (nD) are examined. In this paper, we define distance functions based on neighborhood sequences on these, higher dimensional generalizations of the hexagonal grid. An algorithm to produce a shortest path based...
متن کامل