Neighborhood Sequences in the Diamond Grid  Algorithms with Four Neighbors
Abstract
In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used. In this paper the diamond grid is considered, that is the threedimensional grid of Carbon atoms in the diamond crystal. This grid can be described by four coordinate values using axes of the directions of atomic bonds. In this way the sum of the coordinate values can be either zero or one. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. The metric and nonmetric properties of some distances based on neighborhood sequences are also discussed. The constrained distance transformation and digital balls obtained by some distance functions are presented.
 Publication:

Lecture Notes in Computer Science
 Pub Date:
 2009
 DOI:
 10.1007/9783642102103_9
 Bibcode:
 2009LNCS.5852..109N