Neighborhood Sequences in the Diamond Grid: Algorithms with Two and Three Neighbors

摘要

In the digital image processing, digital distances are useful; distances based on neighborhood sequences are widely used. In this article, the diamond grid is considered, that is, the three-dimensional grid of carbon atoms in the diamond crystal. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. A formula to compute the distance based on neighborhood sequences with two neighborhood relations is given. The metric and nonmet-ric properties of some distances based on neighborhood sequences are also discussed. Finally, the constrained distance transformation is shown.