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 three-dimensional 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 non-metric properties of some distances based on neighborhood sequences are also discussed. Finally The constrained distance transformation and digital balls obtained by some distance functions are presented. © Springer-Verlag Berlin Heidelberg 2009.
CITATION STYLE
Nagy, B., & Strand, R. (2009). Neighborhood sequences in the diamond grid- Algorithms with four neighbors. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5852 LNCS, pp. 109–121). https://doi.org/10.1007/978-3-642-10210-3_9
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