Neighborhood Sequences in the Diamond Grid – Algorithms with Four Neighbors

  • Benedek Nagy
  • Robin Strand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5852)


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. The constrained distance transformation and digital balls obtained by some distance functions are presented.


digital geometry non-standard grids neighborhood sequences diamond grid distance transform 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Benedek Nagy
    • 1
  • Robin Strand
    • 2
  1. 1.Department of Computer Science, Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.Centre for Image AnalysisUppsala UniversityUppsalaSweden

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