4D Minimal Non-simple Sets

  • C. J. Gau
  • T. Yung Kong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


One method of verifying that a given parallel thinning algorithm “preserves topology” is to show that no iteration ever deletes a minimal non-simple (“MNS”) set of 1’s. The practicality of this method depends on the fact that few types of set can be MNS without being a component. The problem of finding all such types of set has been solved (by Ronse, Hall, Ma, and the authors) for 2D and 3D Cartesian grids, and for 2D hexagonal and 3D face-centered cubic grids. Here we solve this problem for a 4D Cartesian grid, in the case where 80-adjacency is used on 1’s and 8-adjacency on 0’s.


4D xel attachment minimal non-simple MNS parallel thinning 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • C. J. Gau
    • 1
  • T. Yung Kong
    • 2
  1. 1.Department of Computer Science Graduate School and University CenterCity University of New YorkNew YorkUSA
  2. 2.Department of Computer ScienceQueens College City University of New YorkFlushingUSA

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