Minimal Non-simple Sets in 4-Dimensional Binary Images with (8,80)-Adjacency

  • T. Yung Kong
  • Chyi-Jou Gau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)


We first give a definition of simple sets of 1’s in 4D binary images that is consistent with “(8,80)-adjacency”—i.e., the use of 8-adjacency to define connectedness of sets of 1’s and 80-adjacency to define connectedness of sets of 0’s. Using this definition, it is shown that in any 4D binary image every minimal non-simple set of 1’s must be isometric to one of eight sets, the largest of which has just four elements. Our result provides the basis for a fairly general method of verifying that proposed 4D parallel thinning algorithms preserve topology in our “(8,80)” sense. This work complements the authors’ earlier work on 4D minimal non-simple sets, which essentially used “(80,8)-adjacency”—80-adjacency on 1’s and 8-adjacency on 0’s.


Binary Image Euler Number Cartesian Grid Simple Point Proper Face 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • T. Yung Kong
    • 1
  • Chyi-Jou Gau
    • 2
  1. 1.Department of Computer ScienceQueens College, City University of New YorkFlushingU.S.A.
  2. 2.Doctoral Program in Computer Science, Graduate School and University CenterCity University of New YorkNew YorkU.S.A.

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