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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)

Abstract

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.

Keywords

Binary Image Euler Number Cartesian Grid Simple Point Proper Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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