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.
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Kong, T.Y., Gau, CJ. (2004). Minimal Non-simple Sets in 4-Dimensional Binary Images with (8,80)-Adjacency. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_24
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DOI: https://doi.org/10.1007/978-3-540-30503-3_24
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