Abstract
Many applications of digital image processing now deal with three-dimensional images (the third dimension can be time or a spatial dimension). In this paper we develop a topological model for digital three space which can be useful in this context. In particular, we prove a digital, three-dimensional, analogue of the Jordan curve theorem. (The Jordan curve theorem states that a simple closed curve separates the real plane into two connected components.) Our theorem here is a digital topological formulation of the Jordan-Brouwer theorem about surfaces that separate three-dimensional space into two connected components.
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Kopperman, R., Meyer, P.R. & Wilson, R.G. A Jordan surface theorem for three-dimensional digital spaces. Discrete Comput Geom 6, 155–161 (1991). https://doi.org/10.1007/BF02574681
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DOI: https://doi.org/10.1007/BF02574681