Three-Dimensional Digital Topology: The Genus.
MARYLAND UNIV COLLEGE PARK COMPUTER VISION LAB
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This report is one of a series on the geometrical and topological properties of three-dimensional digital images. In this report, we define the genus of a subset of a three-dimensional array and show that the properties of this digital genus are consistent which those of the genus in ordinary continuous topology. Since the approach here is different than that normally used in two dimensions, we also present the two-dimensional case. The derivation of the three-dimensional genus allows us to make explicit what is meant by a hole in an object e.g., the hole in a ring. We also give algorithms for computing the three-dimensional digital genus and discuss the importance of three-dimensional genus in contrast with the two-dimensional genus. Author
- Theoretical Mathematics