On the Characterization of Simple Closed Surfaces in Three-Dimensional Digital Images.
MARYLAND UNIV COLLEGE PARK COMPUTER VISION LAB
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This is a continuation of a series of papers on the digital geometry of three-dimensional digital images. In earlier reports, D. Morgenthaler and A. Rosenfeld gave symmetric definitions for simple surface points under the concepts of 6-connectivity and 26-connectivity, and they non-trivially characterized a simple closed surface i.e., a subset of the image which separates its complement into an inside and an outside as a connected collection of orientable simple surface points. Later, the author and A. Rosenfeld established that the computationally costly assumption of orientability is unnecessary for 6-connectivity by proving that orientability, a local property, is implicitly guaranteed within the 3x3x3-neighborhood definition of a 6-connected simple surface point. However, they also showed that no such guarantee exists for 26-connectivity. In this report, the author completes this investigation of simple closed surfaces by showing that orientability is ensured globally by 26-connectivity. Hence, a simple closed surface may be efficiently charactered as a connected collection of simple surface points regardless of the type of connectivity in consideration. Author
- Theoretical Mathematics