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On the Cellular Convexity of Complexes
June 1981 (vol. 3 no. 6)
pp. 617-625
Chul E. Kim, Department of Computer Science, University of Maryland, College Park, MD 20742.
In this paper we discuss cellular convexity of complexes. A new definition of cellular convexity is given in terms of a geometric property. Then it is proven that a regular complex is celiularly convex if and only if there is a convex plane figure of which it is the cellular image. Hence, the definition of cellular convexity by Sklansky [7] is equivalent to the new definition for the case of regular complexes. The definition of Minsky and Papert [4] is shown to be equivalent to our definition. Therefore, aU definitions are virtually equivalent. It is shown that a regular complex is cellularly convex if and only if its minimum-perimeter polygon does not meet the boundary of the complex. A 0(n) time algorithm is presented to determine the cellular convexity of a complex when it resides in n × m cells and is represented by the run length code.
Citation:
Chul E. Kim, "On the Cellular Convexity of Complexes," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 3, no. 6, pp. 617-625, June 1981, doi:10.1109/TPAMI.1981.4767162
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