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Published in:
2005 | OriginalPaper | Chapter
The Number of Gaps in Binary Pictures
Authors : Valentin E. Brimkov, Angelo Maimone, Giorgio Nordo, Reneta P. Barneva, Reinhard Klette
Published in: Advances in Visual Computing
Publisher: Springer Berlin Heidelberg
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This paper identifies the total number of gaps of object pixels in a binary picture, which solves an open problem in 2D digital geometry (or combinatorial topology of binary pictures). We obtain a formula for the total number of gaps as a function of the number of object pixels (grid squares), vertices (corners of grid squares), holes, connected components, and 2 × 2 squares of pixels. It can be used to test a binary picture (or just one region: e.g., a digital curve) for gap-freeness.