Abstract
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.
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Brimkov, V.E., Maimone, A., Nordo, G., Barneva, R.P., Klette, R. (2005). The Number of Gaps in Binary Pictures. In: Bebis, G., Boyle, R., Koracin, D., Parvin, B. (eds) Advances in Visual Computing. ISVC 2005. Lecture Notes in Computer Science, vol 3804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11595755_5
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DOI: https://doi.org/10.1007/11595755_5
Publisher Name: Springer, Berlin, Heidelberg
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