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.

The number of gaps in binary pictures

MAIMONE, ANGELO
Investigation
;
NORDO, Giorgio
Investigation
;
2005

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/1435630
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