The Number of Gaps in Binary Pictures

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Conference object 01 Jan 2005Publisher:Springer Berlin Heidelberg

Authors: BRIMKOV V. E; MAIMONE, ANGELO; NORDO, Giorgio; BARNEVA R. P; KLETTE R.;

doi: 10.1007/11595755_5

handle: 11570/1435630

The Number of Gaps in Binary Pictures

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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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Keywords

Digital geometry; 2D binary pictures; Gaps; Gap-freeness

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