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An explicit formula for the number of tunnels in digital objects

Valentin Brimkov·Angelo Maimone·Giorgio Nordo
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Abstract

An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2x2 grid squares. It can be used to test for tunnel-freedom a digital object, in particular a digital curve.

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Valentin Brimkov, Angelo Maimone, Giorgio Nordo. 2005-09-07. An explicit formula for the number of tunnels in digital objects. https://arxiv.org/abs/cs/0505084

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