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An explicit formula for the number of tunnels in digital objects

2005/05/31 by Valentin Brimkov, Valentin E. Brimkov, Brimkov, Valentin +4
Computer Science · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Computer Vision and Pattern Recognition (cs.CV) #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #G.2.1 #I.4.6 #I.5.1 #Medical Image Segmentation Techniques #cs.CG #cs.CV #cs.DM

paper · pdf · doi:10.48550/arxiv.cs/0505084

9 pages, 4 figures

openalex publication_date 2005/05/31 · arxiv created 2005/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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