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Determining the Number of Holes of a 2D Digital Component is Easy

Computational Geometry 2012-11-19 v1 Discrete Mathematics Combinatorics

Abstract

The number of holes in a connected component in 2D images is a basic invariant. In this note, a simple formula was proven using our previous results in digital topology (Chen 2004, Chen and Rong (2010). The new is: h=1+(C4C2)/4h =1+ (|C_4|-|C_2|)/4, where h is the number of holes, and CiC_i indicate the set of corner points having ii direct adjacent points in the component.

Keywords

Cite

@article{arxiv.1211.3812,
  title  = {Determining the Number of Holes of a 2D Digital Component is Easy},
  author = {Li M. Chen},
  journal= {arXiv preprint arXiv:1211.3812},
  year   = {2012}
}

Comments

7 pages, 2 figures