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

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: $h=1+(|C_4|-|C_2|)/4$, where h is the number of holes, and $C_i$ indicate the set of corner points having $i$ direct adjacent points in the component.

arXiv comment7 pages, 2 figures

References in corpus (1)

• Genus Computing for 3D digital objects: algorithm and implementation