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

2012/11/16 by Li M. Chen, Chen, Li M.
Computer Science · #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Medical Image Segmentation Techniques #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1211.3812

openalex publication_date 2012/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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+ (|C₄|-|C₂|)/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.

Citations

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

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