Topological Classification of points in $Z^2$ by using Topological Numbers for $2$D discrete binary images

TL;DR

This paper introduces a topological classification system for points in 2D binary images, based on topological numbers, dividing points into six classes with specific configurations.

Contribution

It proposes a novel topological classification method for points in 2D binary images using topological numbers, detailing six distinct classes.

Findings

Six classes of points identified: isolated, interior, simple, curve, 3-curve intersection, 4-curve intersection

Configurations for each class are enumerated

Provides a framework for topological analysis of 2D binary images

Abstract

In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior point, simple point, curve point, point of intersection of 3 curves, point of intersection of 4 curves. The number of configurations of each class is also given.