Simple pairs of points in digital spaces. Topology-preserving transformations of digital spaces by contracting simple pairs of points

TL;DR

This paper introduces a method for contracting simple pairs of points in digital spaces that preserves topology, enabling the transformation of digital manifolds into minimal forms through sequential contractions.

Contribution

It presents a novel approach to topology-preserving contractions of simple point pairs in digital spaces, facilitating digital image thinning and manifold simplification.

Findings

Contraction of simple pairs preserves digital space topology.

Digital n-manifolds can be minimized via simple pair contractions.

Method aids in digital image thinning and skeletonization.

Abstract

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of points based on the notions of a digital contractible space and contractible transformations of digital spaces. We show that the contraction of a simple pair of points preserves local and global topology of a digital space. Relying on the obtained results, we study properties if digital manifolds. In particular, we show that a digital n-manifold can be transformed to its compressed form with the minimal number of points by sequential contractions of simple pairs. Key Words: Graph, digital space, contraction, splitting, simple pair, homotopy, thinning