Digital $n-$Manifolds With Or Without Boundaries

TL;DR

This paper explores the concept of digital manifolds in 2D and 3D digital images, highlighting differences from classical manifolds and discussing related topological concepts like submanifolds and orientation.

Contribution

It provides a comprehensive framework for understanding digital manifolds, emphasizing their properties and differences from continuous manifolds in digital imaging contexts.

Findings

Identifies features of topological manifolds not satisfied in digital versions

Discusses related concepts like submanifolds and orientation in digital images

Provides a general perspective for digital curves and surfaces

Abstract

This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital surfaces. Throughout the study, the features present in topological manifolds but that are not satisfied in the discrete version are specifically underlined. In addition, other concepts closely related to manifolds such as submanifold, orientation, and partition of unity are also discussed in digital images.