Digital n-Manifolds With Or Without Boundaries

2024/12/16 by Melih İs, İs, Melih, İsmet Karaca +1
Computer Science · #Digital Image Processing Techniques #Topological and Geometric Data Analysis #Computer Graphics and Visualization Techniques

paper · pdf · doi:10.48550/arxiv.2412.12008

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.

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