Topology-preserving digitization of n-dimensional objects by constructing cubical models

2015/06/08 by Alexander V. Evako, Evako, Alexander V.
Computer Science · #Computer Graphics and Visualization Techniques #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Medical Image Segmentation Techniques

paper · pdf · doi:10.48550/arxiv.1506.02678

openalex publication_date 2015/06/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous object in its digital counterpart, which is a graph, enabling us to apply notions and operations used in digital imaging to cubical spaces. We formulate a definition of a simple n-cube and prove that deleting or attaching a simple n-cube does not change the homotopy type of a cubical space. Relying on these results, we design a procedure, which preserves basic topological properties of an n-dimensional object, for constructing compressed cubical and digital models.

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