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

Alexander V. Evako

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arXiv · 1506.02678

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

Alexander V. Evako

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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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Alexander V. Evako. 2015-06-08. Topology-preserving digitization of n-dimensional objects by constructing cubical models. https://arxiv.org/abs/1506.02678

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