Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Evako, Alexander V.
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2282938707