Surface-Based Computation of the Euler Characteristic in the BCC Grid(Article)(Open Access)
- aFaculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
- bDepartment of Computer Science, Bioengineering, Robotics, and Systems Engineering, University of Genova, Genova, Italy
Abstract
As opposed to the 3D cubic grid, the body-centered cubic (BCC) grid has some favorable topological properties: each set of voxels in the grid is a 3-manifold, with 2-manifold boundary. Thus, the Euler characteristic of an object O in this grid can be computed as half of the Euler characteristic of its boundary ∂O . We propose three new algorithms to compute the Euler characteristic in the BCC grid with this surface-based approach: one based on (critical point) Morse theory and two based on the discrete Gauss–Bonnet theorem. We provide a comparison between the three new algorithms and the classic approach based on counting the number of cells, either of the 3D object or of its 2D boundary surface. © 2023, The Author(s).
Indexed keywords
| Engineering controlled terms: | Computation theory |
|---|---|
| Engineering uncontrolled terms | 2-manifolds3-manifoldBody-centered cubic gridsCubic gridsDigital topologyDiscrete gauss-bonnet theoremEuler characteristicMorse the-orySurface-basedTopological properties |
| Engineering main heading: | Topology |
Funding details
| Funding sponsor | Funding number | Acronym |
|---|---|---|
| Università degli Studi di Genova | ||
| Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja | 200156,451-03-47/2023- 01/200156 | MPNTR |
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1
Open access funding provided by Universit\u00E0 degli Studi di Genova within the CRUI-CARE Agreement. Lidija \u010Comi\u0107 has received financial support from the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, project number 451-03-47/2023- 01/200156
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2
This work has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the Project No. 451-03-47/2023-01/200156.
- ISSN: 09249907
- CODEN: JMIVE
- Source Type: Journal
- Original language: English
- DOI: 10.1007/s10851-023-01153-y
- Document Type: Article
- Publisher: Springer
Magillo, P.; Department of Computer Science, Bioengineering, Robotics, and Systems Engineering, University of Genova, Genova, Italy;
© Copyright 2023 Elsevier B.V., All rights reserved.
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