The Euler-Poincará formula through contact surfaces of voxelized objects

H. Sánchez-Cruz; H. Sossa-Azuela; U. D. Braumann; E. Bribiesca

doi:10.1016/S1665-6423(13)71515-3

The Euler-Poincará formula through contact surfaces of voxelized objects

H. Sánchez-Cruz, H. Sossa-Azuela, U. D. Braumann, E. Bribiesca

Centro de Investigación en Computación (CIC)

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Two new versions of the Euler-Poincaré formula are proposed considering two new defined cuboids: the tetra-voxel and the octo-voxel, without losing information on the number of vertices and edges. The well-known relationship between contact and enclosing surface concepts, as well as the relationships between vertices, edges and enclosing surfaces, allowed us to compute an innovative algorithm for obtaining alternative versions of the Euler-Poincare formula. This is a very important topological descriptor of 3D binary images. We considered not only topological but geometric aspects. Our method was compared to other proposals, obtaining that our proposed contact surface-based method offers more advantages.

Original language	English
Pages (from-to)	65-78
Number of pages	14
Journal	Journal of Applied Research and Technology
Volume	11
Issue number	1
DOIs	https://doi.org/10.1016/S1665-6423(13)71515-3
State	Published - Feb 2013

Keywords

Contact surfaces
Edges
Euler characteristic
Euler number
Euler-Poincaré
Octo-voxels
Tetra-voxels
Vertices

Access to Document

10.1016/S1665-6423(13)71515-3

Cite this

@article{2ce73c937a6a4b1886baab57d9e1b25d,

title = "The Euler-Poincar{\'a} formula through contact surfaces of voxelized objects",

abstract = "Two new versions of the Euler-Poincar{\'e} formula are proposed considering two new defined cuboids: the tetra-voxel and the octo-voxel, without losing information on the number of vertices and edges. The well-known relationship between contact and enclosing surface concepts, as well as the relationships between vertices, edges and enclosing surfaces, allowed us to compute an innovative algorithm for obtaining alternative versions of the Euler-Poincare formula. This is a very important topological descriptor of 3D binary images. We considered not only topological but geometric aspects. Our method was compared to other proposals, obtaining that our proposed contact surface-based method offers more advantages.",

keywords = "Contact surfaces, Edges, Euler characteristic, Euler number, Euler-Poincar{\'e}, Octo-voxels, Tetra-voxels, Vertices",

author = "H. S{\'a}nchez-Cruz and H. Sossa-Azuela and Braumann, {U. D.} and E. Bribiesca",

year = "2013",

month = feb,

doi = "10.1016/S1665-6423(13)71515-3",

language = "Ingl{\'e}s",

volume = "11",

pages = "65--78",

journal = "Journal of Applied Research and Technology",

issn = "1665-6423",

number = "1",

}

TY - JOUR

T1 - The Euler-Poincará formula through contact surfaces of voxelized objects

AU - Sánchez-Cruz, H.

AU - Sossa-Azuela, H.

AU - Braumann, U. D.

AU - Bribiesca, E.

PY - 2013/2

Y1 - 2013/2

N2 - Two new versions of the Euler-Poincaré formula are proposed considering two new defined cuboids: the tetra-voxel and the octo-voxel, without losing information on the number of vertices and edges. The well-known relationship between contact and enclosing surface concepts, as well as the relationships between vertices, edges and enclosing surfaces, allowed us to compute an innovative algorithm for obtaining alternative versions of the Euler-Poincare formula. This is a very important topological descriptor of 3D binary images. We considered not only topological but geometric aspects. Our method was compared to other proposals, obtaining that our proposed contact surface-based method offers more advantages.

AB - Two new versions of the Euler-Poincaré formula are proposed considering two new defined cuboids: the tetra-voxel and the octo-voxel, without losing information on the number of vertices and edges. The well-known relationship between contact and enclosing surface concepts, as well as the relationships between vertices, edges and enclosing surfaces, allowed us to compute an innovative algorithm for obtaining alternative versions of the Euler-Poincare formula. This is a very important topological descriptor of 3D binary images. We considered not only topological but geometric aspects. Our method was compared to other proposals, obtaining that our proposed contact surface-based method offers more advantages.

KW - Contact surfaces

KW - Edges

KW - Euler characteristic

KW - Euler number

KW - Euler-Poincaré

KW - Octo-voxels

KW - Tetra-voxels

KW - Vertices

UR - http://www.scopus.com/inward/record.url?scp=84881136949&partnerID=8YFLogxK

U2 - 10.1016/S1665-6423(13)71515-3

DO - 10.1016/S1665-6423(13)71515-3

M3 - Artículo

AN - SCOPUS:84881136949

SN - 1665-6423

VL - 11

SP - 65

EP - 78

JO - Journal of Applied Research and Technology

JF - Journal of Applied Research and Technology

IS - 1

ER -

The Euler-Poincará formula through contact surfaces of voxelized objects

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this