Topology preservation on the triangular grid

Péter Kardos, K. Palágyi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

There are exactly three regular planar grids, which are formed by tiling the 2-dimensional Euclidean space with regular triangles, squares, and hexagons. The topology of the square grid is well-understood, but it cannot be said of the remaining two regular sampling schemes. This work deals with the topological properties of digital binary pictures sampled on the triangular grid. Some characterizations of simple pixels and sufficient conditions for topology preserving operators are reported. These results provide the theoretical background to various topological algorithms including thinning, shrinking, generating discrete Voronoi diagrams, and contour smoothing on the triangular grid.

Original languageEnglish
Pages (from-to)53-68
Number of pages16
JournalAnnals of Mathematics and Artificial Intelligence
Volume75
Issue number1-2
DOIs
Publication statusPublished - Jul 19 2014

Fingerprint

Topology Preservation
Triangular Grid
Topology
Grid
Mathematical operators
Pixels
Thinning
Voronoi Diagram
Shrinking
Sampling
Topological Properties
Tiling
Hexagon
Euclidean space
Smoothing
Triangle
Pixel
Binary
Sufficient Conditions
Operator

Keywords

  • Digital topology
  • Discrete geometry
  • Topology preservation
  • Triangular grid

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Topology preservation on the triangular grid. / Kardos, Péter; Palágyi, K.

In: Annals of Mathematics and Artificial Intelligence, Vol. 75, No. 1-2, 19.07.2014, p. 53-68.

Research output: Contribution to journalArticle

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