Topology preservation on the triangular grid

Péter Kardos, Kálmán Palágyi

Research output: Contribution to journalArticle

12 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 - Oct 22 2015

Keywords

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

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

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