The relative neighbourhood graph of a finite planar set

Research output: Contribution to journalArticle

Abstract

The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay (Voronoi) triangulation (DT). It is shown that the RNG is a superset of the MST and a subset of the DT. Two algorithms for obtaining the RNG of n points on the plane are presented. One algorithm runs in 0(n2) time and the other runs in 0(n3) time but works also for the d-dimensional case. Finally, several open problems concerning the RNG in several areas such as geometric complexity, computational perception, and geometric probability, are outlined.

Original languageEnglish (US)
Pages (from-to)261-268
Number of pages8
JournalPattern Recognition
Volume12
Issue number4
DOIs
StatePublished - Jan 1 1980

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Triangulation
Set theory
Computational complexity

Keywords

  • Algorithms
  • Computational perception
  • Delaunay triangulation
  • Dot patterns
  • Geometric complexity Geometric probability
  • Minimal spanning tree
  • Pattern recognition
  • Relative neighbourhood graph
  • Triangulations

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

Cite this

The relative neighbourhood graph of a finite planar set. / Toussaint, Godfried.

In: Pattern Recognition, Vol. 12, No. 4, 01.01.1980, p. 261-268.

Research output: Contribution to journalArticle

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