The relative neighbourhood graph of a finite planar set
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(n 2) time and the other runs in 0(n 3) 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.
- Publication:
-
Pattern Recognition
- Pub Date:
- 1980
- DOI:
- 10.1016/0031-3203(80)90066-7
- Bibcode:
- 1980PatRe..12..261T
- Keywords:
-
- Relative neighbourhood graph;
- Minimal spanning tree;
- Triangulations;
- Delaunay triangulation;
- Dot patterns;
- Computational perception;
- Pattern recognition;
- Algorithms;
- Geometric complexity Geometric probability