Department of Mathematics
Given a spatial point pattern, we use various characteristics of its Voronoi diagram and Delaunay tessellation to extract information of the dependence between points. In particular, we use the characteristics to construct statistics for testing complete spatial randomness. It is shown that the minimum angle of a typical Delaunay triangle is sensitive to both regularity and clustering alternatives, whilst the triangle's area or perimeter is more sensitive to clustering than regularity. These statistics are also sensitive to the Baddeley-Silverman cell process.
Complete spatial randomness, Delaunay tessellation, goodness of fit, spatial point pattern, Voronoi diagram
Source Publication Title
This is the peer reviewed version of the following article: Chiu, S.N. (2003), Spatial Point Pattern Analysis by using Voronoi Diagrams and Delaunay Tessellations – A Comparative Study. Biom. J., 45: 367–376. doi:10.1002/bimj.200390018, which has been published in final form at http://dx.doi.org/10.1002/bimj.200390018. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Research supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project numbers HKBU 2075/98P and HKBU 2048/02P) and an FRG grant of the Hong Kong Baptist University.
Link to Publisher's Edition
Chiu, S. (2003). Spatial point pattern analysis by using Voronoi diagrams and Delaunay tessellations – A comparative study. Biometrical Journal, 45 (3), 367-376. https://doi.org/10.1002/bimj.200390018