A review on anisotropy analysis of spatial point patterns

Authors

Affiliations

Tuomas Rajala

Chalmers University of Technology and the University of Gothenburg

Claudia Redenbach

University of Kaiserslautern

Aila Särkkä

Chalmers University of Technology and the University of Gothenburg

Martina Sormani

University of Kaiserslautern

Abstract

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for anisotropy analysis of (stationary) point patterns in \(\mathbb{R}^2\) and \(\mathbb{R}^3\). We discuss methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis. All techniques are illustrated on both a clustered and a regular example. Finally, we discuss methods for testing for isotropy as well as for estimating preferred directions in a point pattern.

Fig. 8. The anisotropic test sets for the conical (left) and cylindrical (right) K functions, overlaid on top of the Fry plot of the regular example pattern. (this explains everything)