A review on anisotropy analysis of spatial point patterns

TL;DR

This paper reviews nonparametric methods for analyzing anisotropy in spatial point patterns, covering techniques based on summary statistics, spectral, and wavelet analysis, with applications to real examples and testing procedures.

Contribution

It provides a comprehensive overview of existing nonparametric anisotropy analysis methods for stationary point patterns in two and three dimensions.

Findings

Illustrated methods on clustered and regular patterns

Discussed testing for isotropy and estimating directions

Compared various spectral and wavelet techniques

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 $\mathbf{R}^2$ and $\mathbf{R}^3$. 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.