A review on anisotropy analysis of spatial point patterns
Review article, 2018

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 ℝ2 andℝ3. 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.


Spectral analysis

Second-order characteristics

Fry plot

Spatial summary statistics


Tuomas Rajala

University College London (UCL)

Claudia Redenbach

Technische Universität Kaiserslautern

Aila Särkkä

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

M. Sormani

Technische Universität Kaiserslautern

Fraunhofer-Institut fur Techno- und Wirtschaftsmathematk

Spatial Statistics

2211-6753 (ISSN)

Vol. 28 141-168

Subject Categories

Economic Geography

Probability Theory and Statistics

Signal Processing



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