Estimating geometric anisotropy in spatial point patterns
Journal article, 2016

Anisotropy in stationary spatial point patterns is investigated. We develop a two-stage non-parametric method for quantifying geometric anisotropy arising for example when the pattern is compressed or stretched. First, we fit ellipsoids to the pattern of pairwise difference vectors to estimate the direction of anisotropy. Then, we estimate the scale of anisotropy by identifying the back-transformation resulting in the most isotropic pattern. We demonstrate the applicability of the method mainly for regular patterns by numerical examples, and use it to improve the estimation of compression in 3D polar ice air bubble patterns.

Polar ice


Spatial point process


Non-parametric statistics


Tuomas Rajala

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Aila Särkkä

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Claudia Redenbach

Technische Universität Kaiserslautern

Martina Sormani

Fraunhofer-Institut fur Techno- und Wirtschaftsmathematk

Technische Universität Kaiserslautern

Spatial Statistics

2211-6753 (ISSN)

Vol. 15 100-114

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