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
Anisotropy
Spatial point process
Ellipsoid
Non-parametric statistics
Author
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. 15 100-114Subject Categories
Mathematics
Geology
DOI
10.1016/j.spasta.2015.12.005