Estimating geometric anisotropy in spatial point patterns
Abstract:
We present a two-stage non-parametric method for quantifying geometric anisotropy arising
for example when a point pattern is compressed or stretched. First, we fit ellipsoids to the pattern of
point-to-point distance 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
perform a simulation study in 2D to demonstrate the applicability of the method for regular patterns.
Finally, we apply the method to estimate the compression in 3D polar ice air bubble patterns.
Joint work with Tuomas Rajala, Claudia Redenbach and Martina Sormani.
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