Anisotropy analysis of pressed point processes

Abstract

This paper introduces methods for the detection of anisotropies which are caused by compression of regular 3D point patterns. Isotropy tests based on directional summary statistics and estimators for the compression factor are developed. Using simulated data, the dependence of the power of these methods on the intensity, the degree of regularity, and the compression strength is studied. Finally, our methods are applied to the point patterns of centers of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet and an increase of their strength with increasing depth are shown

Statistical methods for identifying anisotropy in the Spodoptera frugiperda spatial distribution

“…Instead of counting all data points falling inside a circle of radius r centered at a data point, we could replace the circle by another geometrical shape (Baddeley et al, 2015). For a unit vector u, the conical directional K-function is defined as where λ is the intensity, and C u (r,θ) denotes a double cone in the direction u with an slant height of length r and an apex angle of size 2θ centered in 0 (Redenbach et al, 2009).…”

A three-dimensional anisotropic point process characterization for pharmaceutical coatings

“…An isotropy test based on replicated data was suggested in Redenbach et al (2009). Directional analyses can also be done by using wavelets (Mateu and Nicolis, 2012) or spectral theory (Møller and Toftaker, 2014;Mugglestone and 55 Renshaw, 1996).…”

“…A directed double cone was introduced as an alternative structure element in Redenbach et al (2009). In Safavimanesh and Redenbach (2016), the cylindrical K-function is compared to a conical alternative for three-dimensional 45 compressed or columnar point patterns, where the conical K-function appeared more suitable for compressed point patterns.…”

Modelling, Estimation and Applications of Second-Order Spatio-Temporal Characteristics of Point Processes

“…There are many varied forms of anisotropy. Orientation analysis is the quantification of the degree of anisotropy in the case of anisotropic point patterns and the detection of inner orientations in case of isotropy (Ohser and Stoyan (1981); Stoyan and Beneš (1991); Mateu (2000); Redenbach et al (2009)). Typical examples of oriented point patterns are patterns in which the points lie randomly in parallel strips of random or constant breadth (anisotropic case) or on an isotropic system of random fibres (inner orientation).…”

“…Harper and Macdonald (2001); Perry et al (2002)), but we can not find connections with spatiotemporal data. In general there is not a large treatment of anisotropy for spatial planar point patterns, and there is currently only one such approach for three-dimensional point patterns (Redenbach et al (2009)). …”