Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances

Structural characteristics of random field threshold exceedance sets (e.g., size, connectivity, and boundary regularity) are used in practice for definition of different indicators in spatial and spatio-temporal risk analysis. In this work, point process techniques are applied to study the structural changes derived from random field deformations and blurring transformations, meaningful from both physical and methodological points of view in a variety of contexts. Specifically, based on simulations from a flexible random field model class, features such as aggregation/inhibition of patterns defined by centroids of connected components, as well as by boundary A-exit points, are investigated in relation to the local contraction/dilation effects of deformation and the smoothing properties of blurring. Supplementary materials accompanying this paper appear online.