A wavelet-based approach to quantify the anisotropy degree of spatial random point configurations

Abstract

A two-dimensional point process, if considered as a random measure, can be expressed as a countable sum of Delta Dirac measures concentrated at some random points. Then a continuous wavelet transform can be applied to obtain information on some structural properties. We introduce the notions of wavelet-based isotropy, main anisotropy direction and anisotropy degree to characterize the implicit anisotropic structure of the point process. We propose several statistical hypothesis tests that are proved to be useful to test for the presence of anisotropy. An application to a real case is also included.