On wavelet-based energy densities for spatial point processes

Abstract

A spatial point process can be considered a random measure and therefore represented as a countable sum of Delta Dirac measures concentrated at some points of the process. Applying a two-dimensional continuous wavelet transform of a point process, we analyse structural properties of the point process by defining new indicators based on partial energy densities. We obtain close forms for these indicators and use them to detect anisotropy in spatial point patterns.