A review on anisotropy analysis of spatial point patterns

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for anisotropy analysis of (stationary) point patterns in $\mathbf{R}^2$ and $\mathbf{R}^3$. We discuss methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis. All techniques are illustrated on both a clustered and a regular example. Finally, we discuss methods for testing for isotropy as well as for estimating preferred directions in a point pattern.Comment: Submitted to Spatial Statistics -journal's special issue of the Spatial Statistics 2017 conferenc

A continuous wavelet-based approach to detect anisotropic properties in spatial point processes

A two-dimensional stochastic point process can be regarded as a random measure and thus represented as a (countable) sum of Delta Dirac measures concentrated at some points. Integration with respect to the point process itself leads to the concept of the continuous wavelet transform of a point process. Applying then suitable translation, rotation and dilation operations through a non unitary operator, we obtain a transformed point process which highlights main properties of the original point process. The choice of the mother wavelet is relevant and we thus conduct a detailed analysis proposing three two-dimensional mother wavelets. We use this approach to detect main directions present in the point process, and to test for anisotropy