Filtering Spatial Point Patterns Using Kernel Densities

Understanding spatial inhomogeneity and clustering in point patterns arises in many contexts, ranging from disease outbreak monitoring to analyzing radiologically-based emphysema in biomedical images. This can often involve classifying individual points as being part of a feature/cluster or as being part of a background noise process. Existing methods for this task can struggle when there are differences in the size and/or density of individual clusters. In this work, we propose employing kernel density estimates of the underlying point process intensity function, using an existing data-driven approach to bandwidth selection, to separate feature points from noise. This is achieved by constructing a null distribution, either through asymptotic properties or Monte Carlo simulation, and comparing kernel density estimates to a given quantile of this distribution. We demonstrate that our method, termed Kernel Density and Simulation based Filtering (KDS-Filt), showed superior performance to existing alternative approaches, especially when there is inhomogeneity in cluster sizes and density. We also show the utility of KDS-Filt for identifying clinically relevant information about the spatial distribution of emphysema in lung computed tomography scans. The KDS-Filt methodology is available as part of the sncp R package, which can be downloaded at https://github.com/stop-pre16/sncp.