Kernel density estimation (KDE): Density of Events implements a spatial kernel density estimator — a standard statistical technique for estimating a probability density function from a set of point samples. Each cell centroid contributes a Gaussian "bump" to the density surface, and the sum of all bumps produces a smooth estimate of the underlying density function. The kernel bandwidth (standard deviation) controls the smoothing: too small and the estimate is noisy (every cell creates its own isolated peak); too large and the estimate is over-smoothed (local hotspots are averaged away).
1/f noise and spatial correlation: Gardner's analysis of 1/f noise reveals that natural spatial patterns — including tissue architecture — exhibit correlations at all scales simultaneously. Cell density in tissue is not random (white noise) nor smoothly varying (low-frequency only), but fractal-like: clusters within clusters across scales. The Gaussian kernel smoothing scale determines which level of this hierarchy you observe — small kernels reveal individual cell clusters, large kernels reveal regional density trends.
Spatial point processes: In spatial statistics, a collection of cell positions is a realization of a spatial point process. A completely random (Poisson) point process produces uniform expected density everywhere. Real tissue departs from this — cells cluster (immune aggregates, tumor nests) or repel (regularly spaced epithelial cells). Density of Events quantifies this departure: regions significantly denser than the Poisson expectation contain true clusters; regions significantly sparser contain true voids.
The tile boundary problem: StrataQuest processes whole-slide images in tiles (Fields of View). At tile boundaries, cells in the adjacent tile are invisible, causing the density computation to underestimate local density at the edges. The border handling parameter (including events from neighboring FOVs) corrects this boundary artifact — analogous to the border handling in nuclei detection.
Density estimation is a standard statistical technique that converts discrete points (cell positions) into a smooth surface (density map). The key parameter is the kernel size — too small and you see noise, too large and you lose local detail. The density map reveals tissue architecture: clusters of immune cells, dense tumor nests, sparse stromal regions, all quantified objectively rather than subjectively.
