Density of Events

The engine builds a continuous surface out of discrete cell positions in four steps:

1. Input. A coded imageLoading... supplies the detected events and their positions.
2. Kernel placement. At each pixel, a Gaussian kernel of the specified radius and standard deviation searches for nearby events. Closer events receive more weight, and events beyond the kernel radius contribute nothing.
3. Density computation. The weighted contributions of the nearby events add up to the density value at that pixel. Together the values form a smooth, continuous surface.
4. Border handling. Events from neighboring Fields of ViewLoading... (default: 100 pixels) are included, so the density does not drop artificially at tile boundaries.

The output is a grayscale image in which pixel brightness encodes local cell density.

Kernel density estimation (KDE): Density of Events is a spatial kernel density estimator, a standard statistical method for estimating a probability density function from point samples. Each cell centroid adds a Gaussian "bump" to the surface, and the bumps sum to a smooth estimate of the underlying density. The kernel bandwidth (standard deviation) sets the smoothing. If it is too small, every cell becomes its own isolated peak; if it is too large, local hotspots average away.

1/f noise and spatial correlation: Tissue architecture is correlated at all scales at once (Gardner's analysis of 1/f noise). Cell density is neither random like white noise nor smoothly varying; it is fractal-like, with clusters inside clusters. The kernel's scale sets which level of that hierarchy you see.

Spatial point processes: In spatial statistics, a set of cell positions is one realization of a spatial point process, and a completely random (Poisson) process has the same expected density everywhere. Real tissue departs from that, because cells cluster (immune aggregates, tumor nests) or repel each other (regularly spaced epithelial cells). Density of Events shows where tissue departs from an even spread: bright regions are crowded and dark regions sparse. Its output is a density map, not a significance test against a random pattern.

The tile boundary problem: StrataQuest processes whole-slide images in tiles, and at a tile's edge the cells of the adjacent tile are out of view, so density reads too low there. The border handling parameter corrects this by including events from neighboring FOVs, much like the border handling in nuclei detectionLoading....

Here is Ki-67 hotspot scoring in breast cancer:

1. Detect all nuclei and classify the Ki-67+ cells by gatingLoading....
2. Run Density of Events on the Ki-67+ coded image, with the kernel radius, which is set in pixels, chosen so the kernel spans a pathological "hotspot".
3. Find the peak density region in the density map.
4. Measure the Ki-67 positivity percentage within that hotspot region.

Scanning the slide by eye for "the most mitotically active area" is a judgment call. The density map finds the densest Ki-67+ region by a fixed rule, so repeated analyses of a slide return the same hotspot, whoever runs them.