Fast Optimized Cluster Algorithm for Localizations (FOCAL): a spatial cluster analysis for super-resolved microscopy

Motivation: Single-molecule localization microscopy (SMLM) microscopy provides images of cellular structure at a resolution an order of magnitude below what can be achieved by conventional diffraction limited techniques. The concomitantly larger data sets generated by SMLM require increasingly efficient image analysis software. Density based clustering algorithms, with the most ubiquitous being DBSCAN, are commonly used to quantitatively assess sub-cellular assemblies. DBSCAN, however, is slow, scaling with the number of localizations like O(n log (n)) at best, and it's performance is highly dependent upon a subjectively selected choice of parameters. Results: We have developed a grid-based clustering algorithm FOCAL, which explicitly accounts for several dominant artifacts arising in SMLM image reconstructions. FOCAL is fast and efficient, scaling like O(n), and only has one set parameter. We assess DBSCAN and FOCAL on experimental dSTORM data of clusters of eukaryotic RNAP II and PALM data of the bacterial protein H-NS, then provide a detailed comparison via simulation. FOCAL performs comparable and often superior to DBSCAN while yielding a significantly faster analysis. Additionally, FOCAL provides a novel method for filtering out of focus clusters from complex SMLM images.