Correlation analysis framework for localization-based superresolution microscopy

Significance Correlation analysis is one of the most widely used image-processing methods. In the quantitative analysis of localization-based superresolution images, there still lacks a generalized coordinate-based correlation analysis framework to take full advantage of the superresolution information. We propose a coordinate-based correlation analysis framework for localization-based superresolution microscopy. We mathematically prove that point-point distance distribution is equivalent to pixel-based correlation function. This framework can be easily extended to model the effect of localization uncertainty, to the time domain and other distance definitions. We demonstrated the versatility and advantages of our framework in three applications of superresolution microscopy: model-free image alignment and averaging for structural analysis, spatiotemporal correlation analysis for mapping molecule diffusion, and quantifying spatial relationships between complex structures. Superresolution images reconstructed from single-molecule localizations can reveal cellular structures close to the macromolecular scale and are now being used routinely in many biomedical research applications. However, because of their coordinate-based representation, a widely applicable and unified analysis platform that can extract a quantitative description and biophysical parameters from these images is yet to be established. Here, we propose a conceptual framework for correlation analysis of coordinate-based superresolution images using distance histograms. We demonstrate the application of this concept in multiple scenarios, including image alignment, tracking of diffusing molecules, as well as for quantification of colocalization, showing its superior performance over existing approaches.