A correlation analysis framework for localization-based super-resolution microscopy

Super-resolution 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 super-resolution 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. Significance statement Correlation analysis is one of the most widely used image processing method. In the quantitative analysis of localization-based super-resolution images, there still lacks a generalized coordinate-based correlation analysis framework to take fully advantage of the super-resolution information. We show a coordinate-based correlation analysis framework for localization-based super-resolution microscopy. This framework is highly general and flexible in that it can be easily extended to model the effect of localization uncertainty, to the time domain and other distance definitions, enabling it to be adapted for a wide range of applications. Our work will greatly benefit the quantitative interpretation of super-resolution images and thus the biological application of super-resolution microscopy.