KCBC - a correlation-based method for co-localization analysis of super-resolution microscopy images using bivariate Ripley's functions.

Motivated by the high demand for co-localization analysis methods for super-resolution microscopy images which are featured with nanoscale precise locational information of molecules, this paper establishes a novel correlation-based method, KCBC, named after the Coordinated-Based Colocalization (CBC) method proposed by Malkusch in 2012, by using bivariate Ripley's functions. The local KCBC values are to quantify the local spatial co-localization of molecules between two species by measuring the correlation of bivariate Ripley's functions over equal-area concentric rings around the base species within a near distance. The mean of local KCBC values is proposed to quantify the co-localization degree of cross-channel to base-channel molecules for the whole image. It could effectively correct the false positives with reduced variance and increased power within the user-defined proximity size. We provide extensive simulation studies under different scenarios to demonstrate the unbiasedness of the KCBC method, and its ability to filter noise signals and random over-counting. Our real data application for super-resolution mitochondria image data illustrates the applicability of our methods with increased effectiveness and power.