  Colocalization aims at characterizing spatial associations between two
fluorescently-tagged biomolecules by quantifying the co-occurrence and
correlation between the two channels acquired in fluorescence microscopy.
Colocalization is presented either as the degree of overlap between the two
channels or the overlays of the red and green images, with areas of yellow
indicating colocalization of the molecules. This problem remains an open issue
in diffraction-limited microscopy and raises new challenges with the emergence
of super-resolution imaging, a microscopic technique awarded by the 2014 Nobel
prize in chemistry. We propose GcoPS, for Geo-coPositioning System, an original
method that exploits the random sets structure of the tagged molecules to
provide an explicit testing procedure. Our simulation study shows that GcoPS
unequivocally outperforms the best competitive methods in adverse situations
(noise, irregularly shaped fluorescent patterns, different optical
resolutions). GcoPS is also much faster, a decisive advantage to face the huge
amount of data in super-resolution imaging. We demonstrate the performances of
GcoPS on two biological real datasets, obtained by conventional
diffraction-limited microscopy technique and by super-resolution technique,
respectively.
