Spherical spatial statistics for 3D fluorescence video-microscopy

Recent work has revealed that, contrary to expectations, the protein machineries responsible for regulating cellular polarity in fission yeast cells localises cortically to the semi-spherical tips of each cell as punctual structures. To quantify this discovery and try and reconcile it with previous findings, a statistical co-localisation framework is set up. We use spatial statistics to analyse collections of punctual objects detected from deconvolved wide-field fluorescence microscopy images as point patterns from their respective spatial point processes. The theory is described for spherical data, as the structures of interest reside on a half-sphere in 3D. Uses include test of complete independence with Monte-Carlo hypothesis testing and comparison between pairs of point collections using bootstrap hypothesis testing. Evaluation on simulated data are performed on top of the targeted biological studies.