  Colocalization analysis aims to study complex spatial associations between
bio-molecules via optical imaging techniques. However, existing colocalization
analysis workflows only assess an average degree of colocalization within a
certain region of interest and ignore the unique and valuable spatial
information offered by microscopy. In the current work, we introduce a new
framework for colocalization analysis that allows us to quantify colocalization
levels at each individual location and automatically identify pixels or regions
where colocalization occurs. The framework, referred to as spatially adaptive
colocalization analysis (SACA), integrates a pixel-wise local kernel model for
colocalization quantification and a multi-scale adaptive propagation-separation
strategy for utilizing spatial information to detect colocalization in a
spatially adaptive fashion. Applications to simulated and real biological
datasets demonstrate the practical merits of SACA in what we hope to be an
easily applicable and robust colocalization analysis method. In addition,
theoretical properties of SACA are investigated to provide rigorous statistical
justification.
