Multichannel microscopy has emerged as a technique for imaging multiple targets (molecules, protein distributions, etc.) simultaneously. Discovering the relative changes in these targets (i.e. distribution of different proteins) is fundamental for understanding cell structure and function. We describe a new method for quantifying and visualizing relationships between multiple targets, from a set of segmented multichannel cells. The method is based on combining the canonical correlation analysis technique with a framework for analyzing images based on the concept of optimal mass transportation. We apply the method towards understanding chromatin distribution in cancer nuclei as a function of nuclear envelope shape. We also show that sub cellular distribution of mitochondria can be used to predict the sub cellular localization of actin fibers in yeast cells. Finally, we also describe the application of the method towards understanding relationships between nuclear and cellular shapes in 2D HeLa cells. We believe that the method could serve as a general tool for mining relationships between different sub cellular protein/molecule distributions as well as organelle shapes.