With the ever-increasing quality and quantity of imaging data in biomedical research comes the demand for computational methodologies that enable efficient and reliable automated extraction of the quantitative information contained within these images. One of the challenges in providing such methodology is the need for tailoring algorithms to the specifics of the data, limiting their areas of application. Here we present a broadly applicable approach to quantification and classification of complex shapes and patterns in biological or other multi-component formations. This approach integrates the mapping of all shape boundaries within an image onto a global information-rich graph and machine learning on the multidimensional measures of the graph. We demonstrated the power of this method by (1) extracting subtle structural differences from visually indistinguishable images in our phenotype rescue experiments using the endothelial tube formations assay, (2) training the algorithm to identify biophysical parameters underlying the formation of different multicellular networks in our simulation model of collective cell behavior, and (3) analyzing the response of U2OS cell cultures to a broad array of small molecule perturbations.