Understanding the multicellular organization of stem cells is vital for determining the mechanisms that coordinate cell fate decision-making during differentiation; these mechanisms range from neighbor-to-neighbor communication to tissue-level biochemical gradients. Current methods for quantifying multicellular patterning tend to capture the spatial properties of cell colonies at a fixed scale and typically rely on human annotation. We present a computational pipeline that utilizes topological data analysis to generate quantitative, multiscale descriptors which capture the shape of data extracted from 2D multichannel microscopy images. By applying our pipeline to certain stem cell colonies, we detected subtle differences in patterning that reflect distinct spatial organization associated with loss of pluripotency. These results yield insight into putative directed cellular organization and morphogen-mediated, neighbor-to-neighbor signaling. Because of its broad applicability to immunofluorescence microscopy images, our pipeline is well-positioned to serve as a general-purpose tool for the quantitative study of multicellular pattern formation.