In biological and medical research, scientists now routinely acquire microscopy images of hundreds of morphologically heterogeneous organoids and are then faced with the task of finding patterns in the image collection, i.e., subsets of organoids that appear similar and potentially represent the same morphological class. We adopt models and algorithms for correlating organoid images, i.e., for quantifying the similarity in appearance and geometry of the organoids they depict, and for clustering organoid images by consolidating conflicting correlations. For correlating organoid images, we adopt and compare two alternatives, a partial quadratic assignment problem and a twin network. For clustering organoid images, we employ the correlation clustering problem. Empirically, we learn the parameters of these models, infer a clustering of organoid images, and quantify the accuracy of the inferred clusters, with respect to a training set and a test set we contribute of state-of-the-art light microscopy images of organoids clustered manually by biologists.