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 adapt models and algorithms to the task of correlating organoid images, i.e., quantifying the similarity in appearance and geometry of the organoids they depict, as well as to the task of clustering organoid images by consolidating conflicting correlations. Toward the correlation of organoid images, we compare two alternatives, a partial quadratic assignment problem and a twin network. Toward the clustering of organoid images, we apply 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.