Follicular lesions of the thyroid remain significant diagnostic challenges in surgical pathology and cytology. The diagnosis often requires considerable resources and ancillary tests including immunohistochemistry, molecular studies, and expert consultation. Visual analyses of nuclear morphological features, generally speaking, have not been helpful in distinguishing this group of lesions. Here we describe a method for distinguishing between follicular lesions of the thyroid based on nuclear morphology. The method utilizes an optimal transport-based linear embedding for segmented nuclei, together with an adaptation of existing classification methods. We show the method outputs assignments (classification results) which are near perfectly correlated with the clinical diagnosis of several lesion types’ lesions utilizing a database of 94 patients in total. Experimental comparisons also show the new method can significantly outperform standard numerical feature-type methods in terms of agreement with the clinical diagnosis gold standard. In addition, the new method could potentially be used to derive insights into biologically meaningful nuclear morphology differences in these lesions. Our methods could be incorporated into a tool for pathologists to aid in distinguishing between follicular lesions of the thyroid. In addition, these results could potentially provide nuclear morphological correlates of biological behavior and reduce health care costs by decreasing histotechnician and pathologist time and obviating the need for ancillary testing.