Many of the useful properties of modern engineering materials are determined by the material's microstructure. Controlling the microstructure requires an understanding of the complex dynamics underlying its evolution during processing. Investigating the thermal and mass transport phenomena responsible for a structure requires establishing a common language to quantitatively represent the microstructures being examined. Although such a common language exists for some of the simple structures, which has allowed these materials to be engineered, there has yet to be a method to represent complex systems, such as the ternary microstructures, which are important for many technologies. Here we show how stereological and data science methods can be combined to quantitatively represent ternary eutectic microstructures relative to a set of exemplars that span the stereological attribute space. Our method uniquely describes ternary eutectic microstructures, allowing images from different studies, with different compositions and processing histories, to be quantitatively compared. By overcoming this long-standing challenge, it becomes possible to begin to make progress toward a quantitatively predictive theory of ternary eutectic growth. We anticipate that the method of quantifying instances of an object relative to a set of exemplars spanning attribute-space will be broadly applied to classify materials structures, and may also find uses in other fields.