We apply recent advances in machine learning and computer vision to a central problem in materials informatics: the statistical representation of microstructural images. We use activations in a pretrained convolutional neural network to provide a high-dimensional characterization of a set of synthetic microstructural images. Next, we use manifold learning to obtain a low-dimensional embedding of this statistical characterization. We show that the low-dimensional embedding extracts the parameters used to generate the images. According to a variety of metrics, the convolutional neural network method yields dramatically better embeddings than the analogous method derived from two-point correlations alone.