Abstract: In this paper, we address the few-shot classification task from a new perspective of optimal matching between image regions. We adopt the Earth Mover's Distance (EMD) as a metric to compute a structural distance between dense image representations to determine image relevance. The EMD generates the optimal matching flows between structural elements that have the minimum matching cost, which is used to represent the image distance for classification. To generate the important weights of elements in the EMD formulation, we design a cross-reference mechanism, which can effectively minimize the impact caused by the cluttered background and large intra-class appearance variations. To handle k-shot classification, we propose to learn a structured fully connected layer that can directly classify dense image representations with the EMD. Based on the implicit function theorem, the EMD can be inserted as a layer into the network for end-to-end training. We conduct comprehensive experiments to validate our algorithm and we set new state-of-the-art performance on four popular few-shot classification benchmarks, namely miniImageNet, tieredImageNet, Fewshot-CIFAR100 (FC100) and Caltech-UCSD Birds-200-2011 (CUB).