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This paper focuses on the matching of local features between images. Given a set of query descriptors and a database of candidate descriptors, the goal is to decide which ones should be matched. This is a crucial issue, since the matching procedure is often a preliminary step for object detection or image matching. In practice, this matching step is often reduced to a specific threshold on the Euclidean distance to the nearest neighbor. Our first contribution is a robust distance between descriptors, relying on the adaptation of the Earth Mover's Distance to circular histograms. It is shown that this distance outperforms classical distances for comparing SIFT-like descriptors, while its time complexity remains reasonable. Our second and main contribution is a statistical framework for the matching procedure, which yields validation thresholds automatically adapted to the complexity of each query descriptor and to the diversity and size of the database. The method makes it possible to detect multiple occurrences, as well as to deal with situations where the target is not present. Its performances are tested through various experiments on a large image database.