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Robust anatomical correspondence detection is a key step in many medical image applications such as image registration and motion correction. In the computer vision field, graph matching techniques have emerged as a powerful approach for correspondence detection. By considering potential correspondences as graph nodes, graph edges can be used to measure the pairwise agreement between possible correspondences. In this paper, we present a novel, hierarchical graph matching method with sparsity constraint to further augment the power of conventional graph matching methods in establishing anatomical correspondences, especially for the cases of large inter-subject variations in medical applications. Specifically, we first propose to measure the pairwise agreement between potential correspondences along a sequence of intensity profiles which reduces the ambiguity in correspondence matching. We next introduce the concept of sparsity on the fuzziness of correspondences to suppress the distraction from misleading matches, which is very important for achieving the accurate, one-to-one correspondences. Finally, we integrate our graph matching method into a hierarchical correspondence matching framework, where we use multiple models to deal with the large inter-subject anatomical variations and gradually refine the correspondence matching results between the tentatively deformed model images and the underlying subject image. Evaluations on both synthetic data and public hand X-ray images indicate that the proposed hierarchical sparse graph matching method yields the best correspondence matching performance in terms of both accuracy and robustness when compared with several conventional graph matching methods.