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Overlapped fingerprints are frequently encountered in latent fingerprints lifted from crime scenes. It is necessary to separate such overlapped fingerprints into component fingerprints so that existing fingerprint matchers can recognize them. The most crucial step in separating overlapped fingerprints is estimation of component orientation fields, which is a challenging problem for existing orientation field estimation algorithms. We propose a robust orientation field estimation algorithm (called the basic algorithm) for latent overlapped fingerprints whose core is the constrained relaxation labeling algorithm. We also propose improved versions of the basic algorithm for two special but frequent cases: 1) the mated template fingerprint of one component fingerprint is known and 2) the two component fingerprints are from the same finger. In both cases, further constraints are used to reduce ambiguity in relaxation labeling. Experimental results on both real and simulated overlapped fingerprints show that the proposed algorithm outperforms the state-of-the-art algorithm in both accuracy and efficiency. The two improved versions also perform better than the basic algorithm in respective cases. The latent overlapped fingerprint database collected for this study is made publicly available for performance evaluation.