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Contactless fingerprint recognition is highly promising and an essential component in the automatic fingerprint identification system. However, due to the inherent characteristic of perspective distortions of contactless fingerprints, achieving a highly accurate contactless fingerprint recognition system is very challenging. In this paper, we propose a robust contactless fingerprint recognition method based on global minutia topology and loose genetic algorithm. In order to avoid the inaccurate minutiae alignment problem suffered in conventional transformation-based methods, the minutiae correspondence is established by optimizing an energy function of the similarity matrix. We define an innovative similarity matrix based on both minutiae and minutia-pairs, which takes the global minutia topology into account. By adopting a distortion-free feature of ridge count to define the similarity, the problem of perspective distortions is effectively overcome. To solve the optimization, we propose a new genetic algorithm (GA) named loose GA with new mutation and crossover operators. We also propose a strict minutia-pair expanding algorithm to enhance the reliability of the minutiae correspondence. For recognition, a metric for measuring comparison scores which takes advantage of both the global topological similarity and the number of corresponding minutiae is proposed. We evaluate our method using two contactless fingerprint benchmark databases and achieve competitive performances in comparison with the state-of-the-art methods.