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Different fingerprint recognition systems store minutiae-based fingerprint templates differently. Some store them inside a small token; some can be found in a server database. As the minutiae template is very compact, many take it for granted that the template does not contain sufficient information for reconstructing the original fingerprint. This paper proposes a scheme to reconstruct a full fingerprint image from the minutiae points based on the amplitude and frequency modulated (AM-FM) fingerprint model. The scheme starts with generating a binary ridge pattern which has a similar ridge flow to that of the original fingerprint. The continuous phase is intuitively reconstructed by removing the spirals in the phase image estimated from the ridge pattern. To reduce the artifacts due to the discontinuity in the continuous phase, a refinement process is introduced for the reconstructed phase image, which is the combination of the continuous phase and the spiral phase (corresponding to the minutiae). Finally, the refined phase image is used to produce a thinned version of the fingerprint, from which a real-look alike gray-scale fingerprint image is reconstructed. The experimental results show that our proposed scheme performs better than the-state-of-the-art technique.