We propose a new mathematical model for human fingerprint images. The model can be summarized by the phrase “fingerprints are holograms”. The model unifies the analysis, compression, classification, matching, and re‐synthesis of fingerprints, in a self‐consistent formalism. The parsimony of this model is demonstrated by the reconstruction of fingerprint images with extreme compression ratios (typically >200x). At the heart of the method is a recently proposed method for demodulating two‐dimensional fringe patterns, such as holograms. Demodulation uses a spiral‐phase quadrature transform combined with a two‐dimensional orientation estimator that also uses spiral‐phase Fourier operators. Finally, the fingerprint decomposition itself achieves compactness by splitting the phase modulation into two unique parts, one of which is a pure spiral‐phase function. Spiral‐phase inexorably emerges as a central theme of the work.

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