This paper proposes an efficient, blind, and robust data hiding scheme which is resilient to both geometric distortion and the general print-scan process, based on a near uniform log-polar mapping (ULPM). In contrast to performing inverse log-polar mapping (a mapping from the log-polar system to the Cartesian system) to the watermark signal or its index as done in the prior works, we apply ULPM to the frequency index ( u , v ) in the Cartesian system to obtain the discrete log-polar coordinate ( l ₁ , l ₂ ), then embed one watermark bit w ( l ₁ , l ₂ ) in the corresponding discrete Fourier transform coefficient c ( u , v ). This mapping of index from the Cartesian system to the log-polar system but embedding the corresponding watermark directly in the Cartesian domain not only completely removes the interpolation distortion and the interference distortion introduced to the watermark signal as observed in some prior works, but also largely expands the cardinality of watermark in the log-polar mapping domain. Both theoretical analysis and experimental results show that the proposed watermarking scheme achieves excellent robustness to geometric distortion, normal signal processing, and the general print-scan process. Compared to existing watermarking schemes, our algorithm offers significant improvement in terms of robustness against general print-scan, receiver operating characteristic (ROC) performance, and efficiency of blind resynchronization.

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