Tenacious tagging of images via Mellin monomials
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We describe a method for attaching persistent metadata to an image. The method can be interpreted as a template-based blind watermarking scheme, robust to common editing operations, namely: cropping, rotation, scaling, stretching, shearing, compression, printing, scanning, noise, and color removal. Robustness is achieved through the reciprocity of the embedding and detection invariants. The embedded patterns are real onedimensional Mellin monomial patterns distributed over two-dimensions. The embedded patterns are scale invariant and can be directly embedded in an image by simple pixel addition. Detection achieves rotation and general affine invariance by signal projection using implicit Radon transformation. Embedded signals contract to one-dimension in the two-dimensional Fourier polar domain. The real signals are detected by correlation with complex Mellin monomial templates. Using a unique template of 4 chirp patterns we detect the affine signature with exquisite sensitivity and moderate security. The practical implementation achieves efficiencies through fast Fourier transform (FFT) correspondences such as the projection-slice theorem, the FFT correlation relation, and fast resampling via the chirp-z transform. The overall method utilizes orthodox spread spectrum patterns for the payload and performs well in terms of the classic robustness-capacity-visibility performance triangle. Tags are entirely imperceptible with a mean SSIM greater than 0.988 in all cases tested. Watermarked images survive almost all Stirmark attacks. The method is ideal for attaching metadata robustly to both digital and analogue images.
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