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Near Perfect Correlation Functions Based on Zero-Sum Projections

Minimal projective ghost functions make good watermark labels for embedding into images. Although fragile to hacking attacks, they are near-to-invisible because of their distributed, random appearance and their binary, zero-mean statistics. They have the strong correlation properties needed to extract a low-intensity watermark from bright image data. We present a method to embed, concurrently, up to (p-1)/2 independent minimal ghosts within the same pxp image space, where p is prime. Compounding ghosts inside the same pxp space increases, by (p-1)/2, the robustness with which these watermarks can be recovered. This result then approaches the optimal peak correlation result obtainable using 2D perfect or near-perfect sequences. However, unlike perfect sequences, minimal ghosts are simple to construct and compound. A large number of independent compounded minimal ghosts can be generated for each prime p, thus each watermark is sufficiently individual to prevent confusion when multiple labels are present.