Set Theoretic Quantization Index Modulation Watermarking

We introduce a set theoretic framework for quantization index modulation (QIM) watermarking and illustrate its potency by designing a semi-fragile watermark that is both visually adaptive and tolerant to compression. We determine the watermarked image to satisfy the multiple constraints of watermark detectability, imperceptibility and robustness to compression using the method of projections onto convex sets (POCS). Mark embedding is performed through implicit quantization of statistical features, specifically the mean, of randomly selected pixel locations from the image. This is accomplished by defining a detectability constraint set that imposes the quantization constraint. We present experimental results demonstrating the efficacy of the technique in the presence of JPEG compression