We introduce a set theoretic framework for watermarking and illustrate its effectiveness by designing a hierarchical semi-fragile watermark that is tolerant to compression and allows tamper localization. Using a quad-tree representation, a spatial resolution hierarchy is established on the image and a watermark is embedded corresponding to each node of the hierarchy. The watermarked image is determined so as to jointly satisfy the multiple constraints of watermark detectability, imperceptibility, and robustness to compression using the method of projections onto convex sets. The spatial hierarchy of watermarks provides a graceful trade-off between robustness and localization under JPEG compression: mild JPEG compression preserves watermarks at all levels of the hierarchy allowing fine localization of malicious changes while aggressive JPEG compression preserves watermarks at coarser levels of the hierarchy still assuring overall image integrity but giving up the capability for localization. Experimental results are presented to illustrate the effectiveness of the method.
Steganographic methods attempt to insert data in multimedia signals in an undetectable fashion. However, these methods often disrupt the underlying signal characteristics, thereby allowing detection under careful steganalysis. Under repeated embedding, disruption of the signal characteristics is the highest for the first embedding and decreases subsequently. That is, the marginal distortions due to repeated embeddings decrease monotonically. We name this general principle as the principle of diminishing marginal distortions (DMD) and illustrate its validity in the audio domain using a morphological distortion metric. The principle of DMD is used to derive a steganalysis tool that detects the presence of hidden messages in uncompressed audio files. Detailed analysis and experimental results are provided for the detection of spread spectrum watermarking and stochastic modulation steganography.
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.
We introduce an optimum watermark embedding technique that satisfies common watermarking requirements such as visual fidelity, sufficient embedding rate, robustness against noise and tolerance to benign signal processing, while optimizing one of these requirements. The algorithm distinguishes itself from other watermark optimization techniques in its flexibility for incorporating constraints and in assuring convergence to the globally optimum point when all constraints are convex. The proposed scheme is a natural extension of set-theoretic watermark design and inherits all the advantages of it. A watermarked image is first obtained by POCS, then optimum watermarked image is determined by an iterative search procedure based on a simple bi-section method. Experimental results are presented to illustrate the effectiveness of the method.Index Terms-Optimum watermark embedding, set theoretic watermark, POCS, vector space projections, spreadspectrum watermark
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