Wavelet-Based Solutions to the Digital Image Watermarking Problem

ly, a watermarking scheme is the six-tuple (X, W, K, G, E, D) where [13] 1. X represents the set of original or host images. 2. W is the set of all watermarks w such that ∃x ∈ X, k ∈ K, w = G(x, k). 3. K is the set of numbers called watermark keys. 4. G is the algorithm that generates W using K and X: G: X × K → W, w = G(x, k) 5. E denotes the encoding algorithm that embeds a watermark w in an image x with some strength α: E: X × W × R → X, xw = E(x, w, α) 6. D is the decoding algorithm that detects whether a watermark w is present in an image x: D: X × W → {0, 1}, D(x, w) =    otherwise 0 in exists if 1 x w A generic watermarking scenario is depicted in Figure 1. The watermark generator takes an original image x and a key k to generate the watermark w. The encoder then embeds w into x to produce a watermarked image xw. The watermarked image is distributed and potentially distorted by image processing operations and targeted watermark attacks. In the last stage of a watermarking scenario, the decoder attempts to ascertain the presence of the original watermark in the distorted image. 2.1.1. Watermark Encoding The watermark encoding algorithm, E, embeds a watermark either in the spatial or a transform domain of an image. Spatial domain watermarking schemes are generally more computationally efficient than the schemes operating in a transform domain. However, transform domain watermarks are far more resistant to various image processing attacks [1]. As a result, almost all recently proposed watermarking schemes operate in a transform domain. A generic transform domain encoder E(x, w, α) works as follows: 1. Let T be the transform in whose domain E operates. Compute T(x) to get transform coefficients v1, v2, ..., vn. 2. For each vi, 1 ≤ i ≤ n, compute vi′ = ƒ(vi, wi, α) 3. Output xw = T (v1′, v2′, ..., vn′) original image watermark watermarked image encoder distortions (image processing, noise, attacks, etc.) distorted image decoder (extractor + decider, detector, verifier, etc.) decision key