Improvement to a Method of Embedding Robust Watermarks into Digital Color

nearly zero. (3) A watermark is randomized so that a pattern of cyclic cross stripes may disappear and an embedded watermark may be inconspicuous. The embedded watermark is extracted by multiplying the conversely randomized image embedding a watermark by the random sequence. (4) An ID pattern is extracted by summing up the products of any part of the random sequence and the corresponding part of a watermark-embedded image so that the ID pattern may correctly extracted. 2. Embedding Method We consider embedding an ID pattern into a color image X (a) = {x ij (a) } with nxm pixels, where (a) denotes color components (a = R, G and B). The ID pattern is a sequence of length h consisting of +1 and –1, where h divides m. Let P be a sequence of length m which is an arrangement of the same m/h ID patterns. We spread the sequence P into an nxm two-dimensional pattern W, which is a watermark, by a random sequence K of length n consisting of real number from –1 to 1 as follows: W K P k p k p k p k p k p T m i j n n m = = ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅           1 1 1 1 (1) where K = (k 1 , k 2 , ···, k n) (–1 ≤ k i ≤ 1), P = (p 1 , p 2 , ···, p m) (p j = +1 or –1) and T represents transpose. As the pattern W is cyclic cross stripes, W is randomized into W'. The pattern W' = {w' ij } is weighted in order to heighten robustness with preserving quality and added to an image as {x ij (a) + A (a) w' ij }, where A (a) is a constant value depending on the SN ratio of a watermark-embedded image. The elements {x ij (a) + A (a) w' ij } of a watermark-embedded image are quantized into integers. We conversely randomize the watermark-embedded image Y (a) = {x ij (a) + A (a) w' ij } into Y' (a) = {x' ij (a) + A (a) w ij } and extract the arrangement P of the ID pattern by multiplying Y' (a) by the random sequence K which is used in Eq.(1), where {x' ij (a) } is a …