Evaluating the visual quality of watermarked images

A recent image quality measure, M-SVD, can express the quality of distorted images either numerically or graphically. Based on the Singular Value Decomposition (SVD), it consistently measures the distortion across different distortion types and within a given distortion type at different distortion levels. The SVD decomposes every real matrix into a product of three matrices A = USV, where U and V are orthogonal matrices, UU = I, VV = I and S = diag(s1, s2, ...). The diagonal entries of S are called the singular values of A, the columns of U are called the left singular vectors of A, and the columns of V are called the right singular vectors of A. M-SVD, as a graphical measure, computes the distance between the singular values of the original image block and the singular values of the distorted image block, where n x n is the block size. If the image size is k x k, we have (k/n) x (k/n) blocks. The set of distances, when displayed in a graph, represents a “distortion map.” The numerical measure is derived from the graphical measure. It computes the global error expressed as a single numerical value. In this paper, we will extend the SVD-based image quality measure to evaluate the visual quality of watermarked images using several watermarking schemes.