The High-Resolution Rate-Distortion Function under the Structural Similarity Index. (2nd November 2010) - Østergaard Østergaard, Jan Jan; Derpich Derpich, Milan S. Milan S.; Channappayya Channappayya, Sumohana S. Sumohana S.
Abstract : We show that the structural similarity (SSIM) index, which is used in image processing to assess the similarity between an image representation and an original reference image, can be formulated as a locally quadratic distortion measure. We, furthermore, show that recent results of Linder and Zamir on the rate-distortion function (RDF) under locally quadratic distortion measures are applicable to this SSIM distortion measure. We finally derive the high-resolution SSIM-RDF and provide a simple method to numerically compute an approximation of the SSIM-RDF of real images.