The high-resolution rate-distortion function under the structural similarity index

Authors:
Jan Østergaard;Milan S. Derpich;Sumohana S. Channappayya
Affiliations:
Department of Electronic Systems, Aalborg University, Alborg, Denmark;Department of Electronic Engineering, Federico Santa María Technical University, Valparaíso, Chile;PacketVideo Corporation, San Diego, CA
Venue:
EURASIP Journal on Advances in Signal Processing - Special issue on theory and application of general linear image processing
Year:
2011

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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.