Structural similarity-based affine approximation and self-similarity of images revisited

Authors:
Dominique Brunet;Edward R. Vrscay;Zhou Wang
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada;Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada;Department of Electrical and Computer Engineering, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada
Venue:
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part II
Year:
2011

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Abstract

Numerical experiments indicate that images, in general, possess a considerable degree of affine self-similarity, that is, blocks are well approximated in root mean square error (RMSE) by a number of other blocks when affine greyscale transformations are employed. This has led to a simple L2-based model of affine image self-similarity which includes the method of fractal image coding (cross-scale, affine greyscale similarity) and the nonlocal means denoising method (same-scale, translational similarity). We revisit this model in terms of the structural similarity (SSIM) image quality measure, first deriving the optimal affine coefficients for SSIM-based approximations, and then applying them to various test images. We show that the SSIM-based model of self-similarity removes the "unfair advantage" of low-variance blocks exhibited in L2- based approximations. We also demonstrate experimentally that the local variance is the principal factor for self-similarity in natural images both in RMSE and in SSIM-based models.