Structural Similarity-Based Affine Approximation and Self-similarity of Images Revisited

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 L-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 Lbased 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.