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 L 2-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 L 2-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.
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Brunet, D., Vrscay, E.R., Wang, Z. (2011). Structural Similarity-Based Affine Approximation and Self-similarity of Images Revisited. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2011. Lecture Notes in Computer Science, vol 6754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21596-4_27
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DOI: https://doi.org/10.1007/978-3-642-21596-4_27
Publisher Name: Springer, Berlin, Heidelberg
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