Geodesic
Comparative analysis of the SSIM index and the pearson coefficient as a criterion for image similarity
Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 1, pp. 76-90.

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In this paper,the SSIM index, which is the most popular measure of the structural image is studied. A mathematical proof that the SSIM index and its linear transformations are not metric functions is given. We demonstrated that this index, as well as any full-reference image comparison function, cannot evaluate the image quality. These functions estimate only some similarity degree between a reference image and its distorted copy. It is proved experimentally that the SSIM index does not always correctly determine similarity of images of the same scene. The Pearson linear correlation is a better tool for similarity analysis and it is faster to calculate. It is experimentally demonstrated that the Pearson correlation better than the SSIM index coincides with the subjective MOS image estimates. It is shown that the Pearson correlation coefficient is non-linearly related to the Euclid metric, but no any linear transformation of the coefficient can be a metric function. Our study proves that the Pearson correlation coefficient is superior to the SSIM index when evaluating image similarity.
Keywords: Image similarity, Image quality, SSIM index, MOS, Metric, Pearson correlation. 
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     title = {Comparative analysis of the {SSIM} index and the pearson coefficient as a criterion for image similarity},
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V. V. Starovoytov; E. E. Eldarova; K. T. Iskakov. Comparative analysis of the SSIM index and the pearson coefficient as a criterion for image similarity. Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 1, pp. 76-90. http://geodesic.mathdoc.fr/item/EJMCA_2020_8_1_a4/