Structural Similarity Index SSIMplified:

Starting instead from a symmetric-antisymmetric reformulation we first show SSIM to be a contrast or visibility function in the classic sense. Furthermore, the previously enigmatic structural covariance is revealed to be the difference of variances. The second step, eliminating the intrinsic quadratic nature of SSIM, allows a near linear correlation with human observer scores, and without invoking the usual, but arbitrary, sigmoid model fitting. We conclude that SSIM can be re-interpreted in terms of perceptual masking: it is essentially equivalent to a normalised error or noise visibility function (NVF), and, furthermore, the NVF alone explains it success in modelling perceptual image quality. We use the term Dissimilarity Quotient (DQ) for the specifically anti/symmetric SSIM derived NVF.