  The Structural Similarity Index (SSIM) is generally considered to be a
milestone in the recent history of Image Quality Assessment (IQA). Alas, SSIM's
accepted development from the product of three heuristic factors continues to
obscure it's real underlying simplicity. 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. It seems that IQA researchers may now have two choices: 1) Continue to use
the complex SSIM formula, but noting that SSIM only works coincidentally since
the covariance term is actually the mean square error (MSE) in disguise. 2) Use
the simplest of all perceptually-masked image quality metrics, namely NVF or
DQ. On this choice Occam is clear: in the absence of differences in predictive
ability, the fewer assumptions that are made, the better.
