Award for 2009. It also received the IEEE Signal Processing Society Sustained Impact Award for 2016, indicative of a paper having an unusually high impact for at least 10 years following its publication. Because of its high adoption by the television industry, the authors of the original SSIM paper were each accorded a Primetime Engineering Emmy Award in 2015 by the Television Academy. Algorithm The SSIM index is calculated on various windows of an image. The measure between two windows and of common size is: with: the pixel sample mean of ; the pixel sample mean of ; the variance of ; the variance of ; the covariance of and ; , two variables to stabilize the division with weak denominator; the dynamic range of the pixel-values (typically this is ); and by default. Formula components The SSIM formula is based on three comparison measurements between the samples of and : luminance (), contrast () and structure (). The individual comparison functions are: with, in addition to above definitions: SSIM is then a weighted combination of those comparative measures: Setting the weights to 1, the formula can be reduced to the form shown above. Mathematical Properties SSIM satisfies the identity of indiscernibles, and symmetry properties, but not the triangle inequality or non-negativity, and thus is not a distance function. However, under certain conditions, SSIM may be converted to a normalized root MSE measure, which is a distance function. The square of such a function is not convex, but is locally convex and quasiconvex, making SSIM a feasible target for optimization. Application of the formula In order to evaluate the image quality, this formula is usually applied only on luma, although it may also be applied on color (e.g., RGB) values or chromatic (e.g. YCbCr) values. The resultant SSIM index is a decimal value between -1 and 1, where 1 indicates perfect similarity, 0 indicates no similarity, and -1 indicates perfect anti-correlation. For an image, it is typically calculated using a sliding Gaussian window of size 11x11 or a block window of size 8×8. The window can be displaced pixel-by-pixel on the image to create an SSIM quality map of the image. In the case of video quality assessment, the authors propose to use only a subgroup of the possible windows to reduce the complexity of the calculation. Variants Multi-Scale SSIM A more advanced form of SSIM, called Multiscale SSIM (MS-SSIM)