On the duality of rate allocation and quality indices

In a recent work, the author proposed to study the performance of still image quality indices such as the SSIM by using them as objective function of rate allocation algorithms. The outcome of that work was not only a multi-scale SSIM optimal JPEG 2000 implementation, but also a first-order approximation of the MS-SSIM that is surprisingly similar to more traditional contrast-sensitivity and visual masking based approaches. It will be seen in this work that the only difference between the latter works and the MS-SSIM index is the choice of the exponent of the masking term, and furthermore, that a slight modification of the SSIM definition reproducing the traditional exponent is able to improve the performance of the index at or below the visual threshold. It is hence demonstrated that the duality of quality indices and rate allocation helps to improve both the visual performance of the compression codec and the performance of the index.