Our team determined that the optimum statistic for comparing and evaluating two images is the SSIM. So is there another ideal criteria for comparing and evaluating the quality of images?
I’m afraid this type of questions is hard to answer, as comparing images is inherently subjective process. What is good in one situation, might be disaster in another. For example, this paper Limitations of the SSIM quality metric in the context of diagnostic imaging describes the poor performance of SSIM for some types of medical scans. Also, “comparing and evaluating the quality of images” requires a solid and formal definition of “quality of image”. For different definitions there might be different optimal techniques.