Mystery behind similarity measures mse and SSIM

Similarity or distance measures play an important role in various pattern recognition applications such as classification, clustering, change detection, information retrieval, energy minimization and optimization problems. We shall analyze theoretically the two most popular quality measures MSE and SSIM used in image processing by showing their origin, similarities/differences and advantages/drawbacks. Both measures depend on the same parameters: sample means, standard deviations and correlation coefficient. It is shown that SSIM originates from two Dice measures and thus inherit their main drawback - dependence on the absolute mean and standard deviation values. Similarly, MSE depends on the absolute standard deviation values. A new similarity measure Composite quality index based on Means, Standard deviations and Correlation coefficient (CMSC) is proposed inheriting advantages of the both measures but at the same time avoiding their drawbacks.