Statistical estimation of the structural similarity index for image quality assessment

Abstract

The structural similarity (SSIM) index has been studied from different perspectives in the last decade. Most of the developments consider its parameters fixed. Because each of these parameters corresponds to the weight of a factor in the final SSIM coefficient, the usual assumption that all parameters are equal to one is questionable. In this article, a new estimation method is proposed from a statistical perspective. The approach we develop is a model-based estimation method so that the usual assumption that all parameters are equal to one can be handled via approximate hypothesis-testing techniques that are properly developed in the context of regression. The method considers nonlinear models with multiplicative noise to explain the root mean square error as a function of the SSIM index. A numerical experiment based on a Monte Carlo simulation is carried out to test whether the parameters are all equal to one and to gain more insight into the performance of the estimates in practice. Our analysis showed that the assumption that the parameters are equal to one is not supported by the data and may lead to a misconception of the closeness between two images.