Since humans usually use contrast, color, and frequency changes in their image quality measures,22 the SSIM uses the luminance, contrast, and structure comparison shown in Fig. 1.8,22 The SSIM of two images and is defined by the combination of three components as follows:8Display Formula
(3)where , , and are the luminance, contrast, and structure comparison functions, respectively, defined by Display Formula
(6)where and denote the mean and the standard deviation of ; and denote the mean and the standard deviation of ; denotes the covariance between and ; and , , and are constants used to avoid instability when the denominators are very close to zero. The values of , , and are in [0, 1] and they indicate higher similarities for each comparison function when the values are close to 1. The local statistics are calculated within the local window having circular symmetric Gaussian weights, which are and as follows: Display Formula
(9)where is an index of the pixels in the Gaussian window and is the total pixel number of the Gaussian window.