Gaussian assumptions for the irradiance probability density in a digital image are often employed but rarely justified. We provide a mathematical justification for these assumptions and indicate the limitations of their use. Beginning with the context-dependent image ensemble considerations introduced by Hunt and Cannon [IEEE Trans. Syst. Man Cybern. SMC-6, 876 (1976)], such an ensemble is found to be accurately modeled as a Gaussian random process with nonstationary mean and nonstationary variance. An ensemble transformation is deduced and confirmed empirically that yields a Gaussian, zero-mean, unit-variance, ergodic random process. This conclusion leads to an image model that predicts that the distribution of image irradiance values after local mean removal is determined only by the distribution of local standard deviation values in the image. An analytic expression is derived for the probability density function of these irradiance values and is validated experimentally. This expression indicates that the distribution of image irradiance values after local mean removal may be assumed to be Gaussian only when the local standard deviation in an image is a nearly stationary quantity.
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