LIMITATIONS OF GAUSSIAN ASSUMPTIONS FOR THE IRRADIANCE DISTRIBUTION IN DIGITAL IMAGERY - NONSTATIONARY IMAGE ENSEMBLE CONSIDERATIONS

Gaussian assumptions for the irradiance probability density in a digit al image are often employed but rarely justified. We provide a mathema tical justification for these assumptions and indicate the limitations of their use. Beginning with the context-dependent image ensemble con siderations introduced by Hunt and Cannon [IEEE Trans. Syst. Man Cyber n. SMC-6, 876 (1976)], such an ensemble is found to be accurately mode led as a Gaussian random process with nonstationary mean and nonstatio nary variance. An ensemble transformation is deduced and confirmed emp irically that yields a Gaussian, zero-mean, unit-variance, ergodic ran dom process. This conclusion leads to an image model that predicts tha t the distribution of image irradiance values after local mean removal is determined only by the distribution of local standard deviation va lues in the image. An analytic expression is derived for the probabili ty density function of these irradiance values and is validated experi mentally. This expression indicates that the distribution of image irr adiance values after local mean removal may be assumed to be Gaussian only when the local standard deviation in an image is a nearly station ary quantity. (C) 1998 Optical Society of America.