Three-parameter probability distribution density for statistical image analysis

Statistical analysis of 2-D image data or data gathered from a scanning radiometer requires that both the non-Gaussian nature and finite sample size of the process be considered. To aid the statistical analysis of this data, a higher moment description density function has been defined, and parameters have been identified with the estimated moments of the data. It is shown that the first two moments may be computed from a knowledge of the Weiner spectrum, whereas all higher moments require the complex spatial frequency spectrum. Parameter identification is carried out for a three-parameter density function and applied to a scene in the IR region, 8-14 microns. Results indicate that a three-parameter distribution density generally provides different probabilities than does a two-parameter Gaussian description if maximum entropy (minimum bias) forms are sought.