Modeling multiscale differential pixel statistics

The statistics of natural images play an important role in many image processing tasks. In particular, statistical assumptions about differences between neighboring pixel values are used extensively in the form of prior information for many diverse applications. The most common assumption is that these pixel difference values can be described be either a Laplace or Generalized Gaussian distribution. The statistical validity of these two assumptions is investigated formally in this paper by means of Chi-squared goodness of fit tests. The Laplace and Generalized Gaussian distributions are seen to deviate from real images, with the main source of error being the large number of zero and close to zero nearby pixel difference values. These values correspond to the relatively uniform areas of the image. A mixture distribution is proposed to retain the edge modeling ability of the Laplace or Generalized Gaussian distribution, and to improve the modeling of the effects introduced by smooth image regions. The Chi-squared tests of fit indicate that the mixture distribution offers a significant improvement in fit.