Generalization of the two-dimensional random checkerboard process

A generalization of the two-dimensional random checkerboard process is described and a complete statistical characterization of its second-order properties provided. In particular, we allow arbitrary correlation between the intensities or gray levels in contiguous square regions. The construction procedure is shown to result in a homogeneous and isotropic two-dimensional random field. Explicit evaluation of the autocorrelation function and power spectral density are provided. The resulting random field provides a useful model for a variety of image processing applications. Several applications are discussed.