Random image syntheses by using a narrow band long-correlation model

This paper presents an extension of the isotropic long-correlation (LC) image model named “narrow band” LC model. Normarlly, the isotropic or the anisotropic LC model whose single spectral peak position is located at the origin is used as an image model. These models are not suitable to describe random images with periodicity. The spectral density of the proposed model has two spectral peaks, which are located at symmetric position with respect to the origin. The spectral peak position is determined by a pair of the parameters in the spatial frequency domain and the spread of the spectral density at each peak position is controlled by the index of the fractional differencing. By adjust this index, various images with any strength of periodicity can be synthesized. The parameter estimations of the proposed narrow band LC model are also performed based on the nonlinear minimization of a criterion that indicates the whiteness of the output image of the model.