Long-correlation image models for textures with circular and elliptical correlation structures

A class of random field model having long-correlation characteristics is introduced. Unlike earlier approaches in long-correlation models, the correlation structure is isotropic or elliptical in this new class of random field model. The new model has an advantage of modeling diverse real textures with less than five model parameters. Further, the model parameters match with intuitive attributes of textures, such as smoothness, pattern size, elongation or orientation of patterns. The new long-correlation models are based on the fractional differencing of a two-dimensional (2-D) autoregressive polynomial defined by eight symmetric neighbors, and they are either persistent or periodic models depending whether the roots of the polynomial are real or imaginary. A comprehensive three-step algorithm for parameter estimation is developed, and the statistical properties of the estimators are also discussed. The validity of the new model in modeling textures is tested by synthesizing images from manually selected parameters as well as parameters estimated from real textures. It is shown that an image with desired attributes can be synthesized by selecting proper values of the parameters. Further, it is shown that the models introduced can be used in modeling wide range of textures by synthesizing images resembling real textures from estimated parameters