Modeling of the texture structural components using 2-D deterministic random fields

The paper presents a unified texture model, which is applicable to a wide variety of texture types found in natural images. This model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and reconstruct the original texture field from these parameters. The model is highly motivated by findings about human vision. The texture field is assumed by a mixed spectral distribution. On the basis of a 2-D Wold like decomposition for homogeneous random fields, the texture field is decomposed into a sum of two mutually orthogonal components: a purely-indeterministic component and a deterministic component. The deterministic component is further orthogonally decomposed into a harmonic component, and a generalized-evanescent component. The purely- indeterministic component is represented by a 2-D, non-symmetrical-half-plane, finite support AR model. The harmonic random field is a sum of 2-D harmonic components of random amplitude and phase. The generalized evanescent field consists of a countable number of wave systems all traveling in directions of rational tangent, and all modulated by 1-D purely- indeterministic processes in the orthogonal dimension. Both analytical and experimental results show that the deterministic components should be parametrized separately from the purely- indeterministic component. The model is very efficient in terms of the number of parameters required to faithfully represent textures. Reconstructed textures are practically indistinguishable from the originals.