A new model for the spatial singularities component of the texture field and parameter estimation and synthesis procedures are presented. The spatial singularities field includes the local-structural components of the texture. The field is modeled by a 2-D compound Poisson-cliques model, after testing the fitness of the proposed model to the detected singularities field. According to this model the spatial singularities field is a 2-D point process where each of the events is a clique. The test of fit is based on a discrete version of the Kolmogorov-Smirnov test. In the analysis procedure the intensity of the 2-D point process is estimated, as well as the empirical distribution function of the clique occurrences. These parameters are then used to synthesize the singularities field.>

Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic one. The purely indeterministic component is shown to have a two-dimensional white-innovations driven MA representation. The two-dimensional deterministic random field can be perfectly predicted from the field's past samples. This field is further orthogonally decomposed into a purely deterministic field that represents the remote past of the field and can thus be perfectly predicted given enough arbitrarily located data samples, and an evanescent component. The evanescent component can be further decomposed into a remote columnwise past component and a column-to-column renewal field.>

A 2-D AR (autoregressive), finite-support, half-plane, causal model for homogeneous random fields is developed and applied to the analysis and synthesis of homogeneous random textures. The conditions under which the finite, discontinuous-support, 2-D Levinson type algorithm can be applied to solve the 2-D normal equations are presented. In the texture analysis case, these conditions are met by first removing all periodic components and subsequently applying a 2-D preemphasis filter. These steps also help reduce the required model order. It is shown that the resulting model is very efficient in terms of both the number of parameters required to achieve a good reconstructed texture (which is usually indistinguishable from the original) and good correlation match.>

A highly nonrestrictive model and procedure for texture analysis and synthesis are presented. The texture is modeled by three independent components: global structural, local structural and stochastic. The texture's global (directional and periodic) components are identified, parameterized and reconstructed through spectral analysis. Local structural components are extracted by parameterizing the line singularities. The stochastic component is modeled, analyzed and synthesized by a 2D half-plane finite-dimension autoregressive model. The model is very efficient in terms of the number of parameters required to represent and reconstruct a given texture faithfully.>

The pinned sine transform (PST) coder described is a practical approximation to the pinned KLT coder. The image is partitioned into two fields: a boundary field, which depends only on the coded block boundaries, and a pinned field, which vanishes at the boundaries and is subsequently sine transformed and compressed. The reconstructed image is continuous across the block boundaries and "blocking effects" are hardly visible. Simulation results are given for fixed and adaptive compression schemes with fair image quality at low bit rates down to 0.3 bits/pel.