2-D autoregressive, finite support, causal model for texture analysis and synthesis

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.