Modeling textured images using generalized long correlation models

The long correlation (LC) models are a general class of random field (RF) models which are able to model correlations which extend over large image regions with few model parameters. The LC models have seen limited use, due to lack of an effective method for estimating the model parameters. In this work, we develop an estimation scheme for a very general form of this model and demonstrate its applicability to texture modeling applications. The relationship of the generalized LC models to other classes of RF models, namely the simultaneous autoregressive (SAR) and Markov random field (MRF) models, is shown. While it is known that the SAR model is a special case of the LC model, we show that the MRF model is also encompassed by this model. Consequently, the LC model may be considered a generalization of the SAR and MRF models.