Considers the problem of estimating parameters of multispectral random field (RF) image models using maximum likelihood (ML) methods. For images with an assumed Gaussian distribution, analytical results are developed for multispectral simultaneous autoregressive (MSAR) and Markov random field (MMRF) models which lead to practical procedures for calculating ML estimates. Although previous work has provided least squares methods for parameter estimation, the superiority of the ML method is evidenced by experimental results provided in this work. The effectiveness of multispectral RF models using ML estimates in modeling color texture images is also demonstrated.

Random field (RF) models have widespread application in image modeling and analysis. The effectiveness of these models is largely dependent on the choice of neighbor sets, which determine the spatial interactions that are represented by the model. We consider the problem of selecting these neighbor sets for simultaneous autoregressive and Gauss-Markov random field models, based on the correlation structure of the image to be modeled. A procedure for identifying appropriate neighbor sets is proposed, and experimental results which demonstrate the viability of this method are presented.

Multispectral extensions to the traditional gray level simultaneous autoregressive (SAR) and Markov random field (MRF) models are considered. Furthermore, a new image model is proposed, the pseudo-Markov model, which retains the characteristics of the multispectral Markov model, yet admits to a simplified parameter estimation method. These models are well-suited to analysis and modeling of color images. For each model considered, procedures are developed for parameter estimation and image synthesis. Experimental results, based on known image models and natural texture samples, substantiate the validity of thee results.

The long correlation (LC) models are a general class of random field (RF) models which are able to model correlations, extending 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 as a generalization of the SAR and MRF models.

We consider the problem of maximum likelihood estimation applied to multispectral random field image models, specifically the multispectral simultaneous autoregressive (MSAR) model. Although previous work has provided least squares methods for parameter estimation, the maximum likelihood method often produces better results. For images with an assumed Gaussian distribution we develop effective procedures for calculating these estimates. Through a series of experiments using known random field models and natural texture samples, the effectiveness of the maximum likelihood approach is demonstrated.

We develop multispectral random field image models for use in image processing applications. The simultaneous autoregressive and Markov random field (MRF) models have been widely used in modeling intensity images. In this work we extend these models to include the more general multispectral case where images are represented by multiple intensity planes. In particular, we focus on the obvious application to color texture modeling using the RGB color model. For each model type we present the model equations, develop methods for synthesizing images based on these models and procedures for estimating the model parameters. In addition, the conditions necessary to ensure model validity are identified. We also provide experimental results which, substantiate the validity of these results. Color images synthesized from these models are shown to have the statistical characteristics implied by the model equations and parameters estimated from these images are very close to the known values from which the images were generated. In further experiments color random field models were fitted to natural texture samples. Images synthesized from these models are observed to be visually similar to the original images.

Random field models have been successfully utilized in many applications requiring texture synthesis, classification, and segmentation. This class of models assumes each image pixel can be represented as a function of neighboring pixels and an additive noise sample. The effectiveness of these models is highly dependent on the choice of neighbor sets. Current approaches to selecting neighbor sets are based on ad-hoc methods. In the paper a systematic method which selects neighbor sets based on the correlation structure of texture images is presented and evaluated.>