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Random field models have arisen in important applications in many diverse fields, including image synthesis and analysis. The automatic description and processing of images is limited by the types of underlying models that are hypothesized for the image. Hence, new random field models and associated techniques are developed. The new class of models includes the traditional simultaneous autoregressive and moving average models, but extends these to comprise a substantially larger new class. Thus, new image textures are representable with convenient small-order parameterizations. In particular, representations with significant correlations between distant locations are achieved. The algorithms for synthesis and estimation, however, require only about the same amount of time as the classical models. The development is facilitated by a new mathematical formulation suitable for problems involving high-dimensional transformations.