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In this paper, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction residuals. This interpretation leads to statistical tests more insightful than the original tests and makes the procedures computationally tractable. This paper also examines a computational structure tailored to one of the algorithms. In particular, we describe a processor based on systolic arrays that realizes the object detection algorithm developed in the paper.