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Progress in object and pattern recognition is based on progress in underlying theory from imaging science, computer vision, statistical signal processing, computational learning theory, and information theory. Information theory can be used both to bound the performance achievable in recognition systems subject to complexity constraints and to motivate system design. Many recognition systems are dynamic and must evolve or adapt to optimize performance subject to system constraints. Based on data collected and results of computations performed at any given time, dynamic resource allocation is a sequence of decisions on continuation or refinement of computational searches, redeployment of sensing resources, or halting. A common metric is the log-likelihood ratio. Any point in a computation involving a fixed quantity of data may be viewed as defining an approximate data model with a corresponding log-likelihood function. Any further computations or data collections yield alternative, refined models. The expected increase in the log-likelihood function equals the relative entropy between the refined approximate model and the current approximate model. Bounds on this relative entropy may be used in design criteria for dynamic resource allocation.