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Consider the problem of visually finding an object in a mostly unknown space with a mobile robot. It is clear that all possible views and images cannot be examined in a practical system. Visual attention is a complex phenomenon; we view it as a mechanism that optimizes the search processes inherent in vision. Here, we describe a particular example of a practical robotic vision system that employs some of these attentive processes. We cast this as an optimization problem, i.e., optimizing the probability of finding the target given a fixed cost limit in terms of total number of robotic actions required to find the visual target. Due to the inherent intractability of this problem, we present an approximate solution and investigate its performance and properties. We conclude that our approach is sufficient to solve this problem and has additional desirable empirical characteristics.