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Due to the fact that objects of interest may be located at many possible locations in the environment, the capacity to efficiently visually search the environment for those objects is an essential visual capacity. The foveated nature of the human visual system requires that humans make fixations in rapid succession to locate targets. In this work, we develop a theory of foveated search for natural images and test the theory on simpler white noise backgrounds. The core of the theory takes advantage of recent work showing that suitably normalized template matching observers detecting targets with position known exactly are approximately optimal for detection in a wide variety of natural background conditions, and that they are consistent with human detection performance. In particular, detectability of targets has been shown to be proportional to a separable product of four factors: the background luminance, contrast …