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Defocus blur is ubiquitous. When objects at one distance are in best focus, objects at other distances are blurred—the greater the distance from the best-focus distance the greater the defocus blur. Furthermore, even when objects are in best focus, there are other factors, including higher-order monochromatic aberrations, chromatic aberrations, and diffraction, which introduce blur and thereby reduce image quality. Although reduced image quality is generally undesirable, there are ways in which it may be useful. For instance, defocus blur could be used as a cue to depth. Specifically, if the level and sign of defocus blur can be estimated from the image of an object, then it is possible to estimate the distance of that object from the from best focus distance. In recent work, we have determined how to optimally estimate the defocus in images of natural scenes. We find that both the magnitude and sign of defocus can be …