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Johannes Burge, Wilson Geisler; Optimal detection and estimation of defocus in natural images. Journal of Vision 2010;10(7):1382. doi: 10.1167/10.7.1382.
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© ARVO (1962-2015); The Authors (2016-present)
Defocus signals are important in many aspects of vision including accommodation, the estimation of scale, distance, and depth, and the control of eye growth. However, little is known about the computations visual systems use to detect and estimate the magnitude of defocus under natural conditions. We investigated how to optimally estimate defocus blur in images of natural scenes, given the optical systems of primates. First, we selected a large set of well-focused natural image patches. Next, we filtered each image patch with point-spread functions derived from a wave-optics model of the primate (human) eye at different levels of defocus. Finally, we used a statistical learning method, based on Bayesian ideal observer theory, to determine the spatial-frequency filters that are optimal for estimating retinal image defocus in natural scenes. We found that near the center of the visual field, the optimal spatial-frequency filters form a systematic set that is concentrated in the range of 5-15 cyc/deg, the range that drives human accommodation. Furthermore, we found that the optimal filters can be closely approximated by a linear combination of a small number of difference-of-Gaussian filters. Cells with such center-surround receptive field structure are commonplace in the early visual system. Thus, retinal neurons sensitive to this frequency range should contribute strongly to the retinal and/or post-retinal mechanisms that detect and estimate defocus. The optimal filters were also used to detect, discriminate, and identify defocus levels for 1 deg natural image patches. Consistent with human psychophysical data, detection thresholds were higher than discrimination thresholds. Also, once defocus exceeds 0.25 diopters, we found that 0.25 diopter changes in defocus can be identified with better than 86% accuracy. The estimated optimal filters are biologically plausible and provide a rigorous starting point for developing principled hypotheses for the neural mechanisms that encode and exploit optical defocus signals.
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