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Brian McCann, Wilson Geisler, Mary Hayhoe; Effect of retinal ganglion cell sampling on the local power spectra of natural images. Journal of Vision 2009;9(8):1045. doi: 10.1167/9.8.1045.
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The retina encodes images with decreasing resolution as a function of eccentricity from the central fovea: ganglion cell density decreases rapidly with eccentricity and the receptive field size of ganglion cells increases rapidly with eccentricity. This architecture imposes substantial computational constraints on the downstream components of the visual system that are involved in estimating scene properties and in selecting eye movements. To understand these constraints it is important to characterize how spatial information extracted by the retina varies with eccentricity. To address this question we collected natural images with a 36 bit camera calibrated to the spectral responses of human photoreceptors and converted them 12 bit gray-scale images. We then estimated the responses of retinal ganglion P cells to the natural images using a model based directly on existing measurements of the optics of the human eye, the sampling density of human ganglion cells, and the receptive field parameters of macaque ganglion cells. Finally, we characterized the relative spatial information in the ganglion cell responses by measuring the local power spectra of the responses at various retinal eccentricities and comparing them to the local power spectra of the responses in the fovea. We find that (i) the local power spectra at all eccentricities are modeled well by a simple two-parameter formula: one parameter controlling the slope of the power spectrum as a function of spatial frequency, the other controlling the intercept (closely related to the overall power), (ii) the slope and intercept observed at any given eccentricity is quite predictive of the “true” (foveal) slope and intercept, and (iii) the uncertainty about the “true” (foveal) power spectrum grows with eccentricity. These natural scene statistics suggest hypotheses for how downstream mechanisms might compensate for the effects of retinal eccentricity and how they might select eye movements in natural tasks.
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