In a recent study of spatial-frequency discrimination [ J. Opt. Soc. Am. 72, 1367 ( 1982)], we reported evidence for the quantization of position in the human visual system with the fundamental unit of quantization being the photo-receptor spacing for spatial frequencies greater than 2 cycles per degree (c/deg). In this paper we extend our measurements to lower spatial frequencies, between 0.3 and 2, which we call the mid-spatial-frequency band, and find that this band of spatial frequencies shows similar evidence for spatial quantization. However, the spacing of the fundamental unit is about 0.056 deg or approximately seven or eight times the spacing of the foveal photoreceptor instead of about 0.008 deg or approximately equal to the spacing of foveal cones. We interpret this as evidence for a class of retinal receptive fields that we call spatial-sampling fields that perform a dual function of neural blurring and spatial sampling. We propose a scaled lattice model of spatial vision that allows apparently scale-free spatial processing while retaining the advantages of linear maps. The model generalizes the notion of hyperacuity to low-resolution tasks for which neural interpolation occurs not only on the photoreceptor sampling lattice to achieve hyperacuity but also on receptive-field sampling lattices to achieve lower resolutions.
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