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Jeremy Freeman, Eero Simoncelli; The radial and tangential extent of spatial metamers. Journal of Vision 2013;13(9):573. doi: 10.1167/13.9.573.
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© ARVO (1962-2015); The Authors (2016-present)
Crowding provides a striking example of the limits of peripheral vision: objects are unrecognizable when spaced closer together than half their eccentricity. It has been suggested that crowding arises because the visual system summarizes spatial information in the periphery statistically (Parks et al., 2001; Pelli & Tillman; 2008; Balas, Nakano, & Rosenholtz, 2009). To test this hypothesis, we previously developed a physiologically-inspired model, in which an image is represented by receptive fields that tile the visual field, grow in size with eccentricity, and combine inputs from primary visual cortex (V1) to represent local higher-order statistical features (Freeman & Simoncelli, 2011). When model receptive fields were set to sizes found in primate area V2, we found that physically distinct images with identical model responses were indistinguishable ͨ2; metameric ͨ2; to human observers. The model provides a quantitative explanation of the dependence of crowding on eccentricity and spacing; here, we generalize it to address the fact that crowding is more pronounced radially than tangentially (Toet & Levi, 1992). We generate pairs of synthetic images matched for model responses within spatial regions, while independently controlling the scaling of these regions (s, ratio of radial extent to eccentricity), and their aspect ratio (a, ratio of radial to circumferential extent). If metamerism depends only on receptive field area (s[sup]2[/sup]/a), combinations of scaling and aspect ratio that yield comparable areas should yield comparable performance. Instead, performance depends strongly on aspect ratio. Images are metameric when matched for moderate scaling (s ͭ6; 0.4ͨ2;0.5) and moderate radial elongation (a ͭ6; 1.5ͨ2;2), whereas images matched for much smaller scaling (s ͭ6; 0.25) and tangential elongation (a ͭ6; 0.5) are reliably discriminated. As in our original experiment, region sizes that yield metamerism are consistent with receptive field scaling in V2, and additionally rely on receptive field radial elongation, offering a new prediction regarding receptive field shapes in V2.
Meeting abstract presented at VSS 2013
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