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Tim Meese, Rob Summers, Alex Baldwin; Theory and data for area summation of contrast with and without uncertainty: Evidence for a noisy integrator model. Journal of Vision 2012;12(9):601. doi: 10.1167/12.9.601.
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Contrast sensitivity improves with the area of a sine-wave grating, but why? The standard account attributes this to spatial probability summation (e.g. A MAX operator) between independent noisy detectors. However, this does not fit well with hierarchical models of neuronal convergence, which suggest a more direct form of spatial integration. Deciding between these alternatives has been difficult because in each case, good model fits to summation functions are achieved with a single free parameter: the level of uncertainty for MAX pooling or the severity of the nonlinear transducer for linear pooling. The slope of the psychometric function also depends on each of these parameters. We cannot control intrinsic uncertainty but did control extrinsic uncertainty by either blocking or interleaving centrally placed target gratings with various diameters (1:32 cycles) using 2IFC and MCS. Area summation curves were steep over the first 8 grating cycles, becoming shallower thereafter. For the smaller stimuli, sensitivity was significantly worse for the interleaved design than for the blocked design suggesting that our manipulation of uncertainty was successful. However, neither stimulus area nor blocking affected the slope of the psychometric function. We derived stochastic model predictions for an inhomogeneous retinal field, noisy mechanisms and extrinsic uncertainty that depended on experimental design. The contrast transducer was either linear (C1.0) or nonlinear (C2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed, or it was proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the energy model) described the summation functions and the slopes of the psychometric functions for both experimental designs. We conclude that in previous studies, the effects of a square-law transducer followed by linear summation of noise with the signal have combined to masquerade as probability summation.
Meeting abstract presented at VSS 2012
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