Modeling lateral geniculate nucleus response with contrast gain control Part 2: analysis

Abstract

Cope, Blakeslee and McCourt (2013) proposed a class of models for LGN ON-cell behavior consisting of a linear response with divisive normalization by local stimulus contrast. Here we analyze a specific model with the linear response defined by a difference-of-Gaussians filter and a circular Gaussian for the gain pool weighting function. For sinusoidal grating stimuli, the parameter region for band-pass behavior of the linear response is determined, the gain control response is shown to act as a switch (changing from “off” to “on” with increasing spatial frequency), and it is shown that large gain pools stabilize the optimal spatial frequency of the total nonlinear response at a fixed value independent of contrast and stimulus magnitude. Under- and super-saturation as well as contrast saturation occur as typical effects of stimulus magnitude. For circular spot stimuli, it is shown that large gain pools stabilize the spot size that yields the maximum response.

The Oriented Difference of Gaussians (ODOG) model of brightness perception: Overview and executable Mathematica notebooks

“…It would, for example, benefit from modifications such as the replacement of ODOG filters with balanced Gabor functions (Cope, Blakeslee & McCourt, 2009), and the substitution of local contrast gain control (Cope, Blakeslee & McCourt, 2013; 2014) for the image-based (global) normalization procedure which is currently implemented. Nonetheless, the utility of the spatial filtering approach lies in the ODOG model’s success in accounting for brightness in a wide variety of stimuli, ranging from simple to complex, without the adjustment of any parameter values, and its parsimony, which acts as a scientifically necessary counterweight to high-level theories which posit only vaguely specified mechanisms such as unconscious inference, perceptual transparency, Gestalt grouping, intrinsic image layer decomposition, and the like.…”

Modeling lateral geniculate nucleus response with contrast gain control Part 1: formulation

“…The formulation is the five-parameter model studied in our companion paper [1], and illustrative results here are taken directly from that paper. A specific formulation is necessary to provide computational results.…”

“…Electrophysiological experiments typically involve drifting gratings across the LGN receptive field while recording spike activity, and the maximum discharge rate per stimulus period can be recovered from the post-stimulus time histogram. The corresponding maximum response of the model, $${\left(\frac{\text{LGN}\left[P\right]}{{\nu }_{\mathrm{normalG}}}\right)}_{\max }≔\underset{{\varphi }_{\mathrm{normalP}}}{\max }true(\frac{\text{LGN[P]}}{{\nu }_{\mathrm{G}}}true)$$ as well as the related quantities ( R [ P ]ν G ) max and ( G [ P ]ν G ) min , are found explicitly in our companion paper [1] and are used in reporting results here. Altogether, the key parameters for sinusoidal grating stimuli are stimulus magnitude ν P , spatial frequency s P , contrast c P , and SNR = ν P /ν G .…”

“…This paper formulates these models and derives their key properties. A companion paper (Cope, Blakeslee and McCourt [1]) provides a detailed analysis of a five-parameter model of this type, and selected results from that companion paper are included here for illustration.…”

“…These examples are drawn from the work of the companion paper [1], which studies a five-parameter model of this class consisting of a difference-of-Gaussians receptive field function [28, 29] and a Gaussian gain pool and the full nonlinear response to sinusoidal grating and circular spot stimuli. An unexpected result follows from the model's intrinsic scale for SNR, which provides a means of studying saturation behavior as SNR varies.…”