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

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

The Oriented Difference of Gaussians (ODOG) model of brightness (perceived intensity) by Blakeslee and McCourt (Vision Research 39:4361-4377, 1999), which is based on linear spatial filtering by oriented receptive fields followed by contrast normalization, has proven highly successful in parsimoniously predicting the perceived intensity (brightness) of regions in complex visual stimuli such as White's effect, which had been believed to defy filter-based explanations. Unlike competing explanations such as anchoring theory, filling-in, edge-integration, or layer decomposition, the spatial filtering approach embodied by the ODOG model readily accounts for the often overlooked but ubiquitous gradient structure of induction which, while most striking in grating induction, also occurs within the test fields of classical simultaneous brightness contrast and the White stimulus. Also, because the ODOG model does not require defined regions of interest, it is generalizable to any stimulus, including natural images. The ODOG model has motivated other researchers to develop modified versions (LODOG and FLODOG), and has served as an important counterweight and proof of concept to constrain high-level theories which rely on less well understood or justified mechanisms such as unconscious inference, transparency, perceptual grouping, and layer decomposition. Here we provide a brief but comprehensive description of the ODOG model as it has been implemented since 1999, as well as working Mathematica (Wolfram, Inc.) notebooks which users can employ to generate ODOG model predictions for their own stimuli.

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

A class of models for lateral geniculate nucleus (LGN) on-cell behavior is proposed. The models consist of a linear filter with divisive normalization by root mean square local contrast and include an intrinsic noise density parameter. The properties of these models are shown to match observed LGN behavior: (1) a linear response to low-magnitude stimuli; (2) a linear response without saturation (luxotonic behavior) for zero-contrast stimuli (homogeneous fields) with increasing magnitude; and (3) response saturation for nonzero contrast stimuli with increasing magnitude. The models possess an intrinsic scale for signal-to-noise ratio (SNR). The models show under and supersaturation, as well as saturation, for sinusoidal grating stimuli with increasing contrast and predict that different SNR regimes will cause a single neuron to show different contrast response curves. A companion paper [1] provides a detailed analysis of the full nonlinear response for sinusoidal grating stimuli and circular spot stimuli.