Nonlinear processing in LGN neurons Bonin, Mante & Carandini (2004)

Summary of this paper They proposed an empirical model of LGN neurons. The model includes “suppressive field” (Levick et al., 1972). They formulated a mathematical model, and then the free parameters were fitted to physiological data. The model with fitted parameters can reproduce a broader range of visual characteristics.

Linear model of the LGN neuron Receptive field is modeled by F(x,t) = Fs(x) Ft(t), where Fs(x) is difference of Gaussian (DoG), and Ft(t) is difference of Gamma functions.

The linear model can explains (some) physiological data. ● Model

Prediction of the linear model is limited. Response of an LGN neuron to a video sequence, and the prediction by a linear model.

Prediction of the linear model is limited (cont’d) Data Linear Model Proposed Model ( )

Proposed model with “suppressive field” H(x,t) S*=c*H G(x) Definitions: Receptive field: the region in the visual field that generates visual response by some elementary visual stimulus (small dot or bar). Suppressive field: it does not generate visual response by itself; it modulates (suppresses) the visual response.

Method of developing the model The authors fitted the model parameters to “canonical” physiological experiments. Spatial- and temporal-frequency selectivity of the receptive field Contrast saturation Mask contrast effect Mask size effect Mask spatial-frequency selectivity The authors further conducted a different kind of experiment on the model given the fitted parameters, which is compared to the physiological experiment. Size and contrast effect of sinusoidal stimuli

Fitting parameters for the receptive field Data Model ●

Fitting parameters for the suppressive field Data Linear Model Proposed Model

The fitted model can predicts visual responses to the verification experiment.

The fitted model can predicts visual responses to the verification experiment (cont’d)

Characteristics of the proposed LGN neuron model H(x,t) G(x) Stimulus selectivity of suppressive field H(x,t) Orientation Controversial Spatial-frequency Low Temporal-frequency High

Improvement of the prediction to a video sequence..

They improved the standard LGN neuron model. Summary [1/2] They improved the standard LGN neuron model. A fundamental question: why the visual system has such characteristics? Gain control ... any theoretical model that derives those characteristics? Previous theoretical studies (but for V1) Statistical independence: Schwartz & Simoncelli (2001) Inference of hidden variables in data generative model: Karklin & Lewicki (2003; 2005)

Suppression in V1 Cross-orientation suppression

Suppression in V1 (cont’d) Surround suppression

Summary of suppressive field in V1 Receptive field (w/ orientation selectivity) Suppressive field w/o orientation selectivity Hotspots of suppressive field Suppressive field w/ the same orientation selectivity as the receptive field

Schwartz & Simoncelli’s model

Karklin & Lewicki’s model

What is the unified theory which explains both LGN and V1? Summary [2/2] What is the unified theory which explains both LGN and V1? What is the effects of the nonlinear LGN properties on V1? (Most) current models/experiments do not take into account follows: Abrupt change of the luminance in time and space. cf. constant mean luminance Non-stationary stimulus, such as a video sequence. cf. stationary stimulus for a few seconds Natural/complex images. cf. sinusoidal gratings