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  provides a detailed analysis of the full nonlinear response for sinusoidal grating stimuli and circular spot stimuli.
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