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A nonlinear model for the visual system is proposed in relation to the dependence of receptive field size on luminance. The model is constructed based on the fact that the exponent of Stevens' brightness function varies depending on the target size. The model consists of two stages; the mechanism of spatial summation and the mechanism of 0.5-power in cascade. The mechanism of 0.5-power is responsible for an exponent 0.5 of the brightness function for the point target. The extent of the spatial summation changes depending on the luminance so that the model yields a brightness function with exponent 0.33 for the infinite target of uniform luminance distribution. The model predicts well the signal transfer function of vision, the charactreristics of the suprathreshold spatial summation and the mean luminance dependence of the spatial frequency characteristics for threshold contrast.