A possible linear filtering model to explain White’s illusion at different grating widths

The perceived lightness of a stimulus depends on its background, a phenomenon known as lightness induction. For instance, the same gray stimulus can look light in one background and dark in another. Moreover, such induction can take place in two directions; in one case, it occurs in the direction of the background lightness known as lightness assimilation, while in the other it occurs opposite to that, known as lightness contrast. The White’s illusion is a typical one which does not completely conform to any of these two processes. In this paper, we have quantified the perceptual strength of the White’s illusion as a function of the width of the background square grating. Based on our results which also corroborate some earlier studies, we propose a linear filtering model inspired from an earlier work dealing with varying Mach band widths. Our model assumes that the for the White’s illusion, where the edges are strong and many in number, and as such the spectrum is rich in high frequency components, the inhibitory surround in the classical Difference-of-Gaussians (DoG) filter gets suppressed, so that the filter essentially reduces to a multi-scale Gaussian one. The simulation results with this model support the present as well as earlier experimental results.