An adaptive scale Gaussian filter to explain White's illusion from the viewpoint of lightness assimilation for a large range of variation in spatial frequency of the grating and aspect ratio of the targets.

The variation between the actual and perceived lightness of a stimulus has strong dependency on its background, a phenomena commonly known as lightness induction in the literature of visual neuroscience and psychology. For instance, a gray patch may perceptually appear to be darker in a background while it looks brighter when the background is reversed. In the literature it is further reported that such variation can take place in two possible ways. In case of stimulus like the Simultaneous Brightness Contrast (SBC), the apparent lightness changes in the direction opposite to that of the background lightness, a phenomenon often referred to as lightness contrast, while in the others like neon colour spreading or checkerboard illusion it occurs opposite to that, and known as lightness assimilation. The White's illusion is a typical one which according to many, does not completely conform to any of these two processes. This paper presents the result of quantification of the perceptual strength of the White's illusion as a function of the width of the background square grating as well as the length of the gray patch. A linear filter model is further proposed to simulate the possible neurophysiological phenomena responsible for this particular visual experience. The model assumes that for the White's illusion, where the edges are strong and quite a few, i.e., the spectrum is rich in high frequency components, the inhibitory surround in the classical Difference-of-Gaussians (DoG) filter gets suppressed, and the filter essentially reduces to an adaptive scale Gaussian kernel that brings about lightness assimilation. The linear filter model with a Gaussian kernel is used to simulate the White's illusion phenomena with wide variation of spatial frequency of the background grating as well as the length of the gray patch. The appropriateness of the model is presented through simulation results, which are highly tuned to the present as well as earlier psychometric results.

A DOG filter model of the occurrence of Mach bands on spatial contrast discontinuities.

The present work proposes a unified model to explain two previously reported properties of the Mach band illusion. The first is the frequently referenced fact that Mach bands are prominently visible at ramps, but practically vanish at intensity steps. The second property, less studied, on the other hand may also be related to the first. It concerns the fact that the width of the illusory Mach bands appears to be a function of the slope of the ramp itself. The model proposed here combines the difference of Gaussians (DOG) model of lateral inhibition in receptive fields with the models of feature detection, based on a holistic approach. The sharpness of discontinuity (SOD) concept for Mach band stimulus has been defined and is related to the slope of the ramp. It is suggested that calculation of SOD leads to an adaptive change in inhibitory surround, a notion that has the support of physiological experiments too.