The Oriented Difference of Gaussian (ODOG) filter of Blakeslee and McCourt has been successfully employed to explain several brightness perception illusions which include illusions of both brightness-contrast type, for example, Simultaneous Brightness Contrast and Grating Induction and the brightness-assimilation type, for example, the White effect and the shifted White effect. Here, we demonstrate some limitations of the ODOG filter in predicting perceived brightness by comparing the ODOG responses to various stimuli (generated by varying two parameters, namely, test patch length and spatial frequency) with experimental observations of the same.

In this paper we present some demonstrations concerning the width of Mach bands and henceforth hypothesize certain relations. We show that it is the variation in width of Mach bands in relation to luminance gradients which is responsible for Mach bands being strong for luminance ramps and weak or vanishing for luminance steps. We present the results of the experiments carried out by us using some of these demonstrations to provide support for our claims.

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A novel modification of the Hermann grid stimulus is demonstrated. It is shown that introduction of extremely tiny squares at the corners of the grid squares in the classical stimulus, keeping the position and orientation of the grid squares fixed, can reduce the strength and even completely wipe out the illusory dark spots. The novel perturbing stimulus was investigated further and a gray-level intensity threshold was measured for the tiny corner squares beyond which the illusory blobs disappear completely. It was also found that this threshold remains practically unchanged over a wide range of grid square size for an observer.

The surface Hamiltonian corresponding to the surface part of a gravitational action has $xp$ structure where $p$ is conjugate momentum of $x$. Moreover, it leads to $TS$ on the horizon of a black hole. Here $T$ and $S$ are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.Comment: Revised version, accepted in Phys. Lett.