Modelling the Mach bands illusion by means of a diffusion model.

Abstract

First, we criticize the validity of the principle of lateral inhibition. Second, on the basis of illusory phenomena and stabilized retinal images, we point out that the retina does not code the absolute luminance; the retina forwards a relative luminance sketch towards higher levels of the visual system. However, at the level of conscious processing the perceptual counterpart of absolute luminance, brightness, is available. Therefore, it is reasonable to assume that a reconstruction process is carried out by the visual system, which recovers the inner representation that corresponds to the retinal light distribution from the coded relative luminance sketch. We provide an illustrative description of a computational model of this reconstruction process. The basis of the reconstruction is a mathematically provable theorem, according to which if image P is produced from image I by Laplacian filtering, and then P is used as the sources and sinks of a homogeneous linear diffusion process, then the equilibrium of the diffusion will be identical to the original image I. We have illustrated this by a one-dimensional heat diffusion example, and by a series of test tubes connected to each other, also in one dimension. Brightness illusions are considered as a side effect of this diffusion-based reconstruction process. If the diffusion process deviates from the principle of homogeneous linearity, then the result of the reconstruction will deviate from the original image I. We showed a concrete illustration of this with regards to the Mach bands illusion: here we violated the principle of homogeneous linearity by means of inserting a small vertical tube serving as a serial resistance between each test tube and the horizontal connecting tube. This violation resulted in a change of water level in the source and the sink test tubes corresponding to the Mach bands illusion.