Modelling the Mach bands illusion by means of a diffusion model

Area of Science:

• Visual Neuroscience
• Computational Vision
• Image Processing

Background:

• The retina processes visual information, but the exact mechanism for reconstructing absolute luminance from relative signals remains unclear.
• Illusory phenomena and stabilized retinal images suggest the retina encodes relative luminance, not absolute values.

Purpose of the Study:

• To challenge the principle of lateral inhibition in visual processing.
• To propose and model a reconstruction process in the visual system that recovers absolute luminance from relative luminance sketches.
• To explain brightness illusions as byproducts of this reconstruction process.

Main Methods:

• Critique of the lateral inhibition principle.
• Analysis of illusory phenomena and stabilized retinal images.
• Development of a computational model based on a diffusion process and a mathematical theorem.
• Illustration using 1D heat diffusion and a physical model of connected test tubes.
• Demonstration of Mach bands illusion by violating homogeneous linearity in the diffusion model.

Main Results:

• The retina transmits a relative luminance sketch, not absolute luminance.
• A diffusion-based reconstruction process can recover the original image from Laplacian-filtered input.
• Brightness illusions, such as Mach bands, can be explained as artifacts of deviations from homogeneous linearity in the diffusion process.

Conclusions:

• The visual system likely reconstructs absolute luminance from relative signals using a process akin to diffusion.
• Deviations in the linearity of this diffusion process explain visual brightness illusions.
• The proposed model offers a new perspective on visual perception and luminance processing.