A Mathematical Principle of Art and Human Vision

The study of visual illusions is an old subject and an important part of the psychology of human visual perception, but hitherto there has been no single principle able to explain radically different kinds of visual illusions conjointly. Such a principle does exist, as is to be shown, and has the virtue of being rigorous: it is the mathematical theory of Fourier analysis. A great many visual illusions are what happen when the visual objects involved undergo certain frequency filtering, a concept deduced from Fourier analysis. Phenomena thus explained belong in these distinct categories: brightness illusions, colour illusions, geometrical illusions, and motion illusions, all of which have been simulated with computer programmes based on this mathematical principle. Visual illusions obeying this principle have in fact been depicted in Western painting for centuries, and art can in certain ways shed light on the quest for the understanding of human vision.

An Analysis of Theoretical Approaches to Geometrical-Optical Illusions

The geometrical optical illusions, such as the Müller-Lyer and the Poggendorff, are simple line drawings, which demonstrate errors as large as 25% when people are asked to match their properties such as size, angles, and line collinearity. They have been tantalizing people for at least 150 years and are still not really understood. Illusion figures have been used to probe the consistency of different perceptual properties and also of perception and action with implications for the theory of two visual systems. Explanations of geometrical illusions tend to invoke either physiological processes or the functional role illusion responses may have when viewing a 3D scene. This chapter examines all of these theoretical issues, discussing evidence for and against the major theories.

The Café Wall Illusion: Local and Global Perception from Multiple Scales to Multiscale

Geometrical illusions are a subclass of optical illusions in which the geometrical characteristics of patterns in particular orientations and angles are distorted and misperceived as a result of low-to-high-level retinal/cortical processing. Modelling the detection of tilt in these illusions, and its strength, is a challenging task and leads to the development of techniques that explain important features of human perception. We present here a predictive and quantitative approach for modelling foveal and peripheral vision for the induced tilt in the Café Wall illusion, in which parallel mortar lines between shifted rows of black and white tiles appear to converge and diverge. Difference of Gaussians is used to define a bioderived filtering model for the responses of retinal simple cells to the stimulus, while an analytical processing pipeline is developed to quantify the angle of tilt in the model and develop confidence intervals around them. Several sampling sizes and aspect ratios are explored to model variant foveal views, and a variety of pattern configurations are tested to model variant Gestalt views. The analysis of our model across this range of test configurations presents a precisely quantified comparison contrasting local tilt detection in the foveal sample sets with pattern-wide Gestalt tilt.