### Introduction

The Proposed Theory

When our visual system interprets the images received by our eyes, it carries out a large number of processes. We can analyze these processes as computations. Many of the computations are estimation processes. In other words we compute - that is estimate - quantities from the images (such as the location of edges and corners, the structure of the scene in view, or the position of the light source) using as input the image data, or the image data processed in some way. Because of the limitations of the visual apparatus the images contain noise, and the visual system has to come up with the best estimate in the presence of noise. However, many of the visual computations are such that, unless the noise is known, the best estimate does not correspond to the true value. In other words, there is systematic error. We say the estimates are biased. The only way to avoid the bias would be to estimate the noise very accurately, which because of the complexity of visual processes, seems to be impossible. Thus, the bias constitutes a general principle, it is the principle of uncertainty of visual processes. Under everyday conditions the errors are not large enough to notice, but in certain patterns, where the error is repeated, it becomes noticeable.

The hypothesis illustrated here is that this principle of uncertainty is the main cause for many optical illusions. In particular:

Geometric Optical Illusions
The very early computational processes are concerned with the extraction of features, such as lines and points, or intersections of lines. Because of bias there is an erroneous estimation, which gives rise to erroneous perception of these features causing illusions with certain patterns.
Illusions of Movement
The basic feature of image sequences is the movement of image points, and this is estimated with bias as well. For cleverly arranged patterns with spatially separated areas having different biases, a segmentation of the pattern and perception of illusory movement can be caused.
Shape Illusions
The processes extracting the shape of the scene in view from image features, called shape from X computations, are estimation processes. The bias can account for many findings in psychophysical experiments on the erroneous estimation of shape. An understanding of the bias allows to create illusory displays.

The bias is a computational problem, and it applies to any vision system. Thus, these illusions experienced by humans, also should be experienced by machines.