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Optical Illusions
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Introduction

Introduction

A new theory of visual illusions

A computational nature.

The theory predicts many of the well known geometric optical illusions

Illusions of movement in line drawings

Illusions of three-dimensional shape

Nearly every illusion has a different cause

Robinson in introduction to geometrical optical illusions "There is no better indicator of the forlornness of this hope [the hope of some to find a general theory] than a thorough review of the illusions themselves "

The scientific study of illusions

Beginning of the nineteenth century when scientists got interested in perception

Illusions have been used as tools in the study of perception

An important strategy in finding out how perception operates is to observe situations in which misperceptions occur. By carefully altering the stimuli and testing the changes in visual perception psychologists tried to gain insight into the principles of perception.

Theories about illusions

On geometric optical illusions: accounting for a number of illusions

Referring to image blurring

The new theory

Slide 2

Introduction The Proposed Theory

Introduction The Proposed Theory

Image interpretation - number of estimation processes

Noise  best estimate

However, the best estimate does not correspond to the true value

The estimates are biased

The principle of uncertainty of visual processes

In certain patterns, where the error is repeated, it becomes noticeable.

The principle of uncertainty is the main cause for many optical illusions

Geometric Optical Illusions

Early computational processes: The extraction of features, such as lines and points, or intersections of lines

An erroneous estimation  erroneous perception

Illusions of Movement

For cleverly arranged patterns with spatially separated areas having different biases

Shape Illusions

Extracting the shape of the scene in view from image features, called shape from X computations

The bias can account for many findings in psychophysical experiments on the erroneous estimation of shape

An understanding the bias allows to create illusory displays.

The bias is a computational problem, and it applies to any vision system

These illusion is experienced by humans, also should be experienced by machines.

Slide 3

Introduction: The Proposed Theory Bias in Linear Estimation

Introduction: The Proposed Theory Bias in Linear Estimation

The constraints underlying visual processes

Formulated as an over-determined linear equations

A x = b where A an n × k matrix, and b an n-dimensional vector denoting measurements, that is the observations, and x a k-dimensional vector denoting the unknowns. The observations are noisy, that is, they are corrupted by errors. We can say that the observations are composed of the true values (A', b') plus the errors (δA, δb) , i.e. A = A' + δA and b = b' + δb. In addition the constraints are not completely true, they are only approximations; in other words there is system error, ε. The constraints for the true value, x', amount to

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