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
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
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.
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