Transcript Optical Illusions

Optical Illusions
KG-VISA
Kyongil Yoon
3/31/2004
Introduction
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http://www.cfar.umd.edu/~fer/optical/index.html
A new theory of visual illusions
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A computational nature.
The theory predicts many of the well known geometric optical illusions
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Nearly every illusion has a different cause
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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
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Beginning of the nineteenth century when scientists got interested in perception
Illusions have been used as tools in the study of perception
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Illusions of movement in line drawings
Illusions of three-dimensional shape
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
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On geometric optical illusions: accounting for a number of illusions
Referring to image blurring
The new theory
Introduction
The Proposed Theory
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Image interpretation - number of estimation processes
Noise  best estimate
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However, the best estimate does not correspond to the true value
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The estimates are biased
The principle of uncertainty of visual processes
In certain patterns, where the error is repeated, it becomes noticeable.
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The principle of uncertainty is the main cause for many optical illusions
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Geometric Optical Illusions
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Illusions of Movement
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For cleverly arranged patterns with spatially separated areas having different biases
Shape Illusions
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Early computational processes: The extraction of features, such as lines and points, or intersections of lines
An erroneous estimation  erroneous perception
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.
Introduction: The Proposed Theory
Bias in Linear Estimation
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The constraints underlying visual processes
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Formulated as an over-determined linear equations
Ax=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
A' x' = b' + ε.
We are dealing with what is called the errors-in-variable model in statistics. We have to use an
estimator, that is a procedure, to solve the equation system. The most common choice is by
means of least squares (LS) estimation. However, it is well known, that LS estimation is biased.
Under some simplifying assumptions (identical and independent random variables δA and
δb with zero mean and variance σ2 ) the LS estimate converges to
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Large variance in δA , an ill-conditioned A', or an x' which is oriented close to the eigenvector of
the smallest singular value of A' all could increase the bias and push the LS solution away from
the real solution. Generally it leads to an underestimation of the parameters.
There are other, more elaborate estimators that could be used. None, however will perform better
if the errors cannot be obtained with high accuracy.
Examples of visual computations which amount to linear equation systems are the estimation of
image motion or optical flow, the estimation of the intersections of lines, and the estimation of
shape from various cues, such as motion, stereo, texture, or patterns.
Errors in Image Intensity:
How images change when smoothed
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As a noisy version of the ideal image signal
We create the most likely image the vision system works
with by smoothing the image
Many illusions can be understood from the behavior of
straight lines and edges
Three cases
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An edge at the border between regions of different intensity,
such as black and white
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A line on a background of different intensity
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No change
Drift apart each other
A gray line between a bright and a dark region
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Move toward each other
Errors in Image Intensity:
Café Wall Illusion
The horizontal mortar lines being tilted
 Effects of smoothing
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Errors in Image Intensity:
Café Wall Illusion
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Local edge detection  linked to longer
lines
Errors in Image Intensity:
Café Wall Illusion
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Counteract the effect
Errors in Image Intensity:
Spring Pattern
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Square grid with black squares
superimposed
Errors in Image Intensity:
Spring Pattern
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Combination of type-1 (single) and type-2
(drift apart) edges
Flash Anim
Errors in Image Intensity:
Waves Pattern
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Black and white checkerboard with small
squares
Flash Anim
Errors in Line Estimation:
The Theory
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Two intersecting lines
Local edge detection
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Intersection point
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Noisy
The point closest to all the lines using
least squares estimation
The estimation of the intersection point
is biased
For an acute angle
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The estimated intersection point is
between the lines.
The bias increases as the angle
decreases.
The component of the bias in the
direction perpendicular to a line
decreases as the number of line
segments along the line increases
Errors in Line Estimation:
Poggendorff Illusion
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The two ends of the straight diagonal
line passing behind the rectangle
appear to be offset
Can be predicted by the bias
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The diagonal line segments
The lines at the border of the rectangle
The illusory effect increases with a
decrease in the acute angle
Java Anim
Errors in Line Estimation:
Zöllner Illusion
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Tilted segments are estimated
Input to the higher computational
processes which fits long line to
the segments
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Parametric studies
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A stronger illusory perception for
more tilted obliques
A stronger illusory effect when
the pattern is rotated by 45
degrees
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In neurophysiological studies,
our cortex responds more to
lines in horizontal and vertical
than oblique orientations
Less response from the main
lines, more bias
Java Anim
Errors in Line Estimation:
Luckiesh Pattern
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Distorted circle
The bias depends on the
direction of the intersecting
lines
Changing the direction of
the background lines
causes a change in the
bias and thus a change in
the estimated curve, with
the circle bumping at
different locations
Java Anim
Errors in Movement:
How image movement is estimated
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Optical flow
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Representation of image motion by comparing sequential
images and estimating how patterns move between images
The movement of the point from the first image to the second
image. It can only be computed where there is detail, or edges,
in the image. And it requires two computational stages to
estimate optical flow.
Normal flow (First stage)
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Through a small aperture, we can only
compute the component of the motion
vector perpendicular the edge
Local information only provides
information about the line
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constraint line:
on which the optical flow vector lies
Errors in Movement:
How image movement is estimated
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Second stage
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Combination of the motion components from
differently oriented edges within a small patch
Estimate the optical flow vector closest to all the
constraint lines
The minimum squared distance from the lines
Over-determined system
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Solution is biased
Does not correspond to
the actual flow
Depends on the features
in the patch, texture
Errors in Movement:
Ouchi Illusion
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Estimated flows of
surrounding area and
inset area are different
Smaller in length than
the actual flow and it
is closer in direction to
the majority of normal
flow vectors in a
region
Errors in Movement:
Ouchi Illusion
Flash Anim
Errors in Movement:
Wheels Illusion
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Every point on the
image moves on a
straight line
through the image
center
Actual flow vectors
are moving radially
from the image
center outwards,
otherwise they are
moving inwards
Errors in Movement:
Wheels Illusion
Errors in Movement:
Wheels Illusion
Errors in Movement:
Wheels Illusion
Errors in Movement:
Spiral Illusion
Spiral rotation around its center
 Not circular
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Contract or expand
Counter-clockwise
Red: actualmotion vector
 Blue: normal flow vectors
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Errors in Movement:
Moving sinusoids
Smooth curves may be
perceived to deform nonrigidly when translated in the
image plane
 Low amplitude: appears to
deform non-rigidly
 High amplitude: perceived as
the true translation
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Flash Anim
Shape from Motion:
The Constraint
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A biased estimate for the surface normal
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Motion parameters
Orientation of the image lines (that is the texture of
the plane)
As a parameterization for the surface normal
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Slant (σ)
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The angle between N and
the negative optical axis
Tilt (τ)
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The angle between the
parallel projection of N on
the image plane and the
image x-axis.
Shape from Motion:
Segmentation of a Plane
due to Erroneous Slant Estimation
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The plane is perceived to be segmented into two differently slanted planes
Upper texture: smaller the slant in the than in the lower one
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Appears to be closer in orientation
Much more bias  a large underestimation of slant