Jenny C A Read

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A Bayesian model of the correspondence problem

• Jenny C A Read
• University of Oxford

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Joseph Fourier Thomas Bayes
1768-1830
1702-1761
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outline

• psychophysical experiments (with Richard Eagle)
• qualitative interpretation
• quantitative modelling
• conclusions

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stereopsis motion
how far?
how fast?
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psychophysical experiments
stereo
motion
monitor
mirror
keypad
observer
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anti-correlated stimuli
black ?? white
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anti-correlated stimuli
motion
stereo
?
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fourier analysis
any image
as a sum of Fourier components.
can equivalently be represented
...of different
spatial frequencies and orientations
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why reversed motion?
correlated
anti-correlated
1st frame
1st frame
2nd frame
2nd frame
motion to right
perceive
motion to left
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example stimuli
1d
2d
all orientations
only vertical orientations
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results with 1d stimuli
MOTION
STEREO
no problem!
100
100
correlated
just below chance weak reversed perceptions
anti-correlated
40
40

• Stereo and motion results are similar.
• Maybe both systems have a similar way of
  combining information from different spatial
  frequency channels.

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results with 2d stimuli
MOTION
STEREO
no problem!
100
100
correlated
anti-correlated
0
50
strong reversed motion
chance

• Stereo and motion results are different.
• Maybe a difference in how systems combine
  information from different orientation channels

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single Fourier component...
contrast-reversed...
...shifted ?/(2cos?)-d to left
...shifted d to right
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crossed (stereo) right (motion)
uncrossed (stereo) left (motion)
true disparity
disparity (stereo) displacement (motion)
disparities reported by different channels
Different orientation channels agree on
direction, but not on magnitude.
STEREO SYSTEM Disagreement on magnitude prevents
clear perception of depth.
MOTION SYSTEM Agreement on direction enables
clear perception of reversed motion.
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the results can be understood qualitativelycan
they be modelled quantitatively?
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what is perception?
physical world
BRAIN
mental representation of the world
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a bayesian model
prior visual experience P(W)
physical world W
Bayes theorem P(WI) P(IW) ? P(I) / P(W)
BRAIN
visual image I
mental representation of the world
noise
knowledge of imaging system P(IW)
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the model
After initial image processing by simple and
complex cells.
each channel assesses the probability of each
possible disparity...
finally output from all channels is combined.
to arrive at a single percept of disparity.
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results stereo
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results motion
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conclusions

• puzzling experimental results
• increasing orientation bandwidth
• enhances reversed motion
• impairs reversed depth
• can be reproduced by this model.
• image processed by array of Fourier channels
• Bayesian probability analysis within each channel
• stereo motion systems differ in how different
  orientation channels are combined.

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