Analysis of Motion

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Analysis of Motion

• Measuring motion in biological vision systems

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Smoothness assumption

• Compute a velocity field that
• is consistent with local measurements of image
  motion (perpendicular components)
• has the least amount of variation possible

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Computing the smoothest velocity field
(Vxi-1, Vyi-1)
motion components Vxiuxi Vyi uyi v?i
(Vxi, Vyi)
(Vxi1, Vyi1)
i-1
i
i1
change in velocity (Vxi1-Vxi, Vyi1-Vyi)
Find (Vxi, Vyi) that minimize S(Vxiuxi Vyiuyi
- v?i)2 ?(Vxi1-Vxi)2 (Vyi1-Vyi)2
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When is the smoothest velocity field correct?
When is it wrong?
motion illusions
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Two-stage motion measurement
motion components ? 2D image motion Movshon,
Adelson, Gizzi Newsome
V1 high of cells selective for direction of
motion (especially in layer that projects to
MT) MT high of cells selective for direction
and speed of motion lesions in MT ? behavioral
deficits in motion tasks
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Testing with sine-wave plaids
moving plaid
Movshon et al. recorded responses of neurons in
area MT to moving plaids with different component
gratings
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The logic behind the experiments
(1)
(2)
(3)
Component cells measure perpendicular components
of motion e.g. selective for vertical features
moving right predicted responses (1)
(2) (3) Pattern cells integrate
motion components e.g. selective for rightward
motion of pattern predicted responses (1)
(2) (3)
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Movshon et al. observations
? Cortical area V1 all neurons behaved like
component cells ? Cortical area MT layers 4
6 component cells layers 2, 3, 5 pattern
cells ? Perceptually, two components are not
integrated if large difference in spatial
frequency large difference in speed components
have different stereo disparity
Evidence for two-stage motion measurement!
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Integrating motion over the image
? integration along contours vs. over 2D
areas Nakayama Silverman
true motion
perceived motion
area features must be close
contour features can be far away
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Recovering 3D structure from motion
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Ambiguity of 3D recovery
birds eye views
We need additional constraint to recover 3D
structure uniquely
rigidity constraint
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Image projections
perspective projection
orthographic projection
Z
Z
X
image plane
X
image plane
(X, Y, Z) ? (X, Y) 3D 2D
(X, Y, Z) ? (X/Z, Y/Z) 3D 2D