1. Measuring motion in biological vision systems
Analysis of Motion
Measuring motion in biological vision systems

2. Smoothness assumption:
Compute a velocity field that:
is consistent with local measurements of image motion (perpendicular components)
has the least amount of variation possible

3. Computing the smoothest velocity field
(Vxi-1, Vyi-1)
motion components:
Vxiuxi + Vyi uyi= vi
(Vxi, Vyi)
(Vxi+1, Vyi+1)
i-1 i
i+1
change in velocity:
(Vxi+1-Vxi, Vyi+1-Vyi)
Find (Vxi, Vyi) that minimize:
Σ(Vxiuxi + Vyiuyi - vi)2 + [(Vxi+1-Vxi)2 + (Vyi+1-Vyi)2]

4. When is the smoothest velocity field correct?
When is it wrong?
motion illusions

5. 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

6. Testing with sine-wave “plaids”
moving plaid
Movshon et al. recorded responses of neurons in area MT to moving plaids with different component gratings

7. 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

8. 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!

9. 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

10. Recovering 3D structure from motion

11. Ambiguity of 3D recovery
birds’ eye views
We need additional constraint to recover 3D structure uniquely
“rigidity constraint”

12. Image projections orthographic projection perspective projectionZ Z X
image plane X
image plane
(X, Y, Z)  (X, Y)
3D D
(X, Y, Z)  (X/Z, Y/Z)
3D D