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Analysis of Motion

Analysis of Motion. Measuring motion in biological vision systems. Smoothness assumption:. Compute a velocity field that: is consistent with local measurements of image motion (perpendicular components) has the least amount of variation possible. Computing the smoothest velocity field.

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Analysis of Motion

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  1. 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 predicted responses: (1) (2) (3)

  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 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

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