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Optical Snow and the Aperture Problem

Optical Snow and the Aperture Problem. Richard Mann School of Computer Science University of Waterloo. Michael Langer School of Computer Science McGill U niversity. Optical flow. J.J. Gibson, The Senses Considered As Perceptual Systems, 1966. Layered motion.

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Optical Snow and the Aperture Problem

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  1. Optical Snow and the Aperture Problem Richard Mann School of Computer Science University of Waterloo Michael Langer School of Computer Science McGill University

  2. Optical flow J.J. Gibson, The Senses Considered As Perceptual Systems, 1966

  3. Layered motion e.g. occlusions, transparency

  4. Motion beyond layers e.g. falling snow

  5. “Optical snow”

  6. “Optical Snow” Lateral egomotion in a 3D cluttered scene

  7. Optical snow

  8. Overview of Talk • background: - Fourier analysis of optical snow - how to estimate direction of optical snow? (Langer and Mann, ICCV ’01)

  9. Overview of Talk • background: - Fourier analysis of optical snow - how to estimate direction of optical snow? (Langer and Mann, ICCV ’01) • new stuff: - aperture problem

  10. Fourier analysis of image translation (Watson & Ahumada ’85) f t t f y f x If image patch is translating with velocity(v , v ) then all power lies on a plane: x y v f + v f + f = 0 x x y y t

  11. Optical Snow Image velocities are (αv , αv ) x y

  12. Fourier analysis of optical snow f t f t “bowtie” f x αv f +αv f + f = 0 x x y y t

  13. Bowtie of falling spheres f t f Θ

  14. Bowtie of bush f t f Θ

  15. Q: How to compute motion direction ?A: rotate a wedge and measure power Minimum of power in wedge occurs when wedge is aligned with the bowtie.

  16. Computing the direction of motion minimum of power motion direction The motion direction is perpendicular to the direction of minimum of power.

  17. Aperture Problem “normal” direction Vertically falling cylinders appear to move in normal direction.

  18. Aperture Problem “normal” direction (max of power) true motion direction

  19. Aperture problem ? falling ellipsoids same power but random phase

  20. Summary • Optical snow: a new motion category • Fourier-based method for detecting direction of motion • Analysis of aperture problem

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