optical snow and the aperture problem
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/1.jpg)
Optical Snow and the Aperture Problem
Richard MannSchool of Computer Science
University of Waterloo
Michael Langer
School of Computer Science
McGill University
![Page 2: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/2.jpg)
Optical flow
J.J. Gibson, The Senses Considered As Perceptual Systems, 1966
![Page 3: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/3.jpg)
Layered motion
e.g. occlusions, transparency
![Page 4: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/4.jpg)
Motion beyond layers
e.g. falling snow
![Page 5: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/5.jpg)
“Optical snow”
![Page 6: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/6.jpg)
“Optical Snow”
Lateral egomotion in a 3D cluttered scene
![Page 7: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/7.jpg)
Optical snow
![Page 8: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/8.jpg)
Overview of Talk
• background: - Fourier analysis of optical snow - how to estimate direction of optical snow? (Langer and Mann, ICCV ’01)
![Page 9: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/9.jpg)
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
![Page 10: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/10.jpg)
Fourier analysis of image translation
v f + v f + f = 0x x y y t
If image patch is translating with velocity (v , v )then all power lies on a plane:
x y
fy
t
(Watson & Ahumada ’85)
f x
f t
![Page 11: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/11.jpg)
Optical Snow
Image velocities are (α v , α v ) x y
![Page 12: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/12.jpg)
α v f + α v f + f = 0x x y y t
ft
f x
ft
Fourier analysis of optical snow
“bowtie”
![Page 13: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/13.jpg)
Bowtie of falling spheres
f Θ
f t
![Page 14: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/14.jpg)
Bowtie of bush
f t
f Θ
![Page 15: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/15.jpg)
Q: How to compute motion direction ?A: rotate a wedge and measure power
Minimum of power in wedge occurswhen wedge is aligned with the bowtie.
![Page 16: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/16.jpg)
Computing the direction of motion
The motion direction is perpendicular to the direction of minimum of power.
motion directionminimum of power
![Page 17: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/17.jpg)
Aperture Problem
Vertically falling cylinders appearto move in normal direction.
“normal”direction
![Page 18: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/18.jpg)
Aperture Problem
true motiondirection
“normal” direction(max of power)
![Page 19: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/19.jpg)
Aperture problem
falling ellipsoids
same power butrandom phase
?
![Page 20: Optical Snow and the Aperture Problem](https://reader036.vdocuments.us/reader036/viewer/2022062502/56814d0a550346895dba423a/html5/thumbnails/20.jpg)
Summary
• Optical snow: a new motion category
• Fourier-based method for detecting direction of motion
• Analysis of aperture problem