Motion and Optical Flow
We live in a moving world
• Perceiving, understanding and predicting motion is an important part of our daily lives
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Motion and perceptual organization
• Even “impoverished” motion data can evoke a strong percept
G. Johansson, “Visual Perception of Biological Motion and a Model For Its Analysis”,
Perception and Psychophysics 14, 201-211, 1973.
Motion and perceptual organization
• Even “impoverished” motion data can evoke a strong percept
G. Johansson, “Visual Perception of Biological Motion and a Model For Its Analysis”,
Perception and Psychophysics 14, 201-211, 1973.
Seeing motion from a static picture?
http://www.ritsumei.ac.jp/~akitaoka/index-e.html
More examples
How is this possible?
• The true mechanism is yet to be revealed
• FMRI data suggest that illusion is related to some component of eye movements
• We don’t expect computer vision to “see” motion from these patterns
The cause of motion
• Three factors in imaging process – Light
– Object – Camera
• Varying either of them causes motion
– Staticcamera,movingobjects(surveillance)
– Moving camera, static scene (3D capture)
– Moving camera, moving scene (sports, movie)
– Static camera, moving objects, moving light (time lapse)
Recovering motion • Feature-tracking
– Extract visual features (corners, textured areas) and “track” them over multiple frames
• Optical flow
– Recover image motion at each pixel from spatio-temporal image
brightness variations (optical flow)
Two problems, one registration method
B. Lucas and T. Kanade. An iterative image registration technique with an application to stereo vision. In Proceedings of the International Joint Conference on Artificial Intelligence, pp. 674–679, 1981.
Feature tracking
• Challenges
– Figure out which features can be tracked
– Efficiently track across frames
– Some points may change appearance over time
(e.g., due to rotation, moving into shadows, etc.)
– Drift: small errors can accumulate as appearance model is updated
– Points may appear or disappear: need to be able to add/delete tracked points
What is Optical Flow?
Definitions
optical flow is a velocity field in the image which
transforms one image into the next image in a
sequence [
flow field
Ambiguity of optical flow
flow (1): true motion
What is Optical Flow?
4 v4 I(t +1)
Optical Flow
Velocity vectors
Optical flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene -Wiki
Optical Flow Research: Timeline
Horn&Schunck Lucas&Kanade many
more methods
Seminal papers
Benchmark:
Barron et.al.
Benchmark:
Galvin et.al.
Optical Flow
I(x,y,t) I(x,y,t+1)
• Given two subsequent frames, estimate the point
translation
• Key assumptions of Lucas-Kanade Tracker
• Brightness constancy: projection of the same point looks the same in every frame
• Small motion: points do not move very far
• Spatial coherence: points move like their neighbors
The brightness constancy constraint
I(x,y,t) I(x,y,t+1) • Brightness Constancy Equation:
I ( x , y , t ) = I ( x + u , y + v , t + 1)
Take Taylor expansion of I(x+u, y+v, t+1) at (x,y,t) to linearize the right side:
Image derivative along x Difference over frames
I(x+u,y+v,t+1)I(x,y,t)+ u+Iy v+ I(x+u,y+v,t+1)−I(x,y,t)=+Ix u+Iy v+It
I u+I v+I 0 →Iu v +I =0 xyt t
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