L11(motion)

# L11(motion) - Motion Field and Optical Flow Ack for the...

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1 May 2006 Motion/Optic Flow 1 Motion Field and Optical Flow Ack, for the slides: Professor Yuan-Fang Wang Professor Octavia Camps May 2006 Motion/Optic Flow 2 Motion Field and Optical Flow • So far, algorithms deal with a single, static image • In real world, a static pattern is a rarity, continuous motion and change are the rule • Human eyes are well-equipped to take advantage of motion or change in an image sequence. – In our discussions, an image sequence is a discrete set of N images, taken at discrete time instants (may or may not be uniformly spaced in time). • Image changes are due to the relative motion between the camera and the scene (illumination being constant).

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2 May 2006 Motion/Optic Flow 3 Example • Ullman’s concentric counter-rotating cylinder experiment • Two concentric cylinders of different radii • W. a random dot pattern on both surfaces (cylinder surfaces and boundaries are not displayed) • Stationary: not able to tell them apart • Counter-rotating: structures apparent May 2006 Motion/Optic Flow 4 • Motion helps in – segmentation (two structures) – identification (two cylinders) Example (cont.)
3 May 2006 Motion/Optic Flow 5 General Scenario Possibilities: camera moving, stationary scene • camera stationary, moving objects • both camera and scene moving May 2006 Motion/Optic Flow 6 Visual Motion • Allows us to compute useful properties of the 3D world, with very little knowledge. • Example: Time to collision

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4 May 2006 Motion/Optic Flow 7 Time to Collision f L v L D o l(t) l(t) An object of height An object of height L L moves with moves with constant velocity constant velocity v: v: •At time At time t=0 the object is at: the object is at: • D(0) = D D(0) = D o •At time At time t it is at it is at •D(t) = D D(t) = D o – vt vt •It will crash with the camera at It will crash with the camera at time: time: • D( D( ± ) = D ) = D o – v ± = 0 = 0 ± = D = D o /v t=0 t=0 t D(t) ² Octavia Camps May 2006 Motion/Optic Flow 8 Time to Collision f L v L D o l(t) l(t) t=0 t=0 t D(t) The image of the object has size l(t): The image of the object has size l(t): Taking derivative Taking derivative wrt wrt time: time: ² Octavia Camps
5 May 2006 Motion/Optic Flow 9 Time to Collision f L v L D o l(t) l(t) t=0 t=0 t D(t) ± Octavia Camps May 2006 Motion/Optic Flow 10 Time to Collision f L v L D o l(t) l(t) t=0 t=0 t D(t) And their ratio is: ± Octavia Camps

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6 May 2006 Motion/Optic Flow 11 Time to Collision f L v L D o l(t) l(t) t=0 t=0 t D(t) And And time to collision time to collision : Can be Can be directly directly measured measured from image from image Can be found, without knowing Can be found, without knowing L or or D o or v !! !!
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L11(motion) - Motion Field and Optical Flow Ack for the...

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