# Lecture-16 - Lecture-16 Computing Motion Trajectories...

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1 Lecture-16 Computing Motion Trajectories http://www.cs.ucf.edu/~vision/papers/ shah/93/SRT93.pdf

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2 Algorithm For Computing Motion Trajectories • Compute tokens using Moravec’s interest operator (intensity constraint). • Remove tokens which are not interesting with respect to motion (optical flow constraint). – Optical flow of a token should differ from the mean optical flow around a small neighborhood.
3 Algorithm For Computing Motion Trajectories • Link optical flows of a token in different frames to obtain motion trajectories. – Use optical flow at a token to predict its location in the next frame. – Search in a small neighborhood around the predicted location in the next frame for a token. • Smooth motion trajectories using Kalman filter. Kalman Filter (Ballistic Model) 0 2 0 2 5 . ) ( 5 . ) ( y t v t a t y x t v t a t x y y x x + + = + + = )) ( ), ( ( ) , , , ( t y t x v v a a y x y x = = y Z ) 5 . ) ( , 5 . ) ( ( ) , ( 0 2 0 2 y t v t a t y x t v t a t x f y y x x - - - - - - = y Z

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4 Kalman Filter (Ballistic Model) ) 1 ( )) ( ) ( ( ) ( )) ( ) 1 ( ( ) ( ) 1 ( ) ( )) 1 ( ) ( ) ( )( ( ) 1 ( ) ( 1 - - = - + - = - - + - = - k P k H k K I k P k H k P H W k H k P k K k k H k Y k K k k T T T Z Z Z T T T f f W f k H k f f k Y y y Z Z Z y 1 k Z Α = = - + - - = ) ( ) 1 ( ) ), ( ( ) (
5 Point Correspondence • Given n video frames taken at different time instants and m points in each frame, the motion correspondence problem deals with a mapping of a point in one frame to another point in the second frame such that no two points map onto the same point

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6 Key Points • Constraints Cost Function • Algorithm Minimize the cost function Constraints Maximum Velocity Consistent Match Common Motion Minimum Velocity Model
7 Proximal Uniformity Constraint • Most objects in the real world follow smooth paths and cover small distance in a small time. – Given a location of point in a frame, its location

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Lecture-16 - Lecture-16 Computing Motion Trajectories...

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