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# Lecture-5 - Lecture-5 Computing Optical Flow Lucas Kanade...

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1 Lecture-5 Computing Optical Flow: Lucas & Kanade Global Flow Lucas & Kanade (Least Squares) Optical flow eq t y x f v f u f - = + 9 9 9 1 1 1 t y x t y x f v f u f f v f u f - = + - = + M - - = 9 1 9 1 9 1 t t y y x x f f v u f f f f M M M t f Au = Consider 3 by 3 window

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2 Lucas & Kanade t T T t T T t f A A A u f A Au A f Au 1 ) ( - = = = 2 ) ( min t yi xi f v f u f + + Lucas & Kanade 0 ) ( 0 ) ( = + + = + + yi ti yi xi xi ti yi xi f f v f u f f f v f u f 2 ) ( min t yi xi f v f u f + +
3 ( f xi u + f yi v + f ti ) f xi = 0 ( f xi u + f yi v + f ti ) f yi = 0 f xi 2 u + f xi f yi v = - f xi f ti f xi f yi u + f yi 2 v = - f yi f ti f xi 2 f xi f yi f xi f yi f yi 2 u v = - f xi f ti - f yi f ti Lucas & Kanade - - = - ti yi ti xi yi yi xi yi xi xi f f f f f f f f f f v u 1 2 2 - - - - - = ti yi ti xi xi yi xi yi xi yi yi xi yi xi f f f f f f f f f f f f f f v u 2 2 2 2 2 ) ( 1 - - = - + - = 2 2 2 2 2 2 2 2 ) ( ) ( yi xi yi xi ti yi xi yi xi ti xi yi xi yi xi ti yi yi xi ti xi yi f f f f f f f f f f f v f f f f f f f f f f f u

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4 Comments Horn-Schunck and Lucas-Kanade optical method works only for small motion. If object moves faster, the brightness changes rapidly, 2x2 or 3x3 masks fail to estimate spatiotemporal derivatives. Pyramids can be used to compute large optical flow vectors.
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