Lecture-4 - Lecture-4 Computing Optical Flow Hamburg Taxi...

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Lecture-4 Computing Optical Flow Hamburg Taxi seq
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Horn&Schunck Optical Flow df ( x , y , t ) dt ! " f " x dx dt # " f " y dy dt # " f " t ! 0 Sequence Image ) , , ( t y x f
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Horn&Schunck Optical Flow Taylor Series f x y t f x y t f x dx f y dy f t dt ( , , ) ( , , ) ! # # # " ) , , ( ) , , ( t dy y x f t y x f # # # ! 0 ! # # f dy f dx f t y x Interpretation of optical flow eq d=normal flow p=parallel flow Equation of st.line 0 ! # # t y x f v f u f y t y x f f u f f v $ $ ! d f ff t xy ! # 22
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Horn&Schunck (contd) variational calculus discrete version min {( ) ( )} % % # # # # # # f u f v f u u v v dxdy x y t x y x y 2 2 2 2 2 & ( ) ( ) ( ) (( ) f u f v f f u f u f v f f v x y t x x y t y # # # ! # # # ! 2 2 0 0 ( ) ( ) ( ) (( ) f u f v f f u u f u f v f f v v x y t x av x y t y # # # $ ! # # # $ ! 0 0 u u f P D v v f P D av x av y !$ P f u f v f D f f x y t xy ! # # ! # # 22 yy xx u u u # ! 2 Algorithm-1 ! k=0 ! Initialize • Repeat until some error measure is satisfied (converges) uv K K 2 2 y x t av y av x f f D f v f u f P # # ! # # ! u u f P D v v f P D av x av y
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Derivatives ! Derivative: Rate of change of some quantity " Speed is a rate of change of a distance " Acceleration is a rate of change of speed Derivative speed acceleration x x f x f x x x f x f dx df !
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Lecture-4 - Lecture-4 Computing Optical Flow Hamburg Taxi...

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