Lecture-15-01-h - Lecture Computing Optical Flow...

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Unformatted text preview: Lecture Computing Optical Flow Horn&Schunck Optical Flow f ( x, y, t ) Image Sequence df ( x, y, t ) ∂f dx ∂f dx ∂f = + + =0 dt ∂x dt ∂y dt ∂t f x u + f y v + f t = 0 brightness constancy eq 1 Horn&Schunck Optical Flow f ( x, y, t ) = f ( x + dx, y + dy, t + dt ) Taylor Series f ( x, y, t ) = f ( x, y, t ) + ∂f ∂f ∂f dx + dy + dt ∂x ∂y ∂t f x dx + f y dy + f t dt = 0 f x u + f y v + f t = 0 brightness constancy eq Interpretation of optical flow eq f xu + f y v + f t = 0 d=normal flow p=parallel flow f f v=- x u- t fy fy d= ft f x2 + f y2 Equation of st.line 2 Horn&Schunck (contd) Ú Ú {( f u + f v + f ) x y 2 t + l (u x2 + u y2 + v x2 + v y2 )}dxdy variational calculus min P D P v = v av - f y D u = uav - f x 2 ( f x u + f y v + f t ) f x + l ( D u) = 0 ( f x u + f y v + f t ) f y + l (( D2 v) = 0 discrete version P = f x uav + f y v av + f t ( f x u + f y v + f t ) f x + l (u - uav ) = 0 ( f x u + f y v + f t ) f y + l ((v - vav ) = 0 D = l + f x2 + f y2 D2u = u xx + u yy Algorithm-1 • k=0 uK vK • Initialize • Repeat until some error measure is satisfied (converges) P D P - fy D k u K = uav-1 - f x K v = v av-1 P = f x uav + f y vav + f t D = l + f x2 + f y2 3 Derivative Masks È- 1 Í- 1 Î È- 1 Í- 1 Î fx 1˘ first image 1˙ ˚ 1˘ second image 1˙ ˚ È- 1 - 1˘ Í 1 1 ˙ first image Î ˚ È- 1 - 1˘ Í 1 1 ˙second image Î ˚ fy È- 1 - 1˘ Í- 1 - 1˙ first image Î ˚ 1 1˘ È Í1 1˙second image Î ˚ ft Synthetic Images 4 Results One iteration 10 iterations l=4 5 ...
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This note was uploaded on 06/12/2011 for the course CAP 5415 taught by Professor Staff during the Fall '08 term at University of Central Florida.

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