OpticalFlow - Motion estimation Image Processing 4 Optical...

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1 Image Processing : 4. Optical Flow Aleix M. Martinez [email protected] Motion estimation Optical flow is used to compute the motion of the pixels of an image sequence. It provides a dense (point to point) pixel correspondance. Correspondence problem : determine where the pixels of an image at time t are in the image at time t+1 . Large number of applications. Two important definitions Motion field: “the 2 -D projection of a 3-D motion onto the image plane.” Optical flow: “the apparent motion of the brightness pattern in an image sequence.” The method of The method of Horn and Schunck This is the most fundamental optical flow algorithm. As you will see, it has several important flaws that makes its use inappropriate in a large number of applications. Most of the other algorithms proposed to date are based on the formulation advanced by Horn and Schunck.
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2 If the brightness is assumed to be constant from frame to frame, then the motion associated to each pixel (x,y) of an image I can be modeled as: This is known as the data conservation constraint . The 1 st -order Taylor expansion ) , , ( ) , , ( t t t v y t u x I z y x I 0 t y x I v I u I  R t y x D dxdy I v I u I E 2 ) ( ) , , ( ) , , ( t t t v y t u x I z y x I t I t y I y x I x t y x I t y x I ) , , ( ) , , ( 0 t 0 t I y I dt dy x
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