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lecture19 - Motion Estimation Optical flow Measurement of...

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1 Motion Estimation Optical flow Measurement of motion at every pixel

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2 Problem definition: optical flow How to estimate pixel motion from image H to image I? Solve pixel correspondence problem given a pixel in H, look for nearby pixels of the same color in I Key assumptions color constancy: a point in H looks the same in I For grayscale images, this is brightness constancy small motion : points do not move very far This is called the optical flow problem Optical flow equation
3 Lukas-Kanade flow Prob: we have more equations than unknowns The summations are over all pixels in the K x K window This technique was first proposed by Lukas & Kanade (1981) described in Trucco & Verri reading Solution: solve least squares problem minimum least squares solution given by solution (in d) of: Iterative Refinement Iterative Lukas-Kanade Algorithm 1. Estimate velocity at each pixel by solving Lucas-Kanade equations 2. Warp H towards I using the estimated flow field - use image warping techniques 3. Repeat until convergence

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4 image I image H Gaussian pyramid of image H Gaussian pyramid of image I image I u=10 pixels u=5 pixels u=2.5 pixels u=1.25 pixels Coarse-to-fine optical flow estimation image I image J Gaussian pyramid of image H Gaussian pyramid of image I image I image H Coarse-to-fine optical flow estimation run iterative L-K run iterative L-K warp & upsample . . .
5 Multi-resolution Lucas Kanade Algorithm Compute Iterative LK at highest level For Each Level i •Take flow u ( i -1), v ( i -1) from level i -1 •Upsample the flow to create u *( i ), v *( i ) matrices of twice resolution for level i . •Multiply u *( i ), v *( i ) by 2 •Compute I t from a block displaced by u *( i ), v *( i ) •Apply LK to get u ’( i ), v ’( i ) (the correction in flow) •Add corrections u ’( i ), v ’( i ) to obtain the flow u ( i ), v ( i ) at i th level, i.e., u ( i )= u *( i )+ u ’( i ), v ( i )= v *( i )+ v ’( i ) Optical Flow Results

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6 Optical Flow Results Optical flow Results
7 Global Flow Global Flow Dominant Motion in the image Motion of all points in the scene

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lecture19 - Motion Estimation Optical flow Measurement of...

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