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# lecture19 - Motion Estimation Optical flow Measurement of...

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Motion Estimation

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Optical flow Measurement of motion at every pixel
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

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Optical flow equation
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:

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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 1. Repeat until convergence
image I Gaussian pyramid of image H Gaussian pyramid of image I image I image H u=10 pixels u=5 pixels u=2.5 pixels u=1.25 pixels Coarse-to-fine optical flow estimation

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image I 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 . . .
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 )

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Optical Flow Results
Optical Flow Results

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Optical flow Results
Global Flow

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Global Flow Dominant Motion in the image Motion of all points in the scene Motion of most of the points in the scene A Component of motion of all points in the scene
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lecture19 - Motion Estimation Optical flow Measurement of...

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