# lec19 - Announcements Motion TA evaluations today HW 4 due...

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1 CS252A, Fall 2010 Computer Vision I Motion Computer Vision I CSE252A Lecture 18 CS252A, Fall 2010 Computer Vision I Announcements TA evaluations today HW 4 due Friday at midnight Will go over final on thurs. CS252A, Fall 2010 Computer Vision I Motion Some problems of motion 1. Correspondence: Where have elements of the image moved between image frames 2. Reconstruction: Given correspondence, what is the 3-D geometry of the scene 3. Segmentation: What are regions of image corresponding to different moving objects 4. Tracking: Where have objects moved in the image? related to correspondence and segmentation. Variations: Small motion (video), Wide-baseline (multi-view) CS252A, Fall 2010 Computer Vision I Rigid Motion: General Case Position and orientation of a rigid body Rotation Matrix & Translation vector Rigid Motion: Velocity Vector: T Angular Velocity Vector: ω (or Ω ) P CS252A, Fall 2010 Computer Vision I Motion Field Equation T : Components of 3-D linear motion ω : Angular velocity vector • (u,v): Image point coordinates • Z: depth • f: focal length CS252A, Fall 2010 Computer Vision I Optical Flow Constraint Equation Assume brightness of patch remains same in both images: Assume small motion: (Taylor expansion of LHS upto first order) Optical Flow: Velocities Displacement: I ( x + u δ t , y + v δ t , t + δ t ) = I ( x , y , t ) I ( x , y , t ) + δ x I x + δ y I y + δ t I t = I ( x , y , t )

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