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Unformatted text preview: 1 CS252A, Fall 2010 Computer Vision I Stereo Computer Vision I CSE252A Lecture 14 CS252A, Fall 2010 Computer Vision I Binocular Stereopsis: Mars Given two images of a scene where relative locations of cameras are known, estimate depth of all common scene points. Two images of Mars CS252A, Fall 2010 Computer Vision I Stereo Vision Outline Offline: Calibrate cameras & determine epipolar geometry Online 1. Acquire stereo images 2. Rectify images to convenient epipolar geometry 3. Establish correspondence 4. Estimate depth A B C D CS252A, Fall 2010 Computer Vision I BINOCULAR STEREO SYSTEM Estimating Depth Z X (0,0) (d,0) Z=f X L X R DISPARITY (X L X R ) Z = (f/X L ) X Z= (f/X R ) (Xd) (f/X L ) X = (f/X R ) (Xd) X = (X L d) / (X L X R ) Z = d f (X L X R ) X = d X L (X L X R ) (Adapted from Hager) X L =f(X/Z) X R =f((Xd)/Z) (X,Z) CS252A, Fall 2010 Computer Vision I Reconstruction: General 3D case Linear Method: find P such that NonLinear Method: find Q minimizing where q=MQ and q=MQ Given two image measurements p and p, estimate P. CS252A, Fall 2010 Computer Vision I Random Dot Stereograms 2 CS252A, Fall 2010 Computer Vision I Epipolar Constraint Potential matches for p have to lie on the corresponding epipolar line l . Potential matches for p have to lie on the corresponding epipolar line l . CS252A, Fall 2010 Computer Vision I Epipolar Geometry Epipolar Plane Epipoles Epipolar Lines Baseline CS252A, Fall 2010 Computer Vision I Epipolar Constraint: Calibrated Case Essential Matrix (LonguetHiggins, 1981) CS252A, Fall 2010 Computer Vision I Calibration Determine intrinsic parameters and extrinsic relation of two cameras. From R 1 , t 1 , R 2 , t 2 estimate the Essential matrix CS252A, Fall 2010 Computer Vision I The Fundamental matrix The epipolar constraint is given by: where p and p are 3D coordinates of the image coordinates of points in the two images. Without calibration, we can still identify corresponding points in two images, but we cant convert to 3D coordinates. However, the relationship between the calibrated cordinates (p,p) and uncalibrated coordinates (q,q) can be expressed as p=Aq, and p=Aq Therefore, we can express the epipolar constraint as: (Aq) T E(Aq) = q T (A T EA)q = q T Fq = 0 where F is called the Fundamental Matrix. where F is called the Fundamental Matrix....
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This note was uploaded on 12/08/2010 for the course CSE 252a taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
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