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lec16 - 1 CS252A, Fall 2010 Computer Vision I Stereo...

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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 ) (X-d) (f/X L ) X = (f/X R ) (X-d) 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((X-d)/Z) (X,Z) CS252A, Fall 2010 Computer Vision I Reconstruction: General 3-D case Linear Method: find P such that Non-Linear 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 (Longuet-Higgins, 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 3-D 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 3-D 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.

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lec16 - 1 CS252A, Fall 2010 Computer Vision I Stereo...

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