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# lec17 - Xbox Kinnect Stereo III Depth map...

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1 CS252A, Fall 2010 Computer Vision I Stereo III Computer Vision I CSE252A Lecture 16 CS252A, Fall 2010 Computer Vision I Xbox Kinnect: Depth map http:// www.youtube.com/watch?v =7QrnwoO1-8A Projected pattern http://www.youtube.com/watch?v=CEep7x-Z4wY 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 can’t 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’=A’q’ Therefore, we can express the epipolar constraint as: (Aq) T E(A’q’) = q T (A T EA’)q’ = q T Fq’ = 0 where F is called the Fundamental Matrix. CS252A, Fall 2010 Computer Vision I Rectification CS252A, Fall 2010 Computer Vision I Image pair rectification simplify stereo matching by warping the images Apply projective transformation H so that epipolar lines correspond to horizontal scanlines e e map epipole e to (1,0,0) try to minimize image distortion Note that rectified images usually not rectangular H CS252A, Fall 2010 Computer Vision I Example: forward motion e e’ courtesy of Andrew Zisserman

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2 CS252A, Fall 2010 Computer Vision I Correspondence Search Algorithm For i = 1:nrows for j=1:ncols best(i,j) = -1 for k = mindisparity:maxdisparity c = Match_Metric(I 1 (i,j),I 2 (i,j+k),winsize) if (c > best(i,j)) best(i,j) = c disparities(i,j) = k end end end end O(nrows * ncols * disparities * winx * winy) CS252A, Fall 2010 Computer Vision I Match Metric Summary MATCH METRIC DEFINITION Normalized Cross-Correlation (NCC) Sum of Squared Dif erences (SSD) Normalized SSD Sum of Absolute Dif erences (SAD) Zero Mean SAD Rank Census These two are actually the same CS252A, Fall 2010 Computer Vision I Some Issues • Ordering • Window size • Window shape • Lighting • Ambiguity • Half occluded regions CS252A, Fall 2010 Computer Vision I Lighting Conditions (Photometric Variations) W ( P l ) W ( P r ) CS252A, Fall 2010 Computer Vision I Ambiguity CS252A, Fall 2010 Computer Vision I Multiple Interpretations Each feature on left epipolar line match one and only one feature on right epipolar line.
3 CS252A, Fall 2010 Computer Vision I Window size W = 3 W = 20 Better results with adaptive window T. Kanade and M. Okutomi, A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment,, Proc. International Conference on Robotics and Automation, 1991.

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lec17 - Xbox Kinnect Stereo III Depth map...

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