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Computer Vision

Computer Vision. Spring 2010 15-385,-685 Instructor: S. Narasimhan WH 5409 T-R 10:30am – 11:50am Lecture #15. Binocular Stereo Lecture #15. Recovering 3D from Images. How can we automatically compute 3D geometry from images? What cues in the image provide 3D information?.

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Computer Vision

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  1. Computer Vision Spring 2010 15-385,-685 Instructor: S. Narasimhan WH 5409 T-R 10:30am – 11:50am Lecture #15

  2. Binocular Stereo Lecture #15

  3. Recovering 3D from Images • How can we automatically compute 3D geometry from images? • What cues in the image provide 3D information?

  4. Visual Cues for 3D • Shading Merle Norman Cosmetics, Los Angeles

  5. Visual Cues for 3D • Shading • Texture The Visual Cliff, by William Vandivert, 1960

  6. Visual Cues for 3D • Shading • Texture • Focus From The Art of Photography, Canon

  7. Visual Cues for 3D • Shading • Texture • Focus • Motion

  8. Visual Cues for 3D • Others: • Highlights • Shadows • Silhouettes • Inter-reflections • Symmetry • Light Polarization • ... • Shading • Texture • Focus • Motion • Shape From X • X = shading, texture, focus, motion, ... • We’ll focus on the motion cue

  9. Stereo Reconstruction • The Stereo Problem • Shape from two (or more) images • Biological motivation known camera viewpoints

  10. Why do we have two eyes? Cyclope vs. Odysseus

  11. 1. Two is better than one

  12. 2. Depth from Convergence

  13. 3. Depth from binocular disparity P: converging point C: object nearer projects to the outside of the P, disparity = + F: object farther projects to the inside of the P, disparity = - Sign and magnitude of disparity

  14. Binocular Stereo

  15. right image baseline left image Assume that we know corresponds to From perspective projection(define the coordinate system as shown above) Disparity and Depth scene

  16. right image baseline left image is the disparity between corresponding left and right image points Disparity and Depth scene • inverse proportional to depth • disparity increases with baseline b

  17. field of view of stereo uncertainty of scenepoint one pixel Optical axes of the two cameras need not be parallel Vergence • Field of view decreases with increase in baseline and vergence • Accuracy increases with baseline and vergence

  18. Binocular Stereo scene point image plane optical center

  19. Binocular Stereo • Basic Principle: Triangulation • Gives reconstruction as intersection of two rays • Requires • calibration • point correspondence

  20. epipolar line epipolar line epipolarplane Stereo Correspondence • Determine Pixel Correspondence • Pairs of points that correspond to same scene point • Epipolar Constraint • Reduces correspondence problem to 1D search along conjugateepipolar lines • Java demo: http://www.ai.sri.com/~luong/research/Meta3DViewer/EpipolarGeo.html

  21. Stereo Image Rectification

  22. Stereo Image Rectification • reproject image planes onto a common • plane parallel to the line between optical centers • pixel motion is horizontal after this transformation • C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999. Details in next lecture

  23. Stereo Rectification

  24. For each epipolar line For each pixel in the left image • Improvement: match windows • This should look familiar... • Correlation, Sum of Squared Difference (SSD), etc. Basic Stereo Algorithm • compare with every pixel on same epipolar line in right image • pick pixel with minimum match cost

  25. W = 3 W = 20 Size of Matching window • Smaller window Good/bad ? • Larger window Good/bad ? • Effect of window size • 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. • D. Scharstein and R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision, 28(2):155-174, July 1998

  26. Stereo Results • Data from University of Tsukuba Scene Ground truth

  27. Results with Window Search Window-based matching (best window size) Ground truth

  28. Better methods exist... • State of the art method • Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, • International Conference on Computer Vision, September 1999. Ground truth

  29. depth map 3D rendering [Szeliski & Kang ‘95] Stereo Example input image (1 of 2)

  30. left image right image depth map Stereo Example H. Tao et al. “Global matching criterion and color segmentation based stereo”

  31. Stereo Example H. Tao et al. “Global matching criterion and color segmentation based stereo”

  32. Stereo Matching • Features vs. Pixels? • Do we extract features prior to matching? Julesz-style Random Dot Stereogram

  33. Range Scanning and Structured Light

  34. Next Class • Binocular Stereo (relative and absolute orientation) • Reading: Horn, Chapter 13.

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