Notes
Slide Show
Outline
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Announcements
    • Project 3 code & artifact due Tuesday
    • Final project proposals due noon Wed (by email)
      • One-page writeup (from project web page), specifying:
        • Your team members
        • Project goals.  Be specific.  Describe the input and output.
        • Brief description of your approach.  If you are implementing or extending a previous method, give the reference and web link to the paper.
        • Will you be using helper code (e.g., available online) or will you implement it all yourself?
        • Evaluation method.  How will you test it?  Which test cases will you use?
        • Breakdown--what will each team-member do?  Ideally, everyone should do something imaging/vision related (it's not good for one team member to focus purely on user-interface, for instance).
        • Special equipment that will be needed.  We may be able to help with cameras, tripods, etc.
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Stereo
  • Readings
    • Szeliski, Chapter 10 (through 10.5)
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Anaglyphs online
  • I used to maintain of list of sites, but too hard to keep up to date.  Instead, see wikipedia page:


  • http://en.wikipedia.org/wiki/Anaglyph_image


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Stereo
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Stereo
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Stereo correspondence
  • Determine Pixel Correspondence
    • Pairs of points that correspond to same scene point
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Fundamental matrix
  • Let p be a point in left image, p’ in right image




  • Epipolar relation
    • p maps to epipolar line l’
    • p’ maps to epipolar line l
  • Epipolar mapping described by a 3x3 matrix F




  • It follows that
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Fundamental matrix
  • This matrix F is called
    • the “Essential Matrix”
      • when image intrinsic parameters are known
    • the “Fundamental Matrix”
      • more generally (uncalibrated case)

  • Can solve for F from point correspondences
    • Each (p, p’) pair gives one linear equation in entries of F



    • 8 points give enough to solve for F (8-point algorithm)
    • see Marc Pollefey’s notes for a nice tutorial

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Stereo image rectification
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Stereo image rectification
  • reproject image planes onto a common
  • plane parallel to the line between optical centers
  • pixel motion is horizontal after this transformation
  • two homographies (3x3 transform), one for each input image reprojection
  • C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.
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Stereo matching algorithms
  • Match Pixels in Conjugate Epipolar Lines
    • Assume brightness constancy
    • This is a tough problem
    • Numerous approaches
      • A good survey and evaluation:  http://www.middlebury.edu/stereo/
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Your basic stereo algorithm
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Window size
    • Smaller window
    • Larger window
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Stereo results
    • Data from University of Tsukuba
    • Similar results on other images without ground truth
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Results with window search
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Better methods exist...
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Stereo as energy minimization
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Stereo as energy minimization
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Depth from disparity
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Video View Interpolation
  • http://research.microsoft.com/users/larryz/videoviewinterpolation.htm
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Real-time stereo
  • Used for robot navigation (and other tasks)
    • Several software-based real-time stereo techniques have been developed (most based on simple discrete search)
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Stereo reconstruction pipeline
  • Steps
    • Calibrate cameras
    • Rectify images
    • Compute disparity
    • Estimate depth
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Active stereo with structured light
  • Project “structured” light patterns onto the object
    • simplifies the correspondence problem
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Active stereo with structured light
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Laser scanning
  • Optical triangulation
    • Project a single stripe of laser light
    • Scan it across the surface of the object
    • This is a very precise version of structured light scanning
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Laser scanned models
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Laser scanned models
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Laser scanned models
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Laser scanned models
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Laser scanned models
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Spacetime Stereo