Computer Vision - Stereo Vision
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Stereo vision allows computing depth from two images captured from different viewpoints. The key is measuring disparity, how much each pixel moves between the two images. Epipolar geometry constrains the possible matches. Basic stereo algorithms match pixels in conjugate epipolar lines. State-of-the-art methods formulate stereo as an energy minimization problem that balances match quality and smoothness in the depth map. Dynamic programming and graph cuts provide good approximations to solve this NP-hard problem. Structured light and laser scanning are alternatives to passive stereo that simplify correspondence.
Computer Vision - Stereo Vision
- 1. Stereo CSCI 455: Computer Vision Single image stereogram, by Niklas Een
- 2. Mark Twain at Pool Table", no date, UCR Museum of Photography
- 3. Stereo • Given two images from different viewpoints – How can we compute the depth of each point in the image? – Based on how much each pixel moves between the two images
- 4. epipolar lines Epipolar geometry (x1, y1) (x2, y1) x2 -x1 = the disparity of pixel (x1, y1) Two images captured by a purely horizontal translating camera (rectified stereo pair)
- 5. Your basic stereo matching algorithm • Match Pixels in Conjugate Epipolar Lines – Assume brightness constancy – This is a challenging problem – Hundreds of approaches • A good survey and evaluation: http://www.middlebury.edu/stereo/
- 6. Your basic stereo algorithm For each epipolar line For each pixel in the left image • compare with every pixel on same epipolar line in right image • pick pixel with minimum match cost Improvement: match windows
- 7. Stereo matching based on SSD SSD dmin d Best matching disparity
- 8. Window size – Smaller window + • – Larger window + • 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. • D. Scharstein and R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision, 28(2):155-174, July 1998 Effect of window size
- 9. Stereo results – Data from University of Tsukuba – Similar results on other images without ground truth Ground truthScene
- 10. Results with window search Window-based matching (best window size) Ground truth
- 11. 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 For the latest and greatest: http://www.middlebury.edu/stereo/
- 12. Stereo as energy minimization • What defines a good stereo correspondence? 1. Match quality • Want each pixel to find a good match in the other image 2. Smoothness • If two pixels are adjacent, they should (usually) move about the same amount
- 13. Stereo as energy minimization • Find disparity map d that minimizes an energy function • Simple pixel / window matching SSD distance between windows I(x, y) and J(x + d(x,y), y)=
- 14. Stereo as energy minimization I(x, y) J(x, y) y = 141 C(x, y, d); the disparity space image (DSI)x d
- 15. Stereo as energy minimization y = 141 x d Simple pixel / window matching: choose the minimum of each column in the DSI independently:
- 16. Greedy selection of best match
- 17. Stereo as energy minimization • Better objective function { { match cost smoothness cost Want each pixel to find a good match in the other image Adjacent pixels should (usually) move about the same amount
- 18. Stereo as energy minimization match cost: smoothness cost: 4-connected neighborhood 8-connected neighborhood : set of neighboring pixels
- 19. Smoothness cost “Potts model” L1 distance How do we choose V?
- 20. Dynamic programming • Can minimize this independently per scanline using dynamic programming (DP) • Basic idea: incrementally build a table of costs D one column at a time : minimum cost of solution such that d(x,y) = i Recurrence: Base case: (L = max disparity)
- 21. Dynamic programming • Finds “smooth”, low-cost path through DPI from left to right y = 141 x d
- 23. Dynamic programming • Can we apply this trick in 2D as well? • No: dx,y-1 and dx-1,y may depend on different values of dx-1,y-1 Slide credit: D. Huttenlocher
- 24. Stereo as a minimization problem • The 2D problem has many local minima – Gradient descent doesn’t work well • And a large search space – n x m image w/ k disparities has knm possible solutions – Finding the global minimum is NP-hard in general • Good approximations exist… we’ll see this soon
- 25. Questions?
- 26. Depth from disparity f x x’ baseline z C C’ X f
- 27. Real-time stereo • Used for robot navigation (and other tasks) – Several real-time stereo techniques have been developed (most based on simple discrete search) Nomad robot searches for meteorites in Antartica http://www.frc.ri.cmu.edu/projects/meteorobot/index.html
- 28. • Camera calibration errors • Poor image resolution • Occlusions • Violations of brightness constancy (specular reflections) • Large motions • Low-contrast image regions Stereo reconstruction pipeline • Steps – Calibrate cameras – Rectify images – Compute disparity – Estimate depth What will cause errors?
- 29. Active stereo with structured light • Project “structured” light patterns onto the object – simplifies the correspondence problem – basis for active depth sensors, such as Kinect and iPhone X (using IR) camera 2 camera 1 projector camera 1 projector Li Zhang’s one-shot stereo
- 30. Active stereo with structured light https://ios.gadgethacks.com/news/watch-iphone-xs-30k-ir-dots-scan-your-face-0180944/
- 31. 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 Digital Michelangelo Project http://graphics.stanford.edu/projects/mich/
- 32. Laser scanned models The Digital Michelangelo Project, Levoy et al.
- 33. Laser scanned models The Digital Michelangelo Project, Levoy et al.
- 34. Laser scanned models The Digital Michelangelo Project, Levoy et al.
- 35. Laser scanned models The Digital Michelangelo Project, Levoy et al.
- 36. Questions?