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Computer Vision

Computer Vision. Stereo Vision. Pinhole Camera. Perspective Projection. Stereo Vision. Two cameras. Known camera positions. Recover depth. scene point. p. p’. image plane. optical center. Correspondences. p. p’. Matrix form of cross product. a =a x i +a y j +a z k.

chanda-roberts
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Computer Vision

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  1. Computer Vision Stereo Vision

  2. Pinhole Camera

  3. Perspective Projection

  4. Stereo Vision • Two cameras. • Known camera positions. • Recover depth. scene point p p’ image plane optical center

  5. Correspondences p p’

  6. Matrix form of cross product a=axi+ayj+azk a×b=|a||b|sin(η)u b=bxi+byj+bzk

  7. The Essential Matrix Essential matrix

  8. Epipolar Line p’ Y2 X2 Z2 O2 Epipole Stereo Constraints M Image plane Y1 p O1 Z1 X1 Focal plane

  9. disparity Depth Z Elevation Zw A Simple Stereo System LEFT CAMERA RIGHT CAMERA baseline Right image: target Left image: reference Zw=0

  10. Stereo View Right View Left View Disparity

  11. Stereo Disparity • The separation between two matching objects is called the stereo disparity.

  12. Parallel Cameras P Z xl xr f pl pr Ol Or Disparity: T T is the stereo baseline

  13. Finding Correspondences

  14. (xl, yl) Correlation Approach LEFT IMAGE • For Each point (xl, yl) in the left image, define a window centered at the point

  15. Correlation Approach RIGHT IMAGE (xl, yl) • … search its corresponding point within a search region in the right image

  16. Correlation Approach RIGHT IMAGE (xr, yr) dx (xl, yl) • … the disparity (dx, dy) is the displacement when the correlation is maximum

  17. ? = g f Most popular Comparing Windows

  18. Comparing Windows Minimize Sum of Squared Differences Maximize Cross correlation

  19. Correspondence Difficulties • Why is the correspondence problem difficult? • Some points in each image will have no corresponding points in the other image. (1) the cameras might have different fields of view. (2) due to occlusion. • A stereo system must be able to determine the image parts that should not be matched.

  20. Structured Light • Structured lighting • Feature-based methods are not applicable when the objects have smooth surfaces (i.e., sparse disparity maps make surface reconstruction difficult). • Patterns of light are projected onto the surface of objects, creating interesting points even in regions which would be otherwise smooth. • Finding and matching such points is simplified by knowing the geometry of the projected patterns.

  21. Stereo results • Data from University of Tsukuba Scene Ground truth (Seitz)

  22. Results with window correlation Estimated depth of field (a fixed-size window) Ground truth (Seitz)

  23. Results with better method • A state of the art method • Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, • International Conference on Computer Vision, September 1999. Ground truth (Seitz)

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