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Stereopsis.md

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Sam Saltwick
October 23 2018
Fall 2018

Steropsis


Why Stereo Vision?

  • 2D images project 3D points into 2D
  • 3D points on the same viewing line have the same 2D image
    • 2D imaging results in depth information loss

Stereo

  • Assumes two cameras with known positions
  • Can recover depth from this information

Recovering Depth

  • Depth recovered with two images and triangulation
  • Find correspondences between images and see where their projective lines meet
  • Solution is not always unique
    • Looking at 3 points -> 9 intersections in space -> 3 possible solutions
  • Find Correspondences and epipolar lines
    • Epipolar lines -> lines formed by the intersection between the plane created by 2 correspondences and their intersection and the camera plane
    • Reduces correspondence problem to 1D search in conjugate epipolar lines

Simplest Case

  • Image planes of cameras are parallel
  • Focal points are at the same height
  • Focal lengths are the same
  • => Epipolar lines are horizontal scan lines

Calculations

$$ \frac{T + x_r - x_l}{Z -f} = \frac{T}{Z} \[1em] Z = f \frac{T}{x_l - x_r} , d = x_l - x_r \implies \boxed{Z = f \frac{T}{d}} $$

  • T is the stereo baseline
  • d measures the difference in retinal position between correspondences
  • Given Z we can compute X and Y

What Correspondences should we match?

  • Objects? Edges? Pixels? Collections of pixels?
  • Slide window along scanline and compare its contents with the reference window in the other image
  • Matching Cost: SSD or normalized correlation
    • Minimize SSD or Maximized Correlation
  • Correspondence at the minimum point of the matching cost
  • Effects of Window Size
    • Window size too small -> A lot of noise
    • Window size too big -> Too much smoothing => loss of detail