ECE 549CS 543: COMPUTER VISON LECTURE 16

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ECE 549/CS 543 COMPUTER VISON LECTURE
16 STEREO I

• The Trifocal Tensor (Recap)
• The Quadrifocal Tensor (Recap)
• Stereo Reconstruction
• The Stereo Fusion Problem

• Reading Chapters 10 and 11
• A list of potential projects is at
• http//www-cvr.ai.uiuc.edu/ponce/fall04/project
  s.pdf
• Homework Weak Calibration due Th. Oct. 21.
• http//www-cvr.ai.uiuc.edu/ponce/fall04/hw3/hw3
  .pdf

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Trinocular Epipolar Constraints
These constraints are not independent!
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Trinocular Epipolar Constraints Transfer
Given p and p , p can be computed as the
solution of linear equations.
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Trifocal Constraints
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Trifocal Constraints
Calibrated Case
All 3x3 minors must be zero!
Trifocal Tensor
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Trifocal Constraints
Uncalibrated Case
Trifocal Tensor
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Trifocal Constraints 3 Points
Pick any two lines l and l through p and p .
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Do it again.
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Properties of the Trifocal Tensor
i
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Estimating the Trifocal Tensor

• Ignore the non-linear constraints and use linear
  least-squares
• a posteriori.
• Impose the constraints a posteriori.

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The backprojections of the two lines do not
define a line!
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Multiple Views (Faugeras and Mourrain, 1995)
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Two Views
Epipolar Constraint
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Three Views
Trifocal Constraint
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Four Views
Quadrifocal Constraint (Triggs, 1995)
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Geometrically, the four rays must intersect in P..
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Quadrifocal Tensor and Lines
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Scale-Restraint Condition from Photogrammetry
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Stereopsis
Figure from US Navy Manual of Basic Optics and
Optical Instruments, prepared by Bureau of Naval
Personnel. Reprinted by Dover Publications, Inc.,
1969.
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Reconstruction

• Linear Method
• find P such that
• Non-Linear Method find Q minimizing

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Rectification
All epipolar lines are parallel in the rectified
image plane.
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Reconstruction from Rectified Images
Disparity du-u.
Depth z -B/d.
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Stereopsis
Figure from US Navy Manual of Basic Optics and
Optical Instruments, prepared by Bureau of Naval
Personnel. Reprinted by Dover Publications, Inc.,
1969.
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Human Stereopsis Reconstruction
d0
Disparity d r-l D-F.
dlt0
In 3D, the horopter.
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Human Stereopsis Reconstruction
What if F is not known?

• Helmoltz (1909)
• There is evidence showing the vergence angles
• cannot be measured precisely.
• Humans get fooled by bas-relief sculptures.
• There is an analytical explanation for this.
• Relative depth can be judged accurately.

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(Binocular) Fusion
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Human Stereopsis Binocular Fusion
How are the correspondences established?

• Julesz (1971) Is the mechanism for binocular
  fusion
• a monocular process or a binocular one??
• There is anecdotal evidence for the latter
  (camouflage).

• Random dot stereograms provide an objective
  answer

BP!