Stereo models

1
Stereo models

• Algebraic models for stereo

2
General stereo environment
A world point P seen by two cameras must lie at
the intersection of two rays in space. (The
algebraic model is 4 linear equations in the 3
unknowns x,y,z, enabling solution for x,y,z.) It
is also common to use 3 cameras the reason will
be seen later on.
3
Baseline stereo carefully aligned cameras
4
Computing (x, y, z) in 3D from corresponding 2D
image points
5
2 calibrated cameras view the same 3D point at
(r1,c1)(r2,c2)
6
Compute closest approach of the two rays use
center point V
Shortest line segment between rays
7
Connector is perpendicular to both imaging rays
8
Solve for the endpoints of the connector
Scaler mult. Fix book
9
Correspondence problem is most difficult aspect

• Can use interest points and cross correlation
• Can limit search to epipolar line
• Can use symbolic matching (Ch 11) to determine
  corresponding points (called structural
  stereopsis)
• apparently humans dont need ss

10
Epipolar constraint
With aligned cameras, search for corresponding
point is 1D along corresponding row of other
camera. So, the match for P1 in image I2 must be
along a given row.
11
Epipolar constraint for non baseline stereo
computation
Need to know relative orientation of cameras C1
and C2
If cameras are not aligned, a 1D search can still
be determined for the corresponding point. P1,
C1, C2 determine a plane that cuts image I2 in a
line P2 will be on that line.
12
Measuring driver body position
4 cameras were used to measure driver position
and posture while driving 2mm accuracy achieved