Stereo models
Algebraic models for stereo
CSE 803 Stockman Fall 2008
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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.
CSE 803 Stockman Fall 2008
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Baseline stereo: carefully aligned
cameras
CSE 803 Stockman Fall 2008
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Computing (x, y, z) in 3D from
corresponding 2D image points
CSE 803 Stockman Fall 2008
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2 calibrated cameras view the
same 3D point at (r1,c1)(r2,c2)
CSE 803 Stockman Fall 2008
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Compute closest approach of the
two rays: use center point V
Shortest
line
segment
between
rays
CSE 803 Stockman Fall 2008
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Connector is perpendicular to
both imaging rays
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Geometric interpretation
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Create a plane perpendicular to ray P; it can
slide along the ray. All lines normal to ray P
are in this plane.
Create a plane perpendicular to ray Q; it can
slide along the ray. All normals to ray Q are in
this plane.
Slide the planes and find that shortest line
segment simultaneously in both planes.
CSE 803 Stockman Fall 2008
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Solve for the endpoints of the
connector
Scaler mult. Fix book
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How to find points Pj and Qj ?
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We assume ray P originates at some fixed image
point [r, c].
The camra matrix is known.
Ray P is defined by 2 linear equations in 3 unknowns
[WPx , WPy, WPZ]
Create a plane perpendicular to ray P; it can slide
along the ray.
Pick some plane, say WPZ = 20 and solve for the
other two 3D coordinates where the ray P pierces this
plane.
Make sure that the ray is not parallel to the picked
plane!
Repeat this process to get two points on ray P and
two points on ray Q; making sure to use the second
803 Stockman
Fall 2008
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camera matrix and CSE
second
image
point for Q.
Correspondence problem is most
difficult aspect
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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 don’t need ss
CSE 803 Stockman Fall 2008
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Epipolar constraint
With aligned cameras, search for corresponding point is
1D along corresponding row of other camera. So, the
match for P1 in image I2CSE
must
be along a given row.
803 Stockman Fall 2008
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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.
CSE 803 Stockman Fall 2008
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Measuring driver body position
4 cameras were used to measure driver position and
posture while driving: 2mm accuracy achieved
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