Computer Vision
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Transcript of Computer Vision
Computer Vision
Stereo Vision
Bahadir K. Gunturk 2
Pinhole Camera
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Perspective Projection
' ' 'x y fx y z
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Stereo Vision
Two cameras. Known camera positions. Recover depth.
scene pointscene point
optical centeroptical center
image planeimage plane
p p’
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Correspondences
p p’
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Matrix form of cross product
20
0 0
y z z y z
z x x z z x
x y y z y x
a b a b a aa b a b a b a a b a b
a b a b a a
( ) 0( ) 0
a a bb a b
a×b=|a||b|sin(η)u a=axi+ayj+azk b=bxi+byj+bzk
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The Essential Matrix
( , ,1)' ( ', ',1)
T
T
p u vp u v
' 0Tp Ep
Essential matrix
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Stereo Constraints
X1
Y1
Z1O1
Image plane
Focal plane
M
p p’Y2
X2
Z2O2
Epipolar Line
Epipole
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A Simple Stereo System
Zw=0
LEFT CAMERA
Left image:reference
Right image:target
RIGHT CAMERA
Elevation Zw
disparity
Depth Z
baseline
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Stereo View
Left View Right View
Disparity
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Stereo Disparity The separation between two matching objects
is called the stereo disparity.
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Parallel Cameras
ZT
fZxxTlr
OOll OOrr
PP
ppll pprr
TT
ZZxxll xxrr
ff
T is the stereo baseline
rlxx
TfZ
rlxxd Disparity:
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Finding Correspondences
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Correlation Approach
For Each point (xl, yl) in the left image, define a window centered at the point
(xl, yl)LEFT IMAGE
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Correlation Approach
… search its corresponding point within a search region in the right image
(xl, yl)RIGHT IMAGE
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Correlation Approach
… the disparity (dx, dy) is the displacement when the correlation is maximum
(xl, yl)dx(xr, yr)RIGHT IMAGE
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Comparing Windows ==??
ff gg
MostMostpopularpopular
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Maximize Cross correlation
Minimize Sum of Squared Differences
Comparing Windows
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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.
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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.
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Stereo results
Ground truthScene
Data from University of Tsukuba
(Seitz)
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Results with window correlation
Estimated depth of field(a fixed-size window)
Ground truth
(Seitz)
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Results with better method
A state of the art methodBoykov et al., Fast Approximate Energy Minimization via Graph Cuts,
International Conference on Computer Vision, September 1999.
Ground truth
(Seitz)