Camera Calibration
EGGN 512 - Computer Vision
Christopher Douglas
Calibration
●
Intrinsic Camera Matrix
●
6+ point correspondence
●
Vanishing Points
●
Planar Calibration Targets
–
Unknown Movement, 2+ Photos
Projection
Projection
Projection
Solving For P
Solving For P
Solving For P
Solving For P
Solving For P
Solving For P
Solving For P
Solving For P
SVD
Solving For P
Solving For P
Solving For P
Solving For P
Solving For K,R
Solving For K,R
Solving For K,R
Solving For K,R
Ideal K Matrix
Undistortion
Undistortion
Undistortion
Undistortion
Empirical Testing
Empirical Testing
Empirical Testing
Empirical Testing
Empirical Testing
Radial Distortion
●
Has an effect on pixels in a radial fashion:
pixels along concentric circles exhibit the same
displacement
●
●
Can be corrected by re-projecting the image
through the apparatus that originally captured it [1]
Can be modeled with a series of parameters,
but the main effect can be captured in just 1 or
2
●
Using more is often unnecessary and may lead to
numerical instability [2]
Modeling Radial Distortion
Modeling Radial Distortion
Modeling Radial Distortion
Solving For Parameters
Solving For Parameters
Solving For Parameters
Solving For Parameters
Empirical Testing
●
For the sake of time and tedium used a
synthetic checkerboard image
●
In real imaging applications, would use a set of
vertical & horizontal lines
–
–
Window panes on a skyscraper
Set of plumb bob lines
Barrel
k1=3.3
400 points (1 line)
k1=3.3032
Pincushion
k1=-.5
400 points (1 line)
k1=-.499917
Barrel (2)
k1=3.3
k2=2
800 points (2 lines)
k1=3.28129
k2=2.30061
Pincushion (2)
k1=-.3
k2=-.1
1200 points (3 lines)
k1=-.300519
k2=-.0992554
Pincushion (2)
k1=-.3
k2=-.1
400 points (1 per smaller square)
k1=-.3014
k2=-.0944613
Pincushion (2)
k1=-.3
k2=-.1
100 points (1 point/4 smaller squares)
k1=-.308349
k2=-.065128
Pincushion (2)
k1=-.3
k2=-.1
25 points (1 point/16 smaller squares)
k1=-.302588
k2=-.0887552
Pincushion (2)
k1=-.3
k2=-.1
11 points (1 point/40 smaller squares)
k1=-.314392
k2-.0580393
Pincushion (2)
k=-.5
k=-.2
164 points
Pincushion (2)
k1=-.5
k2=-.2
170 points
k1=-.499341
k2=-.200759
k1=-.3
k2=-.3
k3=.3
k4=.5
k5=-.1
k6=.4
k7=-.2
Mixed (7)
116 points
k1=-.330333
k2=-.0768392
k1=-.3
k2=-.3
k3=.3
k4=.5
k5=-.1
k6=.4
k7=-.2
Mixed (7)
488 points
k1=-.321327
k2=-.108505
k1=-3
k2=2
k1=-2
k2=3
845 Points
k1=-2.99983
k2=1.99968
845 Points
k1=2.00009
k2=-3.00093
References
●
●
●
●
●
T.A. Clarke, J.G. Fryer. The development of
camera calibration methods and models.
Photogrammetric Record, 16(91):51-66,1998
Z. Zhang. Flexible camera calibration by
viewing a plane from unknown orientations. The
Proceedings of the Seventh IEEE International
Conference on Computer Vision, 666-673, 1999
D.C. Brown, Close-range camera calibration.
Photogrammetric Engineering, 37(8):855-866,
1971
Special Thanks to Jean-Yves Bouguet (Matlab
camera calibration toolkit creator)
And Wikipedia
Questions