A minimal solution to the autocalibration of radial distortion Young Ki Baik (CV Lab.) 2007. 8. 29...
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Transcript of A minimal solution to the autocalibration of radial distortion Young Ki Baik (CV Lab.) 2007. 8. 29...
A minimal solution to the autocalibration oA minimal solution to the autocalibration of radial distortion f radial distortion
Young Ki Baik (CV Lab.)Young Ki Baik (CV Lab.)2007. 8. 29 (Wed)2007. 8. 29 (Wed)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
ReferencesReferencesA minimal solution to the autocalibration of radial distortion
• Zuzana Kukelova and Tomas Pajdla (CVPR2007)
Recent Developments on Direct Relative Orientation• H. Stewenius, C. Engels and D. Nister, Kurt cornelis, Luc Van Gool (I
SPRS Journal of Photogrammetry and Remote Sensing 2006)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Why?Why?… did I select this paper?
• Is fundamental matrix is really best material of real 3D reconstruction?
• Is there any other good solution to replace
fundamental matrix?
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Why?Why?… did I select this paper?
• If fundamental matrix is best solution for 3D reconstruction…
• How can we compute…
accurate fundamental matrix?
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Why?Why?… did I select this paper?
• A recent trend of the MVG is to add …
some constraints!!!
• Autocalibration via Rank-Constrained Estimation of the Absolute Quadric
• M. Chandraker, D. Nister. et. al. (CVPR 2007)
• Minimal Solutions for Panoramic Stitching• Matthew Brown, Richard Hartley, and D. Nister (CVPR 2007)
• An Efficient Minimal Solution for Infinitesimal Camera Motion• Henrik Stewenius, Chris Engels, and D. Nister (CVPR 2007)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
What?What?… is the purpose of this paper?
• Correcting radial distortion
from a pair of distorted real images!!
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Previous work…Previous work…Simultaneous linear estimation of multiple view
geometry and lens distortion • A. Fitzgibbon (CVPR 2001)
A non-iterative method for correcting lens distortion from nine-point correspondences
• H. Li and R. Hartley (OMNIVIS 2005)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Fitzgibbon’s work (CVPR2001)Fitzgibbon’s work (CVPR2001)Assumption
• Radial distortion model (Division model)
21~
d
du r
xx
positionpoint dundistorte:1,, uuu yxx
positionpoint distorted : 1,, ddd yxx
distortion ofcenter thefrom distance : 222ddd yxr
parameter distortion :
• Square pixelSquare pixel• Known Known center of distortioncenter of distortion
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Fitzgibbon’s work (CVPR2001)Fitzgibbon’s work (CVPR2001)Assumption
• Fundamental matrix
8,,1 ,0 iTu
Tu iixFx
333231
232221
131211
fff
fff
fff
F
Scale factorScale factor
Final factor can not be zero !!!Final factor can not be zero !!!
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Fitzgibbon’s work (CVPR2001)Fitzgibbon’s work (CVPR2001)Proposed linear model
• 9 parameters
2311 ,,, ff
9 points algorithm9 points algorithm
•Simultaneous linear estimation of multiple view geometry and lens distortion
- A. Fitzgibbon (CVPR 2001)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Fitzgibbon’s work (CVPR2001)Fitzgibbon’s work (CVPR2001)Using two real distorted imagesFinding initial correspondences
• Cross-correlation• Window size (100x100)
Proposed linear model• Radial distortion param.• MVG param. (F)
RANSAC• Find correct correspondances• Find radial distortion param.• Find geometrical property
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
What?What?… is the difference …
between Fitzgibbon’s work and this paper?
0det F
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
What?What?… is the difference …
between Fitzgibbon’s work and this paper?
• If they succeed their proposed algorithm,If they succeed their proposed algorithm,
8 Points Algorithm8 Points Algorithm
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
What?What?… is the Problem …
to unify constraints?
0det F
0TuTu iixFx 21
~d
du r
xx
Linear Linear equationequation
Too complicatedToo complicated
polynomial polynomial
equationequation
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
How?How?… can solve the complicated polynomial
equation?
•Recent Developments on Direct Relative Orientation
H. Stewenius, C. Engels and D. Nister, Kurt cornelis, Luc Van Gool ( ISPRS Journal of Photogrammetry and Remote Sensing 2006)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Stewenius’ workRelative position
E 02 EEEEEE TT trace
Also complicated polynomial equationAlso complicated polynomial equation
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Stewenius’ workRelative position
• Algebraic geometry tools
• Gröbner basis methodGröbner basis method
• Using Algebraic Geometry•D. Cox, J. Little, and D. O’Shea D. Cox, J. Little, and D. O’Shea (Springer-Verlag, 2005)(Springer-Verlag, 2005)
• Ideals, Varieties, and Algorithms•D. Cox, J. Little, and D. O’Shea D. Cox, J. Little, and D. O’Shea (Springer-Verlag, 2005)(Springer-Verlag, 2005)
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Features of Proposed methodFeatures of Proposed methodUsing an additional constraint
Solving polynomial equations
0det F
Gröbner basis method
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Quantitative results of estimating Quantitative results of estimating Synthetic dataSynthetic data
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Results of real data Results of real data
Distorted imageDistorted image Corrected imageCorrected image
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Contribution of this paperContribution of this paper
Realize the minimal solution• previous 9-point algorithm → 8-point algorithm
Obtain more accurate and stable results
•Additional constraint give more …
A minimal solution to the autocalibration of rA minimal solution to the autocalibration of radial distortionadial distortion
Why?Why?… should this paper have been accepted?
• Idea and contributions of this paper are
not excellent.(-)
•Numerical formulation and results are
good for practical point of view. (+)
•Previous work is well described. (+)
•Paper is well written. (+)