Transcript PPT - Computer Vision Lab.

A minimal solution to the
autocalibration of radial
distortion
Young Ki Baik (CV Lab.)
2007. 8. 29 (Wed)
A minimal solution to the
autocalibration of radial distortion
 References
 A 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 (ISPRS Journal of Photogrammetry and Remote
Sensing 2006)
A minimal solution to the
autocalibration of radial distortion
 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 radial distortion
 Why?
 … did I select this paper?
• If fundamental
reconstruction…
matrix is best solution for 3D
• How can we compute…
accurate fundamental matrix?
A minimal solution to the
autocalibration of radial distortion
 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 radial distortion
 What?
 … is the purpose of this paper?
• Correcting radial distortion
from
a pair of distorted real images!!
A minimal solution to the
autocalibration of radial distortion
 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 radial distortion
 Fitzgibbon’s work (CVPR2001)
 Assumption
• Radial distortion model (Division model)
xu ~
xd
1  r 
2
d
 : distortion parameter
 : undistorte
xu  xu , y•u ,1Square
d point position
pixel
x•d Known
 xd , yd ,center
1: distorted
position
ofpoint
distortion
rd2  xd2  yd2 : distancefrom the center of distortion
A minimal solution to the
autocalibration of radial distortion
 Fitzgibbon’s work (CVPR2001)
 Assumption
• Fundamental matrix
xTui FxuTi  0,
 f11

F   f 21
f
 31
f12
f 22
f 32
i  1,  ,8
f13 

f 23 
f 33 
Scale factor
Final factor can not be zero !!!
A minimal solution to the
autocalibration of radial distortion
 Fitzgibbon’s work (CVPR2001)
 Proposed linear model
• 9 parameters
 , f11,, f 23
9 points algorithm
•Simultaneous linear estimation of multiple
view geometry and lens distortion
- A. Fitzgibbon (CVPR 2001)
A minimal solution to the
autocalibration of radial distortion
 Fitzgibbon’s work (CVPR2001)
 Using two real distorted images
 Finding 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 radial distortion
 What?
 … is
the difference …
between Fitzgibbon’s work and this paper?
detF   0
A minimal solution to the
autocalibration of radial distortion
 What?
 … is
the difference …
between Fitzgibbon’s work and this paper?
• If they succeed their proposed algorithm,
8 Points Algorithm
A minimal solution to the
autocalibration of radial distortion
 What?
 … is
the Problem …
to unify constraints?
xu ~
xd

2
1  rd
detF   0

T
T
x ui Fxui
0
Linear
equation
Too complicated
polynomial
equation
A minimal solution to the
autocalibration of radial distortion
 How?
 … can solve the
equation?
complicated polynomial
•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 200
A minimal solution to the
autocalibration of radial distortion
 Stewenius’ work
 Relative position
E


2EE E  trace EE E  0
T
T
Also complicated polynomial equation
A minimal solution to the
autocalibration of radial distortion
 Stewenius’ work
 Relative position
• Algebraic geometry tools
• Gröbner basis method
• Using Algebraic Geometry
•D. Cox, J. Little, and D. O’Shea
(Springer-Verlag, 2005)
• Ideals, Varieties, and Algorithms
•D. Cox, J. Little, and D. O’Shea
(Springer-Verlag, 2005)
A minimal solution to the
autocalibration of radial distortion
 Features of Proposed method
 Using an additional constraint
detF   0
 Solving polynomial equations
Gröbner basis method
A minimal solution to the
autocalibration of radial distortion
 Quantitative results of estimating 
Synthetic data
A minimal solution to the
autocalibration of radial distortion
 Results of real data
Distorted image
Corrected image
A minimal solution to the
autocalibration of radial distortion
 Contribution 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 radial distortion
 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. (+)