1. A minimal solution to the autocalibration of radial distortion Young Ki Baik (CV Lab.) 2007. 8. 29 (Wed)

2. 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)

3. 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 ?

4. A minimal solution to the autocalibration of radial distortion  Why? … did I select this paper? If fundamental matrix is best solution for 3D reconstruction… How can we compute… accurate fundamental matrix ?

5. 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)

6. 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 !!

7. 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)

8. A minimal solution to the autocalibration of radial distortion  Fitzgibbon’s work (CVPR2001) Assumption Radial distortion model (Division model) Square pixelSquare pixel Known center of distortionKnown center of distortion

9. A minimal solution to the autocalibration of radial distortion  Fitzgibbon’s work (CVPR2001) Assumption Fundamental matrix Scale factor Final factor can not be zero !!!

10. A minimal solution to the autocalibration of radial distortion  Fitzgibbon’s work (CVPR2001) Proposed linear model 9 parameters 9 points algorithm Simultaneous linear estimation of multiple view geometry and lens distortion - A. Fitzgibbon (CVPR 2001)

11. 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

12. A minimal solution to the autocalibration of radial distortion  What? … is the difference … between Fitzgibbon’s work and this paper?

13. 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,If they succeed their proposed algorithm, 8 Points Algorithm

14. A minimal solution to the autocalibration of radial distortion  What? … is the Problem … to unify constraints? Linear equation Too complicated polynomialequation

15. A minimal solution to the autocalibration of radial distortion  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)

16. A minimal solution to the autocalibration of radial distortion   Stewenius’ work Relative position Also complicated polynomial equation

17. A minimal solution to the autocalibration of radial distortion   Stewenius’ work Relative position Algebraic geometry tools Gröbner basis methodGröbner basis method Using Algebraic Geometry D. Cox, J. Little, and D. O’Shea (Springer-Verlag, 2005)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)D. Cox, J. Little, and D. O’Shea (Springer-Verlag, 2005)

18. A minimal solution to the autocalibration of radial distortion  Features of Proposed method Using an additional constraint Solving polynomial equations Gröbner basis method

19. A minimal solution to the autocalibration of radial distortion  Quantitative results of estimating Synthetic data

20. A minimal solution to the autocalibration of radial distortion  Results of real data Distorted image Corrected image

21. 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 …

22. 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. (+)