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A minimal solution to the autocalibration of radial distortion

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).

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A minimal solution to the autocalibration of radial distortion

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  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? • Isfundamental 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? • Iffundamental matrix is best solution for 3D reconstruction… • How can we compute… accuratefundamental 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 pixel Known 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, 8 Points Algorithm

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

  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 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)

  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-pointalgorithm • 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. (+)

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