1 / 24

Computer Engineering YOO GWI HYEON

Camera calibration from multiple view of a 2D object, using a global non linear minimization method. Computer Engineering YOO GWI HYEON. Camera calibration. Abstract We propose this paper a which is based on a camera model that incorporates lens distortion

gladys
Download Presentation

Computer Engineering YOO GWI HYEON

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Camera calibration from multiple view of a 2D object, using a global non linear minimization method Computer Engineering YOO GWI HYEON

  2. Camera calibration • Abstract • We propose this paper a which is based on a camera model that incorporates lens distortion • Which involves a non-linear minimization technique • which can be performed using multiple view of a single 2D object, and subpixel features extraction

  3. Camera calibration • Two factors demanded from camera calibration • Intrinsic parameters • The process of determining the internal camera geometric and optical characteristics • Extrinsic parameters • The 3D position and orientation of the camerawith respect to some predefined world coordinate system

  4. Camera calibration • The achieved calibration accuracy depends • The accuracy of the 3D calibration object or accuracy of the xyz translation stage for moving a planar calibration tile • The accuracy provided on the attributes of 2D features extracted from the image • The numerical method used for estimating the camera parameters

  5. Camera models • Pinhole model • The most widely used camera model • The coordinate of a 3D point P = [x, y, z]T in a world coordinate system and its retinal coordinates P = [u, v]T are related by a perfect perspective transformation (su, sv, s)T = M (X, Y, Z, 1)T

  6. Numerical methods • Three categories of techniques • Closed-Form Solution techniques • The Parameters values are computed directly form analytical formulas • Global Nonlinear Minimization techniques • The parameters are estimated by an iterative algorithm used to minimize linear (or non-linear) criterion provided by set of measurement equations • Two- step Method a closed- form solution • Derived for most of the calibration parameters and some iterative solution is used for the other parameters

  7. Numerical methods • Minimization methods • Initialization step • An approximative solution is computed for all the parameters by a simple technique using a simple camera model • Estimation step • The nonlinear optimization is started with this approximative solution as an initial guess

  8. Camera models • The Pinhole camera model

  9. Camera models • The Pinhole camera model

  10. Camera models • The Pinhole camera model

  11. Numerical methods • Levenberg-Marquardt method • This method can be used with a very approximative initial guess • Main drawback is that it does not provide an accuracy estimate on the computed parameter ɵ

  12. Numerical methods • Extended Kalman Filter(EKF) • It is a recursive method • A well-known drawback of the EKF method is that it is very sensitive about the initial guess and many measurements are often required to ensure a good convergence

  13. Numerical methods • Extended Kalman Filter(EKF)

  14. Numerical methods • Application of Extended KalmanFilter(EKF) • Integrated Navigation System • GPS • Target tracking • Attitude determination • Orbit determination

  15. Numerical methods • Bard-Deming algorithm • Bard-Deming algorithm Canbe prefered to the EKF method, for off line processing, like the calibration step • It is iterative method which considers globally all measurements

  16. Experimental set-up • These Global nonlinear Minimization techniques could be performed in different contexts • Classical calibration • The parameter vector ɵ contains the I intrinsic parameters and only one E transform • Mutiview calibration • The parameter vector contains the I intrinsic parameters and as many Ei transforms as the object position • Object calibration • The parameter vector contains only one E transform

  17. Experimental set-up

  18. Experimental set-up • The calibration function

  19. Experimental set-up • Grey level model • The grey level model of a cross line centered in is given by a mathematical function which depends on 11 parameter • The precise location of the cross center is given by the estimation of these parameters with a non linear minimization of the difference between grey levels of the theoretical shape and the observed one

  20. Experimental results • The evaluation criteria of a calibration method • The stability of the intrinsic parameters when several runs are performed with different positions of the calibration object • several residues provided by the minimization method, i.e. the value of the measurement equation computed with the final parameter estimates • The best criteria: the application.

  21. Experimental results

  22. Experimental results

  23. Experimental results

  24. Conclusion • Several Nonlinear Minimization methods • The best one of the parameter accuracy seems to be the Bard-Deming algorithm, but it is too expensive in memory requirements and in computation time • Levenberg-Marquardt minimization algorithm converges faster • The Extended Kalman Filter requires a good initial guess, but allow to detect the outliers with a probabilistic test, provided that realistic uncertainty model can be exhibited for the extracted point and for the object model

More Related