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Rotation Averaging with Application to Camera-Rig Calibration

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5995))

Abstract

We present a method for calibrating the rotation between two cameras in a camera rig in the case of non-overlapping fields of view and in a globally consistent manner. First, rotation averaging strategies are discussed and an L 1-optimal rotation averaging algorithm is presented which is more robust than the L 2-optimal mean and the direct least squares mean. Second, we alternate between rotation averaging across several views and conjugate rotation averaging to achieve a global solution. Various experiments both on synthetic data and a real camera rig are conducted to evaluate the performance of the proposed algorithm. Experimental results suggest that the proposed algorithm realizes global consistency and a high precision estimate.

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References

  1. Kim, J.H., Li, H., Hartley, R.: Motion estimation for multi-camera systems using global optimization. In: Proc. Comput. Vis. Pattern Recognit., pp. 1–8 (2008)

    Google Scholar 

  2. Kim, J.H., Hartley, R., Frahm, J.M., Pollefeys, M.: Visual odometry for non-overlapping views using second-order cone programming. In: Proc. Asian Conf. on Computer Vision, pp. 353–362 (2007)

    Google Scholar 

  3. Li, H., Hartley, R., Kim, J.H.: A linear approach to motion estimation using generalized camera models. In: Proc. Comput. Vis. Pattern Recognit., pp. 1–8 (2008)

    Google Scholar 

  4. Kumar, R.K., Ilie, A., Frahm, J.-M., Pollefeys, M.: Simple calibration of non-overlapping cameras with a mirror. In: Proc. Comput. Vis. Pattern Recognit., pp. 1–7 (2008)

    Google Scholar 

  5. Esquivel, S., Woelk, F., Koch, R.: Calibration of a multi-camera rig from non-overlapping views. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 82–91. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Govindu, V.M.: Combining two-view constraints for motion estimation. In: Proc. Comput. Vis. Pattern Recognit., pp. 218–225 (2001)

    Google Scholar 

  7. Govindu, V.M.: Lie-algebraic averaging for globally consistent motion estimation. In: Proc. Comput. Vis. Pattern Recognit., pp. 684–691 (2004)

    Google Scholar 

  8. Govindu, V.M.: Robustness in motion averaging. In: Proc. Asian Conf. on Computer Vision, pp. 457–466 (2006)

    Google Scholar 

  9. Tron, R., Vidal, R., Terzis, A.: Distributed pose averaging in camera networks via consensus on SE(3). In: Second ACM/IEEE International Conference on Distributed Smart Cameras, pp. 1–10 (2008)

    Google Scholar 

  10. Tuzel, O., Subbarao, R., Meer, P.: Simultaneous multiple 3d motion estimation via mode finding on Lie groups. In: Int. Conf. Computer Vision, pp. 18–25 (2005)

    Google Scholar 

  11. Moakher, M.: Means and averaging in the group of rotations. SIAM J. Matrix Anal. Appl. 24(1), 1–16 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Martinec, D., Pajdla, T.: Robust rotation and translation estimation in multiview reconstruction. In: Proc. Comput. Vis. Pattern Recognit., pp. 1–8 (2007)

    Google Scholar 

  13. Sarlette, A., Sepulchre, R.: Consensus optimization on manifolds. SIAM J. Control Optim. 48(1), 56–76 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Agrawal, M.: A Lie algebraic approach for consistent pose registration for general euclidean motion. In: Int. Conf. Intelligent Robots and Systems, pp. 1891–1897 (2006)

    Google Scholar 

  15. Devarajan, D., Radke, R.J.: Calibrating distributed camera networks using belief propagation. EURASIP J. Appl. Signal Process. 2007(1) (2007)

    Google Scholar 

  16. Park, F., Martin, B.: Robot sensor calibration: solving AX=XB on the euclidean group. IEEE Transactions on Robotics and Automation 10(5), 717–721 (1994)

    Article  Google Scholar 

  17. Grove, K., Karcher, H., Ruh, E.A.: Jacobi fields and Finsler metrics on compact Lie groups with an application to differentiable pinching problems. Math. Ann. 211, 7–21 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  18. Manton, J.H.: A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups. In: Proceedings of the Eighth Int. Conf. on Control, Automation, Robotics and Vision, Kunming, China, pp. 2211–2216 (2004)

    Google Scholar 

  19. Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization algorithms on matrix manifolds. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  20. Dai, Y., Trumpf, J., Li, H., Barnes, N., Hartley, R.: On rotation averaging in multi-camera systems. Technical report, Northwestern Polytechnical University and Australian National University (2009) (to appear)

    Google Scholar 

  21. Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach. 24, 381–395 (1981)

    MathSciNet  Google Scholar 

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Dai, Y., Trumpf, J., Li, H., Barnes, N., Hartley, R. (2010). Rotation Averaging with Application to Camera-Rig Calibration. In: Zha, H., Taniguchi, Ri., Maybank, S. (eds) Computer Vision – ACCV 2009. ACCV 2009. Lecture Notes in Computer Science, vol 5995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12304-7_32

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  • DOI: https://doi.org/10.1007/978-3-642-12304-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12303-0

  • Online ISBN: 978-3-642-12304-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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