Camera Pose Estimation Using First-Order Curve Differential Geometry

  • Ricardo Fabbri
  • Benjamin B. Kimia
  • Peter J. Giblin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7575)

Abstract

This paper considers and solves the problem of estimating camera pose given a pair of point-tangent correspondences between the 3D scene and the projected image. The problem arises when considering curve geometry as the basis of forming correspondences, computation of structure and calibration, which in its simplest form is a point augmented with the curve tangent. We show that while the standard resectioning problem is solved with a minimum of three points given the intrinsic parameters, when points are augmented with tangent information only two points are required, leading to substantial computational savings, e.g., when used as a minimal engine within ransac. In addition, computational algorithms are developed to find a practical and efficient solution shown to effectively recover camera pose using both synthetic and realistic datasets. The resolution of this problem is intended as a basic building block of future curve-based structure from motion systems, allowing new views to be incrementally registered to a core set of views for which relative pose has already been computed.

Keywords

Pose Estimation Camera Resectioning Differential Geometry 

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References

  1. 1.
    Agarwal, S., Snavely, N., Simon, I., Seitz, S.M., Szeliski, R.: Building Rome in a day. In: ICCV 2009 (2009)Google Scholar
  2. 2.
    Ayache, N., Lustman, L.: Fast and reliable passive trinocular stereovision. In: ICCV 1987 (1987)Google Scholar
  3. 3.
    Bujnak, M., Kukelova, Z., Pajdla, T.: A general solution to the p4p problem for camera with unknown focal length. In: CVPR 2008 (2008)Google Scholar
  4. 4.
    Fabbri, R., Kimia, B.B.: High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 645–660. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Fabbri, R., Kimia, B.B.: 3D curve sketch: Flexible curve-based stereo reconstruction and calibration. In: CVPR 2010 (2010)Google Scholar
  6. 6.
    Finsterwalder, S., Scheufele, W.: Das ruckwartseinschneiden im raum. Sebastian Finsterwalder zum 75, 86–100 (1937)Google Scholar
  7. 7.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Grunert, J.A.: Das pothenotische problem in erweiterter gestalt nebst Über seine anwendungen in der geodäsie. Archiv der für Mathematik and Physik 1, 238–248 (1841)Google Scholar
  9. 9.
    Haralick, R.M., Lee, C.-N., Ottenberg, K., Nölle, M.: Review and analysis of solutions of the three point perspective pose estimation problem. IJCV 13(3), 331–356 (1994)CrossRefGoogle Scholar
  10. 10.
    Harris, C., Stephens, M.: A combined edge and corner detector. In: Alvey Vision Conference (1988)Google Scholar
  11. 11.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2000)Google Scholar
  12. 12.
    Horaud, R., Conio, B., Leboulleux, O., Lacolle, B.: An analytic solution for the p4p problem. CVGIP 47(1), 33–44 (1989)Google Scholar
  13. 13.
    Hu, Z.Y., Wu, F.C.: A note on the number of solutions of the noncoplanar p4p problem. PAMI 24(4), 550–555 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kahl, F., Heyden, A.: Using conic correspondence in two images to estimate the epipolar geometry. In: ICCV 1998 (1998)Google Scholar
  15. 15.
    Kaminski, J.Y., Shashua, A.: Multiple view geometry of general algebraic curves. IJCV 56(3), 195–219 (2004)CrossRefGoogle Scholar
  16. 16.
    Longuet-Higgins, H.C.: A computer algorithm for reconstructing a scene from two projections. Nature 293, 133–135 (1981)CrossRefGoogle Scholar
  17. 17.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)CrossRefGoogle Scholar
  18. 18.
    Moreels, P., Perona, P.: Evaluation of features detectors and descriptors based on 3D objects. IJCV 73(3), 263–284 (2007)CrossRefGoogle Scholar
  19. 19.
    Porrill, J., Pollard, S.: Curve matching and stereo calibration. IVC 9(1), 45–50 (1991)CrossRefGoogle Scholar
  20. 20.
    Robert, L., Faugeras, O.D.: Curve-based stereo: figural continuity and curvature. In: CVPR 1991 (1991)Google Scholar
  21. 21.
    Sinha, S.N., Pollefeys, M., McMillan, L.: Camera network calibration from dynamic silhouettes. In: CVPR 2004 (2004)Google Scholar
  22. 22.
    Tamrakar, A., Kimia, B.B.: No grouping left behind: From edges to curve fragments. In: ICCV 2007 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ricardo Fabbri
    • 1
  • Benjamin B. Kimia
    • 1
  • Peter J. Giblin
    • 2
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA
  2. 2.University of LiverpoolLiverpoolUK

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