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International Workshop on Robot Vision

RobVis 2001: Robot Vision pp 237–244Cite as

Trifocal Tensors with Grassmann-Cayley Algebra

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1998))

Abstract

In this paper we study trifocal tensors with Grassmann-Cayley algebra. We propose a new method to derive relations among epipoles, fundamental tensors and trifocal tensors of three pinhole cameras. By this method we can find some new constraints satisfied by trifocal tensors.

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References

  1. E. Bayro-Corrochano, J. Lasenby, G. Sommer: Geometric Algebra: a framework for computing point and line correspondences and projective structure using nuncalibrated cameras. In: Proc. of ICPR’96, Vienna, Vol. I, (1996) 334–338.

    Google Scholar 

  2. O. Faugeras, B. Mourrain: On the geometry and algebra of the point and line correspondences between n images. In: Proc. ICCV’95, (1995) 951–956.

    Google Scholar 

  3. O. Faugeras, B. Mourrain: On the geometry and algebra of the point and line correspondences between n images. Technical report 2665, INRIA (1995).

    Google Scholar 

  4. O. Faugeras, T. Papadopoulo: Grassmann-Cayley algebra for modelling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Technical report 3225, INRIA (1997).

    Google Scholar 

  5. O. Faugeras, T. Papadopoulo: A nonlinear method for estimating the projective geometry of three views. In: Proc. ICCV’98 (1998).

    Google Scholar 

  6. R. Hartley: Lines and points in three views-an integrated approach. In: Proc. of ARPA Image Understanding Workshop, Defense Advanced Research Projects Agency, Morgan Kaufmann Publ. Inc. (1994).

    Google Scholar 

  7. D. Hestenes, R. Ziegler: Projective geometry with Clifford algebra. Acta Appl. Math. 23 (1991) 25–63.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Li and Y. Wu (2000): Outer product factorization in Clifford algebra. Proc. of ATCM’99, Guangzhou, pp. 255–264.

    Google Scholar 

  9. H. Li and G. Sommer (2000): Coordinate-free projective geometry for computer vision. In Geometric Computing with Clifford Algebra, G. Sommer (Ed.), Springer Heidelberg, pp. 415–454.

    Google Scholar 

  10. A. Shashua: Trilinearity in visual recognition by alignment. In: LNCS 800, J.-O. Eklundh (Ed.), Springer, (1994) 479–484.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, P. R. China

    Hongbo Li

Authors
  1. Hongbo Li
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Editor information

Editors and Affiliations

  1. Center for Image Technology and Robotics (CITR Tamaki), The University of Auckland, Tamaki Campus, Building 731, 1005, Auckland, New Zealand

    Reinhard Klette

  2. Department of Computer Science, The Hebrew University of Jerusalem, Givat Ram, Ross Building, 91904, Jerusalem, Israel

    Shmuel Peleg

  3. Institut für Informatik, Universitäet Kiel, Preusserstr.1-9, 24105, Kiel, Germany

    Gerald Sommer

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© 2001 Springer-Verlag Berlin Heidelberg

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Li, H. (2001). Trifocal Tensors with Grassmann-Cayley Algebra. In: Klette, R., Peleg, S., Sommer, G. (eds) Robot Vision. RobVis 2001. Lecture Notes in Computer Science, vol 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44690-7_29

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  • DOI: https://doi.org/10.1007/3-540-44690-7_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41694-4

  • Online ISBN: 978-3-540-44690-3

  • eBook Packages: Springer Book Archive

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