Abstract
Projective reconstruction recovers projective coordinates of 3D scene points from their several projections in 2D images. We introduce a method for the projective reconstruction based on concatenation of trifocal constraints around a reference view. This configuration simplifies computations significantly. The method uses only linear estimates which stay “close” to image data. The method requires correspondences only across triplets of views. However, it is not symmetrical with respect to views. The reference view plays a special role. The method can be viewed as a generalization of Hartley”s algorithm [11], or as a particular application of Triggs’ [21] closure relations.
This research is supported by the Grant Agency of the Czech Republic under the grants 102/97/0480, 102/97/0855, and 201/97/0437, and by the Czech Ministry of Education under the grant VS 96049.
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References
S. Avidan and A. Shashua. Threading fundamental matrices. In ECCV-98, Frieburg, Germany, June 1998. Springer-Verlag.
P. Beardsley, P. Torr, and A. Zisserman. 3D model acquisition from extended image sequences. In Bernard Buxton and Roberto Cippola, editors, ECCV-96. Springer-Verlag, 1996.
D. Bondyfalat, B. Mourrain, and V.Y. Pan. Controlled iterative methods for solving polynomials systems. ISSAC’98. ACM Press, 1998.
J. Buriánek. Korespondence pro virtualní kameru. Master’s thesis, Czech Technical University, FEL ČVUT, Karlovo náměstí 13, Praha, Czech Republic, 1998. In Czech.
O. Faugeras. Three-Dimensional Computer Vision: A Geometric Viewpoint. The MIT Press, 1993.
O. Faugeras and T. Papadopoulo. Grassmann-Cayley algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Technical Report 3225, INRIA, Jully 1997.
O. Faugeras and B. Mourrain. The geometry and algebra of the point and line correspondences between n images. Technical Report RR-2665, INRIA-Sophia Antipolis, Octobre 1995.
Fitzgibbon, A.W. and Cross, G. and Zisserman, A. Automatic 3D Model Construction for Turn-Table Sequences. SMILE98, Freiburg, Germany, Springer-Verlag LNCS 1506, June 1998.
R. I. Hartley. Computation of the quadrifocal tensor. In ECCV-98, volume I, pages 20–35. Springer Verlag, 1998.
R. I. Hartley. Projective reconstruction from line correspondences. Technical report, GE-Corporate Research and Development, P.O. Box 8, Schenectady, NY, 12301., 1995.
R.I. Hartley. Lines and points in three views and the trifocal tensor. International Journal of Computer Vision, 22(2):125–140, March 1997.
A. Heyden. A common framework for multiple view tensors. In ECCV-98, volume I, pages 3–19. Springer Verlag, 1998.
A. Heyden. Reduced multilinear constraints-theory and experiments. International Journal of Computer Vision, 30:5–26, 1998.
R.H. Lewis and P.F. Stiller. Solving the recognition problem for six lines using the Dixon resultant. Preprint submitted to Elsevier Preprint, 1999.
M. Pollefeys, R. Koch, and L. VanGool. Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. In ICCV98, page Session 1.4, 1998.
L. Quan. Invariants of 6 points and projective reconstruction from 3 uncalibrated images. PAMI, 17(1):34–46, January 1995.
A. Shashua. Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. In International Workshop on Algebraic Frames For The Perception Action Cycle (AFPAC97), Kiel Germany, September 1997.
A. Shashua and S. Avidan. The rank 4 constraint in multiple (⩾3) view geometry. In Bernard Buxton and Roberto Cipolla, editors, ECCV-96, pages 196–206. Springer Verlag, April 1996.
A. Shashua and M. Werman. Fundamental tensor: On the geometry of three perspective views. Technical report, Hebrew University of Jerusalem, Institut of Computer Science, 91904 Jerusalem, Israel, 1995.
P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In ECCV-96. Springer-Verlag, 1996.
B. Triggs. Linear projective reconstruction from matching tensors. Technical report, Edinburgh, 1996. British Machine Vision Conference.
B. Triggs. The geometry of projective reconstruction I: Matching constraints and the joint image. Technical report, 1995. unpublished report.
M. Urban, T. Pajdla, and V. Hlaváč. Projective reconstruction from multiple views. Technical Report CTU-CMP-1999-5, CMP, FEL CVUT, Karlovo náměstý 13, Praha, Czech Republic, December 1999.
T. Werner, T. Pajdla, and M. Urban. Rec3d: Toolbox for 3d reconstruction from uncalibrated 2d views. Technical Report CTU-CMP-1999-4, Czech Technical University, FEL CVUT, Karlovo náměstí 13, Praha, Czech Republic, December 1999.
Zhengyou Zhang. Determining the epipolar geometry and its uncertainty: A review. IJCV, 1997.
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Urban, M., Pajdla, T., Hlaváč, V. (2000). Projective Reconstruction from N Views Having One View in Common. In: Triggs, B., Zisserman, A., Szeliski, R. (eds) Vision Algorithms: Theory and Practice. IWVA 1999. Lecture Notes in Computer Science, vol 1883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44480-7_8
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