Abstract
In this work, a new affine invariant of parallelograms is introduced, and the explicit constraint equations between the intrinsic matrix of a camera and the similar invariants of a parallelogram or a parallelepiped are established using this affine invariant. Camera calibration and 3D reconstruction from parallelograms are systematically studied based on these constraints. The proposed theoretical results and algorithms have wide applicability as parallelograms and parallelepipeds are not rare in man-made scenes. Experimental results on synthetic and real images validate the proposed approaches.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdel-Aziz, Y.I., Karara, H.M.: Direct linear transformation from comparator coordinates into object space coordinates. In: ASP Symposimy on Colse-Range Photogrammetry, pp. 1–18 (1971)
Tsai, R., Lenz, R.K.: A technique for fully automous and efficient 3d robotics hand/eye calibration. IEEE Trans. Robotics and Automation 5, 345–358 (1989)
Tsai, R.: An efficient and accurate camera calibration technique for 3d machine vision. In: Proc. CVPR, pp. 364–374 (1986)
Zhang, Z.: Flexible camera calibration by viewing a plane from unknown orientations. In: Proc.ICCV, pp. 666–673 (1999)
Sturm, P., Maybank, S.J.: On plane-based camera calibration: A general algorithm, singularities, applications. In: Proc. CVPR, pp. 432–437 (1999)
Zhang, Z.: Camera calibration with one-dimensional objects. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 161–174. Springer, Heidelberg (2002)
Maybank, S.J., Faugeras, O.D.: A theory of self-calibration of a moving camera. IJCV 8, 123–152 (1992)
Hartley, R.I.: Estimation of relative camera positions for uncalibrated cameras. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 579–587. Springer, Heidelberg (1992)
Hartley, R.I.: An algorithm for self calibration from several views. In: Proc. CVPR, pp. 908–912 (1994)
Pollefeys, M., Gool, L., Osterlinck, A.: The modulus constraint: a new constraint for self-calibration. In: Proc. ICPR, pp. 31–42 (1996)
Pollefeys, M., Gool, L.: A stratified approach to metric self-calibration. In: Proc. CVPR, pp. 407–412 (1997)
Hartley, R.I., Agapite, L., Hayman, E., Reid, I.: Camera calibration and search for infinity. In: Proc. ICCV, pp. 510–517 (1999)
Triggs, B.: Auto-calibration and the absolute quadric. In: Proc. CVPR, pp. 609–614 (1997)
Caprile, B., Torre, V.: Using vanishing points for camera calibration. IJCV 4, 127–140 (1990)
Chen, C., Yu, C., Hung, Y.: New calibration-free approach for augmented reality based on parameterized cuboid structure. In: Proc. ICCV, pp. 30–37 (1999)
Wilczkowiak, M., Sturm, P., Boyer, E.: Using geometric constraints through parallelepipeds for calbration and 3d modeling. IEEE-T PAMI 27, 194–207 (2005)
Hartely, R.: Self-calibration of stationary cameras. IJCV 22, 5–23 (1997)
Wolfe, W.J., Mathis, D.: The perspective view of three points. IEEE-T PAMI 13, 66–73 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, F.C., Duan, F.Q., Hu, Z.Y. (2006). An Affine Invariant of Parallelograms and Its Application to Camera Calibration and 3D Reconstruction. In: Leonardis, A., Bischof, H., Pinz, A. (eds) Computer Vision – ECCV 2006. ECCV 2006. Lecture Notes in Computer Science, vol 3952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11744047_15
Download citation
DOI: https://doi.org/10.1007/11744047_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33834-5
Online ISBN: 978-3-540-33835-2
eBook Packages: Computer ScienceComputer Science (R0)