Abstract
The popularly used DLT method sometimes fails to give reliable camera parameter estimation. It is therefore important to detect the unreliability and provide the corresponding solutions. Based on a complete framework of invariance for six points, we construct two evaluation functions to detect the unreliability. The two evaluation functions do not involve any computations for the camera projective matrix or optical center and thus are efficient to perform the detection. Then, the guidelines corresponding to the different detection results are presented. In particular, a filtering RANSAC method to remove the detected unreliable points is provided. The filtering RANSAC proves to be successful in removing the unreliable points even if these points are of a large proportion.
Similar content being viewed by others
References
Abdel-Aziz, Y. I., & Karara, H. M. (1971). Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry. In Proceedings of the ASP/UI symposium on close range photogrammetry (pp. 1–18).
Bayro-Corrochano, E., & Banarer, V. (2002). A geometric approach for the theory and applications of 3D projective invariants. Journal of Mathematical Imaging and Vision, 16(2), 131–154.
Buchanan, T. (1992). The projection of six points from 2-space and 3-space. Preprint, Eberstadt, Troyesstr. 78, D-6100 Darmstadt, Germany. http://www.iks.hs-merseburg.de/~buchanan/pubs/Coble.pdf.
Carlsson, S. (1995). View variation and linear invariants in 2-D and 3-D (Tech. Rep. ISRN KTH/NA/P–95/22–SE), December 1995.
Carlsson, S. (1998). Symmetry in perspective. In ECCV (pp. 249–263).
Coble, A. B. (1922). Associated sets of points. Transactions of the American Mathematical Society, 24(1), 1–20.
Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern classification. (2nd ed.). New York: Wiley-Interscience.
Förstner, W. (1987). Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 40(3), 273–310.
Hartley, R., & Zisserman, A. (2000). Multiple view geometry in computer vision. Cambridge: Cambridge University Press.
Kahl, F., & Henrion, D. (2007). Globally optimal estimates for geometric reconstruction problems. International Journal of Computer Vision, 74(1), 3–15.
Quan, L. (1995). Invariants of six points and projective reconstruction from three uncalibrated images. IEEE Transactions on Pattern Recognition and Machine Intelligence, 17(1), 34–46.
Semple, J., & Kneebone, G. (1952). Algebraic projective geometry. Oxford: Oxford University Press.
Slama, C. (1980). Manual of photogrammetry (4th ed.). Falls Church: American Society of Photogrammetry.
Sutherland, I. E. (1963). Sketchpad: a man-machine graphical communications system (Technical report 296). MIT Lincoln Laboratory. Also published by Garland publishing, New York (1980).
Weng, J., Huang, T. S., & Ahuja, N. (1989). Motion and structure from two perspective views: algorithms, error analysis, and error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5), 451–476.
Wu, Y. H. (2001). Bracket algebra, affine bracket algebra, and automated geometric theorem proving. PhD dissertation, Institute of Systems Science, Chinese Academy of Sciences, Beijing.
Wu, Y. H., & Hu, Z. Y. (2003). The invariant representations of a quadric cone and a twisted cubic. IEEE Transactions on Pattern Recognition and Machine Intelligence, 25(10), 1329–1332.
Wu, Y. H., & Hu, Z. Y. (2005). A unified and complete framework of invariance for six points. In H. Li, P. J. Olver, & G. Sommer (Eds.), Lecture notes in computer science : Vol. 3519. Computer algebra and geometric algebra with applications (pp. 403–417). Berlin: Springer.
Wu, Y. H., & Hu, Z. Y. (2006). A robust method to recognize critical configuration for camera calibration. Image and Vision Computing, 24(12), 1313–1318.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, Y., Li, Y. & Hu, Z. Detecting and Handling Unreliable Points for Camera Parameter Estimation. Int J Comput Vis 79, 209–223 (2008). https://doi.org/10.1007/s11263-007-0114-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11263-007-0114-4