Abstract
Until very recently it was believed that visual tasks require camera calibration. More recently it has been shown that various visual or visually-guided robotics tasks may be carried out using only a projective representation characterized by the projective invariants. This paper studies different algebraic and geometric methods of computation of projective invariants of points and/or lines using only informations obtained by a pair of uncalibrated cameras. We develop combinations of those projective invariants which are insensitive to permutations of the geometric primitives of each of the basic configurations and test our methods on real data in the case of the six points configuration.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. Carlsson. Multiple image invariants using the double algebra. In J. Mundy and A. Zissermann, editors, Proceeding of the DARPA-ESPRIT workshop on Applications of Invariants in Computer Vision, Azores, Portugal, pages 335–350, October 1993.
G. Csurka. Modelisation projective des objets tridimensionnels en vision par ordinateur. These de doctorat, Université de Nice — Sophia Antipolis. April 1996.
G. Csurka and O. Faugeras. Computing three-dimensional projective invariants from a pair of images using the grassmann-cayley algebra. Image and Vision Computing, 1997. to appear.
P. Doubilet, G.C. Rota, and J. Stein. On the foundations of combinatorial theory: Ix combinatorial methods in invariant theory. Studies in Applied Mathematics, 53:185–216, 1974.
R. Hartley. Invariants of lines in space. In Proceedings of darpa Image Understanding Workshop, pages 737–744, 1993.
R. Hartley and P. Sturm. Triangulation. In Proceedings of arpa Image Understanding Workshop, Monterey, California, pages 957–966, November 1994.
R. Horaud, F. Dornaika, and B. Espiau. Visually guided object grasping. ieee Transactions on Robotics and Automation, 1997. submitted.
P. Meer, S. Ramakrishna, and R. Lenz. Correspondence of coplanar features through p 2-invariant representations. In Proceedings of the 12th International Conference on Pattern Recognition, Jerusalem, Israel, pages A 196 202, 1994.
L. Morin. Quelques contributions des invariants projectifs à la vision par ordinateur. Thèse de doctorat, Institut National Polytechnique de Grenoble, January 1993.
C. Rothwell, O. Faugeras, and G. Csurka. A comparison of projective reconstruction methods for pairs of views. Computer Vision and Image Understanding, 1997. to appear.
J.G. Semple and G.T. Kneebone. Algebraic Projective Geometry. Oxford Science Publication, 1952.
U. Uenohara and T. Kanade. Geometric invariants for verification in 3-d object tracking. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Osaka, Japan, volume II, pages 785–790, November 1996.
C. Zeller and O. Faugeras. Applications of non-metric vision to some visual guided tasks. In Proceedings of the 12th International Conference on Pattern Recognition, Jerusalem, Israel, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Csurka, G., Faugeras, O. (1997). Computing projective and permutation invariants of points and lines. In: Sommer, G., Daniilidis, K., Pauli, J. (eds) Computer Analysis of Images and Patterns. CAIP 1997. Lecture Notes in Computer Science, vol 1296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63460-6_101
Download citation
DOI: https://doi.org/10.1007/3-540-63460-6_101
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63460-7
Online ISBN: 978-3-540-69556-1
eBook Packages: Springer Book Archive