Abstract
We introduce the concept of self-calibration of a 1D projective camera from point correspondences, and describe a method for uniquely determining the two internal parameters of a 1D camera based on the trifocal tensor of three 1D images. The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images, and solving for the roots of a cubic polynomial in one variable. Interestingly enough, we prove that a 2D camera undergoing a planar motion reduces to a 1D camera. From this observation, we deduce a new method for self-calibrating a 2D camera using planar motions.
Both the self-calibration method for a 1D camera and its applications for 2D camera calibration are demonstrated on real image sequences. Other applications including 2D affine camera self-calibration are also discussed.
Chapter PDF
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
M. Armstrong, A. Zisserman, and R. Hartley. Self-calibration from image triplets. ECCV, 3–16, 1996.
M. Armstrong. Self-calibration from image sequences. Ph.D. Thesis, University of Oxford, 1996.
P.A. Beardsley and A. Zisserman. Affine calibration of mobile vehicles. Europe-China Workshop on GMICV, 214–221. 1995.
T. Buchanan. The twisted cubic and camera calibration. CVGIP, 42(1):130–132, 1988.
O. Faugeras. Stratification of three-dimensional vision: Projective, affine and metric representations. JOSA, 12:465–484, 1995.
O. Faugeras and S. Maybank. Motion from point matches: Multiplicity of solutions. IJCV, 3(4):225–246, 1990.
O. Faugeras and B. Mourrain. About the correspondences of points between n images. Workshop on Representation of Visual Scenes, 37–44, 1995.
R. Hartley. In defence of the 8-point algorithm. ICCV, 1064–1070, 1995.
R.I. Hartley. A linear method for reconstruction from lines and points. ICCV, 882–887, 1995.
A. Heyden. Geometry and Algebra of Multiple Projective Transformations. Ph.D. thesis, Lund University, 1995.
Q.-T. Luong and O. Faugeras. Self-calibration of a moving camera from point correspondences and fundamental matrices. IJCV, 22(3):261–289, 1997.
S.J. Maybank and O.D. Faugeras. A theory of self calibration of a moving camera. IJCV, 8(2):123–151, 1992.
R. Mohr, B. Boufama, and P. Brand. Understanding positioning from multiple images. AI, (78):213–238, 1995.
L. Quan. Uncalibrated 1D projective camera and 3D affine reconstruction of lines. CVPR, 60–65, 1997.
L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. Trans. PAMI, 19(8):834–845, 1997.
L. Quan. Algebraic Relations among Matching Constraints of Multiple Images. Technical Report INRIA, RR-3345, Jan. 1998 (also TR Lifia-Imag 1995).
A. Shashua. Algebraic functions for recognition. Trans. PAMI, 17(8):779–789, 1995.
M. Spetsakis and J. Aloimonos. A unified theory of structure from motion. DARPA Image Understanding Workshop, 271–283, 1990.
P. Sturm. Vision 3D non calibrée: contributions à la reconstruction projective et étude des mouvements critiques pour l'auto-calibrage. Ph.D. Thesis, INPG, 1997.
P.H.S. Torr and A. Zissermann. Performance characterization of fundamental matrix estimation under image degradation. MVA, 9:321–333, 1997.
B. Triggs. Matching constraints and the joint image. ICCV, 338–343, 1995.
Cyril Zeller and Olivier Faugeras. Camera self-calibration from video sequences: the Kruppa equations revisited. Research Report 2793, INRIA, February 1996.
Z. Zhang, R. Deriche, O. Faugeras, and Q.T. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. AI, 78:87–119, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Faugeras, O., Quan, L., Sturm, P. (1998). Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055658
Download citation
DOI: https://doi.org/10.1007/BFb0055658
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64569-6
Online ISBN: 978-3-540-69354-3
eBook Packages: Springer Book Archive