Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera
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.
KeywordsPlanar Motion Internal Parameter Optical Center Principal Point Point Correspondence
Unable to display preview. Download preview PDF.
- 1.M. Armstrong, A. Zisserman, and R. Hartley. Self-calibration from image triplets. ECCV, 3–16, 1996.Google Scholar
- 2.M. Armstrong. Self-calibration from image sequences. Ph.D. Thesis, University of Oxford, 1996.Google Scholar
- 3.P.A. Beardsley and A. Zisserman. Affine calibration of mobile vehicles. Europe-China Workshop on GMICV, 214–221. 1995.Google Scholar
- 5.O. Faugeras. Stratification of three-dimensional vision: Projective, affine and metric representations. JOSA, 12:465–484, 1995.Google Scholar
- 7.O. Faugeras and B. Mourrain. About the correspondences of points between n images. Workshop on Representation of Visual Scenes, 37–44, 1995.Google Scholar
- 8.R. Hartley. In defence of the 8-point algorithm. ICCV, 1064–1070, 1995.Google Scholar
- 9.R.I. Hartley. A linear method for reconstruction from lines and points. ICCV, 882–887, 1995.Google Scholar
- 10.A. Heyden. Geometry and Algebra of Multiple Projective Transformations. Ph.D. thesis, Lund University, 1995.Google Scholar
- 13.R. Mohr, B. Boufama, and P. Brand. Understanding positioning from multiple images. AI, (78):213–238, 1995.Google Scholar
- 14.L. Quan. Uncalibrated 1D projective camera and 3D affine reconstruction of lines. CVPR, 60–65, 1997.Google Scholar
- 15.L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. Trans. PAMI, 19(8):834–845, 1997.Google Scholar
- 16.L. Quan. Algebraic Relations among Matching Constraints of Multiple Images. Technical Report INRIA, RR-3345, Jan. 1998 (also TR Lifia-Imag 1995).Google Scholar
- 17.A. Shashua. Algebraic functions for recognition. Trans. PAMI, 17(8):779–789, 1995.Google Scholar
- 18.M. Spetsakis and J. Aloimonos. A unified theory of structure from motion. DARPA Image Understanding Workshop, 271–283, 1990.Google Scholar
- 19.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.Google Scholar
- 20.P.H.S. Torr and A. Zissermann. Performance characterization of fundamental matrix estimation under image degradation. MVA, 9:321–333, 1997.Google Scholar
- 21.B. Triggs. Matching constraints and the joint image. ICCV, 338–343, 1995.Google Scholar
- 22.Cyril Zeller and Olivier Faugeras. Camera self-calibration from video sequences: the Kruppa equations revisited. Research Report 2793, INRIA, February 1996.Google Scholar
- 23.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.Google Scholar