Conic reconstruction and correspondence from two views

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 18, Issue 2, 1996, Pages 151-160

  Quan, Long ^a  

^a LIFIA CNRS INR1A   (France)

Author keywords

Conic; Reconstruction; Stereo correspondence

Indexed keywords

CAMERAS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; IMAGE ANALYSIS; IMAGE RECONSTRUCTION; LINEAR ALGEBRA; POLYNOMIALS; STABILITY;

CAMERA VIEWS; CLOSED FORM SOLUTION; CONIC CORRESPONDENCE; CONIC RECONSTRUCTION; IMAGE FEATURES; PROJECTION RECONSTRUCTION;

STEREO VISION;

EID: 0030081091     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.481540     Document Type: Article

References (29)

1. K. Kanatani and W. Liu, "3D interpretation of conies and orthogonality," Computer Vision, Graphics and Image Processing, vol. 58, no. 58, pp. 286-301,1993.
2. F.L. Bookstein, "Fitting conic sections to scattered data," Computer Graphics and Image Processing, vol. 9, pp. 56-71,1979.
3. [31 S. Ma, "Conies-based stereo, motion estimation, and pose determination," Int'l J. Computer Vision, vol. 10, no. 1, pp. 7-25,1993.
4. R. Safaee-Rad, I. Tchoukanov, B. Benhabib, and K.C. Smith, "3D pose estimation from a quadratic curved feature in two perspective views," Proc. llth Int'l Conf. Pattern Recognition, The Hague, pp. 341-344,1992.
5. Geometric Invariance in Computer Vision, J.L. Mundy and A. Zisserman, eds. Cambridge, Mass.: MIT Press, 1992.
6. A. Zisserman, C. Marines, D.A. Forsyth, J.L. Mundy, and C.A. Rotwell, "Relative motion and pose from invariants," Proc. British Machine Vision Conf., Oxford, pp. 7-12, Sept. 1990.
7. M. Ferri, F. Mangili, and G. Viano, "Projective pose estimation of linear and quadratic primitives in monocular computer vision," Computer Vision, Graphics and Image Processing, vol. 58, no. 1, pp. 66-84, July 1993.
8. S.J. Maybank, "The projection of two non-coplanar conies," Geometric Invariance in Computer Vision, ]. Mundy and A. Zisserman, eds., pp. 105-119. Cambridge, Mass.: MIT Press, 1992.
9. L. Quan, "Algebraic and geometric invariant of a pair of noncoplanar conies in space," J. Mathematical Imaging and Vision, vol. 5, no. 3, pp. 263-267,1995.
10. L. Quan, "Invariant of a pair of non-coplanar conies in space: Definition, geometric interpretation and computation," Proc. Fifth M'l CoJ. Computer Vision, pp. 926-931, Cambridge, Mass., 1995.
11. S.D. Ma, S.H. Si, and Z.Y. Chen, "Quadric curve based stereo," Proc. Tlth Int'l Conf. Pattern Recognition, pp. 1-4, The Hague, 1992.
12. O. Faugeras, Three-Dimensional Computer Vision-A Geometric Viewpoint, Artificial intelligence. Cambridge, Mass.: M.I.T. Press, 1993.
13. R.I. Hartley, "Projective reconstruction and invariants from multiple images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 1,036-1,041, Oct. 1994.
14. Q.T. Luong and T. Vieville, "Canonic representations for the geometries of multiple projective views," Proc. Third European Conf. Computer Vision, pp. 589-599, Stockholm, May 1994.
15. H.C. Longuet-Higgins, "A computer algorithm for reconstructing a scene from two projections," Nature, vol. 293, pp. 133-135,1981.
16. K.Y. Isai and T.S. Huang, "Uniqueness and estimation of 3D motion parameters of rigid bodies with curved surfaces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 13-27,1984.
17. O.D. Faugeras, Q.T. Luong, and S.J. Maybank, "Camera selfcalibration: Theory and experiments," Proc. Second European Conf. Computer Vision, G. Sandini, ed., pp. 321-334, Santa Margherita Ligure, Italy, May 1992.
18. Q.T. Luong, "Matrice fondamentale et autocalibration en vision par ordinateur," Thèse de doctorat, Université de Paris-Sud, Orsay, France, Dec. 1992.
19. R. Hartley, R. Gupta, and T. Chang, "Stereo from uncalibrated cameras," Proc. Conf. Computer Vision and Pattern Recognition, pp. 761-764, Urbana-Champaign, 111., 1992.
20. J.G. Semple and G.T. Knecbone, Algebraic Projective- Geometry. Oxford Science Publication, 1952.
21. P. Lancaster, Lambda-matrices and Vibrating Systems. Pergamon Press, 1966.
22. G.H. Golub and C.F. Van Loan, Matrix Computation. Baltimore: Johns Hopkins Univ. Press, 1989.
23. F. Uhlig, "A canonical form for a pair of real symmetric matrices that generate a non singular pencil," Linear Algebra and Its Applications, vol. 14, pp. 189-209,1976.
24. D. Forsyth, J.L. Mundy, A. Zisserman, C. Coelho, A. Heller, and C. Rothwell, "Invariant descriptors for 3D object recognition and pose," IEEF. Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 10, pp. 971-991, Oct. 1991.
25. L. Quan, P. Gros, and R. Mohr, "Invariants of a pair of conies revisited," Image and Vision Computing, vol. 10, no. 5, pp. 319-323, June 1992.
26. L. Robert and O. Faugeras, "Relative 3D positionning and 3D convex hull computation from a weakly calibrated stereo pair," Proc. Fourth Int'l Conf. Computer Vision, pp. 540-544, Berlin, May 1993.
27. R.I. Hartley, "Cheirality invariants," Proc. of DARPA Image Understanding Workshop, pp. 745-753,1993.
28. K. Kanatani, Geometric Computation for Machine Vision. Oxford: Oxford Science Publications, 1993.
29. L. Quan and R. Mohr, "Using geometric model guided active contour method for traffic sign detection," Proc. IAPR Int'l Workshop Machine Vision Application, Tokyo, 1990.