The critical sets of lines for camera displacement estimation: A mixed euclidean-projective and constructive approach

International Journal of Computer Vision

Volumn 23, Issue 1, 1997, Pages 17-44

  Navab, Nassir ^a   Faugeras, Olivier D ^b  

^a SIEMENS CORPORATE RESEARCH   (United States)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CAMERAS; COMPUTATIONAL GEOMETRY; IMAGE ANALYSIS; IMAGE RECONSTRUCTION;

CAMERA DISPLACEMENT ESTIMATION;

COMPUTER VISION;

EID: 0031141034     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007911807871     Document Type: Article

References (52)

1. Abdel-Aziz, Y.I. and Karara, H.M. 1971. Direct linear transformation into object space coordinates in close-range photogrammetry. In Proceedings of the Symposium on Close-Range Photogrammetry, University of Illinois at Urbana-Champaign, Urbana, Illinois, pp. 1-18.
2. Adiv, G. 1985. Determining three-dimensional motion and structure from optical flow generated by several moving objects. IEEE Trans. PAMI, 7:384-401.
3. Brown, C. 1971. Close-range camera calibration. Photogrammetric Engineering, 37(8):855-866.
4. Buchanan, T. 1992a. Critical sets for 3d reconstruction using lines. In Proc. Second European Conf. on Comput. Vision, Santa Margherita Ligure, Italy, pp. 730-738.
5. 3(c). Geometricae Dedicata, 44:223-232.
6. Chasles, M. 1855. Question No. 296. Nouv. Ann. Math., 14:50.
7. Faig, W, 1975. Calibration of close range photogrammetry systems: Mathematical formulation. Photogrammetric Engineering and Remote Sensing, 41(12):1479-1486.
8. Faugeras, O. 1993. Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press: Cambridge, MA.
9. Faugeras, O.D. and Toscani, G. 1986. The calibration problem for stereo. In Proc. IEEE Conf. Comput. Vision Pattern Recog., Miami, FL, pp. 15-20. IEEE.
10. Faugeras, O.D., Lustman, F., and Toscani, G. 1987. Motion and structure from motion from point and line matches. In Proc. First Int'l Conf. Comput. Vision, London, UK, pp. 25-34.
11. Faugeras, O.D. and Maybank, S. 1990. Motion from point matches: Multiplicity of solutions. The International Journal of Computer Vision, 4(3):225-246. Also INRIA Tech. Report 1157.
12. Faugeras, O.D., Navab, N., and Deriche, R. 1990. On the information contained in the motion field of lines and the cooperation between motion and stereo. International Journal on Imaging Systems and Technology, 2:356-370.
13. Finsterwalder, S. 1987. Die geometrischen grundlagen der photogrammetrie. Jahresber. Der Deutschen Math. Vereinigung, 6(2):1-41.
14. Hildreth, E.C. 1983. The Measurement of Visual Motion. MIT Press: Cambridge, MA.
15. Hofmann, W. 1950. Das problem der "Gefährlichen Flächen" in theorie und pr axis. Ph.D. thesis, Fakultät für Bauwesen der technischen Hochschule Mü nchen.
16. Horn, B.K.P. 1987. Motion fields are hardly ever ambiguous. Int'l J. Comput. Vision, 1(3):263-278.
17. Horn, B.K.P. 1990. Relative orientation. Int'l J. Comput. Vision, 4(1):59-78.
18. Horn, B.K.P. and Schunk, B.G. 1981. Determining optical flow. Artif. Intell., 20:199-228.
19. Kanatani, K. 1992. Geometric Computation for Machine Vision. Oxford University Press.
20. Krames, J. 1940. Zur ermittlung eines objektes aus zwei perspektiven. (Ein Beitra g zur Theorie der "gefährlichen Örter.). Monatshefte für Mathematik und Physik, 49:327-354.
21. Liu, Y. and Huang, T.S. 1986. Estimation of rigid body motion using straight line correspondences: Further results. In Proc. 8th Int'l Conf. Pattern Recog., Paris, France, pp. 306-307. IEEE.
22. Liu, Y. and Huang, T.S. 1988a. Estimation of rigid body motion using straight line correspondences. Comput. Vision, Graphics Image Process., 43(1):37-52.
23. Liu, Y. and Huang, T.S. 1988b. A linear algorithm for determining motion and structure from line correspondences. Comput. Vision, Graphics Image Process., 44(1):35-57.
24. Liu, Y., Huang, T.S., and Faugeras, O.D. 1990. Determination of camera location from 2-D to 3-D line and point correspondences. IEEE Trans. PAMI, 12(1):28-37.
25. Longuet-Higgins, H.C. 1981. A computer algorithm for reconstructing a scene from two projections. Nature, 293:133-135.
26. Longuet-Higgins, H.C. 1984. The reconstruction of a scene from two projections-configurations that defeat the 8-point algorithm. In Proc. First Conf. Artif. Intell. Applications, Denver, Colorado, pp. 395-397.
27. Longuet-Higgins, H.C. 1988. Multiple interpretations of a pair of images of a surface. Proc. Roy. Soc. Lond. A., Vol. 418, pp. 1-15.
28. Luong, T. and Faugeras, O. 1994. A stability analysis of the fundamental matrix. In 3rd European Conference on Computer Vision, Stockholm, accepted.
29. Maybank, S.J. 1987. A theoretical study of optical flow. Ph.D. thesis, Birkbeck College, University of London, London, UK.
30. Maybank, S.J. 1990. The projective geometry of ambiguous surfaces. Proceedings of the Royal Society London, A, Vol. 332, pp. 1-47.
31. Maybank, S.J. 1992. Theory of Reconstruction from Image Motion. Springer-Verlag.
32. Navab, N. 1993. Visual motion of lines, and cooperation between motion and stereo. Dissertation, University of Paris XI, Orsay, Paris, France (in English).
33. Navab, N. and Faugeras, O.D. 1993. Monocular pose determination from lines: Critical sets and maximum number of solutions. In Proc. IEEE Conf. Comput. Vision Pattern Recog., New York, USA. IEEE Computer Society, pp. 254-260.
34. Navab, N., Faugeras, O.D., and Vieville, T. 1993. The critical sets of lines for camera displacement estimation: A mixed euclidean-projective and constructive approach. In Proc. Fourth Int'l Conf. Comput. Vision, Berlin, Germany. IEEE.
35. Negahdaripour, S. 1989. Critical surface pairs and triplets. Int'l J. Comput. Vision, 3(4):293-312.
36. Okamoto, A. 1981. Orientation and construction of models, Part I: The orientation problem in close-range photogrammetry. Photogrammetric Engineering and Remote Sensing, 47(10):1437-1454.
37. Okamoto, A. 1984. The model construction problem using the collinearity condition. Photogrammetric Engineering and Remote Sensing, L(6):705-711.
38. Semple, J.G. and Roth, L. 1949. Introduction to Algebraic Geometry. Oxford Clarendon Press. Reprinted 1987.
39. Semple, J.G. and Kneebone, G.T. 1952. Algebraic Projective Geometry. Oxford Clarendon Press. Reprinted 1979.
40. Spetsakis, M.E. and Aloimonos, J. 1990. Structure from motion using line correspondences. Int'l J. Comput. Vision, 4:171-183.
41. Sturm Rudolf. 1909. Die Lehre Von Den Geometrischen Verwandischaften. Leipzig-Berlin, B.G. Teubner.
42. Subbarao, M. 1987. Solution and uniqueness of image flow equations for rigid curved surfaces in motion. In Proc. First Int'l Conf. Comput. Vision, London, UK, pp. 687-692. IEEE.
43. Tsai, R. 1986. An efficient and accurate camera calibration technique for 3D machine vision. In Proc. IEEE Conf. Comput. Vision Pattern Recog., Miami, FL. IEEE, pp. 364-374.
44. Tsai, R. and Huang, T.S. 1982. Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular value decomposition. IEEE Trans. ASSP, 30.
45. Tsai, R.Y. and Huang, T.S. 1984. Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surface. IEEE Trans. PAMI, 6(1):13-26.
46. Viéville, T. and Faugeras, O. 1990. Feed-forward recovery of motion and structure from a sequence of 2D-lines matches. In Proc. Third Int'l Conf. Comput. Vision, Osaka, Japan, pp. 517-520.
47. Waxman, A.M. and Duncan, J.H. 1986. Binocular image flows: Steps toward stereo-motion fusion. IEEE Trans. PAMI, 8(6):715-729.
48. Weng, J., Ahuja, N., and Huang, T.S. 1992. Motion and structure from line correspondences: Closed-form solution, uniqueness and optimization. IEEE Trans. PAMI, 14(3).
49. Wolf, P.R. Elements of Photogrammetry. McGraw-Hill: New York, 2nd edition.
50. Wong, K.W. 1975. Mathematical formulation and digital analysis in close-range pho togrammetry. Photogrammetric Engineering and remote Sensing, 41(11):1355-1373.
51. Wunderlich, W. 1941. Zur Eindeutigkeitsfrage der hauptaufgabe der Photogrammetrie. Monatshefte für Mathematik und Physik, 50:151-164.
52. Zeller, M. 1952. Textbook of Photogrammetry. H.K. Lewis & Company: London.