Affine shape representation from motion through reference points
Tóm tắt
This paper shows how an affine representation of spatial configuration is obtained from a pair of projection views. Calibration of cameras and knowledge of the camera's motion are not necessary; however, some preselected reference points and their correspondences are needed. Projective and affine geometry invariants are trickily manipulated to do the affine reconstruction. The method is thus geometrically constructive. When it is compared with the solution proposed in 1989 by J.J. Koenderink and A.J. Van Doorn (“Affine Structure from Motion,” Technical Report, Utrect University), the method provides a viewpoint-independent affine representation under parallel projections. Further, we investigate the central-projection case in which, with three additional special reference points, the same affine reconstruction can be done. We also discuss some important applications of this viewpoint independence of shape representation.
Tài liệu tham khảo
J.J. Koenderink and A.J. Van Doorn, “Affine Structure from Motion,” To appear inJournal of the Optical Society of America, 1992.
R. Mohr. and E. Arbogast, “It Can be Done without Camera Calibration,”Patt. Recognition Lett., vol. 12, 1991, pp. 39–43.
R. Mohr, L. Morin, C. Inglebert, and L. Quan, “Geometric Solutions to 3D Vision Problems,” inIntegration and Control in Real Time Active Vision, BRA Series 1991, J. L. Crowley, E. Granum, R. Storer, and A. Duller, eds., Berlin: Springer-Verlag, 1991.
L. Quan and R. Mohr, “Towards structure from motion for linear features through reference points,” inProc. IEEE Workshop on Visual Motion, Washington, DC: IEEE Computer Society, 1991, pp. 249–254.
O.D. Faugeras and G. Toscani, “Camera Calibration for 3D Computer Vision,” inProc. International Workshop on Machine Vision and Machine Intelligence, Tokyo, 1987.
R. Tsai, “A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses,”IEEE. Robotics Automat. vol. RA-3, 1987, pp. 323–344.
H.S.M. Coxeter,Introduction to Geometry, New York: John Wiley, 1980.
J.G. Semple and G.T. Kneebone,Algebraic Projective Geometry, London: Oxford University Press, 1979.