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Issue No.02 - February (2009 vol.31)
pp: 370-375
Graziano Chesi , University of Hong Kong, Hong Kong
ABSTRACT
This paper proposes a new approach to estimate the camera displacement of stereo vision systems via minimization of the algebraic error over the essential matrices manifold. The proposed approach is based on the use of homogeneous forms and linear matrix inequality (LMI) optimizations, and has the advantages of not presenting local minima and not introducing approximations of nonlinear terms. Numerical investigations carried out with both synthetic and real data show that the proposed approach provides significantly better results than SVD methods as well as minimizations of the algebraic error over the essential matrices manifold via both gradient descent and simplex search algorithms.
INDEX TERMS
3D/stereo scene analysis, Motion
CITATION
Graziano Chesi, "Camera Displacement via Constrained Minimization of the Algebraic Error", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 2, pp. 370-375, February 2009, doi:10.1109/TPAMI.2008.198
REFERENCES
[1] O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, 1993.
[2] C. Taylor and J. Ostrowski, “Robust Vision-Based Pose Control,” Proc. IEEE Int'l Conf. Robotics and Automation, pp. 2734-2740, 2000.
[3] G. Chesi, K. Hashimoto, D. Prattichizzo, and A. Vicino, “Keeping Features in the Field of View in Eye-in-Hand Visual Servoing: A Switching Approach,” IEEE Trans. Robotics, vol. 20, no. 5, pp. 908-913, 2004.
[4] E. Malis, F. Chaumette, and S. Boudet, “2 1/2 D Visual Servoing,” IEEE Trans. Robotics and Automation, vol. 15, no. 2, pp. 238-250, 1999.
[5] G. Chesi and A. Vicino, “Visual Servoing for Large Camera Displacements,” IEEE Trans. Robotics, vol. 20, no. 4, pp. 724-735, 2004.
[6] Y. Mezouar and F. Chaumette, “Path Planning for Robust Image-Based Control,” IEEE Trans. Robotics and Automation, vol. 18, no. 4, pp. 534-549, 2002.
[7] G. Chesi and Y.S. Hung, “Global Path-Planning for Constrained and Optimal Visual Servoing,” IEEE Trans. Robotics, vol. 23, no. 5, pp. 1050-1060, 2007.
[8] G. Chesi and K. Hashimoto, “A Simple Technique for Improving Camera Displacement Estimation in Eye-in-Hand Visual Servoing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1239-1242, Sept. 2004.
[9] J. Weng, T. Huang, and N. Ahuja, “Motion and Structure from Two Perspective Views: Algorithms, Error Analysis, and Error Estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 5, pp. 451-476, May 1989.
[10] R. Hartley and A. Zisserman, Multiple View in Computer Vision. Cambridge Univ. Press, 2000.
[11] R. Deriche, Z. Zhang, Q.-T. Luong, and O. Faugeras, “Robust Recovery of the Epipolar Geometry for an Uncalibrated Stereo Rig,” Proc. Third European Conf. Computer Vision, 1994.
[12] Z. Zhang, “Determining the Epipolar Geometry and Its Uncertainty—A Review,” Int'l J. Computer Vision, vol. 27, no. 2, pp. 161-195, 1998.
[13] U. Helmke, K. Huper, P.-Y. Lee, and J. Moore, “Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold,” Int'l J. Computer Vision, vol. 74, no. 2, pp. 117-136, 2007.
[14] R. Hartley and F. Kahl, “Global Optimization through Searching Rotation Space and Optimal Estimation of the Essential Matrix,” Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[15] G. Chesi, A. Tesi, A. Vicino, and R. Genesio, “On Convexification of Some Minimum Distance Problems,” Proc. Fifth European Control Conf., 1999.
[16] G. Chesi, A. Garulli, A. Tesi, and A. Vicino, “Solving Quadratic Distance Problems: An LMI-Based Approach,” IEEE Trans. Automatic Control, vol. 48, no. 2, pp. 200-212, 2003.
[17] G. Chesi, A. Garulli, A. Vicino, and R. Cipolla, “Estimating the Fundamental Matrix via Constrained Least-Squares: A Convex Approach,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 3, pp. 397-401, Mar. 2002.
[18] G. Chesi and Y.S. Hung, “Image Noise Induced Errors in Camera Positioning,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 8, pp. 1476-1480, Aug. 2007.
[19] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
[20] Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming. SIAM, 1994.
[21] G. Chesi, A. Garulli, A. Tesi, and A. Vicino, “Characterizing the Solution Set of Polynomial Systems in Terms of Homogeneous Forms: An LMI Approach,” Int'l J. Robust and Nonlinear Control, vol. 13, no. 13, pp. 1239-1257, 2003.
[22] T. Huang and A. Netravali, “Motion and Structure from Feature Correspondences: A Review,” Proc. IEEE, vol. 82, no. 2, pp. 252-268, 1994.
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