CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2010 vol.32 Issue No.10 - October

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Issue No.10 - October (2010 vol.32)

pp: 1907-1914

John Lim , NICTA and Australian National University, Canberra

Nick Barnes , NICTA, Australian National University, Canberra and Bionic Vision Australia

Hongdong Li , NICTA, Australian National University, Canberra and Bionic Vision Australia

ABSTRACT

This paper introduces a novel antipodal-epipolar constraint on relative camera motion. By using antipodal points, which are available in large Field-of-View cameras, the translational and rotational motions of a camera are geometrically decoupled, allowing them to be separately estimated as two problems in smaller dimensions. We present a new formulation based on discrete camera motions, which works over a larger range of motions compared to previous differential techniques using antipodal points. The use of our constraints is demonstrated with two robust and practical algorithms, one based on RANSAC and the other based on Hough-like voting. As an application of the motion decoupling property, we also present a new structure-from-motion algorithm that does not require explicitly estimating rotation (it uses only the translation found with our methods). Finally, experiments involving simulations and real image sequences will demonstrate that our algorithms perform accurately and robustly, with some advantages over the state-of-the-art.

INDEX TERMS

Multiview geometry, antipodal points, epipolar constraint, structure and motion, Hough, robust estimation.

CITATION

John Lim, Nick Barnes, Hongdong Li, "Estimating Relative Camera Motion from the Antipodal-Epipolar Constraint",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.32, no. 10, pp. 1907-1914, October 2010, doi:10.1109/TPAMI.2010.113REFERENCES

- [1] K. Prazdny, "Egomotion and Relative Depth Map from Optical Flow"
Biological Cybernetics, vol. 36, pp. 87-102, 1980.- [2] J. Gluckman and S.K. Nayar, "Ego-Motion and Omnidirectional Cameras,"
Proc. IEEE Int'l Conf. Computer Vision, 1998.- [3] G.L. Mariottini and D. Prattichizzo, "Image-Based Visual Servoing with Central Catadioptric Camera"
Int'l J. Robotics Research, vol. 27, pp. 41-57, 2008.- [4] R. Hartley and A. Zisserman,
Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2004.- [5] H. Stewénius, C. Engels, and D. Nistér, "An Efficient Minimal Solution for Infinitesimal Camera Motion,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2007.- [6] J.C. Bazina, C. Demonceaux, P. Vasseur, and I.S. Kweon, "Motion Estimation by Decoupling Rotation and Translation in Catadioptric Vision,"
Computer Vision and Image Understanding, vol. 114, no. 2, pp. 254-273, 2010.- [7] M. Antone and S. Teller, "Automatic Recovery of Relative Camera Rotations for Urban Scenes,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2000.- [8] H. Longuet-Higgins, "A Computer Algorithm for Reconstruction of a Scene from Two Projections"
Nature, vol. 293, pp. 133-135, 1981.- [9] R. Hartley, "In Defence of the 8-Point Algorithm,"
Proc. Fifth Int'l Conf. Computer Vision, pp. 1064-1075, 1995.- [10] D. Nister, "An Efficient Solution to the Five-Point Relative Pose Problem,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 6, pp. 756-770, June 2004.- [11] Z. Kukelova, M. Bujnak, and T. Pajdla, "Polynomial Eigenvalue Solutions to the 5-pt and 6-pt Relative Pose Problems,"
Proc. British Machine Vision Conf., 2008.- [12] H. Li and R. Hartley, "Five-Point Motion Estimation Made Easy,"
Proc. Int'l Conf. Pattern Recognition, pp. 630-633, http://users.cecs.anu.edu.au%7Ehongdong, 2006.- [13] R. Hartley and F. Kahl, "Global Optimization through Searching Rotation Space and Optimal Estimation of the Essential Matrix,"
Proc. IEEE Int'l Conf. Computer Vision, 2007.- [14] R. Hartley and F. Kahl, "Global Optimization through Rotation Space Search"
Int'l J. Computer Vision, vol. 82, no. 1, pp. 64-79, 2009.- [15] Q.-T. Luong, R. Deriche, O.D. Faugeras, and T. Papadopoulo, "On Determining the Fundamental Matrix: Analysis of Different Methods and Experimental Results," Technical Report RR-1894, INRIA, 1993.
- [16] Z. Zhang, "Determining the Epipolar Geometry and Its Uncertainty: A Review," Technical Report RR-2927, INRIA, 1996.
- [17] A. Jepson and D. Heeger, "Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation"
Int'l J. Computer Vision, vol. 7, no. 2, pp. 95-117, 1992.- [18] K. Kanatani, Y. Shimizu, N. Ohta, M.J. Brooks, W. Chojnacki, and A. van den Hengel, "Fundamental Matrix from Optical Flow: Optimal Computation and Reliability Evaluation"
J. Electronic Imaging, vol. 9, no. 2, pp. 194-202, 2000.- [19] C. Tomasi and J. Shi, "Direction of Heading from Image Deformations,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 422-427, 1993.- [20] C. Fermüller and Y. Aloimonos, "Qualitative Egomotion"
Int'l J. Computer Vision, vol. 15, pp. 7-29, 1995.- [21] A.R. Bruss and B.K. Horn, "Passive Navigation"
Computer Vision, Graphics, and Image Processing, vol. 21, pp. 3-20, 1983.- [22] J.H. Rieger and D.T. Lawton, "Processing Differential Image Motion"
J. Optical Soc. Am. A, vol. 2, no. 2, pp. 354-359, 1985.- [23] K. Prazdny, "On the Information in Optical Flows"
Computer Graphics and Image Processing, vol. 22, pp. 239-259, 1983.- [24] J. Oliensis, "A Critique of Structure-from-Motion Algorithms"
Computer Vision and Image Understanding, vol. 80, no. 2, pp. 172-214, 2000.- [25] J. Oliensis and G. Yakup, "New Algorithms for Two-Frame Structure from Motion,"
Proc. IEEE Int'l Conf. Computer Vision, pp. 737-744, 1999.- [26] J. Oliensis, "Exact Two-Image Structure from Motion"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1618-1633, Dec. 2002.- [27] R. Hartley and P. Sturm, "Triangulation"
Computer Vision and Image Understanding, vol. 68, no. 2, pp. 146-157, 1997.- [28] K. Kanatani,
Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier, 1996.- [29] M.A. Fischler and R.C. Bolles, "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography"
Comm. ACM, vol. 24, no. 6, pp. 381-395, June 1981.- [30] P.H.S. Torr and A. Zisserman, "MLESAC: A New Robust Estimator with Application to Estimating Image Geometry"
J. Computer Vision and Image Understanding, vol. 78, no. 1, pp. 138-156, 2000.- [31] J. Matas and O. Chum, "Randomized RANSAC with $T_{d,d}$ Test"
Image and Vision Computing, vol. 22, no. 10, pp. 837-842, Sept. 2004.- [32] O. Chum and J. Matas, "Optimal Randomized RANSAC,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 8 pp. 1472-1482, Aug. 2008.- [33] D. Nistér, "Preemptive RANSAC for Live Structure and Motion Estimation"
Machine Vision Applications, vol. 16, no. 5, pp. 321-329, 2005.- [34] P. Rousseeuw, "Least Median of Squares Regression"
J. Am. Statistical Assoc., vol. 79, pp. 871-880, 1984.- [35] J. Lim and N. Barnes, "Estimation of the Epipole Using Optical Flow at Antipodal Points,"
Computer Vision and Image Understanding, vol. 114, no. 2, pp. 245-253, 2010.- [36] J. Lim and N. Barnes, "Directions of Egomotion from Antipodal Points,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.- [37] C.X. Hu and L.F. Cheong, "Linear Quasi-Parallax SfM Using Laterally-Placed Eyes"
Int'l J. Computer Vision, vol. 84, no. 1, pp. 21-39, 2009.- [38] J. Lim and N. Barnes, "Estimation of the Epipole Using Optical Flow at Antipodal Points,"
Proc. Workshop on Omnidirectional Vision Camera Networks and Non-Classical Cameras, 2007.- [39] I. Thomas and E. Simoncelli, "Linear Structure from Motion," technical report, IRCS, Univ. of Pennsylvania, 1994.
- [40] D.H. Ballard and O.A. Kimball, "Rigid Body Motion from Depth and Optical Flow"
Computer Vision, Graphics, and Image Processing, vol. 22, pp. 95-115, 1984.- [41] A. Makadia, C. Geyer, S. Sastry, and K. Daniilidis, "Radon-Based Structure from Motion without Correspondences,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2005.- [42] R.J.M. den Hollander and A. Hanjalic, "A Combined RANSAC-Hough Transform Algorithm for Fundamental Matrix Estimation,"
Proc. 18th British Machine Vision Conf., 2007.- [43] B. Triggs, "Plane$+$ Parallax, Tensors and Factorization,"
Proc. European Conf. Computer Vision, pp. 522-538, 2000.- [44] C. Rother and S. Carlsson, "Linear Multi View Reconstruction and Camera Recovery,"
Proc. IEEE Int'l Conf. Computer Vision, pp. 42-50, 2001.- [45] B. Triggs, P.F. McLauchlan, R. Hartley, and A. Fitzgibbon, "Bundle Adjustment—a Modern Synthesis,"
Proc. Int'l Workshop Vision Algorithms, pp. 298-372, 1999.- [46] P.D. Kovesi, "MATLAB and Octave Functions for Computer Vision and Image Processing," http://www.csse.uwa.edu.au/%7Epk/research matlabfns/, 2009.
- [47] Point Grey Research, http:/www.ptgrey.com, 2009.
- [48] D. Lowe, SIFT Code: http://www.cs.ubc.ca/%7Elowekeypoints/, 2009.
- [49] E. Tola, V. Lepetit, and P. Fua, "A Fast Local Descriptor for Dense Matching,"
Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.- [50] H. Li, "Consensus Set Maximization with Guaranteed Global Optimality for Robust Geometry Estimation,"
Proc. IEEE Int'l Conf. Computer Vision, 2009. |