| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
Camera Calibration from Surfaces of Revolution
February 2003 (vol. 25 no. 2)
pp. 147-161
Abstract—This paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution. Camera calibration is the process of determining the intrinsic or internal parameters (i.e., aspect ratio, focal length, and principal point) of a camera, and it is important for both motion estimation and metric reconstruction of 3D models. In this paper, a novel and simple calibration technique is introduced, which is based on exploiting the symmetry of images of surfaces of revolution. Traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern (such as a calibration grid). The use of surfaces of revolution, which are commonly found in daily life (e.g., bowls and vases), makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects. In this paper, it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio, focal length, and principal point of a camera with fixed intrinsic parameters. The algorithms presented in this paper have been implemented and tested with both synthetic and real data. Experimental results show that the camera calibration method presented here is both practical and accurate.
[1] O.D. Faugeras and G. Toscani, “The Calibration Problem for Stereo,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 15-20, June 1986.
[2] R. Tsai, "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses," IEEE J. Robotics and Automation, vol. 3, no. 4, pp. 323-344, Aug. 1987.
[3] R.K. Lenz and R.Y. Tsai, “Techniques for Calibration of the Scale Factor and Image Center for High Accuracy 3D Machine Vision Metrology,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 713-720, Sept. 1988.
[4] Z. Zhang, A Flexible New Technique for Camera Calibration IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1330-1334, Nov. 2000.
[5] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2000.
[6] O.D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint.Cambridge, Mass.: MIT Press, 1993.
[7] B. Caprile and V. Torre, “Using Vanishing Points for Camera Calibration,” Int'l J. Computer Vision, vol. 4, no. 2, pp. 127-140, Mar. 1990.
[8] R. Cipolla, T.W. Drummond, and D. Robertson, “Camera Calibration from Vanishing Points in Images of Architectural Scenes,” Proc. British Machine Vision Conf., T. Pridmore and D. Elliman, eds., vol. 2, pp. 382-391, Sept. 1999.
[9] D. Liebowitz and A. Zisserman, “Combining Scene and Auto-Calibration Constraints,” Proc. Seventh Int'l Conf. Computer Vision, pp. 293-300, Sept. 1999.
[10] A. Zisserman, D. Forsyth, J.L. Mundy, and C.A. Rothwell, “Recognizing General Curved Objects Efficiently,” Geometric Invariance in Computer Vision, J.L. Mundy and A. Zisserman, eds., Artificial Intelligence Series, chapter 11, Cambridge, Mass.: MIT Press, pp. 228-251, 1992.
[11] J. Liu, J.L. Mundy, D.A. Forsyth, A. Zisserman, and C.A. Rothwell, “Efficient Recognition of Rotationally Symmetric Surface and Straight Homogeneous Generalized Cylinders,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 123-129, June 1993.
[12] J.L. Mundy and A. Zisserman, “Repeated Structures: Image Correspondence Constraints and 3D Structure Recovery,” Proc. Applications of Invariance in Computer Vision, Second Joint European-US Workshop, J.L. Mundy, A. Zisserman, and D. Forsyth, eds., vol. 825, pp. 89-106, Oct. 1993.
[13] A. Zisserman, J.L. Mundy, D.A. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke, “Class-Based Grouping in Perspective Images,” Proc. Fifth Int'l Conf. Computer Vision, pp. 183-188, June 1995.
[14] R.W. Curwen, C.V. Stewart, and J.L. Mundy, “Recognition of Plane Projective Symmetry,” Proc. Sixth Int'l Conf. Computer Vision, pp. 1115-1122, Jan. 1998.
[15] K.-Y.K. Wong, P.R.S. Mendonça, and R. Cipolla, “Camera Calibration from Symmetry,” The Mathematics of Surfaces IX, R. Cipolla and R. Martin, eds., Cambridge, UK: Springer-Verlag, pp. 214-226, Sept. 2000.
[16] D.C. Brown, “Close-Range Camera Calibration,” Photogrammetric Eng., vol. 37, no. 8, pp. 855-866, Aug. 1971.
[17] I. Sobel, “On Calibrating Computer Controlled Cameras for Perceiving 3-D Scenes,” Artificial Intelligence, vol. 5, no. 2, pp. 185-198, June 1974.
[18] W. Faig, “Calibration of Close-Range Photogrammetry System: Mathematical Formulation,” Photogrammetric Eng. and Remote Sensing, vol. 41, no. 12, pp. 1479-1486, Dec. 1975.
[19] Y.I. Abdel-Aziz and H.M. Karara, “Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates in Close-Range Photogrammetry,” Proc. ASP/UI Symp. Close-Range Photogrammetry, pp. 1-18, Jan. 1971.
[20] S.J. Maybank and O.D. Faugeras, “A Theory of Self-Calibration of a Moving Camera,” Int'l J. Computer Vision, vol. 8. no. 2, pp. 123-152, Aug. 1992.
[21] Q.-T. Luong and O. Faugeras, “Camera Calibration, Scene Motion and Structure Recovery from Point Correspondences and Fundamental Matrices,” Int'l J. Computer Vision, vol. 22, no. 3, pp. 261-289, 1997.
[22] B. Triggs, “Autocalibration and the Absolute Quadric,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 609-614, June 1997.
[23] M. Pollefeys, R. Koch, and L. VanGool, “Self-Calibration and Metric Reconstruction Inspite of Varying and Unknown Intrinsic Camera Parameters,” Int'l J. Computer Vision, vol. 32, no. 1, pp. 7-25, Aug. 1999.
[24] L. deAgapito, E. Hayman, and I.D. Reid, “Self-Calibration of Rotating and Zooming Cameras,” Int'l J. Computer Vision, vol. 45, no. 2, pp. 107-127, Nov. 2001.
[25] M. Armstrong, A. Zisserman, and R. Hartley, “Self-Calibration from Image Triplets,” Proc. Fourth European Conf. Computer Vision, B. Buxton and R. Cipolla, eds., vol. 1064, pp. 3-16, Apr. 1996.
[26] L. G. Roberts, “Machine Perception of Three-Dimensional Solids,” Optical and Electro-Optical Information Processing, J.T. Tippett, D.A. Berkowitz, L.C. Clapp, C.J. Koester, and A. Vanderburgh, Jr., eds., pp. 159-197, MIT Press, 1965.
[27] P.R.S. Mendonça, K.-Y.K. Wong, and R. Cipolla, “Recovery of Circular Motion from Profiles of Surfaces,” Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds., vol. 1883, pp. 151-167, Sept. 1999.
[28] P.R.S. Mendonça, K.-Y.K. Wong, and R. Cipolla, “Epipolar Geometry from Profiles under Circular Motion,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 604-616, June 2001.
[29] J.G. Semple and G.T. Kneebone, Algebraic Projective Geometry. Oxford, UK: Clarendon Press, 1998, originally published in 1952.
[30] H.S.M. Coxeter, Introduction to Geometry, second ed. New York: Wiley and Sons, 1989.
[31] J.R. Kender and T. Kanade, “Mapping Image Properties into Shape Constraints: Skewed Symmetry, Affine-Transformable Patterns, and the Shape-from-Texture Paradigm,” Human and Machine Vision, J. Beck, B. Hope, and A. Rosenfeld, eds., pp. 237-257, New York: Academic Press, 1983.
[32] D.P. Mukherjee, A. Zisserman, and J.M. Brady, “Shape from Symmetry—Detecting and Exploiting Symmetry in Affine Images,” Philisophical Trans. Royal Soc. London A, vol. 351, pp. 77-106, 1995.
[33] T.J. Cham and R. Cipolla, “Geometric Saliency of Curve Correspondences and Grouping of Symmetric Contours,” Proc. Fourth European Conf. Computer Vision, B. Buxton and R. Cipolla, eds., pp. 385-398, Apr. 1996.
[34] J. Sato and R. Cipolla, “Affine Integral Invariants for Extracting Symmetry Axes,” Image and Vision Computing, vol. 15, no. 8, pp. 627-635, Aug. 1997.
[35] A. Zisserman, D. Liebowitz, and M. Armstrong, “Resolving Ambiguities in Auto-Calibration,” Philisophical Trans. Royal Soc. London A, vol. 356, no. 1740, pp. 1193-1211, 1998.
[36] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[37] M. Wright, A.W. Fitzgibbon, P.J. Giblin, and R.B. Fisher, “Convex Hulls, Occluding Contours, Aspect Graphs and the Hough Transform,” Image and Vision Computing, vol. 14, no. 8, pp. 627-634, Aug. 1996.
[38] R. Glacahet, M. Dhome, and J.T. Lapreste, “Finding the Perspective Projection of an Axis of Revolution,” Pattern Recognition Letters, vol. 12, pp. 693-700, Nov. 1991.
[39] W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C. Cambridge Univ. Press, 1992.
[40] F. Kirwan, Complex Algebraic Curves. Cambridge, UK: Cambridge Univ. Press, 1992.
[41] J. Plücker, System der Analytischen Geometrie : Auf neue Betrachtungsweisen Gegrundet und Insbesonderer eine Ausfuhrliche Theorie der Curven Dritter Ordnung Enthaltend. Berlin, 1835.
[42] T.W. Sederberg, D.C. Anderson, and R.N. Goldman, “Implicit Representation of Parametric Curves and Surfaces,” Computer Vision, Graphics, and Image Processing, vol. 28, no. 1, pp. 72-84, Oct. 1984.
[43] G. Cross and A. Zisserman, “Quadric Reconstruction from Dual-Space Geometry,” Proc. Sixth Int'l Conf. Computer Vision, pp. 25-31, Jan. 1998.
[44] A.W. Fitzgibbon, G. Cross, and A. Zisserman, “Automatic 3D Model Construction for Turn-Table Sequences,” Proc. 3D Structure from Multiple Images of Large-Scale Environments, European Workshop, SMILE '98, R. Koch and L. Van Gool, eds., vol. 1506, pp. 155-170, June 1998.
Index Terms:
Camera calibration, surface of revolution, harmonic homology, absolute conic, vanishing point.
Citation:
Kwan-Yee K. Wong, Paulo R.S. Mendonça, Roberto Cipolla, "Camera Calibration from Surfaces of Revolution," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 147-161, Feb. 2003, doi:10.1109/TPAMI.2003.1177148
