A fast method for calibrating video-based motion analysers using only a rigid bar

  • N. A. Borghese
  • P. Cerveri
  • P. Rigiroli


Video-camera systems are widely used in biomechanics and clinical fields to measure the 3D kinematic measurements of human motion. To be used, they need to be calibrated, that is the parameters which geometrically define the cameras have to be determined. It is shown here how this can be achieved by surveying a rigid bar in motion inside the working volume, and in a very short time: less than 15 s on a Pentium III. The exterior parameters are estimated through the coplanarity constraint, the camera focal lengths through the properties of epipolar geometry and the principal points with a fast evolutionary optimisation which guarantees convergence when the initial principal points cannot be adequately estimated. The method has been widely tested on simulated and real data. Results show that its accuracy is comparable with that obtained using methods based on points of known 3D coordinates (DLT): 0.37 mm RMS error over a volume with a diagonal ≈1.5m. A preferential absolute reference system is obtained from the same bar motion data and is used to guide an intelligent decimation of the data. Finally, the role that the principal points play in achieving a high accuracy, which is questioned in the computer vision domain, is assessed through simulations.


Motion analysis Stereo cameras Calibration Epipolar geometry Optimisation Evolution strategies 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Azarbayejani, A., andPentland, A. (1995): ‘Recursive estimation of motion, structure, and focal length’,IEEE Trans. Patt. Anal. Machine Intell.,17, pp. 562–575CrossRefGoogle Scholar
  2. Borghese, N. A., andFerrigno, G. (1990): ‘An algorithm for 3D automatic movement detection by means of standard TV cameras’,IEEE Trans. Biomed. Eng.,37, pp. 1221–1225CrossRefGoogle Scholar
  3. Borghese, N. A., andPerona, P. (1993): ‘Calibration of a stereo system with points of unknown location’, Proceedings of the XIVth International Conference of the Society of Biomechanics ISB, Paris, pp. 202–203Google Scholar
  4. Borghese N. A., Cerveri, P., andFerrigno, G. (1997): ‘Statistical comparison of ILSSC versus DLT in the calibration of a photogrammetric stereo-system’,J. Biomech.,30, pp. 409–413CrossRefGoogle Scholar
  5. Cerveri, P., Ferrigno, G., andBorghese N. A. (1999): ‘Evolution strategies and epipolar geometry for dynamic calibration of photogrammetric camera system’,Med. Biol. Eng. Comput.,37, (Suppl. 2), pp. 830–831Google Scholar
  6. Cerveri, P., Borghese, N. A., andPedotti, A. (1998): ‘Complete calibration of a stereo photogrammetric system through control points of unknown coordinates’,J. Biomech.,31, pp. 935–940CrossRefGoogle Scholar
  7. Challis, J. H., andKerwin, D. G. (1992): ‘Accuracy assessment and control point configuration when using the DLT for photogrammetry’,J. Biomech.,25, pp. 1053–1058Google Scholar
  8. Dapena, J., Everett, A. H., andMiller, J. A. (1982): ‘Three-dimensional cinematography with control object of unknown shape’,J. Biomech.,15, pp. 11–19Google Scholar
  9. Faugeras, O. D. (1993): ‘Three-dimensional computer vision’ (MIT Press, Cambridge, MA)Google Scholar
  10. Faugeras, O. D. (1995): ‘Stratification of three-dimensional vision: projective, affine, and metric representations’,J. Opt. Soc. Am. A,12, pp. 465–484Google Scholar
  11. Ferrigno, G., Borghese, N. A., andPedotti, A. (1990): ‘Pattern recognition in 3D automatic human motion analysis’,ISPRS J. Photogr. Rem. Sens.,45, pp. 227–246Google Scholar
  12. Hartley, R. I. (1992): ‘Estimation of relative positions for uncalibrated cameras. Computer vision-ECCV '92’ LNCS-Series, Vol. 588, Springer-Verlag, pp. 579–587Google Scholar
  13. Hartley, R. I. (1997): ‘Self-calibration of stationary cameras’,Int. J. Comput. Vision,22, pp. 5–23Google Scholar
  14. Hu, X., andAhuja, N. (1994): ‘Matching point features with ordered geometric, rigidity, and disparity constraints’,IEEE Trans. Patt. Anal. Machine Intell.,16, pp. 1041–1049Google Scholar
  15. Lenz, R. K., andTsai, R. Y. (1988): ‘Techniques for calibration of the scale factor and image center for high accuracy 3D machine vision metrology’,IEEE Trans. Patt. Anal. Machine Intell.,10, pp. 713–720CrossRefGoogle Scholar
  16. Luong, Q. T., andFaugeras, O. D. (1996): ‘The fundamental matrix: theory, algorithms, and stability analysis’,Int. J. Comput. Vision,17, pp. 43–76CrossRefGoogle Scholar
  17. Maas, H.-G. (1997): ‘Image sequence based automatic multicamera system calibration techniques’, IAPRS, Vol. 32, Part 5Google Scholar
  18. Marzan, G. T., andKarara, H. M. (1975): ‘A computer program for direct linear transformation solution of the collinearity condition, and some application of it’. Proceedings of Symposium on Close-range Photographic Systems, Champaign, ILGoogle Scholar
  19. Mendonca, P. R., andCipolla, R. (1999): ‘A simple technique for self-calibration’. Proceedings of IEEE Conference CVPR, Fort Collins, Colorado, pp. 145–151Google Scholar
  20. Weng, J., Cohen, P., andHenriou, M. (1992): ‘Camera calibration with distortion models and accuracy evaluation’,IEEE Trans. Patt. Anal. Machine Intell.,14, pp. 965–979Google Scholar
  21. Winter, D. (1990): ‘Biomechanics and motor control of human movement’ (Wiley & Sons)Google Scholar
  22. Wolf, P. R. (1983): ‘Elements of photogrammetry’ (McGraw-Hill, New York)Google Scholar

Copyright information

© IFMBE 2001

Authors and Affiliations

  1. 1.Istituto Neuroscienze e Bioimmagini CNR, Laboratory of Human Motion Analysis and Virtual Reality, MAVRScientific Institute H. S. RaffaeleMilanItaly
  2. 2.Bioengineering DepartmentPolitecnico di Milano and Foundazione Don GnocchiMilanItaly

Personalised recommendations