Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Maybank, Stephen J. (2005)
Publisher: Springer
Languages: English
Types: Article
Subjects: csis
A conditional probability density function is defined for measurements arising from a projective transformation of the line. The conditional density is a member of a parameterised family of densities in which the parameter takes values in the three dimensional manifold of projective transformations of the line. The Fisher information of the family defines on the manifold a Riemannian metric known as the Fisher-Rao metric. The Fisher-Rao metric has an approximation which is accurate if the variance of the measurement errors is small. It is shown that the manifold of parameter values has a finite volume under the approximating metric. \ud These results are the basis of a simple algorithm for detecting those projective transformations of the line which are compatible with a given set of measurements. The algorithm searches a finite list of representative parameter values for those values compatible with the measurements. Experiments with the algorithm suggest that it can detect a projective transformation of the line even when the correspondences between the components of the measurements in the domain and the range of the projective transformation are unknown.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. Abramowitz, M. and Stegun, I.A. (eds.) 1965. Handbook of Mathematical Functions with formulas, graphs, and mathematical tables. Dover.
    • 2. Amari, S.-I. 1985. Di®erential-Geometrical Methods in Statistics. Lecture Notes in Computer Science, 28. Springer.
    • 3. Chavel, I. 1984. Eigenvalues in Riemannian Geometry. Academic Press Inc.
    • 4. Cover, T.M. and Thomas, J.A. 1991. Elements of Information Theory. John Wiley and Sons.
    • 5. Faugeras, O.D. 1993. Three-Dimensional Computer Vision. MIT Press.
    • 6. Ferryman, J.M. 2001. PETS'2001 database. Available at http://www.visualsurveillance.org/PETS2001.
    • 7. Fisher, R.A. 1922. On the mathematical foundations of theoretical statistics. Phil. Trans. R. Soc. Lond., Series A, 222, pp. 309-368.
    • 8. Forsyth, D.A. and Ponce, J. 2003. Computer Vision, a modern approach. Prentice Hall.
    • 9. Gallot, S., Hulin, D. and LaFontaine, J. 1990. Riemannian Geometry. 2nd edition, Universitext, Springer.
    • 10. Golub, G.H. and Van Loan, C.F. 1996. Matrix Computations. The John Hopkins University Press.
    • 11. Gonzalez, R.C. and Woods, R.E. (2002) Digital Image Processing. 2nd Edition. Prentice Hall.
    • 12. Hartley, R. and Zisserman, A. 2000. Multiple View Geometry in Computer Vision. Cambridge University Press.
    • 13. Kanatani, K. 1996 Statistical Computation for Geometric Optimization: theory and practice. Elsevier.
    • 14. Kotz, S. and Johnson, N.L. (eds.) 1992. Breakthroughs in Statistics. Vol. 1. foundations and basic theory. Springer Series in Statistics, Springer-Verlag.
    • 15. Maybank, S.J. 2003. Fisher information and model selection for projective transformations of the line. Proceedings of the Royal Society of London, Series A, 459, pp. 1-21.
    • 16. Maybank, S.J. 2004. Detection of image structures using the Fisher information and the Rao metric. IEEE Trans. Pattern Analysis and Machine Intelligence, 26, No. 12.
    • 17. Myung, J., Balasubramanian, V. and Pitt, M.A. 2000. Counting probability distributions: di®erential geometry and model selection. Proc. National Academy of Science, 97, no. 21, pp. 11170-11175.
    • 18. Rao, C.R. 1945. Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc., 37, pp. 81-91.
    • 19. Semple, J.G. and Kneebone, G.T. 1952. Algebraic Projective Geometry. Clarendon Press.
    • 20. Torr, P.H.S. and Murray, D.W. 1993, Statistical detection of nonrigid motion. Image and Vision Computing, 11, pp. 180-187.
    • 21. Werman, M. and Keren, D. 1999. A novel Bayesian method for ¯tting parametric and non-parametric models to noisy data. Proc. Computer Vision and Pattern Recognition, Fort Collins, Colorado, June 1999, 2, pp. 552-558.
    • 22. Wolfram, S. 2003. The Mathematica Book. 5th Edition, Wolfram Media.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article