The Fisher-Rao metric for projective transformations of the line

International Journal of Computer Vision

Volumn 63, Issue 3, 2005, Pages 191-206

  Maybank, Stephen J ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Asymptotic expansion; Canonical volume; Fisher Rao metric; Heat equation; Probability of false detection; Projective transformation of the line; Riemannian manifold

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; MATRIX ALGEBRA; SET THEORY;

ASYMPTOTIC EXPANSION; CANONICAL VOLUME; FISHER-RAO METRIC; RIEMANNIAN MANIFOLD;

COMPUTER VISION;

EID: 24044525228     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11263-005-6877-6     Document Type: Article

References (22)

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. Differential-Geometrical Methods in Statistics. Lecture Notes in Computer Science, Vol. 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. Land., Series A, 222:309-368.
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 edn. 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, 459:1-21.
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(12).
17. Myung, J., Balasubramanian, V. and Pitt, M.A. 2000. Counting probability distributions: differential geometry and model selection. Proc. National Academy of Science, 97(21): 11170-11175.
18. Rao, C.R. 1945. Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc., 37:81-91.
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, 11:180-187.
21. Werman, M. and Keren, D. 1999. A novel Bayesian method for fitting parametric and non-parametric models to noisy data. Proc. Computer Vision and Pattern Recognition, Fort Collins, Colorado, 1999, 2:552-558.
22. Wolfram, S. 2003. The Mathematica Book. 5th edition, Wolfram Media.