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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.
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.
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.