Queen Mary Vision Laboratory seminar

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Application of Fisher Information to Line Detection

Dr Steve Maybank

The University of Reading (*)

(*) Steve will very soon be joining Birkbeck College, University of

London as a Professor.

http://www.cvg.cs.rdg.ac.uk/~sjm/

Wednesday 26th November, 1-2 pm

Room CS-338

ABSTRACT:

Let p(x|theta) be a density for data x conditional on a parameter theta.

x and theta take values in different manifolds, D and T. The manifold D

carries a Riemannian metric which assists in the description of the

measurement errors. In the simplest cases, the metric on D is Euclidean

and the measurement errors are described using a Gaussian density.

The manifold T is given a Riemannian metric derived from p(x|theta).

This metric is the Fisher information, or Rao metric as it is known in

statistics. The metric has a statistical meaning: let p(x|theta) and

p(x|theta+Delta) be two densities. If theta and theta+Del are close

together in the Rao metric on T, then it is likely that any measurement

x compatible with p(x|theta) will also be compatible with p(x|theta+Del).

The Fisher information is approximated by the leading order term in an

asymptotic expansion of the Fisher information. The approximation is

accurate provided the noise level is low. The number ng of lines needed

for line detection is of the order

ng = (volume of T) / (volume of neighbourhood of a single point in t)

The above theory leads to a simple algorithm for line detection: check

each of the ng lines to see if the image D contains data which support

the presence of the line. In practical applications ng is of the order

of 5,000.