Dr Steve Maybank

Queen Mary Vision Laboratory seminar

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.


Wednesday 26th November, 1-2 pm
Room CS-338


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.