Application of the Fisher-Rao Metric to Structure Detection

Abstract - Certain structure detection problems can be solved by sampling a parameter space for the different structures at a finite number of points and checking each point to see if the corresponding structure has a sufficient number of inlying measurements. The measurement space is a Riemannian manifold and the measurements relevant to a given structure are near to or on a submanifold which constitutes the structure. The probability density function for the errors in the measurements is described using a generalisation of the Gaussian density to Riemannian manifolds. The conditional probability density function for the measurements yields the Fisher information which defines a metric, known as the Fisher-Rao metric, on the parameter space. The main result is a derivation of an asymptotic approximation to the Fisher-Rao metric, under the assumption that the measurement noise is small. Using this approximation to the Fisher-Rao metric, the parameter space is sampled, such that each po...

• Type: Journal
• Year: 2006
• Where: JMIV
• Authors: Stephen J. Maybank
• Keywords: JMIV 2006, Measurement, Parameter Space, Probability Density Function