Cramer-Rao Lower Bounds for Estimation of a Circular Arc Center and Its Radius

doi:10.1006/gmip.1995.1043

Graphical Models and Image Processing

Volume 57, Issue 6, November 1995, Pages 527-532

Graphical Models and...

https://doi.org/10.1006/gmip.1995.1043 Get rights and content

Abstract

The problem of determining the coordinates of a circle and its radius from a set of measurements of its arc is of practical interest. We derive the expression that gives the Cramer-Rao lower bounds of these estimates. These bounds are a function of the noise factor, the number of measurements, and the arc length. Simulation results have corroborated the derivations and shown that the estimator of [S. M. Thomas and Y. T. Chan, Comput. Vision Graphics Image Process. 45, 1989, 362-370] achieve the lower bounds.

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NoteCramer-Rao Lower Bounds for Estimation of a Circular Arc Center and Its Radius

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Cramer-Rao Lower Bounds for Estimation of a Circular Arc Center and Its Radius