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|Title:||Maximum-likelihood circle-parameter estimation via convolution|
|Author:||Zelniker, Emanuel Emil|
Clarkson, I. Vaughan L.
|Citation:||Digital image computing : techniques and applications ; proceedings of the VIIth Biennial Australian Pattern Recognition Society Conference, DICTA 2003 / Sun C., Talbot H., Ourselin S. and Adriaansen T. (eds.), pp. 509-518.|
|Conference Name:||Australian Pattern Recognition Society. Conference (7th : 2003 : Sydney, N.S.W.)|
|School/Discipline:||School of Computer Science|
|Emanuel E. Zelniker and I. Vaughan L. Clarkson|
|Abstract:||In this paper, we present an interpretation of the Maximum Likelihood Estimator (MLE) and the Delogne-K˚asa Estimator (DKE) for circle-parameter estimation via convolution. Under a certain model for theoretical images, this convolution is an exact description of the MLE. We use our convolution based MLE approach to find good starting estimates for the parameters of a circle, that is, the centre and radius. It is then possible to treat these estimates as preliminary estimates into the Newton-Raphson method which further refines these circle estimates and enables sub-pixel accuracy. We present closed form solutions to the Cram´er-Rao Lower Bound of each estimator and discuss fitting circles to noisy points along a full circle as well as along arcs. We compare our method to the DKE which uses a least squares approach to solve for the circle parameters.|
|Keywords:||circle-parameter estimation; convolution; estimators; likelihood|
|Appears in Collections:||Computer Science publications|
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