A note on conic fitting by the gradient weighted least-squares estimation: refined eigenvector solution

Authors:
G. Y. Wang;Z. Houkes;B. Zheng;X. Li
Affiliations:
Department of Electrical Engineering, Ocean University of Qingdao, Yushan Road 5, Qingdao. 266003 China;Measurement and Instrumentation Laboratory, Faculty of Electrical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Department of Electrical Engineering, Ocean University of Qingdao, Yushan Road 5, Qingdao. 266003 China;Department of Electrical Engineering, Ocean University of Qingdao, Yushan Road 5, Qingdao. 266003 China
Venue:
Pattern Recognition Letters
Year:
2002

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Abstract

The gradient weighted least-squares criterion is a popular criterion for conic fitting. When the non-linear minimisation problem is solved using the eigenvector method, the minimum is not reached and the resulting solution is an approximation. In this paper, we refine the existing eigenvector method so that the minimisation of the non-linear problem becomes exactly. Consequently we apply the refined algorithm to the re-normalisation approach, by which the new iterative scheme yields to bias-corrected solution but based on the exact minimiser of the cost function. Experimental results show the improved performance of the proposed algorithm.