Statistical Performance Analysis and Improvement of Conic Fitting Algorithm
Yang Zhong · Journal of Shanghai, Maritime University · 2003
The traditional procedure of conic fitting utilizes the standard Eigen Value Decomposition (EVD) algorithm. By means of the statistical analysis, we know that, when the technique is utilized to fit a digital conic, it has the disadvantages of very big estimation bias and mse. Its reason is that the data noise is not white and the condition number of the ACF matrix of the data observation is extremely big. Thus, the effective measure ment to improve the performance of a conic fitting algorithm is whitening the data noise and regulation transformation. This theoretic analysis has strongly supported the regularized EVD algorithm developed by Hartley. Then, we develop a dimension reduced EVD algorithm. The theoretical analysis and computer simulations have demonstrated that the technique has the advantages of intrinsical functions to whiten the data noise and to regulate the condition number of the ACF matrix of the data observation so that it can give a non biased estimation of conic parameter with very small mse. Furthermore, it has neither whitening transformation nor regulation transformation. At the same time, the dimension number of the optimization procedure is reduced from 6 to 2. Therefore the computation complex is largely simplified.