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The results of ellipse fitting can be considerably distorted by outliers in the fitted point set.To tackle this problem, three improved ellipse fitting algorithms, one of which is based on least trimmed square, and the other two on dual point removal, are proposed.The least trimmed square algorithm starts from a random sample of the original complete fitted set, and then in each iteration, new fitted set is formed by points with the least residual errors, till the process converges to an ellipse fitting a subset whose members are mostly non-outliers.Dual point removal algorithms, on the other hand, starts from the whole fitted set, removes the two points respectively with the maximal positive and the minimal negative residual errors, and halts when the number of points in the remaining set does not exceeds a user-defined threshold.The two proposed algorithms and existing methods are compared on an image base of actual accessories.Experimental results show that when the number of reserved ellipse points is relatively small, the dual removal-based algorithms present the best fitting accuracies, but are slower than the least trimmed square fitting algorithm.When the best performance with parameter tuning is concerned, however, the least trimmed square algorithm achieves a shape-location matching accuracy of 0.62 pixels and an orientation matching accuracy of 0.6°, at an average execution time of 6.5ms, outperforming other algorithms.Other advantages of the proposed algorithms include the small number of algorithm parameters, the intuitiveness of the parameters, and the insensitivity of the algorithm performance to the parameters.These experimental results provide solid evidences for the effectiveness of the proposed algorithms, especially the least trimmed square algorithm.

The presence of outliers would inevitably lead to distorted analysis and inappropriate prediction, especially for multiple outliers in high-dimensional regression, where the high dimensionality of the data might amplify the chance of an observation or multiple observations being outlying. Noting that the detection of outliers is not only necessary but also important in high-dimensional regression analysis, we, in this paper, propose a feasible outlier detection approach in sparse high-dimensional linear regression model. Firstly, we search a clean subset by use of the sure independence screening method and the least trimmed square regression estimates. Then, we define a high-dimensional outlier detection measure and propose a multiple outliers detection approach through multiple testing procedures. In addition, to enhance efficiency, we refine the outlier detection rule after obtaining a relatively reliable non-outlier subset based on the initial detection approach. By comparison studies based on Monte Carlo simulation, it is shown that the proposed method performs well for detecting multiple outliers in sparse high-dimensional linear regression model. We further illustrate the application of the proposed method by empirical analysis of a real-life protein and gene expression data. [ABSTRACT FROM PUBLISHER]

In regression analysis least square (LS) estimator fails because of its sensitivity to unusual observations present in the data. Robust estimation provides alternative estimates which are insensitive and efficient, when the data are not normally distributed or polluted with distant observations usually called outliers. To cope with the problem of outliers is more challenging in nonlinear regression (NLRM) than linear regression. In this study, least trimmed absolute (LTA) estimator which is a robust and high breakdown estimator is adopted for nonlinear regression model fitting. Bias and mean square error is used to check the efficiency of the proposed estimator. The performance of the estimator is compared with LS and existing robust M-estimators using simulated data sets and real world problems. It has been observed that LTA is efficient in case of contaminated data sets as compared to LS and M estimator. Furthermore, it has been concluded that in case of 40% contamination LTA outperforms LS and M estimator, while in case of 20% outliers LTA and M estimators perform equally well. In regard to clean data sets, LS, LTA and M estimator performs equally well. Conclusion has been made on the basis of simulated data sets as well as real data sets. [ABSTRACT FROM AUTHOR]