IEEE Trans Image Process - Approximate least trimmed sum of squares fitting and applications in image analysis.

Tópicos

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Resumo

The least trimmed sum of squares (LTS) regression estimation criterion is a robust statistical method for model fitting in the presence of outliers. Compared with the classical least squares estimator, which uses the entire data set for regression and is consequently sensitive to outliers, LTS identifies the outliers and fits to the remaining data points for improved accuracy. Exactly solving an LTS problem is NP-hard, but as we show here, LTS can be formulated as a concave minimization problem. Since it is usually tractable to globally solve a convex minimization or concave maximization problem in polynomial time, inspired by , we instead solve LTS' approximate complementary problem, which is convex minimization. We show that this complementary problem can be efficiently solved as a second order cone program. We thus propose an iterative procedure to approximately solve the original LTS problem. Our extensive experiments demonstrate that the proposed method is robust, efficient and scalable in dealing with problems where data are contaminated with outliers. We show several applications of our method in image analysis.

Resumo Limpo

least trim sum squar lts regress estim criterion robust statist method model fit presenc outlier compar classic least squar estim use entir data set regress consequ sensit outlier lts identifi outlier fit remain data point improv accuraci exact solv lts problem nphard show lts can formul concav minim problem sinc usual tractabl global solv convex minim concav maxim problem polynomi time inspir instead solv lts approxim complementari problem convex minim show complementari problem can effici solv second order cone program thus propos iter procedur approxim solv origin lts problem extens experi demonstr propos method robust effici scalabl deal problem data contamin outlier show sever applic method imag analysi

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