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Type: Journal article
Title: Approximate least trimmed sum of squares fitting and applications in image analysis
Author: Shen, F.
Shen, C.
Van Den Hengel, A.
Tang, Z.
Citation: IEEE Transactions on Image Processing, 2013; 22(5):1836-1847
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2013
ISSN: 1057-7149
Statement of
Fumin Shen, Chunhua Shen, Anton van den Hengel and Zhenmin Tang
Abstract: 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 [1], 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.
Keywords: Least trimmed sum of squares (LTS) regression
outlier removal
robust model fitting
second order cone programming
semidefinite programming
Rights: © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
DOI: 10.1109/TIP.2013.2237914
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