Robust line fitting using LMedS clustering

Abstract

AbstractThe authors propose a robust clustering method based on the Least Median of Squares principle. This is a general‐purpose method, and is efficient for finding a majority structure using dictionary sorting and a smallest square region enclosing for a set of data points. In addition, the authors propose a robust line fitting algorithm using this method. The fitting problem is solved through a dual transform of a pair of points selected from data space to a parameter space, and then clustering the mapped points. Moreover, a function to identify outliers based on the size of the square region converging in the parameter space is defined, and is used to distinguish between normal values and outliers. The proposed method enables robust line fitting for data points found in images or in files. The resulting line statistically satisfies the least median condition. Furthermore, line fitting to groups of points with a high outlier percentage is also possible. Here, outliers and normal values are removed in sequence. The validity of the proposed method has been shown based on the results of simulation experiments. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(14): 92–100, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1225