Outlier removal by Convex optimization for L-infinity approaches

Abstract

This paper is about removing outliers without iterations in L ∈∞∈ optimization. Existing L ∈∞∈ outlier removal method requires iterative removal of the set of measurements with greatest residual during L ∈∞∈ minimization. In the method presented in this paper, on the other hand, a threshold is preset once for the maximum residual error in a manner similar to RANSAC, and the measurements yielding greater residuals than the threshold are taken to be outliers. We examine two feasibility test algorithms: 1) one that minimizes the maximum infeasibility and 2) the other that minimizes the sum of infeasibilities (SOI). Both of these can be used for feasibility test in conjunction with the bisection algorithm which attains the L ∈∞∈ optimum. We note that the SOI method has an interesting characteristic due to its L1-norm minimization nature. It tries to estimate a robust solution while maximizing the number of feasible constraints. The infeasible constraints are found to be due mostly to outliers. Once we set a threshold, the SOI algorithm sorts out outliers from the data set without any repetition and substantial reduction of computation time can be achieved compared to the iterative method. Experiments with synthetic as well as real objects demonstrate the effectiveness of the SOI method. We suggest that the SOI method precede the outlier-sensitive L ∈∞∈ optimization. © 2009 Springer Berlin Heidelberg.