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Outlier Removal by Convex Optimization for L-Infinity Approaches

机译：凸优化去除L-Infinity方法的异常值

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摘要

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 arc taken to be outliers. We examine two feasibility test algorithms: 1) one that minimizes the maximum in-feasibility 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 Ll-norm minimization nature. It tries to estimate a robust solution while maximizing the number of feasible constraints. The infea-sible 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.
机译：本文旨在消除L_∞优化中没有迭代的离群值。现有的L_∞离群值去除方法需要在最小化L_∞的过程中迭代去除残差最大的一组测量值。另一方面，在本文提出的方法中，以与RANSAC相似的方式为最大残留误差预设了一次阈值，并且所产生的残差大于阈值弧，这被认为是异常值。我们研究了两种可行性测试算法：1）一种使最大的不可行性最小化，以及2）另一种使不可行性总和（SOI）最小化。这两种方法都可以与实现L_∞最优的二等分算法一起用于可行性测试。我们注意到，SOI方法由于其L1-范数最小化性质而具有有趣的特征。它尝试在最大化可行约束的数量的同时，估计一种可靠的解决方案。发现不可行的约束主要是由于离群值。一旦设置了阈值，SOI算法就可以从数据集中挑选出异常值，而无需任何重复，并且与迭代方法相比，可以大大减少计算时间。用合成物体和真实物体进行的实验证明了SOI方法的有效性。我们建议SOI方法先于离群敏感的L_∞优化。

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