Recently, there has been interest in solving geometric vision problems such as triangulation and camera resectioning using L\infty minimization. One key advantage of using the L\infty norm rather than the L2 norm is that the L\infty cost function has a single minimum unlike the commonly used L2 cost function which typically has multiple local minima. However, one drawback of using L\infty minimization is that it is not robust to outliers. By minimizing the L\infty norm instead of the L2 norm, we are, in essence, fitting the outliers and not the good data. Therefore, before one can perform L\infty optimization on a problem, it is first necessary to remove outliers. A popular (but generally unsound) method of removing outliers is to minimize the cost function using standard optimization techniques; then if the residual error is too great, remove the offending measurements and continue. Although this method can fail for simple L2 optimization problems, we show in this paper that for a wide class of L\infty problems it is a valid technique. It is proved that the set of measurements with greatest residual must contain at least one outlier. Thus, if we keep throwing out the measurements with greatest residual, we will eventually remove all outliers in the data. We test this hypothesis on the multiview reconstruction problem and show that even simple strategies for throwing out these maximum residual measurements are effective in removing outliers.

Recently, there has been interest in formulating various geometric problems in Computer Vision as L\infty optimization problems. The advantage of this approach is that under L\infty norm, such problems typically have a single minimum, and may be efficiently solved using Second-Order Cone Programming (SOCP). This paper shows that such techniques may be used effectively on the problem of determining the track of a camera given observations of features in the environment. The approach to this problem involves two steps: determination of the orientation of the camera by estimation of relative orientation between pairs of views, followed by determination of the translation of the camera. This paper focusses on the second step, that of determining the motion of the camera. It is shown that it may be solved effectively by using SOCP to reconcile translation estimates obtained for pairs or triples of views. In addition, it is observed that the individual translation estimates are not known with equal certainty in all directions. To account for this anisotropy in uncertainty, we introduce the use of covariances into the L\infty optimization framework.