Recovering Camera Motion Using L\infty Minimization

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.