L-infinity norm minimization in the multiview triangulation

Abstract

Triangulation is an important part of numerous computer vision systems. The multiview triangulation problem is often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show how to recast multiview triangulation as quasi-convex optimization under the L-infinity norm. It is shown that the L-infinity norm cost function is significantly simpler than the L2 cost. In particular L-infinity norm minimization involves finding the minimum of a cost function with a single global minimum on a convex parameter domain. These problems can be efficiently solved using second-order cone programming. We carried out experiment with real data to show that L-infinity norm minimization provides a more accurate estimate and superior to previous approaches. © 2010 Springer-Verlag.