An Efficient Meta-Algorithm for Triangulation

Abstract

Triangulation by $\ell _\infty$ minimisation has become established in computer vision. State-of-the-art $\ell _\infty$ triangulation algorithms exploit the quasiconvexity of the cost function to derive iterative update rules that deliver the global minimum. Such algorithms, however, can be computationally costly for large problem instances that contain many image measurements. In this paper, we exploit the fact that $\ell _\infty$ triangulation is an instance of generalised linear programs (GLP) to speed up the optimisation. Specifically, the solution of GLPs can be obtained as the solution on a small subset of the data called the support set. A meta-algorithm is then constructed to efficiently find the support set of a set of image measurements for triangulation. We demonstrate that, on practical datasets, using the meta-algorithm in conjunction with all existing $\ell _\infty$ triangulation solvers provides faster convergence than directly executing the triangulation routines on the full set of measurements.