Multiple-View Geometry Under the Linfinity-Norm

Fredrik Kahl, Richard I. Hartley

Abstract: This paper presents a new framework for solving geometric structure and motion problems based on the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -norm. Instead of using the common sum-of-squares cost function, that is, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm, the model-fitting errors are measured using the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -norm. Unlike traditional methods based on L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.