Multiple View Geometry and L-infinity Optimization


April 19, 2005


Frederik Kahl




In this talk, a framework for solving geometric reconstruction problems in computer vision will be presented based on the L-infinity norm. Instead of using the common sum-of-squares cost-function, that is, the L-2 norm, the model-fitting errors are measured using the L-infinity norm. Unlike traditional methods based on L-2, this framework allows for efficient computation of global estimates. It will be shown that a class of geometric structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as a quasi-convex optimization problem within the framework. These problems can be efficiently solved using Second Order Cone Programming (SOCP) and Bisection which are standard techniques in convex optimization. The methods have been validated on real data in different settings with small and large dimensions and with excellent performance.


Frederik Kahl

Frederik Kahl’s main research area is Computer Vision. In particular, he really likes theoretical problems, but more practical ones can also be interesting. Currently, he is working on geometric vision problems, photometric stereo, surface reconstruction and learning at the University of California, San Diego, where he is a Visiting Research Fellow with David Kriegman’s research group. Previously he held a postdoctoral position at the Australian National University, RSISE, Canberra, Australia. He received his PhD in 2001 from the, Lund Institute of Technology, Sweden. He is a one of the foundesr of Cognimatics AB.