Projective Least-Squares: Global Solutions with Local Optimization

Recent work in multiple view geometry has focused on obtaining globally optimal solutions at the price of computational time efciency. On the other hand, traditional bundle adjustment algorithms have been found to provide good solutions even though there may be multiple local minima. In this paper we justify this observation by giving a simple sufcient condition for global optimality that can be used to verify that a solution obtained from any local method is indeed global. The method is tested on numerous problem instances of both synthetic and real data sets. In the vast majority of cases we are able to verify that the solutions are optimal, in particular for small-scale problems. We also develop a branch and bound procedure that goes beyond verication. In cases where the sufcient condition does not hold, the algorithm returns either of the following two results: (i) a certicate of global optimality for the local solution or (ii) the global solution.

• Type: Conference
• Year: 2009
• Where: CVPR
• Authors: Carl Olsson, Fredrik Kahl, Richard I. Hartley
• Keywords: Computer Vision, CVPR 2009, Projective Least-Squares