Globally Optimal Estimates for Geometric Reconstruction Problems

We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality - or a combination of both - we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.

• Type: Conference
• Year: 2005
• Where: ICCV
• Authors: Fredrik Kahl, Didier Henrion
• Keywords: Classical Vision Problems, Computer Vision, Convex Relaxations, Geometric Reconstruction Problems, Global Optimum, ICCV 2005, Non-convex Optimization Problems