Practical global optimization for multiview geometry

This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and hemography estimation. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L-2-norm of reprojection errors which is optimal under Gaussian noise as well as the more robust L-1-norm which is less sensitive to outliers. The efficacy of our algorithm is empirically demonstrated by good performance on experiments for both synthetic and real data. An open source MATLAB toolbox that implements the algorithm is also made available to facilitate further research.