Abstract.
This paper presents a practical method for finding the provably globally optimal solution to numerous problems in pro jective geometry including multiview triangulation, camera resectioning and ho- mography 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 for- mulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L2 -norm of repro jection errors which is optimal under Gaussian noise as well as the more robust L1 -norm which is less sensitive to outliers. The eficacy of our algorithm is empirically demon- strated 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.