Fast and Stable Algebraic Solution to L2 Three-View Triangulation
Zuzana Kúkelová, Tomáš Pajdla, Martin Bujnak · 2013
In this paper we provide a new fast and stable algebraic solution to the problem of L2triangulation from three views. We use Lagrange multipliers to formulate the search for the minima of the L2objective function subject to equality constraints. Interestingly, we show that by relaxing the triangulation such that we do not require a single point in 3D, we get, after a linear correction, a solver that is faster, more stable and practically as accurate as the state-of-the-art L2-optimal algebraic solvers [24, 7, 8, 9]. In our formulation, we obtain a system of eight polynomial equations in eight unknowns, which we solve using the Groebner basis method. We get less (31) solutions than was the number (47-66) of solutions obtained in [24, 7, 8, 9] and our solver is more robust than [8, 9] w.r.t. critical configurations. We evaluate the precision and speed of our solver on both synthetic and real datasets.