Fast and Stable Algebraic Solution to L2 Three-View Triangulation

In this paper we provide a new fast and stable algebraic solution to the problem of L₂ triangulation from three views. We use Lagrange multipliers to formulate the search for the minima of the L₂ objective 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.