Closed-Form Optimal Two-View Triangulation Based on Angular Errors

Seong Hun Lee, Javier Civera

Abstract:

In this paper, we study closed-form optimal solutions to
two-view triangulation with known internal calibration and
pose. By formulating the triangulation problem as L1 and
L∞ minimization of angular reprojection errors, we derive
the exact closed-form solutions that guarantee global optimality under respective cost functions. To the best of our
knowledge, we are the first to present such solutions. Since
the angular error is rotationally invariant, our solutions can
be applied for any type of central cameras, be it perspective,
fisheye or omnidirectional. Our methods also require significantly less computation than the existing optimal methods.
Experimental results on synthetic and real datasets validate
our theoretical derivations.