Closed-Form Optimal Two-View Triangulation Based on Angular Errors
This provides a computationally efficient solution for 3D point reconstruction from images across various camera types, but it is incremental as it builds on known triangulation frameworks.
The paper tackles the problem of two-view triangulation by deriving closed-form optimal solutions based on angular reprojection errors, achieving global optimality under L1 and L∞ cost functions with significantly reduced computation compared to existing methods.
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 $L_1$ and $L_\infty$ 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.