Even with good initialization, extrinsic parameters $(R, t)$ are never perfect. Numerical Refinement Uses iterative solvers to find the global minimum of the alignment error.
In VPS, we typically minimize the Reprojection Error—the distance between where a point *should* be in the camera frame and where it was *observed*.
LM is the industry-standard algorithm for these "non-linear least squares" problems. It acts like a hybrid between Gradient Descent and the Gauss-Newton method, offering both stability and fast convergence.
Iterative Error Minimization