Fast and globally convergent pose estimation from video images

TLDR

Determining the rigid transformation between 2D images and known 3D geometry is a classical photogrammetry problem, yet existing iterative methods lack guaranteed convergence and proper handling of rotation orthonormality. The authors aim to reformulate pose estimation as minimizing an error metric based on object‑space collinearity. They derive an iterative algorithm that directly computes orthogonal rotation matrices using object‑space collinearity error, ensuring global convergence. Experiments show the method is computationally efficient, as accurate as state‑of‑the‑art optimization techniques, and more robust to outliers.

Abstract

Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers.