Abstract: The pose estimation problem is one of the key problems in computer graphics, machine vision, and photogrammetry. It is to estimate the rotation and translation between a camera and  an object based on  given 3D-to-2D reference points. Recently, with the help of a quaternion model, semidefinite programming relaxation (SDR) and sum-of-square relaxation (SOS) are proposed in literature.  In this paper, by adding redundant constraints to the original problem, we develop a Lagrangian dual model for pose estimation, which can be reformulated as a semidefinite program. We use SeDuMi to solve these three models. They are captured in matrices of 117\times32 (SDR), 266\times70 (SOS) and  81\times 12 (Dual), respectively. Numerical results show that our method is not only fast but also very efficient.

Key words: pose estimation, Lagrangian dual, semidefinite programming