Relative Pose Estimation of Calibrated Cameras with Known $\mathrm{SE}(3)$ Invariants
This work addresses a domain-specific problem in computer vision for applications like robotics or augmented reality, offering incremental improvements in flexibility and convenience by eliminating the need for extrinsic calibration.
The paper tackles the problem of relative pose estimation for calibrated cameras by incorporating known SE(3) invariants, reducing the minimal number of point pairs needed and improving efficiency and robustness in experiments on synthetic and real data.
The $\mathrm{SE}(3)$ invariants of a pose include its rotation angle and screw translation. In this paper, we present a complete comprehensive study of the relative pose estimation problem for a calibrated camera constrained by known $\mathrm{SE}(3)$ invariant, which involves 5 minimal problems in total. These problems reduces the minimal number of point pairs for relative pose estimation and improves the estimation efficiency and robustness. The $\mathrm{SE}(3)$ invariant constraints can come from extra sensor measurements or motion assumption. Different from conventional relative pose estimation with extra constraints, no extrinsic calibration is required to transform the constraints to the camera frame. This advantage comes from the invariance of $\mathrm{SE}(3)$ invariants cross different coordinate systems on a rigid body and makes the solvers more convenient and flexible in practical applications. Besides proposing the concept of relative pose estimation constrained by $\mathrm{SE}(3)$ invariants, we present a comprehensive study of existing polynomial formulations for relative pose estimation and discover their relationship. Different formulations are carefully chosen for each proposed problems to achieve best efficiency. Experiments on synthetic and real data shows performance improvement compared to conventional relative pose estimation methods.