Trajectory representation and landmark projection for continuous-time structure from motion

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a C2-continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on SO(3) and on R3, and a joint spline on SE(3), and show that the latter implicitly couples the direction of translation and rotation. Such an assumption can make good sense for a camera mounted on a robot arm, but not for hand-held or body-mounted cameras. Our experiments in the Spline Fusion framework show that a split spline on R3andSO(3) is preferable over an SE(3) spline in all tested cases. Finally, we investigate the problem of landmark reprojection on rolling shutter cameras, and show that the tested reprojection methods give similar quality, whereas their computational load varies by a factor of two.