Department of Electrical Engineering (ISY)

Trajectory Representation and Landmark Projection for Continuous-Time Structure from Motion

Hannes Ovrén, Per-Erik Forssén
International Journal of Robotics Research
Volume 38, Number 6, Pages 686-701
May 2019

Abstract

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 analyse the behaviour 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 R³+SO(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, while their computational load varies by a factor of 2.

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Bibtex entry

@Article{ovren19,
  author = {Hannes Ovr\'en and Per-Erik Forss\'en},
  title = {Trajectory Representation and Landmark Projection for Continuous-Time Structure from Motion},
  journal = 	 {International Journal of Robotics Research},
  year = 	 {2019},
  volume = 	 {38},
  number = 	 {6},
  pages = 	 {686-701},
  month = 	 {May},
  note = {Accepted 2019-01-23.},
  publisher =    {{SAGE} Publishing},
  url =          {https://doi.org/10.1177/0278364919839765}
}