  Structure from motion algorithms have an inherent limitation that the
reconstruction can only be determined up to the unknown scale factor. Modern
mobile devices are equipped with an inertial measurement unit (IMU), which can
be used for estimating the scale of the reconstruction. We propose a method
that recovers the metric scale given inertial measurements and camera poses. In
the process, we also perform a temporal and spatial alignment of the camera and
the IMU. Therefore, our solution can be easily combined with any existing
visual reconstruction software. The method can cope with noisy camera pose
estimates, typically caused by motion blur or rolling shutter artifacts, via
utilizing a Rauch-Tung-Striebel (RTS) smoother. Furthermore, the scale
estimation is performed in the frequency domain, which provides more robustness
to inaccurate sensor time stamps and noisy IMU samples than the previously used
time domain representation. In contrast to previous methods, our approach has
no parameters that need to be tuned for achieving a good performance. In the
experiments, we show that the algorithm outperforms the state-of-the-art in
both accuracy and convergence speed of the scale estimate. The accuracy of the
scale is around $1\%$ from the ground truth depending on the recording. We also
demonstrate that our method can improve the scale accuracy of the Project
Tango's build-in motion tracking.
