  In this paper we derive and test a probability-based weighting that can
balance residuals of different types in spline fitting. In contrast to previous
formulations, the proposed spline error weighting scheme also incorporates a
prediction of the approximation error of the spline fit. We demonstrate the
effectiveness of the prediction in a synthetic experiment, and apply it to
visual-inertial fusion on rolling shutter cameras. This results in a method
that can estimate 3D structure with metric scale on generic first-person
videos. We also propose a quality measure for spline fitting, that can be used
to automatically select the knot spacing. Experiments verify that the obtained
trajectory quality corresponds well with the requested quality. Finally, by
linearly scaling the weights, we show that the proposed spline error weighting
minimizes the estimation errors on real sequences, in terms of scale and
end-point errors.
