# Spline Error Weighting for Robust Visual-Inertial Fusion

arXiv: https://arxiv.org/abs/1804.04820 · HTML: https://mlsanity.com/paper/1804.04820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2018.

## Built on by (most cited first, 3 of 3)

- [Revisiting Rolling Shutter Bundle Adjustment: Toward Accurate and Fast Solution](https://mlsanity.com/paper/2209.08503/) (2022)
- [Asynchronous Multi-View SLAM](https://mlsanity.com/paper/2101.06562/) (2021)
- [Continuous-Time vs. Discrete-Time Vision-based SLAM: A Comparative Study](https://mlsanity.com/paper/2202.08894/) (2022)

## Abstract (arXiv)

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.