# Efficient Globally-Optimal Correspondence-Less Visual Odometry for Planar Ground Vehicles

arXiv: https://arxiv.org/abs/2203.00291 · HTML: https://mlsanity.com/paper/2203.00291/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [GOGMA: Globally-Optimal Gaussian Mixture Alignment](https://mlsanity.com/paper/1603.00150/) (2016)
- [The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation](https://mlsanity.com/paper/1812.01232/) (2018)
- [Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence](https://mlsanity.com/paper/1709.09384/) (2017)

## Built on by (most cited first, 5 of 5)

- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Globally-Optimal Event Camera Motion Estimation](https://mlsanity.com/paper/2203.03914/) (2022)
- [Relative Pose for Nonrigid Multi-Perspective Cameras: The Static Case](https://mlsanity.com/paper/2401.09140/) (2024)

## Abstract (arXiv)

The motion of planar ground vehicles is often non-holonomic, and as a result may be modelled by the 2 DoF Ackermann steering model. We analyse the feasibility of estimating such motion with a downward facing camera that exerts fronto-parallel motion with respect to the ground plane. This turns the motion estimation into a simple image registration problem in which we only have to identify a 2-parameter planar homography. However, one difficulty that arises from this setup is that ground-plane features are indistinctive and thus hard to match between successive views. We encountered this difficulty by introducing the first globally-optimal, correspondence-less solution to plane-based Ackermann motion estimation. The solution relies on the branch-and-bound optimisation technique. Through the low-dimensional parametrisation, a derivation of tight bounds, and an efficient implementation, we demonstrate how this technique is eventually amenable to accurate real-time motion estimation. We prove its property of global optimality and analyse the impact of assuming a locally constant centre of rotation. Our results on real data finally demonstrate a significant advantage over the more traditional, correspondence-based hypothesise-and-test schemes.