# Probabilistic Degeneracy Detection for Point-to-Plane Error Minimization

arXiv: https://arxiv.org/abs/2410.10784 · HTML: https://mlsanity.com/paper/2410.10784/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration](https://mlsanity.com/paper/2509.06285/) (2025)

## Abstract (arXiv)

Degeneracies arising from uninformative geometry are known to deteriorate LiDAR-based localization and mapping. This work introduces a new probabilistic method to detect and mitigate the effect of degeneracies in point-to-plane error minimization. The noise on the Hessian of the point-to-plane optimization problem is characterized by the noise on points and surface normals used in its construction. We exploit this characterization to quantify the probability of a direction being degenerate. The degeneracy-detection procedure is used in a new real-time degeneracy-aware iterative closest point algorithm for LiDAR registration, in which we smoothly attenuate updates in degenerate directions. The method's parameters are selected based on the noise characteristics provided in the LiDAR's datasheet. We validate the approach in four real-world experiments, demonstrating that it outperforms state-of-the-art methods at detecting and mitigating the adverse effects of degeneracies. For the benefit of the community, we release the code for the method at: github.com/ntnu-arl/drpm.