# Global Data Association for SLAM with 3D Grassmannian Manifold Objects

arXiv: https://arxiv.org/abs/2205.08556 · HTML: https://mlsanity.com/paper/2205.08556/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2022.

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

- [GraffMatch: Global Matching of 3D Lines and Planes for Wide Baseline LiDAR Registration](https://mlsanity.com/paper/2212.12745/) (2022)
- [CLIPPER: Robust Data Association without an Initial Guess](https://mlsanity.com/paper/2402.07284/) (2024)
- [View-Invariant Localization using Semantic Objects in Changing Environments](https://mlsanity.com/paper/2209.14426/) (2022)
- [Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold](https://mlsanity.com/paper/2507.17998/) (2025)
- [RoEL: Robust Event-based 3D Line Reconstruction](https://mlsanity.com/paper/2602.18258/) (2026)

## Abstract (arXiv)

Using pole and plane objects in lidar SLAM can increase accuracy and decrease map storage requirements compared to commonly-used point cloud maps. However, place recognition and geometric verification using these landmarks is challenging due to the requirement for global matching without an initial guess. Existing works typically only leverage either pole or plane landmarks, limiting application to a restricted set of environments. We present a global data association method for loop closure in lidar scans using 3D line and plane objects simultaneously and in a unified manner. The main novelty of this paper is in the representation of line and plane objects extracted from lidar scans on the manifold of affine subspaces, known as the affine Grassmannian. Line and plane correspondences are matched using our graph-based data association framework and subsequently registered in the least-squares sense. Compared to pole-only approaches and plane-only approaches, our 3D affine Grassmannian method yields a 71% and 325% increase respectively to loop closure recall at 100% precision on the KITTI dataset and can provide frame alignment with less than 10 cm and 1 deg of error.