# An Efficient Planar Bundle Adjustment Algorithm

arXiv: https://arxiv.org/abs/2006.00187 · HTML: https://mlsanity.com/paper/2006.00187/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2020.

## Built on by (most cited first, 10 of 10)

- [GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation](https://mlsanity.com/paper/2407.13537/) (2024)
- [VIP-SLAM: An Efficient Tightly-Coupled RGB-D Visual Inertial Planar SLAM](https://mlsanity.com/paper/2207.01158/) (2022)
- [Efficient Second-Order Plane Adjustment](https://mlsanity.com/paper/2211.11542/) (2022)
- [Incremental Abstraction in Distributed Probabilistic SLAM Graphs](https://mlsanity.com/paper/2109.06241/) (2021)
- [CNN-Augmented Visual-Inertial SLAM with Planar Constraints](https://mlsanity.com/paper/2205.02940/) (2022)
- [LMBAO: A Landmark Map for Bundle Adjustment Odometry in LiDAR SLAM](https://mlsanity.com/paper/2209.08810/) (2022)
- [An Efficient Plane Extraction Approach for Bundle Adjustment on LiDAR Point clouds](https://mlsanity.com/paper/2305.00287/) (2023)
- [Robust Second-order LiDAR Bundle Adjustment Algorithm Using Mean Squared Group Metric](https://mlsanity.com/paper/2409.01856/) (2024)
- [Micro-Structures Graph-Based Point Cloud Registration for Balancing Efficiency and Accuracy](https://mlsanity.com/paper/2410.21857/) (2024)
- [A novel algorithm for optimizing bundle adjustment in image sequence alignment](https://mlsanity.com/paper/2411.06343/) (2024)

## Abstract (arXiv)

This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem Planar Bundle Adjustment (PBA), due to the similarity between this problem and the original Bundle Adjustment (BA) in visual reconstruction. As planes ubiquitously exist in the man-made environment, they are generally used as landmarks in SLAM algorithms for various depth sensors. PBA is important to reduce drift and improve the quality of the map. However, directly adopting the well-established BA framework in visual reconstruction will result in a very inefficient solution for PBA. This is because a 3D point only has one observation at a camera pose. In contrast, a depth sensor can record hundreds of points in a plane at a time, which results in a very large nonlinear least-squares problem even for a small-scale space. Fortunately, we find that there exist a special structure of the PBA problem. We introduce a reduced Jacobian matrix and a reduced residual vector, and prove that they can replace the original Jacobian matrix and residual vector in the generally adopted Levenberg-Marquardt (LM) algorithm. This significantly reduces the computational cost. Besides, when planes are combined with other features for 3D reconstruction, the reduced Jacobian matrix and residual vector can also replace the corresponding parts derived from planes. Our experimental results verify that our algorithm can significantly reduce the computational time compared to the solution using the traditional BA framework. Besides, our algorithm is faster, more accuracy, and more robust to initialization errors compared to the start-of-the-art solution using the plane-to-plane cost