Efficient and Distributed Large-Scale Point Cloud Bundle Adjustment via Majorization-Minimization

TL;DR

This work tackles the prohibitive cubic time and memory scaling of large-scale point cloud BA by introducing BALM3.0, which applies a majorization-minimization surrogate based on point-to-plane residuals to completely decouple LiDAR scan poses. The surrogate yields a block-diagonal (diagonal) Hessian, enabling per-pose LM updates in parallel and reducing the linear solve from O($M_p^3$) to O($M_p$) in practice. The authors formalize the surrogate, derive its first- and second-order derivatives, prove convergence, and implement both a single-device and a distributed framework (via ROS/SFTP) that optimizes very large datasets across multiple consumer laptops. Extensive simulations and benchmark evaluations on public datasets show BALM3.0 achieves the same optimal residual as BALM2 with up to 704x speedups and dramatically lower memory usage, while the distributed framework demonstrates map consistency and feasible bandwidth usage across devices. The results indicate BALM3.0 is practical for scalable, distributed large-scale mapping and point to GPU acceleration and GNSS/RTK integration as promising future directions.

Abstract

Point cloud bundle adjustment is critical in large-scale point cloud mapping. However, it is both computationally and memory intensive, with its complexity growing cubically as the number of scan poses increases. This paper presents BALM3.0, an efficient and distributed large-scale point cloud bundle adjustment method. The proposed method employs the majorization-minimization algorithm to decouple the scan poses in the bundle adjustment process, thus performing the point cloud bundle adjustment on large-scale data with improved computational efficiency. The key difficulty of applying majorization-minimization on bundle adjustment is to identify the proper surrogate cost function. In this paper, the proposed surrogate cost function is based on the point-to-plane distance. The primary advantages of decoupling the scan poses via a majorization-minimization algorithm stem from two key aspects. First, the decoupling of scan poses reduces the optimization time complexity from cubic to linear, significantly enhancing the computational efficiency of the bundle adjustment process in large-scale environments. Second, it lays the theoretical foundation for distributed bundle adjustment. By distributing both data and computation across multiple devices, this approach helps overcome the limitations posed by large memory and computational requirements, which may be difficult for a single device to handle. The proposed method is extensively evaluated in both simulated and real-world environments. The results demonstrate that the proposed method achieves the same optimal residual with comparable accuracy while offering up to 704 times faster optimization speed and reducing memory usage to 1/8. Furthermore, this paper also presented and implemented a distributed bundle adjustment framework and successfully optimized large-scale data (21,436 poses with 70 GB point clouds) with four consumer-level laptops.

Figures (14)

• Figure 1: Explanation of key technical details in majorization-minimization: (a) Optimizing the upper surrogate cost function $c(\mathbf{T}|\mathbf{T}^{(k)})$ yields a state $\mathbf{T}^{(k+1)}$ that ensures $c(\mathbf{T}^{(k+1)}) \leq c(\mathbf{T}^{(k)})$, thus decreasing the original cost function $c(\mathbf{T})$. (b) Compared to the original cost function, the upper surrogate cost function features a block-diagonal Hessian matrix, reducing the solving time from cubic to linear.
• Figure 2: Pipeline of the proposed distributed bundle adjustment framework.
• Figure 3: Devices used in distributed bundle adjustment experiment.
• Figure 4: An example of our simulation environment. (a) shows the initial poses and point clouds. (b) shows the optimized one.
• Figure 5: Result of the convergence evaluation under simulation environment. The results demonstrate that the proposed method converges, at a significantly higher speed, to the same point-to-plane residual as BALM2.

Theorems & Definitions (5)

• Lemma 1
• Theorem 1
• Theorem 2
• Corollary 1
• Remark 1