Decentralization and Acceleration Enables Large-Scale Bundle Adjustment (2305.07026v3)

Abstract: Scaling to arbitrarily large bundle adjustment problems requires data and compute to be distributed across multiple devices. Centralized methods in prior works are only able to solve small or medium size problems due to overhead in computation and communication. In this paper, we present a fully decentralized method that alleviates computation and communication bottlenecks to solve arbitrarily large bundle adjustment problems. We achieve this by reformulating the reprojection error and deriving a novel surrogate function that decouples optimization variables from different devices. This function makes it possible to use majorization minimization techniques and reduces bundle adjustment to independent optimization subproblems that can be solved in parallel. We further apply Nesterov's acceleration and adaptive restart to improve convergence while maintaining its theoretical guarantees. Despite limited peer-to-peer communication, our method has provable convergence to first-order critical points under mild conditions. On extensive benchmarks with public datasets, our method converges much faster than decentralized baselines with similar memory usage and communication load. Compared to centralized baselines using a single device, our method, while being decentralized, yields more accurate solutions with significant speedups of up to 953.7x over Ceres and 174.6x over DeepLM. Code: https://joeaortiz.github.io/daba.

• The paper introduces a decentralized framework that distributes computation across devices to overcome central processing bottlenecks.
• The paper reformulates the reprojection error and applies majorization minimization to decouple variables and ensure stable, convergent optimization.
• The paper integrates Nesterov’s acceleration with adaptive restart, achieving remarkable speedups of up to 953.7x in benchmark tests.

Decentralization and Acceleration Enables Large-Scale Bundle Adjustment

The paper presents a novel approach to addressing the computational and communication challenges associated with large-scale bundle adjustment problems by employing decentralization and acceleration techniques. The authors introduce a decentralized method that alleviates the bottlenecks inherent in centralized systems.

Key Contributions

1. Decentralized Framework: The paper develops a decentralized approach to bundle adjustment, eliminating the need for a central processing unit and relying solely on peer-to-peer communication. This allows the method to efficiently manage large-scale problems by distributing data and computational tasks across multiple devices.
2. Reprojection Error Reformulation: A novel reprojection error is derived, enabling the decoupling of optimization variables across devices. This facilitates the reduction of the global optimization problem into independent subproblems that can be processed in parallel, significantly enhancing scalability.
3. Majorization Minimization: By applying majorization minimization techniques, the paper constructs surrogate functions that upper bound the original objective function. This ensures that each iteration of the proposed method results in a non-increasing sequence of objective function values, leading to convergence.
4. Acceleration Techniques: The introduction of Nesterov's acceleration and adaptive restart strategies enhances the convergence speed while retaining theoretical guarantees. These techniques mitigate the slow convergence typically associated with first-order methods in decentralized systems.

Numerical Results and Claims

The decentralized method, referred to as Decentralized and Accelerated Bundle Adjustment (DABA), demonstrates remarkable performance improvements in extensive benchmarks on public datasets. Compared to centralized methods, DABA achieves significant speedups—up to 953.7x over certain baselines—while also providing more accurate solutions.

Implications and Future Directions

The implications of this research are substantial for applications in robotics, computer vision, and related fields where large-scale bundle adjustment is critical. By eliminating the necessity for a central device, the method significantly reduces communication overhead and allows for more efficient utilization of parallel computing resources.

Future work could explore the relaxation of local minimum conditions, extension of the method to accommodate other geometric constructs such as lines and planes, and its implementation in multi-robot systems for 3D reconstruction tasks.

This paper represents a meaningful contribution to the field by addressing the inherent limitations of centralized methods and providing a scalable solution for large-scale optimization problems in bundle adjustment. The authors’ use of decentralization and innovative error reformulation forms a solid foundation for further advancements in this area.