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://github.com/facebookresearch/DABA.

翻译：将任意大规模光束法平差问题扩展至多设备，需分布式处理数据与计算。现有集中式方法因计算与通信开销，仅能解决中小规模问题。本文提出一种全去中心化方法，通过缓解计算与通信瓶颈，可求解任意大规模光束法平差问题。我们通过重新表述重投影误差并推导新型替代函数，实现不同设备优化变量的解耦。该函数支持使用最小化最大化技术，将光束法平差转化为可并行求解的独立优化子问题。进一步采用涅斯捷罗夫加速与自适应重启策略，在保持理论保证的同时提升收敛速度。尽管采用受限点对点通信，我们的方法在温和条件下可证明收敛至一阶临界点。在公共数据集的广泛基准测试中，本方法在内存占用与通信负载相近的条件下，收敛速度远快于去中心化基线方法。与使用单设备的集中式基线相比，本方法在去中心化场景下仍能获得更精确的解，相比Ceres加速高达953.7倍，相比DeepLM加速174.6倍。代码：https://github.com/facebookresearch/DABA。