Abstract
We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex optimization on the spherical manifold of quaternions with posterior sampling, in order to provide both reliable initial poses and uncertainty estimates that are informative about the quality of individual solutions. We devise rigorous theoretical convergence guarantees for our method and extensively evaluate it on synthetic and real benchmark datasets. Besides its elegance in formulation and theory, we show that our method is robust to missing data, noise and the estimated uncertainties capture intuitive properties of the data.
Abstract (translated)
我们引入了回火测地马尔可夫链蒙特卡罗（TG-MCMC）算法来初始化在各种场景中出现的姿态图优化问题，如SFM（运动结构）或SLAM（同时定位和映射）。TG-MCMC首先将四元数球面流形上的渐近全局非凸优化与后验抽样相结合，以便提供可靠的初始位置和不确定度估计，这些估计可提供有关个别解质量的信息。我们为我们的方法设计了严格的理论收敛保证，并在合成和真实的基准数据集上对其进行了广泛的评估。除了公式和理论上的优雅之外，我们还证明了我们的方法对缺失数据、噪声和估计的不确定性具有鲁棒性，能够捕获数据的直观特性。
URL
https://arxiv.org/abs/1805.12279
