论文标题
通过最佳运输对旋转的概率度量同步
Synchronizing Probability Measures on Rotations via Optimal Transport
论文作者
论文摘要
我们介绍了一个新的范式，$ \ textit {measure synchronization} $，用于与MEATUR-valued Edges同步图。我们将此问题提出，因为在相对旋转的概率度量方面最大化了周期一致性。 In particular, we aim at estimating marginal distributions of absolute orientations by synchronizing the $\textit{conditional}$ ones, which are defined on the Riemannian manifold of quaternions. Such graph optimization on distributions-on-manifolds enables a natural treatment of multimodal hypotheses, ambiguities and uncertainties arising in many computer vision applications such as SLAM, SfM, and object pose estimation. We first formally define the problem as a generalization of the classical rotation graph synchronization, where in our case the vertices denote probability measures over rotations. We then measure the quality of the synchronization by using Sinkhorn divergences, which reduces to other popular metrics such as Wasserstein distance or the maximum mean discrepancy as limit cases.我们提出了一种非参数riemannian粒子优化方法来解决该问题。 Even though the problem is non-convex, by drawing a connection to the recently proposed sparse optimization methods, we show that the proposed algorithm converges to the global optimum in a special case of the problem under certain conditions.我们的定性和定量实验显示了我们方法的有效性，我们为同步研究带来了新的观点。
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative rotations. In particular, we aim at estimating marginal distributions of absolute orientations by synchronizing the $\textit{conditional}$ ones, which are defined on the Riemannian manifold of quaternions. Such graph optimization on distributions-on-manifolds enables a natural treatment of multimodal hypotheses, ambiguities and uncertainties arising in many computer vision applications such as SLAM, SfM, and object pose estimation. We first formally define the problem as a generalization of the classical rotation graph synchronization, where in our case the vertices denote probability measures over rotations. We then measure the quality of the synchronization by using Sinkhorn divergences, which reduces to other popular metrics such as Wasserstein distance or the maximum mean discrepancy as limit cases. We propose a nonparametric Riemannian particle optimization approach to solve the problem. Even though the problem is non-convex, by drawing a connection to the recently proposed sparse optimization methods, we show that the proposed algorithm converges to the global optimum in a special case of the problem under certain conditions. Our qualitative and quantitative experiments show the validity of our approach and we bring in new perspectives to the study of synchronization.
