Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the
classical angular synchronization problem consists of recovering unknown angles
$\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements
of the form $(\theta_i^* - \theta_j^*) \mod 2\pi$, for all $\{i,j\} \in
\mathcal{E}$. This problem arises in a variety of applications, including
computer vision, time synchronization of distributed networks, and ranking from
pairwise comparisons. In this paper, we consider a dynamic version of this
problem where the angles, and also the measurement graphs evolve over $T$ time
points. Assuming a smoothness condition on the evolution of the latent angles,
we derive three algorithms for joint estimation of the angles over all time
points. Moreover, for one of the algorithms, we establish non-asymptotic
recovery guarantees for the mean-squared error (MSE) under different
statistical models. In particular, we show that the MSE converges to zero as
$T$ increases under milder conditions than in the static setting. This includes
the setting where the measurement graphs are highly sparse and disconnected,
and also when the measurement noise is large and can potentially increase with
$T$. We complement our theoretical results with experiments on synthetic data.

在本文中，我们考虑了角度同步问题的动态版本，其中角度和测量图在 T 个时间点上演变。在假设潜在角度的演变具有平滑性条件的基础上，我们推导了三种算法来联合估计所有时间点的角度。此外，对于其中一种算法，我们在不同统计模型下建立了均方误差（MSE）的非渐近恢复保证。特别是，我们证明了在较静态设置下更温和的条件下，MSE 随着 T 的增加收敛于零。这包括测量图高度稀疏且不连通的情况，以及测量噪声较大且可能随着 T 的增加而增加的情况。我们通过对合成数据进行实验来补充我们的理论结果。

平滑约束下的动态角度同步

Dynamic angular synchronization under smoothness constraints

We propose a unified formulation for the problem of 3D human pose estimation
from a single raw RGB image that reasons jointly about 2D joint estimation and
3D pose reconstruction to improve both tasks. We take an integrated approach
that fuses probabilistic knowledge of 3D human pose with a multi-stage CNN
architecture and uses the knowledge of plausible 3D landmark locations to
refine the search for better 2D locations. The entire process is trained
end-to-end, is extremely efficient and obtains state- of-the-art results on
Human3.6M outperforming previous approaches both on 2D and 3D errors.

本文提出了一种用于从单个 RGB 图像中估计人类姿势的统一方法，通过联合推理 2D 关节估计和 3D 姿势重建来改善两个任务，并使用可信的 3D 地标位置知识来对更好的 2D 位置进行搜索，并通过多级卷积神经网络架构综合了 3D 人体姿势的概率知识，并在 Human3.6M 数据集上进行了端到端的训练，最终获得了在 2D 和 3D 误差上优于之前方法的最新结果。