Given an unordered list of 2D or 3D point trajectories corrupted by noise and partial observations, in this paper we introduce a framework to simultaneously recover the incomplete motion tracks and group the points into spatially and temporally coherent clusters. This advances existing work, which only addresses partial problems and without considering a unified and unsupervised solution. We cast this problem as a matrix completion one, in which point tracks are arranged into a matrix with the missing entries set as zeros. In order to perform the double clustering, the measurement matrix is assumed to be drawn from a dual union of spatiotemporal subspaces. The bases and the dimensionality for these subspaces, the affinity matrices used to encode the temporal and spatial clusters to which each point belongs, and the non-visible tracks, are then jointly estimated via augmented Lagrange multipliers in polynomial time. A thorough evaluation on incomplete motion tracks for multiple-object typologies shows that the accuracy of the matrix we recover compares favorably to that obtained with existing low-rank matrix completion methods, specially under noisy measurements. In addition, besides recovering the incomplete tracks, the point trajectories are directly grouped into different object instances, and a number of semantically meaningful temporal primitive actions are automatically discovered.

给定一个被噪声和部分观察破坏的 2D 或 3D 点轨迹的无序列表，在本文中，我们引入了一个框架来同时恢复不完整的运动轨迹并将这些点分组为空间和时间相干的簇。这推进了现有的工作，这些工作只解决了部分问题，而没有考虑统一和无监督的解决方案。我们将此问题视为矩阵完成问题，其中点轨迹被排列成一个矩阵，其中缺失的条目设置为零。为了执行双重聚类，假设测量矩阵是从时空子空间的双重联合中提取的。这些子空间的基数和维数，用于编码每个点所属的时间和空间集群的亲和矩阵，以及不可见的轨迹，然后在多项式时间内通过增广拉格朗日乘数联合估计。对多目标类型的不完整运动轨迹的全面评估表明，我们恢复的矩阵的准确性与使用现有低秩矩阵完成方法获得的准确性相比具有优势，特别是在噪声测量下。此外，除了恢复不完整的轨迹外，点轨迹被直接分组到不同的对象实例中，并自动发现了一些语义上有意义的时间原始动作。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 特别是在噪声测量下。此外，除了恢复不完整的轨迹外，点轨迹被直接分组到不同的对象实例中，并自动发现了一些语义上有意义的时间原始动作。特别是在噪声测量下。此外，除了恢复不完整的轨迹外，点轨迹被直接分组到不同的对象实例中，并自动发现了一些语义上有意义的时间原始动作。