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 spatio-temporal 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.


computer vision, optimisation.

Author keywords

Point Track Completion, Spatio-Temporal Clustering, Augmented Lagrangian Multiplier

Scientific reference

A. Agudo, V. Lepetit and F. Moreno-Noguer. Simultaneous completion and spatiotemporal grouping of corrupted motion tracks. The Visual Computer, 2021, to appear.