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The interest in 3D dynamical tracking is growing in fields such as robotics,biology and fluid dynamics. Recently, a major source of progress in 3D trackinghas been the study of collective behaviour in biological systems, where thetrajectories of individual animals moving within large and dense groups need tobe reconstructed to understand the behavioural interaction rules. Experimentaldata in this field are generally noisy and at low spatial resolution, so thatindividuals appear as small featureless objects and trajectories must beretrieved by making use of epipolar information only. Moreover, opticalocclusions often occur: in a multi-camera system one or more objects becomeindistinguishable in one view, potentially jeopardizing the conservation ofidentity over long-time trajectories. The most advanced 3D tracking algorithmsovercome optical occlusions making use of set-cover techniques, which howeverhave to solve NP-hard optimization problems. Moreover, current methods are notable to cope with occlusions arising from actual physical proximity of objectsin 3D space. Here, we present a new method designed to work directly in 3Dspace and time, creating (3D+1) clouds of points representing the fullspatio-temporal evolution of the moving targets. We can then use a simpleconnected components labeling routine, which is linear in time, to solveoptical occlusions, hence lowering from NP to P the complexity of the problem.Finally, we use normalized cut spectral clustering to tackle 3D physicalproximity.

Towards a tracking algorithm based on the clustering of spatio-temporal clouds of points