Tracking multiple moving targets allows quantitative measure of the dynamic
behavior in systems as diverse as animal groups in biology, turbulence in fluid
dynamics and crowd and traffic control. In three dimensions, tracking several
targets becomes increasingly hard since optical occlusions are very likely,
i.e. two featureless targets frequently overlap for several frames. Occlusions
are particularly frequent in biological groups such as bird flocks, fish
schools, and insect swarms, a fact that has severely limited collective animal
behavior field studies in the past. This paper presents a 3D tracking method
that is robust in the case of severe occlusions. To ensure robustness, we adopt
a global optimization approach that works on all objects and frames at once. To
achieve practicality and scalability, we employ a divide and conquer
formulation, thanks to which the computational complexity of the problem is
reduced by orders of magnitude. We tested our algorithm with synthetic data,
with experimental data of bird flocks and insect swarms and with public
benchmark datasets, and show that our system yields high quality trajectories
for hundreds of moving targets with severe overlap. The results obtained on
very heterogeneous data show the potential applicability of our method to the
most diverse experimental situations.Comment: 13 pages, 6 figures, 3 tables. Version 3 was slightly shortened, and
new comprative results on the public datasets (thermal infrared videos of
flying bats) by Z. Wu and coworkers (2014) were included. in A. Attanasi et
al., "GReTA - A Novel Global and Recursive Tracking Algorithm in Three
Dimensions", IEEE Trans. Pattern Anal. Mach. Intell., vol.37 (2015
