Solving the data association problem in multi-object tracking by Fourier analysis on the symmetric group
In addition to modeling the position of individual targets, multi-object tracking must also address the combinatorial problem of matching objects to corresponding tracks. In general, maintaining a probability distribution over all n! possibilities is clearly infeasible, while just maintaining an n×n matrix of “first order marginals” is a very impoverished representation. In this work we explain how to harness the theory of harmonic analysis on the symmetric group to get a hierarchy of approximations of increasing fidelity to this problem. Importatantly, not only are such band-limited approxima- tions theoretically well justifiable, but they also admit efficient observations updates based on some ideas from Clausen’s FFT for the symmetric group. Experiments show that our algebraic approach can outperform more con- ventional solutions to the data association problem while still remaining computationalliy feasible for n in the 30-40 range.