Minimum Cost Multi-Way Data Association for Optimizing Multitarget Tracking of Interacting Objects

This paper presents a general formulation for a minimum cost data association problem which associates data features via one-to-one, m-to-one and one-to-n links with minimum total cost of the links. A motivating example is a problem of tracking multiple interacting nanoparticles imaged on video frames, where particles can aggregate into one particle or a particle can be split into multiple particles. Many existing multitarget tracking methods are capable of tracking non-interacting targets or tracking interacting targets of restricted degrees of interactions. The proposed formulation solves a multitarget tracking problem for general degrees of inter-object interactions. The formulation is in the form of a binary integer programming problem. We propose a polynomial time solution approach that can obtain a good relaxation solution of the binary integer programming, so the approach can be applied for multitarget tracking problems of a moderate size (for hundreds of targets over tens of time frames). The resulting solution is always integral and obtains a better duality gap than the simple linear relaxation solution of the corresponding problem. The proposed method was validated through applications to simulated multitarget tracking problems and a real multitarget tracking problem.