Optimal Object Association in the Dempster–Shafer Framework

Object association is a crucial step in target tracking and data fusion applications. This task can be formalized as the search for a relation between two sets (e.g., a sets of tracks and a set of observations) in such a way that each object in one set is matched with at most one object in the other set. In this paper, this problem is tackled using the formalism of belief functions. Evidence about the possible association of each object pair, usually obtained by comparing the values of some attributes, is modeled by a Dempster–Shafer mass function defined in the frame of all possible relations. These mass functions are combined using Dempster's rule, and the relation with maximal plausibility is found by solving an integer linear programming problem. This problem is shown to be equivalent to a linear assignment problem, which can be solved in polynomial time using, for example, the Hungarian algorithm. This method is demonstrated using simulated and real data. The 3-D extension of this problem (with three object sets) is also formalized and is shown to be NP-Hard.