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Applications, ranging from tracking molecular motion within cells toanalyzing complex animal foraging behavior, require algorithms for associatinga collection of spot-like particles in one image with particles contained inanother image. These associations are often made via network flow algorithms.However, it is often the case that many candidate association solutions (theoutput of network flow algorithms) have nearly optimal scores; in this case,the optimal assignment solution is of dubious quality. Algorithms for reliablycomputing the uncertainty of candidate association solutions areunder-developed in situations where many particles are tracked over multipleframes of data. This is due in part to the fact that exact uncertaintyquantification (UQ) in large association problems is computationallyintractable because the exact computation exhibits exponential dependence onthe number of particles tracked. We introduce a technique that can accuratelyand efficiently quantify association ambiguity (i.e., UQ for discreteassociation problems) without requiring the evaluation of the cost of eachfeasible association solution. Our method can readily be wrapped aroundexisting tracking algorithms and can efficiently handle a variety of 2Dassociation problems. The applications presented are focused on trackingmolecules in live cells. Our method is validated via both simulations andexperiments. The experimental applications aim to accurately form tracks andquantify diffusion of quantum dot labeled proteins from \emph{in vivo}measurements; here association problems involving cost matrices possessinghundreds to thousands of rows/columns are encountered. For such large-scaleproblems, we discuss how our approach can efficiently and accurately quantifyinherent uncertainty in candidate data associations.

Uncertainty Quantification of Discrete Association Problems in Image Sequence-based Tracking