The Linear Assignment Problem (LAP) trackers implemented here follow a stripped down version of the renowned method contributed by Jaqaman and colleagues. We repeat here the ideas found in the reference paper, then stresses the differences with the nominal implementation. Particle-linking happens in two step: track segments creation from frame-to-frame particle linking, then track segments linking to achieve gap closing. The mathematical formulation used for both steps is linear assignment problem (LAP): a cost matrix is assembled contained all possible assignment costs. Actual assignments are retrieved by solving this matrix for minimal total cost. We describe first how cost matrices are arranged, then how individual costs are calculated (from http://fiji.sc/TrackMate).
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