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Optimal transport (OT) is a prominent framework for point set registration, that is, to align points in two sets. Point set registration becomes particularly difficult when points are organized into objects and the correspondence among the objects is to be established. The registration of pixels must maintain consistency at the object level despite the possibility of object division, merging, and substantial alteration in size and shape over time. Existing approaches in OT exploit either similarity in shape for the entire set of points or spatial closeness of individual points, but not the two simultaneously. We propose a new weighted Gromov--Wasserstein distance (WGWD) to combine both sources of information. Importantly, we use a bipartite graph partitioning strategy to regularize OT in order to achieve object-level consistency and to enhance computational efficiency. We apply the method to cell tracking, specifically, the task of …

SCOTT: Shape-Location Combined Tracking with Optimal Transport