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Together with my co-authors, we have released two papers accepted at SIGGRAPH 2016, that are related to optimal transport and its applications in computer graphics and imaging.
With Nicolas and Marco we propose in Wasserstein Barycentric Coordinates: Histogram Regression Using Optimal Transport a way to compute barycentric coordinates for histograms, according to the geometry defined by optimal transport (the so-called Wasserstein distance. It is useful to perform vizualization and to navigate in collections of histograms, and also enables to compute “projections” on a geodesic simplex defined by these histograms. The main contribution is a computationally tractable optimization scheme, that makes use of recursive differentiation of Sinkhorn’s algorithm.
With Justin, Vova and Suvrit, we propose in
Entropic Metric Alignment for Correspondence Problems a fast iterative scaling algorithm to approximate the solution of quadratic assignment problems. It iteratively solves an entropic regularization of optimal transport, which in turn can be solved using Sinkhorn’s algorithm, and is similar to the “softassign” algorithm.