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A fast algorithm for Earth Mover's Distance based on optimal transport and L1 type Regularization
Wuchen Li, Stanley Osher, Wilfrid Gangbo
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We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar L₁ type minimization. We use a regularization which gives us a unique solution for this L₁ type problem. The new regularized minimization is very similar to problems which have been solved in the fields of compressed sensing and image processing, where several fast methods are available. In this paper, we adopt a primal-dual algorithm designed there, which uses very simple updates at each iteration and is shown to converge very rapidly. Several numerical examples are provided.
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