A Gradient Descent Solution to the Monge-Kantorovich Problem
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چکیده
We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into an unconstrained minimization of a convex, continuous functional, for which the derivative can be explicitly found. The Monge-Kantorovich problem has applications in many fields; examples from image warping and medical imaging are shown. Mathematics Subject Classification: 49D10
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تاریخ انتشار 2005