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Rick Chartrand, Kevin R Vixie, Brendt Wohlberg, and Erik M Bollt (2007)

A gradient descent solution to the Monge-Kantorovich problem

submitted.

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.
LA-UR-04-6305
http://math.lanl.gov/~rick/Publications/chartrand-2005-monge.shtml
 
by Katharine Chartrand — last modified 2007-05-19 04:14