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Volume 17,     Number 3,     Fall 2009

 

VOLUMETRIC IMAGE REGISTRATION
METHODS BASED ON SOLVING THE
MONGE-AMPÈRE EQUATION
M. SULMAN, J. F. WILLIAMS, M. F. BEG AND R. D. RUSSELL

Abstract. Two new approaches for solving the image registration problem are investigated. Both use optimal warping and an elastic registration approach and are based on solving the Monge-Ampère equation fundamental to the Monge-Kantorovich theory for optimal mass transport. The key idea of the first method is to find a steady state solution to the parabolic Monge-Amp`ere equation. The second approach uses a fluid mechanics formulation of the optimal mass transfer problem. Several examples are given to demonstrate the performance of the methods.

 

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