Elastic image registration with exact mass preservation
  We establish a new framework for image registration, which is based on linear elasticity and optimal mass transportation theory. We combine these two arguments in order to obtain a PDE constrained optimization problem that is analytically investigated and further discretized with the finite difference method and solved by an inexact SQP algorithm. This requires to solve in each step a large sparse linear system, which has a saddle point form. Motivated by stability arguments we use a fully staggered grid for the discretization of the displacement vector field. Artificial and real world examples are presented to underline the numerical robustness of the method. 
Jaros{\l}aw Wlaz{\l}o, Robert Fe{\ss}ler, Ren\'e Pinnau, Norbert   Siedow, Oliver Tse
math.OC