A multigrid method for elastic image registration with additional structural constraints [Elektronische Ressource] / vorgelegt von Lars Hömke

A multigrid method for elastic imageregistration with additional structuralconstraintsInaugural-DissertationzurErlangung des Doktorgrades derMathematisch-Naturwissenschaftlichen Fakultat¤der Heinrich-Heine Universitat¤ Dusseldorf¤vorgelegt vonLars Homk¤ eaus Dusseldorf¤August 2006Aus dem Mathematischen Institut¤ ¤der Heinrich-Heine Universitat DusseldorfGedruckt mit der Genehmigung derMathematisch-Naturwissenschaftlichen Fakultat¤ der Heinrich-Heine¤ ¤Universitat DusseldorfReferent: Prof. Dr. rer. nat. Kristian WitschKoreferent: Prof. Dr. rer. nat. Bernd Fischer (Universitat¤ zu Lubeck)¤Tag der mundlichen¤ Prufung:¤ 08.12.2006c 2006Lars Homk¤ eAll Rights ReservedAbstractThis thesis deals with the solution of a nonlinear inverse problem arising in digitalimage registration. In image registration one seeks to compute a transformationbetween two images such that they become more similar in some sense.In the rst part, we de ne the problem as the minimization of a regularized non-linear least-squares functional, which measures the image difference and smooth-ness of the transformation. The nonlinear functional is linearized around a currentapproximation in order to obtain well-posed linear subproblems. The Hessian isreplaced by an approximation that leads to an inexact Newton-type method, specif-ically a regularized Gauss-Newton method. A related gradient descent method isderived in the same framework for the purpose of comparison.