A direct method for the solutionof an optimal control problem arising from image registration

Marcus Wagner

doi:10.3934/naco.2012.2.487

Article Contents

2012, Volume 2, Issue 3: 487-510. Doi: 10.3934/naco.2012.2.487

This issue Previous Article Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems Next Article Quadratic order conditions for bang-singular extremals

A direct method for the solution of an optimal control problem arising from image registration

Marcus Wagner^1,

1.
University of Leipzig, Department of Mathematics, P. O. B. 10 09 20, D-04009 Leipzig

Received: October 2011

Revised: February 2012

Published: August 2012

Abstract / Introduction Related Papers Cited by

Abstract

In the present paper, the the elastic/hyperelastic image registration problem is treated as a multidimensional control problem of Dieudonné-Rashevsky type. For its numerical solution, we describe a direct method based on discretization methods and large-scale optimization techniques. Selected numerical results will be presented and discussed. The quality of the results obtained with the optimal control method competes well with those generated from a standard variational method.

Keywords:

Image registration,
linear-elastic and hyperelastic regularization,
optimal control problem,
hard constraints,
direct methods.

Mathematics Subject Classification: Primary: 49J20, 68U10, 74B05, 74B20; Secondary: 26B25, 49M37.

Citation:

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