American Institute of Mathematical Sciences

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August  2010, 4(3): 505-522. doi: 10.3934/ipi.2010.4.505

A variational setting for volume constrained image registration

Christiane Pöschl 1, , Jan Modersitzki 2, and  Otmar Scherzer 3,

1. 

Departament de Tecnologia, Universitat Pompeu Fabra, Edificio Tánger, Tánger 122-140, 08018 Barcelona, Spain
2. 

Institute of Mathematics and Image Computing, Universität Lübeck, Wallstr. 40, 23560 Lübeck, Germany
3. 

Computational Science Center, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria

Received  February 2009 Revised  March 2010 Published  July 2010

We consider image registration, which is the determination of a geometrical transformation between two data sets. In this paper we propose constrained variational methods which aim for controlling the change of area or volume under registration transformation. We prove an existence result, convergence of a finite element method, and present a simple numerical example for volume-preserving registration.
Keywords: image registration, area and volume preserving registration., constrained regularization.
Mathematics Subject Classification: Primary: 68U10; Secondary: 65N2.
Citation: Christiane Pöschl, Jan Modersitzki, Otmar Scherzer. A variational setting for volume constrained image registration. Inverse Problems and Imaging, 2010, 4 (3) : 505-522. doi: 10.3934/ipi.2010.4.505
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