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Non-linear Image Registration

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Book cover Handbook of Mathematical Methods in Imaging

Abstract

Image registration is to automatically establish geometrical correspondences between two images. It is an essential task in almost all areas involving imaging. This chapter reviews mathematical techniques for nonlinear image registration and presents a general, unified, and flexible approach. Taking into account that image registration is an ill-posed problem, the presented approach is based on a variational formulation and particular emphasis is given to regularization functionals motivated by mathematical elasticity. Starting out from one of the most commonly used linear elastic models, its limitations and extensions to nonlinear regularization functionals based on the theory of hyperelastic materials are considered. A detailed existence proof for hyperelastic image registration problems illustrates key concepts of polyconvex variational calculus. Numerical challenges in solving hyperelastic registration problems are discussed and a stable discretization that guarantees meaningful solutions is derived. Finally, two case studies highlight the potential of hyperelastic image registration for medical imaging applications.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, 30322, Atlanta, GA, USA

    Lars Ruthotto

  2. Institute of Mathematics and Image Computing, University of Lübeck, Ratzeburger Allee 160, 23562, Luebeck, Germany

    Jan Modersitzki

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  1. Lars Ruthotto
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  2. Jan Modersitzki
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Correspondence to Lars Ruthotto .

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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Ruthotto, L., Modersitzki, J. (2015). Non-linear Image Registration. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_39

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