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An Efficient Numerical Method for Mean Curvature-Based Image Registration Model

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problemsNumerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Jin Zhang,
Ke Chen,
Fang Chen and
Bo Yu
Jin Zhang*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P R China
Ke Chen*
Affiliation:
Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, United Kingdom
Fang Chen*
Affiliation:
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, P R China
Bo Yu*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P R China
*
*Corresponding author. Email addresses:zhangjinsunny321@163.com (J. Zhang), k.chen@liv.ac.uk (K. Chen), chenfreesky@126.com (F. Chen), yubo@dlut.edu.cn (B. Yu)
*Corresponding author. Email addresses:zhangjinsunny321@163.com (J. Zhang), k.chen@liv.ac.uk (K. Chen), chenfreesky@126.com (F. Chen), yubo@dlut.edu.cn (B. Yu)
*Corresponding author. Email addresses:zhangjinsunny321@163.com (J. Zhang), k.chen@liv.ac.uk (K. Chen), chenfreesky@126.com (F. Chen), yubo@dlut.edu.cn (B. Yu)
*Corresponding author. Email addresses:zhangjinsunny321@163.com (J. Zhang), k.chen@liv.ac.uk (K. Chen), chenfreesky@126.com (F. Chen), yubo@dlut.edu.cn (B. Yu)

Abstract

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Mean curvature-based image registration model firstly proposed by Chumchob-Chen-Brito (2011) offered a better regularizer technique for both smooth and nonsmooth deformation fields. However, it is extremely challenging to solve efficiently this model and the existing methods are slow or become efficient only with strong assumptions on the smoothing parameter β. In this paper, we take a different solution approach. Firstly, we discretize the joint energy functional, following an idea of relaxed fixed point is implemented and combine with Gauss-Newton scheme with Armijo's Linear Search for solving the discretized mean curvature model and further to combine with a multilevel method to achieve fast convergence. Numerical experiments not only confirm that our proposed method is efficient and stable, but also it can give more satisfying registration results according to image quality.

Keywords

Deformable image registrationregularizationmultilevelmean curvature

MSC classification

Secondary:65F10: Iterative methods for linear systems65M55: Multigrid methods; domain decomposition68U10: Image processing

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017, pp. 125 - 142
Copyright
Copyright © Global-Science Press 2017 

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