Volume 7, Issue 1
An Efficient Numerical Method for Mean Curvature-Based Image Registration Model

Jin Zhang, Ke Chen, Fang Chen & Bo Yu

East Asian J. Appl. Math., 7 (2017), pp. 125-142.

Published online: 2018-02

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  • Abstract

Mean curvature-based image registration model firstly proposed by ChumchobChen-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 registration, regularization, multilevel, mean curvature.

  • AMS Subject Headings

65F10, 65M55, 68U10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-125, author = {}, title = {An Efficient Numerical Method for Mean Curvature-Based Image Registration Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {125--142}, abstract = {

Mean curvature-based image registration model firstly proposed by ChumchobChen-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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200816.031216a}, url = {http://global-sci.org/intro/article_detail/eajam/10739.html} }
TY - JOUR T1 - An Efficient Numerical Method for Mean Curvature-Based Image Registration Model JO - East Asian Journal on Applied Mathematics VL - 1 SP - 125 EP - 142 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.200816.031216a UR - https://global-sci.org/intro/article_detail/eajam/10739.html KW - Deformable image registration, regularization, multilevel, mean curvature. AB -

Mean curvature-based image registration model firstly proposed by ChumchobChen-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.

Jin Zhang, Ke Chen, Fang Chen & Bo Yu. (2020). An Efficient Numerical Method for Mean Curvature-Based Image Registration Model. East Asian Journal on Applied Mathematics. 7 (1). 125-142. doi:10.4208/eajam.200816.031216a
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