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Volume 2, Issue 4
3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Tiril P. Gurholt & Xuecheng Tai

DOI: 10.4208/nmtma.2009.m9003s

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 403-420.

Published online: 2009-02

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  • Abstract

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.

  • Keywords

Piecewise constant level set method, energy minimization, graph cut, segmentation, three-dimensional.

  • AMS Subject Headings

65K10, 49K20, 49K35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-403, author = {Tiril P. Gurholt and Xuecheng Tai}, title = {3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {4}, pages = {403--420}, abstract = {

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9003s}, url = {http://global-sci.org/intro/article_detail/nmtma/6031.html} }
TY - JOUR T1 - 3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization AU - Tiril P. Gurholt & Xuecheng Tai JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 403 EP - 420 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m9003s UR - https://global-sci.org/intro/article_detail/nmtma/6031.html KW - Piecewise constant level set method, energy minimization, graph cut, segmentation, three-dimensional. AB -

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.

Tiril P. Gurholt and Xuecheng Tai. (2009). 3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization. Numerical Mathematics: Theory, Methods and Applications. 2 (4). 403-420. doi:10.4208/nmtma.2009.m9003s
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