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Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning
1. | Department of Computer Science and Department of Mechanical Engineering, University of California at Santa Barbara, CA 93106-5070, United States |
2. | Department of Mathematics, Stanford University, Stanford, CA 94305-2125 |
3. | Siemens Medical Solutions, Med SW West, 755 College Road East, Princeton, NJ 08540, United States |
4. | Department of Radiation Oncology, Stanford University, Stanford, CA 94305, United States, United States |
[1] |
Esther Klann, Ronny Ramlau, Wolfgang Ring. A Mumford-Shah level-set approach for the inversion and segmentation of SPECT/CT data. Inverse Problems and Imaging, 2011, 5 (1) : 137-166. doi: 10.3934/ipi.2011.5.137 |
[2] |
Li Shen, Eric Todd Quinto, Shiqiang Wang, Ming Jiang. Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography. Inverse Problems and Imaging, 2018, 12 (6) : 1343-1364. doi: 10.3934/ipi.2018056 |
[3] |
Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems and Imaging, 2021, 15 (3) : 387-413. doi: 10.3934/ipi.2020073 |
[4] |
Antonin Chambolle, Francesco Doveri. Minimizing movements of the Mumford and Shah energy. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 153-174. doi: 10.3934/dcds.1997.3.153 |
[5] |
Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems and Imaging, 2021, 15 (2) : 315-338. doi: 10.3934/ipi.2020070 |
[6] |
Yoshikazu Giga, Hiroyoshi Mitake, Hung V. Tran. Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3983-3999. doi: 10.3934/dcdsb.2019228 |
[7] |
Giovanna Citti, Maria Manfredini, Alessandro Sarti. Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. Communications on Pure and Applied Analysis, 2010, 9 (4) : 905-927. doi: 10.3934/cpaa.2010.9.905 |
[8] |
Zhenlin Guo, Ping Lin, Guangrong Ji, Yangfan Wang. Retinal vessel segmentation using a finite element based binary level set method. Inverse Problems and Imaging, 2014, 8 (2) : 459-473. doi: 10.3934/ipi.2014.8.459 |
[9] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1047-1069. doi: 10.3934/dcds.2008.21.1047 |
[10] |
Zhenhua Zhao, Yining Zhu, Jiansheng Yang, Ming Jiang. Mumford-Shah-TV functional with application in X-ray interior tomography. Inverse Problems and Imaging, 2018, 12 (2) : 331-348. doi: 10.3934/ipi.2018015 |
[11] |
Tetsuya Ishiwata, Takeshi Ohtsuka. Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 893-907. doi: 10.3934/dcdss.2020390 |
[12] |
Ye Yuan, Yan Ren, Xiaodong Liu, Jing Wang. Approach to image segmentation based on interval neutrosophic set. Numerical Algebra, Control and Optimization, 2020, 10 (1) : 1-11. doi: 10.3934/naco.2019028 |
[13] |
Bin Dong, Aichi Chien, Yu Mao, Jian Ye, Fernando Vinuela, Stanley Osher. Level set based brain aneurysm capturing in 3D. Inverse Problems and Imaging, 2010, 4 (2) : 241-255. doi: 10.3934/ipi.2010.4.241 |
[14] |
Jiangfeng Huang, Zhiliang Deng, Liwei Xu. A Bayesian level set method for an inverse medium scattering problem in acoustics. Inverse Problems and Imaging, 2021, 15 (5) : 1077-1097. doi: 10.3934/ipi.2021029 |
[15] |
Dietmar Szolnoki. Set oriented methods for computing reachable sets and control sets. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 361-382. doi: 10.3934/dcdsb.2003.3.361 |
[16] |
Peter Frolkovič, Viera Kleinová. A new numerical method for level set motion in normal direction used in optical flow estimation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 851-863. doi: 10.3934/dcdss.2020347 |
[17] |
Wangtao Lu, Shingyu Leung, Jianliang Qian. An improved fast local level set method for three-dimensional inverse gravimetry. Inverse Problems and Imaging, 2015, 9 (2) : 479-509. doi: 10.3934/ipi.2015.9.479 |
[18] |
D. Motreanu, Donal O'Regan, Nikolaos S. Papageorgiou. A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1791-1816. doi: 10.3934/cpaa.2011.10.1791 |
[19] |
Enrique Fernández-Cara, Juan Límaco, Laurent Prouvée. Optimal control of a two-equation model of radiotherapy. Mathematical Control and Related Fields, 2018, 8 (1) : 117-133. doi: 10.3934/mcrf.2018005 |
[20] |
Juan Carlos López Alfonso, Giuseppe Buttazzo, Bosco García-Archilla, Miguel A. Herrero, Luis Núñez. A class of optimization problems in radiotherapy dosimetry planning. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1651-1672. doi: 10.3934/dcdsb.2012.17.1651 |
2018 Impact Factor: 1.313
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