From restoration by topological gradient to medical image segmentation via an asymptotic expansion
Tài liệu tham khảo
Alessandrini, 1996, Unique determination of multiple cracks by two measurements, SIAM J. Control Optim., 34, 913, 10.1137/S0363012994262853
Ammari, 2001, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II - The full Maxwell equations, J. Math. Pure Appl., 80, 769, 10.1016/S0021-7824(01)01217-X
Amstutz, 2005, Crack detection by the topological gradient method, Control Cybern., 34, 119
Amstutz, 2003, The topological asymptotic for the Helmoltz equation, SIAM J. Control Optim., 42, 1523, 10.1137/S0363012902406801
Andrieux, 1996, Identification of planar cracks by complete overdetermined data: Inversion formulae, Inverse Problems, 12, 553, 10.1088/0266-5611/12/5/002
Aubert, 2001, vol. 147
Auroux, 2007, A topological asymptotic analysis for the regularized grey-level image classification problem, Math. Model. Numer. Anal., 41, 607, 10.1051/m2an:2007027
Auroux, 2006, A one-shot inpainting algorithm based on the topological asymptotic analysis, Comput. Appl. Math., 25, 1
Belhachmi, 2007, Stability and uniqueness for the crack identification problem, SIAM J. Control Optim., 46, 253, 10.1137/S0363012904441179
Ben Abda, 1999, Identification of 2D cracks by elastic boundary measurements, Inverse Problems, 15, 67, 10.1088/0266-5611/15/1/011
Ben Abda, 2002, Line-segment cracks recovery from incomplete boundary data, Inverse Problems, 18, 1057, 10.1088/0266-5611/18/4/308
Blake, 1998
Bruhl, 2001, Crack detection using electrostatic measurements, Math. Model. Numer. Anal., 35, 595, 10.1051/m2an:2001128
K. Bryan, M.S. Vogelius, A review of selected works on crack identification, in: Proceedings of the IMA workshop on Geometric Methods in Inverse Problems and PDE Control, August 2001
A.P. Calderón, On an inverse boundary value problem, in: Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), Soc. Brasil. Mat., Rio de Janeiro, Brasil, 1980, pp. 65–73
Catté, 1992, Image selective smoothing and edge detection by non linear diffusion, SIAM J. Numer. Anal., 29, 182, 10.1137/0729012
Duncan, 2000, Medical image analysis: Progress over two decades and the challenges ahead, IEEE Trans. Pattern Anal. Mach. Intell., 22, 85, 10.1109/34.824822
Friedman, 1989, Determining cracks by boundary measurements, Indiana Univ. Math. J., 38, 527, 10.1512/iumj.1989.38.38025
Friedman, 1989, Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem of continuous dependence, Arch. Ration. Mech. Anal., 105, 299, 10.1007/BF00281494
Garreau, 2001, The topological asymptotic for PDE systems: The elasticity case, SIAM J. Control Optim., 39, 1756, 10.1137/S0363012900369538
Guillaume, 2002, From compressible to incompressible materials via an asymptotic expansion, Numer. Math., 91, 649, 10.1007/s002110100347
Guillaume, 2002, The topological asymptotic expansion for the Dirichlet problem, SIAM J. Control Optim., 41, 1042, 10.1137/S0363012901384193
Guillaume, 2004, The topological sensitivity and shape optimization for the Stokes equations, SIAM J. Control Optim., 43, 1, 10.1137/S0363012902411210
Jaafar Belaid, 2006, Image restoration and edge detection by topological asymptotic expansion, C. R. Acad. Sci. Sér. I, 342, 313
L. Jaafar Belaid, M. Jaoua, M. Masmoudi, L. Siala, Application of the topological gradient to image restoration and edge detection, Eng. Anal. Bound. Elem. (2008) (in press)
Kohn, 1987, Relaxation of a variational method for impedance computed tomography, Commun. Pure Appl. Math., 40, 745, 10.1002/cpa.3160400605
Kubo, 1990, Inverse problems and the electric potential computed tomography method as one of their application
M. Masmoudi, The topological asymptotic, Computational Methods for Control Applications, in: R. Glowinski, H. Karawada, J. Periaux (Eds.), GAKUTO Internat. Ser. Math. Sci. Appl. vol. 16, Tokyo, Japan, 2001, pp. 53–72
T. McInerney, D. Terzopoulos, Medical image segmentation using topologically adaptable surfaces, in: Proc. CVRMed’97, Grenoble, France, 1997
Mumford, 1989, Optimal approximations by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42, 577, 10.1002/cpa.3160420503
Nishimura, 1991, A boundary integral equation method for an inverse problem related to crack detection, Internat. J. Numer. Methods Engrg., 32, 1371, 10.1002/nme.1620320702
Perona, 1990, Scale space and Edge detection detection using Anisotropic diffusion, IEEE Trans. Pattern Analy. Mach. Intell., 12, 629, 10.1109/34.56205
D.L. Pham, C. Xu, J.L. Prince, A survey of current methods in medical image segmentation, Tech. Report Johns Hopkins Univ., JHU/ECE 99-01 (1999)
Samet, 2003, The topological asymptotic for the helmholtz equation, SIAM J. Control Optim., 42, 1523, 10.1137/S0363012902406801
Santosa, 1991, A computational algorithm to determine cracks from electrostatic boundary measurements, Internat. J. Engrg. Sci., 29, 917, 10.1016/0020-7225(91)90166-Z
Sethian, 1999, Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials sciences
Sokolowski, 2002, Topological derivatives of shape functionals for elasticity systems, Internat. Ser. Numer. Math, 139, 231
Wei, 2004, A fast snake model based on non-linear diffusion for medical image segmentation, Comput. Med. Imaging Graph., 28, 109, 10.1016/j.compmedimag.2003.12.002
Weickert, 1996, Theoretical foundations of anisotropic diffusion in image processing, Computing, Suppl., 11, 221, 10.1007/978-3-7091-6586-7_13
J. Weickert, Anisotropic diffusion in image processing, Ph.D. Thesis, University of Kaiserslautern, Germany, 1996
Weickert, 2001, Efficient image segmentation using partial differential equations and morphology, Pattern Recognit., 34, 1813, 10.1016/S0031-3203(00)00109-6
Yezzi, 1997, A Geometric Snake Model for Segmentation of Medical Imagery, IEEE Trans. Med. Imaging, 16, 199, 10.1109/42.563665