Viscosity solutions for geodesic active contour under geometrical conditions

References

• Apprato , D. 2004 . Segmentation of medical image sequence under constraints: application to non-invasive assessment of pulmonary arterial hypertension . Int. J. Comput. Math. , 5 : 527 – 536 .
   Google Scholar
• Alvarez , L. , Lions , P.-L. and Morel , J.-M. 1992 . Image selective smoothing and edge detection by nonlinear diffusion . SIAM J. Numer. Anal. , 29 ( 3 ) : 845 – 866 .
   Web of Science ®Google Scholar
• Barles , G. 1999 . Nonlinear neumann boundary conditions for quasilinear degenerate elliptic equations and applications . J. Differential Eq. , 34 : 191 – 224 .
   Google Scholar
• Barles , G. 1994 . Solutions de viscosité des Équations de Hamilton-Jacobi , Berlin : Springer-Verlag .
   Google Scholar
• Caselles , V. , Catté , F. , Coll , C. and Dibos , F. 1993 . A geometric model for active contours in image processing . Numer. Math. , 66 : 1 – 31 .
   Web of Science ®Google Scholar
• Caselles , V. , Kimmel , R. and Sapiro , G. 1997 . Geodesic active contours . Int. J. Computer Vision , 22–1 : 61 – 87 .
   Google Scholar
• Chan , T. and Vese , L. 2001 . Active contours without edges . IEEE Trans Image Process , 10 ( 2 ) : 266 – 277 .
   PubMed Web of Science ®Google Scholar
• Chan , T. F. , Shen , J. and Vese , L. 2003 . Variational PDE models in image processing . Notices of the American Mathematical Society , 50 ( 1 ) : 14 – 26 .
   Google Scholar
• Cohen , L. D. 1991 . On active contours models and balloons . Comput. Vision, graph image process image understand , 53 ( 2 ) : 211 – 218 .
   Web of Science ®Google Scholar
• Crandall , M. G. , Ishii , H. and Lions , P-L. 1992 . User's guide to viscosity solutions of second order partial differential equations . Bullet. Am. Math. Soc. , 27 ( 1 ) : 1 – 69 .
   Web of Science ®Google Scholar
• Dubrovin , B. A. , Fomenko , A. T. and Novikov , S. P. 1992 . “ Modern geometry methods and applications ” . In The Geometry of Surfaces, Transformation Groups, and Fields , Springer-Verlag . Part I
   Google Scholar
• Freidlin , M. 1985 . Functional Differential Equations of Parabolic Type , Princeton University Press .
   Google Scholar
• Gout , C. and Le Guyader , C. 2006 . Segmentation of complex geophysical structures with well data . Comput. Geosci. , 10 ( 4 ) : 361 – 372 .
   Google Scholar
• Gout , C. and Vieira-Testé , S. 2003 . An algorithm for segmentation under interpolation conditions using deformable models . Int. J. Comput. Math. , 80 ( 1 ) : 47 – 54 .
   Web of Science ®Google Scholar
• Gout , C. , Le Guyader , C. and Vese , L. 2005 . Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods . Numer. Algorithms , 39 ( 1–3 ) : 155 – 173 .
   Web of Science ®Google Scholar
• Ishii , H. and Sato , M.-H. 2004 . Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain . Nonlinear Anal. , 57 : 1077 – 1098 .
   Google Scholar
• Kass , M. , Witkin , A. and Terzopoulos , D. 1987 . Snakes: Active contour models . Int. J. Comput. Vision , 1 ( 4 ) : 133 – 144 .
   Google Scholar
• Kichenassamy , S. Proceedings of the International Conference on Computer Vision ICCV . Gradient Flows and Geometric Active Contour Models , pp. 810 – 815 .
   Google Scholar
• Le Guyader , C. and Vese , L. 2007 . Self-repelling snakes for topology-preserving segmentation models , submitted
   Google Scholar
• Le Guyader , C. 2004 . Imagerie Mathématique: Segmentation sous contraintes géométriques, Théory et Applications , INSA Rouen . Thèse de Doctorat
   Google Scholar
• Le Guyader , C. , Apprato , D. and Gout , C. 2005 . Using a level set approach for image segmentation under interpolation conditions . Numer. Algorithms , 39 ( 1–3 ) : 221 – 235 .
   Google Scholar
• Osher , S. and Fedkiw , R. 2003 . Level Set Methods and Dynamic Implicit Surfaces , Springer Verlag .
   Google Scholar
• Osher , S. and Sethian , J. A. 1998 . Fronts propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations . J. Comput. Phys. , 79 : 12 – 49 .
   Web of Science ®Google Scholar
• Sethian , J. A. 1999 . Level Set Methods and Fast Marching Methods: Evolving interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science , London : Cambridge University Press .
   Google Scholar
• Yatziv , L. , Bartesaghi , A. and Sapiro , G. 2006 . A fast O(N) implementation of the fast marching algorithm . J. Comput. Phys. , 212 : 393 – 399 .
   Google Scholar
• Zhao , H.-K. 2000 . Implicit and non parametric shape reconstruction from unorganized data using a variational level set method . Comput. Vision Image Understand , 80 ( 3 ) : 295 – 314 .
   Web of Science ®Google Scholar