Segmentation of complex geophysical structures with well data

Computational Geosciences

Volumn 10, Issue 4, 2006, Pages 361-372

  Gout, Christian ^a,b   Le Guyader, Carole ^c  

^a Université de Valenciennes et du Hainaut Cambrésis   (France)

^b UNIVERSITY OF HAWAII   (United States)

^c INSA DE RENNES   (France)

Author keywords

Geodesic active contour; Interpolation of points; Level set method; Viscosity solution

Indexed keywords

EID: 47749107528     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-006-9029-3     Document Type: Article

References (40)

1. Adalsteinsson, D., Sethian, J.: A fast level set method for propagating interfaces. J. Comput. Phys. 118(2), 269-277 (1995)
2. k reconstruction of surfaces from partial data. Math. Geol. 32(8), 969-983 (2000)
3. Apprato, D., Gout, C., Komatitsch, D.: A new method for Ck approximation from a set of curves: Application to ship track data in the Marianas trench. Math. Geol. 34(7), 831-843 (2002)
4. Apprato, D., Ducassou, D., Gout, C., Laffon, E., Le Guyader, C.: Segmentation of Medical Images Sequence for Non Invasive Assessment of Pulmonary Arterial Hypertension, http://www.univ-pau.fr/~cgout/chubdx/ index1.htm, (2004)
5. Alvarez, L., Lions, P.L., Morel, J.M.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(3), 845-866 (1992)
6. Barles, G.: Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications. J. Diff. Eq. 154, 191-224 (1999)
7. Barles, G.: Solutions de viscosité des équations de Hamilton-Jacobi. Springer, Berlin Heidelberg New York (1994)
8. Caselles, V., Catté, V., Coll, C., Dibos, C., Dibos, F.: A geometric model for active contours in image processing. Numer. Math. 66, 1-31 (1993)
9. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vision 22-1, 61-87 (1997)
10. Caselles, V., Kimmel, R., Sapiro, G., Sbert, G., Sbert, C.: Minimal surfaces: A geometric three-dimensional segmentation approach. Numer. Math. 77(4), 423-451 (1997)
11. Chan, T., Vese, L.: An Efficient Variational Multiphase Motion for the Mumford-Shah segmentation mode. IEEE Asilomar Conf. Signals Syst. Comput. 1, 490-494 (2000)
12. Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266-277 (2001)
13. Chen, Y., Giga, Y., Goto, S.: Uniqueness and existence of ciscosity solutions of generalized mean curvature flow equations. J. Diff. Geom. 33(3), 749-786 (1991)
14. Cohen, L.D.: On active contours models and balloons. Computer Vis. Graph. Image Process. Image Understand. 53(2), 211-218 (1991)
15. Crandall, M.G., Ishii, H., Lions, P.L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27(1), 1-69 (1992)
16. Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277(1), 1-42 (1983)
17. Gout, C.: C k surface reconstruction from surface patches. Comput. Math. Appl. 44 (3-4), 389-406 (2002)
18. Gout, C., Le Guyader, C., Vese, L.: Image Segmentation under Interpolation conditions, Preprint, 44 pp., CAM-IPAM, Univ. of California at Los Angeles (2003)
19. Gout, C., Le Guyader, C., Vese, L.: Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods, Numer. Algorithms 39 (1-3), 155-173 (2005)
20. Gout, C., Komatitsch, D.: Surface fitting of rapidly varying data using rank coding: Application to geophysical surfaces. Math. Geol. 32(7), 873-888 (2000)
21. Le Guyader, C.: Imagerie Mathématique: Segmentation sous contraintes géométriques, Théory et Applications, Thèse de Doctorat, INSA Rouen (2004)
22. Le Guyader, C., Apprato, D., Gout, C.: Using a level set approach for image segmentation under interpolation conditions. Numer. Algorithms 39 (1-3), 221-235 (2005)
23. Hvistendahl Karlsen, K., Lie, K.A., Risebro, N.H.: A fast marching method for reservoir simulation. Comput. Geosci. 4(2), 185-206 (2000)
24. Ishii, H., Sato, M.H.: Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain, Preprint, Univ. Waseda, Japan, (2001)
25. Kichenassamy, S., Kumar, A., Olver, P. J., Tannenbaum, A., Yezzi, A.: Gradient Flows and Geometric Active Contour Models. In: Proceedings of the International Conference on Computer Vision ICCV, pp. 810-815 (1995)
26. Malladi, R., Sethian, J. A., Vemuri, B. C.: Shape modeling with front propagation: A level set approach. IEEE Trans. Patt. Anal. Mach. Int. 17(2), 158-175 (1995)
27. Monsen, E., Randen, T., Sønneland, L., Odegard, J.: Geological Model Building: A Hierarchical Segmentation Approach in Mathematical Methods and Modelling in Hydrocarbon Exploration and Production, Series: Mathematics in Industry, Vol. 7 Iske, Armin; Randen, Trygve (Eds.), (2005)
28. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. Int. J. Comput. Vision 1(4), 133-144 (1987)
29. Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, Berlin Heidelberg New York (2003)
30. Osher, S., Sethian, J.: A Fronts propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 12-49 (1988)
31. Randen, T., Monsen, E., Signer, C., Abrahamsen, A., Hansen, J., Sæter, J., Schlaf, J., Sønneland, L.: Three-dimensional texture attributes for seismic data analysis, in 70th Annual International Meeting, Society of Exploration Geophysics Expanded Abstracts, pp. 668-671, Calgary, Canada (2000)
32. Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science. Cambridge University Press, Londres (1999)
33. Sethian, J.A.: Evolution, Implementation and application of level set and fast marching methods for advancing fronts. J. Comput. Phys. 169 (2), 503-555 (2001)
34. Sethian, J.A.: A review of recent numerical algorithms for surface s moving with curvature dependent flows. J. Differential Geom. 31, 131-161 (1989)
35. Siddiqi, K., Lauziere, Y. B., Tannenbaum, A., Zucker, S. W.: Area and length minimizing flows for shape segmentation. IEEE Trans Image Processing 7 (3), 433-443 (1998)
36. Symes, W.: The Rice Inversion Project, http://www.trip.caam.rice.edu/ and http://www.trip.caam.rice.edu/txt/tripinfo/other_list.html (2005)
37. Weickert, J., Kühne, G.: Fast methods for implicit active contours models, Preprint 61, Universität des Saarlandes, Saarbrücken (2002)
38. Yatziv, L., Bartesaghi, A., Sapiro, G.: A fast O(N) implementation of the fast marching algorithm. J. Comp. Phys. 212, 393-399 (2006)
39. Zhao, H.K., Osher, S., Merriman, B., Kang, M.: Implicit and non parametric shape reconstruction from unorganized data using a variational level set method. Comput. Vision Image Understand. 80 (3), 295-314 (2000)
40. Zhao, H.K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179-195 (1986)