A grid based particle method for evolution of open curves and surfaces

Journal of Computational Physics

Volumn 228, Issue 20, 2009, Pages 7706-7728

  Leung, Shingyu ^a   Zhao, Hongkai ^b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Eulerian mesh; Lagrangian particles; Open curves; Open surfaces

Indexed keywords

LAGRANGE MULTIPLIERS; MESH GENERATION; NUMERICAL METHODS;

CURVE AND SURFACE; EULERIAN MESH; GRID-BASED; LAGRANGIAN PARTICLES; MESHLESS; MODELING MOTIONS; OPEN CURVE; OPEN SURFACE; PARTICLE METHODS; TWO-DIMENSIONS;

IMAGE SEGMENTATION;

EID: 69049101846     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.07.017     Document Type: Article

References (25)

1. Aubert G., and Kornprobst P. Mathematical Problems in Image Processing - Partial Differential Equations and the Calculus of Variations (2006), Springer
2. S. Basu, D.P. Mukherjee, S.T. Acton, Implicit evolution of open ended curves, in: IEEE International Conference on Image Processing, vol. 1, 2007, pp. 261-264.
3. Bell J.B., Colella P., and Glaz H.M. A second order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257-283
4. Bresson X., Esedoglu S., Vandergheynst P., Thiran J.-P., and Osher S. Fast global minimization of the active Contour/Snake model. J. Math. Imaging Vision 28 (2007) 151-167
5. Burchard P., Cheng L.-T., Merriman B., and Osher S. Motion of curves in three spatial dimensions using a level set approach. J. Comput. Phys. 170 2 (2001) 720-741
6. Burton W.K., Cabrera N., and Frank F.C. The growth of crystals and the equilibrium structure of their surface. Philos. Trans. Roy. Soc. Lond. 243A (1951) 299-358
7. Caselles V., Kimmel R., and Sapiro G. Geodesic active contours. Int. J. Comput. Vision 22 1 (1997) 61-79
8. Chan T.F., Esedoḡlu S., and Nikolova M. Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66 (2006) 1632-1648
9. Cheng L.-T., Burchard P., Merriman B., and Osher S. Motion of curves constrained on surfaces using a level-set approach. J. Comput. Phys. 175 (2002) 604-644
10. Enright D., Fedkiw R., Ferziger J., and Mitchell I. A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183 (2002) 83-116
11. Fua P., and Leclerc Y.G. Model driven edge detection. Machine Vision Appl. 3 (1990) 45-56
12. Gilles J., and Collin B. Fast probabilistic snake algorithm. ICIP 3 (2003) 14-17
13. Gomes J., and Faugeras O. Using the vector distance functions to evolve manifolds of arbitrary codimension. Lect. Notes Comput. Sci. 2106 (2001) 1-13
14. Hieber S., and Koumoutsakos P. A lagrangian particle level set method. J. Comput. Phys. 210 (2005) 342-367
15. Kass M., Witkin A., and Terzopoulos D. Snakes: active contour models. Int. J. Comput. Vision 1 4 (1988) 321-331
16. S. Leung, S. Osher, Fast global minimization of the active contour model with tv-inpainting and two-phase denoising, in: Proceeding of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2005, pp. 149-160.
17. Leung S., and Zhao H.K. A grid based particle method for moving interface problems. J. Comput. Phys. 228 (2009) 2993-3024
18. LeVeque R. High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33 (1996) 627
19. Min C., and Gibou F. A second order accurate level set method on non-graded adaptive cartesian grids. J. Comput. Phys. 225 (2007) 300-321
20. Osher S., and Fedkiw R.P. Level Set Methods and Dynamic Implicit Surfaces (2003), Springer-Verlag, New York
21. Osher S.J., and Sethian J.A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12-49
22. Sapiro G. Geometric Partial Differential Equations and Image Analysis (2001), Cambridge University Press
23. Smereka P. Spiral crystal growth. Physica D 138 (2000) 282-301
24. Solem J.E., and Heyden A. Reconstructing open surfaces from image data. Int. J. Comput. Vision 69 (2006) 267-275
25. Ventura G., Xu J.X., and Belytschoko T. A vector level set method and new discontinuity approximations for crack growth by EFG. Int. J. Numer. Methods Eng. 54 (2002) 923-944