New variational formulations for level set evolution without reinitialization with applications to image segmentation

Journal of Mathematical Imaging and Vision

Volumn 41, Issue 3, 2011, Pages 194-209

  Liu, Chunxiao ^a   Dong, Fangfang ^b   Zhu, Shengfeng ^c   Kong, Dexing ^c   Liu, Kefeng ^a  

^a ZHEJIANG UNIVERSITY   (China)

^b ZHEJIANG GONGSHANG UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY   (China)

Author keywords

Additive operator splitting; Augmented Lagrangian method; Chan Vese model; Level set method; Projection Lagrangian method; Reinitialization

Indexed keywords

ADDITIVE OPERATOR SPLITTING; AUGMENTED LAGRANGIAN METHODS; CHAN-VESE MODEL; LAGRANGIAN METHODS; LEVEL SET METHOD; REINITIALIZATION;

ALGORITHMS; CONSTRAINED OPTIMIZATION; DROP BREAKUP; IMAGE SEGMENTATION; LEVEL MEASUREMENT; NUMERICAL METHODS;

LAGRANGE MULTIPLIERS;

EID: 84855530359     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-011-0269-z     Document Type: Article

References (36)

1. Osher, S., Sethian, J.A.: Fronts propagation with curvature depen-dent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12-49 (1988)
2. Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163, 489-528 (2000)
3. Osher, S., Santosa, F.: Level set methods for optimization prob-lems involving geometry and constraints I. frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171, 272-288 (2001) (Pubitemid 33667119)
4. Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two phase flow. J. Comput. Phys. 114, 146-159 (1994) (Pubitemid 124013478)
5. Santosa, F.: A level-set approach for inverse problems involving obstacles. ESAIM Control Optim. Calc. Var. 1, 17-33 (1996)
6. Chan, T.F., Tai, X.-C.: Level set and total variation regulariza-tion for elliptic inverse problems with discontinuous coefficients. J. Comput. Phys. 193, 40-66 (2003) (Pubitemid 37468957)
7. Fedkiw, R.P., Sapiro, G., Shu, C.-W.: Shock capturing, level sets, and PDE based methods in computer vision and image processing: a review of Osher's contributions. J. Comput. Phys. 185, 309-341 (2003) (Pubitemid 36309100)
8. Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Berlin (2003)
9. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)
10. Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, Berlin (2003)
11. Tai,X.-C.,Chan,T.F.: A survey on multiple level setmethod swith applications for identifying piecewise constant functions. Int. J. Numer. Anal. Mod. 1, 25-48 (2004)
12. Gomes, J., Faugeras, O.: Reconciling distance functions and level sets. J. Vis. Commun. Image Represent. 11, 209-223 (2000)
13. Lie, J., Lysaker, M., Tai, X.-C.: A binary level set model and some applications to Mumford-Shah image segmentation. IEEE Trans. Image Process. 15, 1171-1181 (2006)
14. Li, C., Xu, C., Gui, C., Fox, M.D.: Level set evolution without reinitialization: a new variational formulation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 430-436 (2005)
15. Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10, 266-277 (2001) (Pubitemid 32254596)
16. Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591-1595 (1996) (Pubitemid 26075170)
17. Sethian, J.A.: Fast marching methods. SIAM Rev. 41, 199-235 (1999)
18. Tsai, Y.-H.R., Cheng, L.-T., Osher, S., Zhao, H.-K.: Fast sweep-ing algorithms for a class of Hamilton-Jacobi equations. SIAM J. Numer. Anal. 41, 673-694 (2003)
19. Adalsteinsson, D., Sethian, J.A.: The fast construction ofexten-sion velocities in level set methods. J. Comput. Phys. 148, 2-22 (1999)
20. Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A PDE-based fast local level set method. J. Comput. Phys. 155, 410-438 (1999)
21. Lie, J., Lysaker, M., Tai, X.-C.: A variant of the level set method and applications to image segmentation. Math. Comput. 75, 1155-1174 (2006) (Pubitemid 44116291)
22. Zhu, S., Wu, Q., Liu, C.: Variational piecewise constant level set methods for shape optimization of a two-density drum. J. Comput. Phys. 229, 5062-5089 (2010)
23. Zhu, S., Liu, C., Wu, Q.: Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum. Com-put. Methods Appl. Mech. Eng. 199, 2970-2986 (2010)
24. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
25. Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2, 323-343 (2009)
26. Huang, Y., Ng, M.,Wen, Y.: A new total variation method for mul-tiplicative noise removal. SIAM J. Imaging Sci. 2, 20-40 (2009)
27. Bioucas-Dias, J.M., Figueiredo, M.A.T.: Multiplicative noise re-moval using variable aplitting and constrained optimization. IEEE Trans. Image Process. 19, 1720-1730 (2010)
28. Chan, T.F., Sandberg, B.Y., Vese, L.A.: Active contours without edges for vector-valued images. J. Vis. Commun. Image Repre-sent. 11, 130-141 (2000)
29. Vese, L.A., Chan, T.F.: A multiphase level set framework for im-age segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50, 271-293 (2002) (Pubitemid 35377416)
30. Sussman, M., Fatemi, E.: An efficient, interface preserving level set redistancing algorithm and its application to interfacial incom-pressible fluid flow. SIAM J. Sci. Comput. 20, 1165-1191 (1999) (Pubitemid 32251212)
31. Zhao, H.K., Chan, T.F., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179-195 (1996) (Pubitemid 126162336)
32. Tai, X.-C., Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. UCLA CAM Report 09-05 (2009)
33. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577-685 (1989)
34. Lu, T., Neittaanmäki, P., Tai, X.-C.: A parallel splitting up method and its application to Navier-Stokes equations. Appl. Math. Lett. 4, 25-29 (1991)
35. Weickert, J., Romeny, B.M., Viergever, M.A.: Efficient and reli-able schemes for nonlinear diffusion filtering. IEEE Trans. Image Process. 7, 398-410 (1998) (Pubitemid 128745358)
36. Wang, X., Huang, D., Xu, H.: An efficient local Chan-Vese model forimage segmentation. Pattern Recognit. 43, 603-618 (2010)