Multigrid geometric active contour models

IEEE Transactions on Image Processing

Volumn 16, Issue 1, 2007, Pages 229-240

  Papandreou, George ^a   Maragos, Petros ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Geometric active contours; Image segmentation; Implicit explicit schemes; Level sets; Multigrid; Partial differential equations

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER VISION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

GEOMETRIC ACTIVE CONTOURS; IMPLICIT-EXPLICIT TIME INTEGRATION; MULTIGRID;

IMAGE SEGMENTATION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL;

EID: 33847740315     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2006.884952     Document Type: Article

References (64)

1. M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models," Int. J. Comput. Vis., vol. 1, no. 4, pp. 321-331, 1988.
2. A. Blake and M. Isard, Active Contours. New York: Springer, 1997.
3. T. McInerney and D. Terzopoulos, "T-snakes: Topology adaptive snakes," Med. Image Anal., vol. 4, pp. 73-91, 2000.
4. V. Caselles, F. Catte, T. Coll, and F. Dibos, "A geometric model for active contours," Numer. Math., vol. 66, pp. 1-31, 1993.
5. R. Malladi, J. A. Sethian, and B. C. Vemuri, "Shape modelling with front propagation: A level set approach," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 2, pp. 158-175, Feb. 1995.
6. V. Casettes, R. Kimmel, and G. Sapiro, "Geodesic active contours," Int. J. Comput. Vis., vol. 22, no. 1, pp. 61-79, 1997.
7. A. Yezzi, S. Kichenassamy, A. Kumar, P. Olver, and A. Tannenbaum, "A geometric snake model for segmentation of medical imagery," IEEE Trans. Med. Imag., vol. 16, no. 2, pp. 199-209, Apr. 1997.
8. T. Chan and L. Vese, "Active contours without edges," IEEE Trans. Image Process., vol. 10, no. 2, pp. 266-277, Feb. 2001.
9. A. Tsai, A. Yezzi, and A. Willsky, "Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification," IEEE Trans. Image Process., vol. 10, no. 8, pp. 1169-1186, Aug. 2001.
10. L. A. Vese and T. F. Chan, "A multiphase level set framework for image segmentation using the Mumford and Shah model," Int. J. Comput. Vis., vol. 50, no. 3, pp. 271-293, 2002.
11. D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems," Commun. Pure Appl. Math., vol. 42, no. 5, pp. 577-685, 1989.
12. S.-C. Zhu and A. Yuille, "Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation," IEEE Trans. Pattern Anal. Mach. Intell, vol. 18, no. 9, pp. 884-900, Sep. 1996.
13. N. Paragios and R. Deriche, "Geodesic active regions: A new framework to deal with frame partition problems in computer vision," J. Vis. Commun. Image Represent., vol. 13, no. 1-2, pp. 249-268, 2002.
14. A. Yezzi, A. Tsai, and A. Willsky, "A statistical approach to snakes for bimodal and trimodal imagery," in Proc. Int. Conf. Computer Vision, 1999, vol. 2, pp. 898-903.
15. M. Rousson, T. Brox, and R. Deriche, "Active unsupervised texture segmentation on a diffusion based feature space," in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2003, vol. II, pp. 699-704.
16. 2S: Deformable regions driven by an Eulerian accurate minimization method for image and video segmentation," Int. J. Comput. Vis., vol. 53, no. 1, pp. 45-70, 2003.
17. I. Kokkinos, G. Evangelopoulos, and P. Maragos, "Modulation-feature based textured image segmentation using curve evolution," in Proc. Int. Conf. Image Processing, 2004, vol. 2, pp. 1201-1204.
18. M. Leventon, E. Grimson, and O. Faugeras, "Statistical shape influence in geodesic active contours," in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2000, vol. 1, pp. 316-323.
19. D. Cremers, F. Tischhäuser, J. Weickert, and C. Schnörr, "Diffusion snakes: Introducing statistical shape knowledge into the Mumford-Shah functional," Int. J. Comput. Vis., vol. 50, no. 3, pp. 295-313, 2002.
20. M. Rousson and N. Paragios, "Shape priors for level set representations," in Proc. Eur. Conf. Computer Vision, 2002, vol. 2, pp. 78-92.
21. I. Kokkinos and P. Maragos, "An expectation maximization approach to the synergy between image segmentation and object categorization," in Proc. Int. Conf. Computer Vision, 2005, vol. I, pp. 617-624.
22. S. Osher and J. A. Sethian, "Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys, vol. 79, pp. 12-49, 1988.
23. V. Kolmogorov and Y. Boykov, "What metrics can be approximated by geo-cuts, or global optimization of length/area and flux," in Proc. Int. Conf. Computer Vision, 2005, pp. 564-571.
24. L. D. Cohen and R. Kimmel, "Global minimum for active contour models: A minimal path approach," Int. J. Comput. Vis., vol. 24, no. 1, pp. 57-78, 1997.
25. J. A. Sethian, Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1999.
26. M. Sussman, P. Smereka, and S. Osher, "A level set approach for computing solutions to incompressible two-phase flow," J. Comput. Phys, vol. 114, pp. 146-159, 1994.
27. D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, "A PDE-based fast local level set method," J. Comput. Phys, vol. 155, pp. 410-438, 1999.
28. D. Geiger, A. Gupta, L. A. Costa, and J. Vlontzos, "Dynamic programming for detecting, tracking, and matching deformable contours," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 3, pp. 294-302, Mar. 1995.
29. T. Lu, P. Neittaanmäki, and X.-C. Tai, "A parallel splitting up method and its application to Navier-Stokes equations," Appl. Math. Lett., vol. 4, no. 2, pp. 25-29, 1991.
30. J. Weickert, B. t. H. Romeny, and M. Viergever, "Efficient and reliable schemes for nonlinear diffusion filtering," IEEE Trans. Image Process., vol. 7, no. 3, pp. 398-410, Mar. 1998.
31. R. Goldenberg, R. Kimmel, E. Rivlin, and M. Rudzsky, "Fast geodesic active contours," IEEE Trans. Image Process., vol. 10, no. 10, pp. 1467-1475, Oct. 2001.
32. J. Weickert and G. Kühne, "Fast methods for implicit active contour models," in Geometric Level Set Methods in Imaging, Vision and Graphics, S. Osher and N. Paragios, Eds. New York: Springer, 2003.
33. U. M. Ascher, S. J. Ruuth, and B. T. R. Wetton, "Implicit-explicit methods for time-dependent partial differential equations," SIAM J. Numer. Anal., vol. 32, no. 3, pp. 797-823, 1995.
34. U. Trottenberg, C. Oosterlee, and A. Schüller, Multigrid. New York: Academic, 2001.
35. S. Acton, "Multigrid anisotropic diffusion," IEEE Trans. Image Process., vol. 7, no. 3, pp. 280-291, Mar. 1998.
36. P. Felzenszwalb and D. Huttenlocher, "Distance Transforms of Sampled Functions," Tech. Rep. TR2004-1963, Cornell Comput. Inf. Sci., Cornell Univ., Ithaca, NY, 2004.
37. A. Kenigsberg, "A multigrid approach for fast geodesic active contours," presented at the Copper Mountain Conf. Multigrid Methods, 2001.
38. A. Kenigsberg, R. Kimmel, and I. Yavneh, "A Multigrid Approach for Fast Geodesic Active Contours," Tech. Rep. CIS-2004-06, Technion-Israel Inst. Technol., Haifa, 2004.
39. G. Papandreou and P. Maragos, "A fast multigrid implicit algorithm for the evolution of geodesic active contours," in Proc. IEEE Conf. Computer Vision and Pattern Recognit., 2004, vol. II, pp. 689-694.
40. L. D. Cohen, "On active contour models and balloons," Comput. Vis. Graph. Image Process.: Image Understand., vol. 53, no. 2, pp. 211-218, 1991.
41. R. Kimmel and A. M. Bruckstein, "Regularized laplacian zero crossings as optimal edge integrators," Int. J. Comput. Vis., vol. 53, no. 3, pp. 225-243, 2003.
42. P. Maragos and M. A. Butt, "Curve evolution, differential morphology, and distance transforms applied to multiscale and eikonal problems," Fundam. Inf., vol. 41, pp. 91-129, 2000.
43. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes. Cambridge, U.K.: Cambridge Univ. Press, 1992.
44. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. New York: Springer-Verlag, 2003.
45. J. Weickert, Anisotropic Diffusion in Image Processing. Stuttgart, Germany: Teubner-Verlag, 1998.
46. W. Ames, Numerical Methods for Partial Differential Equations, 3rd ed. New York: Academic, 1992.
47. D. Barash, T. Schlick, M. Israeli, and R. Kimmel, "Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps," J. Math. Imag. Vis., vol. 19, no. 1, pp. 33-48, 2003.
48. P. Maragos, "PDEs for morphological scale-spaces and eikonal applications," in The Image and Video Processing Handbook, A. Bovik, Ed., 2nd ed. New York: Academic, 2005, ch. 4.16.
49. C. Xu and J. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process., vol. 7, no. 3, pp. 359-369, Mar. 1998.
50. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, "Comparing images using the Hausdorff distance," IEEE Trans. Pattern Anal. Mach. Intell., vol. 15, no. 9, pp. 850-863, Sep. 1993.
51. A. Brandt, "Multi-level adaptive solutions to boundary-value problems," Math. Comput., vol. 31, no. 138, pp. 333-390, 1977.
52. W. L. Briggs, V. E. Henson, and S. F. McCormick A Multigrid Tutorial, 2nd ed. Philadelphia, PA: SIAM, 2000.
53. P. Wesseling, An Introduction to Multigrid Methods. New York: Wiley, 1992.
54. D. Terzopoulos, "Image analysis using multigrid relaxation methods," IEEE Trans. Pattern Anal. Mach. Intell., vol. 8, no. 2, pp. 129-139, Mar. 1986.
55. A. Bruhn, J. Weickert, C. Feddern, T. Kohlberger, and C. Schjörr, "Variational optical flow computation in real-time," IEEE Trans. Image Process., vol. 14, no. 5, pp. 608-615, May 2005.
56. E. Sharon, A. Brandt, and R. Basri, "Fast multiscale image segmentation," in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2000, vol. 1, pp. 70-77.
57. R. Kimmel and I. Yavneh, "An algebraic multigrid approach for image analysis," SIAM J. Sci. Comput., vol. 24, no. 4, pp. 1218-1231, 2003.
58. F. Heitz, P. Pérez, and P. Bouthemy, "Multiscale minimization of global energy functions in some visual recovery problems," Comput. Vis. Graph. Image Process.: Image Understand., vol. 59, no. 1, pp. 125-134, 1994.
59. B. Leroy, I. L. Herlin, and L. Cohen, "Multiresolution algorithms for active contour models," in Proc. Int. Conf Anal. Optimiz. Syst., 1996, pp. 58-65.
60. A. Willsky, "Multiresolution markov models for signal and image processing," Proc. IEEE, vol. 90, no. 8, pp. 1396-1458, Aug. 2002.
61. R. E. Alcouffe, A. Brandt, J. E. Dendy, and J. W. Painter, "The multigrid method for the diffusion equation with strongly discontinuous coefficients," SIAM J. Sci. Statist. Comput., vol. 2, pp. 430-454, 1981.
62. P. M. d. Zeeuw, "Matrix-dependent prolongations and restrictions in a blackbox multigrid solver," J. Comput. Appl. Math., vol. 33, pp. 1-27, 1990.
63. J. W. Ruge and K. Stüben, "Algebraic multigrid," in Multigrid Methods, S. Mc Cormick, Ed. Philadelphia, PA: SIAM, 1987.
64. Y. Shapira, Matrix-Based Multigrid. Norwell, MA: Kluwer, 2003.