Image segmentation and selective smoothing by using Mumford-Shah model

IEEE Transactions on Image Processing

Volumn 14, Issue 10, 2005, Pages 1537-1549

  Gao, Song ^a   Bui, Tien D ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

Curve evolution; Image segmentation and denoising; Level set methods; Mumford Shah functional

Indexed keywords

APPROXIMATION THEORY; EQUATIONS OF MOTION; ESTIMATION; EVOLUTIONARY ALGORITHMS; IMAGE QUALITY; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; POISSON EQUATION; SIGNAL TO NOISE RATIO; SPURIOUS SIGNAL NOISE;

CURVE EVOLUTION EQUATIONS; IMAGE DENOISING; IMAGE SMOOTHING METHOD; MUMFORD-SHAH FUNCTIONAL; NOISY IMAGES;

IMAGE SEGMENTATION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; SIGNAL PROCESSING; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 27744506546     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.852200     Document Type: Article

References (26)

1. L. Alvarez, P. L. Lions, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion II," SIAM J. Numer Anal., vol. 29, no.3, pp.845-866, 1992.
2. G. Aubert and R Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. New York: Springer, 2002, vol. 147.
3. T. D. Bui and G. Y. Chen, "Translation invariant denoising using multiwavelets," IEEE Trans. Signal Process., vol. 46, no. 12, pp. 3414-3420, Dec. 1998.
4. V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic active contours," Int. J. Comput. Vis., vol. 22, pp. 61-79, 1997.
5. F. Catte, R L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., vol. 29, no. 1, pp. 182-193, 1992.
6. T. F. Chan and L. A. Vese, "Active contours without edges," IEEE Trans. Image Process., vol. 10, no. 2, pp. 266-277, Feb. 2001.
7. T. F. Chan and S. Esedoglu, "A multiscale algorithm for Mumford-Shah image segmentation," Univ. California, Los Angeles, CAM, 03-77, 2003.
8. D. Freedman and T. Zhang, "Active contours for tracking distributions," IEEE Trans. Image Process., vol. 13, no. 4, pp. 518-526, Apr. 2004.
9. M. Kass, A. Witkin, and D, Terzopoulos, "Snakes: Active contour models," Int. J. Comput. Vis., vol. 1, pp. 321-331, 1988.
10. B. B. Kimia and K. Siddiqi, "Geometric heat equation and nonlinear diffusion of shapes and images," Comput. Vis. Image Understand., vol. 64, no.3, pp.305-322, 1996.
11. R. Malladi and J. A. Sethian, "Image processing via level set curvature flow," in Proc. Nat. Acad. Sci. USA, vol. 92, Jul. 1995, pp. 7046-7050.
12. R. Malladi and J. A. Sethian, "Image processing: Flows under Min/Max curvature and mean curvature," Graph. Models Image Process., vol. 58, no. 2, pp. 127-141, 1996.
13. A. Mansouri and J. Konrad, "Multiple motion segmentation with level sets," IEEE Trans. Image Process., vol. 12, no. 2, pp. 266-277, Feb. 2003.
14. P. Mrazek, J. Weickert, and G. Steidl, "Correspondences between wavelet shrinkage and nonlinear diffusion," in Scale-Space 2003, L. D. Griffin and M. Lillholm, Eds. New York: Springer, 2003, vol. 2695, Lecture Notes in Computer Science, pp. 101-116.
15. D. Mumford and J. Shah, "Optimal approximation by piecewise smooth functions and associated variational problems," Comm. Pure Appl. Math, vol. 42, pp. 577-685, 1989.
16. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 5, pp. 629-639, May 1990.
17. J. A. Sethian, Level Set Methods and Fast Marching Methods. Cambridge, MA: Cambridge Univ. Press, 1999.
18. B. Song and T. F. Chan, "A fast algorithm for level set based optimization," Univ. California, Los Angeles, CAM, 02-68, 2002.
19. A. Tsai, A. Yezzi, and A. S. Willsky, "Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification," IEEE Tran. Image Process., vol. 10, no. 8, pp. 1169-1186, Aug. 2001.
20. L. 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.
21. J. Weickert,Anisotropic Diffusion in Image Processing. Stuttgart,Germany: Taeubner, 1998.
22. J. Weickert, "Theoretical foundations of anisotropic diffusion in image processing," Comput. Suppl., vol. 11, pp. 221-236, 1996.
23. J. Weickert and C. Schnörr, "PDE-based preprocessing of medical images," Künstliche Intell., no. 3, pp. 5-10, 2000.
24. N. N. Yanenko, The Method of Fractional Steps. New York: Springer-Verlag, 1971.
25. A. Yezzi, L. Zollei, and T. Kapur, "A variational framework for integrating segmentation and registration through active contours," Med. Image Anal., vol. 7, pp. 171-185, 2003.
26. S. 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.