Edge preserving regularization for the pde-based piecewise smooth mumford-shah algorithm

Imaging Science Journal

Volumn 57, Issue 3, 2009, Pages 119-127

  Zhang, Ying Jie ^b   Geb, Li Ling ^a  

^a XI'AN UNIVERSITY OF TECHNOLOGY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Edge preserving regularization; Level sets; Mumford shah models; Segmentation

Indexed keywords

EID: 70350247330     PISSN: 13682199     EISSN: 1743131X     Source Type: Journal    
DOI: 10.1179/174313109X362460     Document Type: Article

References (26)

1. Mumford, D. and Shah, J. Optimal approximations by piecewise smooth functions and associated variational problems.Commun. PureAppl.Math., 1989, 42, 577-685.
2. Kass, M., Witkin, A. and Terzopoulos, D. Snakes: active contour models. Int. J. Comput. Vision, 1988, 1, 321-331.
3. Perona, P. and Malik, P. Scale space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Anal. Mach. Intell., 1990, 12, 629-639.
4. Geman, S. and Geman, D. Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Patt. Anal. Mach. Intell., 1984, 6, 721-741.
5. You, Y. and Kaveh, M. A regularization approach to joint blur identification and image restoration. IEEE Trans. Image Process., 1996, 5, 416-428.
6. Jayant, S. A common framework for curve evolution, segmentation and anisotropic diffusion, Proc. Int. Conf. on 'Computer vision and pattern recognition': CVPR'96, San Francisco, CA, USA, June 1996, IEEE, pp. 136- 142.
7. Sethian, J. A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science, 1999, 2nd edition (Cambridge: Cambridge University Press).
8. Chan, T. F. and Vese, L. A. A level set algorithm for minimizing the Mumford-Shah functional in image processing, Proc. 1st IEEE Workshop on 'Variational and level set methods in computer vision': VLMS '01, Vancouver, Canada, July 2001, IEEE Computer Society, pp. 161-168.
9. Chan, T. and Vese, L. Active contours without edges. IEEE Trans. Image Process., 2001, 10, 266- 277.
10. Tikhonov, A. N. and Arsenin, V. Y. Solutions of illposed problems. SIAM Rev., 1979, 21, (2), 266-267.
11. Weickert, J. and Scharr, H. A scheme for coherenceenhancing diffusion filtering with optimized rotation invariance. J. Visual Commun. Image Represent., 2002, 13, 103-118.
12. Weeratunga, S. and Kamath, C. PDE-based non-linear diffusion techniques for denoising scientific and industrial images: an empirical study, Proc. Conf. on 'Image processing: algorithms and systems: electronic imaging', San Jose, CA, USA, January 2002, US Department of Energy, pp. 279-290.
13. Teboul, S., Féraud, L. B., Aubert, G. and Barlaud, M. Variational approach for edge-preserving regularization using coupled PDE's. IEEE Trans. Image Process., 1998, 7, 387-397.
14. Tsai, A., Yezzi, A. J. and Willsky, A. S. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. Image Process., 2001, 10, 1169-1186.
15. Osher, S. and Sethian, J. A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys., 1988, 79, 12-49.
16. Choi, J., Kim, G., Park, P., Wang, G. and Kim, S. Efficient PDE-based segmentation algorithms and their application to CT images. J. Korean Inst. Plant Eng., 2003, 1-17.
17. Geman, S. and Mcclure, D. E. Bayesian image analysis: an application to single photon emission tomography, Proc. 'Statistical Computing Section, Washington, DC, USA, American Statistical Association, August 1985, pp. 12-18.
18. Ji, S. and Park, H. Image segmentation of color image based on region coherency, Proc. Int. Conf. on 'Image processing', Chicago, IL, USA, October 1998, IEEE, Vol. 1, pp. 80-83.
19. Haddon, J. and Boyce, J. Image segmentation by unifying region and boundary information. IEEE Trans. Patt. Anal. Mach. Intell., 1990, 12, 929-948.
20. Haris, K., Efstratiadis, S., Maglaveras, N. and Katsaggelos, A. Hybrid image segmentation using watersheds and fast region merging. IEEE Trans. Image Process., 1998, 7, 1684-1699.
21. Kichenassamy, S., Kumar, A., Oliver, P., Tannenbaum, A. and Yezzi, A. Conformal curvature flows: from phase transitions to active vision Arch. Ration. Mech. Anal., 1996, 134, 275-301.
22. Marr, D. and Hildreth, E. Theory of edge detection. Proc. R. Soc. Lond. B, 1980, 207B, 187-217.
23. Hill, P., Canagarajah, C. and Bull, D. Texture gradient based watershed segmentation, Proc. IEEE Int. Conf. on 'Acoustics, speech, and signal processing': ICASSP'02, Orlando, FL, USA, May 2002, University of Florida, Vol. 4, pp. 3381-3384.
24. Osher, S. and Fedkiw, R. Level Set Methods and Dynamic Implicit Surfaces, 2003 (New York, Springer- Verlag).
25. Vese, L. A. and Chan, T. F. A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vision, 2002, 50, 271- 293.
26. Rudin, L, Osher, S. and Fatemi, E. Nonlinear total variation based noise removal algorithms. Physica D, 1992, 60D, 259-268.