Improved Mumford-Shah model and its applications to image processing with the piecewise constant level set method

Zidonghua Xuebao/Acta Automatica Sinica

Volumn 33, Issue 12, 2007, Pages 1259-1262

  Song, Jin Ping ^a   Li, Shuai Jie ^a  

^a HENAN UNIVERSITY   (China)

Author keywords

Denoising; Level set; Mumford Shah model; Piecewise constant level set method (PCLSM); Segmentation

Indexed keywords

COMPUTER VISION; IMAGE SEGMENTATION;

DENOISING; GRADIENT DESCENT METHOD; MUMFORD-SHAH MODEL; PIECEWISE CONSTANT LEVEL SET METHOD (PCLSM); SEGMENTATION;

IMAGE PROCESSING;

EID: 38049186791     PISSN: 02544156     EISSN: None     Source Type: Journal    
DOI: 10.1360/aas-007-1259     Document Type: Article

References (13)

1. Osher S, Sethian J A. Fronts propagating with, curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 1988, 79: 12-49.
2. Tai X C, Chan T F. A survey on multiple level set methods with applications for identifying piecewise constant functions. International Journal of Numerical Analysis and Modeling, 2004, 1(1): 25-47.
3. Burger M, Osher S J. A Survey on Level Set Methods for Inverse Problems and Optimal Design. CAM Report 04-02, Department of Mathematica, University of California, Los Angeles, USA, 2004.
4. Osher S, Fedkiw R P. Level set methods: an overview and some recent results. Journal of Computational Physics, 2001, 169(2): 463-502
5. Lie J, Lysaker M, Tai X C. A variant of the level set method and applications to image segmentation. Mathematics for Computation, 2006, 75(255): 1155-1174.
6. Lie J, Lysaker M, Tai X C. A binary level set model and some applications for Mumford-Shah image segmentation. IEEE Transactions on Image Processing, 2006, 15(5): 1171-1181.
7. Lie J, Lysaker M, Tai X C. Piecewise constant level set methods and image segmentation. Lecture Notes in Computer Science, 2005, 3459: 573-584.
8. Nielsen L K, Tai X C, Aannosen S I, Espedal M. A binary level set model for elliptic inverse problems with discontinuous coefficients. International Journal of Numerical Analysis and Modeling, 2005, 4(1): 74-99.
9. Tai X C, Li H W. A piecewise constant level set methods for elliptic inverse problems. Applied Numerical Mathematics, 2007, 57(5-7): 686-696.
10. Tai X C, Yao C H. Fast Piecewise Constant Level Set Methods (PCLSM) with Newton Updating. CAM-Report-05-52, Applied Mathematics, University of California, Los Angeles, USA, 2005.
11. Mumford D, Shah J. Optimal approximation by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 1989, 42(5): 577-685.
12. Aubert G, Vese L. A variational method in image recovery. SIAM Journal of Numerical Analysis, 1997, 34(5): 1948-1979.
13. Kornprobst P, Deriche R, Aubert G. Nonlinear operators in image restoration. In: Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition. San Juan, Puerto Rico: IEEE, 1997. 325-331.