Full Text:   <1136>

CLC number: O175.3,TN911.73

On-line Access: 

Received: 2002-10-20

Revision Accepted: 2003-01-22

Crosschecked: 0000-00-00

Cited: 4

Clicked: 3408

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.1 P.123~128


Image segmentation based on Mumford-Shah functional

Author(s):  CHEN Xu-feng, GUAN Zhi-cheng

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   chxfhz@21cn.com, amaguan@zju.edu.cn

Key Words:  Image segmentational, Mumford-Shah functional, Viscosity solution, Level set method

Share this article to: More

CHEN Xu-feng, GUAN Zhi-cheng. Image segmentation based on Mumford-Shah functional[J]. Journal of Zhejiang University Science A, 2004, 5(1): 123~128.

@article{title="Image segmentation based on Mumford-Shah functional",
author="CHEN Xu-feng, GUAN Zhi-cheng",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Image segmentation based on Mumford-Shah functional
%A CHEN Xu-feng
%A GUAN Zhi-cheng
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 1
%P 123~128
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0123

T1 - Image segmentation based on Mumford-Shah functional
A1 - CHEN Xu-feng
A1 - GUAN Zhi-cheng
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 1
SP - 123
EP - 128
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0123

In this paper, the authors propose a new model for active contours segmentation in a given image, based on mumford-Shah functional (Mumford and Shah, 1989). The model is composed of a system of differential and integral equations. By the experimental results we can keep the advantages of Chan and Vese's model (Chan and Vese, 2001) and avoid the regularization for Dirac function. More importantly, in theory we prove that the system has a unique viscosity solution.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Ambrosio, L. and Tortorelli, V. M., 1992. On the approximation of free discontinuity problems. Boll. U.M.I., 6B(7):105-123.

[2] Alvarez, L., Lions, P. L. and Morel, J. M., 1992. Image selective smoothing and edge detection by nonlinear deffusions. SIAM J. Numer. Anal., 29(3):845-866.

[3] Barcelos, C. A. Z. and Chen, Y., 2000. Heat flows and related minimization problem in image restoration. Computer and Mathematics with Application, 39:81-97.

[4] Bourdin, B., 1999. Image segmentation with a finite element method. M2AN Math. Model. Numer. Anal., 33(2):229-244.

[5] Bourdin, B. and Chamboll, A., 2000. Implementation of a finite-elements approximation of the Mumford-Shah functional. Numer. Math., 85(4):609-646.

[6] Chambolle, A., 1995. Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations. SIAM J. Appl. Math., 55(3):827-863.

[7] Chambolle, A. and Maso, G. D., 1999. Discrete approximation of the Mumford-Shah functional in dimension two. M2AN Math. Model. Numer. Anal., 33(4):651-672.

[8] Chambolle, A., 1999. Finite-differences discretizations of the Mumford-Shah functional. M2AN Math. Model. Numer. Anal., 33(2):261-288.

[9] Chan, T. F. and Vese, L. A., 2001. Active contours without edges. IEEE Trans. on Image Processing, 10(2):266-277.

[10] Chang, Y. C., Hou, T. Y., Merriman, B. and Osher, S., 1996. A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. Journal of Computational Physics, 124:449-464.

[11] Chen, Y., Vemuri, B. C. and Wang, L., 2000. Image denoising and segmentation via nonlinear diffusion. Computer and Mathematics with Application, 39:131-149.

[12] Guichard, F. and Morel, J. M., 1998. Image Iterative Smoothing and P.D.E's. Notes de cours du Centre Emile Borel.

[13] IEEE Trans. on Image Processing, 1998. 7(3).

[14] Ladyzhenskaya, O. A., Solonnikov, V. A. and Uraltseva, N. N., 1968. Linear and Quasilinear Equations of Parabolic Type, American Math. Society, Providence RI.

[15] Malladi, R., Sethian, J. A. and Vemuri, B. C., 1995. Shape Modeling with front propagation: a level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2).

[16] March, R., 1992. Visual reconstruction with discontinuities using variational methods. Image Vision Comput., 10:30-38.

[17] Mumford, D. and Shah, J., 1989. Optimal approximations by Piecewise Smooth Functions and associated variational problems. Comm. Pure Appl. Math., 42(5):577-685.

[18] Osher, S. and Sethian, J. A., 1988. Fronts propagating with curvature depender speed: algorithms based on Hamilton-Jacobi formulation. J. of Computational Physics, 79:12-49.

[19] Sussman, M., Smerka, P. and Osher, S., 1994. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114:146-159.

[20] Weickert, J., 1998. Efficient Image Segmentation using Partial Differential Equations and Morphology. Technical Report DIKU-TR-98/10, Department of Computer Science, University of Copenhagen.

[21] Whitaker, R. T., 2000. A level-set approach to Image blending. IEEE Transactions on Image Processing, 9(11).

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE