Finite-differences discretizations of the Mumford-Shah functional
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 2, pp. 261-288.
@article{M2AN_1999__33_2_261_0,
     author = {Chambolle, Antonin},
     title = {Finite-differences discretizations of the {Mumford-Shah} functional},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {261--288},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {2},
     year = {1999},
     zbl = {0947.65076},
     mrnumber = {1700035},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_2_261_0/}
}
TY  - JOUR
AU  - Chambolle, Antonin
TI  - Finite-differences discretizations of the Mumford-Shah functional
JO  - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY  - 1999
DA  - 1999///
SP  - 261
EP  - 288
VL  - 33
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_2_261_0/
UR  - https://zbmath.org/?q=an%3A0947.65076
UR  - https://www.ams.org/mathscinet-getitem?mr=1700035
LA  - en
ID  - M2AN_1999__33_2_261_0
ER  - 
%0 Journal Article
%A Chambolle, Antonin
%T Finite-differences discretizations of the Mumford-Shah functional
%J ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
%D 1999
%P 261-288
%V 33
%N 2
%I EDP-Sciences
%G en
%F M2AN_1999__33_2_261_0
Chambolle, Antonin. Finite-differences discretizations of the Mumford-Shah functional. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 2, pp. 261-288. http://www.numdam.org/item/M2AN_1999__33_2_261_0/

[1] L. Ambrosio A compactness theorem for a new class of functions with bounded variation. Boll. Un. Mat. Ital. (7) 3 (1989) 857 881. | MR | Zbl

[2] L. Ambrosio Variational problems in SBV and image segmentation. Acta Appl. Math. 17 (1989) 1-40. | MR | Zbl

[3] L. Ambrosio Existence theory for a new class of vanational problems Arc. Rational Mech. Anal. 111 (1990) 291-322. | MR | Zbl

[4] L. Ambrosio and V. M. Tortorelli Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence Comm. Pure Appl. Math. 43 (1990) 999-1036. | MR | Zbl

[5] L. Ambrosio and V. M. Tortorelli On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. (7) 6 (1992)105-123. | MR | Zbl

[6] G. Aubert, M. Barlaud, P. Charbonnier and L. Blanc-Féraud Deterministic edge-preserving regularization in computed imaging. Technical report. TR#94-01, I3S, CNRS URA 1376 Sophia-Antipohs, France (1994).

[7] A. Blake and A. Zisserman Visual Reconstruction. MIT Press (1987). | MR

[8] B. Bourdin and A. Chambolle Implementation of a flnite-elements approximation of the Mumford Shah functional Technical report 9844, Ceremade, University of Paris-Dauphine, 1998; preprint LPMTM, University of Paris Nord, 1998, Numer. Math. (to appear). | MR

[9] A. Chambolle Un théorème de Γ-convergence pour la segmentation des signaux. C. R. Acad. Sci. Paris 314 (1992) 191-196. | MR | Zbl

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

[11] A. Chambolle and G. Dal Maso Discrete approximation of the Mumford-Shah functional in dimension two Technical Report. 9820, Ceremade, University of Paris-Dauphine, 1998 preprint SISSA 29/98/M, Trieste RAIRO Model. Math. Anal. Numer.(to appear). | Numdam | MR | Zbl

[12] G. Dal Maso An introduction to Γ-convergence Birkhäuser, Boston (1993). | MR | Zbl

[13] E. De Giorgi, M. Carriero and A. Leaci Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195-218. | MR | Zbl

[14] L. C. Evans and R. F. Ganepy Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992). | MR | Zbl

[15] H. Federer Geometric Measure Theory. Springer Verlag, New York (1969). | MR | Zbl

[16] D. Geiger and F. Girosi Parallel and determmistic algorithms for MRFs: surface reconstruction. IEEE Trans. PAMI 13 (1991) 401-412.

[17] D. Geiger and A. Yuille A common framework for image segmentation. Internat J. Comput. Vision 6 (1991) 227-243.

[18] D. Geman and G. Reynolds Constrained image restoration and the recovery of discontinuities. IEEE Trans. PAMI 3 (1992) 367-383.

[19] S. Geman and D. Geman. Stochatic relaxation, Gibbs distributions, and the Bayesian restoration of image. IEEE Trans. PAMI 6 (1984). | Zbl

[20] E. Giusti. Minimal surfaces and functions of bounded variation. Birkhäuser, Boston (1984). | MR | Zbl

[21] M. Gobbino. Finite difference approximation of the Mumford-Shah functional.Comm. Pure Appl. Math. 51 (1998) 197-228. | MR | Zbl

[22] D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989) 577-685. | MR | Zbl

[23] C. R. Vogel and M. E. Oman. Iterative methods for total variation denoismg, in Procedings of the Colorado Conference on Iterative Methods (1994). | Zbl

[24] W. P. Ziemer. Weakly Differentiable Functions. Springer-Verlag, Berlin (1989). | MR | Zbl