The Mumford-Shah conjecture in image processing
Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1995-1996), Exposé no. 813, p. 221-242
@incollection{SB_1995-1996__38__221_0,
     author = {Morel, Jean-Michel},
     title = {The Mumford-Shah conjecture in image processing},
     booktitle = {S\'eminaire Bourbaki : volume 1995/96, expos\'es 805-819},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     year = {1995-1996},
     note = {talk:813},
     pages = {221-242},
     zbl = {0879.49002},
     mrnumber = {1472541},
     language = {en},
     url = {http://www.numdam.org/item/SB_1995-1996__38__221_0}
}
Morel, Jean-Michel. The Mumford-Shah conjecture in image processing, dans Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1995-1996), Exposé no. 813, pp. 221-242. http://www.numdam.org/item/SB_1995-1996__38__221_0/

[ACF] H.W. Alt, L.A. Caffarelli and A. Friedman - Variational problems with two phases and their free boundary, Trans. A.M.S. 282, 431-461, 1984. | MR 732100 | Zbl 0844.35137

[Amb1] L. Ambrosio - A compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. It., 3-B , 857-881, 1989. | MR 1032614 | Zbl 0767.49001

[Amb2] L. Ambrosio - Existence theory for a new class of variational problems, Arch. Rational Mech. Anal. 111, 291-322, 1990. | MR 1068374 | Zbl 0711.49064

[Amb3] L. Ambrosio - Variational problems in SBV, Acta Applicandae Mathem. 17, 1-40, 1989. | MR 1029833 | Zbl 0697.49004

[Amb4] L. Ambrosio - A new proof of SB V compactness theorem, Calc. Var. 3, 127-137, 1995. | MR 1384840 | Zbl 0837.49011

[AP] L. Ambrosio and D. Pallara - Partial regularity of free discontinuity sets I, preprint, Universita di Pisa, October 1994.

[AFP] L. Ambrosio, N. Fusco and D. Pallara - Partial regularity of free discontinuity sets II, Preprint 21, 1995, Universita degli Studi di Napoli "Federico II".

[AmbTo] L. Ambrosio and V.M. Tortorelli - Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math. 43, 999-1036, 1991. | Zbl 0722.49020

[BlatM2] J. Blat, and J.-M. Morel - Elliptic problems in image segmentation and their relation to fracture theory, Proceedings of the Int. Conf. on nonlinear elliptic and parabolic problems, Nancy 88, Longman 1989. | MR 1035009 | Zbl 0727.35040

[BZ] A. Blake and A. Zisserman - Visual reconstruction, MIT Press, 1987. | MR 919733

[Bo] A. Bonnet - On the regularity of edges in the Mumford-Shah model for image segmentation, preprint, 1995.

[Br] K.A. Brakke - The motion of a surface by its mean curvature, Princeton U.P., 1978. | MR 485012 | Zbl 0386.53047

[CaLe1] M. Carriero and A. Leaci - Sk-valued maps minimizing the Lp norm of the gradient with free discontinuities, Ann. Sc. Norm. Pisa, s.IV 18 , 321-352, 1991. | Numdam | MR 1145314 | Zbl 0753.49018

[CaLe2] M. Carriero, A. Leaci, D. Pallara and E. Pascali - Euler conditions for a minimum problem with free discontinuity surfaces, Preprint Dipartimento di Matematica, Lecce, 1988.

[CaLe] M. Carriero and A. Leaci - Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Analysis TMA 15, 661-677, 1990. | MR 1073957 | Zbl 0713.49003

[CaLT] M. Carriero, A. Leaci and F. Tomarelli - Plastic free discontinuity and Special Bounded Hessian, C. R. Acad. Sci. Paris, t. 314, s.I, 595-600, 1992. | MR 1158743 | Zbl 0794.49011

[CarDeGL] M. Carriero, E. De Giorgi and A. Leaci - Existence theorem for a minimum problem with free discontinuity set, Arch. Rat. Mech. Anal., vol. 108, 1989. | MR 1012174 | Zbl 0682.49002

[Cham] A. Chambolle - Un théorème de r-convergence pour la segmentation des signaux, C.R.Acad.Sci. Paris 314, S I, 191-196, 1992. | MR 1150831 | Zbl 0772.49010

[DalMMS1] G. Dal Maso, J.-M. Morel and S. Solimini - Une approche variationnelle en traitement d'images: résultats d'existence et d'approximation, C.R. Acad. Sci. Paris, t. 308, Série I, p. 549-554, 1989. | MR 999453 | Zbl 0682.49003

[DalMMS2] G. Dal Maso, J.-M. Morel and S. Solimini - A variational method in image segmentation: existence and approximation results, Acta Matematica, Vol. 168, 89-151, 1992. | MR 1149865 | Zbl 0772.49006

[Da] G. David - C1 arcs for minimizers of the Mumford-Shah functional. To appear in SIAM J. Appl. Math., 1996. | MR 1389754 | Zbl 0870.49020

[DaSe1] G. David and S. Semmes - On the singular set of minimizers of Mumford-Shah functional. To appear in Journal de Mathématiques Pures et Appliquées (1993)

[DaSe2] G. David and S. Semmes - Uniform rectifiability and singular sets. To appear, Annales de l'IHES. | Numdam | MR 1404317 | Zbl 0908.49030

[DeGi0] E. De Giorgi - Free Discontinuity Problems in Calculus of Variations, in: Frontiers in pure and applied Mathematics, a collection of papers dedicated to J.-L. Lions on the occasion of his 60th birthday, R. Dautray ed., 55-61, North Holland, 1991. | MR 1110593 | Zbl 0758.49002

[DeGiAm] E. De Giorgi and L. Ambrosio - Un nuovo tipo di funzionale del Calcolo delle Variazioni, Atti Accad. Naz. Lincei, s.8 82 , 199-210, 1988. | MR 1152641 | Zbl 0715.49014

[DeGiCL] E. De Giorgi, M. Carriero and A. Leaci - Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal. 108, 195-218, 1989. | MR 1012174 | Zbl 0682.49002

[Dib] F. Dibos - Uniform rectifiability of image segmentations obtained by variational method. To appear in Journal de Mathematiques Pures et Appliquées, 1993. | Zbl 0860.49030

[DibK] F. Dibos and G. Koepfler - Propriété de régularité des contours d'une image segmentée, C.R. Acad. Sci. Paris, t. 313, Série I, p. 573-578, 1991. | MR 1133487 | Zbl 0779.49004

[DiSé] F. Dibos and E. Séré - Approximating Mumford-Shah minimizers. Preprint, CEREMADE, 1994.

[GG] D. Geman and S. Geman - Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741, 1984. | Zbl 0573.62030

[Gi] E. Giusti - Minimal surfaces and functions with bounded variations, Birkhäuser, Boston, 1984. | MR 775682 | Zbl 0545.49018

[Jo] P. Jones - Rectifiable sets and the traveling salesman problem, Invent. Mathematicae 102, 1-16, 1990. | MR 1069238 | Zbl 0731.30018

[Kn] J.K. Knowles - A note on the energy release rate in quasi-static elastic crack propagation, SIAM J. Appl. Math. 41, 401-412, 1981. | MR 639122 | Zbl 0469.73082

[Lea] A. Leaci - Free discontinuity problems with unbounded data: the two dimensional case, Manuscripta Math. 75, 429-441, 1992. | MR 1168179 | Zbl 0774.49009

[Lég] J.-C. Léger - Une remarque sur la régularité d'une image segmentée, Journal de Mathématiques Pures et Appliquées, 1993. | Zbl 0861.49006

[Li] F.H. Lin - Variational problems with free interfaces, Calc. Var. 1, 149-168, 1993. | MR 1261721 | Zbl 0794.49038

[MaTa] U. Massari and I. Tamanini - Regularity properties of optimal segmentations, J. Reine Angew. Math. 420, 61-84, 1991. | MR 1124566 | Zbl 0729.49004

[MoS1] J.-M. Morel and S. Solimini - Segmentation of images by variational methods: a constructive approach, Rev. Matematica de la Universidad Complutense de Madrid, Vol.1, n° 1,2,3, 169-182, 1988. | MR 977048 | Zbl 0679.68205

[MoS2] J.-M. Morel and S. Solimini - Segmentation d'images par méthode variationnelle: une preuve constructive d'existence, C. R. Acad. Sci. Paris Série I, 1988. | Zbl 0676.68051

[MoS3] J.-M. Morel and S. Solimini - Variational methods in image segmentation, Birkhäuser, Boston, 1994. | MR 1321598

[MumS1] D. Mumford and J. Shah - Boundary detection by minimizing funcionals, IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, 1985.

[MumS2] D. Mumford and J. Shah - Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Communications on Pure and Applied Mathematics. vol. XLII No.4, 1989. | MR 997568 | Zbl 0691.49036

[MumS3] D. Mumford and J. Shah - Boundary detection by minimizing functionals, Image Understanding, 1988, Ed. S. Ullman and W. Richards.

[So] S. Solimini - Functionals with surface terms on a free singular set, Nonlinear partial differential equations and applications, College de France Seminar, Pitman, 1993. | MR 1291853 | Zbl 0817.49016

[Zi] W.P. Ziemer - Weakly differentiable functions, Springer Verlag, Berlin, 1989. | MR 1014685 | Zbl 0692.46022