no. 2
Image segmentation with a finite element method
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 229-244 
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     author = {Bourdin, Blaise},
     title = {Image segmentation with a finite element method},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {229--244},
     year = {1999},
     publisher = {EDP Sciences},
     volume = {33},
     number = {2},
     mrnumber = {1700033},
     zbl = {0947.65075},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1999__33_2_229_0/}
}
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Bourdin, Blaise. Image segmentation with a finite element method. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 229-244. https://www.numdam.org/item/M2AN_1999__33_2_229_0/

[1] 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. | Zbl | MR

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

[3] G. Belletmi and A. Coscia, Discrete approximation of a free discontinuity problem. Num. Funct. Anal. Optim. 15 (1994) 201-224. | Zbl | MR

[4] A. Bonnet, On the regularity of the edge set of Mumford-Shah minimizers. Prog. in Nonlinear Differential Equation and Their Applications 25 (1996) 93-103. | Zbl | MR

[5] H. Brezis, Analyse fonctionnelle. Masson (1989). | Zbl | MR

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

[7] P. G. Ciarlet, The finite element method for ellipttc problems. North-Holland (1987). | Zbl | MR

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

[9] F. Dibos and E. Séré, An approximation result for the minimizers of the Mumford-Shah functional. Boll. Un. Mat. Ital. A 11 (1997). | Zbl | MR

[10] L. C. Evans and R Gariepy, Measure theory and fine properties of functions. CRC Press, Boca Raton (1992). | Zbl | MR

[11] S. Finzi-Vita and P. Perugia, Some numerical experiments on the variational approach to image segmentation, in Proc. of the Second European Workshop on Image Processing and Mean Curvature Motion, Palma de Mallorca (1995) 233-240.

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

[13] T. J. Richardson and S. K. Mitter, A variational formulation based edge focusing algorithm. Sadhana Acad. P. Eng. S. 22(1997) 553-574. | Zbl | MR