On the regularity of edges in image segmentation
Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 4, pp. 485-528.
@article{AIHPC_1996__13_4_485_0,
author = {Bonnet, A.},
title = {On the regularity of edges in image segmentation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {485--528},
publisher = {Gauthier-Villars},
volume = {13},
number = {4},
year = {1996},
zbl = {0883.49004},
mrnumber = {1404319},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1996__13_4_485_0/}
}
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Bonnet, A. On the regularity of edges in image segmentation. Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 4, pp. 485-528. http://archive.numdam.org/item/AIHPC_1996__13_4_485_0/

[1] H.W. Alt, L.A. Caffarelli and A. Friedman, Variational problems with two Phases and their free boundary, Trans. Am. Math. Soc., Vol. 282, 1984, pp. 431-461. | MR | Zbl

[2] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rat. Mech. Anal., Vol. 111, 1990, pp. 291-322. | MR | Zbl

[3] L. Ambrosio and D. Pallara, Partial regularity of free discontinuity sets I, to appear. | Numdam | MR | Zbl

[4] L. Ambrosio, N. Fusco and D. Pallara, Partial regularity of free discontinuity sets II, to appear. | Numdam | MR | Zbl

[5] G. Congedo and I. Tamanini, On the existence of solutions to a problem in multidimensional segmentation, Ann. Inst. Henri Poincaré, Vol. 8, 2, 1991, pp. 175-195. | Numdam | MR | Zbl

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

[7] G. David and S. Semmes, On the singular sets of minimisers of the Mumford-Shah functional, to appear in J. Math. Pures Appl. | MR | Zbl

[8] G. David, C1-arcs for minimisers of the Mumford-Shah functional, to appear. | MR | Zbl

[9] F. Dibos, Uniform rectifiability of image segmentations obtained by a variational method, J. Math. Pures and Appl., Vol. 73, 1994, pp. 389-412. | MR | Zbl

[10] F. Dibos and G. Koepfler, Color segmentation using a variational formulation, preprint CEREMADE.

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

[12] L. Evans and R. Gariepy, Measure theory and fine properties of functions, London: CRC Press, 1992. | MR | Zbl

[13] K.J. Falconer, The geometry of fractal sets, Cambridge University Press, 1985. | MR | Zbl

[14] H. Federer, Geometric measure theory, Springer-Verlag, 1969. | MR | Zbl

[15] G. Hardy, J.E. Littlewood and G. Pólya, Inequalities Second Edition, Cambridge university Press. | JFM | MR | Zbl

[16] U. Massari and I. Tamanini, Regularity properties of optimal segmentations, Journ. reine angew. Math., Vol. 420, 1991, pp. 61-84. | MR | Zbl

[17] J.-M. Morel and S. Solimini, Variational methods in Image Segmentation, Birkhauser, 1994. | MR | Zbl

[18] C.B. Morrey Jr., Multiple integrals in the calculus of variations, Springer-Verlag, 1966. | MR | Zbl

[19] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. on Pure and Appl. Math., Vol. XLII, n° 4, 1989. | MR | Zbl