@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},
volume = {13},
year = {1996},
pages = {485-528},
mrnumber = {1404319},
zbl = {0883.49004},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1996__13_4_485_0}
}
Bonnet, A. On the regularity of edges in image segmentation. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) pp. 485-528. http://gdmltest.u-ga.fr/item/AIHPC_1996__13_4_485_0/
[1] , and , Variational problems with two Phases and their free boundary, Trans. Am. Math. Soc., Vol. 282, 1984, pp. 431-461. | MR 732100 | Zbl 0844.35137
[2] , Existence theory for a new class of variational problems, Arch. Rat. Mech. Anal., Vol. 111, 1990, pp. 291-322. | MR 1068374 | Zbl 0711.49064
[3] and , Partial regularity of free discontinuity sets I, to appear. | Numdam | MR 1475771 | Zbl 0896.49023
[4] , and , Partial regularity of free discontinuity sets II, to appear. | Numdam | MR 1475772 | Zbl 0896.49024
[5] and , On the existence of solutions to a problem in multidimensional segmentation, Ann. Inst. Henri Poincaré, Vol. 8, 2, 1991, pp. 175-195. | Numdam | MR 1096603 | Zbl 0729.49003
[6] , and , A variational method in image segmentation: existence and approximation results, Acta Matematica, Vol. 168, 1992, pp. 89-151. | MR 1149865 | Zbl 0772.49006
[7] and , On the singular sets of minimisers of the Mumford-Shah functional, to appear in J. Math. Pures Appl. | MR 1251061 | Zbl 0853.49010
[8] , C1-arcs for minimisers of the Mumford-Shah functional, to appear. | MR 1389754 | Zbl 0870.49020
[9] , Uniform rectifiability of image segmentations obtained by a variational method, J. Math. Pures and Appl., Vol. 73, 1994, pp. 389-412. | MR 1290493 | Zbl 0860.49030
[10] and , Color segmentation using a variational formulation, preprint CEREMADE.
[11] , and , Existence theorem for a minimum problem with free discontinuity set, Arch. Rat. Mech. Anal., Vol. 108, 1989, pp. 195-218. | MR 1012174 | Zbl 0682.49002
[12] and , Measure theory and fine properties of functions, London: CRC Press, 1992. | MR 1158660 | Zbl 0804.28001
[13] , The geometry of fractal sets, Cambridge University Press, 1985. | MR 867284 | Zbl 0587.28004
[14] , Geometric measure theory, Springer-Verlag, 1969. | MR 257325 | Zbl 0176.00801
[15] , and , Inequalities Second Edition, Cambridge university Press. | JFM 60.0169.01 | MR 944909 | Zbl 0010.10703
[16] and , Regularity properties of optimal segmentations, Journ. reine angew. Math., Vol. 420, 1991, pp. 61-84. | MR 1124566 | Zbl 0729.49004
[17] and , Variational methods in Image Segmentation, Birkhauser, 1994. | MR 1321598 | Zbl 0827.68111
[18] , Multiple integrals in the calculus of variations, Springer-Verlag, 1966. | MR 202511 | Zbl 0142.38701
[19] and , Optimal approximations by piecewise smooth functions and associated variational problems, Comm. on Pure and Appl. Math., Vol. XLII, n° 4, 1989. | MR 997568 | Zbl 0691.49036