@article{AIHPC_2002__19_5_631_0, author = {David, Guy and L\'eger, Jean-Christophe}, title = {Monotonicity and separation for the {Mumford-Shah} problem}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {631--682}, publisher = {Elsevier}, volume = {19}, number = {5}, year = {2002}, zbl = {1038.49022}, language = {en}, url = {http://archive.numdam.org/item/AIHPC_2002__19_5_631_0/} }
TY - JOUR AU - David, Guy AU - Léger, Jean-Christophe TI - Monotonicity and separation for the Mumford-Shah problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2002 SP - 631 EP - 682 VL - 19 IS - 5 PB - Elsevier UR - http://archive.numdam.org/item/AIHPC_2002__19_5_631_0/ LA - en ID - AIHPC_2002__19_5_631_0 ER -
David, Guy; Léger, Jean-Christophe. Monotonicity and separation for the Mumford-Shah problem. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 5, pp. 631-682. http://archive.numdam.org/item/AIHPC_2002__19_5_631_0/
[1] Existence theory for a new class of variational problems, Arch. Rational Mech. Anal. 111 (1990) 291-322. | MR | Zbl
,[2] Partial regularity of free discontinuity sets I, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997) 1-38. | EuDML | Numdam | MR | Zbl
, ,[3] Partial regularity of free discontinuity sets II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997) 39-62. | EuDML | Numdam | MR | Zbl
, , ,[4] On the regularity of edges in image segmentation, Ann. Inst. H. Poincaré, Analyse Non Linéaire 13 (4) (1996) 485-528. | EuDML | Numdam | MR | Zbl
,[5] Cracktip is a global Mumford-Shah minimizer, Astérisque, 274, SMF, 2001. | Numdam | MR | Zbl
, ,[6] A variational method in image segmentation: Existence and approximation results, Acta Math. 168 (1992) 89-151. | MR | Zbl
, , ,[7] C1 arcs for minimizers of the Mumford-Shah functional, SIAM. J. Appl. Math. 56 (3) (1996) 783-888. | MR | Zbl
,[8] Analysis of and on Uniformly Rectifiable Sets, AMS Series of Mathematical Surveys and Monographs, 38, 1993. | MR | Zbl
, ,[9] On the singular sets of minimizers of the Mumford-Shah functional, J. Math. Pures Appl. 75 (1996) 299-342. | MR | Zbl
, ,[10] Problemi con discontinuità libera, Int. Symp. Renato Caccioppoli, Napoli, Sept. 20-22, 1989, Ricerche Mat. (suppl.) 40 (1991) 203-214. | Zbl
,[11] Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal. 108 (1989) 195-218. | MR | Zbl
, , ,[12] The Geometry of Fractal Sets, Cambridge University Press, 1984. | MR | Zbl
,[13] Geometric Measure Theory, Grundlehren der Mathematischen Wissenschaften, 153, Springer-Verlag, 1969. | MR | Zbl
,[14] Inequalities, Cambridge University Press, 1952. | JFM | MR
, , ,[15] Flatness and finiteness in the Mumford-Shah problem, J. Math. Pures Appl. (9) 78 (4) (1999) 431-459. | MR | Zbl
,[16] Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18 (2001) 639-673. | Numdam | MR | Zbl
, , ,[17] Blow-up techniques and regularity near the boundary for free discontinuity problems, Advanced Nonlinear Studies 1 (2) (2001). | MR | Zbl
, ,[18] Geometry of Sets and Measures in Euclidean Space, Cambridge Studies in Advanced Mathematics, 44, Cambridge University Press, 1995. | MR | Zbl
,[19] Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989) 577-685. | MR | Zbl
, ,[20] Elements of the Topology of Plane Sets of Points, Cambridge University Press, New York, 1961. | MR | Zbl
,