The uniqueness as a generic property for some one-dimensional segmentation problems
Rendiconti del Seminario Matematico della Università di Padova, Tome 88 (1992) , pp. 151-173.
@article{RSMUP_1992__88__151_0,
author = {Amar, Micol and De Cicco, Virginia},
title = {The uniqueness as a generic property for some one-dimensional segmentation problems},
journal = {Rendiconti del Seminario Matematico della Universit\a di Padova},
pages = {151--173},
publisher = {Seminario Matematico of the University of Padua},
volume = {88},
year = {1992},
zbl = {0783.49014},
mrnumber = {1209122},
language = {en},
url = {http://www.numdam.org/item/RSMUP_1992__88__151_0/}
}
Amar, Micol; De Cicco, Virginia. The uniqueness as a generic property for some one-dimensional segmentation problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 88 (1992) , pp. 151-173. http://www.numdam.org/item/RSMUP_1992__88__151_0/`

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

[2] L. Ambrosio, Variational problems in SBV, Acta Applicandae Mathematicae, 17 (1989), pp. 1-40. | MR 1029833 | Zbl 0697.49004

[3] L. Ambrosio - V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, to appear on Comm. Pure Appl. Math. | Zbl 0722.49020

[4] M. Carriero - E. Pascali, Uniqueness of the one-dimensional bounce problem as a generic property in L1([0, T]; R), Boll. Un. Mat. It. (6), 1-A (1982), pp. 87-91. | MR 652366 | Zbl 0477.73005

[5] G. Congedo - I. Tamanini, On the existence of solutions to a problem in image segmentation, to appear.

[6] G. Dal Maso - J.M. Morel - S. Solimini, A variational method in image segmentation: existence and approximation results, to appear on Acta Mathematica. | MR 1149865 | Zbl 0772.49006

[7] E. De Giorgi - M. Carriero- A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal., (3), 108 (1989), pp. 195-218. | MR 1012174 | Zbl 0682.49002

[8] A. Lasota - J. A. YORKE, The generic property of existence of solutions of differential equations in Banach spaces, J. Diff. Eq., 13 (1973), pp. 1-12. | MR 335994 | Zbl 0259.34070

[9] J.M. Morel - S. SOLIMINI, Segmentation of images by variational methods: a constructive approach, Revista Matem. de la Univ. Complutense de Madrid, 1 (1988), pp. 169-182. | MR 977048 | Zbl 0679.68205

[10] J.M. Morel - S. Solimini, Segmentation d'images par méthode variationelle: une preuve constructive d'existence, C.R. Acad. Sci. Paris, 308, Série I (1989), pp. 465-470. | MR 994693 | Zbl 0676.68051

[11] D. Mumford - J. SHAH, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 42 (1989), pp. 577-685. | MR 997568 | Zbl 0691.49036

[12] D. Mumford - J. Shah, Boundary detection by minimizing functionals, Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, 1985.

[13] W. Orlicz, Zur Theorie der Differentialgleichung y' = f(x, y), Bull. Acad. Polon. Sci. (1932), pp. 221-228. | Zbl 0006.30401

[14] J. Shah, Segmentation by minimizing functionals: smoothing properties, to appear.

[15] G. Vidossich, Existence, uniqueness and approximation of fixed points as a generic property, Bull. Soc. Math. Brasil, 5 (1974), pp. 17-29. | MR 397710 | Zbl 0349.47042