On the existence of solutions to a problem in multidimensional segmentation

G. Congedo; I. Tamanini

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 2, page 175-195
  • ISSN: 0294-1449

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Congedo, G., and Tamanini, I.. "On the existence of solutions to a problem in multidimensional segmentation." Annales de l'I.H.P. Analyse non linéaire 8.2 (1991): 175-195. <http://eudml.org/doc/78249>.

@article{Congedo1991,
author = {Congedo, G., Tamanini, I.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {image segmentation in computer vision; Minimal boundary problems with free discontinuity},
language = {eng},
number = {2},
pages = {175-195},
publisher = {Gauthier-Villars},
title = {On the existence of solutions to a problem in multidimensional segmentation},
url = {http://eudml.org/doc/78249},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Congedo, G.
AU - Tamanini, I.
TI - On the existence of solutions to a problem in multidimensional segmentation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 2
SP - 175
EP - 195
LA - eng
KW - image segmentation in computer vision; Minimal boundary problems with free discontinuity
UR - http://eudml.org/doc/78249
ER -

References

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  5. [B-M] J. Blat and J.M. Morel, Elliptic Problems in Image Segmentation (to appear). 
  6. [C-T1] G. Congedo and I. Tamanini, Note sulla regolarità dei minimi di funzionali del tipo dell'area, Rend. Accad. Naz. XL, 106, Vol. XII, fasc. 17, 1988, pp. 239-257. Zbl0674.49031MR985069
  7. [C-T2] G. Congedo and I. Tamanini, Density Theorems for Local Minimizers of Area-Type Functionals (to appear). Zbl0753.49019MR1142542
  8. [DeG] E. De Giorgi, Free Discontinuity Problems in Calculus of Variations, Proceedings of the meeting in J. L. Lions's honour, Paris, 1988 (to appear). Zbl0758.49002
  9. [DeG-A] E. De Giorgi and L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei (to appear). 
  10. [DeG-C-L] 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. Zbl0682.49002MR1012174
  11. [DeG-C-P] E. De Giorgi, F. Colombini and L.C. Piccinini, Frontiere orientate di misura minima e questioni collegate, Editrice Tecnico Scientifica, Pisa, 1972. Zbl0296.49031
  12. [DeG-C-T] E. De Giorgi, G. Congedo and I. Tamanini, Problemi di regolarità per un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei (to appear). 
  13. [F] H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin, 1969. Zbl0176.00801MR257325
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  15. [M-M] U. Massari and M. Miranda, Minimal Surfaces of Codimension 1, North-Holland, Amsterdam, 1984. Zbl0565.49030MR795963
  16. [M-T] U. Massari, I. Tamanini, paper in preparation. 
  17. [Mo-S] J.M. Morel and S. Solimini, Segmentation of Images by Variational Methods: a Constructive Approach, Rev. Mat. Univ. ComplutenseMadrid, Vol. 1, 1988, pp. 169-182. Zbl0679.68205MR977048
  18. [M-S] D. Mumford and J. Shah, Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 577-685. Zbl0691.49036MR997568
  19. [S] L. Simon, Lectures on Geometric Measure Theory, Center for Math. Analysis, Australian National University, Vol., 3, 1983. Zbl0546.49019MR756417
  20. [T1] J.E. Taylor, The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces, Annals Math., 103, 1976, pp. 489-539. Zbl0335.49032MR428181
  21. [T2] J.E. Taylor, Cristalline Variational Problems, Bull. A.M.S., Vol. 84, 1978, pp. 568-588. Zbl0392.49022MR493671

Citations in EuDML Documents

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  1. Gian Paolo Leonardi, Suddivisioni ottimali di domini n-dimensionali
  2. Luca Rondi, Fadil Santosa, Enhanced electrical impedance tomography via the Mumford–Shah functional
  3. Ana Cristina Barroso, José Matias, On a volume constrained variational problem in SBV 2 ( Ω ) : part I
  4. A. Bonnet, On the regularity of edges in image segmentation
  5. Luca Rondi, Fadil Santosa, Enhanced Electrical Impedance Tomography the Mumford–Shah Functional
  6. Italo Tamanini, Giuseppe Congedo, Density theorems for local minimizers of area-type functionals
  7. Ana Cristina Barroso, José Matias, On a Volume Constrained Variational Problem in SBV²(Ω): Part I
  8. Raphaël Cerf, Ágoston Pisztora, Phase coexistence in Ising, Potts and percolation models
  9. Italo Tamanini, Giuseppe Congedo, Optimal segmentation of unbounded functions
  10. Giuseppe Congedo, Italo Tamanini, Problemi di partizioni ottimali con dati illimitati

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