Image segmentation with a finite element method

Blaise Bourdin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 2, page 229-244
  • ISSN: 0764-583X

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Bourdin, Blaise. "Image segmentation with a finite element method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.2 (1999): 229-244. <http://eudml.org/doc/193918>.

@article{Bourdin1999,
author = {Bourdin, Blaise},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Mumford-Shah functional; image segmentation; finite element method; convergence; numerial results},
language = {eng},
number = {2},
pages = {229-244},
publisher = {Dunod},
title = {Image segmentation with a finite element method},
url = {http://eudml.org/doc/193918},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Bourdin, Blaise
TI - Image segmentation with a finite element method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 2
SP - 229
EP - 244
LA - eng
KW - Mumford-Shah functional; image segmentation; finite element method; convergence; numerial results
UR - http://eudml.org/doc/193918
ER -

References

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  2. [2] L. Ambrosio and V. M. Tortorelli, On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. VI-B (1992) 105-123. Zbl0776.49029MR1164940
  3. [3] G. Belletmi and A. Coscia, Discrete approximation of a free discontinuity problem. Num. Funct. Anal. Optim. 15 (1994) 201-224. Zbl0806.49002MR1272202
  4. [4] A. Bonnet, On the regularity of the edge set of Mumford-Shah minimizers. Prog. in Nonlinear Differential Equation and Their Applications 25 (1996) 93-103. Zbl0916.49030MR1414491
  5. [5] H. Brezis, Analyse fonctionnelle. Masson (1989). Zbl0511.46001MR697382
  6. [6] A. Chambolle, Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations. SIAM J. Appl. Math. 55 (1995) 827-863. Zbl0830.49015MR1331589
  7. [7] P. G. Ciarlet, The finite element method for ellipttc problems. North-Holland (1987). Zbl0383.65058MR520174
  8. [8] E. De-Giorgi, M. Carnero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195-218. Zbl0682.49002MR1012174
  9. [9] F. Dibos and E. Séré, An approximation result for the minimizers of the Mumford-Shah functional. Boll. Un. Mat. Ital. A 11 (1997). Zbl0873.49008MR1438364
  10. [10] L. C. Evans and R Gariepy, Measure theory and fine properties of functions. CRC Press, Boca Raton (1992). Zbl0804.28001MR1158660
  11. [11] S. Finzi-Vita and P. Perugia, Some numerical experiments on the variational approach to image segmentation, in Proc. of the Second European Workshop on Image Processing and Mean Curvature Motion, Palma de Mallorca (1995) 233-240. 
  12. [12] D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems Comm. Pure Appl. Math. XLII (1989) 577-685. Zbl0691.49036MR997568
  13. [13] T. J. Richardson and S. K. Mitter, A variational formulation based edge focusing algorithm. Sadhana Acad. P. Eng. S. 22(1997) 553-574. Zbl1075.68664MR1610027

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