Comptes Rendus
no. 5
Partial Differential Equations/Calculus of Variations
Image restoration and edge detection by topological asymptotic expansion

Presented by: Pierre-Louis Lions

Lamia Jaafar Belaid1; Mohamed Jaoua1, 2; Mohamed Masmoudi3; Lassaad Siala1
1 LAMSIN-ENIT, École Nationale d'Ingénieurs de Tunis, B.P. 37, 1002 Le Belvedere, Tunis, Tunisia
2 Université de Nice, parc Valrose, 28, avenue Valrose, 06108 Nice cedex 2, France
3 UMR MIG, Université Paul-Sabatier, CNRS UMR 5640 MIP, 31062 Toulouse cedex 9, France
Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 313-318.

A new method for edge detection and image restoration is proposed. This method is based on topological gradient approach. Experimental results obtained on noisy images illustrate the capabilities of this promising method in image processing.

Une nouvelle méthode de restauration d'images avec détection de contours est proposée. Cette méthode est basée sur l'approche du gradient topologique. Des résultats expérimentaux obtenus sur des images bruitées illustrent les possibilités de cette approche prometteuse dans le domaine du traîtement d'images.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.12.009

Lamia Jaafar Belaid 1; Mohamed Jaoua 1, 2; Mohamed Masmoudi 3; Lassaad Siala 1

1 LAMSIN-ENIT, École Nationale d'Ingénieurs de Tunis, B.P. 37, 1002 Le Belvedere, Tunis, Tunisia
2 Université de Nice, parc Valrose, 28, avenue Valrose, 06108 Nice cedex 2, France
3 UMR MIG, Université Paul-Sabatier, CNRS UMR 5640 MIP, 31062 Toulouse cedex 9, France 
@article{CRMATH_2006__342_5_313_0,
     author = {Lamia Jaafar Belaid and Mohamed Jaoua and Mohamed Masmoudi and Lassaad Siala},
     title = {Image restoration and edge detection by topological asymptotic expansion},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {313--318},
     publisher = {Elsevier},
     volume = {342},
     number = {5},
     year = {2006},
     doi = {10.1016/j.crma.2005.12.009},
     language = {en},
}
TY  - JOUR
AU  - Lamia Jaafar Belaid
AU  - Mohamed Jaoua
AU  - Mohamed Masmoudi
AU  - Lassaad Siala
TI  - Image restoration and edge detection by topological asymptotic expansion
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 313
EP  - 318
VL  - 342
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crma.2005.12.009
LA  - en
ID  - CRMATH_2006__342_5_313_0
ER  - 
%0 Journal Article
%A Lamia Jaafar Belaid
%A Mohamed Jaoua
%A Mohamed Masmoudi
%A Lassaad Siala
%T Image restoration and edge detection by topological asymptotic expansion
%J Comptes Rendus. Mathématique
%D 2006
%P 313-318
%V 342
%N 5
%I Elsevier
%R 10.1016/j.crma.2005.12.009
%G en
%F CRMATH_2006__342_5_313_0
Lamia Jaafar Belaid; Mohamed Jaoua; Mohamed Masmoudi; Lassaad Siala. Image restoration and edge detection by topological asymptotic expansion. Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 313-318. doi : 10.1016/j.crma.2005.12.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.009/

[1] S. Amstutz, I. Horchani, M. Masmoudi, Crack detection by the topological gradient method, Recent Advances in Shape and Topology Optimization, Special issue J. Control and Cybernetics, in press

[2] G. Aubert; P. Kornprobst Mathematical Problems in Image Processing, Appl. Math. Sci., vol. 147, Springer-Verlag, 2001

[3] F. Catté; T. Coll; P.L. Lions; J.M. Morel Image selective smoothing and edge detection by non linear diffusion, SIAM J. Numer. Anal., Volume 29 (1992), pp. 182-193

[4] H.W. Engl; C.W. Groetsch Inverse an Ill Posed Problems, Academic Press, New York, 1987

[5] M. Masmoudi The topological asymptotic (H. Kawarada; J. Périaux, eds.), Computational Methods for Control Applications, GAKUTO Intern. Ser., 2002

[6] P. Perona; J. Malik Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Analysis and Machine Intelligence, Volume 12 (1990), pp. 629-639

[7] J. Weikert Anisotropic Diffusion in Image Processing, ECMI Series, Teubner, Stuttgart, Germany, 1998

Cited by Sources:

Comments - Policy