A topological asymptotic analysis for the regularized grey-level image classification problem
Didier Auroux; Lamia Jaafar Belaid; Mohamed Masmoudi
ESAIM: Mathematical Modelling and Numerical Analysis (2007)
- Volume: 41, Issue: 3, page 607-625
- ISSN: 0764-583X
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topAuroux, Didier, Belaid, Lamia Jaafar, and Masmoudi, Mohamed. "A topological asymptotic analysis for the regularized grey-level image classification problem." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 607-625. <http://eudml.org/doc/250065>.
@article{Auroux2007,
abstract = {
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical
variational approach without and with a regularization term in order to
smooth the contours of the classified image. Then we present the general
topological asymptotic analysis, and we finally introduce its application to
the grey-level image classification problem.
},
author = {Auroux, Didier, Belaid, Lamia Jaafar, Masmoudi, Mohamed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Image classification; topological asymptotic expansion; image restoration.},
language = {eng},
month = {8},
number = {3},
pages = {607-625},
publisher = {EDP Sciences},
title = {A topological asymptotic analysis for the regularized grey-level image classification problem},
url = {http://eudml.org/doc/250065},
volume = {41},
year = {2007},
}
TY - JOUR
AU - Auroux, Didier
AU - Belaid, Lamia Jaafar
AU - Masmoudi, Mohamed
TI - A topological asymptotic analysis for the regularized grey-level image classification problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/8//
PB - EDP Sciences
VL - 41
IS - 3
SP - 607
EP - 625
AB -
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical
variational approach without and with a regularization term in order to
smooth the contours of the classified image. Then we present the general
topological asymptotic analysis, and we finally introduce its application to
the grey-level image classification problem.
LA - eng
KW - Image classification; topological asymptotic expansion; image restoration.
UR - http://eudml.org/doc/250065
ER -
References
top- G. Allaire, Shape optimization by the homogenization method. Applied Mathematical Sciences 146, Springer (2002).
- G. Allaire and R. Kohn, Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur. J. Mech. A Solids12 (1993) 839–878.
- G. Allaire, F. Jouve and A.-M. Toader, A level-set method for shape optimization. C. R. Acad. Sci. Sér. I334 (2002) 1125–1130.
- G. Allaire, F. de Gournay, F. Jouve and A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method, Internal report, n° 555, CMAP, École polytechnique. Control Cybern.34 (2005) 59-80.
- H. Ammari, M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II - The full Maxwell equations. J. Math. Pures Appl.80 (2001) 769–814.
- S. Amstutz, I. Horchani and M. Masmoudi, Crack detection by the topological gradient method. Control Cybern.34 (2005) 119-138.
- G. Aubert and J.-F. Aujol, Optimal partitions, regularized solutions, and application to image classification. Appl. Anal.84 (2005) 15–35.
- G. Aubert and P. Kornprobst, Mathematical problems in image processing. Applied Mathematical Sciences 147, Springer-Verlag, New York (2002).
- J.-F. Aujol, G. Aubert and L. Blanc-Féraud, Wavelet-based level set evolution for classification of textured images. IEEE Trans. Image Process.12 (2003) 1634–1641.
- M. Bendsoe, Optimal topology design of continuum structure: an introduction. Technical report, Department of Mathematics, Technical University of Denmark, Lyngby, Denmark (1996).
- M. Berthod, Z. Kato, S. Yu and J. Zerubia, Bayesian image classification using Markov random fields. Image Vision Comput.14 (1996) 285–293.
- C.A. Bouman and M. Shapiro, A multiscale random field model for Bayesian image segmentation. IEEE Trans. Image Process.3 (1994) 162–177.
- P.G. Ciarlet, Finite Element Method for Elliptic Problems. North Holland (2002).
- L. Cohen, E. Bardinet and N. Ayache, Surface reconstruction using active contour models. SPIE Int. Symp. Optics, Imaging and Instrumentation, San Diego California USA (July 1993).
- R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Collection CEA, Masson, Paris (1987).
- X. Descombes, R. Morris and J. Zerubia, Some improvements to Bayesian image segmentation – Part one: modelling. Traitement du signal14 (1997) 373–382.
- X. Descombes, R. Morris and J. Zerubia, Some improvements to Bayesian image segmentation – Part two: classification. Traitement du signal14 (1997) 383–395.
- A. Friedman and M.S. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem of continuous dependance. Arch. Rational Mech. Anal.105 (1989) 299–326.
- S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: The elasticity case. SIAM J. Control Optim.39 (1991) 17–49.
- L. Jaafar Belaid, M. Jaoua, M. Masmoudi and L. Siala, Image restoration and edge detection by topological asymptotic expansion. C. R. Acad. Sci. Paris. Ser. I Math.342 (2006) 313–318.
- Z. Kato, Modélisations markoviennes multirésolutions en vision par ordinateur - Application à la segmentation d'images SPOT. Ph.D. thesis, INRIA, Sophia Antipolis, France (1994).
- M. Masmoudi, The topological asymptotic, in Computational Methods for Control Applications, R. Glowinski, H. Karawada and J. Periaux Eds., GAKUTO Internat. Ser. Math. Sci. Appl.16, Tokyo, Japan (2001) 53–72.
- D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math.42 (1989) 577–685.
- N. Paragios and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation. Int. Jour. Computer Vision46 (2002) 223–247.
- T. Pavlidis and Y.-T. Liow, Integrating region growing and edge detection. IEEE Trans. Pattern Anal. Machine Intelligence12 (1990) 225–233.
- P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intelligence12 (1990) 629–638.
- B. Samet, S. Amstutz and M. Masmoudi, The topological asymptotic for the Helmholtz equation. SIAM J. Control Optim.42 (2003) 1523–1544.
- C. Samson, L. Blanc-Féraud, G. Aubert and J. Zerubia, A level set method for image classification. Int. J. Comput. Vision40 (2000) 187–197.
- C. Samson, L. Blanc-Féraud, G. Aubert and J. Zerubia, A variational model for image classification and restauration. IEEE Trans. Pattern Anal. Machine Intelligence22 (2000) 460–472.
- J.A. Sethian, Level set methods evolving interfaces in geometry, fluid mechanics, computer vision, and materials science. Cambride University Press (1996).
- J. Sokolowski and A. Zochowski, Topological derivatives of shape functionals for elasticity systems. Int. Ser. Numer. Math.139 (2002) 231–244.
- S. Solimini and J.M. Morel, Variational methods in image segmentation. Birkhauser (1995).
- L. Vese and T. Chan, Reduced Non-Convex Functional Approximations for Image Restoration and Segmentation. UCLA CAM Report 97–56 (1997).
- M.Y. Wang, D. Wang and A. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Engrg.192 (2003) 227–246.
- J. Weickert, Efficient image segmentation using partial differential equations and morphology. Pattern Recogn.34 (2001) 1813–1824.
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