Time-delay regularization of anisotropic diffusion and image processing
Abdelmounim Belahmidi; Antonin Chambolle
- Volume: 39, Issue: 2, page 231-251
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topBelahmidi, Abdelmounim, and Chambolle, Antonin. "Time-delay regularization of anisotropic diffusion and image processing." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.2 (2005): 231-251. <http://eudml.org/doc/245424>.
@article{Belahmidi2005,
abstract = {We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.},
author = {Belahmidi, Abdelmounim, Chambolle, Antonin},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {image restoration; edge detection; Perona-Malik equation; time-delay regularization},
language = {eng},
number = {2},
pages = {231-251},
publisher = {EDP-Sciences},
title = {Time-delay regularization of anisotropic diffusion and image processing},
url = {http://eudml.org/doc/245424},
volume = {39},
year = {2005},
}
TY - JOUR
AU - Belahmidi, Abdelmounim
AU - Chambolle, Antonin
TI - Time-delay regularization of anisotropic diffusion and image processing
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 2
SP - 231
EP - 251
AB - We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
LA - eng
KW - image restoration; edge detection; Perona-Malik equation; time-delay regularization
UR - http://eudml.org/doc/245424
ER -
References
top- [1] L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel, Axioms and fundamental equations of image processing. Arch. Rational Mech. Anal. 123 (1993) 199–257. Zbl0788.68153
- [2] A. Belahmidi, Équations aux dérivées partielles appliquées à la restauration et à l’agrandissement des images. Ph.D. thesis, CEREMADE, Université de Paris-Dauphine, Paris (2003). Available at http://tel.ccsd.cnrs.fr.
- [3] J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (1986) 679–698.
- [4] F. Catté, P.-L. Lions, J.-M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29 (1992) 182–193. Zbl0746.65091
- [5] P.G. Ciarlet, Introduction à l’analyse numérique matricielle et à l’optimisation. Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris (1982). Zbl0488.65001
- [6] G.H. Cottet and M. El-Ayyadi, A volterra type model for image processing. IEEE Trans. Image Process. 7 (1998) 292–303.
- [7] S. Esedoḡlu, An analysis of the Perona-Malik scheme. Comm. Pure Appl. Math. 54 (2001) 1442–1487. Zbl1031.68133
- [8] Y. Giga and S. Goto, Motion of hypersurfaces and geometric equations. J. Math. Soc. Japan 44 (1992) 99–111. Zbl0739.53005
- [9] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. Zbl1042.35002MR1814364
- [10] E. Heinz, An elementary analytic theory of the degree of mapping in -dimensional space. J. Math. Mech. 8 (1959) 231–247. Zbl0085.17105
- [11] K. Höllig and J.A. Nohel, A diffusion equation with a nonmonotone constitutive function, in Systems of nonlinear partial differential equations (Oxford, 1982), Reidel, Dordrecht. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 111 (1983) 409–422. Zbl0531.35045
- [12] O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques, volume 13 of Mathématiques & Applications (Berlin). Springer-Verlag, Paris (1993). Zbl0797.58005MR1276944
- [13] B. Kawohl and N. Kutev, Maximum and comparison principle for one-dimensional anisotropic diffusion. Math. Ann. 311 (1998) 107–123. Zbl0909.35025
- [14] S. Kichenassamy, The Perona-Malik paradox. SIAM J. Appl. Math. 57 (1997) 1328–1342. Zbl0887.35071
- [15] D. Marr and E. Hildreth, Theory of edge detection. Proc. Roy. Soc. London B. 207 (1980) 187–217.
- [16] N.G. Meyers, An e-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 17 (1963) 189–206. Zbl0127.31904
- [17] M. Nitzberg and T. Shiota, Nonlinear image filtering with edge and corner enhancement. IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 826–833.
- [18] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629–639.
- [19] R.T. Whitaker and S.M. Pizer, A multi-scale approach to nonuniform diffusion. CVGIP: Image Underst. 57 (1993) 99–110.
- [20] Y. You, W. Xu, A. Tannenbaum and M. Kaveh, Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5 (1996) 1539–1553.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.