A volterra type model for image processing

IEEE Transactions on Image Processing

Volumn 7, Issue 3, 1998, Pages 292-303

  Cottet, Georges Henri ^a   El Ayyadi, Mohamed ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Adaptive neural network; Image restoration; Nonlinear diffusion; Selective filter; Time delay regularization

Indexed keywords

IMAGE PROCESSING; LEARNING SYSTEMS; MATHEMATICAL MODELS; NEURAL NETWORKS; NUMERICAL METHODS;

ADAPTIVE NEURAL NETWORKS; NONLINEAR DIFFUSION;

IMAGE RECONSTRUCTION;

EID: 0032028943     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.661179     Document Type: Article

References (17)

1. L. Alvarez, F. Guichard, P.-L. Lions, and J.-M. Morel, "Axioms and fundamental equations in image processing," Arch. Rational Mech. Anal., vol. 123, pp. 199-257, 1993.
2. L. Alvarez, P.-L. Lions, and J.-M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion II," SIAM J. Numer. Anal., vol. 29, pp. 845-866, 1992.
3. F. Catté, J.-M. Morel, P.-L. Lions, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., vol. 29, pp. 182-193, 1992.
4. G.-H. Cottet, "Modèles de réaction-diffusion pour des réseaux de neurones stochastiques et déterministes," C. R. Acad. Sci. Paris, vol. 312, 1991.
5. _, "Neural networks: Continuous approach and applications to image processing," J. Biol. Syst., vol. 3, pp. 1131-1139, 1995.
6. G.-H. Cottet and M. El Ayyadi, "Nonlinear PDE operators with memory terms for image processing," in Proc. Third IEEE Int. Conf. Image Processing, 1996, pp. I-481-I-484.
7. G.-H. Cottet and L. Germain, "Combining nonlinear diffusion with reaction for image processing," Math. Comput., vol. 61, pp. 659-673, 1993.
8. P. Degond and S. Mas-Gallic, "The weighted particle method for convection-diffusion equations. II: The anisotropic case," Math. Comput., vol. 53, pp. 485-508, 1989.
9. R. Edwards, "Approximation of neural network dynamics by reaction-diffusion equations," Math. Methods Appl. Sci., vol. 19, pp. 651-677, 1996.
10. M. El Ayyadi, F. Leitner, G.-H. Cottet, and J. Demongeot, "Image segmentation using snake-splines and nonlinear diffusion operators," preprint, 1995.
11. M. Nitzberg, D. Mumford, and T. Shiota, "Filtering, segmentation and depth," in Lecture Notes in Computer Science, vol. 662. New York: Springer-Verlag, 1993.
12. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 629-630, 1990.
13. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica-D, vol. 60, pp. 259-268, 1992.
14. J. Shah, "A common framework for curve evolution, segmentation and anisotropic diffusion," in IEEE Conf. Computer Vision and Pattern Recognition, 1996.
15. J. Weickert, "Scale-space properties of nonlinear diffusion filtering with a diffusion tensor," preprint, 1994.
16. _, "Anisotropic diffusion in image processing," Ph.D. dissertation, Univ. Kaiserslautern, Germany, 1996.
17. D. Zaharie, personal communication.