F. Alvarez, P. L. Guichard, and J. M. Lions, Axiomatisation et nouveaux op erateurs de la morphologie math ematique, C. R. Acad. Sci, p.2655268, 1992.

F. Alvarez, P. L. Guichard, and J. M. Lions, Axiomes et equations fondamentales du traitement d'images, Analyse multi echelle et E.D.P.. C. R. Acad

. Sci, Paris, t. 315, S erie I:1355138, 1992.

F. Alvarez, P. L. Guichard, and J. M. Lions, Equations fondamentales de l'analyse multi echelle des lms, C. R. Acad. Sci, p.114551148, 1992.

F. Alvarez, P. L. Guichard, and J. M. Lions, Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, vol.11, issue.3, 1993.
DOI : 10.1007/BF00375127

P. L. Alvarez and J. M. Lions, Image selective smoothing and edge detection by nonlinear diiusion, II. SIAM J. Numer. Anal, vol.293, p.8455866, 1992.

L. Alvarez and . Mazorra, Signal and image restoration using shock lters and anisotropic diiusion, SIAM J. Numer. Anal, vol.312, p.5900605, 1994.

J. M. Alvarez, Anisotropic diiusion Geometry-driven diiusion in computer vision, 1994.

J. M. Alvarez, Formalization and computational aspects of image analysis, Acta Numerica, vol.1, p.1159, 1994.
DOI : 10.1137/0729052

J. Alvarez and . Esclar-n, Image Quantization using Reaction-Diiusion Equations, SIAM J. Appl. Math, vol.571, p.1533175, 1997.

H. Amit, H. Gutfreund, and . Sompolinsky, Storing innnite numbers of patterns in a spin glass model of neural network, Phys. Rev. Lett, vol.55, p.153001533, 1985.

J. Y. Anh, H. T. Shi, and . Tsui, Scaling Theorems for Zero Crossings of Bandlimited Signals Kernel for Scale-Space Filtering, IEEE Trans. Pattern Anal. & Machine Intell. IEEE Trans. Pattern Anal. & Machine Intell, vol.18, issue.8, p.309932026633, 1986.

C. Ballester, V. Caselles, and M. Gonz-alez, AAne Invariant Segmentation by V ariational Method, SIAM J. Appl. Math, vol.561, p.2944325, 1996.

L. Benabid, P. Cinquin, J. F. Lebas, J. Demongeot, and J. De-rougemont, A computer driven robot for stereotactic surgery connected to cat-scan magnetic resonance imaging. Technological design and preliminary results, Applied Neurophysiology, vol.50, p.1533154, 1987.

O. Berthommier, T. Francois, T. Coll, I. Herve, J. Marque et al., Asymptotic Behavior of Neural Networks and Image Processing, Self-Organization, Emerging properties and Learning, p.2199230, 1991.
DOI : 10.1007/978-1-4615-3778-6_15

. Blankenship, Real-Time Enhancement of Medical Ultrasound Images, 1987.
DOI : 10.1007/978-1-4613-0725-9_18

J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. & Machine Intell, vol.8, p.6799698, 1986.

F. Caselles, T. Catt-e, F. Coll, and . Dibos, A geometric model for active contours in image processing, Numerische Mathematik, vol.36, issue.4, p.1133, 1993.
DOI : 10.1007/BF01385685

B. Caselles and J. M. Coll, Junction detection and ltering: a morphological approach, Proc. third IEEE Int. Conf. on Image Processing, pp.4933496-96, 1996.

R. Caselles, G. Kimmel, and . Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, p.694469995, 1995.
DOI : 10.1109/ICCV.1995.466871

V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, p.61179, 1997.
DOI : 10.1109/ICCV.1995.466871

V. Caselles and J. M. , An Axiomatic Approach to Image Interpolation, IEEE Trans. Image Processing, 1997.

C. Caselles and . Sbert, What is the Best Causal Scale Space for Three-Dimensional Images?, SIAM Journal on Applied Mathematics, vol.56, issue.4, p.119991246, 1996.
DOI : 10.1137/S0036139994269352

F. Catt-e and . Dibos, A Morphological Scheme for Mean Curvature Motion and Application to Anisotropic Diiusion and Motion of Level Sets, Proc. third IEEE Int. Conf. on Image Processing, pp.26630-94, 1994.

J. Catt-e, P. Morel, T. Lions, and . Coll, Image selectives smoothing and edge detection by nonlinear diiusion, SIAM J. Numer. Anal, vol.29, p.1822193, 1992.

P. Chambolle and . Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, vol.76, issue.2, p.1677188, 1997.
DOI : 10.1007/s002110050258

-. Chua and L. Yang, Cellular neural networks: applications, IEEE Transactions on Circuits and Systems, vol.35, issue.10, p.127331290, 1988.
DOI : 10.1109/31.7601

L. Chua and L. Yang, Cellular neural networks: theory, IEEE Transactions on Circuits and Systems, vol.35, issue.10, p.125771272, 1988.
DOI : 10.1109/31.7600

I. Cohen, Mod eles d eformables 2D et 3D : application a la segmentation d'images m edicales, 1992

D. Cohen, On active contour models and balloons, CVGIP: Image Understanding, vol.53, issue.2, p.2111218, 1991.
DOI : 10.1016/1049-9660(91)90028-N

M. Cohen, Sustained Oscillation in a Symetric Cooperative-Competitive Neural Networ: Disproof of a conjecture about Content Adressable Memory, Neural Network, vol.1, p.2177221, 1988.

M. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage bye competitive neural networks, IEEE Trans. Systems Man & Cybernetics, issue.5, p.12815, 1983.

M. Cohen and S. Grossberg, Neural Dynamics of brightness perception: Features, boundaries, diiusion and resonance, Perception and Psychophysics, vol.36, p.4288456, 1984.

F. Cohignac, F. Eve, C. Guichard, and J. M. Lopez, Numerical analysis of the fundamental equation of image processing, 1992.

G. Cottet and M. Ayyadi, Nonlinear PDE operators with memory terms for image processing, Proceedings of 3rd IEEE International Conference on Image Processing, pp.4811484-96, 1996.
DOI : 10.1109/ICIP.1996.559538

G. Cottet and M. Ayyadi, A Volterra type model for image processing, IEEE Transactions on Image Processing, vol.7, issue.3, 1997.
DOI : 10.1109/83.661179

G. Bibliographie, J. Cottet, M. Demongeot, F. Ayyadi, and . Leitner, Image segmentation using snake-splines and anisotropic diiusion operators, 1996.

H. Cottet, Mod ele de r eaction-diiusion pour des r eseaux de neurones stochastiques et d eterministes, C.R.Acad.Sc, vol.312, p.2177221, 1991.

H. Cottet, NEURAL NETWORKS: CONTINUOUS APPROACH AND APPLICATIONS TO IMAGE PROCESSING, Journal of Biological Systems, vol.03, issue.04, p.113111139, 1995.
DOI : 10.1142/S0218339095001027

H. Cottet and L. Germain, Image processing through reaction combined with nonlinear diiusion, Math. Comp, vol.61, p.6599673, 1993.

S. Degond and . Mas-gallic, The weighted particle method for convection-diiusion equations. II: The anisotropic case, Math. Comp, vol.53, p.4855508, 1989.

. Deriche, Using Canny's criteria to derive a recursively implemented optimal edge detector, International Journal of Computer Vision, vol.1, issue.2, p.1677187, 1987.
DOI : 10.1007/BF00123164

. Dibos, Analyse multi echelle i n variante par transformations projective, RT 9505, 1995.

W. Dong, Dynamic Properties of Neural Networks, 1991.

W. Dong and J. J. Hoppeld, Dynamic properties of neural networks with adapting synapses, Network: Computation in Neural Systems, v olume 33, p.2677283, 1992.

W. Dong and J. J. Hoppeld, Dynamics of interconnection development within visual cortex, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks, p.85590, 1992.
DOI : 10.1109/IJCNN.1992.227186

. Edwards, Neural Networks and Neural Fields: Discrete and Continuous Space Neural Models, 1994.

. Edwards, Approximation of Neural Network Dynamics by Reaction-Diiusion Equations, Math. Meth. Appl. Sci, vol.19, 1996.

. Faugeras, Sur l' evolution de courbes simples du plan projectif r eel, C. R. Acad. Sci. Paris, t, vol.317, p.5655570, 1993.

. Faugeras, Three-Dimensional Computer Vision; a Geometric Viewpoint, 1993.

O. Faugeras and M. Hebert, The Representation, Recognition, and Locating of 3-D Objects, The International Journal of Robotics Research, vol.5, issue.3, p.25552, 1986.
DOI : 10.1177/027836498600500302

R. Faugeras and . Keriven, Some recent results on the projective e v olution of 2-D curves, Proc. third IEEE Int. Conf. on Image Processing, pp.13316-95, 1995.

M. J. Florack, The Syntactical Structure of Scalar Image, 1993.

C. G. Egout, Techniques Evolutionnaires pour l'apprentissage des R eseaux de Neurones a Coeecients R eels, 1992

D. Geman and . Geman, Stochastic relaxation, Gibbs distributions,and the Bayesian restoration of images, IEEE Trans. Pattern Anal. & Machine Intell, vol.6, p.7211741, 1984.

O. Gerig, R. Ubler, F. A. Kikinis, and . Jolesz, Nonlinear anisotropic ltering of MRI data, IEEE Trans. Medical Imaging, vol.11, p.2211232, 1992.

. Grossberg, Adaptive pattern classiication and universal recoding: I. Parallel developement and coding of neural feature detectors, Biological Cybernetics, vol.23, pp.1211-134, 1976.

. Grossberg, Competition, decision, and consensus, Journal of Mathematical Analysis and Applications, vol.66, p.4700493, 1978.

. Grossberg, Nonlinear neural networks: Principles, mechanisms, and architectures, Neural Networks, vol.1, issue.1, p.17761, 1988.
DOI : 10.1016/0893-6080(88)90021-4

O. Hebb, The Organization of Behavior: A Neuropsychological Theory, 1948.

M. Hirsch, Systems of diierential equation that are competitive or cooperative I: Limit sets, SIAM Journal of Mathematical Analysis, vol.13, p.1677179, 1982.

M. Hirsch, Systems of diierential equation that are competitive or cooperative I I : Convergence almost everywhere, SIAM Journal of Mathematical Analysis, vol.16, pp.4233-439, 1985.

M. Hirsch, Convergent activation dynamics in continuous time networks, Neural Networks, vol.2, issue.5, p.3311349, 1989.
DOI : 10.1016/0893-6080(89)90018-X

J. Hoppeld, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A, p.255442558, 1982.

J. Hoppeld, Neurons with graded response have collective computational properties like those of two-states neurons, Proc. Nat. Acad. Sci. U.S.A, p.308883092, 1984.

R. A. Hummel, Representations bazed on zero-crossings in scale space, IEEE Conf. Computer Vision & Pattern Recognition CVPR'86, p.2044209, 1986.

H. Illner and . Neunzert, Relative e n tropy maximization and directed diiusion equations, Math. Meth. Appl. Sci, vol.16, p.5455554, 1993.

J. Illner and . Tie, On directed diiusion with measurable background, Math. Meth. Appl. Sci, vol.16, p.6811690, 1993.

A. Kass, D. Witkin, and . Terzopoulous, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, p.3211332, 1988.
DOI : 10.1007/BF00133570

A. R. Kimia, S. W. Tannenbaum, and . Zucker, On the Evolution of Curves via a F unction of Curvature. I. The Classical Case, J. of Mathematical Analysis and Applications, vol.1632, p.4388458, 1992.

A. R. Kimia, S. W. Tannenbaum, and . Zucker, Shapes, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space, International Journal of Computer Vision, vol.1, issue.1, p.1899224, 1995.
DOI : 10.1007/BF01451741

. Kimmel, Curve E v olution on Surfaces, 1995.

J. Koenderink, The sructure of images, Biol. Cybernet, vol.50, p.3633370, 1984.

. Kohonen, Self-Organization and Associative Memory, 1984.

H. Kurosawa, Y. Tsuchiya, H. Maruyama, K. Ohtsuka, and . Nakazato, A new bi-level reproduction of continuous tone images, Proc. 3rd Interna. Conf. Image Processing and its Applications, p.82286, 1986.

T. Li and . Chen, Nonlinear diiusion with multiple edginess thresholds, Pattern Recognition, vol.27, p.102991037, 1994.

L. Lions, S. Osher, and L. Rudin, Denoising and Deblurring Algorithms with Constrained Nonlinear PDE's, SIAM J. Numer. Anal

E. Marr and . Hildreth, Theory of edge detection. Pro, Roy. Soc. London Ser. B, vol.207, p.1877217, 1980.

J. Morel and S. Solimini, Variational methods in imagesegmentation, Birkhh auser, 1994.

J. Mumford and . Shah, Boundary detection by minimizing functionals. IEEE Conf. Computer Vision & Pattern Recognition CVPR'85, p.22226, 1985.

J. Mumford and . Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, p.5777685, 1989.
DOI : 10.1002/cpa.3160420503

D. Nitzberg, T. Mumford, and . Shiota, Filtering, segmentation and depth, Lecture Notes in Comp. Science, vol.662, 1993.
DOI : 10.1007/3-540-56484-5

T. Nitzberg and . Shiota, Nonlinear image filtering with edge and corner enhancement, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.8, p.8266833, 1992.
DOI : 10.1109/34.149593

. Nordstrr-om, Biased anisotropic diiusion -a unifed regularization and diiusion approach to edge detection, Image Vision Comput, vol.8, p.3188327, 1990.

L. Osher and . Rudin, Feature-oriented image enhancement using shock lters, SIAM J. Numer. Anal, vol.27, p.9199940, 1990.

L. Osher and . Rudin, Shock and Other Nonlinear Filtering Applied to Image Processing, Proc. SPIE Application of Digital Image Processing XIV, p.16622, 1991.

J. Osher and . Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, p.12249, 1988.
DOI : 10.1016/0021-9991(88)90002-2

P. Erona and J. Malik, Scale-space and edge detection using anisotropic diiusion, Proc. IEEE Comp. Soc. Workshop on Computer Vision, p.16622, 1987.

P. Erona and J. Malik, A network for multiscale image segmentation, Proc. IEEE Int. Symp. Circuit and Systems ISCAS-88, p.256552568, 1988.

P. Erona and J. Malik, Scale-space and edge detection using anisotropic diiusion, IEEE Trans. Pattern Anal. & Machine Intell, vol.12, p.6299639, 1990.

P. Erona, T. Shiota, and J. Malik, Anisotropic diiusion, Geometry-driven diiusion in computer vision, 1994.

J. Pineda, Generalization of Backpropagation to Recurrent and Higher Order Neural Networks, Neural Information Processing Systems Conference, p.6022611, 1987.

B. Price, P. , and A. Oosterlinck, Application of reaction-diiusion equations to image processing, Proc. 3rd Interna. Conf. Image Processing and its Applications, p.49953, 1989.

. Rudin, Images, numerical analysis of singularities, and shock lters, 1987.

L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, p.2599268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

D. Rumelhart, G. Hinton, and R. Williams, Learning Internal Representations by Error Propagation, Parallel Distribued P r ocessing, p.2199230, 1986.
DOI : 10.1016/B978-1-4832-1446-7.50035-2

J. S. Saint-marc, G. Chen, and . Medioni, Adaptive smoothing: a general tool for early vision, IEEE Trans. Pattern Anal. & Machine Intell, vol.13, p.5144529, 1990.

A. Sapiro and . Tannenbaum, AAne invariant scalespace, Int. J. of Computer Vision, vol.11, p.24444, 1993.

A. Sapiro and . Tannenbaum, On AAne Plane Curve E v olution, J. of Functional Analysis, vol.1191, p.799119, 1993.

A. Sapiro and . Tannenbaum, Area and length preserving geometric invariant scale-space, IEEE Trans. Pattern Anal. & Machine Intell, vol.17, p.67772, 1995.

. Shah, A Common Framework for Curve E v olution, Segmentation and Anisotropic Diiusion, IEEE Conf. on Computer Vision and Pattern Recognition, 1996.

. Shah, Curve E v olution and Segmentation Functionals: Application to Color Images, Proc. third IEEE Int. Conf. Image Processing, p.96, 1996.

M. Ter-haar-romeny, Geometry-driven diiusion in computer vision, 1994.

M. Ter-haar-romeny, L. M. Florack, J. J. Koenderink, and M. A. Viergever, Scale space: Its natural operators and diierential invariants Information processing in medical imaging, Lecture Notes in Comp. Science, p.511, 1991.

J. Van-hemmen, Spin-glass models of a neural network, Physical Review A, vol.34, issue.4, pp.34355-3445, 1986.
DOI : 10.1103/PhysRevA.34.3435

J. Weickert, Anisotropic Diiusion Filters for Image Processing: Based Quality Control, 1993.

J. Weickert, Scale-space properties of nonlinear diiusion ltering with a diiusion tensor, 1994.

J. Weickert, Multiscale texture enhancement, Computer analysis of images and patterns, p.2300237, 1995.
DOI : 10.1007/3-540-60268-2_301

J. Weickert, Anisotropic Diiusion in Image Processing, 1996.

M. A. Weickert, B. M. Viergever, and . Ter-haar-romeny, Conservative image transformations with restoration and scale-space properties, Proceedings of 3rd IEEE International Conference on Image Processing, pp.4655468-96, 1996.
DOI : 10.1109/ICIP.1996.559534

G. Whitaker and . Gerig, Vector-valued diiusion. B.M. ter Haar Romeny Ed., Geometry-driven diiusion in computer vision, 1994.

T. Whitaker, Geometry-Limited Diiusion in the characterization of Geometric Patches in Images, CVGIP: Image Understanding, p.1111120, 1993.

T. Whitaker and M. A. Abidi, A Weighted Sum of Curvatures for Image Denoising : A Comparative Analysis, IEEE Trans. Image Processing, p.page submitted, 1996.

T. Whitaker and S. M. Pizer, A m ultiscale approach t o n o n uniform diiusion, CVGIP: Image Understanding, p.999110, 1993.

. Wiggins, Global Biiurcations and Chaos: Analytic Methods, 1988.

P. Witkin, Scale-space ltering, Proc. of IJCAI, p.101991021, 1983.

B. Xu, Global Convergence and Asymptotic Stability of Asymmetric Hoppeld Neural Networks, Journal of Mathematical Analysis and Applications, vol.191, pp.4055-427, 1995.

Y. and T. Poggio, Scaling theorems for zero crossings, IEEE Trans. Pattern Anal. & Machine Intell, vol.8, 1986.