@. D. Tschumperlé and R. Deriche, Orthonormal Vector Sets Regularization with PDE's and Applications, International Journal of Computer Vision), 2002.

@. C. Chefd-'hotel, D. Tschumperlé, R. Deriche, and O. Faugeras, Manifold Constrained Partial Differential Equations and Geometric Integration Methods in Image Processing

@. D. International-conference-papers, R. Tschumperlé, and . Deriche, Constrained and Unconstrained PDEs for Vector Image Restoration, Proceedings of SCIA'2001 (Scandinavian Conference on Image Analysis), pp.153-160

@. D. Tschumperlé and R. Deriche, Regularization of orthonormal vector sets using coupled PDE's, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp.3-10
DOI : 10.1109/VLSM.2001.938875

@. D. Tschumperlé and R. Deriche, Diffusion tensor regularization with constraints preservation, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001
DOI : 10.1109/CVPR.2001.990631

@. D. Tschumperlé and R. Deriche, Constrained Flows of Matrix-Valued Functions : Application to Diffusion Tensor Reg- ularization, Proceedings of ECCV'2002 (European Conference on Computer Vision)

@. D. Tschumperlé and R. Deriche, Vector-valued image regularization with PDE's: a common framework for different applications, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings., 2003.
DOI : 10.1109/CVPR.2003.1211415

@. D. Tschumperlé and R. Deriche, DT-MRI Images : Estimation, Regularization and Application. To appear in EURO- CAST', Neuroinformatics and Neuroimaging, 2003.

@. D. National-conference-papers, R. Tschumperlé, and . Deriche, Restauration d'images vectorielles par EDP, Proceedings of RFIA'2000 (Conférence sur la Reconnaissance des Formes et l'Intelligence Artificielle)

@. D. Tschumperlé and R. Deriche, Régularisation par EDP de Champs de Vecteurs Orthonormes et Applications, Proceedings of RFIA'2002 (Conférence sur la Reconnaissance des Formes et l'Intelligence Artificielle)

@. D. Tschumperlé and R. Deriche, EDP, Images multivalues Contraintes et Applications, Proceedings of " Le traitement

R. Report, @. D. Tschumperlé, and R. Deriche, Vector-Valued Image Regularization with PDE's : A Common Framework for Different Applications, INRIA Research Report No Projet ODYSEE, vol.4657, 2002.

J. F. Abramatic and L. M. Silverman, Non linear restoration of noisy images, IEEE Trans. Patern Analysis and Machine Intelligence, vol.4, issue.2, pp.141-149, 1982.

L. Alvarez, R. Deriche, T. Papadopoulo, and J. Sanchez, Symmetrical dense optical flow estimation with occlusion detection, proceedings of ECCV'02, pp.721-735

L. Alvarez, R. Deriche, and F. Santana, Recursivity and PDE's in image processing, Proceedings 15th International Conference on Pattern Recognition, pp.242-248, 2000.

L. Alvarez, R. Deriche, J. Weickert, and J. , Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and Scale-Space Based Approach, Journal of Visual Communication and Image Representation, vol.13, issue.1-2, 2000.
DOI : 10.1006/jvci.2001.0482

URL : https://hal.archives-ouvertes.fr/inria-00072780

L. Alvarez, J. Esclarín, M. Lefebure, and J. Sánchez, A pde model for computing the optical flow, Proceedings of CEDYA XVI, 1999.

L. Alvarez, F. Guichard, P. L. Lions, and J. M. , Axioms and fundamental equations of image processing. Archive for Rational Mechanics and Analysis, pp.199-257, 1993.

L. Alvarez, P. L. Lions, and J. M. , Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.845-866, 1992.
DOI : 10.1137/0729052

L. Alvarez and L. Mazorra, Signal and Image Restoration Using Shock Filters and Anisotropic Diffusion, SIAM Journal on Numerical Analysis, vol.31, issue.2, pp.590-605, 1994.
DOI : 10.1137/0731032

L. Alvarez, J. Weickert, and J. , A Scale-Space Approach to Nonlocal Optical Flow Calculations
DOI : 10.1007/3-540-48236-9_21

L. Alvarez, J. Weickert, and J. , Reliable estimation of dense optical flow fields with large displacements, International Journal of Computer Vision, vol.39, issue.1, pp.41-56, 2000.
DOI : 10.1023/A:1008170101536

Y. Amit, A Nonlinear Variational Problem for Image Matching, SIAM Journal on Scientific Computing, vol.15, issue.1, 1994.
DOI : 10.1137/0915014

H. C. Andrews and B. R. Hunt, Digital Image Restoration. Signal Processing, N.J, 1977.

G. Aubert, M. Barlaud, O. Faugeras, and J. Besson, Image segmentation using active contours: calculus of variations or shape optimization?, SIAM Journal on Applied Mathematics, 2002.

G. Aubert, L. Blanc-féraud, M. Barlaud, and P. Charbonnier, A deterministic algorithm for edge-preserving computed imaging using Legendre transform, Proceedings of the 12th IAPR International Conference on Pattern Recognition (Cat. No.94CH3440-5), pp.188-191, 1994.
DOI : 10.1109/ICPR.1994.577154

G. Aubert, R. Deriche, and P. Kornprobst, Computing Optical Flow via Variational Techniques, SIAM Journal on Applied Mathematics, vol.60, issue.1, pp.156-182, 1999.
DOI : 10.1137/S0036139998340170

G. Aubert and P. Kornprobst, A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$, SIAM Journal on Mathematical Analysis, vol.30, issue.6, pp.1282-1308, 1999.
DOI : 10.1137/S003614109834123X

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Applied Mathematical Sciences, vol.147, 2002.

D. Barash, Bilateral filtering and anisotropic diffusion : Towards a unified viewpoint, 2000.

F. Barbaresco, Spatial denoising of statistical parameters estimation by beltrami diffusion on embedding siegel space, 2002.

M. Barlaud and C. Labit, Compression et codage des images et des vidéos, 2002.

M. Bart and . Ter-haar-romeny, Geometry-driven diffusion in computer vision. Computational imaging and vision, 1994.

J. Becker, T. Preusser, and M. Rumpf, PDE methods in flow simulation post processing, Computing and Visualization in Science, vol.3, issue.3, pp.159-167, 2000.
DOI : 10.1007/PL00013547

M. Bertalmio, L. T. Cheng, S. Osher, and G. Sapiro, Variational Problems and Partial Differential Equations on Implicit Surfaces, Journal of Computational Physics, vol.174, issue.2, 2000.
DOI : 10.1006/jcph.2001.6937

M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.417-424, 2000.
DOI : 10.1145/344779.344972

URL : https://hal.archives-ouvertes.fr/hal-00522652

M. Bertalmio, G. Sapiro, L. Cheng, and S. Osher, Variational problems and PDE's on implicit surfaces, IEEE Workshop on Variational and Level Set Methods VLSM'01, pp.186-193

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, Robust anisotropic diffusion, Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis, pp.421-432, 1998.
DOI : 10.1109/83.661192

L. Blanc-feraud, P. Charbonnier, G. Aubert, and M. Barlaud, Nonlinear image processing: modeling and fast algorithm for regularization with edge detection, Proceedings., International Conference on Image Processing, pp.474-477, 1995.
DOI : 10.1109/ICIP.1995.529749

P. Blomgren, Color TV: total variation methods for restoration of vector-valued images, IEEE Transactions on Image Processing, vol.7, issue.3, 1998.
DOI : 10.1109/83.661180

P. Blomgren and T. F. Chan, Color TV: total variation methods for restoration of vector-valued images, Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis, pp.304-309, 1998.
DOI : 10.1109/83.661180

J. Bride and P. Meer, Global registration via direct methods: a statistical approach, Proceedings of CVPR'01, 2001.

D. Buerkle, T. Preusser, and M. Rumpf, Transport and diffusion in timedependent flow visualization, Proceedings IEEE Visualization, 2001.

V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, pp.61-79, 1997.
DOI : 10.1109/ICCV.1995.466871

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Introduction To The Special Issue On Partial Differential Equations And Geometry-driven Diffusion In Image Processing And Analysis, IEEE Transactions on Image Processing, vol.7, issue.3, pp.269-273, 1998.
DOI : 10.1109/TIP.1998.661176

A. Chambolle and P. L. Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, vol.76, issue.2, pp.167-188, 1997.
DOI : 10.1007/s002110050258

T. Chan, S. H. Kang, and J. Shen, Euler's elastica and curvature based inpainting, SIAM J. Appl. Math, 2002.

T. Chan and J. Shen, Variational restoration of non-flat image features : Models and algorithms, Research Report. Computational and applied mathematics department of mathematics Los Angeles, 1999.

T. Chan and J. Shen, Mathematical models for local deterministic inpaintings, 2000.

T. Chan and J. Shen, Non-texture inpaintings by curvature-driven diffusions (cdd), 2000.

T. Chan and L. Vese, Image segmentation using level sets and the piecewiseconstant Mumford?Shah model, 2000.

T. F. Chan, S. H. Kang, and J. Shen, Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color Models, Journal of Visual Communication and Image Representation, vol.12, issue.4, 2000.
DOI : 10.1006/jvci.2001.0491

T. F. Chan and J. Shen, Non-texture inpainting by curvature-driven diffusions (cdd)

P. Charbonnier, G. Aubert, M. Blanc-féraud, and M. Barlaud, Two deterministic half-quadratic regularization algorithms for computed imaging, Proceedings of 1st International Conference on Image Processing, pp.168-172, 1994.
DOI : 10.1109/ICIP.1994.413553

P. Charbonnier, L. Blanc-féraud, G. Aubert, and M. Barlaud, Deterministic edge-preserving regularization in computed imaging, IEEE Transactions on Image Processing, vol.6, issue.2, pp.298-311, 1997.
DOI : 10.1109/83.551699

P. Charbonnier, L. Blanc-feraud, and M. Barlaud, Noisy image restoration using multiresolution markov random fields, Journal of Visual Communication and Image Representation, vol.3, issue.4, pp.338-346, 1992.
DOI : 10.1016/1047-3203(92)90037-T

C. Chefd-'hotel, D. Tschumperlé, R. Deriche, and O. Faugeras, Constrained flows on matrix-valued functions : application to diffusion tensor regularization, Proceedings of ECCV'02, 2002.

C. Chefd-'hotel, G. Hermosillo, and O. Faugeras, A variational approach to multimodal image matching, IEEE Workshop on Variational and Level Set Methods VLSM'01, pp.21-28
URL : https://hal.archives-ouvertes.fr/inria-00072513

M. T. Chu, Constructing Symmetric Nonnegative Matrices with Prescribed Eigenvalues by Differential Equations, SIAM Journal on Mathematical Analysis, vol.22, issue.5, 1990.
DOI : 10.1137/0522088

M. T. Chu, A list of matrix flows with applications, 1990.
DOI : 10.1090/fic/003/07

M. T. Chu, Matrix differential equations: a continuous realization process for linear algebra problems, Nonlinear Analysis: Theory, Methods & Applications, vol.18, issue.12, 1990.
DOI : 10.1016/0362-546X(92)90157-A

M. T. Chu, On a differential equation approach to the weighted orthogonal procrustes problem, 1990.

M. Clerc, O. Faugeras, R. Keriven, J. Kybic, and T. Papadopoulo, A level set method for the inverse eeg/meg problem, Proceedings of the 8th International Conference on Functional Mapping of the Human Brain, 2002.

I. Cohen, Nonlinear variational method for optical flow computation, Scandinavian Conference on Image Analysis, pp.523-530, 1993.
URL : https://hal.archives-ouvertes.fr/inria-00615717

L. D. Cohen, On Active Contour Models, 1989.
DOI : 10.1007/978-3-642-77225-2_31

URL : https://hal.archives-ouvertes.fr/inria-00075484

C. Connolly and T. Fliess, A study of efficiency and accuracy in the transformation from RGB to CIELAB color space, IEEE Transactions on Image Processing, vol.6, issue.7, 1997.
DOI : 10.1109/83.597279

G. H. Cottet and L. Germain, Image processing through reaction combined with nonlinear diffusion, Mathematics of Computation, vol.61, issue.204, pp.61659-673, 1993.
DOI : 10.1090/S0025-5718-1993-1195422-2

O. Coulon, D. C. Alexander, and S. R. Arridge, A geometrical approach to 3d diffusion tensor magnetic resonance image regularisation, 2001.

O. Coulon, D. C. Alexander, and S. R. Arridge, A Regularization Scheme for Diffusion Tensor Magnetic Resonance Images, XVIIth International Conferenceon Information Processing in Medical Imaging, 2001.
DOI : 10.1007/3-540-45729-1_8

R. Deriche, Using Canny's criteria to derive a recursively implemented optimal edge detector, International Journal of Computer Vision, vol.1, issue.2, pp.167-187, 1987.
DOI : 10.1007/BF00123164

R. Deriche, Fast algorithms for low-level vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.1, issue.12, pp.78-88, 1990.

R. Deriche, Recursively Implementing the Gaussian and Its Derivatives, Proc. Second International Conference On Image Processing, pp.263-267, 1992.

R. Deriche, Recursively implementing the gaussian and its derivatives, 1993.

R. Deriche and O. Faugeras, Les EDP en traitement des images et vision par ordinateur A more complete version of this Research Report has appeared in the French Revue, Traitement du Signal, vol.13, issue.6, 1995.

R. Deriche, P. Kornprobst, and G. Aubert, Optical-flow estimation while preserving its discontinuities: A variational approach, Proceedings of the 2nd Asian Conference on Computer Vision ACCV'95, pp.71-80
DOI : 10.1007/3-540-60793-5_63

F. Devernay, Vision stéréoscopique et propriétés différentielles des surfaces, 1997.

U. Diewald, T. Preusser, and M. Rumpf, Anisotropic diffusion in vector field visualization on Euclidean domains and surfaces, IEEE Transactions on Visualization and Computer Graphics, vol.6, issue.2, pp.139-149, 2000.
DOI : 10.1109/2945.856995

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

O. Faugeras, F. Clément, R. Deriche, R. Keriven, T. Papadopoulo et al., The inverse EEG and MEG problems: The adjoint space approach I: The continuous case, 1999.

O. Faugeras, Q. T. Luong, and T. Papadopoulo, The Geometry of Multiple Images, 2001.

O. D. Faugeras and G. Hermosillo, Well-posedness of eight problems of multimodal statistical image-matching, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072352

L. Florack, Image Structure, 1997.
DOI : 10.1007/978-94-015-8845-4

G. B. Folland, Fourier Analysis and its Applications. The Wadsworth & Brooks, 1992.

M. A. Förstner and E. Gülch, A fast operator for detection and precise location of distinct points, corners and centers of circular features, Proceedings of the Intercommission Workshop of the International Society for Photogrammetry and Remote Sensing, 1987.

B. R. Frieden, Restoring with Maximum Likelihood and Maximum Entropy*, Journal of the Optical Society of America, vol.62, issue.4, pp.511-518, 1972.
DOI : 10.1364/JOSA.62.000511

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, issue.6, pp.721-741, 1984.

S. Geman and D. E. Mcclure, Bayesian Image Analysis, Amer. Statist. Assoc, pp.12-18, 1985.
DOI : 10.1007/978-3-642-82657-3_30

G. Gerig, O. Kubler, R. Kikinis, and F. Jolesz, Nonlinear anisotropic filtering of MRI data, IEEE Transactions on Medical Imaging, vol.11, issue.2, pp.221-231, 1992.
DOI : 10.1109/42.141646

G. Gilboa, N. Sochen, and Y. Zeevi, Forward-and-backward diffusion processes for adaptative image enhancement and denoising, IEEE Transactions on Image Processing, 2002.

G. Gilboa, N. Sochen, and Y. Zeevi, Regularized Shock Filters and Complex Diffusion, Proceedings of ECCV'02, pp.399-413
DOI : 10.1007/3-540-47969-4_27

G. Gilboa, N. Sochen, and Y. Y. Zeevi, Complex Diffusion Processes for Image Filtering, Proceedings of ECCV'02

G. H. Golub and C. F. Van-loan, Matrix computations, 1983.

J. Gomes, Implicit representations of evolving manifolds in computer vision, 2001.

A. Gouze, M. Antonini, and M. Barlaud, Quincunx filtering lifting scheme for image coding, SPIE, Visual Communications and Image Processing, 1999.

G. H. Granlund and H. Knutsson, Signal Processing for Computer Vision, 1995.
DOI : 10.1007/978-1-4757-2377-9

P. J. Green, Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Transactions on Medical Imaging, vol.9, issue.1, pp.84-93, 1990.
DOI : 10.1109/42.52985

J. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations, 1923.

A. B. Hamza, G. R. Unal, and H. Krim, Towards a unified estimation theme: probabilistic vs. variational. Signal Processing Magazine Special Issue, 2002.

G. Hermosillo, O. Faugeras, and J. Gomes, Unfolding the Cerebral Cortex Using Level Set Methods, Scale-Space Theories in Computer Vision, pp.58-69, 1999.
DOI : 10.1007/3-540-48236-9_6

G. Hermosillo, Variational Methods for Multimodal Image Matching INRIA, The document is accessible at ftp://ftp-sop.inria.fr /robotvis, 2002.

B. K. Horn, Height and gradient from shading, International Journal of Computer Vision, vol.238, issue.1, pp.37-75, 1990.
DOI : 10.1007/BF00056771

B. R. Hunt, The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer, IEEE Transactions on Computers, vol.22, issue.9, pp.805-812, 1973.
DOI : 10.1109/TC.1973.5009169

S. Jehan-besson, M. Barlaud, and G. Aubert, Video object segmentation using Eulerian region-based active contours, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, pp.353-360, 2001.
DOI : 10.1109/ICCV.2001.937540

J. Consortium, W. Page, and K. Kanatani, Automatic singularity test for motion analysis by an information criterion, Proceedings of the 4th European Conference on Computer Vision, pp.697-708, 1996.

M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, First International Conference on Computer Vision, pp.259-268, 1987.
DOI : 10.1007/BF00133570

S. Kichenassamy, The Perona--Malik Paradox, SIAM Journal on Applied Mathematics, vol.57, issue.5, pp.1328-1342, 1997.
DOI : 10.1137/S003613999529558X

URL : https://hal.archives-ouvertes.fr/hal-00002600

R. Kimmel, R. Malladi, and N. Sochen, Image processing via the beltrami operator, Proceedings of the 3rd Asian Conference on Computer Vision, pp.574-581, 1998.
DOI : 10.1007/3-540-63930-6_169

R. Kimmel, R. Malladi, and N. Sochen, Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images, International Journal of Computer Vision, vol.39, issue.2, pp.111-129, 2000.
DOI : 10.1023/A:1008171026419

R. Kimmel and N. Sochen, Geometric-Variational Approach for Color Image Enhancement and Segmentation, Scale-Space Theories in Computer Vision, Second International Conference, Scale-Space'99, volume 1682 of Lecture Note in Computer Science, pp.295-305, 1999.
DOI : 10.1007/3-540-48236-9_26

R. Kimmel and N. Sochen, Orientation diffusion or how to comb a porcupine Accepted to special issue on PDEs in Image Processing, Journal of Visual Communication and Image Representation, 2000.

R. Kimmel and N. Sochen, Orientation Diffusion or How to Comb a Porcupine, Journal of Visual Communication and Image Representation, vol.13, issue.1-2, 2001.
DOI : 10.1006/jvci.2001.0501

J. J. Koenderink, The structure of images, Biological Cybernetics, vol.27, issue.269, pp.363-370, 1984.
DOI : 10.1007/BF00336961

P. Kornprobst, Calcul de flot optique avec préservation des discontinuités

P. Kornprobst, ContributionsàContributions`Contributionsà la Restauration d'Images etàet`età l'Analyse de Séquences: Approches Variationnelles et Solutions de Viscosité, 1998.

P. Kornprobst, R. Deriche, and G. Aubert, Image restoration via PDE's, First Annual Symposium on Enabling Technologies for Law Enforcement and Security - SPIE Conference 2942 : Investigative Image Processing, 1996.

P. Kornprobst, R. Deriche, and G. Aubert, Nonlinear operators in image restoration, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.325-331, 1997.
DOI : 10.1109/CVPR.1997.609344

P. Kornprobst, R. Deriche, and G. Aubert, EDP, débruitage et réhaussement en traitement d'image: Analyse et contributions, 11ème Congrés RFIA, pp.277-286, 1998.

A. Koschan, A comparative study on color edge detection, Proceedings of the 2nd Asian Conference on Computer Vision, ACCV'95, pp.574-578

D. and L. Bihan, Methods and Applications of Diffusion MRI, Magnetic Resonance Imaging and Spectroscopy in Medicine and Biology, 2000.
DOI : 10.1002/9780470034590.emrstm0309

Y. Leedan and P. Meer, Heteroscedastic regression in computer vision: problems with bilinear constraint, The International Journal of Computer Vision, vol.37, issue.2, pp.1-24, 2000.

M. Lefébure and L. Cohen, Optical Flow and Image Registration: A New Local Rigidity Approach for Global Minimization, Energy Minimization Methods in Computer Vision and Pattern Recognition, 2001.
DOI : 10.1007/3-540-44745-8_39

T. Lindeberg, Scale-Space Theory in Computer Vision, 1994.
DOI : 10.1007/978-1-4757-6465-9

L. M. Lorigo, O. D. Faugeras, W. E. Grimson, R. Keriven, R. Kikinis et al., CURVES: Curve evolution for vessel segmentation, Medical Image Analysis, vol.5, issue.3, pp.195-206, 2001.
DOI : 10.1016/S1361-8415(01)00040-8

L. Lucido, R. Deriche, L. Alvarez, and V. Rigaud, Sur quelques schémas numériques de résolution d'´ equations aux dérivées partielles pour le traitement d'images, 1997.

G. Medioni, M. S. Lee, and C. K. Tang, A Computational Framework for Segmentation and Grouping, 2000.

J. M. Morel and S. Solimini, Segmentation of image: by variational methods: A constructive approach, Revista Matem??tica Complutense, vol.1, issue.1, pp.169-182, 1988.
DOI : 10.5209/rev_REMA.1988.v1.n1.18194

D. Mumford and J. Shah, Boundary detection by minimizing functionals, Proceedings of the International Conference on Computer Vision and Pattern Recognition, pp.22-26, 1985.

H. Nagel, On the estimation of optical flow: Relations between different approaches and some new results, Artificial Intelligence, vol.33, issue.3, pp.299-324, 1987.
DOI : 10.1016/0004-3702(87)90041-5

M. Ng, R. Chan, and W. Tang, A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions, SIAM Journal on Scientific Computing, vol.21, issue.3, pp.851-866, 2000.
DOI : 10.1137/S1064827598341384

M. Nielsen, L. Florack, and R. Deriche, Regularization, scale-space, and edge detection filters, Related ECCV:96 article available, pp.291-308, 1997.
DOI : 10.1007/3-540-61123-1_128

M. Nikolova, Local Strong Homogeneity of a Regularized Estimator, SIAM Journal on Applied Mathematics, vol.61, issue.2, pp.633-658, 2000.
DOI : 10.1137/S0036139997327794

M. Nikolova and M. Ng, Fast image reconstruction algorithms combining halfquadratic regularization and preconditioning, Proceedings of the International Conference on Image Processing, 2001.

S. Osher and R. Fedkiw, The Level Set Method and Dynamic Implicit Surfaces, 2002.

S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision and Graphics, 2002.

S. Osher and L. I. Rudin, Feature-Oriented Image Enhancement Using Shock Filters, SIAM Journal on Numerical Analysis, vol.27, issue.4, pp.919-940, 1990.
DOI : 10.1137/0727053

T. Papadopoulo and M. I. Lourakis, Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications, Research Report, vol.3961, 2000.
DOI : 10.1007/3-540-45054-8_36

URL : https://hal.archives-ouvertes.fr/inria-00072686

N. Paragios and R. Deriche, ARTemis: A Geodesic Active Contour Tracker, IEEE Conference on Computer Vision and Pattern Recognition, the demo session, 1998.

N. Paragios and R. Deriche, A PDE-based level-set approach for detection and tracking of moving objects, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.1139-1145, 1998.
DOI : 10.1109/ICCV.1998.710859

URL : https://hal.archives-ouvertes.fr/inria-00073515

N. Paragios and R. Deriche, Geodesic active contours for supervised texture segmentation, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149), 1999.
DOI : 10.1109/CVPR.1999.784715

N. Paragios and R. Deriche, Geodesic active contours and level sets for the detection and tracking of moving objects, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.3, pp.266-280, 2000.
DOI : 10.1109/34.841758

N. Paragios and R. Deriche, Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision, Journal of Visual Communication and Image Representation, vol.13, issue.1-2, 2001.
DOI : 10.1006/jvci.2001.0475

N. Paragios and R. Deriche, Geodesic active regions and level set methods forsupervised texture segmentation, International Journal of Computer Vision, vol.46, issue.3, p.223, 2002.
DOI : 10.1023/A:1014080923068

N. Paragios, Geodesic Active Regions and Level Set Methods: Contributions and Applications on Artificial Vision, 2000.

A. Pardo and G. Sapiro, Vector probability diffusion, Proceedings of the International Conference on Image Processing, 2000.

X. Pennec, Registration of uncertain geometric features: Estimating the pose and its accuracy, Proceedings of the First Image Registration Workshop, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00615789

P. Perona, Orientation diffusions, IEEE Transactions on Image Processing, vol.7, issue.3, pp.457-467, 1998.
DOI : 10.1109/83.661195

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

. Poseidon, The lifeguards third eye

C. Poupon, Détection des faisceaux de fibres de la substance blanche pour l'´ etude de la connectivité anatomique cérébrale, 1999.

C. Poupon, J. Mangin, V. Frouin, J. Regis, F. Poupon et al., Regularization of MR diffusion tensor maps for tracking brain white matter bundles, Medical Image Computing and Computer-Assisted Intervention-MICCAI'98, number 1496 in Lecture Notes in Computer Science, pp.489-498, 1998.
DOI : 10.1109/TPAMI.1984.4767596

C. A. Poynton, Poynton's colour faq (www.inforamp.net/ poynton) Web page, 1995.

E. Prados, O. Faugeras, and E. Rouy, Shape from Shading and Viscosity Solutions, 2002.
DOI : 10.1007/3-540-47967-8_53

URL : https://hal.archives-ouvertes.fr/inria-00394240

E. Prados, O. Faugeras, and E. Rouy, Shape from Shading and Viscosity Solutions, Proceedings of ECCV'02, 2002.
DOI : 10.1007/3-540-47967-8_53

URL : https://hal.archives-ouvertes.fr/inria-00394240

. Realviz, Web-site

A. Roche, G. Malandain, X. Pennec, and N. Ayache, Multimodal image registration by maximization of the correlation ratio, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00073311

M. Rousson and R. Deriche, A variational framework for active and adaptative segmentation of vector valued images, Workshop on Motion and Video Computing, 2002. Proceedings., 2002.
DOI : 10.1109/MOTION.2002.1182214

URL : https://hal.archives-ouvertes.fr/inria-00072073

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

G. Sapiro, Vector-valued active contours, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.680-685, 1996.
DOI : 10.1109/CVPR.1996.517146

G. Sapiro, Color Snakes, Computer Vision and Image Understanding, vol.68, issue.2, 1997.
DOI : 10.1006/cviu.1997.0562

G. Sapiro, Geometric Partial Differential Equations and Image Analysis, 2001.
DOI : 10.1017/CBO9780511626319

G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images with applications to color filtering, IEEE Transactions on Image Processing, vol.5, issue.11, pp.1582-1585, 1996.
DOI : 10.1109/83.541429

H. Scharr and J. Weickert, An Anisotropic Diffusion Algorithm with Optimized Rotation Invariance, Mustererkennung, pp.460-467, 2000.
DOI : 10.1007/978-3-642-59802-9_58

J. A. Sethian, Level Set Methods, 1996.

J. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996.
DOI : 10.1109/CVPR.1996.517065

J. Shah, Curve evolution and segmentation functionals: application to color images, Proceedings of 3rd IEEE International Conference on Image Processing, pp.461-464, 1996.
DOI : 10.1109/ICIP.1996.559533

N. Sochen, On affine invariance in the Beltrami framework for vision, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp.51-56
DOI : 10.1109/VLSM.2001.938881

N. Sochen, R. Kimmel, and A. M. Bruckstein, Diffusions and confusions in signal and image processing, Journal of Mathematical Imaging and Vision, vol.14, issue.3, pp.195-209, 2001.
DOI : 10.1023/A:1011277827470

N. Sochen, R. Kimmel, and R. Malladi, From high energy physics to low level vision, 1996.

N. Sochen, R. Kimmel, and R. Malladi, A general framework for low level vision, IEEE Transactions on Image Processing, vol.7, issue.3, pp.310-318, 1998.
DOI : 10.1109/83.661181

I. Sokolnikoff, Tensor Analysis ? Theory and Applications, 2n Ed, 1964.

B. Tang, G. Sapiro, and V. Caselles, Diffusion of general data on non-flat manifolds via harmonic maps theory : The direction diffusion case, International Journal of Computer Vision, vol.36, issue.2, pp.149-161, 2000.
DOI : 10.1023/A:1008152115986

S. Teboul, L. Blanc-féraud, G. Aubert, and M. Barlaud, Variational approach for edge-preserving regularization using coupled PDEs, IEEE Transactions on Image Processing, vol.7, issue.3, pp.387-397, 1998.
DOI : 10.1109/83.661189

A. N. Tikhonov, Regularization of incorrectly posed problems, Soviet. Math. Dokl, vol.4, pp.1624-1627, 1963.

C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.839-846, 1998.
DOI : 10.1109/ICCV.1998.710815

A. Trouvé and L. Younes, Mise en correspondance par difféomorphismes en une dimension: définition et maximisation de fonctionnelles, 12ème Congrès RFIA'00

D. Tschumperlé and R. Deriche, Restauration d'images vectorielles par EDP, 12ème Congrès RFIA'00, pp.247-256

D. Tschumperlé and R. Deriche, Constrained and unconstrained pde's for vector image restoration, Proceedings of the 10th Scandinavian Conference on Image Analysis, pp.153-160, 2001.

D. Tschumperlé and R. Deriche, Diffusion tensor regularization with constraints preservation, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, 2001.
DOI : 10.1109/CVPR.2001.990631

D. Tschumperlé and R. Deriche, Regularization of orthonormal vector sets using coupled PDE's, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp.3-10
DOI : 10.1109/VLSM.2001.938875

D. Tschumperlé and R. Deriche, Diffusion PDEs on vector-valued images, IEEE Signal Processing Magazine, vol.19, issue.5, pp.16-25, 2002.
DOI : 10.1109/MSP.2002.1028349

D. Tschumperlé and R. Deriche, Orthonormal Vector Sets Regularization with PDE's and Aplications, Internation Journal of Computer Vision (IJCV, Special Issue VLSM, 2002.

D. Tschumperlé and R. Deriche, Régularisation par EDP de champs de vecteurs orthonormés et applications, 13ème Congrès RFIA'02, 2002.

H. Urakawa, Calculus of Variations and Harmonic Maps, Translations of Mathematical Monographs, vol.132, 1993.

B. Vemuri, Y. Chen, M. Rao, T. Mcgraw, T. Mareci et al., Fiber tract mapping from diffusion tensor MRI, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001.
DOI : 10.1109/VLSM.2001.938885

L. A. Vese and S. Osher, -Harmonic Flows and Applications to Image Processing, SIAM Journal on Numerical Analysis, vol.40, issue.6, 2001.
DOI : 10.1137/S0036142901396715

URL : https://hal.archives-ouvertes.fr/inria-00590199

P. Viola, Alignement by Maximisation of Mutual Information, 1995.

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

J. Weickert, Theoretical Foundations of Anisotropic Diffusion in Image Processing, Computing Supplement, vol.11, pp.221-236, 1996.
DOI : 10.1007/978-3-7091-6586-7_13

J. Weickert, Coherence-enhancing diffusion of colour images, 7th National Symposium on Pattern Recognition and Image Analysis, 1997.
DOI : 10.1016/S0262-8856(98)00102-4

J. Weickert, A review of nonlinear diffusion filtering. Scale-Space Theory in Computer Vision, Lecture Notes in Comp, Science, vol.1252, pp.3-28, 1997.

J. Weickert, Anisotropic Diffusion in Image Processing, 1998.

J. Weickert and B. Benhamouda, A semidiscrete nonlinear scale-space theory and its relation to the Perona?Malik paradox Advances in Computer Vision, pp.1-10, 1997.

J. Weickert and B. Benhamouda, Why the peronamalik filter works, 1997.

J. Weickert and T. Brox, Diffusion and regularization of vector- and matrix-valued images, 2002.
DOI : 10.1090/conm/313/05378

J. Weickert and C. Schnörr, A theoretical framework for convex regularizers in pde-based computation of image motion, International Journal of Computer Vision, vol.45, issue.3, pp.245-264, 2001.
DOI : 10.1023/A:1013614317973

P. Wesseling, Principles of Computational Fluid Dynamics, 2000.
DOI : 10.1007/978-3-642-05146-3

A. P. Witkin, SCALE-SPACE FILTERING, International Joint Conference on Artificial Intelligence, pp.1019-1021, 1983.
DOI : 10.1016/B978-0-08-051581-6.50036-2

C. Wurster, Computers : An illustrated History. Unknown, 2002.

S. and D. Zenzo, A note on the gradient of a multi-image, Computer Vision, Graphics, and Image Processing, pp.116-125, 1986.
DOI : 10.1016/0734-189X(86)90223-9