Publications of Gilles Aubert
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G. Aubert-R. Tahraoui. Théorèmes d'existence en calcul
des variations; C.RA.S, T 285, 1977.
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G. Aubert-R. Tahraoui. Théorèmes d'existence pour des
problèmes du calcul des variations du type... ; Journal of Differential
Equations, Vol 133, 1 ,1977.
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G. Aubert-R. Tahraoui. Sur la minimisation d'une fonctionnelle non convexe,
non différentiable en dimension 1; Bolletino UMI, 5, 17B, 1980.
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G. Aubert-R. Tahraoui. Quelques remarques sur un problème d'élasticité non linéaire; Annales de la Faculté des Sciences de Toulouse,
Vol 4, 1982.
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G. Aubert-R. Tahraoui. Fermeture de certains ensembles de contrainte
en élasticité non linéaire plane; C.R.A.S, T 290,
1980.
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G. Aubert-R. Tahraoui. Sur la fermeture de certains ensembles de contrainte
en élasticité non linéaire; Arch.Ration.Mech.Anal,
Vol 97, 1, 1987.
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G. Aubert-R. Tahraoui. Conditions nécessaires de faible fermeture
et de 1-rang convexité en 3-D; Rendiconti del Circolo di Palermo,
Série 2, T 34, 1985.
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G. Aubert-R. Tahraoui. Sur quelques résultats d'existence en
optimisation non convexe; C.R.A.S, T 297, 1984.
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G. Aubert-R. Tahraoui. Résultats d'existence en optimisation
non convexe; Applicable Analysis, Vol 18, 1984.
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G. Aubert. On a counter example of a rank-one convex function which
is not polyconvex; Proc.Royal.Society of Edimburgh, 106A, 1987.
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G. Aubert. Quelques remarques sur les notions de polyconvexité
et de 1-rang convexité en dimensions 2 et 3; M2AN, Vol 122, 1988.
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G. Aubert. Sur une équation quasilinéaire non elliptique
d'ordre 2; Annales IHP, Analyse non linéaire, Vol 8, 1991.
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G. Aubert-R. Tahraoui. Young measures and relaxation of functional for
integrands f(x,u(x),u'(x)); Journal of Differential and Integral Equations,
Vol 9, n° 1, Janv 96, p 27-44.
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G. Aubert. Necessary and sufficient conditions for isotropic rank-one
convex functions in dimension two; Journal of Elasticity, Vol 39, 1995,
p 21-46.
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G. Aubert- M. Barlaud- M.L Blanc-Féraud-P.Charbonnier. Deterministic
edge-preserving regularization in computed imaging; I.E.E.E Transaction
on Image Processing Vol 5, n°12, fev 1997.
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G.Aubert-R Tahraoui: Mesures de Young et conditions d'optimalité pour des fonctionnelles non convexes; C.R.A.S, t321, Série I, 1995,
p 659-662.
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G.Aubert-R Tahraoui: Young measures , relaxation of functionals and
existence results without lower semi-continuity, Advances in Differential
Equations, Vol 3, N°2, Mars 1998.
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G.Aubert-L. Vese:Variational
methods in image restauration; SIAM Journal of Numerical Analysis,
34(5), oct 1997.
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G.Aubert-R.Deriche-P.Kornprobst: Discontinuities Preserving in Optical
Flow estimation, Proceedings of the 2nd Asian Conference on Computer Vision,
Vol 2, Singapore, dec 1995.
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G.Aubert- M. Barlaud- L. Blanc-Féraud- S. Teboul: Variationalijcv.ps
approach for edge preserving regularization using coupled PDE' , IEEE Trans.
Image. Process, Special isssue on PDE and geometry-driven diffusion in
image processing and analysis, March 98, Vol 7, n°3.
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G. Aubert - P. Kornprobst : A mathematical study of the regularized
optical flow problem in the space BV, SIAM Journal of Mathematical Analysis,Vol
30, p1282-1308, 1999.
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G.Aubert -R. Deriche - P. Kornprobst: Computing
optical flow via variational techniques, SIAM Journal on Applied Mathematics,
Vol 60, n°1, p156-182, 2000.
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G. Aubert- R.Deriche- P. Kornprobst : Image sequence analysis via partial
differential equations, Journal of Mathematical Imaging and Vision, Vol
11, n° 1, sept 1999.
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G. Aubert - L . Blanc-Féraud - Ch. Samson J. Zérubia :
A variational model for image classification and restoration, IEEE, Pattern
Analysis and Machine Intelligenc e, Vol 22, N°5, May 2000.
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G. Aubert L. Blanc-Féraud : Some remarks on the equivalence between
classical snakes and geodesic active contours, Int. Jour. Computer Vision,
Vol 34, N° ,1999.
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G. Aubert- M. Barlaud- E. Debreuve- J. Darcourt : Space -time segmentation
using level set active contours applied to myocardial gated SPECT, IEEE
Transactions on Medical Imaging. Vol 20,July 2001, 7, p643-59.
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G. Aubert - L. Blanc-Féraud - Ch. Samson J. Zérubia :
A level set model for image classification, Int. Jour. Computer Vision,
Vol 40, N° 3, 2000.
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G. Aubert - M. Barlaud - S. Jehan : Deformable
Regions driven by an Eulerian Accurate Minimization Method for image and
video Segmentation, Int. Jour. Compu. Vision 53, 2003.
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G. Aubert - L . Blanc -Féraud - Ch. Samson - J. Zérubia:
Deux modèles Variationnels pour la Classification d'images Multi-Spectrales,Traitement du signal, Vol 18, N°5-6, 2001.
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G. Aubert- P. Kornprobst : Mathematical
Problems in Image Processing: Partial Differential Equations and the Calculus
of Variations, , Springer Verlag, Applied Mathematical Sciences, Vol
147, November 2001.
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G. Aubert - M. Barlaud;- S. Jehan: A 3-step algorithm using region-based active contours for video object detection, Eurasip Journal on Applied Signal Processing, Special issue on Image Analysis for multi-media, Vol 2002, n° 6, June 2002.
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G. Aubert- M. Barlaud- E. Debreuve- J. Darcourt: Non-parametric and non-rigid registration method applied to myocardial gated SPECT, IEEE Transaction on Nuclear Sciences, Vol 49, n°3, June2002.
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G. Aubert - M. Barlaud- O. Faugeras - S. Jehan: Image segmentation using active contours: calculus of variations or shape gradient, Siam Journal on Applied Mathematics, Vol 63, n° 6, 2003.
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G. Aubert - L. Blanc Féraud - Riccardo March: Gamma
- convergence of discrete functionals with nonconvex perturbation for image classification, Siam Journal on Numerical Analysis, Vol 42, n° 3, 2004.
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G. Aubert - J.F. Aujol - L. Blanc-Féraud - A. Chambolle: Image Decomposition into a bounded variation component and an oscillating component, Journal of Mathematical Imaging and Vision, 22, p71-88, 2005.
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G. Aubert - J.F. Aujol - L. Blanc-Féraud: Wavelet-Based level set evolution for classification of textured images, IEEE Transaction on Image Processing Vol.12, n°12, 2003.
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G. Aubert - J.F. Aujol: Modeling very oscillating signals. Application to image processing, Applied Mathematics Optimization, Vol 51, N°2, March/April 2005.
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G. Aubert - M. Barlaud - M. Gastaud, Combining Shape Prior and Statistical Features for Active Contours Segmentation, IEEE Trans. on Circuit System Video Tecnnology, Vol 14, n°5, 2004.
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G. Aubert - J. F. Aujol : Optimal partitions, regularization and application to image classification, Applicable Analysis, Vol 84, n°1, 2005.
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G. Aubert - M. Barlaud- E. Debreuve - M. Gastaud - S. Jehan - F. Precioso : From snakes to region active contours defined by region dependent parameters, Applied Optics, Vol 43, Issue 2, January 2004.
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G. Aubert - M. Barlaud;- A. Herbulot - S. Jehan-Besson : Shape gradient for image and video segmentation : The Handbook of Mathematical Models in Computer Vision,chapter 18, Springer Verlag, 2005.
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G. Aubert - M. Barlaud - E. Debreuve - T. Roy : Segmentation of a vector field: Dominant parameter and shape optimization, Journal of Mathematical Imaging and Vision, Vol 24, N°2, mars 2006.
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G. Aubert - M. Barlaud- S. Duffner - A. Herbulot - S. Jehan-Besson : Segmentation of vectorial image features using shape gradients and information measures, Journal of Mathematical Imaging and Vision,Vol 25, 2006.
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G. Aubert - J.F. Aujol - L. Blanc-Féraud : Detecting codimension-two objects in an image with Ginzburg-Landau models, International Journal of Computer Vision, Vol 65, N°1-2, 2005.
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G. Aubert - L. Blanc-Féraud - Riccardo March: An approximation of the Mumford-Shah energy by a family of discrete edge-preserving functionals, Nonlinear Analysis, Theory, Methods and Applications, Vol 64, Issue 9, may 2006.
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G. Aubert - P. Kornprobst: Mathematics in Image Processing, chapter of Encyclopedia of Mathematical Physics, Elsevier (editors J.P. Françoise, G. Naber, T.S. Tsun), 2006.
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G. Aubert- P. Kornprobst: Le traitement des images numériques, chapitre de l'Encyclopédie de l'Informatique et des Systèmes d'Information, Vuibert 2006.
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G. Aubert - M. Barlaud- E. Debreuve - M; Gastaud: Using the shape gradient for active contour segmentation: from the continuous to the discrete formulation, Journal of Mathematical Imaging and Vision, Vol 28, N°1, May 2007.
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G. Aubert - L. Blanc-Féraud - P. Weiss: Efficient schemes for total variation minimization under constraints in image processing, SIAM Journal of Scientific Computing, Vol 31, Issue3, 2009.
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G. Aubert - J.F. Aujol: A variational appoach to remove multiplicative noise, SIAM Journal on Applied Mathematics, Vol 68, Issue 4, 2008.
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G. Aubert - P. Kornprobst: Can the nonlocal characterization of Sobolev spaces by Bourgain etal be useful for solving variational problems ? SIAM Journal of Numerical Analysis, Vol 47, Issue 2, 2009.
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G. Aubert - M. Barlaud - S. Boltz - E. Debreuve - A. Herbulot: Motion and appearance nonparametric joint entropy for video segmentation, International Journal Computer Vision, Vol 80, Issue 2, 2008.
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G. Aubert - A. El Hamidi - C. Ghannam - M. Menard: On a class of ill-posed problems in image processing, Journal of Mathematical Analysis and Applications, Vol 352, 2009.
 
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G. Aubert - L. Blanc-Féraud - D. Graziani: A formal Gamma-convergence approach for the detection of points in 2D images, SIAM Journal on Imaging Sciences, Vol 3, N° 3, 2010.
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G. Aubert - J. Fadili - S. Jehan Besson - F. Lecellier - M. Revenu - E. Saloux: Region-based active contours with exponential, family observations, Journal of Mathematical Imaging and Vision,Vol36,N°1,2010.
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G. Aubert - D. Graziani: Variational approximation for detecting point-like target problems, ESSAIM-COCV,Vol 17, N°4, 2011.
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G. Aubert - L. Blanc-Féraud - A. Fournier - P. Weiss: On the illumination invariance of the level lines under directed light. Application to change detection, SIAM Journal on Imaging Science,Vol 4,N°1, 2011.
 
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G. Aubert - L. Blanc-Féraud - D. Graziani: Analysis of a new variational model to restore point-like singularities in imaging, to appear in Appl. Math. Opt, 2012.
 
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G. Aubert - D. Graziani: A relaxation result for an inhomogeneous functional preserving point-like and curve-like singularities in image procesing, International Journal of Maths,Vol 23, N° 12, 2012.
 
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G. Aubert - J.F Aujol, Poisson Skeleton Revisited: A New Mathematical Perspective, to appear in JMIV.