Publications of Gilles Aubert


  1. G. Aubert-R. Tahraoui. Théorèmes d'existence en calcul des variations; C.RA.S, T 285, 1977.
  2. G. Aubert-R. Tahraoui. Théorèmes d'existence pour des problèmes du calcul des variations du type... ; Journal of Differential Equations, Vol 133, 1 ,1977.
  3. G. Aubert-R. Tahraoui. Sur la minimisation d'une fonctionnelle non convexe, non différentiable en dimension 1; Bolletino UMI, 5, 17B, 1980.
  4. G. Aubert-R. Tahraoui. Quelques remarques sur un problème d'élasticité non linéaire; Annales de la Faculté des Sciences de Toulouse, Vol 4, 1982.
  5. G. Aubert-R. Tahraoui. Fermeture de certains ensembles de contrainte en élasticité non linéaire plane; C.R.A.S, T 290, 1980.

  7. G. Aubert-R. Tahraoui. Sur la fermeture de certains ensembles de contrainte en élasticité non linéaire; Arch.Ration.Mech.Anal, Vol 97, 1, 1987.
  8. 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.
  9. G. Aubert-R. Tahraoui. Sur quelques résultats d'existence en optimisation non convexe; C.R.A.S, T 297, 1984.
  10. G. Aubert-R. Tahraoui. Résultats d'existence en optimisation non convexe; Applicable Analysis, Vol 18, 1984.
  11. G. Aubert. On a counter example of a rank-one convex function which is not polyconvex; Proc.Royal.Society of Edimburgh, 106A, 1987.
  12. G. Aubert. Quelques remarques sur les notions de polyconvexité et de 1-rang convexité en dimensions 2 et 3; M2AN, Vol 122, 1988.
  13. G. Aubert. Sur une équation quasilinéaire non elliptique d'ordre 2; Annales IHP, Analyse non linéaire, Vol 8, 1991.
  14. 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.
  15. G. Aubert. Necessary and sufficient conditions for isotropic rank-one convex functions in dimension two; Journal of Elasticity, Vol 39, 1995, p 21-46.
  16. 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.
  17. 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.
  18. 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.
  19. G.Aubert-L. Vese:Variational methods in image restauration; SIAM Journal of Numerical Analysis, 34(5), oct 1997.
  20. 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.
  21. G.Aubert- M. Barlaud- L. Blanc-Féraud- S. Teboul: 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.
  22. 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.
  23. publications.html G.Aubert -R. Deriche - P. Kornprobst: Computing optical flow via variational techniques, SIAM Journal on Applied Mathematics, Vol 60, n°1, p156-182, 2000.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. G. Aubert - J.F. Aujol: Modeling very oscillating signals. Application to image processing, Applied Mathematics Optimization, Vol 51, N°2, March/April 2005.
  39. 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.
  40. G. Aubert - J. F. Aujol : Optimal partitions, regularization and application to image classification, Applicable Analysis, Vol 84, n°1, 2005.
  41. 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.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. G. Aubert- P. Kornprobst: Le traitement des images numériques, chapitre de l'Encyclopédie de l'Informatique et des Systèmes d'Information, Vuibert 2006.
  49. 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.
  50. 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.
  51. G. Aubert - J.F. Aujol: A variational appoach to remove multiplicative noise, SIAM Journal on Applied Mathematics, Vol 68, Issue 4, 2008.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. G. Aubert - D. Graziani: Variational approximation for detecting point-like target problems, ESSAIM-COCV,Vol 17, N°4, 2011.
  58. 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.
  59. 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.
  60. 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.
  61. G. Aubert - J.F Aujol, Poisson Skeleton Revisited: A New Mathematical Perspective, to appear in JMIV.