Publication Cover
Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 1
22
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Optimal partitions, regularized solutions, and application to image classification

&
Pages 15-35 | Received 03 May 2004, Published online: 15 Aug 2006

References

  • Adams R 1975 Sobolev Spaces. Pure and Applied Mathematics New York Academic Press, Inc
  • Ambrosio L 1997 Corso introduttivo alla teoria geometrica della misura ed alle superfici minime Scuola Normale Superiore Lecture Notes Pisa
  • Ambrosio L Caselles V Masnou S Morel JM 1999 Connected components of sets of finite perimeter and applications to image processing
  • Ambrosio L Fusco N Pallara D 2000 Oxford Mathematical Monographs, Oxford University Press
  • Aubert G Blanc L-Féraud March R Gamma-convergence of discrete functionals with non convex perturbation for image classification. To appear in SIAM Journal on Numerical Analysis
  • Aubert G Kornprobst P 2002 Mathematical Problems in Image Processing volume 147 of Applied Mathematical Sciences Berlin Springer-Verlag
  • Aubert , G and Vese , L . 1997 . A variational method in image recovery . SIAM Journal on Numerical Analysis , 34 : 1948 – 1979 .
  • Aujol , JF , Aubert , G and Blanc-Feraud , L . 2003 . Wavelet-based level set evolution for classification of textured images . IEEE Transactions on Image Processing , 12 ( 12 ) : 1634 – 1641 .
  • Brezis H 1983 Analyse fonctionnelle. Theorie et applications Mathématiques appliquées pour la maitrise Masson
  • Chan TF Vese LA 2001 Active contours without edges IEEE Transactions on Image Processing 10 2 266 277 February
  • Congedo , G and Tamanini , I . 1991 . On the existence of solutions to problem in multidimensional segmentation . Ann. Inst. Henri Poincare , 8 ( 2 ) : 175 – 195 .
  • Ekelaud I Temam R 1976 Convex Analysis and Variational Problems, North Holland Amsterdam
  • Evans LC Gariepy RF 1992 Measure theory and fine properties of functions. volume 19 of Studies in Advanced Mathematics Bocca Raton CRC Press
  • Giusti E 1994 Minimal Surfaces and Functions of Bounded Variation Boston Birkhauser
  • Ladyzenskaja OA Ural’Ceva NN 1968 Linear and Quasilinear Elliptic Equations. Mathematics in Science and Engineering New York Academic Press Inc
  • Ladyzenskaja , OA and Ural’Ceva , NN . 1970 . Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations . Communications in Pure and Applied Mathematics , 23 : 677 – 703 .
  • Massari , U . 1974 . Esistenza e regolarita delle ipersuperfici di curvatura madia assegnata in rn . Archive for Rational Mechanics and Analysis , 55 : 357 – 382 .
  • Massari U Miranda M 1984 Minimal Surfaces of Codimension One, North Holland
  • Massari , U and Tamanini , I . 1991 . Regularity properties of optimal segmentations . Journal fur die Reine und Angewandte Mathematik , 420 : 61 – 84 .
  • Morel JM Solimini S 1995 Variational Methods in Image Segmentation, volume 14 of Progress in Nonlinear Differential Equations and Their Applications Boston Birkhauser
  • Paragios , N and Deriche , R . 2002 . Geodesic active regions and level set methods for supervised texture segmentation . International Journal of Computer Vision , 46 ( 3 ) : 223 – 247 .
  • Samson , C , Blanc-Féraud , L , Aubert , G and Zerubia , J . 2000 . A level set method for image classification . International Journal of Computer Vision , 40 ( 3 ) : 187 – 197 .
  • Temam , R . 1971 . Solutions généralisées de certaines équations de type hypersurfaces minima . Archive for Rational Mechanics and Analysis , 44 : 121 – 156 .
  • Vese , LA and Chan , TF . 2002 . A multiphase level set framework for image segmentation using the Mumford and Shah model . International Journal of Computer Vision , 50 ( 3 ) : 271 – 293 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.