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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 2
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Articles

Non-unique solutions for a convex TVL1 problem in image segmentation

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Pages 232-248 | Received 24 Jan 2018, Accepted 11 Jun 2018, Published online: 14 Jul 2018

References

  • Chan T. F., Esedoglu S.. Aspects of total variation regularized L1 function approximation. SIAM J Appl Math. 2005;65:51817–1837. doi: 10.1137/040604297
  • Alter F, Caselles V, Chambolle A. A characterization of convex calibrable sets in RN. Math Ann. 2005;332:329–366. doi: 10.1007/s00208-004-0628-9
  • Chambolle A. An algorithm for mean curvature motion. Interfaces Free Bound. 2004;6:195–218. doi: 10.4171/IFB/97
  • Chan T.F., Vese L.A.. Active contours without edges. IEEE Trans Imag Proc. 2001;10:266–277. doi: 10.1109/83.902291
  • Caselles V, Catté F, Coll T, Dibos F. A geometric model for active contours in image processing. Numer Math. 1993;66:1–31. doi: 10.1007/BF01385685
  • Caselles V, Kimmel R, Sapiro G. On geodesic active contours. Int J Comput Vis. 1997;22:61–79. doi: 10.1023/A:1007979827043
  • Kass M, Witkin A, Terzopoulos D. Snakes: Active contour models. Int J Comput Vis. 1988;1:321–331. doi: 10.1007/BF00133570
  • Malladi R, Sethian JA, Vemuri BC. Topology-independent shape modeling scheme, Geometric Methods in Computer Vision II, 1993;2031
  • Chan T, Esedoglu S, Nikolova M. Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J Appl Math. 2006;66(5):1632–1648. doi: 10.1137/040615286
  • Bresson X, Esedoglu S, Vandergheynst P, Thiran JP, Osher S. Fast Global Minimization of the Active Contour/Snake Model. J Math Imaging Vis. 2007;28(2):151–167. doi: 10.1007/s10851-007-0002-0
  • Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D. 1992;60:259–268. doi: 10.1016/0167-2789(92)90242-F
  • Vese V. A Study in the BV Space of a Denoising-Deblurring Variational Problem. Appl Math Optim. 2001;44:131–161. doi: 10.1007/s00245-001-0017-7
  • Caselles V, Chambolle A, Novaga M. The discontinuity set of solutions of the TV denoising problem and some extensions. SIAM Multiscale Model Simul. 2007;6(3):879–894. doi: 10.1137/070683003
  • Caselles V, Chambolle A, Novaga M. Regularity for solutions of the total variation denoising problem. Rev Mat Iberoamericana. 2011;27(1):233–252. doi: 10.4171/RMI/634
  • Chambolle A. An Algorithm for Total Variation Minimization and Applications. J Math Imaging Vis. 2004;20:89–97. doi: 10.1023/B:JMIV.0000011320.81911.38
  • Chambolle A, Pock T. A first-order primal-dual algorithm for convex problems with applications to imaging. J Math Imaging Vis. 2011;40:120–145. doi: 10.1007/s10851-010-0251-1
  • Evans C, Gariepy R. Measure Theory and Fine Properties of Functions. Boca Raton: CRC Press, Inc.; 1992. (Stud. Adv. Math.)).
  • Giusti E. Minimal Surfaces and Functions of Bounded Variation. Boston: Birkhäuser; 1984.
  • Caselles V, Chambolle A, Moll S, Novaga M. A chracterization of convex calibrable sets in RN with respect to anisotropic norms. Ann Inst Henri Poincare-Anal Non Lineaire. 2008;25:803–832. doi: 10.1016/j.anihpc.2008.04.003
  • Carlier G, Comte M. On a weighted total variation minimization problem. J Funct Anal. 2007;250:214–226. doi: 10.1016/j.jfa.2007.05.022

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