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Comparison of minimization methods for nonsmooth image segmentation Cover

Comparison of minimization methods for nonsmooth image segmentation

By: L. Antonelli and  V. De Simone  
Open Access
|Mar 2018

References

  1. 1. T. Chan and L. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266-277, 2001.10.1109/83.90229118249617
  2. 2. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol. 45, no. 2, pp. 577-685, 1989.10.1002/cpa.3160420503
  3. 3. T. Chan, S. Esedofiglu, and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, vol. 66, no. 5, pp. 1632|1648, 2006.
  4. 4. X. Bresson, S. Esedofiglu, P. Vandergheynst, J.-P. Thiran, and S. Osher, Fast global minimization of the active contour/snake model, Journal of Mathematical Imaging and Vision, vol. 28, no. 2, pp. 151-167, 2007.10.1007/s10851-007-0002-0
  5. 5. R. Yildizofiglu, J.-F. Aujol, and N. Papadakis, Active contours without level sets, in ICIP 2012 - IEEE International Conference on Image Pro- cessing (Orlando, FL, Sept. 30 - Oct. 3, 2012), pp. 2549-2552, IEEE, 2012.
  6. 6. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, vol. 40, no. 1, pp. 120-145, 2011.10.1007/s10851-010-0251-1
  7. 7. J. Yuan, E. Bae, and X. Tai, A study on continous max-ow and mincut approaches, in Computer Vision and Pattern Recognition, pp. 2217- 2224, IEEE, 2010.
  8. 8. G. Paul, J. Cardinale, and I. F. Sbalzarini, Coupling image restoration and segmentation: A generalized linear model/bregman perspective, In- ternational Journal of Computer Vision, vol. 104, pp. 69-93, 2013.10.1007/s11263-013-0615-2
  9. 9. L. Antonelli, V. De Simone, and D. di Serafino, On the application of the spectral projected gradient method in image segmentation, J. Math. Imaging Vis., vol. 54, pp. 106-116, Jan. 2016.10.1007/s10851-015-0591-y
  10. 10. A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Img. Sci., vol. 2, pp. 183-202, Mar. 2009.10.1137/080716542
  11. 11. E. Birgin, J. Martfifinez, and M. Raydan, Spectral projected gradient methods: review and perspectives, Journal of Statistical Software, vol. 60, no. 3, 2014.10.18637/jss.v060.i03
  12. 12. J. Barzilai and J. Borwein, Two-point step size gradient methods, IMA Journal of Numerical Analysis, vol. 8, pp. 141-148, 1988.10.1093/imanum/8.1.141
  13. 13. D. di Serafino, V. Ruggiero, G. Toraldo, and L. Zanni, On the steplength selection in gradient methods for unconstrained optimization, Applied Mathematics and Computation, 2017.10.1016/j.amc.2017.07.037
  14. 14. L. Grippo, F. Lampariello, and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM Journal on Numerical Analysis, vol. 23, no. 4, pp. 707-716, 1986.10.1137/0723046
  15. 15. T. Goldstein, X. Bresson, and S. Osher, Geometric applications of the split Bregman method: segmentation and surface reconstruction, Jour- nal of Scientific Computing, vol. 45, no. 1-3, pp. 272-293, 2010.10.1007/s10915-009-9331-z
  16. 16. L. Bregman, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathemati- cal Physics, vol. 7, pp. 69-93, 1967.10.1016/0041-5553(67)90040-7
  17. 17. S. Setzer, Split bregman algorithm, douglas-rachford splitting and frame shrinkage, in Proc. of the Second International Conference on Scale Space Methods and Variational Methods in Computer, vol. 5567, pp. 464-476, 2009.
  18. 18. O. Güler, New proximal point algorithms for convex minimization, SIAM Journal on Optimization, vol. 2, no. 4, pp. 649-664, 1992.10.1137/0802032
  19. 19. Y. Nesterov, A method of solving a convex programming problem with convergence rate o (1/k2), Soviet Mathematics Doklady, vol. 27, pp. 372- 376, 1983.
  20. 20. G. Peyrfie, The numerical tours of signal processing, Advanced Computational Signal and Image Processing IEEE Computing in Science and Engineering, vol. 13, no. 4, pp. 94-97, 2011.10.1109/MCSE.2011.71
  21. 21. D. Martin, C. Fowlkes, D. Tal, and J. Malik, A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics, in Proc. 8th Int'l Conf. Computer Vision, vol. 2, pp. 416-423, July 2001.
  22. 22. W. M. Rand, Objective criteria for the evaluation of clustering methods, Journal of the American Statistical Association, vol. 66, no. 336, pp. 846-850, 1971.10.1080/01621459.1971.10482356
Language: English
Page range: 68 - 86
Submitted on: Aug 1, 2017
Accepted on: Feb 2, 2018
Published on: Mar 24, 2018
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2018 L. Antonelli, V. De Simone, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.