Open Access

Comparison of minimization methods for nonsmooth image segmentation


Cite

1. T. Chan and L. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266-277, 2001.10.1109/83.90229118249617Search in Google Scholar

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.3160420503Search in Google Scholar

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.Search in Google Scholar

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/s10851-007-0002-0Search in Google Scholar

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.Search in Google Scholar

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/s10851-010-0251-1Search in Google Scholar

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.Search in Google Scholar

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/s11263-013-0615-2Search in Google Scholar

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-ySearch in Google Scholar

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. 2009.10.1137/080716542Search in Google Scholar

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.i03Search in Google Scholar

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/8.1.141Search in Google Scholar

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.2017.07.037Search in Google Scholar

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, 1986.10.1137/0723046Search in Google Scholar

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-zSearch in Google Scholar

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)90040-7Search in Google Scholar

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.Search in Google Scholar

18. O. Güler, New proximal point algorithms for convex minimization, SIAM Journal on Optimization, vol. 2, no. 4, pp. 649-664, 1992.10.1137/0802032Search in Google Scholar

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.Search in Google Scholar

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.2011.71Search in Google Scholar

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.Search in Google Scholar

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, 1971.10.1080/01621459.1971.10482356Search in Google Scholar

eISSN:
2038-0909
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, Numerical and Computational Mathematics, Applied Mathematics