volume | PIER Journals

Abstract

This paper present a fast algorithm for synthetic aperture radar (SAR) image segmentation based on the augmented Lagrangian method (ALM). The proposed approach considers the segmentation of SAR images as an energy minimization problem in a variational framework. The energy functional is formulated based on the statistical characteristic of SAR images. The total variation regularization is used to impose the smoothness constraint of the segmentation result. To solve the optimization problem efficiently, the energy functional is firstly modified to be convex and differentiable by using convex relaxing and variable splitting techniques, and then the constrained optimization problem is converted to an unconstrained one by using the ALM. Finally the energy is minimized with an iterative minimization algorithm. The effectiveness of the proposed algorithm is validated by experiments on both synthetic and real SAR images.

1. Oliver, C. and S. Quegan, Understanding Synthetic Aperture Radar Images, Artech House, 1998.

2. Mishra, P., D. Singh, and Y. Yamaguchi, "Land cove classification of PALSAR images by knowledge based decision tree classifier and supervised classifiers based on SAR observation," Progress In Electromagnetics Research B, Vol. 30, 47-70, 2011.

3. Tian, B., D.-Y. Zhu, and Z.-D. Zhu, "A novel moving target detection approach for dual-channel SAR system," Progress In Electromagnetics Research, Vol. 115, 191-206, 2011.

4. Jin, Y.-Q., "Polarimetric scattering modeling and information retrieval of SAR remote sensing --- A review of FDU work," Progress In Electromagnetics Research, Vol. 104, 333-384, 2010.
doi:10.2528/PIER10020101

5. Caselles, V., R. Kimmel, and G. Sapiro, "Geodesic active contours," Int. J. Computer Vision, Vol. 22, No. 1, 61-79, 1997.
doi:10.1023/A:1007979827043

6. Zhu, S. C. and A. Yuille, "Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation," IEEE Trans. Pattern Anal. Mach. Intell., Vol. 18, No. 9, 884-900, Sept. 1996.
doi:10.1109/34.537343

7. Chan, T. and L. Vese, "Active contour without edges," IEEE Trans. Image Process., Vol. 10, No. 2, 266-277, 2001.
doi:10.1109/83.902291

8. Paragios, N. and R. Deriche, "Geodesic active regions and level set methods for supervised texture segmentation," Int. J. Computer Vision, Vol. 46, No. 3, 223-247, 2002.
doi:10.1023/A:1014080923068

9. Cremers, D., M. Rousson, and R. Deriche, "A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape," Int. J. Computer Vision, Vol. 72, No. 2, 195-215, 2007.
doi:10.1007/s11263-006-8711-1

10. Ayed, I. B., A. Mitiche, and Z. Belhadj, "Multiregion level-set partitioning of synthetic aperture radar images," IEEE Trans. Pattern Anal. Mach. Intell., Vol. 27, No. 5, 793-800, 2005.
doi:10.1109/TPAMI.2005.106

11. Shuai, Y., H. Sun, and G. Xu, "SAR image segmentation based on level set with stationary global minimum," IEEE Geosci. Remote Sens. Lett., Vol. 5, No. 4, 644-648, 2008.
doi:10.1109/LGRS.2008.2001768

12. Ayed, I. B., N. Hennane, and A. Mitiche, "Unsupervised variational image segmentation classification using a Weibull observation model," IEEE Trans. Image Process., Vol. 15, No. 11, 3431-3439, 2006.
doi:10.1109/TIP.2006.881961

13. Silveira, M. and S. Heleno, "Separation between water and land in SAR image using region based level set," IEEE Trans. Geoscience and Remote Sensing, Vol. 6, No. 3, 471-475, 2009.
doi:10.1109/LGRS.2009.2017283

14. Frery, A. C., H. J. Muller, C. C. F. Yanasse, and S. J. S. Sant'Anna, "A model for extremely heterogeneous clutter," IEEE Trans. Geoscience and Remote Sensing, Vol. 35, No. 3, 648-659, 1997.
doi:10.1109/36.581981

15. Frery, A. C. and F. Yanasse, "Alternative distributions for the multiplicative model in SAR images," International Geoscience and Remote Sensing Symposium, Vol. 1, 169-171, 1995.

16. Tison, C., J.-M. Nicolas, F. Tupin, and H. Maitre, "A new statistical model for Markovian classification of urban areas in high-resolution SAR images," IEEE Trans. Geoscience and Remote Sensing, Vol. 42, No. 10, 2046-2057, 2004.
doi:10.1109/TGRS.2004.834630

17. Feng, J., Z. Cao, and Y. P, "A G⁰ statistical model based level set approach for SAR image segmentation," Proc. EUSAR, 841-844, 2010.

18. Malladi, R., J. A. Sethian, and B. C. Vemuri, "Shape modeling with front propagation: A level set approach," IEEE Trans. Pattern Anal. Mach. Intell., Vol. 17, No. 2, 158-175, 1995.
doi:10.1109/34.368173

19. Li, C., C. Xu, C. Gui, and M. D. Fox, "Level set evolution without re-initialization: A new variational formulation," Proc. CVPR, Vol. 1, 430-436, 2005.

20. Goldenberg, R., R. Kimmel, E. Rivlin, and M. Rudzsky, "Fast geodesic active contours," IEEE Trans. Image Process., Vol. 10, No. 10, 1467-1475, 2001.
doi:10.1109/83.951533

21. Shi, Y. and W. C. Karl, "A real-time algorithm for the approximation of level-set-based curve evolution," IEEE Trans. Image Process., Vol. 17, No. 5, 645-656, 2008.
doi:10.1109/TIP.2008.920737

22. Chan, T. F., S. Esedoglu, and M. Nikolova, "Algorithms for finding global minimizers of image segmentation and denoising models," SIAM J. Appl. Math, Vol. 66, No. 5, 1632-1648, 2006.
doi:10.1137/040615286

23. Bresson, X., S. Esedoglu, P. Vandergheynst, et al. "Fast global minimization of the active contour/snake model," J. Math. Imaging. Vision., Vol. 28, No. 2, 151-167, 2007.
doi:10.1007/s10851-007-0002-0

24. Wu, C. and X. C. Tai, "Augmented lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models," SIAM J. Imaging Sci., Vol. 3, No. 3, 300-339, 2010.
doi:10.1137/090767558

25. Afonso, M. V., J. M. Bioucas-Dias, and M. A. T. Figueiredo, "An augmented lagrangian approach to the constrained optimization formulation of imaging inverse problems," IEEE Trans. Image Process., Vol. 20, No. 3, 681-695, 2011.
doi:10.1109/TIP.2010.2076294

26. Chambolle, A., "An algorithm for total variation minimization and application," J. Math. Imaging. Vision., Vol. 20, No. 1--2, 89-97, 2004.

27. Rudin, L., S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, Vol. 60, 259-268, 1992.
doi:10.1016/0167-2789(92)90242-F

28. Beck, A. and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denosing and deblurring problems," IEEE Trans. Image Process., Vol. 18, No. 11, 2419-2434, 2009.
doi:10.1109/TIP.2009.2028250

29. Nocedal, J. and S. J. Wright, Numerical Optimization, 2nd Ed., Springer-Verlag, 2006.

30. Powell, M., "A method for nonlinear constraints in minimization problems," Optimization, 283-298, R. Fletcher Edition, Academic, New York, 1969.

31. Bertsekas, D. P., "Multiplier methods: A survey," Automatica, Vol. 12, 133-145, 1976.
doi:10.1016/0005-1098(76)90077-7

Dr. Jilan Feng

Dr. Zongjie Cao

Dr. Yiming Pi