①(State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China) ②(Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China) ③(College of Science, National University of Defense Technology, Changsha 410073, China)
Based on the idea that objects in a given image can be segmented by removing the background part, an unconstrained convex minimization problem is proposed. The penalization term added in the construction procedure of the proposed problem is proven to be viable, which is demonstrated by the experiment. At the computational level, a fixed-point operator and the corresponding algorithm are proposed by applying the theory of subdifferential and proximity operators, and Opial -averaged theorem. And then the convergence proof of the algorithm is given. Comparisons with other classical models show that the proposed segmentation model is more accurate. And the experiments also demonstrate that the fixed-point algorithm is faster than the gradient descent method and the split Bregman method. Moreover, the algorithm is robust to the initial curve and noise.
李伟斌,易贤,宋松和. 一种图像分割的快速不动点算法[J]. 电子与信息学报, 2015, 37(10): 2390-2396.
Li Wei-bin, Yi Xian, Song Song-he. Fast Fixed-point Algorithm for Image Segmentation. JEIT, 2015, 37(10): 2390-2396.
Zhu W, Tai X, and Chan T. Image segmentation using Euler’s Elastica as the regularization[J]. Journal of Scientific Computing, 2013, 15(2): 414-438.
[2]
Yuan J, Bae E, Tai X, et al.. A spatially continuous max-flow and min-cut framework for binary labeling problems[J]. Numerische Mathmatik, 2014, 126(3): 559-587.
Zhang Ze-jun and Shui Peng-lang. A new fast SAR image segmentation algorithm based on grid coding and region merging[J]. Journal of Electronics & Information Technology, 2014, 36(4): 974-980.
Zhao Xue-mei, Li Yu, and Zhao Quan-hua. Image segmentation by fuzzy clustering algorithm combining hidden Markov random field and Gaussian regression model[J]. Journal of Electronics & Information Technology, 2014, 36(11): 2730-2736.
Li Wei-bin, Gao Er, and Song Song-he. A global minimization method for image segmentation[J]. Journal of Electronics & Information Technology, 2013, 35(4): 791-796.
[6]
Li Wei-bin, Song Song-he, and Luo Feng. Fast image segmentation by convex minimisation and split Bregman method[J]. Electronics Letters, 2013, 49(17): 1073-1074.
[7]
Goldstein T and Osher S. The split Bregman method for 1 regularized problems[J]. SIAM Journal on Imaging Sciences, 2008, 2(2): 323-343.
[8]
Micchelli C, Shen L, and Xu Y. Proximity algorithms for image models: denosing[J]. Inverse Problems, 2011, 27(4): 45009-45038.
[9]
Osher S and Fedkiw R. Level Sset Methods and Dynamic Implicit Surfaces[M]. New York: Springer Verlag, 2002: 4-22.
[10]
Bertsekas D. Nonlinear Programming[M]. Belmont: Athena Scientific, 2003: 209-210.
[11]
Z?linescu C. Convex Analysis in General Vector Spaces[M]. River Edge: World Scientific, 2002: 79-88.
[12]
Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings[J]. Bulletin American Mathematical Society, 1967, 73: 591-597.
[13]
Chan T, Esedoglu S, and Nikolova M. Algorithms for finding global minimizers of image segmentation and denoising models[J]. SIAM Journal on Applied Mathematics, 2006, 66(5): 1632-1648.
[14]
Bresson X, Esedoglu S, Vandergheynst P, et al.. Fast global minimization of the active contour/snake models[J]. Journal of Mathematical Imaging and Vision, 2007, 28(2): 151-167.
[15]
Goldstein T, Bresson X, and Osher S. Geometric applications of the split Bregman method: segmentation and surface reconstruction[J]. SIAM Journal on Scientific Computing, 2010, 45(1-3): 272-293.
[16]
Alpert S, Galun M, Basri R, et al.. Image segmentation by probabilistic bottom-up aggregation and cue integration[C]. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Minneapolis, 2007: 1-8.