Abstract—In this paper, we propose a variational model of multiphase image segmentation using n binary label functions for n regions. This framework is subject to a constraint to avoid the vacuum and overlapping problem. Firstly, we solve the simple problem without the constraint. In order to improve the computation efficiency of the unconstrained problem, we design the Split Bregman algorithm in the alternating minimization, which transforms the unconstrained model into a series of simple Euler-Lagrange equations. These equations are solved via Gauss-Seidel iterative method or expressed as generalized thresholding formulas in analytical forms. Secondly, we project the results above onto the constraint using Lagrange multiplier method. Due to the linear structure of the constraint, we can also solve the projection scheme quickly. Finally, numerical results on 2D and 3D images demonstrate that our proposed Split-Bregman-Projection (SBP) algorithm is competitive in terms of quality and efficiency compared to other methods.
Index Terms—Active contour model, lagrange multiplier, split bregman, binary label function, multiphase segmentation
The authors are with the College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong China, and also with the College of Information Engineering, Qingdao, Shandong China (e-mail: clliuqdu@ gmail.com; e-mail: zhengyg206@163.com; e-mail: zkpan@qdu.edu.cn; e-mail: doctorwgd@gmail.com).
Cite: Cunliang Liu, Yongguo Zheng, Zhenkuan Pan, and Guodong Wang, "A Fast Algorithm for Multiphase Image Segmentation: The Split-Bregman-Projection Algorithm," International Journal of Modeling and Optimization vol. 2, no. 1, pp. 1-6, 2012.
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