Fast B-ultrasound Image Segmentation Based on a Convex Relaxation Method
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摘要: 利用活动轮廓线方法进行图像分割的一个重要缺陷是目标函数是非凸的, 这不仅使得分割结果容易陷于局部极小, 而且还使得一些快速算法无法开展.本文首先从贝叶斯风险估计的方法出发,针对B超幅度图像, 给出一种基于Rayleigh分布的活动轮廓线模型. 然后结合凸松弛的方法,得到一个新的放松的凸模型.原有模型和放松后模型的关系可由定理1给出. 最后结合分裂Bregman算法, 给出基于B超分割模型的快速算法.与传统梯度下降法相比较,本文提出的算法不仅能得到全局最优解,而且在算法收敛速度上也 大大优于梯度下降法.Abstract: One main drawback of active contour method applied to image segmentation is that the objective function is not convex. The solution of a non-convex minimization problem is prone to get stuck in a local minima, and some fast algorithms to convex optimization problems can not be used in a non-convex active contour model. Using a Bayesian risk method, this paper presents a new level set model for B-ultrasound image segmentation based on a Rayleigh distribution. The directly obtained model is not convex. However, we can get a new relaxed convex model by using a convex relaxation method. The relation between the directly obtained model and the relaxed convex model is given by a theorem. Then, a split Bregman algorithm is incorporated to propose a fast algorithm to solve the relaxed convex model. Compared with the traditional gradient descent method, the proposed method can not only get a global minima, but also is quite faster than gradient descent method.
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Key words:
- Medical B ultrasound /
- active contour /
- Bayesian risk /
- convex relaxation /
- split Bregman
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[1] Zhu S C, Yuille A L. Region competition: unifying snakes, region growing and Bayes/MDL for multiband image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996, 18(9): 884-900[2] Paragios N, Deriche R. Geodesic active regions and level set methods for supervised texture segmentation. International Journal of Computer Vision, 2002, 46(3): 223-247[3] Kass M, Witkin A P, Terzopoulos D. Snakes: active contour models. International Journal of Computer Vision, 1988, 1(4): 321-331[4] Caselles V, Kimmel R, Sapiro G. Geodesic active contours. International Journal of Computer Vision, 1997, 22(1): 61 -79[5] Mumford D, Shah J. Optical approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 1989, 42(5): 577-684[6] Liu Guo-Cai, Wang Yao-Nan, Duan Xuan-Chu. Knowledge based hierarchical Mumford-Shah model for vector-valued image segmentation. Acta Automatica Sinica, 2009, 35(4): 356-363(刘国才, 王耀南, 段宣初. 基于知识的多层Mumford-Shah向量值图像分割模型. 自动化学报, 2009, 35(4): 356-363)[7] Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Processing, 2001, 10(2): 266-277[8] Zhong T, Tagare H D, Beaty J D. Evaluation of four probability distribution models for speckle in clinical cardiac ultrasound images. IEEE Transactions on Medical Imaging, 2006, 25(11): 1483-1491[9] Sarti A, Corsi C, Mazzini E, Lamberti C. Maximum likelihood segmentation of ultrasound images with Rayleigh distribution. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2005, 52(6): 947-960[10] Liu Bo, Huang Jian-Hua, Tang Xiang-Long, Liu Jia-Feng, Zhang Ying-Tao. Combining global probability density difference and local gray level fitting for ultrasound image segmentation. Acta Automatica Sinica, 2010, 36(7): 951-959(刘博, 黄剑华, 唐降龙, 刘家锋, 张英涛. 结合全局概率密度差异与局部灰度拟合的超声图像分割. 自动化学报, 2010, 36(7): 951- 959)[11] Han Shou-Dong, Zhao Yong, Tao Wen-Bing, Sang Nong. Gaussian super-pixel based fast image segmentation using graph cuts. Acta Automatica Sinica, 2011, 37(1): 11-20(韩守东, 赵勇, 陶文兵, 桑农. 基于高斯超像素的快速Graph Cuts图像分割方法. 自动化学报, 2011, 37(1): 11-20)[12] Li C M, Huang R, Ding Z H, Gatenby J C, Metaxas D N, Gore J C. A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI. IEEE Transactions on Image Processing, 2011, 20(7): 2007-2016[13] Nikolova M, Esedoglu S, Chan T F. Algorithms for finding global minimizers of image segmentation and denosing models. SIAM Journal on Applied Mathematics, 2006, 66(5): 1632-1648[14] Bresson X, Esedoglu S, Vandergheynst P, Thiran J P, Osher S. Fast global minimization of the active contour/snake model. Journal of Mathematical Imaging and Vision, 2007, 28(2): 151-167[15] Goldstein T, Bresson X, Osher S. Geometric applications of split Bregman method: segmentation and surface reconstruction. Journal of Scientific Computing, 2009, 45(1-3): 272-293[16] Nambakhsh M S, Yuan J, Ayed I B, Punithakumar K, Goela A, Islam A, Peters T, Shuo L. A convex max-flow segmentation of LV using subject-specific distributions on cardiac MRI. In: Proceedings of the 22nd International Conference on Information Processing in Medical Imaging. Kloster Irsee, Germany: Springer, 2011. 171-183[17] Wanger R F, Smith S W, Sandrik J M, Lopez H. Statistics of speckle in ultrasound B-scans. IEEE Transactions on Sonics and Ultrasonics, 1983, 30(3): 156-163[18] Burckhardt C B. Speckle in ultrasound B-mode scans. IEEE Transactions on Sonics and Ultrasonics, 1978, 25(1): 1-6[19] Casella G, Berger R L. Statistical Inference. California: Wadsworth, 1990. 373-413[20] Goldstein T, Osher S. The split Bregman algorithm for L_{1}-regularized problems. SIAM Journal on Imaging Sciences, 2009, 2(2): 323-343[21] Osher S, Burger M, Goldfarb D, Xu J J, Yin W T. An iterative regularization method for total variation-based image restoration. Multiscale Modeling and Simulation, 2005, 4(2): 460-489[22] Setzer S, Steidla G, Teuber T. Deblurring Poissonian images by split Bregman techniques. Journal of Visual Communication and Image Representation, 2010, 21(3): 193-199[23] Setzer S. Operator splittings, Bregman methods and frame shrinkage in image processing. International Journal of Computer Vision, 2011, 92(3): 265-280[24] Cai J F, Osher S, Shen Z W. Split Bregman methods and frame based image restoration. Multiscale Modeling and Simulation, 2010, 8(2): 337-370[25] Jensen J A. Field: a program for simulating ultrasound systems. Medical and Biological Engineering and Computing, 1996, 34(S1): 351-353[26] Jensen J A, Svendsen N B. Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 1992, 39(2): 262-267
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