山东大学学报 (工学版) ›› 2022, Vol. 52 ›› Issue (4): 54-68.doi: 10.6040/j.issn.1672-3961.0.2021.532
• • 上一篇
董璐璐,宋金涛,魏伟波,潘振宽*
DONG Lulu, SONG Jintao, WEI Weibo, PAN Zhenkuan*
摘要： 针对多相图像分割变分模型的局部极值问题,采用函数提升方法实现模型的全局优化。基于笛卡尔流思想和校准理论,将离散的标签函数提升为二值超水平集函数。利用二值标签函数凸松弛技术,设计标签函数子问题的凸优化方法,通过原-对偶算法和投影算法简化计算以提高计算效率。对多幅多相灰度图像和彩色图像进行分割试验,结果表明:所提模型的能量极小值较原模型直接计算结果小得多,与最小值的误差仅为0、0.426%、0.040%等。改进后的方法几乎不依赖初始水平集的设置和试验参数的选择,可以得到全局最小值;所提算法的迭代次数大大减少,计算效率显著提高。
中图分类号:
| [1] 房巾莉, 吕毅斌, 王樱子, 等. 基于水平集的医学图像分割算法[J]. 电子科技, 2021, 34(2): 12-20. FANG Jinli, LÜ Yibin, WANG Yingzi, et al. Medical image segmentation algorithm based on level set[J]. Electronic Science and Technology, 2021, 34(2): 12-20. [2] 李晓慧, 汪西莉. 结合目标局部和全局特征的CV遥感图像分割模型[J]. 图学学报, 2020, 41(6): 905-916. LI Xiaohui, WANG Xili. CV image segmentation model combining with local and global features of the target[J]. Journal of Graphics, 2020, 41(6):905-916. [3] 刘步实, 吕永波, 吕万钧,等. 基于MS-RG混合图像分割模型的道路检测研究[J]. 交通运输系统工程与信息, 2019, 19(2): 60-65. LIU Bushi, LÜ Yongbo, LÜ Wanjun, et al. Research on road detection based on MS-RG hybrid image segmentation model[J]. Journal of Transportation Systems Engineering and Information Technology, 2019, 19(2): 60-65. [4] BAE E, YUAN J, TAI X C. Simultaneous convex optimization of regions and region parameters in image segmentation models[M]. Berlin, Germany: Springer, 2013: 421-438. [5] 刘花香, 方江雄, 肖静,等. 基于全局凸优化变分模型的快速多相图像分割方法: ZL2015102501678[P]. 2015-08-12. [6] BENNINGHOFF H, GARCKE H. Segmentation of three-dimensional images with parametric active surfaces and topology changes[J]. Journal of Scientific Computing, 2017, 72(3): 1333-1367. [7] POTTS R B. Some generalized order-disorder transformations[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1952, 48(1): 106-109. [8] SAMSON C, BLANC-FÉRAUD L, ZERUBIA J, et al. A level set model for image classification[J]. International Journal of Computer Vision, 1999, 40(3): 187-197. [9] 潘振宽, 李华, 魏伟波, 等. 三维图像多相分割的变分水平集方法[J]. 计算机学报, 2009, 32(12): 2464-2474. PAN Zhenkuan, LI Hua, WEI Weibo, et al. A variational level set method of multiphase segmentation for 3D images[J]. Chinese Journal of Computers, 2009, 32(12): 2464-2474. [10] VESE L A, CHAN T F. A multiphase level set framework for image segmentation using the Mumford and Shah model[J]. International Journal of Computer Vision, 2002, 50(3): 271-293. [11] CHUNG G, VESE L A. Energy minimization based segmentation and denoising using a multilayer level set approach[C] // Proceedings of the 5th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition. St. Augustine, USA: Springer, 2005: 439-455. [12] CHAN T F, ESEDOGLU S, NIKOLOVA M. Algorithms for finding global minimizers of image segmentation and denoising models[J]. SIAM Journal on Applied Mathematics, 2006, 66(5): 1632-1648. [13] LIE J, LYSAKER M, TAI X C. A binary level set model and some applications to Mumford-Shah image segmentation[J]. IEEE Transactions on Image Processing, 2006, 15(5): 1171-1181. [14] LIE J, LYSAKER M, TAI X C. A piecewise constant level set framework[J]. International Journal of Numerical Analysis and Modeling, 2005, 2(4): 422-438. [15] POCK T, SCHOENEMANN T, GRABER G, et al. A convex formulation of continuous multi-label problems[C] // Proceedings of Computer Vision: ECCV 2008, 10th European Conference on Computer Vision. Marseille, France: Springer, 2008: 792-805. [16] BROWN E S, CHAN T F, BRESSON X. Completely convex formulation of the Chan-Vese image segmentation model[J]. International Journal of Computer Vision, 2012, 98(1): 103-121. [17] POCK T, CREMERS D, BISCHOF H, et al. Global solutions of variational models with convex regularization[J]. SIAM Journal on Imaging Sciences, 2010, 3(4): 1122-1145. [18] STREKALOVSKIY E, CHAMBOLLE A, CREMERS D. Convex relaxation of vectorial problems with coupled regularization[J]. SIAM Journal on Imaging Sciences, 2014, 7(1): 294-336. [19] MOLLENHOFF T, LAUDE E, MOELLER M, et al. Sublabel-accurate relaxation of nonconvex energies[C] //Proceedings of 2016 IEEE Conference on Computer Vision and Pattern Recognition(CVPR). Las Vegas, USA: IEEE, 2016: 3948-3956. [20] MOLLENHOFF T, CREMERS D. Sublabel-accurate discretization of nonconvex free-discontinuity problems[C] // Proceedings of 2017 IEEE International Conference on Computer Vision(ICCV). Venice, Italy: IEEE, 2017: 1192-1200. [21] LOEWENHAUSER B, LELLMANN J. Functional lifting for variational problems with higher-order regularization[M]. Cham, Switzerland: Springer, 2018: 101-120. [22] VOGT T, LELLMANN J. Functional liftings of vectorial variational problems with laplacian regularization[C] //Proceedings of Scale Space and Variational Methods in Computer Vision. Cham, Switzerland: Springer International Publishing, 2019: 559-571. [23] CONDAT L, KITAHARA D, HIRABAYASHI A. A convex lifting approach to image phase unwrapping[C] //Proceedings of ICASSP 2019: 2019 IEEE International Conference on Acoustics, Speech and Signal Processing(ICASSP). Brighton, UK: IEEE, 2019: 1852-1856. [24] VOGT T, STREKALOVSKIY E, CREMERS D, et al. Lifting methods for Manifold-Valued variational problems[M]. Cham, Switzerland: Springer, 2020: 95-119. [25] WU T, GU X, SHAO J,et al. Color image segmentation based on a convex k-means approach[J]. IET Image Processing, 2021, 15(8): 1596-1606. [26] CHAMBOLLE A, POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging[J]. Journal of Mathematical Imaging and Vision, 2011, 40(1): 120-145. [27] KHATIBINIA M, ROODSARABI M. Structural topology optimization based on hybrid of piecewise constant level set method and isogeometric analysis[J]. International Journal of Optimization in Civil Engineering, 2020, 10(3): 493-512. |
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