最大流方法在图像去噪和分割中的研究进展
Progress of Max-Flow Method in Image Denoising and Segmentation
DOI: 10.12677/jisp.2013.22003, PDF, HTML,    国家自然科学基金支持
作者: 王小欢*, 杨晓艺, 宋锦萍：河南大学数学与信息科学学院，开封
关键词: 最大流；图像去噪；图像分割；Max-Flow; Image Denoising; Image Segmentation
摘要:  近年来，基于能量泛函的图像去噪和分割模型得到广泛的关注，解决这类模型的有力工具之一是最大流方法。本文分别介绍离散的和连续的最大流方法，包括能量泛函最小化问题转化为最大流问题的基本步骤，以及相应最大流问题的求解方法，并展望最大流方法的发展前景。
Abstract: In recent years, image denoising and segmentation model based on energy functional received widely atten- tion. Max-flow method is one of the most powerful tools to solve this kind of model. Discrete and continuous max-flow methods are introduced, they both include the basic steps in which energy functional minimization problem transformed to max-flow problem, and the solutions of the corresponding max-flow problem are also reviewed. In addition, the de- velopment of max-flow method are also discussed.

文章引用：王小欢, 杨晓艺, 宋锦萍. 最大流方法在图像去噪和分割中的研究进展[J]. 图像与信号处理, 2013, 2(2): 19-23. http://dx.doi.org/10.12677/jisp.2013.22003

参考文献

[1] 刘松涛, 殷福亮. 基于图割的图像分割方法及其新进展[J]. 自动化学报, 2012, 38(6): 911-922.
[2] 杨建功, 汪西莉. 一种结合图割与双水平集的图像分割方法[J]. 计算机工程与应用, 2012, 48(3): 195-197.
[3] D. Greig, B. Porteous and A. Ssheult. Exact maximum a poste- riori estimation for binary images. Journal of the Royal Statisti- cal Society, Series B, 1989, 51(2): 271-279.
[4] Y. Bovkov, M. P. Jolly. Interactive organ segmentation using graph cuts. Proceeding of the 3rd International Conference on Medical Image Computing and Computer-Assisted Intervention, Pittsburgh: Springer, 2000: 276-286.
[5] T. P. Gurholt, X.-C. Tai. 3D multiphase piecewise constant level set method based on graph cut minimization. Numerical Mathe- matics: Theory, Methods and Applications, 2009, 2: 403-420.
[6] E. Bae, J. Shi and X.-C. Tai. Graph cuts for curvature based image denoising. IEEE Transactions on Image Processing, 2009: 1-30.
[7] J. C. Picard, H. D. Ratliff. Minimum cuts and related problems. Networks, 1975, 5(4): 357-370.
[8] Y. Bovkov, O. Veksler. Graph cuts in vision and graphics: Theo- ries and applications. Handbook of Mathematical Models in Computer Vision, NewYork: Springer, 2006: 79-96.
[9] B. V. Cherkassky, A. V. Goldberg. On implementing the pushrelabel method for the maximum flow problem.Algorithmica,1997,19(4):390-410.
[10] Goldberg A V,Tarjan R E.A new approach to the maximum-flow problem.Journal of the ACM,1988,35(4):921-940.
[11] Ford L,Fulkerson D.Flows in Networks.Princeton:Princeton University Press, 1962.
[12] Dinic E A. Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Mathematics- Doklady, 1970, 11(5): 1277-1280.
[13] Y. Boykov, O. Veksler and R. Zabih. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Ana- lysis and Machine Intelligence, 2001, 23(11): 1222-1239.
[14] V. Kolmogorov. What metrics can be approximated by geo-cuts or global optimization of length/area and flux. ICCV, 2005: 564- 571.
[15] G. Strang. Maximal flow through a domain. Mathematics Pro- gramming, 1983, 26: 123-143.
[16] G. Strang. Maximum flows and minimum cuts in the plane. Advances in Mechanics and Mathematics, 2008, III: 1-11.
[17] B. Appleton, H. Talbot. Globally optimal surfaces by continuous maximal flows. Digital Image Computing: Techniques and Applications, 2003: 987-996.
[18] B. Appleton, H. Talbot. Globally minimal surfaces by continu- ous maximal flows. IEEE PAMI, 2006: 28.
[19] T. Chan, S. Esedoglu and M. Nikolova. Algoritms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics, 2006, 66(5): 1632-1648.
[20] E. Bae, J. Yuan and X.-C. Tai. Convex relaxation for multipartitioning problems using a dual approach. Technical Report CAM 09-75, UCLA, CAM, 2009 September.
[21] J. Lellmann, J. Kappes, J. Yuan, F. Becker and C. Schnorr. Con- vex multi-class image labeling by sim-plex-constrained total va- riation. Technical Report, HIC, IWR, University Heidelberg, 2008 November.
[22] T. Pock, A. Chambolle, H. Bischof and D. Cremers. A convex relaxation approach for computing minimal partitions. CVPR, Miami, 2009.
[23] J. Yuan, E. Bae and X.-C. Tai. A study on continuous max-flow and min-cut approaches. IEEE, 2010: 2217-2224.