Variational level set methods for multiphase image segmentation based on piecewise constant

doi:10.7523/j.issn.2095-6134.2012.6.005

Abstract

Abstract: A multiphase image segmentation model with the noise removal ability is proposed based on the variational level set mehod. The new model can complete the segmentation and the denoising process simultaneously. Therefore it can reduce the execution time of image segmentation. On the other hand, we construct the characteristic function of the regional division based on the decimal-binary number conversion. Finally, the proposed model is applied to the segmentation of the synthetic images and medical images. The experimental results show that the proposed model can extract the targets from the noise image faster than Chan-Vese model.

Key words: denoising, multiphase image segmentation, level set, characteristic functions

CLC Number:

TP391

LI Zhong-Wei, NI Ming-Jiu. Variational level set methods for multiphase image segmentation based on piecewise constant[J]. , 2012, (6): 750-756.

References

[1] Chan T F, Shen J. Image processing and analysis: variational, PDE, wavelet, and stochastic methods [M]. Philadelphia: Siam, 2006.
[2] Paragios N, Chen Y, Faugeras O. The handbook of mathematical models in computer vision [M]. New York: Springer Verlag, 2005.
[3] Osher S, Paragios N. Geometric level set methods in imaging vision and graphics [M]. New York: Springer Verlag, 2003.
[4] Aubert G, Kornprobst P. Mathematical problems in image processing: partial differential equations and the calculus of variations [M]. New York: Springer Verlag, 2002.
[5] Mumford D, Shah J. Optimal approximation by piecewise smooth functions and associated variational problems [J]. Comm Pure Appl Math, 1989, 42:577-685.
[6] Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations [J]. J Comput Phys, 1988, 79(1): 12-49.
[7] Vese L A, Chan T F. A multiphase level set framework for image segmentation using the Mumford and Shah model [J]. Int J of Comput Vis, 2002, 50(3):271-293.
[8] Dabiel C, Stefano S. Motion competition: a variational approach to piecewise parametric motion segmentation [J]. Int J of Comput Vis, 2005, 62(3):249-265.
[9] Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J]. Phys D, 1992, 60:259-268.
[10] Andreu F, Caselles V, Diaz J I, et al. Some qualitative properties of the total variation flow [J]. J Funct Anal, 2002, 188(2):516-547.
[11] Whitaker R T, Pizer S M. A multi-scale approach to nonuniform diffusion [J]. Comput Vis Graph Image Process, 1993, 57:99-110.
[12] Chan T F, Marquina M, Mulet P. High-order total variation-based image restoration [J].J Sci Comput, 2000, 22:503-516.
[13] You Y L, Kaveh M. Fourth-order partial differential equation for noise removal [J]. IEEE Trans Image Process, 2000, 9:1723-1730.
[14] Zhao H K, Chan T F, Merriman B, et al. A variational level set approach to multiphase motion [J]. J Comput Phys, 1996, 127:179-195.
[15] Samson C, Blanc-Feraud L, Aubert G, et al. A level set model for image classification [J]. Int J Comput Vis, 2000, 40 (3): 187-197.
[16] Lie J, Lysaker M, Tai X C. A binary level set model and some applications to Mumford-Shah image segmentation [J]. IEEE Trans Image Process, 2006, 15(5):1171-1181.
[17] Li J, Yang X, Shi P F. A fast level set approach to image segmentation based on Mumford-Shah model [J]. Chin J Comput, 2002, 25(11):1175-1183 (in Chinese). 李俊,杨新,施鹏飞. 基于Mumford-Shah模型的快速水平集分割方法 [J]. 计算机学报, 2002, 25(11): 1175-1183.
[18] Xiao L, Wu H Z, Wei Z H, et al. A new level set method of piecewise smooth Mumford-Shah model for image segmentation [J]. J Comput Res Dev, 2004, 41(1): 129-135 (in Chinese) 肖亮,吴慧中,韦志辉,等. 图像分割中分段光滑Mumford-Shah模型的水平集算法 [J]. 计算机研究与发展, 2004, 41(1):129-135.
[19] Zhu F P, Tian J, Lin Y, et al. Medical image segmentation based on level set method [J]. J Softw, 2002, 13(9): 1866-1872 (in Chinese). 朱付平,田捷,林瑶,等. 基于Level Set方法的医学图像分割 [J]. 软件学报,2002, 13(9):1866-1872.
[20] Chen B, Lai J H. Active contour models on image segmentation: a survey [J]. J Image Graph, 2007, 12(1): 11-20 (in Chinese). 陈波,赖剑煌. 用于图像分割的活动轮廓模型综述[J]. 中国图像图形学报, 2007, 12(1):11-20.