基于偏微分方程的生物信息图像处理方法研究
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摘要
生物信息图像处理是生物工程学科的一个分支,包括生物信息处理技术、生物图像处理与分析等,是生物工程领域中发展最迅速的学科方向之一。生物信息图像分析致力于从生物图像或生物图像序列中提取数字信息,在生命科学领域有广泛的应用。然而生物信息图像往往存在一定的噪声,为了后续图像分析与处理,通常需要首先对输入图像进行去噪增强处理,从而改善图像质量,然后进行分割定位处理。一方面,生物信息图像去噪要求既能去除图像的模糊和噪声,又需要保持图像的细节,传统的滤波方法难以处理这类问题。另一方面,对于生物信息图像来说,其特有的复杂性和多样性使其分割方法不能统一,传统的阈值分割方法和分水岭标记变换等方法针对复杂的生物信息图像来说会导致分割失败。
近年来,偏微分方程理论(Partial Differential Equations,PDE)因其严格的数学理论基础已经在图像处理的各个领域得到了广泛应用,并取得了一系列研究成果。针对生物信息图像,结合偏微分方程理论,本文主要的研究工作如下：
1.针对生物信息图像经过传统PDE模型会产生孤立点和噪声强化等缺点,提出了一种基于各向异性扩散方程的图像去噪方法。利用形态学重建技术对正则项进行约束,达到了抑制图像边界移动的目的；并根据梯度阈值范围不同,采用两种扩散系数来加强图像边缘的细节信息；为了减少不必要的扩散,将阈值参数记为时间的函数,减少了去噪时间。实验结果表明,该方法能保留更多的图像边缘细节,在信噪比方面要优于传统的PDE去噪模型。
2.针对全变分模型易受到噪声影响,在图像处理过程中会丢失重要的细节信息的问题,提出一种适合生物信息图像的全变分去噪增强模型。利用形态学重建先验知识约束正则化项,提高了TV正则项指数；通过给平滑项增加新的自适应系数的方法,增强了生物信息图像的边缘结构。模型分析和实验结果均表明,提出的全变分模型在去噪性能方面优于传统PDE模型。该模型还可以作为一种有效的图像预处理手段,与分水岭标记变换结合可以准确高效的提取到生物信息图像的目标区域。
3.由于生物信息图像具有目标分散、边缘模糊的特点,为了快速准确的分离图像目标区域,提出了一种基于水平距离正则项的主动轮廓分割模型。该模型利用不同的正则化函数分别对全局拟合项和局部拟合项进行约束,进一步提高了分割精度；并设计新的边缘停止函数来保护生物信息图像的弱边缘,防止边缘泄露；为了进一步消除水平集函数的重新初始化过程,模型中通过使用一种含有两个极小值的水平距离正则项来对能量泛函进行约束,可以在迭代中采用较大的时间步伐,提高曲线的演化速度。实验结果表明该分割模型对演化参数的设置不敏感,能有效保护生物信息图像的弱边缘,具有很强的分割鲁棒性。
4.针对生物信息图像会出现灰度不均匀性、亮度不一致性的问题,提出了一种结合区域邻域信息的局部二值拟合图像分割模型。通过在全局拟合项中添加像素邻域影响项,使分割模型能够以较少的迭代次数分割亮度不一致的生物信息图像。同时,为了保证水平集方法中的精确计算,能量泛函中通过添加距离正则项来消除水平集函数的重新初始化过程。实验结果表明该模型具有不容易陷入局部极小值区域、水平集迭代次数少、对初始轮廓位置不敏感等优点。
Image processing of biological information is a branch of the bio-engineering disciplines, including biological information processing technology, biotechnology, image processing and analysis, Biological image processing and analysis, which is one of the fastest growing disciplines in the field of bio-engineering direction. Image analysis of biological information is committed to the digital information extracted from biological images or biological image sequences, there is a wide range of applications in the field of life sciences. However, biological information images often have a certain amount of noise, for subsequent image segmentation, it needs enhance the input image edge and improve image quality as well. On one hand, the biological information image filtering requires not only to remove blurring and noises, but also to keep the details of the image, while the traditional filtering methods are difficult to deal with such issues. On the other hand, nowadays, there has not been one unified scheme biological information image segmentation due to its unique complexity and diversity, traditional threshold segmentation method and watershed mark transform method are not suitable for complex biological images, and they will lead to segmentation failure.
In recent years, the theory of partial differential equations has been widely used in various areas of image processing and achieved a great deal of achievements because of its strict mathematical theory. For images of biological information, combined with the theory of partial differential equations, the research work of this thesis are as follows:
1. The traditional partial differential equations denoising model for biological information image may produce isolated point and noise enhancement, to solve the above problem, an improved anisotropic diffusion equation denosing model is designed. Firstly it uses morphological reconstruction technique to process the regularization item of images and then use the two diffusion coefficients respectively to handle edge region and non-edge region of image differently. Furthermore, in order to reduce unnecessary diffusion time, the threshold parameter is recorded as a function of time. The results of experiments show that the new method is able to retain more edge details, and it has better signal-to-noise ratio than the traditional PDE denoising model.
2. A problem of the total variation model is that it is easy to be affected of the noise in the image processing, which may lead to miss some important details, to solve the problem, an adaptable total variational denoising and enhancement model of the biological information image is proposed. The adaptive smoothing term can smooth the edge area and the flat areas in different degree keep the details on edges. The analysis of the new model and the experimental results show that the proposed variational model has better performance than the traditiona PDE models, and it is an efficient pre-processing method for image, a watershed transformation segmentation method with markers can extract the object region of biological information image by using the new model.
3. Biological information image edge of the target area is usually blur, in order to segment the biological information image quickly and accurately, a novel active contour model for image segmentation using distance regularized term is proposed in the article. The model uses two different regularization functions for the global fitting term and the local fitting term to improve the accuracy of segmentation. A new edge stopping function is proposed to protect the weak edges of image. A distance regularization term using a function with two minimums is designed to eliminate the re-initialization of the level set function in the process of iterations. And also, a big time step is used to increase the speed of the evolution. The experimental results show that the new segmentation model is not sensitive to the settings of parameters and it can protect the weak edges of the biological information image effectively, and it has a strong segmentation robustness.
4. A combination of regional neighborhood local binary fitting image segmentation model is proposed to segment biological information image to deal with the gray scale inhomogeneity and brightness inconsistency of the image, the new model uses the global fitting term which adds pixel neighborhood impact items to divide the biological information image fastly. Meanwhile, in order to ensure accurate calculation of the level set method, the energy functional uses distance regularization term to eliminate the re-initialization of the level set evolution process. The experimental results show that the model is not easy to fall into the local minimum regions, it has fewer iterations of evolution and is not sensitive to the location of the initial contour.
近年来,偏微分方程理论(Partial Differential Equations,PDE)因其严格的数学理论基础已经在图像处理的各个领域得到了广泛应用,并取得了一系列研究成果。针对生物信息图像,结合偏微分方程理论,本文主要的研究工作如下：
1.针对生物信息图像经过传统PDE模型会产生孤立点和噪声强化等缺点,提出了一种基于各向异性扩散方程的图像去噪方法。利用形态学重建技术对正则项进行约束,达到了抑制图像边界移动的目的；并根据梯度阈值范围不同,采用两种扩散系数来加强图像边缘的细节信息；为了减少不必要的扩散,将阈值参数记为时间的函数,减少了去噪时间。实验结果表明,该方法能保留更多的图像边缘细节,在信噪比方面要优于传统的PDE去噪模型。
2.针对全变分模型易受到噪声影响,在图像处理过程中会丢失重要的细节信息的问题,提出一种适合生物信息图像的全变分去噪增强模型。利用形态学重建先验知识约束正则化项,提高了TV正则项指数；通过给平滑项增加新的自适应系数的方法,增强了生物信息图像的边缘结构。模型分析和实验结果均表明,提出的全变分模型在去噪性能方面优于传统PDE模型。该模型还可以作为一种有效的图像预处理手段,与分水岭标记变换结合可以准确高效的提取到生物信息图像的目标区域。
3.由于生物信息图像具有目标分散、边缘模糊的特点,为了快速准确的分离图像目标区域,提出了一种基于水平距离正则项的主动轮廓分割模型。该模型利用不同的正则化函数分别对全局拟合项和局部拟合项进行约束,进一步提高了分割精度；并设计新的边缘停止函数来保护生物信息图像的弱边缘,防止边缘泄露；为了进一步消除水平集函数的重新初始化过程,模型中通过使用一种含有两个极小值的水平距离正则项来对能量泛函进行约束,可以在迭代中采用较大的时间步伐,提高曲线的演化速度。实验结果表明该分割模型对演化参数的设置不敏感,能有效保护生物信息图像的弱边缘,具有很强的分割鲁棒性。
4.针对生物信息图像会出现灰度不均匀性、亮度不一致性的问题,提出了一种结合区域邻域信息的局部二值拟合图像分割模型。通过在全局拟合项中添加像素邻域影响项,使分割模型能够以较少的迭代次数分割亮度不一致的生物信息图像。同时,为了保证水平集方法中的精确计算,能量泛函中通过添加距离正则项来消除水平集函数的重新初始化过程。实验结果表明该模型具有不容易陷入局部极小值区域、水平集迭代次数少、对初始轮廓位置不敏感等优点。
Image processing of biological information is a branch of the bio-engineering disciplines, including biological information processing technology, biotechnology, image processing and analysis, Biological image processing and analysis, which is one of the fastest growing disciplines in the field of bio-engineering direction. Image analysis of biological information is committed to the digital information extracted from biological images or biological image sequences, there is a wide range of applications in the field of life sciences. However, biological information images often have a certain amount of noise, for subsequent image segmentation, it needs enhance the input image edge and improve image quality as well. On one hand, the biological information image filtering requires not only to remove blurring and noises, but also to keep the details of the image, while the traditional filtering methods are difficult to deal with such issues. On the other hand, nowadays, there has not been one unified scheme biological information image segmentation due to its unique complexity and diversity, traditional threshold segmentation method and watershed mark transform method are not suitable for complex biological images, and they will lead to segmentation failure.
In recent years, the theory of partial differential equations has been widely used in various areas of image processing and achieved a great deal of achievements because of its strict mathematical theory. For images of biological information, combined with the theory of partial differential equations, the research work of this thesis are as follows:
1. The traditional partial differential equations denoising model for biological information image may produce isolated point and noise enhancement, to solve the above problem, an improved anisotropic diffusion equation denosing model is designed. Firstly it uses morphological reconstruction technique to process the regularization item of images and then use the two diffusion coefficients respectively to handle edge region and non-edge region of image differently. Furthermore, in order to reduce unnecessary diffusion time, the threshold parameter is recorded as a function of time. The results of experiments show that the new method is able to retain more edge details, and it has better signal-to-noise ratio than the traditional PDE denoising model.
2. A problem of the total variation model is that it is easy to be affected of the noise in the image processing, which may lead to miss some important details, to solve the problem, an adaptable total variational denoising and enhancement model of the biological information image is proposed. The adaptive smoothing term can smooth the edge area and the flat areas in different degree keep the details on edges. The analysis of the new model and the experimental results show that the proposed variational model has better performance than the traditiona PDE models, and it is an efficient pre-processing method for image, a watershed transformation segmentation method with markers can extract the object region of biological information image by using the new model.
3. Biological information image edge of the target area is usually blur, in order to segment the biological information image quickly and accurately, a novel active contour model for image segmentation using distance regularized term is proposed in the article. The model uses two different regularization functions for the global fitting term and the local fitting term to improve the accuracy of segmentation. A new edge stopping function is proposed to protect the weak edges of image. A distance regularization term using a function with two minimums is designed to eliminate the re-initialization of the level set function in the process of iterations. And also, a big time step is used to increase the speed of the evolution. The experimental results show that the new segmentation model is not sensitive to the settings of parameters and it can protect the weak edges of the biological information image effectively, and it has a strong segmentation robustness.
4. A combination of regional neighborhood local binary fitting image segmentation model is proposed to segment biological information image to deal with the gray scale inhomogeneity and brightness inconsistency of the image, the new model uses the global fitting term which adds pixel neighborhood impact items to divide the biological information image fastly. Meanwhile, in order to ensure accurate calculation of the level set method, the energy functional uses distance regularization term to eliminate the re-initialization of the level set evolution process. The experimental results show that the model is not easy to fall into the local minimum regions, it has fewer iterations of evolution and is not sensitive to the location of the initial contour.
引文
[1]陈绮.生物信息学中计算机技术应用.北京：电子工业出版社,2010.
[2]T.Charlie Hodgman et al.Bioinfomatics.北京：科学出版社,2012.
[3]肖特利弗著.罗述谦译.生物医学信息学.北京：科学出版社,2011.
[4]郭业才.生物医学信息与图像处理.北京：科学出版社,2010.
[5]Akay, M.,Marsh, A.. Information Technologies in Medicine, Medical Simulation and Education. Wiley-IEEE Press,2001.
[6]Webb, A. Introduction to Biomedical Imaging. Wiley-IEEE Press,2003. Berners-Lee T, Handler T and Lassila O. The semantic web. American:Scientific American,2001.
[7]赵法荣.影响CT增强扫描效果因素分析及解决对策.中国实用神经疾病杂志,2007,10(1)：148-148.
[8]黄继英,染星原.磁共振成像原理.西安：陕西科学技术出版社,1998.
[9]Zeyun Yu, Ming Xu, Zhanheng Gao.Biomedical image segmentation via constrained graph cuts and pre-segmentation. Engineering in Medicine and Biology Society,2011 Annual International Conference of the IEEE Digital Object Identifier,2011:5714-5717.
[10]Ceylan, M., Ozbay, Y., Yildirim, E.A new approach for biomedical image segmentation:Combined complex-valued artificial neural network case study:Lung segmentation on chest CT images.5th Cairo International Biomedical Engineering Conference,2010:33-36.
[11]刁宏志.针叶材年轮细胞图像识别及几何参数建模的研究：(博士学位论文).哈尔滨：东北林业大学,2008.
[12]马义德.生物信息的数字图像处理技术研究：(硕士学位论文).苏州：苏州大学,2001.
[13]秦树伟.白细胞显微图像的分类识别研究：(硕士学位论文).苏州：苏州大学,2007.
[14]冯晨.基于分形维数的中国海常见浮游植物细胞图像特征提取：(博士学位论文).青岛：中国海洋大学,2007.
[15]尹聪.真彩色细胞显微图像自动识别技术的研究：(硕士学位论文).济南：山东大学,2008.
[16]卢艳芝.重叠细胞分割技术研究：(硕士学位论文).长沙：湖南师范大学,2008.
[17]程军娜.基于形态学多尺度图像分析的海藻细胞图像分割及特征提取：(博士学位论文).青岛：中国海洋大学,2010.
[18]李宏,任建敏.生物显微图像分析与处理研究.重庆工商大学学报(自然科学版),2006,23(1)：15-20.
[19]郑仙斌,徐向东,陆祖康.一种用于植物细胞的显微图像处理系统.仪器仪表学报,2002,23(6)：655-656.
[20]谭裴.磁共振成像中的运动伪影消除方法研究：(博士学位论文).合肥：中国科学技术大学,2009.
[21]Liu, Juan Moulin, Pierre.Complexity-regularized image denoising. IEEE International Conference on Image Processing,1997,2:370-373.
[22]Pesquet, J.-C. Empirical wavelet estimator for image denoising. Conference Record of the Asilomar, Conference on Signals, Systems and Computers,1998,1:91-94.
[23]Mihcak, M.Kivanc Kozintsev,Igor,Ramchandran, Kannan, Moulin, Pierre. Low-complexity image denoising based on statistical modeling of wavelet coefficients.IEEE Signal Processing Letters, 1999,6(12):300-303.
[24]W.K.Pratt, Wiley, Digital Image Processing. New York, NY, USA,1978.
[25]刘刚.matlab数字图像处理.北京：机械工业出版社,2010.
[26]宋余庆.数字医学图像,北京：清华大学出版社,2008.
[27]高立群.图像分割若干问题的研究与应用：(博士学位论文).沈阳：东北大学,2009.
[28]章毓晋.图像工程(中册)图像分析.北京：清华大学出版社,2005.
[29]林瑶,田捷.医学图像分割方法综述.模式识别与人工智能,2002,15(2)：192-204.
[30]Thomas M.Cover.Joy A.Thomas信息论基础.北京：清华大学出版社,2003.
[31]Vincenzo Piuri, Fabio Scotti, Morphological Classification of Blood Leucocytes by Microscope Images, IEEE CIMSA,2004:103-108.
[32]杨福生.小波变换的工程分析与应用.北京：科学出版社,2000.
[33]马义德,史飞,李廉等.一种基于脉冲耦合神经网络的脉冲噪声滤波器设计.生物医学工程学杂志,2004,21(6)：1019-1023.
[34]Gabor D, Information theory in electron microscopy.Laboratory Investigation,1965,(14):801-807.
[35]Jain A K. Partial Differential Equation and Finite-Difference Methods in Image Processing, Parl: Image Representation.optimization theory and application,1977,23:65-91.
[36]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京：科学出版社,2006.
[37]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[38]Catte F, Lions P, Morel J. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis,1992,29:182-193.
[39]林宙辰,石青云.一个能去噪和保持真实感的各向异性扩散方程.计算机学报,1999,22(11)：1133-1137.
[40]Jian Ling, Alan C. Bovik. Smoothing Low-SNR Molecular Images Via Anisotropic Median-Diffusion. IEEE Transactions On Medical Imaging,2002,21(4):377-384.
[41]C. Andrew Segall, Scott T. Acton. Morphological Anisotropic Diffusion.International Conference on Image Processing,1997, (26-29)3:348-351.
[42]L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physical D,1992,60:259-268.
[43]L. Rudin, S. Osher. Total variation based image restoration with free local constraints. IEEE ICIP In Processing,1994,(I):31-35.
[44]Tony F. Chan, H.M. Zhou, Raymond H. Chan, Continuation Method for Total Variation Denoising Problems, UCLA CAM Report,1995.
[45]余丽红,冯衍秋,陈武凡.基于自适应正则化的全变分去噪算法.中国图象图形学报,2009,(14)10：1950-1954.
[46]陈利霞,宋国乡,丁宣浩,王旭东.改进的总变分去噪算法.光子学报,2009,38(4)：1001-1004.
[47]李玲,胡学刚,蒋伟.一种基于LIP的全变分图像去噪新模型.四川师范大学学报(自然科学版).2011,34(1)：134-138.
[48]Pouya Dehghani Tafti, Ricard Delgado-Gonzalo, Aurelien F. Stalder, Michael Unser.Variational enhancement and denosing of flow field images.The eighth IEEE International Symposium on Biomedical Imaging.2011:1061-1064.
[49]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models. Internatioanl Journal of Computer Vision,1988,1:321-331.
[50]林颖.基于水平集方法的图像分割关键技术研究：(博士学位论文).哈尔滨：哈尔滨工和大学,2010.
[51]J.A. Sethian, Level Set Methods and Fast Marching Methods:Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. NewYork USA:Cambridge University Press,1996.
[52]S.Osher, J.A.Sethian, Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics.1988,79(1):12-49.
[53]A.R.Mansouri, A.Mitiche, C.Vazquez.Multi-region competition:A level set extension of region competition to multiple region image partitioning.Computer Vision and Image Understanding, 2006,101:137-150.
[54]王大鹏.基于水平集的图像分割技术研究：(硕士学位论文).合肥：安徽大学,2011.
[55]李俊.杨新.施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法.计算机学报,2002,25(11)：1176-1183.
[56]D.Mumford, J.Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math,1989,42:577-685.
[57]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. International Journal of Computer Vision, 1997,22(1):61-79.
[58]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics,1989, (42):577-685.
[59]Ambrosio L, Fusco N,Pallara D.Functions of Bounded Variation and Free Dis-continuity Problems.Oxford:Clarendon Press,2000:71-97.
[60]Morel J M, Solimini S. Variational Methods in Image Segmentation.Boston:Birkhauser Boston, 1995:113-123.
[61]Chan T, Vese L, Active contours without edges. IEEE Transactions on Image Processing 2001, 10(2):266-77.
[62]David Adalsteinsson, David Adalsteinsson, James A. Sethian, James A. Sethian. A Fast Level Set Method for Propagating Interfaces. Journal of Computational Physics,1994,118(2):203-231.
[63]王峥,杨新,李俊,施鹏飞.基于水平集人机交互模型的医学图像分割.模式识别与人工智能,2002,15(4)：392-396.
[64]Li C M, Xu C Y, Gui Changfen. Level set Evolution without Re-initialization:a New Varitional Formulation.Computer Vision and Pattern Recognition,2005,1:430-436.
[65]LiWang, Chunming Li, Quansen Sun, Deshen Xia, Chiu-Yen Kao, Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation, Computerized Medical Imaging and Graphics,2009,33:520-531.
[66]Li C, Kao C, Gore J, Ding Z. Implicit active contours driven by local binary fitting energy. In: Proceedings of IEEE conference on computer vision and patternrecognition (CVPR).2007:1-7.
[67]高静.基于形态学分水岭算法的细胞图像分割：(硕士学位论文).长春：吉林大学,2008.
[68]陈伟斌,张鑫,陈胜勇.基于形态学重构算法的细胞图像边缘检测.计算机与数字程,2008,36(12),135-137.
[69]尹诗白,赵祥模,王卫星,孙小蓉.荧光彩色医学细胞图像分割及其染色体的提取和识别.四川大学学报(工程科学版),2011,43(1)：133-138.
[70]HU Chan,JIANG Li-Jun,BO Jiang.Wavelet Transform and Morphology Image Segmentation Algorism for Blood Cell.4th IEEE Conference on Industrial Electronics and Applications,2009:542-545.
[71]Hui Kong, Metin Gurcan, Kamel Belkacem-Boussaid.Partitioning Histopathological Images:An Integrated Framework for Supervised Color-Texture Segmentation and Cell Splitting.IEEE Transation on medical imaging,2011,30(9):1661-1677.
[72]贾迪,杨金柱,曹鹏,张一匕,赵大哲,于戈,一种具有边缘保护的MRI影像同步去噪增强算法.小型微型计算机系统,2011,32(10)：2064-2067.
[73]牛和明,杜茜,张建勋,一种自适应全变分图像去噪算法.模式识别与人工智能,2011.24(6)：798-803.
[74]Yaniv Gal, Andrew J. H. Mehnert, Andrew P. Bradley, Kerry McMahon, Dominic Kennedy, Stuart Crozier, Denoising of Dynamic Contrast-Enhanced MR Images Using Dynamic Nonlocal Means, IEEE Transactions on medical imaging,2010,29(2):302-310.
[75]蒙建军,靳艳红,基于KFCM算法对MRI图像分割的研究,湖北民族学院学报(自然科学版)2011,29(1)：108-111.
[76]宋利伟,宋朝昀,庄天戈,基于分水岭算法的磁共振脑图像自动分割,上海交通大学学报,2003,,37(11)：1754-1756.
[77]H. P. Ng, S. H. Ong, K. W. C. Foong, P. S. Goh, W. L. Nowinski, Masseter segmentation using an improved watershed algorithm with un supervised classification,Computers in Biology and Medicine.2008,38:171-184.
[78]林相波.基于非刚性配准的图像分割研究及其在脑部MRI图像中的应用：(博士学位论文).大连：大连理工大学.2010.
[79]李小兵.MRI图像脑肿瘤分割与EEG脑癫痫检测的研究：(博士学位论文).大连：大连理工大学.2010.
[80]S.E. Yuksel, A. El-Baz. A.A. Farag, M.E.A. El-Ghar, T.A. Eldiasty, M.A. Ghoneim, A Kidney Segmentation Framework for Dynamic Contrast Enhanced Magnetic Resonance Imaging.International Congress Series on Automatic detection of renal rejection after kidney transplantation,2005:773-778.
[81]Frank G. Zolner, Rosario Sance, Peter Rogelj, Maria J. Ledesma-Carbayo, Jarle Rovik, Andres Santos, Arvid Lundervold. Assessment of 3D DCE-MRI of the kidneys using non-rigid image registration and segmentation of voxel time courses. Computerized Medical Imaging and Graphics,2009,33:171-181.
[82]Ting Song, Vivian S. Lee, Henry Rusinek, Manmeen Kaur, Andrew F. Laine. Automatic 4-D Registration in Dynamic MR Renography. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference,2005:3067-3070.
[83]Dongjiao LV, Jie Zhang. Dynamic Contrast-Enhanced Magnetic Resonance Images of the kidney.IEEE Engineering In Medicine And Biology Magazine,2008,8:36-41.
[84]章日康.基于偏微分方程及变分水平集的图像分割：(硕士学位论文).西安：电子科技大学,2008.
[85]金大年.基于水平集的医学图像分割算法研究：(硕士学位论文).广州：第一军医大学,2005.
[86]Elliott PJ. Knapamn JM, SehlegeW. Interactive Image Segmentation for Radiation Treamtnet Planning.IBM Systems Journal,1992,31(4):620-634.
[87]宋余庆.数字医学图像,北京：清华大学出版社.2008.
[88]J.A.Sethian.Level Set Methods and Fast Marching Methods. Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Seienees. Cambridge, U.K.:Cambridge University Press.1966.
[89]S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces.New York:Springer-Verlag Express,2002.
[90]Gabor D, Information theory in electron microscopy.Laboratory Investigation,1965,(14):801-807.
[91]Jain A K. Partial Differential Equation and Finite-Difference Methods in Image Processing, Parl: Image Representation.optimization theory and application,1977,23:65-91.
[92]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[93]汪伟.基于各向异性扩散的数字图像处理研究：(硕士学位论文).合肥：中国科学科技大学,2009.
[94]姜东焕,冯象初,宋国乡.基于形态学算子的各向异性扩散方程.西安电子科技大学学报(自然科学版).2006,(33)1：121-124.
[95]Serra Jean. Image Analysis and Mathematical Morphology.USA:Academic Press,1982.
[96]P Soille, Morphological Image Analysis:Principles and Applications, Berlin, Germany: Springer-Verlag,2003.
[97]熊金涛,孙乾松,李良超,杨建宇.一种基于自适应双向扩散过程的无源毫米波图像去噪与增强.红外与毫米波学报,2011.30(6)：556-560.
[98]陈文斌,程晋译.图像处理与分析：变分.PDE.小波及随机方法.北京：科学出版社.2011.
[99]罗俊召,陈立平,罗震.基于半隐式格式的水平集法连续体结构形状和拓扑优化方法.固体力学学报,2008.29(2)：175-180.
[100]M.A.Mohamed,B.M.EI-Den.Implementation of image fusion techniques using FPGA, IJCSNS International Journal of Computer Science and Network Security,2010,10(5):95-102.
[101]PJin LI, P PYanwei WANG, P P Jie WEI, P Dada WANG, PHong YU.A FNL Means De-noise Algorithm Based on Gradient Calibration.International Journal of Advancements in Computing Technology,2011,3(9):147-154.
[102]钱伟长.变分法及有限元(上册).北京：科学出版社,1980.
[103]老大中.变分法基础.北京：国防工业出版社,2007.
[104]郭彦伶.基于全变分(TV)的彩色图像增强：(硕士学位论文).西安：西北大学,2009.
[105]Courant R, Friedrichs K O, Lewy H. On the partial differentail equation of mathematical physics. IBMJ,1967,11:215-243.
[106]Chan T, shen JH. Mathematical model for local non-texture inpainting. Siam journal on applied mathematics,2001,62(3)1019-1043.
[107]袁慰平,孙志忠,吴宏伟,计算方法与实习.南京：东南大学出版社.2000.
[108]Serra Jean. Image Analysis and Mathematical Morphology. USA:Academic Press,1982.
[109]Vincent, L., and Soille, P. Watersheds in digital spaces:an e_cient algorithm based on immersion simulations. IEEE Transactions on pattern analysis and machine intelligence,1991.13(6):583-598.
[110]Jos B.T.M. Roerdink, Arnold Meijster.The Watershed Transform:Definitions, Algorithms and Parallelization Strategies.Fundamenta Informaticae,2001,41:187-228.
[111]冯林,管慧娟,孙焘,滕弘飞,基于分水岭变换和核聚类算法的图像分割,大连理工大学学报,2006,46(6)：851-856.
[112]Pousse, A. Chavanelle, J. Mixed wavelet-watershed method for nodule detection in high resolution scintigraphy, IEEE Transactions on Nuclear Science,2006,53 (3):1096-1101.
[113]Meyer, F. Topographic distance and watershed lines.Signal Processing,1994,38:113-125.
[114]Soille P. Morphological image analysis principles and applications.Berlin, Germany:Springer Verlag, 1999.
[115]齐丽娜,张博,王战凯.最大类间方差法在图像处理中的应用.无线电工程,2006,36(7)：25-26.
[116]王晓峰.水平集方法及其在图像分割中的应用研究：(硕士学位论文).合肥：中国科学技术大学,2009.
[117]刘秀平,常先堂,李治隆.一种基于边缘和区域信息的变分水平集图像分割方法.大连理工大学学报.2008,48(5)：754-758.
[118]C. Li, C. Xu, C. Gui, and M. D. Fox. Distance Regularized Level Set Evolution and its Application to Image Segmentation. IEEE Transactions on Image Processing,2010,19(2):3243-3254.
[119]陆金甫,关治.偏微分方程数值解法.北京：清华大学出版社.2004.
[120]Li C,Kao C,Gore J.C,Ding Z.Minimization of region-scalable fitting energy for segmentation. IEEE Transactions on Image Processing,2008,17(10):1940-1949.
[121]Li Wang, Chunming Li, Quansen Sun, Deshen Xia, Chiu-Yen Kao, Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. Computerized Medical Imaging and Graphics,2009,33:520-531.
[122]X.F. Wang, D-S.Huang, H.Xu. An efficient local Chan-Vese model for image segmentation. Pattern Recognition,2010,43:603-618.
[2]T.Charlie Hodgman et al.Bioinfomatics.北京：科学出版社,2012.
[3]肖特利弗著.罗述谦译.生物医学信息学.北京：科学出版社,2011.
[4]郭业才.生物医学信息与图像处理.北京：科学出版社,2010.
[5]Akay, M.,Marsh, A.. Information Technologies in Medicine, Medical Simulation and Education. Wiley-IEEE Press,2001.
[6]Webb, A. Introduction to Biomedical Imaging. Wiley-IEEE Press,2003. Berners-Lee T, Handler T and Lassila O. The semantic web. American:Scientific American,2001.
[7]赵法荣.影响CT增强扫描效果因素分析及解决对策.中国实用神经疾病杂志,2007,10(1)：148-148.
[8]黄继英,染星原.磁共振成像原理.西安：陕西科学技术出版社,1998.
[9]Zeyun Yu, Ming Xu, Zhanheng Gao.Biomedical image segmentation via constrained graph cuts and pre-segmentation. Engineering in Medicine and Biology Society,2011 Annual International Conference of the IEEE Digital Object Identifier,2011:5714-5717.
[10]Ceylan, M., Ozbay, Y., Yildirim, E.A new approach for biomedical image segmentation:Combined complex-valued artificial neural network case study:Lung segmentation on chest CT images.5th Cairo International Biomedical Engineering Conference,2010:33-36.
[11]刁宏志.针叶材年轮细胞图像识别及几何参数建模的研究：(博士学位论文).哈尔滨：东北林业大学,2008.
[12]马义德.生物信息的数字图像处理技术研究：(硕士学位论文).苏州：苏州大学,2001.
[13]秦树伟.白细胞显微图像的分类识别研究：(硕士学位论文).苏州：苏州大学,2007.
[14]冯晨.基于分形维数的中国海常见浮游植物细胞图像特征提取：(博士学位论文).青岛：中国海洋大学,2007.
[15]尹聪.真彩色细胞显微图像自动识别技术的研究：(硕士学位论文).济南：山东大学,2008.
[16]卢艳芝.重叠细胞分割技术研究：(硕士学位论文).长沙：湖南师范大学,2008.
[17]程军娜.基于形态学多尺度图像分析的海藻细胞图像分割及特征提取：(博士学位论文).青岛：中国海洋大学,2010.
[18]李宏,任建敏.生物显微图像分析与处理研究.重庆工商大学学报(自然科学版),2006,23(1)：15-20.
[19]郑仙斌,徐向东,陆祖康.一种用于植物细胞的显微图像处理系统.仪器仪表学报,2002,23(6)：655-656.
[20]谭裴.磁共振成像中的运动伪影消除方法研究：(博士学位论文).合肥：中国科学技术大学,2009.
[21]Liu, Juan Moulin, Pierre.Complexity-regularized image denoising. IEEE International Conference on Image Processing,1997,2:370-373.
[22]Pesquet, J.-C. Empirical wavelet estimator for image denoising. Conference Record of the Asilomar, Conference on Signals, Systems and Computers,1998,1:91-94.
[23]Mihcak, M.Kivanc Kozintsev,Igor,Ramchandran, Kannan, Moulin, Pierre. Low-complexity image denoising based on statistical modeling of wavelet coefficients.IEEE Signal Processing Letters, 1999,6(12):300-303.
[24]W.K.Pratt, Wiley, Digital Image Processing. New York, NY, USA,1978.
[25]刘刚.matlab数字图像处理.北京：机械工业出版社,2010.
[26]宋余庆.数字医学图像,北京：清华大学出版社,2008.
[27]高立群.图像分割若干问题的研究与应用：(博士学位论文).沈阳：东北大学,2009.
[28]章毓晋.图像工程(中册)图像分析.北京：清华大学出版社,2005.
[29]林瑶,田捷.医学图像分割方法综述.模式识别与人工智能,2002,15(2)：192-204.
[30]Thomas M.Cover.Joy A.Thomas信息论基础.北京：清华大学出版社,2003.
[31]Vincenzo Piuri, Fabio Scotti, Morphological Classification of Blood Leucocytes by Microscope Images, IEEE CIMSA,2004:103-108.
[32]杨福生.小波变换的工程分析与应用.北京：科学出版社,2000.
[33]马义德,史飞,李廉等.一种基于脉冲耦合神经网络的脉冲噪声滤波器设计.生物医学工程学杂志,2004,21(6)：1019-1023.
[34]Gabor D, Information theory in electron microscopy.Laboratory Investigation,1965,(14):801-807.
[35]Jain A K. Partial Differential Equation and Finite-Difference Methods in Image Processing, Parl: Image Representation.optimization theory and application,1977,23:65-91.
[36]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京：科学出版社,2006.
[37]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[38]Catte F, Lions P, Morel J. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis,1992,29:182-193.
[39]林宙辰,石青云.一个能去噪和保持真实感的各向异性扩散方程.计算机学报,1999,22(11)：1133-1137.
[40]Jian Ling, Alan C. Bovik. Smoothing Low-SNR Molecular Images Via Anisotropic Median-Diffusion. IEEE Transactions On Medical Imaging,2002,21(4):377-384.
[41]C. Andrew Segall, Scott T. Acton. Morphological Anisotropic Diffusion.International Conference on Image Processing,1997, (26-29)3:348-351.
[42]L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physical D,1992,60:259-268.
[43]L. Rudin, S. Osher. Total variation based image restoration with free local constraints. IEEE ICIP In Processing,1994,(I):31-35.
[44]Tony F. Chan, H.M. Zhou, Raymond H. Chan, Continuation Method for Total Variation Denoising Problems, UCLA CAM Report,1995.
[45]余丽红,冯衍秋,陈武凡.基于自适应正则化的全变分去噪算法.中国图象图形学报,2009,(14)10：1950-1954.
[46]陈利霞,宋国乡,丁宣浩,王旭东.改进的总变分去噪算法.光子学报,2009,38(4)：1001-1004.
[47]李玲,胡学刚,蒋伟.一种基于LIP的全变分图像去噪新模型.四川师范大学学报(自然科学版).2011,34(1)：134-138.
[48]Pouya Dehghani Tafti, Ricard Delgado-Gonzalo, Aurelien F. Stalder, Michael Unser.Variational enhancement and denosing of flow field images.The eighth IEEE International Symposium on Biomedical Imaging.2011:1061-1064.
[49]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models. Internatioanl Journal of Computer Vision,1988,1:321-331.
[50]林颖.基于水平集方法的图像分割关键技术研究：(博士学位论文).哈尔滨：哈尔滨工和大学,2010.
[51]J.A. Sethian, Level Set Methods and Fast Marching Methods:Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. NewYork USA:Cambridge University Press,1996.
[52]S.Osher, J.A.Sethian, Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics.1988,79(1):12-49.
[53]A.R.Mansouri, A.Mitiche, C.Vazquez.Multi-region competition:A level set extension of region competition to multiple region image partitioning.Computer Vision and Image Understanding, 2006,101:137-150.
[54]王大鹏.基于水平集的图像分割技术研究：(硕士学位论文).合肥：安徽大学,2011.
[55]李俊.杨新.施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法.计算机学报,2002,25(11)：1176-1183.
[56]D.Mumford, J.Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math,1989,42:577-685.
[57]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. International Journal of Computer Vision, 1997,22(1):61-79.
[58]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics,1989, (42):577-685.
[59]Ambrosio L, Fusco N,Pallara D.Functions of Bounded Variation and Free Dis-continuity Problems.Oxford:Clarendon Press,2000:71-97.
[60]Morel J M, Solimini S. Variational Methods in Image Segmentation.Boston:Birkhauser Boston, 1995:113-123.
[61]Chan T, Vese L, Active contours without edges. IEEE Transactions on Image Processing 2001, 10(2):266-77.
[62]David Adalsteinsson, David Adalsteinsson, James A. Sethian, James A. Sethian. A Fast Level Set Method for Propagating Interfaces. Journal of Computational Physics,1994,118(2):203-231.
[63]王峥,杨新,李俊,施鹏飞.基于水平集人机交互模型的医学图像分割.模式识别与人工智能,2002,15(4)：392-396.
[64]Li C M, Xu C Y, Gui Changfen. Level set Evolution without Re-initialization:a New Varitional Formulation.Computer Vision and Pattern Recognition,2005,1:430-436.
[65]LiWang, Chunming Li, Quansen Sun, Deshen Xia, Chiu-Yen Kao, Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation, Computerized Medical Imaging and Graphics,2009,33:520-531.
[66]Li C, Kao C, Gore J, Ding Z. Implicit active contours driven by local binary fitting energy. In: Proceedings of IEEE conference on computer vision and patternrecognition (CVPR).2007:1-7.
[67]高静.基于形态学分水岭算法的细胞图像分割：(硕士学位论文).长春：吉林大学,2008.
[68]陈伟斌,张鑫,陈胜勇.基于形态学重构算法的细胞图像边缘检测.计算机与数字程,2008,36(12),135-137.
[69]尹诗白,赵祥模,王卫星,孙小蓉.荧光彩色医学细胞图像分割及其染色体的提取和识别.四川大学学报(工程科学版),2011,43(1)：133-138.
[70]HU Chan,JIANG Li-Jun,BO Jiang.Wavelet Transform and Morphology Image Segmentation Algorism for Blood Cell.4th IEEE Conference on Industrial Electronics and Applications,2009:542-545.
[71]Hui Kong, Metin Gurcan, Kamel Belkacem-Boussaid.Partitioning Histopathological Images:An Integrated Framework for Supervised Color-Texture Segmentation and Cell Splitting.IEEE Transation on medical imaging,2011,30(9):1661-1677.
[72]贾迪,杨金柱,曹鹏,张一匕,赵大哲,于戈,一种具有边缘保护的MRI影像同步去噪增强算法.小型微型计算机系统,2011,32(10)：2064-2067.
[73]牛和明,杜茜,张建勋,一种自适应全变分图像去噪算法.模式识别与人工智能,2011.24(6)：798-803.
[74]Yaniv Gal, Andrew J. H. Mehnert, Andrew P. Bradley, Kerry McMahon, Dominic Kennedy, Stuart Crozier, Denoising of Dynamic Contrast-Enhanced MR Images Using Dynamic Nonlocal Means, IEEE Transactions on medical imaging,2010,29(2):302-310.
[75]蒙建军,靳艳红,基于KFCM算法对MRI图像分割的研究,湖北民族学院学报(自然科学版)2011,29(1)：108-111.
[76]宋利伟,宋朝昀,庄天戈,基于分水岭算法的磁共振脑图像自动分割,上海交通大学学报,2003,,37(11)：1754-1756.
[77]H. P. Ng, S. H. Ong, K. W. C. Foong, P. S. Goh, W. L. Nowinski, Masseter segmentation using an improved watershed algorithm with un supervised classification,Computers in Biology and Medicine.2008,38:171-184.
[78]林相波.基于非刚性配准的图像分割研究及其在脑部MRI图像中的应用：(博士学位论文).大连：大连理工大学.2010.
[79]李小兵.MRI图像脑肿瘤分割与EEG脑癫痫检测的研究：(博士学位论文).大连：大连理工大学.2010.
[80]S.E. Yuksel, A. El-Baz. A.A. Farag, M.E.A. El-Ghar, T.A. Eldiasty, M.A. Ghoneim, A Kidney Segmentation Framework for Dynamic Contrast Enhanced Magnetic Resonance Imaging.International Congress Series on Automatic detection of renal rejection after kidney transplantation,2005:773-778.
[81]Frank G. Zolner, Rosario Sance, Peter Rogelj, Maria J. Ledesma-Carbayo, Jarle Rovik, Andres Santos, Arvid Lundervold. Assessment of 3D DCE-MRI of the kidneys using non-rigid image registration and segmentation of voxel time courses. Computerized Medical Imaging and Graphics,2009,33:171-181.
[82]Ting Song, Vivian S. Lee, Henry Rusinek, Manmeen Kaur, Andrew F. Laine. Automatic 4-D Registration in Dynamic MR Renography. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference,2005:3067-3070.
[83]Dongjiao LV, Jie Zhang. Dynamic Contrast-Enhanced Magnetic Resonance Images of the kidney.IEEE Engineering In Medicine And Biology Magazine,2008,8:36-41.
[84]章日康.基于偏微分方程及变分水平集的图像分割：(硕士学位论文).西安：电子科技大学,2008.
[85]金大年.基于水平集的医学图像分割算法研究：(硕士学位论文).广州：第一军医大学,2005.
[86]Elliott PJ. Knapamn JM, SehlegeW. Interactive Image Segmentation for Radiation Treamtnet Planning.IBM Systems Journal,1992,31(4):620-634.
[87]宋余庆.数字医学图像,北京：清华大学出版社.2008.
[88]J.A.Sethian.Level Set Methods and Fast Marching Methods. Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Seienees. Cambridge, U.K.:Cambridge University Press.1966.
[89]S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces.New York:Springer-Verlag Express,2002.
[90]Gabor D, Information theory in electron microscopy.Laboratory Investigation,1965,(14):801-807.
[91]Jain A K. Partial Differential Equation and Finite-Difference Methods in Image Processing, Parl: Image Representation.optimization theory and application,1977,23:65-91.
[92]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[93]汪伟.基于各向异性扩散的数字图像处理研究：(硕士学位论文).合肥：中国科学科技大学,2009.
[94]姜东焕,冯象初,宋国乡.基于形态学算子的各向异性扩散方程.西安电子科技大学学报(自然科学版).2006,(33)1：121-124.
[95]Serra Jean. Image Analysis and Mathematical Morphology.USA:Academic Press,1982.
[96]P Soille, Morphological Image Analysis:Principles and Applications, Berlin, Germany: Springer-Verlag,2003.
[97]熊金涛,孙乾松,李良超,杨建宇.一种基于自适应双向扩散过程的无源毫米波图像去噪与增强.红外与毫米波学报,2011.30(6)：556-560.
[98]陈文斌,程晋译.图像处理与分析：变分.PDE.小波及随机方法.北京：科学出版社.2011.
[99]罗俊召,陈立平,罗震.基于半隐式格式的水平集法连续体结构形状和拓扑优化方法.固体力学学报,2008.29(2)：175-180.
[100]M.A.Mohamed,B.M.EI-Den.Implementation of image fusion techniques using FPGA, IJCSNS International Journal of Computer Science and Network Security,2010,10(5):95-102.
[101]PJin LI, P PYanwei WANG, P P Jie WEI, P Dada WANG, PHong YU.A FNL Means De-noise Algorithm Based on Gradient Calibration.International Journal of Advancements in Computing Technology,2011,3(9):147-154.
[102]钱伟长.变分法及有限元(上册).北京：科学出版社,1980.
[103]老大中.变分法基础.北京：国防工业出版社,2007.
[104]郭彦伶.基于全变分(TV)的彩色图像增强：(硕士学位论文).西安：西北大学,2009.
[105]Courant R, Friedrichs K O, Lewy H. On the partial differentail equation of mathematical physics. IBMJ,1967,11:215-243.
[106]Chan T, shen JH. Mathematical model for local non-texture inpainting. Siam journal on applied mathematics,2001,62(3)1019-1043.
[107]袁慰平,孙志忠,吴宏伟,计算方法与实习.南京：东南大学出版社.2000.
[108]Serra Jean. Image Analysis and Mathematical Morphology. USA:Academic Press,1982.
[109]Vincent, L., and Soille, P. Watersheds in digital spaces:an e_cient algorithm based on immersion simulations. IEEE Transactions on pattern analysis and machine intelligence,1991.13(6):583-598.
[110]Jos B.T.M. Roerdink, Arnold Meijster.The Watershed Transform:Definitions, Algorithms and Parallelization Strategies.Fundamenta Informaticae,2001,41:187-228.
[111]冯林,管慧娟,孙焘,滕弘飞,基于分水岭变换和核聚类算法的图像分割,大连理工大学学报,2006,46(6)：851-856.
[112]Pousse, A. Chavanelle, J. Mixed wavelet-watershed method for nodule detection in high resolution scintigraphy, IEEE Transactions on Nuclear Science,2006,53 (3):1096-1101.
[113]Meyer, F. Topographic distance and watershed lines.Signal Processing,1994,38:113-125.
[114]Soille P. Morphological image analysis principles and applications.Berlin, Germany:Springer Verlag, 1999.
[115]齐丽娜,张博,王战凯.最大类间方差法在图像处理中的应用.无线电工程,2006,36(7)：25-26.
[116]王晓峰.水平集方法及其在图像分割中的应用研究：(硕士学位论文).合肥：中国科学技术大学,2009.
[117]刘秀平,常先堂,李治隆.一种基于边缘和区域信息的变分水平集图像分割方法.大连理工大学学报.2008,48(5)：754-758.
[118]C. Li, C. Xu, C. Gui, and M. D. Fox. Distance Regularized Level Set Evolution and its Application to Image Segmentation. IEEE Transactions on Image Processing,2010,19(2):3243-3254.
[119]陆金甫,关治.偏微分方程数值解法.北京：清华大学出版社.2004.
[120]Li C,Kao C,Gore J.C,Ding Z.Minimization of region-scalable fitting energy for segmentation. IEEE Transactions on Image Processing,2008,17(10):1940-1949.
[121]Li Wang, Chunming Li, Quansen Sun, Deshen Xia, Chiu-Yen Kao, Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. Computerized Medical Imaging and Graphics,2009,33:520-531.
[122]X.F. Wang, D-S.Huang, H.Xu. An efficient local Chan-Vese model for image segmentation. Pattern Recognition,2010,43:603-618.
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