基于泛函极值的图像分割算法研究
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摘要
本文以基于泛函极值的图像分割算法为研究对象,主要研究泛函极值的求解策略。
首先,研究经典的Otsu算法,从运算量上阐释穷举策略对算法的影响,在此基础上提出改进算法,即基于模拟退火算法的多阈值图像分割,这一部分是本文的创新点所在。为了提高Otsu算法的运算效率,提出了两个方法,分别是引入模拟退火算法和引入先验的图像分类信息,使运算量随阈值个数的几何级数增长转化为近似的线性增长。然后研究基于变分法求解泛函极值的图像分割算法,即可变轮廓模型,研究了可变轮廓模型的两个分支,即Snake模型和利用水平集方法的几何可变轮廓模型及两类算法之间的联系。对在性能上具有代表性的两个模型做了具体介绍。
其次,针对图像照度不均所致的部分区域误分割问题,研究构建基于互信息的能量泛函的分割方法,对以互信息与类间方差构建的能量泛函的性能进行了分析。
本文在Matlab701平台上,对Otsu算法及改进算法的实验结果进行对比分析,对基于互信息的图像分割方法和可变轮廓模型算法的处理结果分别进行分析。
This paper chooses algorithm of image segmentation based on functional extreme as its research subject.
First of all, the classical Otsu algorithm is taken for the research of algorithm based on Exhaustive Attack searching and functional extreme. Throuth the investigation of a deficiency of speed, the affection from Exhaustive Attack searching to the operation quantity of the algorithm is analysed, and this draw forth the second stage of a research of algorithm based on Intelligence Optimum Algorithm and functional extreme which conclude the originality of this paper. In this stage two tactics is proposed, that is an injection of simulated annealing and also an injection of metempirical classification information of images. This makes a chage for increase of operation quantity as the number of threshold from geometric progression to analogous linear progression. Then the research is carried out with algorithm based on variations, named deformable contour models. Two kinds of deformable model algorithms are studied, and more research are done on two typical models which differ in the function i.
In this paper in order to conquer the problem of mis-segmentation of partial region, a method of using mutual information to construct a new functional is proposed.
Experiment results of Otsu and the processed algorithm has been discussed on matlab 701, and also the result of the method based on mutual information and deformable contour models are analysed.
首先,研究经典的Otsu算法,从运算量上阐释穷举策略对算法的影响,在此基础上提出改进算法,即基于模拟退火算法的多阈值图像分割,这一部分是本文的创新点所在。为了提高Otsu算法的运算效率,提出了两个方法,分别是引入模拟退火算法和引入先验的图像分类信息,使运算量随阈值个数的几何级数增长转化为近似的线性增长。然后研究基于变分法求解泛函极值的图像分割算法,即可变轮廓模型,研究了可变轮廓模型的两个分支,即Snake模型和利用水平集方法的几何可变轮廓模型及两类算法之间的联系。对在性能上具有代表性的两个模型做了具体介绍。
其次,针对图像照度不均所致的部分区域误分割问题,研究构建基于互信息的能量泛函的分割方法,对以互信息与类间方差构建的能量泛函的性能进行了分析。
本文在Matlab701平台上,对Otsu算法及改进算法的实验结果进行对比分析,对基于互信息的图像分割方法和可变轮廓模型算法的处理结果分别进行分析。
This paper chooses algorithm of image segmentation based on functional extreme as its research subject.
First of all, the classical Otsu algorithm is taken for the research of algorithm based on Exhaustive Attack searching and functional extreme. Throuth the investigation of a deficiency of speed, the affection from Exhaustive Attack searching to the operation quantity of the algorithm is analysed, and this draw forth the second stage of a research of algorithm based on Intelligence Optimum Algorithm and functional extreme which conclude the originality of this paper. In this stage two tactics is proposed, that is an injection of simulated annealing and also an injection of metempirical classification information of images. This makes a chage for increase of operation quantity as the number of threshold from geometric progression to analogous linear progression. Then the research is carried out with algorithm based on variations, named deformable contour models. Two kinds of deformable model algorithms are studied, and more research are done on two typical models which differ in the function i.
In this paper in order to conquer the problem of mis-segmentation of partial region, a method of using mutual information to construct a new functional is proposed.
Experiment results of Otsu and the processed algorithm has been discussed on matlab 701, and also the result of the method based on mutual information and deformable contour models are analysed.
引文
[1]田村秀行,金喜子,乔双.计算机图像处理.北京:科学出版社,2004
[2]张云飞,张晔.利用二维熵自动确定图像分割的阈值.哈尔滨工业大学学报,2006,27(3):353-356
[3]周德龙,潘泉,张洪才,等.最大熵阈值处理算法.软件学报,2001,12(9):1420-1422
[4]卢振泰,陈武凡,吕庆文.基于互信息量的寄生虫卵图像自动优化分割.计算机应用研究,2007,24(11):301-302
[5]冯斌,王璋,孙俊.基于改进粒子群算法的二维阈值图像分割.计算机应用研究,2008,25(8):2402-2404
[6]L.Garc(?)ap(?)rez,M.C.Garc(?)aalegre,J.Marchant,et al.Dynamic threshold selection for image segmentation of natural structures based upon a performance criterion.3ECPA-3 European Conf.on Precision Agriculture,2001,Montpellier,2001
[7]Agus Zainal Arifin,Akira Asano.Image segmentation by histogram thresholding using hierarchical cluster analysis.Pattern Recognition Letters,2006,27(13):1515-1521
[8]Shu-Kay Ng,Geoffrey J.McLachlan.Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images.Pattern Recognition,37(8):1573-1589
[9]赵伟,张姝,李文辉.基于K-means算法的高性能空间索引方法.计算机工程,2008,34(20):4-6
[10]张硕 彭冬亮.基于数学形态学的细胞图像分割.杭州电子科技大学学报,2008,28(6):52-55
[11]王宇,陈殿仁,沈美丽等.基于形态学梯度重构和标记提取的分水岭图像分割.中国图象图形学报,2008,13(11):2176-2180
[12]A.Singh,D.Goldgof,and D.Terzopoulos,Deformable Models in Medical Image Analysis.Los Alamitos,CA:IEEE Computer Society,1998
[13]张辉,戴芳,赵凤群等.基于Snake模型的复杂区域图像分割.激光与红外,2008,38(4):404-406
[14]Michael kass,Andrew witkin,Demetri terzopoulos.Snakes:Active Contour Models.Int.J.Computer Vision,1998,1(4):321-331.
[15]R.Malladi,J.A.Sethian,and B.C.Vemuri.Shape modelling with front propagation:A levelset approach.IEEE Transactions on Pattern Analysis and Machine Intelligence,1995,17(2):158-175
[16]NOBUYUKI OTSU.A threshold selection method from gray-level histograms.IEEE Transactions on Systems,Man and Cybernetics,1979,9(1):62-66
[17]王凌.智能优化算法及其应用.北京:清华大学出版社,2001
[18]S.KIRKPATRICK,C.D.GELATT JR.,M.P.VECCHI.Optimization by simulated annealing.Science,1983,220(4598):671-680
[19]吕国英.算法设计与分析.北京:清华大学出版社出版.2006
[20]李哲岩,张永曙.变分法及其应用.西安:西北工业大学出版社,1989
[21]吴迪光.变分法.北京:高等教育出版社,1987
[22]M.Alper Selvera,Aykut Kocaoglu,Guleser K.Demir,etc.Patient oriented and robust automatic liver segmentation for pre-evaluation of liver transplantation.Computers in Biology and Medicine,2008,38:765-784
[23]吕庆文,陈武凡.基于互信息量的图像分割.计算机学报.2008,9(2):296-301
[24]王永波,陈继荣.二维Otsu阈值分割算法的改进及应用.计算机仿真.2008,25(4):263-267
[25]李峰,一种基于K-L变换和Otsu阈值选择的彩色图像分割算法.计算机应用,2007,27:93-94
[26]时平,王毅,赵海涛等.基于数学形态学和Otsu方法的VHP数据心脏图像分割,生物医学工程学杂志,2007,24(5):996-1000
[27]范九伦,赵凤,张雪峰.三维Otsu阈值分割方法的递推算法.电子学报,2007,35(7):1398-1402
[28]吴世英,虞欣.基于智能遗传算法和Otsu法的多目标图像分割方法.测绘信息与工程,2006,31(4):47-49
[29]吴强辉,石毅力,付长安.基于OTSU的显微图像自适应域值分割算法.医疗卫生装备,2006,27(3):22-24
[30]Deng-Yuan Huang,Chia-Hung Wang.Optimal multi-level thresholding using a two-stage Otsu optimization approach.Pattern Recognition Letters,2009,30(3):275-284
[31]汪海洋,潘德炉,夏德深.二维Otsu自适应阈值选取算法的快速实现.自动化学报,2007,33(9):968-971
[32]高齐圣,张嗣瀛,潘德惠.参数设计的模拟退火并行计算法,系统工程理论与实践,2000,8:41-44
[33]黄樟灿,陈思多,康立山,陈毓屏.基于模拟退火算法的曲面最短路径求解.武汉大学学报(理学版).2000,46(3):273-276
[34]蒋龙聪,刘江平.模拟退火算法及其改进.工程地球物理学报.2007,4(2):135-140
[35]李振涛,王淑玲,张国立.利用遗传模拟退火算法优化神经网络结构,计算机工程与应用,2007,43(36):74-76
[36]Zhengwen He,Nengmin Wang,Tao Jia,etc.Simulated annealing and tabu search for multi-mode project payment scheduling,European Journal of Operational Research,2009,198(3):688-696
[37]Sungho Mun,Yoon-Ho Cho.Noise barrier optimization using a simulated annealing algorithm.Applied Acoustics,2009,70(8):1094-1098
[38]Xiutang Geng,Jin Xu,Jianhua Xiao,etc.A simple simulated annealing algorithm for the maximum clique problem.Information Sciences,2007,177(22):5064-5071
[39]罗述谦,李响.基于最大互信息的多模医学图像配准.中国图象图形学报,2000,5(A):551-558
[40]Andy Tsai,William M Wells,Clare C Tempany,W E L Grimson,A Willsky.Mutual information in coupled multi-shape model for medical image segmentation.Med Image Anal.2004,8(4):429-45
[41]Huawen Liu,Jigui Sun,Lei Liuand,etc.Feature selection with dynamic mutual information.Pattern Recognition,2009,42(7):1330-1339
[42]A.Kuijper.Mutual information aspects of scale space images.Pattern Recognition,2004,37(12):2361-2373
[43]Badong Chen,Jinchun Hu,Hongbo Li,etc.Adaptive filtering under maximum mutual information criterion.Neurocomputing,2008,71(16):3680-3684
[44]VICENT CASELLES,Francine Catte,Tomeu Coll,Francoise Dibos.A geometric model for active contours.Numer.Math,1993,66(1):1-31
[45]J.Kim,J.Fisher,A.Yezzi,M.Cetin,and A.Willsky,Nonparametric methods for image segmentation using information theory and curve evolution,in Proc.ICIP,2002
[46]Conglin Lu,Yan Cao,David Mumford.Surface Evolution under Curvature Flows.Journal of Visual Communication and Image Representation,2002,13(1):65-81
[47]Scott Thompson,Azriel Rosenfeld.Discrete,nonlinear curvature-dependent contour evolution.Pattern Recognition,1998,31(12):1949-1959
[48]A.Yezzi,S.Kichenassamy,A.Kumar,P.Olver,and A.Tennenbaum,A geometric Snake model for segmentation of medical imagery,IEEE Trans.Med.Imag.,1997,16:199-209
[49]V.I.Arnold.Geometrical Methods in the Theory of Ordinary Differential Equations,New York:Springer-Verlag,1983.
[50]刘(王景).图像分割方法研究-可变形模型在超声心动图分割中的应用:[硕士学位论文].南京:东南大学,2000
[51]Chenyang Xu,Jerry L.Prince.Generalized gradient vector flow external forces for active contours.Signal Processing,1998,71:131-139
[52]VICENT CASELLES,RON KIMMEL,GUILLERMO SAPIRO.Geodesic Active Contours.International Journal of Computer Vision,1997,22(1):61-79
[53]Tony F.Chan,Luminita A.Vese.Active Contours Without Edges.IEEE TRANSACTIONS ON IMAGE PROCESSING,2001,10(2):266-277
[54]C.Li,C.Kao,J.Gore,etc.Implicit active contours driven by local binary fitting energy.Proceedings of IEEE Conference on Computer Vision and Pattern Recognition(CVPR),2007
[55]Jinshan Tang.A multi-direction GVF snake for the segmentation of skin cancer images.Pattern Recognition,2009,42(6):1172-1179
[56]李晓光,沈兰荪,LAM Kin-Man,etc.一种基于GVF各向异性扩散模型的图像放大算法.电子学报,2008,36(9):1755-1758
[57]伍林,葛云.结合NGVF信息和互信息的图像配准方法.激光与红外,2008,38(9):939-941
[58]张晖,董育宁,夏洋.一种基于改进的GVF—Snake模型的车辆跟踪算法.模式识别与人工智能,2007,20(3):388-393
[59]Chunming Li,Chenyang Xu,Changfeng Gui,and Martin D.Fox.Level Set Evolution Without Re-initialization:A New Variational Formulation.Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
[60]Cui Hua,Gao Liqun.Geodesic active contour,inertia and initial speed.Pattern Recognition Letters,2008,29(16):2197-2205
[61]Xiuyang Zhao,Yansheng Yin,Bo Yang,etc.Level set and geodesic active contours based measurement of material removal between serial sections.Computational Materials Science,2007,39(4):857-861
[2]张云飞,张晔.利用二维熵自动确定图像分割的阈值.哈尔滨工业大学学报,2006,27(3):353-356
[3]周德龙,潘泉,张洪才,等.最大熵阈值处理算法.软件学报,2001,12(9):1420-1422
[4]卢振泰,陈武凡,吕庆文.基于互信息量的寄生虫卵图像自动优化分割.计算机应用研究,2007,24(11):301-302
[5]冯斌,王璋,孙俊.基于改进粒子群算法的二维阈值图像分割.计算机应用研究,2008,25(8):2402-2404
[6]L.Garc(?)ap(?)rez,M.C.Garc(?)aalegre,J.Marchant,et al.Dynamic threshold selection for image segmentation of natural structures based upon a performance criterion.3ECPA-3 European Conf.on Precision Agriculture,2001,Montpellier,2001
[7]Agus Zainal Arifin,Akira Asano.Image segmentation by histogram thresholding using hierarchical cluster analysis.Pattern Recognition Letters,2006,27(13):1515-1521
[8]Shu-Kay Ng,Geoffrey J.McLachlan.Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images.Pattern Recognition,37(8):1573-1589
[9]赵伟,张姝,李文辉.基于K-means算法的高性能空间索引方法.计算机工程,2008,34(20):4-6
[10]张硕 彭冬亮.基于数学形态学的细胞图像分割.杭州电子科技大学学报,2008,28(6):52-55
[11]王宇,陈殿仁,沈美丽等.基于形态学梯度重构和标记提取的分水岭图像分割.中国图象图形学报,2008,13(11):2176-2180
[12]A.Singh,D.Goldgof,and D.Terzopoulos,Deformable Models in Medical Image Analysis.Los Alamitos,CA:IEEE Computer Society,1998
[13]张辉,戴芳,赵凤群等.基于Snake模型的复杂区域图像分割.激光与红外,2008,38(4):404-406
[14]Michael kass,Andrew witkin,Demetri terzopoulos.Snakes:Active Contour Models.Int.J.Computer Vision,1998,1(4):321-331.
[15]R.Malladi,J.A.Sethian,and B.C.Vemuri.Shape modelling with front propagation:A levelset approach.IEEE Transactions on Pattern Analysis and Machine Intelligence,1995,17(2):158-175
[16]NOBUYUKI OTSU.A threshold selection method from gray-level histograms.IEEE Transactions on Systems,Man and Cybernetics,1979,9(1):62-66
[17]王凌.智能优化算法及其应用.北京:清华大学出版社,2001
[18]S.KIRKPATRICK,C.D.GELATT JR.,M.P.VECCHI.Optimization by simulated annealing.Science,1983,220(4598):671-680
[19]吕国英.算法设计与分析.北京:清华大学出版社出版.2006
[20]李哲岩,张永曙.变分法及其应用.西安:西北工业大学出版社,1989
[21]吴迪光.变分法.北京:高等教育出版社,1987
[22]M.Alper Selvera,Aykut Kocaoglu,Guleser K.Demir,etc.Patient oriented and robust automatic liver segmentation for pre-evaluation of liver transplantation.Computers in Biology and Medicine,2008,38:765-784
[23]吕庆文,陈武凡.基于互信息量的图像分割.计算机学报.2008,9(2):296-301
[24]王永波,陈继荣.二维Otsu阈值分割算法的改进及应用.计算机仿真.2008,25(4):263-267
[25]李峰,一种基于K-L变换和Otsu阈值选择的彩色图像分割算法.计算机应用,2007,27:93-94
[26]时平,王毅,赵海涛等.基于数学形态学和Otsu方法的VHP数据心脏图像分割,生物医学工程学杂志,2007,24(5):996-1000
[27]范九伦,赵凤,张雪峰.三维Otsu阈值分割方法的递推算法.电子学报,2007,35(7):1398-1402
[28]吴世英,虞欣.基于智能遗传算法和Otsu法的多目标图像分割方法.测绘信息与工程,2006,31(4):47-49
[29]吴强辉,石毅力,付长安.基于OTSU的显微图像自适应域值分割算法.医疗卫生装备,2006,27(3):22-24
[30]Deng-Yuan Huang,Chia-Hung Wang.Optimal multi-level thresholding using a two-stage Otsu optimization approach.Pattern Recognition Letters,2009,30(3):275-284
[31]汪海洋,潘德炉,夏德深.二维Otsu自适应阈值选取算法的快速实现.自动化学报,2007,33(9):968-971
[32]高齐圣,张嗣瀛,潘德惠.参数设计的模拟退火并行计算法,系统工程理论与实践,2000,8:41-44
[33]黄樟灿,陈思多,康立山,陈毓屏.基于模拟退火算法的曲面最短路径求解.武汉大学学报(理学版).2000,46(3):273-276
[34]蒋龙聪,刘江平.模拟退火算法及其改进.工程地球物理学报.2007,4(2):135-140
[35]李振涛,王淑玲,张国立.利用遗传模拟退火算法优化神经网络结构,计算机工程与应用,2007,43(36):74-76
[36]Zhengwen He,Nengmin Wang,Tao Jia,etc.Simulated annealing and tabu search for multi-mode project payment scheduling,European Journal of Operational Research,2009,198(3):688-696
[37]Sungho Mun,Yoon-Ho Cho.Noise barrier optimization using a simulated annealing algorithm.Applied Acoustics,2009,70(8):1094-1098
[38]Xiutang Geng,Jin Xu,Jianhua Xiao,etc.A simple simulated annealing algorithm for the maximum clique problem.Information Sciences,2007,177(22):5064-5071
[39]罗述谦,李响.基于最大互信息的多模医学图像配准.中国图象图形学报,2000,5(A):551-558
[40]Andy Tsai,William M Wells,Clare C Tempany,W E L Grimson,A Willsky.Mutual information in coupled multi-shape model for medical image segmentation.Med Image Anal.2004,8(4):429-45
[41]Huawen Liu,Jigui Sun,Lei Liuand,etc.Feature selection with dynamic mutual information.Pattern Recognition,2009,42(7):1330-1339
[42]A.Kuijper.Mutual information aspects of scale space images.Pattern Recognition,2004,37(12):2361-2373
[43]Badong Chen,Jinchun Hu,Hongbo Li,etc.Adaptive filtering under maximum mutual information criterion.Neurocomputing,2008,71(16):3680-3684
[44]VICENT CASELLES,Francine Catte,Tomeu Coll,Francoise Dibos.A geometric model for active contours.Numer.Math,1993,66(1):1-31
[45]J.Kim,J.Fisher,A.Yezzi,M.Cetin,and A.Willsky,Nonparametric methods for image segmentation using information theory and curve evolution,in Proc.ICIP,2002
[46]Conglin Lu,Yan Cao,David Mumford.Surface Evolution under Curvature Flows.Journal of Visual Communication and Image Representation,2002,13(1):65-81
[47]Scott Thompson,Azriel Rosenfeld.Discrete,nonlinear curvature-dependent contour evolution.Pattern Recognition,1998,31(12):1949-1959
[48]A.Yezzi,S.Kichenassamy,A.Kumar,P.Olver,and A.Tennenbaum,A geometric Snake model for segmentation of medical imagery,IEEE Trans.Med.Imag.,1997,16:199-209
[49]V.I.Arnold.Geometrical Methods in the Theory of Ordinary Differential Equations,New York:Springer-Verlag,1983.
[50]刘(王景).图像分割方法研究-可变形模型在超声心动图分割中的应用:[硕士学位论文].南京:东南大学,2000
[51]Chenyang Xu,Jerry L.Prince.Generalized gradient vector flow external forces for active contours.Signal Processing,1998,71:131-139
[52]VICENT CASELLES,RON KIMMEL,GUILLERMO SAPIRO.Geodesic Active Contours.International Journal of Computer Vision,1997,22(1):61-79
[53]Tony F.Chan,Luminita A.Vese.Active Contours Without Edges.IEEE TRANSACTIONS ON IMAGE PROCESSING,2001,10(2):266-277
[54]C.Li,C.Kao,J.Gore,etc.Implicit active contours driven by local binary fitting energy.Proceedings of IEEE Conference on Computer Vision and Pattern Recognition(CVPR),2007
[55]Jinshan Tang.A multi-direction GVF snake for the segmentation of skin cancer images.Pattern Recognition,2009,42(6):1172-1179
[56]李晓光,沈兰荪,LAM Kin-Man,etc.一种基于GVF各向异性扩散模型的图像放大算法.电子学报,2008,36(9):1755-1758
[57]伍林,葛云.结合NGVF信息和互信息的图像配准方法.激光与红外,2008,38(9):939-941
[58]张晖,董育宁,夏洋.一种基于改进的GVF—Snake模型的车辆跟踪算法.模式识别与人工智能,2007,20(3):388-393
[59]Chunming Li,Chenyang Xu,Changfeng Gui,and Martin D.Fox.Level Set Evolution Without Re-initialization:A New Variational Formulation.Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
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