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I摘要图像分割是图像处理中极为关键的一步．图像分割的目的是将图像中我们感兴趣的部分从整幅图像中分离出来，因此分割能力的好坏直接影响了了之后的图像处理效果．自2001年C-V模型被提出以来，基于偏微分方程的图像分割算法开始得以推广．而这也是本文重点研究的方向．在本论文中，我们首先对传统的图像分割方法进行了简单的阐述并描述了基于偏微分方程的图像分割算法的发展情况．然后重点分析了基于偏微分方程的图像分割算法的基础理论，介绍了在以Kass等人提出的活动轮廓模型的基础上，产生的两个基于区域的几何活动轮廓模型：C-V模型和LBF模型，并解释其工作原理．C-V模型是全局模型，但只能处理二值图像，因此噪音对它的影响极大．LBF模型是C-V模型的改进型，它是局部几何活动轮廓模型，将整块图像先分割成无数小块，通过偏微分方程的计算每个小块得出的值，然后将其相加，它能处理多灰度值的图像包括带噪声的图像．本文在理论研究的基础上，运用Matlab对涉及到的算法进行仿真实验．通过实验结果来验证本文的各中方法的图像分割效果．关键词：偏微分方程；图像分割；C-V模型；水平集方法；LBF模型IIAbstractImagesegmentationisaveryimportantstepinimageprocessing.Thegoalofimagesegmentationistosegmentthetargetimagefromtheoriginalimage,soimagesegmentationabilitydirectlyaffectsthequalityoftheimageprocessingresults.SincetheC-Vmodelwasproposedin2001,theimagesegmentationalgorithmbasedonpartialdifferentialequationshasbeenpopularized,whichisthekeyresearchdirectionofthisthesis.Inthepaper,wefirstbrieflydescribethetraditionalimagesegmentationmethodsanddescribethedevelopmentofimagesegmentationalgorithmbasedonpartialdifferentialequations.Andthenweanalyzethebasistheoryofimagesegmentationalgorithmbasedonpartialdifferentialequation.BasedontheactivecontourmodelproposedbyKassetal,thetwogeometricactivecontourmodelsbasedonregionareintroduced:theC-VmodelandtheLBFmodelandexplainitsworkingprinciple..C-Vmodelisaglobalmodel,butitcanonlydealwiththetwovalueimage.Therefore,thenoisehasagreatinfluenceonit.TheLBFmodelisanimprovedC-Vmodel,whichisalocalgeometricactivecontourmodel.Itdividetheentireimageintonumeroussmallpieces,throughthepartialdifferentialequationstocalculatethevalueofeachsmallpiece,andthenaddit.Itcanhandlemultiplegrayvaluesoftheimageandnoisingimage.Basedonthetheoreticalstudy,weuseMatlabtocompletethesimulationexperimentsfortheinvolvedalgorithms.Theimagesegmentationeffectsinthispaperareillustratedbytheexperimentresults.Keywords:partialdifferentialequation;imagesegmentation;C-Vmodel;levelsetmethod;LBFmodelIII目录摘要.......................................................................................................................................IAbstract................................................................................................................................II1绪论................................................................................................................................11.1研究背景及意义..................................................................................................11.2图像分割技术的研究现状..................................................................................12传统图像分割方法........................................................................................................22.1阈值分割方法......................................................................................................22.2边缘检测方法......................................................................................................42.3区域分割法..........................................................................................................52.3.1区域生长....................................................................................................52.3.2区域分裂——合并....................................................................................62.4形态学分水岭法..................................................................................................72.5图像分割中的偏微分方程方法..........................................................................93基于偏微分方程的图像分割........................................................................................93.1偏微分方程的引入..............................................................................................93.2曲线演化理论....................................................................................................103.3水平集方法........................................................................................................113.4基于偏微分方程的理论模型............................................................................133.5C-V模型............................................................................................................143.5.1Mumford-Shah模型................................................................................143.5.2C-V模型..................................................................................................143.5.3LBF模型.................................................................................................174总结与展望..................................................................................................................194.1总结....................................................................................................................194.2展望....................................................................................................................20参考文献............................................................................................................................21致谢....................................................................................................................................22中原工学院毕业论文11绪论1.1研究背景及意义