毕业论文―基于偏微分方程的图像平滑方法的研究

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成都理工大学毕业设计(论文)I基于偏微分方程的图像平滑方法的研究作者姓名:刘洋专业班级:信息与计算科学2008070201指导教师:王茂芝摘要在信息化的社会里,图像在信息传播中所起的作用越来越大。所以,消除在图像采集和传输过程中而产生的噪声,保证图像受污染度最小,成了数字图像处理领域里的重要部分,图像平滑作为图像处理中的重要环节,也逐渐受到人们的关注,图像平滑的目的主要是消除噪声。本文详细介绍了图像平滑的发展,图像平滑方法按空间域和频率域的分类及各种方法的特点,由于传统的这些方法在去噪的同时会破坏图像的重要特征从而引出了基于偏微分方程的图像平滑方法。首先介绍图像处理应用时的常用函数及其用法;其次详细阐述了几种去噪算法原理及特点;最后运用Matlab软件对一张含噪图片(含高斯噪声或椒盐噪声)进行仿真去噪,本文分别从各向同性扩散方程和各向异性扩散方程对基于偏微分方程的图像平滑方法进行研究,进一步完善图像平滑方法,以达到平滑效果更理想的目的。关键词:图像平滑;偏微分方程;各向同性扩散;各向异性扩散成都理工大学毕业设计(论文)IIBasedonpartialdifferentialequationsforimagesmoothingmethodAbstractIntheinformationsociety,theroleofimageinthedisseminationofinformation.Therefore,toeliminatethenoiseintheimageacquisitionandtransmissionprocesstoensurethatanimportantpartoftheimagecontaminatedminimum,hasbecomethefieldofdigitalimageprocessing,imagesmoothingasanimportantlinkinimageprocessing,butalsograduallybytheattention,smooththeimagemainpurposeistoeliminatenoise.Thispaperdescribesthedevelopmentofimagesmoothing,imagesmoothingmethodaccordingtotheclassificationofthespaceandfrequencydomainsandthecharacteristicsofthevariousmethods,thesemethodsduetothetraditionaldenoisingwillalsounderminetheimageoftheimportantcharacteristicswhichleadsbasedonpartialdifferentialequationsimageSmoothingMethod.Firstintroducedthecommonfunctionsandtheirusageinimageprocessingapplications;elaboratedtheprincipleandcharacteristicsofseveraldenoisingalgorithm;Matlabsoftwareonanoisyimage(withGaussiannoiseorsaltandpeppernoise)simulationdenoisingInthispaper,researchfromtheisotropicdiffusionequationandanisotropicdiffusionforimagesmoothingmethodbasedonpartialdifferentialequations,andfurtherimprovetheimagesmoothingmethodinordertoachievethepurposeofbettersmoothingeffectKeywords:Imagesmoothing;partialdifferentialequations;isotropicdiffusion;anisotropicdiffusion成都理工大学毕业设计(论文)III目录第1章前言·················································································11.1课题研究背景··········································································11.2图像平滑的研究现状·································································21.2.1领域平均法········································································21.2.2低通滤波法········································································31.2.3多图像平均法····································································41.2.4中值滤波法·······································································41.2.5各向同性扩散方程······························································61.2.6各向异性扩散方程······························································61.3本文的研究目标和主要内容························································7第2章偏微分方程基础知识······························································82.1偏微分方程的导出与定解··························································82.1.1偏微分方程的概念······························································82.1.2几个典型的数学物理方程·····················································82.1.3初边值问题·······································································92.2热传导方程初值问题的求解······················································122.3二阶偏微分方程的分类与化简···················································132.3.1二阶偏微分方程的分类·······················································132.3.2二阶偏微分方程的化简·······················································152.4与图像处理有关的偏微分方程的例子···········································15第3章图像的基本知识···································································173.1图像介绍··············································································173.1.1图像概述··········································································173.1.2图像分类··········································································183.2静态灰度图像的数学模型·························································183.2.1静态灰度图像的连续模型····················································183.2.2灰度图像的离散模型··························································203.3静态彩色图像的数学模型·························································203.3.1静态灰度图像的连续模型····················································203.3.2彩色图像的数学模型··························································20成都理工大学毕业设计(论文)IV3.4动态图像的数学模型·······························································213.5数字图像的采集·····································································213.6图像格式··············································································23第4章数字图像处理的基本知识·······················································274.1数字图像处理的概述·······························································274.1.1数字图像处理技术的发展····················································274.1.2数字图像处理技术的流程····················································274.1.3低层图像处理···································································284.2滤波和滤波器········································································294.3图像增强算法········································································304.3.1平滑空间滤波···································································304.3.2锐化空间滤波·····························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