数学形态学发展及应用

摘要摘要数学形态学兴起于20世纪60年代，是一种新型的非线性算子，它着重研究图像的几何结构，由于视觉信息理解都是基于对象几何特性的，因此它更适合视觉信息的处理和分析，这类相互作用由两种基本运算腐蚀和膨胀及它们的组合运算来完成。为了跟踪国际前沿，发展我国的非线性信号处理技术，进一步研究形态学理论和应用技术及非常必要而有实际意义的。本文首先深入地讨论了数学形态学的基本理论，详细介绍了数学形态学的起源、发展；从二值形态学推广到灰度形态学，并分析和介绍了数学形态学在图像处理中的具体应用,并对数学形态学的现状和未来发展方向进行总结。具体论述步骤分为以下几个方面：1学习和总结了数学形态学的基本理论。2研究了二值形态学、灰度形态学、彩色形态学的算法理论。3列举并总结数学形态学在图像分割、边缘检测及图像滤波等方面的应用。4对两种图像的边缘检测进行简单的MATLAB实现。5对数学形态学的现状及发展方向进行总结和展望。关键词：数学形态学二值图像灰度图像彩色形态学边缘检测图像分割形态滤波ABSTRACTABSTRACTMathematicsmorphologyroseinthesixtiesofthe20thcentury,itwasakindofnew-typenon-linearoperator.Itstudiesthegeometrystructureoftheimage,becausevisioninformationiscomprehendedbasedongeometrycharacteristicsofthetarget,soitissuitablefortheinformationprocessingandanalyseofthevision.Thiskindofinteractionisaccomplishedbytwokindsofbasicoperation;erosionanddilation.Inordertofollowtheinternationalfrontanddevelopthenon-linearsignalprocessingtechnologyofourcountry,studythemorphologytheoryandapplicationtechnologyareverynecessaryandhaveactualmeaningfurther.Aboveallinthispaperthebasictheoryofmathematicalmorphologyisdiscussed,thenweintroduceoriginofmathematicsmorphologyfrombinarymorphologytograymorphologyandextensivelystudyltsdiffentoperatorsandquality.Itsapplicationinimageprocessingisanalysedandintroducedaswell.Thenittallyupthepresentconditionanddevelopdirectionofthemathematicsmorphology.Concretediscussasteptoisdividedintoafewaspectsasfollows：1Studyandsummarythebasictheoriesofmathematicsmorphology.2Investigatethetheoriesofbinarymorphology.grayscalemorphologyandcolormorphology.3Enumerateandtallyuptheappliedinimagesegmentation.edgedetectionandmorphologicalfilter.4Carryouttheedgedetectionoftwokindsofimagewithmatlab.5Summaryandoutlookthepresentconditionanddevelopingdirectionofmathematicsmorphology.Keywords：Mathematicsmorphology.Binaryimage.Grayscaleinage.Colormorphology.Edgedetection.Imagesegmentation.Morphologicalfilter.目录i目录第一章绪论........................................................11.1引言....................................................................................................................11.2数学形态学发展简史........................................................................................1第二章数学形态学基本理论..........................................52.1引言....................................................................................................................52.2二值形态学........................................................................................................52.2.1二值腐蚀...................................................................................................52.2.2二值膨胀...................................................................................................62.2.3二值开运算...............................................................................................72.2.4二值闭运算...............................................................................................82.3灰值形态学........................................................................................................92.3.1灰值腐蚀...................................................................................................92.3.2灰值膨胀.................................................................................................102.3.3灰值开运算.............................................................................................122.3.4灰值闭运算.............................................................................................122.3.5灰值形态学梯度.....................................................................................142.4彩色形态学......................................................................................................152.4.1彩色形态学简介.....................................................................................152.4.2分量法.....................................................................................................162.4.3HLS法..................................................................................................162.4.5彩色形态学总结.....................................................................................182.5本章小结..........................................................................................................18第三章数学形态学的应用...........................................213.1引言..................................................................................................................213.1.1数学形态学在图像处理中的主要应用.................................................213.1.2图像边缘检测.........................................................................................21ii数学形态学的发展及应用研究3.1.3图像分割................................................................................................223.1.4噪声滤除................................................................................................233.2数学形态学应用于图像边缘检测.................................................................233.2.1图像边缘定义........................................................................................233.2.2基本的形态学边缘检测算子...................................