题目基于MATLAB数字图像边缘检测技术

研究条件在大学四年专业学习的基础上阅读有关软件使用方法以及数字图像处理等方面的书籍；掌握编程语言，熟练利用计算机进行仿真工作目的：本设计要求在熟练应用软件的基础上，学习并应用目前较分析，掌握基于的数字图像处理边缘检测方法。 图像处理-能力提高与应用案例》[M].：航空航天大学，第1版，2014.01.[3]飞思科技产品研发中心.基础与提高[M].：电子工业91-吴术路.基于Sobel算子图像边缘检测的实现[J].电脑知识与技术（435 掌握语言和各种数字图像边缘检测仿真技术，实现基于的数字图检测已经用于军事，医学，，通信等方面，并且，在不远的将来会涉及到的行业。是英文MatrixLaboratory(短阵)的缩写，它的第1版(Dos1.0)1984年。以商品形式出现后，仅短短几年，就以其的UMIST，瑞典的LUNDSIMNON，德国的KEDDC）纷纷淘汰，而改20已经为际控界认标准算件。九十代期，国上3， 功出 是一功能分大的统是集数值计算、图形管理、程序开发为一体的环境，广泛应用与自动控制、数字信号处理、模拟与数字通信、时间序列分析等领域。本课题的主要任务就是基于数字图像边缘检测技术处理图像，学习有关软件使用方法以及数字图像处理等方面的书籍，掌握编程语言，熟练利用计算机进行仿真设计。在熟练应用软件的基础上，学习并应用目前常用的数字图像处握基于的数字图像处理边缘检测方法，实现基于的数字图本课题要求熟练应用软件的基础上，学习并应用目前常用的数Canny算子检测图像边缘等多种方法，并对它们各自的优缺点及适用对Canny在.： ：1[3]基础与提高 ：电子工 研究[J].现代电子技术，2011，34（4）：91-[5吴术路.基于Sobel算子图像边缘检测的实现[J].（19）：5314-[6靳鹏飞.一种改进的Sobel图像边缘检测算法[J].应用光学，2008,29（4）：35-，，常青.基于Canny算子的红外图像边缘检测研究[J]. 将若干常用的边缘检测方法应用于一张人物和一张风景的边缘检测仿真实Theimageedgeisthemostbasicfeatureoftheimage.Theedgeisdiscontinuitywhichreferstothelocalcharacteristicsofimage,Grayorstructuralinformationsuchasthemutation.Edgedetectionisaterminologyinimageprocessingandcomputervision,andtheedgedetectionplaysanimportantroleindigitalimageprocessing.Theessenceofedgedetectionistoextracttheboundarybetweenobjectandbackgroundintheimagebysomealgorithm,particularlyintheareasoffeaturedetectionandfeatureextraction,torefertoalgorithmswhichaimatidentifyingpointsinadigitalimageatwhichtheimagebrightnesschangessharplyormoreformallyhasdiscontinuities.Thetopicofthisresearchisdigitalimageedgedetectiontechnologywhichbased languageprogramming,andseveralcommonlyusededgedetectionmethodwasappliedtoacharacterpictureandasceneryphoto，dotheedgedetectionsimulationexperiments,includingafirstorderdifferentialoperatormethodandsecondorderdifferentialoperatormethodsuchasedgedetectionmethod.Aftertheexperiments，comparisonwiththeresultoftheresearch,gettheirrespectivefeaturesandapplicablescope.:edgedetectionmethod;digitalimageprocessing; ;differentialoperatormethod 绪 课题来源及意 国内外发展现 研究目 研究内 图像边缘的定 图像边缘检测的主要算 soble边缘算 Roberts边缘算 prewitt边缘算 canny边缘算 log边缘算 的发展历 的基本功能及特 的图像处理基本操 一阶微分算 二阶微分算 仿真实现的总 第一章绪论数字图像处理技术于20世纪20年代，经过半个多世纪的发展，目前已经广泛地用于工业、医疗、航空航天、军事、地理等各个领域，在国民经济中发挥着越来越重要的作用。目前，随着的发展、数字化地球概念的提出以及因1.0)于1984年。以商品形式出现后，仅短短几年，就以其良好的开放性和运行的可靠性，使原先控制领域里的封闭式软件包（如英国的UMIST，瑞典的LUNDSIMNONKEDDC）纷纷淘汰，而改以为平台加以重建。在时间进入20世纪九十年代的时候，已经成为国际控制界公认的标在数值计算方面独占鳌头，经过发展，功能不断强大、成熟，可以看出研究目本课题的主要任务就是基于数字图像边缘检测技术处理图像，学习熟练利用计算机进行仿真设计。在熟练应用软件的基础上，学习并应用目前常用的数字图像处理中的边缘检测方法，并对它们各自的优缺点及适用对象进行比较分析，掌握基于的数字图像处理边缘检测方法，实现基于的数字图像处理仿真研究内本课题要求熟练应用软件的基础上，学习并应用目前常用的数字图Canny掌握基于的数字图像处理边缘检测方法。第二章 2-1理想边缘图示图像边缘检测的主要算2-2边缘检测的流程图下是对集中经典的边缘检测算子进行分析。其中有一阶微分算子：Sobel边缘检测分算子：LOG边缘检测算子。Sobel边缘算以待增强f(i,j的任意像素(i,j)为中心33像素窗口，分别计算窗xySxf(i1,j1)2f(i1,j)f(i1,j1)f(i1,j1)2f(i1,j)f(i1,j（2-Syf(i1,j1)2f(i,j1)f(i1,j1)f(i1,j1)2f(i,j1)f(i1,j式（2-增强后的图像在(i.j)处的灰度值S2S 2f'(i,jS2S2S 2 Sx

12

1 Sy 0

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Sobel算子容易在空间上实现，Sobel算子利用像素点上下，左右邻点的灰度加权算法，根据在边缘点处达到极值这一现象进行边缘的检测，Sobel算子受噪声的RobertsRoberts算子根据计算梯度的原理，采用对角线方向相邻两像差得到该算子，如图2-3所示。f(i,f(i1,f(i,jf(i1,j

Gxf(i1,j1)f(i,j)Gyf(i,j1)f(i1,

Gf(i,j)f(i,jf(i1,j1)f(i,j)f(i,j1)f(i1, 式（2-其中Gx和Gy 0 Gx 0

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式（2- 0Prewittf'(i,j)(S

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111 111Canny边缘算Canny算子边缘检测的基本原理是：采用二维函数的任一方向上的一阶方Canny边缘检测算子是一种最优边缘检测算子。其实现检测图像边缘的步骤与用滤波器平滑图像 2f(x,y)

2

图像g为 gfk2f 式（2-12）表示模糊图像f经算子锐化以后得到新图像g。k的选择要合理，太大会使图像中的轮廓边缘产生过冲；k太小，锐化不明显。f(xy2f(x,y)

f(i1,j)

f(i,

式（2-f(i1,j)f(i,j)f(i,j)f(i1,f(i1,j)f(i1,j)2f(i,2f(x,y)

f(i,j1)f(i,j1)2f(i,

式（2- 2f(x,y)2f(x,

式（2-f(i1,j)f(i1,j)f(i,j1)f(i,j1)4f(i, 1f(i1,j)f(i1,j)f(i,j1)f(i,j1)f(i,5f(i, g(i,j)f(i,j2f(i, 式（2-5f(i,j)f(i1,j)f(i1,j)f(i,j1)f(i,j可见，数字图像在(i,j)点的算子，可以由(i,j)点灰度值减去该点领域平均灰度值来求得。当k1时，拉锐化后的图像为gf2f。 3.1的发展历由Matrix(矩阵)与Laboratory()两个单词的前三个字母组成。20世纪70年代后期，时任新墨西哥大学计算机系的CleveMoler博士讲述线性代数课程时，发现应用其他编程软件很不方便，为了减轻学生的编程负担，他和他的同事构思并为学生设计了一组调用LINPACK和EISPACK数据库的通俗易用的借口，这就是用FORTRAN编写萌芽状态的。之后几年,作为免费软件在的基本功能及特Language）、工作环境（theWorkingEnvironment）、数学库函数（theMathLibrary）、用用程序借口（theApplicationInterface）和图形句柄系统（HandleGraphics）。兼有优秀的数值高工作效率、优化设计的强大工具软件。3.4的图像处理基本操对图像的处理功能主要在它的图像处理工具箱（ImageProcessingToolbox）中。图像处理工具箱由一系列支持图像处理操作的函数组成，提供了一套全方位的参照标准算法和图形工具，主要包括ImageWaveletToolboxStatisticsToolboxBioinformaticsToolboxCompiler和COMbuilder，用于进行图像处理、分析、可视化和算法开发，可进行图imadjustim2bwimopen例如本中对数字图像进行边缘检测直接调用图像处理工具箱中的edge可用来检测边界。在编译器内如图3-1所示呈现，仿真结果如图3-2所示。图3-1主界图3-2仿真实第四章数字图像边缘检 子——SobelRobertPrewittCanny以及二阶微分算子——LOG边缘检测算子算法，用语言分别进行编程实现效一阶微分算（I,‘sobel’）BW=edge（I,‘sobel’,thresh）sobel方法的检测方向，可取值horizontal，verticalboth；‘option’不执行细化操作；BW为返回图像的边缘信息。其中，Iroberts’为所用的边缘检测方法；thresh的时候不执行细化操作；BW为返回图像的边缘信息。其中，Iprewitt’为所用的边缘检测方法；threshdirectionsobel方法的检测方向，可取值horizontal，verticalboth；BW为返回图像的边缘信息。BW为返回图像的边缘信息。下面以一张人物和一张景物，对其应用一阶微分算法进行边缘检测仿 4-1I=imread('D:\Users\ZXD\Desktop\设计\leehom.jpg')；%读入图像 4-2灰度图像 4-30.00sobel 4-50.01sobel 4-60.05sobel 4-70.1sobel 4-80.2sobel通过对以上几对Sobel算子算法仿真效果图的4-5中阈值为0.01的边缘检测图像效果0.01检测出来的边缘太多以至于不便于观察边缘 4-90.00Roberts 4-100.001Roberts 4-110.01Roberts 4-120.05Roberts 4-130.1Roberts 4-140.2Roberts通过对以上几对Roberts算子算法仿真效4-12中阈值0.05的边缘检测图像效果比较明阈值小于0.05检测出的边缘太多以至于不便于观察边缘， 4-150.00Prewitt 4-160.001Prewitt 4-170.005Prewitt 4-180.01Prewitt 4-200.1Prewitt 4-210.00Canny 4-220.01Canny 4-230.05Canny 4-240.1Canny 4-250.2Canny 4-260.3Canny0.05二阶微分算是指滤波器的标准差，默认值为2；BW为返回图像的边缘信息。 4-280.001LOG 4-290.005LOG 通过对以上几对LOG算子算法仿真效果图的观察，发现图4-27中阈值为0.00的边缘检测效果和4-28阈值为0.001的边缘检测效果中比阈值大于0.001检测Sobel算子根据像素点上下、左右邻点灰度差，在边缘处达到极值这一现Roberts算子采用对角线方向相邻两像差近似梯度幅值检测边缘。检测水Prewitt是Canny算子所具备的。简单，但会增强图像中噪声的干扰，边缘检测和抗噪声干扰之间的成为这类方本主要简单学习研究了、基于的数字图像边缘检测技术。对边缘提取的基础理论知识进行了系统的阐述。选取几种常用边缘提取方法用在这次设计中我遇到了很多问题，比如程序的编写，软件的用。通过在馆、互联网查阅资料以及学习相关知识，最终在老师和同学这个过程中，要有足够的自信，遇到问题不要气馁，多学多问，没有战胜不了的。参考文[1].《图像处理-能力提高与应用案例》[M].：航空航天大学，第1，2014.01.[2]，赵海滨.《 图像处理实例详解》[M].：，第1版,2013.07. [4].常用图像边缘检测方法及研究[J].现代电子技术，2011，34（4）：91-吴术路.基于Sobel算子图像边缘检测的实现[J].电脑知识与技术靳鹏飞.一种改进的Sobel图像边缘检测算法[J].应用光学，2008,29（4）：35-，，常青.基于Canny算子的红外图像边缘检测研究[J].激光与红外，2007， 数字图像边缘检测算子的研究[J].机械工自动化.数字图像边缘检测方法的探讨[J].测绘通报,2006,3：40-42..灰度图像边缘检测算法的性能评价[D].沈阳工业大学.2007.生,,.一种基于积分变换的边缘检测算法[J].中国图象图形学报..在数字图象处理中的应用[J].电脑知识与技术.2008,1(1):29-,,等.基于多结构元的噪声污染灰度图像边缘检测研究[J].大学学报(工学版),2003,49(3):45-49..图像处理中边缘检测算法的研究[J].科技信息.2008,(4):30-XUXian-ling,LINYi-shui.Applicationof inDingitalImageProcessing[J].MODERN袁,,周雪花,等.基于Sobel算子的图像边缘检测研究[J].激光与红.数字图像处理[M].:大学版社求是科技.7.0从入门到精通[M].:人民邮电,2006: [20]张德丰 外文资DigitalImageProcessingandEdgeDigitalImageInterestindigitalimageprocessingmethodsstemsfromtwoprincipalapplicationareas:improvementofpictorialinformationforhumaninterpretation;andprocessingofimagedataforstorage,transmission,andrepresentationforautonomousmachineperception.Animagemaybedefinedasatwo-dimensionalfunction,f(x,y),wherexandyarespatial(plane)coordinates,andtheamplitudeoffatanypairofcoordinates(x,y)iscalledtheintensityorgrayleveloftheimageatthatpoint.Whenx,y,andtheamplitudevaluesoffareallfinite,discreteties,wecalltheimageadigitalimage.Thefieldofdigitalimageprocessingreferstoprocessingdigitalimagesbymeansofadigitalcomputer.Notethatadigitalimageiscomposedofafinitenumberofelements,eachofwhichhasaparticularlocationandvalue.Theseelementsarereferredtoaspictureelements,imageelements,pels,andpixels.Pixelisthetermmostwidelyusedtodenotetheelementsofadigitalimage.Visionisthemostadvancedofoursenses,soitisnotsurprisingthatimagesplaythesinglemostimportantroleinhumanperception.However,unlikehumans,whoarelimitedtothevisualbandoftheelectromagnetic(EM)spectrum,imagingmachinescoveralmosttheentireEMspectrum,rangingfromgammatoradiowaves.Theycanoperateonimagesgeneratedbysourcesthathumansarenotaccustomedtoassociatingwithimages.Theseincludeultrasound,electronmicroscopy,andcomputergeneratedimages.Thus,digitalimageprocessing passesawideandvariedfieldofapplications.Thereisnogeneralagreementamongauthorsregardingwhereimageprocessingstopsandotherrelatedareas,suchasimageysisandcomputervision,start.Sometimesadistinctionismadebydefiningimageprocessingasadisciplineinwhichboththeinputandoutputofaprocessareimages.Webelievethistobealimitingandsomewhatartificialboundary.Forexample,underthisdefinition,eventhetrivialtaskofcomputingtheaverageintensityofanimage(whichyieldsasinglenumber)wouldnotbeconsideredanimageprocessingoperation.Ontheotherhand,therearefieldssuchascomputervisionwhoseultimategoalistousecomputerstoemulatehumanvision,includinglearningandbeingabletomakeinferencesandtakeactionsbasedonvisualinputs.Thisareaitselfisabranchofartificialinligence(AI)whoseobjectiveistoemulatehumaninligence.ThefieldofAIisinitsearlieststagesofinfancyintermsofdevelopment,withprogresshavingbeenmuchslowerthanoriginallyanticipated.Theareaofimageysis(alsocalledimageunderstanding)isinbetweenimageprocessingandcomputervision.Therearenoclearcutboundariesinthecontinuumfromimageprocessingatoneendtocomputervisionattheother.However,oneusefulparadigmistoconsiderthreetypesofcomputerizedprocessesinthiscontinuum:low,mid,andhighlevelprocesses.Low-levelprocessesinvolveprimitiveoperationssuchasimagepreprocessingtoreducenoise,contrastenhancement,andimagesharpening.Alow-levelprocessischaracterizedbythefactthatbothitsinputsandoutputsareimages.Mid-levelprocessingonimagesinvolvestaskssuchassegmentation(partitioninganimageintoregionsorobjects),descriptionofthoseobjectstoreducethemtoaformsuitableforcomputerprocessing,andclassification(recognition)ofindividualobjects.Amidlevelprocessischaracterizedbythefactthatitsinputsgenerallyareimages,butitsoutputsareattributesextractedfromthoseimages(e.g.,edges,contours,andtheidentityofindividualobjects).Finally,higherlevelprocessinginvolves“makingsense”ofanensembleofrecognizedobjects,asinimageysis,and,atthefarendofthecontinuum,performingthecognitivefunctionsnormallyassociatedwithvision.Basedontheprecedingcomments,weseethatalogicalplaceofoverlapbetweenimageprocessingandimageysisistheareaofrecognitionofindividualregionsorobjectsinanimage.Thus,whatwecallinthisbookdigitalimageprocessing processeswhoseinputsandoutputsareimagesand,inaddition, passesprocessesthatextractattributesfromimages,uptoandincludingtherecognitionofindividualobjects.Asasimpleillustrationtoclarifytheseconcepts,considertheareaofautomatedysisoftext.Theprocessesofacquiringanimageoftheareacontainingthetext,preprocessingthatimage,extracting(segmenting)theindividualcharacters,describingthecharactersinaformsuitableforcomputerprocessing,andrecognizingthoseindividualcharactersareinthescopeofwhatwecalldigitalimageprocessinginthisbook.Makingsenseofthecontentofthepagemaybeviewedasbeingintheofimageysisandevencomputervision,dependingonthelevelofcomplexityimpliedbythestatement“makingsense.”Aswill eevidentshortly,digitalimageprocessing,aswehavedefinedit,isusedsuccessfullyinabroadrangeofareasofexceptionalsocialandeconomicvalue.Theareasofapplicationofdigitalimageprocessingaresovariedthatsomeformoforganizationisdesirableinattemptingtocapturethebreadthofthisfield.Oneofthesimplestwaystodevelopabasicunderstandingoftheextentofimageprocessingapplicationsistocategorizeimagesaccordingtotheirsource(e.g.,visual,X-ray,andsoon).Theprincipalenergysourceforimagesinusetodayistheelectromagneticenergyspectrum.Otherimportantsourcesofenergyincludeacoustic,ultrasonic,andelectronic(intheformofelectronbeamsusedinelectronmicroscopy).Syntheticimages,usedformodelingandvisualization,aregeneratedbycomputer.InthissectionwediscussbrieflyhowimagesaregeneratedinthesevariouscategoriesandtheareasinwhichtheyareImagesbasedonradiationfromtheEMspectrumarethemostfamiliar,especiallyimagesintheX-rayandvisualbandsofthespectrum.Electromagneticwavescanbeconceptualizedaspropagatingsinusoidalwavesofvaryingwavelengths,ortheycanbethoughtofasastreamofmasslessparticles,eachtravelinginawavelikepatternandmovingatthespeedoflight.Eachmasslessparticlecontainsacertainamount(orbundle)ofenergy.Eachbundleofenergyiscalledaphoton.Ifspectralbandsaregroupedaccordingtoenergyperphoton,weobtainthespectrumshowninfig.below,rangingfromgammarays(highestenergy)atoneendtoradiowaves(lowestenergy)attheother.ThebandsareshownshadedtoconveythefactthatbandsoftheEMspectrumarenotdistinctbutrathertransitionsmoothlyfromonetotheother.Imageacquisitionisthefirstprocess.Notethatacquisitioncouldbeassimpleasbeinggivenanimagethatisalreadyindigitalform.Generally,theimageacquisitionstageinvolvespreprocessing,suchasscaling.Imageenhancementisamongthesimplestandmostappealingareasofdigitalimageprocessing.Basically,theideabehindenhancementtechniquesistobringoutdetailthatisobscured,orsimplytohighlightcertainfeaturesofinterestinanimage.Afamiliarexampleofenhancementiswhenweincreasethecontrastofanimagebecause“itlooksbetter.”Itisimportanttokeepinmindthatenhancementisaverysubjectiveareaofimageprocessing.Imagerestorationisanareathatalsodealswithimprovingtheappearanceofanimage.However,unlikeenhancement,whichissubjective,imagerestorationisobjective,inthesensethatrestorationtechniquestendtobebasedonmathematicalorprobabilisticmodelsofimagedegradation.Enhancement,ontheotherhand,isbasedonhumansubjectivepreferencesregardingwhatconstitutesa“good”enhancementresult.ColorimageprocessingisanareathathasbeengaininginimportancebecauseofthesignificantincreaseintheuseofdigitalimagesovertheInternet.Itcoversanumberoffundamentalconceptsincolormodelsandbasiccolorprocessinginadigital.Colorisusedalsoinlaterchaptersasthebasisforextractingfeaturesofinterestinanimage.Waveletsarethefoundationforrepresentingimagesinvariousdegreesofresolution.Inparticular,thismaterialisusedinthisbookforimagedatacompressionandforFigCompression,asthenameimplies,dealswithtechniquesforreducingthestoragerequiredtosaveanimage,orthebandwidthrequiredtotransmiit.Althoughstoragetechnologyhasimprovedsignificantlyoverthepastdecade,thesamecannotbesaidfortransmissioncapacity.ThisistrueparticularlyinusesoftheInternet,whicharecharacterizedbysignificantpictorialcontent.Imagecompressionisfamiliar(perhapsinadvertently)tomostusersofcomputersintheformofimagefileextensions,suchasthejpgfileextensionusedintheJPEG(JointPhotographicExpertsGroup)imagecompressionMorphologicalprocessingdealswithtoolsforextractingimagecomponentsthatareusefulintherepresentationanddescriptionofshape.Thematerialinthischapterbeginsatransitionfromprocessesthatoutputimagestoprocessesthatoutputimageattributes.Segmentationprocedurespartitionanimageintoitsconstituentpartsorobjects.Ingeneral,autonomoussegmentationisoneofthemostdifficulttasksindigitalimageprocessing.Aruggedsegmentationprocedurebringstheprocessalongwaytowardsuccessfulsolutionofimagingproblemsthatrequireobjectstobeidentifiedindividually.Ontheotherhand,weakorerraticsegmentationalgorithmsalmostalwaysguaranteeeventualfailure.Ingeneral,themoreaccuratethesegmentation,themorelikelyrecognitionistosucceed.Representationanddescriptionalmostalwaysfollowtheoutputofasegmentationstage,whichusuallyisrawpixeldata,constitutingeithertheboundaryofaregion(i.e.,thesetofpixelsseparatingoneimageregionfromanother)orallthepointsintheregionitself.Ineithercase,convertingthedatatoaformsuitableforcomputerprocessingisnecessary.Thefirstdecisionthatmustbemadeiswhetherthedatashouldberepresentedasaboundaryorasacompleteregion.Boundaryrepresentationisappropriatewhenthefocusisonexternalshapecharacteristics,suchascornersandinflections.Regionalrepresentationisappropriatewhenthefocusisoninternalproperties,suchastextureorskeletalshape.Insomeapplications,theserepresentationscomplementeachother.Choosingarepresentationisonlypartofthesolutionfortransformingrawdataintoaformsuitableforsubsequentcomputerprocessing.Amethodmustalsobespecifiedfordescribingthedatasothatfeaturesofinterestarehighlighted.Description,alsocalledfeatureselection,dealswithextractingattributesthatresultinsometativeinformationofinterestorarebasicfordifferentiatingoneclassofobjectsfromanother.Recognitionistheprocessthatassignsalabel(e.g.,“vehicle”)toanobjectbasedonitsdescriptors.Asdetailedbefore,weconcludeourcoverageofdigitalimageprocessingwiththedevelopmentofmethodsforrecognitionofindividualobjects.SofarwehavesaidnothingabouttheneedforpriorknowledgeorabouttheinteractionbetweentheknowledgebaseandtheprocessingmodulesinFig2above.Knowledgeaboutaproblemiscodedintoanimageprocessingsystemintheformofaknowledgedatabase.Thisknowledgemaybeassimpleasdetailingregionsofanimagewheretheinformationofinterestisknowntobelocated,thuslimitingthesearchthathastobeconductedinseekingthatinformation.Theknowledgebasealsocanbequitecomplex,suchasaninterrelatedlistofallmajorpossibledefectsinamaterialsinspectionproblemoranimagedatabasecontaininghigh-resolutionsaliteimagesofaregioninconnectionwithchange-detectionapplications.Inadditiontoguidingtheoperationofeachprocessingmodule,theknowledgebasealsocontrolstheinteractionbetweenmodules.ThisdistinctionismadeinFig2abovebytheuseofdouble-headedarrowsbetweentheprocessingmodulesandtheknowledgebase,asopposedtosingle-headedarrowslinkingtheprocessingmodules.EdgeEdgedetectionisaterminologyinimageprocessingandcomputervision,particularlyintheareasoffeaturedetectionandfeatureextraction,torefertoalgorithmswhichaimatidentifyingpointsinadigitalimageatwhichtheimagebrightnesschangessharplyormoreformallyhasdiscontinuities.Althoughpointandlinedetectioncertainlyareimportantinanydiscussiononsegmentation,edgedectectionisbyfarthemostcommonapproachfordetectingmeaningfuldiscountiesingraylevel.Althoughcertainliteraturehasconsideredthedetectionofidealstepedges,theedgesobtainedfromnaturalimagesareusuallynotatallidealstepedges.Insteadtheyarenormallyaffectedbyoneorseveralofthefollowingeffects:1.focalblurcausedbyafinitedepth-of-fieldandfinitepointspreadfunction;2.penumbralblurcausedbyshadowscreatedbylightsourcesofnon-zeroradius;3.shadingatasmoothobjectedge;4.localspecularitiesorinterreflectionsinthevicinityofobjectedges.Atypicaledgemightforinstancebetheborderbetweenablockofredcolorandablockofyellow.Incontrastaline(ascanbeextractedbyaridgedetector)canbeasmallnumberofpixelsofadifferentcoloronanotherwiseunchangingbackground.Foraline,theremaythereforeusuallybeoneedgeoneachsideoftheline.Toillustratewhyedgedetectionisnotatrivialtask,letusconsidertheproblemofdetectingedgesinthefollowingone-dimensionalsignal.Here,wemayintuitivelysaythatthereshouldbeanedgebetweenthe4thand5thpixels.5764Iftheintensitydifferenceweresmallerbetweenthe4thandthe5thpixelsandiftheintensitydifferencesbetweentheadjacentneighbouringpixelswerehigher,itwouldnotbeaseasytosaythatthereshouldbeanedgeinthecorrespondingregion.Moreover,onecouldarguethatthiscaseisoneinwhichthereareseveraledges.Hence,tofirmlystateaspecificthresholdonhowlargetheintensitychangebetweentwoneighbouringpixelsmustbeforustosaythatthereshouldbeanedgebetweenthesepixelsisnotalwaysasimpleproblem.Indeed,thisisoneofthereasonswhyedgedetectionmaybeanon-trivialproblemunlesstheobjectsinthesceneareparticularlysimpleandtheilluminationconditionscanbewellcontrolled.Therearemanymethodsforedgedetection,butmostofthemcanbegroupedintotwocategories,search-basedandzero-crossingbased.Thesearch-basedmethodsdetectedgesbyfirstcomputingameasureofedgestrength,usuallyafirst-orderderivativeexpressionsuchasthegradientmagnitude,andthensearchingforlocaldirectional ofthegradientmagnitudeusingacomputedestimateofthelocalorientationoftheedge,usuallythegradientdirection.Thezero-crossingbasedmethodssearchforzerocrossingsinasecond-orderderivativeexpressioncomputedfromtheimageinordertofindedges,usuallythezero-crossingsoftheLaplacianorthezero-crossingsofanon-lineardifferentialexpression,aswillbedescribedinthesectionondifferentialedgedetectionfollowingbelow.Asapre-processingsteptoedgedetection,asmoothingstage,typicallyGaussiansmoothing,isalmostalwaysapplied(seealsonoisereduction).Theedgedetectionmethodsthathavebeenpublishedmainlydifferinthetypesofsmoothingfiltersthatareappliedandthewaythemeasuresofedgestrengtharecomputed.Asmanyedgedetectionmethodsrelyonthecomputationofimagegradients,theyalsodifferinthetypesoffiltersusedforcomputinggradientestimatesinthex-andy-directions.Oncewehavecomputedameasureofedgestrength(typicallythegradientmagnitude),thenextstageistoapplyathreshold,todecidewhetheredgesarepresentornotatanimagepoint.Thelowerthethreshold,themoreedgeswillbedetected,andtheresultwillbeincreasinglysusceptibletonoise,andalsotopickingoutirrelevantfeaturesfromtheimage.Converselyahighthresholdmaymisssubtleedges,orresultinfragmentededges.Iftheedgethresholdingisappliedtojustthegradientmagnitudeimage,theresultingedgeswillingeneralbethickandsometypeofedgethinningpost-processingisnecessary.Foredgesdetectedwithnon-umsuppressionhowever,theedgecurvesarethinbydefinitionandtheedgepixelscanbelinkedintoedgepolygonbyanedgelinking(edgetracking)procedure.Onadiscretegrid,thenon-umsuppressionstagecanbeimplementedbyestimatingthegradientdirectionusingfirst-orderderivatives,thenroundingoffthegradientdirectiontomultiplesof45degrees,andfinallycomparingthevaluesofthegradientmagnitudeintheestimatedgradientdirection.Acommonlyusedapproachtohandletheproblemofappropriatethresholdsforthresholdingisbyusingthresholdingwithhysteresis.Thismethodusesmultiplethresholdstofindedges.Webeginbyusingtheupperthresholdtofindthestartofanedge.Oncewehaveastartpoint,wethentracethepathoftheedgethroughtheimagepixelbypixel,markinganedgewheneverweareabovethelowerthreshold.Westopmarkingouredgeonlywhenthevaluefallsbelowourlowerthreshold.Thisapproachmakestheassumptionthatedgesarelikelytobeincontinuouscurves,andallowsustofollowafaintsectionofanedgewehavepreviouslyseen,withoutmeaningthateverynoisypixelintheimageismarkeddownasanedge.Still,however,wehavetheproblemofchoosingappropriatethresholdingparameters,andsuitable