1第十章圖像分割

ImageSegmentation張運楚信息與電氣工程學(xué)院

2OutlineDetectionofgrayleveldiscontinuitiesEdgelinkingandboundarydetectionThresholdingRegion-BasedSegmentationSegmentationbyMorphologicalWatershedsTheUseofMotioninSegmentation3Revisit-GoalsofimageprocessingImageimprovement–lowlevelImageProcessingImprovementofpictorialinformationforhumaninterpretation(Improvingthevisualappearanceofimagestoahumanviewer)Imageanalysis–highlevelImageProcessingProcessingofscenedataforautonomousmachineperception(Preparingimagesformeasurementofthefeaturesandstructurespresent)ExtractinginformationfromanimageStep1:segmenttheimage

objectsorregions(Regionofinterest)Step2:describeandrepresentthesegmentedregionsinaformsuitableforcomputerprocessingStep3:imagerecognitionandinterpretation4Imageanalysis5Whatissegmentation?DefinitionSubdividesanimageintoitsconstituentregionsorobjects從圖像中提取出所需的語義對象(semanticobject)將圖像劃分成若干有一定含義的區(qū)域Heavilyrelyononeoftwopropertiesofintensityvalues:Discontinuity----Partitionbasedonabruptchangesinintensity,e.g.edgesinanimagepoint/line/edge/cornerdetectionSimilarity----Partitionbasedonintensitysimilarity.thresholdingregiongrowing/splitting/merging67圖像分割示例8Extractmotionobjectsfromasequenceofimages9圖像分割難度分割依賴于低層視覺，同時又依賴于高層視覺。圖象分割是計算視覺和圖像理解中的最基本問題之一，也是該領(lǐng)域國際學(xué)術(shù)界公認(rèn)的將會長期存在的最困難的問題之一。圖象分割之所以困難的一個重要原因是其并不完全屬于圖像特征提取問題，它還涉及到各種圖像特征的知覺組織(PerceptualGrouping)。從一般意義上來說，只有對圖像內(nèi)容的徹底理解，才能產(chǎn)生完美的分割。通過對環(huán)境進(jìn)行適度控制和選擇適當(dāng)?shù)膫鞲衅鳎梢越档蛨D象分割的難度。101110.1基礎(chǔ)知識LetRrepresenttheentireregion.WemayviewsegmentationasaprocessthatpartitionsRintonsubregions,R1,R2,…,Rn,suchthatHere,Q(Ri)isalogicalpredicatedefinedoverthepointsinregionsetRi.Condition(d)dealswiththepropertiesthatmustbesatisfiedbythepixelsinasegmentedregion.Segmentationmustbecomplete,thatis,Everypixelmustbeinaregion.Regionmustbedisjoint.12示例：基于不連續(xù)性和相似性的灰度圖像分割44的子塊基于區(qū)域特征-標(biāo)準(zhǔn)差1310.2DetectionofDiscontinuitiesWewanttoextract3basictypesofgray-leveldiscontinuityinadigitalimage:PointsLinesEdgesThemostcommonwaytolookfordiscontinuitiesistorunamaskthroughtheimage--spatialfiltering.Theresponseofthemaskatanypointintheimageisgivenby14突變檢測（一階微分）梯度定義對于圖像函數(shù)f(x,y)，它在點(x,y)處的梯度是一個矢量，定義為：

梯度的兩個重要性質(zhì)是：

（1）梯度的方向在函數(shù)f(x,y)最大變化率的方向上。（2）梯度的模用由下式算出：15對數(shù)字圖像來講，f(x,y)的二階偏微分可表示為：突變檢測（二階微分

拉普拉斯算子）16拉普拉斯算子實現(xiàn)模板

Whichgivesanisotropicresultforrotationsinincrementsof90°Whichgivesanisotropicresultforrotationsinincrementsof45°17181.PointDetection

Isolatedpoint(孤立點)–apointwhosegraylevelissignificantlydifferentfromitsbackgroundandwhichislocatedinahomogeneousornearlyhomogeneousarea.Anisolatedpointsdetectedatthelocationonwhichthemaskiscenteredif

|R(x,y)|≥TwhereTisanonnegativethresholdandRistheresponseofthemask.此處采用拉普拉斯模板。從而產(chǎn)生一個二值圖像：19Exampleofpointdetection拉普拉斯模板20用拉普拉斯模板進(jìn)行線檢測2.Linedetection21Masksforlinesofdifferentdirections:Respondmorestronglytolinesofonepixelthickofthedesignateddirection.Ifinterestedinlinesofanydirections,runall4masksandselectthehighestresponse.Ifinterestedonlyinlinesofaspecificdirection(e.g.vertical),useonlythemaskassociatedwiththatdirection.Thresholdtheoutput.22Illustrationoflinedetection233.EdgeDetection物體的邊緣是以圖像的局部特征不連續(xù)的形式出現(xiàn)的，也就是指圖像局部亮度變化最顯著的部分，例如灰度值的突變、顏色的突變、紋理結(jié)構(gòu)的突變等，同時物體的邊緣也是不同區(qū)域的分界處。在Marr的視覺計算理論框架中，抽取二維圖像上的邊緣、角點、紋理等基本特征，是整個系統(tǒng)框架中的第一步。這些特征所組成的圖稱為基元圖。Yuille等指出，在不同“尺度”意義下的邊緣點，在一定條件下包含了原圖像的全部信息。24邊緣的形成與分類A類--空間曲面上的不連續(xù)點B類--由不同材料或相同材料不同顏色產(chǎn)生的C類--物體與背景的分界線，一般稱為輪廓線D類--陰影引起的邊緣右圖畫出了一幅圖像中的邊緣點，僅僅根據(jù)這些邊緣點，就能識別出三維物體，可見邊緣點確實包含了圖像中的大量信息。圖像中的邊緣點

25在各邊緣線的兩邊，圖像的灰度值有明顯的不同。26ModelofEdgeAsetofconnectedpixelsthatlieontheboundary

betweentworegions.Localconcept271stand2nd

DerivativeofgraylevelThemagnitudeofthefirstderivativecanbeusedtodetectthepresenceofanedgeatapointinanimage(i.e.,todetermineifapointisonaramp).Thesignofthesecondderivativecanbeusedtodeterminewhetheranedgepixelliesonthedarkorlightsideofanedge.Producing2valuesforeveryedgeinanimage(anundesirablefeature).Centerofathickedgeislocatedatthezerocrossing.28Example:Behaviorofthefirstandsecondderivatives

aroundanoisyedgeFairlylittlenoisecanhavesignificantimpactonthetwokeyderivatives.Andthesecondderivativeisevenmoresensitivetonoise.Imagesmoothingshouldbeaseriousconsiderationpriortotheuseofderivatives.Effectofnoise29邊緣檢測的基本步驟對圖像進(jìn)行平滑處理-降噪邊緣點的檢測，以提取圖像中所有的邊緣候選點邊緣定位，從候選邊緣點中確認(rèn)真正的邊緣點30FirstDerivative:GradientOperatorsThegradientofanimagef(x,y)atlocation(x,y)isdefinedasSomepropertiesaboutgradientvectorGradientvectordirection:Itpointsinthedirectionofmaximumrateofchangeofimageat(x,y).MagnitudeM(x,y):givesthemaximumrateofincreaseofperunitdistanceinthedirectionof

f.Thedirectionangleofthegradientvector

f,

(x,y).31Anedgeelementisassociatedwith2components:magnitudeofthegradientvector

f.edgedirection,thedirectionofanedgeat(x,y)isperpendiculartothedirectionofthegradientvectorat(x,y).32

水平垂直差分法RobertGradientSobel算子：Prewitt算子：SomebasicgradientoperatorsBetternoise-suppression(x,y)33Somebasicgradientoperators(cont’d)34Example:

IllustrationoftheSobelgradientanditscomponent35IllustrationoftheSobelgradient(cont’d)–smoothedtheimagepriortoedgedetection36IllustrationoftheSobelgradient(cont’d)-Diagonaledgedetection37IllustrationoftheSobelgradient(cont’d)-Thresholding38SecondDerivative:LaplacianOperatorTheLaplacianoperator(

2)isaverypopularoperatorapproximatingthesecondderivative.Laplacianoperatoratlocation(x,y)isdefinedasLaplacianoperatorisnon-directional(isotropic).39IssueswithLaplacianProblems:UnacceptablysensitivetonoiseMagnitudeofLaplacianresultsindoubleedgesDoesnotprovidegradient,socan’tdetectedgedirectionFixes:SmoothingUsingzero-crossingpropertyforedgelocationNotforgradientdirection,butforestablishingwhetherapixelisonthedarkorlightsideofandedge40Marr-HildrethEdgeDetection

Smoothing-LaplacianofGaussian(LoG)ConsiderthentheLaplacianofanimagef(x,y)smoothedbyaGaussian.ThisoperatorisabbreviatedasLoG,fromLaplacianofGaussian:Theorderofdifferentiationandconvolutioncanbeinterchangedduetolinearityoftheoperations:41LaplacianofGaussian(cont’d)42LaplacianofGaussian(cont’d)Becauseofitsshape,theLoGoperatoriscommonlycalledaMexicanhat.43Example:EdgefindingbyzerocrossingSmooththeimageusingGaussianlow-passfiltertoreducenoise.Thencalculatethe2ndderivativeusingLaplacianoperator.Finally,findthezero-crossing.Advantages:noisereductioncapability;edgesarethinner.Drawbacks:edgesformnumerousclosedloops(spaghettieffect);computationcomplex.44CannyEdgeDetector(坎尼邊緣檢測器)Canny在1986年寫的一篇論文中給出了3個準(zhǔn)則：（1）信噪比準(zhǔn)則（2）定位精度準(zhǔn)則（3）單邊緣響應(yīng)準(zhǔn)則具體步驟：

首先用2D高斯濾波模板進(jìn)行卷積以平滑圖像；

利用微分算子，計算梯度的幅值和方向；Canny,J.AComputationalApproachtoEdgeDetection.IEEETrans.onPatternAnalysisandMachineIntelligence,1986,8(6):679-698.45

對梯度幅值進(jìn)行非極大值抑制。即遍歷梯度幅值圖像，若某個像素的梯度幅值與其梯度方向上前后兩個像素的梯度幅值相比不是最大，那么這個像素值置為0，即不是邊緣；

使用雙閾值算法檢測和連接邊緣。即使用累計直方圖計算兩個閾值，凡是梯度的幅值大于高閾值的一定是邊緣；凡是梯度的幅值小于低閾值的一定不是邊緣。如果檢測結(jié)果大于低閾值但又小于高閾值，那就要看這個像素的鄰接像素中有沒有超過高閾值的邊緣像素，如果有，則該像素就是邊緣，否則就不是邊緣。46Anedgeelementisassociatedwith2components:magnitudeofthegradientvector,

f.edgedirection,thedirectionofanedgeat(x,y)isperpendiculartothedirectionofthegradientvectorat(x,y).47Example:Cannyedgedetector48EdgelinkingandboundarydetectionDetectionofdiscontinuityusing1stderivativeProvidinggradientandmagnitudeZerocrossing(2ndderivativeusingLaplacian)ForedgelocationNogradientinformationSensitivetonoiseSmoothingusingGaussianfilter(LoG)Howtodealwithgapsinedges?Howtodealwithnoiseinedges?Linkingpointsbydeterminingwhethertheylieonacurveofaspecificshape.LocalProcessingGlobalProcessingviatheHoughTransform491.LocalProcessingAnalyzethecharacteristicsoftheedgepixelsinasmallneighborhoodItsmagnitudeItsdirectionAllpointsthataresimilaraccordingtoasetofpredefinedcriteriaarelinked,forminganedgeofpixelsthatsharethosecriteria.Asetofsimilaritycriteria,forexample:Anedgepixelat(s,t)inapredefinedneighborhoodof(x,y),issimilarinmagnitudeofgradienttothepixelat(x,y),ifandhasananglesimilartothepixelat(x,y),if,E-nonnegativethreshold,A-nonnegativeanglethreshold50邊緣連接的簡化步驟計算輸入圖像f(x,y)的梯度幅度陣列M(x,y)和梯度角度陣列

(x,y)。按下式形成一幅二值圖像g：其中TM是梯度幅度閾值，A是選定的角度方向，TA是與A相關(guān)的可接受的梯度角度方向變化范圍。掃描g的各行，并在每一行中填充不超過指定長度K的縫隙。如檢測任何其他方向

的縫隙，以該角度旋轉(zhuǎn)圖像g，并應(yīng)用步驟3中的水平掃描過程，然后再恢復(fù)g。51Example:

Edge-pointlinkingbasedonlocalprocessingTM=30%最大梯度值A(chǔ)=90

TA=45

52Matlabfunctionfilter2Imfilterfpecialedge53GlobalProcessingviatheHoughTransform

霍夫變換Resultsofedge-detectionmethodsmaycontainsparsepoints,insteadofstraightlinesorcurves.Therefore,needtofitalinetotheedgepoints.Efficientsolution:HoughTransformImagespace

parameterspaceOriginallyforfindinglinesEasilyvariedtofindothershapesReference:DudaRO,HartPE.UseoftheHoughTransformationtoDetectLinesandCurvesinPictures[J].CommunicationsoftheACM,1972,15(1):11–15.張運楚.基于存在概率圖的圓檢測方法.計算機工程與應(yīng)用,2006,42(29),49-51.54HoughTransformConsiderapoint(xi,yi)andthegeneralequationofastraightlineinslope-interceptform:

yi=axi

+bQ:Howmanylinesmaypassthrough(xi,yi)?Re-writingtheequationin“ab-plane”—parameterspace:b=-xia+yiQ:Howmanylinesdowegetforafixed(xi,yi)in“ab-plane”?Nowgivenanotherpoint(xj,yj),Howtofindtheparameter(a’,b’)whichdefinesthelinethatcontainsbothpoints?55HoughTransform(cont’d)Allpointsonthelinepassingthrough(xi,yi)and(xj,yj),havelinesinparameterspacethatintersectat(a',b').56HoughTransform(con’t)PollingalledgepointsforlinesProblem:theslopeapproachesinfinityasthelineapproachesthehorizontal.57HoughTransform(cont’d)Needanotherparameterizationscheme.Nowconsider:

istheshortestdistancefromthelinetotheorigin,and

istheangle.58HoughTransform(cont’d)Choosingadiscretesetofvaluesof

and

.Constructanaccumulatorarray,initializedwith0foreachentry.Picturethisprocessasavotingprocess.59Example:detectlineviaHoughTransform60DetectingLinesUsingtheHoughTransform(Matlab)houghhoughpeakshoughlines61Example:detectcircleviaHoughTransform6210.3Thresholding閾值分割：利用圖像中要提取的目標(biāo)物與其背景在灰度特性上的差異，把圖像視為具有不同灰度級的兩類區(qū)域(目標(biāo)和背景)的組合，選取一個合適的閾值，以確定圖像中每個像素點應(yīng)該屬于目標(biāo)還是背景區(qū)域，從而產(chǎn)生相應(yīng)的二值圖像，稱單閾值分割。如果圖像中有多個灰度值不同的區(qū)域，那么可以選擇一系列的閾值以將每個像素分到合適的類別中去，這種用多個閾值分割的方法稱為多閾值分割。63ExampleOriginalHistogramResultofsegmentationSinglethresholdDualthresholds64GeneralFormulationofThresholdingAthresholdedimageg(x,y)isdefinedasWhenTdependsonlyonf(x,y),thethresholdiscalledglobal.IfTdependsonbothf(x,y)andp(x,y),thethresholdislocal.IfTdependsonthespatialcoordinates(x,y),thethresholdiscalleddynamicoradaptive.SomelocalpropertyGrayscalevalue65雙閾值分割：圖像中含有三個支配模式的直方圖，可以設(shè)置兩個閾值實現(xiàn)多閾值分割：66Noiseeffect67TheRoleofIlluminationNon-uniformillumination68Thresholdingmethod:categoriesbySankurThresholdNumberBi-levelMulti-levelSpatialvarianceGlobalthreshold:thresholdstheentireimagewithasinglethresholdvalue.Localthreshold:partitionsagivenimageintosubimagesanddeterminesathresholdforeachofthesesubimages.PointdependentorregiondependentFixedoradaptivethresholdM.SezginandB.Sankur,ImageThresholdingTechniques:ASurveyOverCategories69Thresholdingmethod(cont’d)AccordingtheinformationexploitedHistogramshapebased:peaks,valleysandcurvatures.Clusteringbased:pixelsaremodeledasamixtureoftwoGaussians.EntropybasedObjectattributebasedThespatialmethodsusehigh-orderprobabilitydistributionorcorrelationbetweenpixelsLocalmethods70ThresholdingMethoddiscussedBasicGlobalThresholdingBasicAdaptiveThresholdingOtsu’sMethodUsedbythefunctiongraythreshinMatlab71BasicGlobalThresholdingSelectaninitialestimateforTSegmenttheimageusingTtogenerate2regions,G1&G2.G1consistingofallpixelswithgraylevelvalues>TG2consistingofallpixelswithgraylevelvalues

TComputetheaveragegraylevelvaluesm1andm2forthepixelsinregionsG1andG2,respectively.Computeanewthresholdvalue:T=(m

1+m

2)/2Repeatthesteps2through4untilthedifferenceinTinsuccessiveiterationsissmallerthanapredefinedparameterT0(i.e.Tconverges).72HowtoselecttheinitialTIfforegroundandbackgroundoccupycomparableareas,averagegraylevelmightbegood.Iftheareasnotcomparable,midwaybetweenmaxandmingraylevelmightbebetter.73ExampleInitialTistheaveragegraylevel,ThefinalTis125.4with3iterationsvalley74Otsu’sMethod

Otsu法（大津法）由大津于1979年提出的最優(yōu)閾值方法是一種在判決分析或最小二乘法原理的基礎(chǔ)上推導(dǎo)出來的最大類間方差法。令{0,1,2,…,L-1}表示一幅大小為M

N像素的L個不同的灰度級，ni

表示圖像中灰度級為i的像素個數(shù),M

N=n0+n2+…+nL-1表示圖像的總像素數(shù)。圖像的灰度直方圖被歸一化后視為灰度級的概率分布：75Otsu’sMethod(cont’d)選擇T(k)=k為分割閾值，它把把圖像中的所有像素按灰度級分成兩類C1和C2，即：

那么C1和C2發(fā)生的概率可由下式給出：76Otsu’sMethod(cont’d)兩類像素的灰度均值和方差分別為：式中mG為圖像像素灰度總體平均值77Otsu’sMethod(cont’d)兩類像素的灰度方差分別為：為了評估閾值k的優(yōu)劣，Otsu使用類間方差和總體方差定義了兩類像素的可分性測度：78Otsu’sMethod(cont’d)

兩類像素的類間方差和總體方差分別為：

由于總體方差與閾值k

無關(guān)，因此，常通過最大化來獲取最優(yōu)閾值kopt，即：79Otsu’sMethod(cont’d)80ExampleofOtsu’sMethod81用圖像平滑改善全局閾值處理

ExampleofOtsu’sMethod(Noisyimage)82ExampleofOtsu’sMethod(failed)酵母菌83利用邊緣改進(jìn)全局閾值處理利用邊緣性質(zhì)，將原來的直方圖變換成具有更深波谷的直方圖，或者使波谷變換成波峰，使得谷點或峰點更易檢測到。由微分算子的性質(zhì)可以推知，目標(biāo)與背景內(nèi)部像素的梯度小，而目標(biāo)與背景之間的邊界像素的梯度大。因此，可以根據(jù)像素的梯度值或作出一個加權(quán)直方圖。84用梯度信息改進(jìn)圖像分割的步驟：計算圖像f(x,y)的邊緣圖像g(x,y)

，梯度幅度或拉普拉斯的絕對值均可。選擇閾值T。對g(x,y)

進(jìn)行閾值處理，產(chǎn)生一幅二值圖像gT(x,y)

。僅用f(x,y)中對應(yīng)于gT(x,y)

中像素值為1的位置像素計算直方圖。用上述直方圖計算閾值（如Otsu方法），對圖像f(x,y)

進(jìn)行分割。85Example1:Gradientmagnitudebased86Example2:AbsoluteLaplacianbased87Matlabimplementationgraythresh

im2bw88BasicAdaptiveThresholdingGlobalthresholdingoftenfailsinthecaseofunevenillumination.globalthresholding89AnapproachforhandlingsuchasituationistoDividetheimageintosubimagesDetermineadifferentthresholdTtosegmenteachsubimage.Thekeyissues:Howtosubdividetheimage?Howtoestimatethethresholdforeachsubimage?90ExampleofBasicAdaptiveThresholdingAsimplepartition,obtainedbysubdividingtheimageintofourequalparts,andthensubdividingeachpartbyfouragain.subimages91ExampleofBasicAdaptiveThresholding

(cont’d)HowtodealwiththeSubimages?Observation:Type1:Forallsubimages,ifthegraylevelvarianceis<75donotcontainobjectboundaryType2:Forallsubimages,ifthegraylevelvarianceis>100containobjectboundaryAllsubimagesoftype1aremergedandthresholdedusingasinglethresholdvalueEachsubimageoftype2isthresholdedindependently.Allthresholdingisdoneusingbasicglobalmethod.92(cont’d)ResultofBasicAdaptiveThresholdingFailedsubimage93(cont’d)Furthersubdividing9410.4Region-BasedSegmentationFindregionsdirectlybymeansofregionsimilarity&connectivity.TherearefewsuchalgorithmsRegiongrowingRegionsplittingandmerging95RegiongrowingGroupspixelsorsubregionsintolargerregionsbasedonpredefinedcriteria(graytoneortexture).Basicmethod:

Startwithasetof“seed”pointsandfromthese,growregionsbyappendingtoeachseedthoseneighboringpixelsthathavepropertiessimilartotheseed,suchasspecificrangesofgraylevelorcolor.Problemsinregiongrowing:SelectionoftheseedsCriteriaofsimilarityGraylevel’ssimilarity/connectivity/texture/momentsFormulationofastoppingrule

Growingaregionshouldstopwhennomorepixelssatisfythecriteriaforinclusioninthatregion96Example:ApplicationofRegiongrowingseedregions97Example:ApplicationofRegiongrowing(cont’d)Step1:Determinetheinitialseedpoints.Allpixelshavinggray-levelvaluesof255.Step2:Choosecriteriaforregiongrowing.Theabsolutegray-leveldifferencebetweenanypixelandtheseedhadtobelessthan65.Tobeincludedinoneoftheregions,thepixelhadtobe8-connectedtoatleastonepixelinthatregion.Ifapixelwasfoundtobeconnectedtomorethanoneregion,theregionsweremerged.Step3:Formulationofastoppingrule.Inthiscase,itwasnotnecessarytospecifyanystoppingrule.Becausethecriteriaforregiongrowingweresufficient.98RegionsplittingandmergingSplitting:Startingwiththeentireregion.RrepresenttheentireregionandselectapredicateP.IfP(R)=FALSE,dividetheimageintoquadrantsIfPisstillFALSEforanyquadrant,subdividethatquadrantintosubquadrantsandsoon.Theresultisaquadtree.99Merging:Ifonlysplitting,itislikelythatadjacentregionshaveidenticalproperties.Somergingisallowed,aswellassplitting.TwoadjacentregionsRiandRjaremergedonlyifP(Ri∪Rj)=TRUE.AlgorithmSplittinginto4disjointquadrantsforanyregionRiforwhich

P(Ri)=FALSEMerginganyadjacentregionsRjandRkforwhichP(Rj∪Rk)=TRUE.Stopwhennofurthermergingandsplittingispossible.(a)(b)(c)(d)Regionsplittingandmerging(cont’d)100Example10110.5SegmentationbyMorphologicalWatershedsVisualizetheimagein3Dtopography(地形)spatialcoordinatesandgraylevels.Insuchatopographicinterpretation,thereare3typesofpoints:PointsbelongingtoaregionalminimumPointsatwhichadropofwaterwouldfalltoasingleminimum.(Thecatchmentbasin(匯水盆)orwatershed(分水嶺)ofthatminimum.)Pointsatwhichadropofwaterwouldbeequallylikelytofalltomorethanoneminimum.(Thedividelinesorwatershedlines.)WatershedlinesCatchmentbasinsOriginalimageTopographicview102Visualizetheimagein3Dtopography(地形)103(Cont’d)Theobjectiveistofindwatershedlines.Theideaissimple:Supposethataholeispunchedineachregionalminimumandthattheentiretopographyisfloodedfrombelowbylettingwaterrisethroughtheholesatauniformrate.Whenrisingwaterindistinctcatchmentbasinsisaboutthemerge,adamisbuilttopreventmerging.Thesedamboundariescorrespondtothewatershedlines.104IllustrationofWatershedsSegmentationLongerdamconstructedWaterstartmerging,soshorterdamconstructedFinalresult105ApplicationofWatershedSegmentationWatershedalgorithmisoftenappliedtothegradientofanimage,ratherthantotheimageitself.RegionalminimaofcatchmentbasinscorrelatenicelywiththesmallvalueofthegradientcorrespondingtheobjectsofinterestBoundariesarehighlightedasthewatershedlines.Theimportantpropertyisthatthewatershedlinesformaconnectedpath,thusgivingcontinuousboundariesbetweenregions.Oneoftheprincipalapplication:extractionofnearlyuniform(bloblike)objectsfromthebackground.106Example_1ofWatershedSegmentationthegradientofanimage107Example_2ofWatershedSegmentationDuetonoiseandotherlocalirregularitiesofthegradient,oversegmentationmightoccur.108Example_2ofWatershedSegmentation(cont’d)Asolutionistolimitthenumberofregionalminima.Usemarkerstospecifytheonlyallowedregionalminima.Aregionthatissurroundedbypointsofhigher“altitude”;Suchthatthepointsintheregionformaconnectedcomponent;Andinwhichallthepointsintheconnectedcomponenthavethesamegray-levelvalue.internalmarkersexternalmarkers10910.6TheUseofMotioninSegmentationMotionisapowerfulcueusedbyhumansandmanyanimalstoextractobjectsofinterestfromabackgroundofirrelevantdetail.Motionarisesfromarelativedisplacementbetweenthesensingsystemandthescenebeingviewed.RoboticapplicationsAutonomousnavigation