同济大学摄影测量学课件

1,Photogrammetry摄影测量学,关泽群,同济大学测量与国土信息工程系,Chapter5DigitalImageandFeatureExtraction,Contents,5.1ImageSamplingandResampling5.2PointFeatureExtraction5.3LineFeatureExtraction,4,DIGITALIMAGERY,Adigitalimageisaregulararrayofpixels,orpictureelements,andisdescribedintermsofitsgeometryanditsradiometry.数字影像是一个灰度矩阵g,矩阵中每个元素gi,j,是一个灰度值,对应着光学影像或实体的一个微小区域,称为像元素或像元或像素（Pixel=Pictureelement）。各像元素的灰度值gi,j,代表其影像经采样与量化了的“灰度级”,数字影像或数字化影像,6,ToObtainDigitalImage,Eachpixelofadigitalimageisadirectorindirectsampleofthecontinuousincidentlightdistribution.Adigitalsensorsamplesincidentlightdirectly.(可以直接装在空间飞行器中的扫描式传感器、数码相机、以及加有特殊装置的工业摄像机直接获得)Anexampleofindirectsamplingisscanningapieceoffilmandconvertingitintoadigitalimage.(也可利用影像数字化器（如扫描仪等）对摄取的像片经过采样、量化获得地形测图中航测通常使用),7,Pixelsmaybearrangedinanyregularpattern,butinpracticemostsamplinggridsaresquareorrectangular(一般为矩形格网).Hexagonalgrids(六角形格网)havesometheoreticaladvantagesbuthaveseldombeenimplemented.Theratiobetweenpixelwidthandpixelheightisknownastheaspectratio（纵横比）;asquarepixelhasanaspectratioofone.,Pixel,IFOVandGSD,8,Digitalimagesareoftendescribedintermsoftheirpixelsize,butcanalsobespecifiedintermsoftheinstantaneousfieldofview(IFOV)瞬时视场,whichistheangledeterminedbythepixelsizeandthefocallength.AsshowninFig.,asthefocallengthdecreasesorthepixelsizeincreases,theIFOVincreases.,Figure.Instantaneousfieldofview(IFOV)andgroundsampledistance(GSD),AlargerIFOVmeansthatonepixelcoversalargerportionofthesceneor,equivalently,thattheimagewillhavelowerspatialresolution.,9,Figure.Instantaneousfieldofview(IFOV)andgroundsampledistance(GSD),Instantaneousfieldofview(IFOV)瞬时视场groundsampledistance(GSD)地面采样间隔(距离),Anothermeasurerelatedtopixelsizeisthegroundsampledistance(GSD),whichistheprojectionofthepixelsizeontothegroundplane(Fig.).,Pixel,IFOVandGSD,10,Thisisoftenusederroneouslyasasynonymforresolution.Infact,theresolutionofadigitalimageisdeterminedbyboththesensorgeometryandbyfactorsexternaltothesensor,suchasatmosphericconditions,platformmotion,etc.TheactualresolutionmaybeasgoodasindicatedbytheGSD,butinpracticalapplicationsitisoftenlower.,Pixel,IFOVandGSD,11,IFOVandGSDCalculation,Asatelliteimagingsystemhaspixelsthatare0.015ramsquareandafocallengthof1000mm.Whatis(theIFOV?WhatistheGSDatnadir,assuminganorbitalaltitudeof650km?,SOLUTIONTheIFOVis,andtheGSDisGSD=IFOV(650,000)=9.75m,1.DigitalImageSampling,13,Digitalimagessampleacontinuousanaloginputimageatdiscretepointsandassignadiscreteintensityvalueateachpoint.Howcanwedeterminewhetheralltheinformationintheoriginalimageispresentinitssampleddigitalformor,equivalently,whatspatialsamplingrateisrequiredtofullycapturetheinput?,14,Theanswertothisquestionreliesonsamplingtheory.Samplingtheorystatesthataband-limitedsignalwithahighestfrequencyofcanbeexactlyreconstructedwithasamplingrateof2.（当采样频率大于信号中最高频率的2倍时，采样之后的数字信号完整地保留了原始信号中的信息）Intermsofwavelength,asignalwithaminimumwavelengthofmustbesampledwithasamplespacingofnogreaterthan/2.ThetheoreticalminimumsamplingraterequiredisknownastheNyquistrate.,15,Whathappensifwedontsampleatahighenoughrate?Thehigher-frequencycomponentsofthesignal,whichcorrespondtothefinedetailsintheimage,areincorrectlyinterpretedaslower-frequencycomponents.Theseerroneouscomponentsconfusetheoverallsignalreconstruction,aphenomenonknownasaliasing（混淆）.,16,Fordigitalimages,thelensandthepixelbothactasapertures,limitingthemaximumdetailvisibleintheimage.Formostaerialcameras,thelens(andfilm,ifascannerisused)usuallyhavemuchhigherresolutionthanthecommonlyusedpixelsizescanrecord,sothepixelsizedeterminestheeffectiveaperture.,DigitalImageSampling,Sampling对实际连续函数模型离散化的量测过程Samplingpoint被量测的“点”是小的区域-像素Samplinginterval矩形的长与宽通常称为像素的大小,Samplingtheorem(One-dimensionalimage）,Band-limitedfunction,SamplingProcessing,Samplinginterval-x,fliscutofffrequency(Nyquistrate),当采样间隔能使在函数g(x)中存在的最高频率中每周期取有两个样本时，则根据采样数据可以完全恢复原函数g(x),DigitalImageExpression,Frequencydomain,Fouriertransform,2.DigitalImageResampling,23,DIGITALIMAGERESAMPLING,Weoftenneedtoresampleadigitalimageintoadifferentgeometry,forexample,tocreateanorthophoto.Anytypeofgeometrictransformation,includingsimilarity,affine,projective,polynomial,etc.,canbeappliedtoadigitalimageinexactlythesamewayastoanytwo-dimensionalsetofcoordinates.,Imagematching,Referenceimages(主图像)Matchingimage(辅图像),25,However,oncewehavecalculatedthenewimagecoordinates,whichareoftenfractional,wemustdecidewhichgrayvaluetoassigntothem.Anewvaluemustbeinterpolatedfromthepixelsneighboringthecoordinates;anumberofmathematicaltechniquesareavailable.,Imageresamplingtheorem,当欲知不位于矩阵（采样）点上的原始函数g(x,y)的数值时就需进行内插，此时称为重采样（resampling）,Non-samplingpoint,Imageresamplingmethod,Digitalimage,Sincsamplingfunction,28,Threecommonresamplingmethods:,Bi-linearinterpolationBi-cubicconvolution(costofmorecomputation.)Nearestneighborinterpolation,Bi-linearinterpolation,Convolutionkernelisatrianglefunction,11,12,21,22,p,Y,X,y1,y2,a,b,y,1-y,x,1-x,x2,x1,Bi-linearinterpolation,Bi-linearinterpolationcomputation,Hadamardproduct,Weightedaverage,Bi-linearinterpolationcomputation,Bi-cubicconvolution,Convolutionkernelisacubicfunction,p,11,12,13,14,21,31,41,22,23,24,32,33,34,42,43,44,Y,x,y,x,Bi-cubicconvolutiondemo,Bi-cubicconvolutioncomputation,Bi-cubicconvolutioncomputation,Nearestneighborinterpolation,直接取与P(x,y)点位置最近像元N的灰质值为核点的灰度作为采样值,Acomparisonofthreeresamplingmethods,最邻近像元法最简单，计算速度快且能不破坏原始影像的灰度信息。但其几何精度较差，。前两种方法几何精度较好，但计算时间较长，特别是双三次卷积法较费时，在一般值况下用双线性插值法较宜。,3.LocatingConjugateEpipolarlinesandImageResampling,AccordingtotheprinciplesofanalyticalphotogrammetryAccordingtothecoplanaritycondition,Twomethodsforlocatingconjugateepipolarlines,Photographicbaseline,Coordinatetransformation,Accordingtotheprinciplesofanalyticalphotogrammetry,Tiltimage,Horizontalimage,v=某常数即表示某一核线,C=v,在“水平”影像上获取核线影像,u=kSamplinginterval,LocatingepipolarlinesinHorizontalimage,同名核线的v坐标值相等,Locatingconjugatepoints,核线的重排列（重采样）,是否是采样点？,Horizontalimage,Tiltimage,Epipolarlinerearrangement(resampling),Linearinterpolationdemo,Linearinterpolation,Epipolarline,y1,k,Thenearestpixelmethod,n1tgK,Epipolarlinerearrangement(resampling),对每条核线而言K是常数,Linearinterpolation,AccordingtotheprinciplesofanalyticalphotogrammetryAccordingtothecoplanaritycondition,Twomethodsforlocatingconjugateepipolarlines,MathematicalConceptsinPhotogrammetry,49,交汇确定地面点坐标,INTERSECTION(SpaceIntersection空间前方交会),Intersectionreferstothedeterminationofapointspositioninobjectspacebyintersectingtheimageraysfromtwoormoreimages.,50,TheCoplanaritygeometry,Figureillustratesapairofoverlappingframephotographsandapairofconjugateimagepoints.,Theepipolargeometry,C,C,x,xandXarecoplanar,A,S1,S2,l1,a1,a2,l2,Conjugateepipolarlines,anepipolarplane=planecontainingbaseline(1-Dfamily),anepipolarline=intersectionofepipolarplanewithimage(alwayscomeincorrespondingpairs),Conjugatepointsisatconjugateepipolarlines,Theepipolargeometry,s1,s2,p,Conjugateepipolarlinesinthetiltimages,x,y,z,u,q,v,w,p,q,Locatingleftepipolarline,Theequationofleftepipolarline,Theequationofrightepipolarline,Locatingrightepipolarline,Parameterdetermination,Relativelyorienteddouble-image,Contents,5.1ImageSamplingandResampling5.2PointFeatureExtraction5.3LineFeatureExtraction,PointFeatureExtraction,Pointfeaturessuchasdefinitepoints,cornerpointshavehighaccuracy.Theoperatorforpointfeatureextractionisusuallycalledtheinterestoperator.,Pointfeaturewithgreyvaluedifferences,Moravecoperator,Moravec于1977年提出利用灰度方差提取点特征的算子,r,c,（1）GettheinterestvalueIV,（2）IfthevalueMislargerthanathresholdgiven,thenthepointistakenasacandidatepoint,Moravecoperatortakeawindowof5x5pixelwiththepixelasthecentreandthequadraticsumsofgreyvaluedifferencesalongthefourmajordirections.,确定窗口大小,（3）Featurepointistakenfromtheextremumpointofcandidatepoint,Forstneroperator,计算各像素的Roberts梯度和像素（c，r）为中心的一个窗口的灰度协方差矩阵，在影像中寻找具有尽可能小而接近圆的误差椭圆的点作为特征点。,（l）CalculateRobertsgradientofpixels,Forstneroperatorsteps,（2）Obtainthecovariancematrixfordisplacements,（3）Gettheinterestvalueqandw,DetN代表矩阵N之行列式,trN代表矩阵N之迹,(4）Obtaincandidatepoint,当同时，该像元为待选点,（5）Featurepointistakenfromtheextremumpointofcandidatepoint,即在一个适当窗口中选择最大的待选点,Contents,5.1ImageSamplingandResampling5.2PointFeatureExtraction5.3LineFeatureExtraction,LineFeatureExtraction,线特征是指影像的“边缘”与“线”,“边缘”可定义为影像局部区域特征不相同的那些区域间的分界线，而“线”则可以认为是具有很小宽度的其中间区域具有相同的影像特征的边缘对,Differenceoperator、Laplaceoperator、LOGoperatoretc.areusualmethods,LinefeatureforHouse,Linefeatureforroad,Linefeaturewithgreyvaluedifferences,一、Differenceoperator,1Gradientoperator,Differenceoperator,对于一给定的阈值T，当时，则认为像素（i，j）是边缘上的点。,近似,Robertsgradientoperator,Directionaldifferenceoperator,Directionoflineandedge,Sobeloperator,考察它上下、左右邻点灰度的加权差。与之接近的邻点的权大：,PrewittoperatorandSobeloperator,加大模扳抑制噪声,Prewittoperator,Sobeloperator,Secondorderdifferenceoperator,Directionalsecondorderdifferenceoperator,Laplaceoperator,ConvolutionkernelMask,取其符号变化的点，即通过零的点为边缘点，因此通常也称其为零交叉（zero-Crossing）点,Laplaceoperator,Laplacianofgaussianoperator（LOG）,首先用高斯函数先进行低通滤波，然后利用拉普拉斯算子进行高通滤波并提取零交叉点，,Gaussianfunction,Low-passfilters,Edgedetection,LOG算子以为卷积核，对原灰度函数进行卷积运算后提取零交叉点为边缘,Laplacianofgaussianoperator（LOG）,Sobel,Makecomparisonbetweenedg