圖像處理與控制系統(tǒng)課件

圖像處理與控制系統(tǒng)授課教師：祝海江電子郵箱：辦公地點(diǎn)：科技樓502室簡介2004年6月畢業(yè)于中國科學(xué)院自動化研究所模式識別國家重點(diǎn)實(shí)驗(yàn)室模式識別與智能系統(tǒng)專業(yè)，獲得工學(xué)博士學(xué)位；同年7月進(jìn)入北京化工大學(xué)信息科學(xué)與技術(shù)學(xué)院工作；2006.6-2007.6在日本巖手大學(xué)工學(xué)部任客座研究員；主要從事機(jī)器視覺、圖像處理、信號處理與檢測等方向的教學(xué)與科研工作。承擔(dān)國家自然科學(xué)基金、教育部留學(xué)回國人員科研啟動基金、中央高?；究蒲袠I(yè)務(wù)費(fèi)等國家和省部級課題?？萍紭?02研究室常規(guī)計(jì)算機(jī)控制系統(tǒng)u計(jì)算機(jī)保持器廣義對象測量變送器e(kT)u(kT)y單回路計(jì)算機(jī)控制系統(tǒng)示意圖ym采樣器A/DD/A計(jì)算機(jī)系統(tǒng)設(shè)定值r基于圖像處理的控制系統(tǒng)系統(tǒng)框圖：控制平臺/控制策略執(zhí)行機(jī)構(gòu)被控對象攝像頭圖像處理模塊數(shù)模轉(zhuǎn)換數(shù)字圖像處理概述圖像獲取圖像增強(qiáng)與濾波圖像分割圖像特征提取本田公司最新開發(fā)的新型機(jī)器人“阿西莫”

世界第一個機(jī)器人藝人“Ever-2Muse”ThegoalofDigitalImageProcessingistoenabletheprocessofrecognition.TheultimategoalofDIPistoenableacomputingmachinetorecognizeatleastgeometricalsizes,shapesandotherobjectsasinhumanvisionDIPisabranchofArtificialIntelligence(AI).AnattempttoemulatehumanvisioniscalledweakAI.ToexactlyproduceahumanreplicaelectronicallyiscalledstrongAI.什么是數(shù)字圖像處理（DigitalImageProcessing）?原始圖像噪聲圖像低通濾波后的圖像原始圖像直方圖增強(qiáng)圖像邊緣檢測（Robertoperator）邊緣檢測（Sobeloperator)數(shù)字圖像處理的應(yīng)用1.InFlexibleManufacturingSystems:ProductInspection（產(chǎn)品檢測）Assembly（裝配）VehicleGuidance（車輛導(dǎo)航）2.InBiomedicalEngineering:AnalyzingChromosome（染色體分析）Tomography（斷層攝影術(shù)）X-rayAnalysis（X射線分析）醫(yī)療產(chǎn)品檢測3.InMilitaryAreas:BombDisposal（炸彈處理）Infra-redNightVision（紅外線夜視）RadarImageProcessing（雷達(dá)圖像處理）TargetIdentification（目標(biāo)識別）4.InCivilianAreas:Telecommunications（可視化通訊）Firefighting（消防）Fingerprintdetection(指紋識別)IntelligentVehicleHighwaySystem（智能交通系統(tǒng)）FingerprintDetectionSystem5.InCommercialAreas:BarCodeReader（條形碼閱讀器）TextReader（文本閱讀器）Multimedia（多媒體）6.InScientificExperiments:FingerprintDetection（指紋識別）SpaceExploration（太空探索）GeographicStudies（地理學(xué)）Archaeology（考古學(xué)）Physics（物理）簡要?dú)v史回顧1920圖像在倫敦與紐約之間經(jīng)由海底電纜傳輸1921照相復(fù)制技術(shù)產(chǎn)生1929圖像亮度級別從5增加到15，圖像復(fù)制技術(shù)改進(jìn)1964計(jì)算機(jī)首次應(yīng)用到處理圖像中JetPropulsionLab(JPL)Now數(shù)字圖像處理及模式識別在許多領(lǐng)域廣泛應(yīng)用數(shù)字圖像處理系統(tǒng)回顧1.ImageCapturingSystem（圖像獲取系統(tǒng)）2.ImageEnhancementSystem（圖像增強(qiáng)系統(tǒng)）3.FeatureExtractionSystem（特征提取系統(tǒng)）4.FeatureRepresentationandDescriptionSystem（特征表示與描述系統(tǒng)）5.ObjectClassificationSystem（目標(biāo)分類系統(tǒng)）圖像獲取400800BlueGreenRedInfrared紅外線Ultraviolet紫外線VisiblelightX-raysWavelength(nanometers)成像方式Radiance光輝Irradiance發(fā)光點(diǎn)光源相機(jī)目標(biāo)傳感器NZOpticalaxisSurfacenormalPixelPixelPixelDigitalimage196Graylevel92圖像坐標(biāo)系統(tǒng)

crI[0,0]I[M-1,0]I[M-1,N-1]rasteroriented

光柵導(dǎo)向usesrowandcolumncoordinatesstartingat[0,0]fromthetopleftxyF[0,0]F[M-1,N-1]Cartesian笛卡爾coordinateframewith[0,0]atthelowerleftxy[0,0][W/2,H/2][-W/2,-H/2]Cartesiancoordinateframewith[0,0]attheimagecenterRelationshipofpixelcenterpoint[x,y]toareaelementsampledinarrayelementI[i,j][x0,y0][x0+ix,y0+jy]F[i,j]F[i+1,j]圖像類型1:模擬圖像

Ananalogimageisa2DimageF(x,y)which -hasinfinite

precisioninspatialparameters

xandy,and -infinite

precisioninintensityateachspatialpoint(x,y).yxf(xi,yi)=Realnumberxi=Realnumberyi=Realnumber2:數(shù)字圖像

Adigitalimageisa2D

imageI[r,c]representedbyadiscrete2Darrayofintensitysamples,eachofwhichisrepresentedusingalimitedprecision.Itiscommontorecordintensityasan8?bit(1?byte)numberwhichallowsvaluesof0to255.256differentlevelsisusuallyalltheprecisionavailable-fromthesensorand-alsoisusuallyenoughtosatisfytheconsumer.

yxf(xi,yi)=Integerxi=Integeryi=Integer3:Apicturefunction

isamathematicalrepresentation

f(x,y)ofapictureasafunctionoftwospatialvariablesxandy.

xandyarerealvaluesdefiningpointsofthepicture.

f(x,y)isusuallyalsoarealvaluedefiningtheintensityofthepictureatpoint(x,y).

4:單色灰度圖像Agray?scaleimage

isamonochromedigitalimagef(x,y)withone

intensityvalue

perpixel.f(x,y)=0f(x,y)=89f(x,y)=2185:彩色圖像Amultispectralimage

isa2DimageM[x,y],whichhasavectorofvaluesateachspatialpointorpixel.Iftheimageisactuallyacolorimage,thenthevectorhas3elements.I=0.11R+0.59G+0.3B6:二值圖像Abinaryimageisadigitalimagewithallpixelvalues0or1.圖BA像xyf(x,y)=1f(x,y)=07:分類圖像Alabeledimage

isadigitalimageL[r,c]whosepixelvaluesaresymbols.Thesymbolvalueofapixeldenotestheoutcomeofsomedecisionmadeforthatpixel.OriginalimageLabeledimageBoundariesoftheextractedfaceregionOriginalimage(tiger)Labeledimage1:標(biāo)稱分辨度

ThenominalresolutionofaCCDsensoristhesizeofthesceneelementthatimagestoasinglepixelontheimageplane.Eachpixelofadigitalimagerepresentsasampleofsomeelementalregionoftherealimage.圖像度量與量化（數(shù)字化）pixel3DSceneLensImagePlaneSizeofsceneelementpixelIfthepixel

isprojected

fromtheimageplane

backouttothesourcematerialinthescene,thenthesizeofthatsceneelementisthenominalresolution標(biāo)稱分辨度

ofthesensor.pixel3DSceneLensImagePlaneForexample,ifa10inchsquaresheetofpaperisimagedtoforma500500digitalimage,thenthenominalresolutionofthesensoris0.02inches(10/500=0.02).1010inch25005002:分辨率Thetermresolution

referstotheprecisionofthesensorinmakingmeasurements,butisformallydefinedindifferentways.Ifdefinedinrealworldterms,itmayjustbethenominalresolution,asin“theresolutionofthisscannerisonemeterontheground”O(jiān)ritmaybeinthenumberoflinepairspermillimeterthatcanberesolvedordistinguishedinthesensedimage.3:視野Thefieldofviewofasensor(FOV)isthesizeofthescenethatitcansense,forexample10inchesby10inches.(a)Digitalimagewith127rowsof176columns;(b)(6388)createdbyaveragingeach22neighborhoodof(a)andreplicatingtheaveragetoproducea22averageblock;(c)(3144)createdinsamemannerfrom(b);

and(d)(1522)createdinsamemannerfrom(c).Effectivenominalresolutionsare(127176),(6388),

(3144),and(1522)respectively.AquantizerisanAnalog-to-Digitaldevicewhichconvertsacontinuous

inputsignalutooneofasetofdiscretelevelscalledreconstructionlevels

rk.Supposetheuliesintherange:umin

u

umaxandwewishtoquantizeuintoL

levels.Thenwedefine

L+1

transitionlevelstk:

t0=umin<t1<……<tL-1<tL=umaxThequantizationstepinvolvesmappingutoitsquantizedvalue,u*,usingtherule: Define{tk,k=0,…,L}asasetofincreasingtransitionordecisionlevelswitht0andtLastheminimumandmaximumvalues,respectively,ofu.ImageQuantization圖像量化（數(shù)字化）Agraphicalrepresentation(staircasemap)ofthequantizationfunctionisasbelow:Usually,L=2B

(B-bitrepresentation).D=tL–t0

=umax-uminiscalledthedynamicrange.ErrorofquantizationclearlydependsonLandD,aswellasonthechoiceofreconstructionlevelsandtransitionlevels.uu*Quantizerrktkuu*rLr0t0tL圖像量化中的一些問題1010arrayofblack(brightness0)andwhite(brightness8)tiles;(b)

Intensitiesrecordedina55imageofpreciselythebrightnessfieldattheabove,whereeachpixelsensestheaverage

brightnessofa22

neighborhoodoftiles;(0+0+0+8)/4=2(0+0+0+8)/4=2(d)Intensitiesrecordedfromtheshiftedcamerainthesamemannerasin(b).(c)Imagesensedbyshifted

cameraonetiledownandonetiletotheright.0000000000000080880(8+0+0+0)/4=2Notethatthequantizedbrightnessvaluesdepend

onboththeactualpixelsizeandpositionrelativetothebrightnessfield;Interpretationoftheactualscenefeatureswillbeproblematicwitheitherimage(b)or(d).(b)(d)Notethatthequantizedbrightnessvaluesdependonboththeactualpixelsizeandpositionrelativetothebrightnessfield.Differentdigitalimages數(shù)字化效果ColourimageGray-scaleimage512X256Gray-scaleimage256X128Theresolutiondependsonthespatialquantization(thenumberofsamplesperinch)Gray-scaleimage64X32Gray-scaleimage32X16Gray-scaleimage128X64Theresolutiondependsonthespatialquantization(thenumberofsamplesperinch)8-Bitimage(256levels)7-Bitimage(128levels)Thequalityoftheimagedependsontheintensityquantization(thenumberofgraylevels)6-Bit(64levels)5-Bit(32levels)4-Bit(16levels)3-Bit(8levels)2-Bitimage(4levels)1-Bitimage(2levels)Thequalityoftheimagedependsontheintensityquantization(thenumberofgraylevels)數(shù)字化效果1.Run?CodedBinaryImages

Run?codingisanefficientcodingschemeforbinaryorlabeledimages:notonlydoesitreducememoryspace,butitcanalsospeedupimageoperations.Example:

ImageRowr

1111111111100000

Run?codeA

8(0)5(1)12(0)3(1)7(0)9(1)5(0)Run?codingisoftenusedforcompressionwithinstandard.圖像格式2.PGM:PortableGrayMapP2#samplesmallpicture8rowsof16columns,maxgrayvalueof192#makinganimageoftheword"Hi".

168192PrintedpictureImagemadeusingalossycompressionalgorithmOneofthesimplestforstoringandexchangingimagedataisthePBMorPortableBitMapfamilyofformats(PBM/PGM,PPNI).

TheimageheaderandpixelinformationareencodedinASCII.3.GIFImageTheGraphicsInterchangeFormat(GIF)originatedfromCompuServe,Inc.IthasbeenusedtoencodeahugenumberofimagesontheWorldWideWeborincurrentdatabases.GIFfilesarerelativelyeasytoworkwith,butcannotbeusedforhigh?precisioncolor,sinceonly8?bitsareusedtoencodecolor.4.TIFFImageTIFForTIFis

verygeneralandverycomplex.Itisusedonallpopularplatformsandisoftentheformatusedbyscanners.Itsupportsmultipleimageswith1to24bitsofcolor

perpixel.TIFForTIFis

availableforeitherlossyorlosslesscompression.5.JPEGFormatforStillPhotosJPEG(JFIF/JFI/JPG)isamorerecentstandardfromtheJointPhotographicExpertsGroup.Themajorpurposeistoprovideforpracticalcompressionofhigh?qualitycolorstillimages.Animagecanhaveupto64K64Kpixelsof24bitseach.6.PostScriptThefamilyofformatsBDF/PDL/EPSstoreimagedatausingprintableASCIIcharactersandareoftenusedwithX11graphicsdisplaysandprinters.PDLisapagedescriptionlanguageEPSisencapsulatedpostscript(originallyfromAdobe),whichiscommonlyusedtocontaingraphicsorimagestobeinsertedintoalargerdocument.7.MPEGFormatforVideoMPEG(MPG/MPEG?1/MPEG?2)isastream?orientedencodingschemeforvideo,audio,text,andgraphics.MPEGstandsforMotionPictureExpertsGroup,aninternationalgroupofrepresentativesfromindustryandgovernments.MPEG?1isprimarilydesignedformultimediasystemsandprovidesforadatarateof0.25Mbitspersecondofcompressedaudioand1.25Mbitsofcompressedvideo.Theseratesaresuitableformultimediaforpopularpersonalcomputers,butaretoolowforhigh?qualityTV.MPEG?2standardprovidesforupto15MbitsperseconddataratestohandlehighdefinitionTVrates.Thecompressionschemetakesadvantageofbothspatialredundancy,asusedinJPEG,andtemporalredundancyandgenerallyprovidesausefulcompressionratioof25to1,with200to1ratiospossible.圖像增強(qiáng)與濾波Animageneedsimprovement

Low?levelfeaturesmustbedetected

圖像增強(qiáng)

例1:圖像中的劃痕被去掉。Scratches例2:亮度增強(qiáng)例3:機(jī)器零件邊緣增強(qiáng)Left

-Originalsensedfingerprint;

Center

-Imageenhancedbydetectionandthinningofridges;

Right

-Identificationofspecialfeaturescalledminutia,whichcanbeusedformatchingtomillionsoffingerprintrepresentationsinadatabase.Example圖像增強(qiáng)操作(1)點(diǎn)操作ContraststretchingNoiseclippingWindowslicingHistogrammodeling(2)掩膜操作NoisesmoothingMedianfilteringSharpingmaskingZooming對比度增強(qiáng)(a)Original(b)Enhanced(b)Enhanced(a)Original(a)Original(b)EnhancedClipingandthresholdingClipingandthresholding反色反色反色直方圖增強(qiáng)

Histogramafterequalization

Originalimage

OriginalhistogramModifiedimage

Originalimage

OriginalhistogramModifiedimage

Histogramafterequalization

(a)Inputimage

(b)Processedimage(c)Inputimage

(d)Processedimage(e)Inputimage

(f)Processedimage

圖像濾波

Often,animageiscomposedofsomeunderlyingidealstructure,whichwewanttodetectanddescribe,togetherwithsomerandom

noiseorartifact,whichwewouldliketoremove.ImagecontainsbothGaussiannoiseandbrightringartifactsImagewithrandomnoiseScratchesImagecontainsartifacts方框?yàn)V波器（BoxFilter）

Definition

:Smoothinganimagebyequally

weightingarectangularneighborhoodofpixelsiscalledusingaboxfilter.

Output-Image[r,c]= Averageofsomeneighborhoodof Input-Image[r,c]

Example:55NeighborhoodFilter-averages25pixelvaluesina55neighborhoodoftheinputimagepixelinordertocreateasmoothedoutputimage.Example80912308081331808030820803040340405050204000+03+08+12+03+05+40+30+09+13+40+40+80+80+00+50+30+80+80+00+20+40+20+30+1825=3080912308081331808030820803040340405050204030鄰閾平均法OriginalImageNoisyImageNAF(3-by-3)NAF(5-by-5)NAF(7-by-7)UsefornoisesmoothingLPfilteringandsubsamplingofimages.AssumingwhitenoiseηwithzeromeanandvarianceThenthespatialaverage:assumingequalweightwhereisthespatialaverageof.Notethathaszeromeanandi.e.NoisepowerisreducedbyafactorofRemark:Neighborhoodaveragingintroducesadistortionintheformofblurring.

(a)Original(b)noisy(c)3×3filter(d)5×5filterSpatialaveragingfiltersforsmoothingimagescontainingGaussiannoise.

Definition

:WhenaGaussianfilterisused,pixel[x,y]isweightedaccordingtox高斯濾波（GaussianFilter）disthedistanceoftheneighborhoodpixel[x,y]fromthecenterpixel[xc,yc]oftheoutputimagewherethefilterisbeingapplied.[xc]g(x)[x]d[x] Ratherthanweightallinputpixelsequally,itisbetter

toreducetheweight

oftheinputpixelswithincreasingdistancefromthecenterpixelI[xc,yc].TheGaussianfilterdoesthisandisperhapsthemostcommonlyusedofallfilters.[xc]xg(x)高斯函數(shù) One-DimensionalGaussianFunction Two-DimensionalGaussianFunctionExample809123080813318080308208030403404050502040001+031+081+121+031+051

+402+302

+092+131+401+402+803+802+001+501+302+802+802+001+201+401+201+301+181

25=5280912308081331808030820803040340405050204052Examples

NoisyimageIdealimagePixelvaluesinrow100ofthenoisyimagePixelvaluesinrow100ofthesmoothedimageNoiseaveragedusinga55neighborhoodExamples

NoisyimageM=32M=16M=8M=2M=128圖像分割1.基于掩膜窗口的分割I(lǐng)magepointsofhighcontrastcanbedetectedbycomputingintensitydifferencesinlocalimageregions.HighcontrastHighcontrastTypically,suchpointsformtheborder(oredge)betweendifferentobjectsorsceneparts.Neighborhood

templatesormaskscanbeused.Westartbyusingone?dimensional(1D)signals.The1Dsignalscouldjustberowsorcolumnsofa2Dimage.(a)(b)BorderDifferencing2DImages(DetectingEdgesof2DImages)

Themaximumchangeofthecontrastinthe2Dpicturefunctionf(x,y)

occursalongthedirectionofthegradient

梯度

ofthefunction.(Edge)HighcontrastThedirectionofthe

gradient

梯度Mathematicformulaofthegradient:

Gradientmagnitudeor

GradientdirectionfxfyfLower/HigherintensitiesHigher/Lowerintensitiesfxfyf三種掩膜窗口:Sobelmasks210-1-2-1100Mx=0-12-10110-2My=110-1-1-11000-11-10110-1Mx=My=PrewittmasksMx=My=Robertmasks10-1-11000OriginalImage-LenaEnhancedLenabyHistogramEuqalizationEdgemapbyRobertoperatorEdgemapbySobeloperatorStep-1.Compute:MaskMx

isoverlaidonimageneighborhoodN8[x,y]

sothateachintensityNij

canbemultipliedbyweightMij;Finallyalltheseproductsaresummed.Prewittmasks644215356612143865fxfyfN8[x,y]110-1-1-1100Mx=Step-2.Compute:MaskMy

isoverlaidonimageneighborhoodN8[x,y]

sothateachintensityNij

canbemultipliedbyweightMij;Finallyalltheseproductsaresummed.644215356612143865fxfyfN8[x,y]0-11-10110-1My=Step-3.Compute:

Gradientmagnitude

Gradientdirection110-1-1-1100Mx=0-11-10110-1My=LowerintensitiesHigherintensities644215356612143865fxfyfN8[x,y]ExampleImageofJudithPrewittGradientimage

showingresultusingthePrewitt33operator(a)(b)Sobelmasks:theSobeloperatorrepresentsmany,butnotall,oftheimageedges.210-1-2-1100Mx=0-12-10110-2My= (a)Imageofnoisysquaredandrings,(b)Codingofgradientdirectioncomputedby33Sobeloperator.(a)(b)ExampleAninputimage(a)issmoothedusingGaussianfiltersofsize(b)=4,and(c)=1

beforeperformingedgedetection.Moredetailandmorenoiseisshownforthesmallerfilter.(b)(c)(a)=4=1Example: (a)ImageofthegreatarchinSt.Louis; (b)resultsofCannyoperatorwith=1; (c)resultsofCannyoperatorwith=4;(a)(b)(c)ExamplesImageofMao’sMemorial.ResultofapplyingCannyoperatorwith=1.Resultof=2.

Someobjectsaredetectedverywell,soaresomeshadows.(a)(b)(c)DifferentHistograms2.基于閾值的分割Tofindthethreshold,Letthehistogrambep(z)Find2localmaximaonp(z)thatareatleastsomeminimumdistanceapart;z1,z2sayFindz3betweenz1andz2atwhichp(z3)ismin.Checkthatp(z3)/[min(p(z1),p(z2))]tobesmallChoosez3tobethethresholdIfprobabilitydistributionofthe2regionisknown,thenwecanuseBayesiandecisiontheorytofindthethreshold. Letwi=pixelbelongstoregionI ThenchoosezsuchthatP(w1︱z)=P(w2︱z) ApplyBayesrule:

i.e.Selectzsuchthatp(z︱w2)P(w2)=p(z︱w1)P(w1)HistogramrepresentingobjectondarkbackgroundOriginalImage-LenaBinaryLenabyOtsuLenaHistogramThresholdat50Thresholdat165Thresholdat80圖像特征提取漢字識別的困難

LargeinDataSetComplexinStructure1.ALargeSetofCharacters:English: 26lettersRussian: 32lettersGreek: 24lettersChinese: 3,000-7,000charactersareoftenusedStandardinP.O.China:6,763Thefirstlevel:3,755,Thesecondlevel:3,0087,000-10,000Chrs.arecollectedinsmalldictionaries70,000ChelargestcontemporarydictionaryInthelonghistoryofChina,thetotalnumberofChinesecharactersbecamelargerandlargerCellularFeatureExtractionPreprocessingNeuralTreeClassification008109212597191832302Input:Chinesecharacter“tree”......Features(Matrix)什么是特征?在模式識別中，特征指的是把兩類或多類目標(biāo)區(qū)別開來的一種描述方法。

Featuresarefunctionsofthemeasurementsperformedonaclassofobjectsthatenablethatclasstobedistinguishedfromotherclassesinthesamegeneralcategory.ExampleForpolygonsthenumberofverticesthenumberofsidesThelengthsofsidesthevaluesoftheanglesverticesideqPurposeoffeatureselection:

reducedimensionalityofrepresentation

minimizemeasurementextractioncosts

assessthepotentialperformanceofthepatternrecognitionsystemimprovesystem'sperformanceThreeingredientsinfeatureselection/extractionfeatureevaluationcriteriadimensionalityofthefeaturespaceoptimizationprocedure如何選擇特征?(1)Aformal,number-crunchingapproach:forstatisticalPR.(2)Designfeatureswithsemanticcontents,someintuitivewaycorrespondtohumanperceptionoftheobjects:forstructuralPRExamples:(1)ProjectionFourierTransformFeaturesof750123467(2)

00555S00555ABHKVT={0,5}VN={S,A,B,H,K}P:S0A,A0B,B5H,H5K,K5

Featuresof7DensityFeaturesApatternimageisdividedintoNNsub-images

N=4N=4WWi(CellularFeature)N=4N=4Calculatethe

densityofeachsub-image

Howmanyimagepixelsineachsub-imageProjectionsInpatternrecognition,thetermprojectionusuallyreferstomappinganimageintoawaveform

Thevaluesofthewaveformarethesumsoftheimagepointsalong

particular

directionsAccordingtodirections,3projectionshavebeendeveloped:

HorizontalandverticalprojectionRingprojectionCentralprojectionProjectionsFormulaoftheprojection:istheprojectiondirection,Risareaofimage[z]isafunctionsuchthatxytProjectionsofsomeparticulardirections=0°,45°,90°and135°:tf(t)tf(t)Horizontalandvertical

Projections2-Dobjectisconvertedintotwo1-Dsignals

tf(t)tf(t)Orthogonaltransform(Fouriertransform)isusedtoobtainnumericalfeaturesFeatureVectorsVa

=

{va1,va2,...,van,}Vb

=

{vb1,vb2,...,vbn,}Vc

=

{vc1,vc2,...,vcn,}………………..Vz

=

{vz1,vz2,...,vzn,}Theprojectionisrotationsensitive779881047riCenterofgravityrk4911p(r)rp(ri)ri0rkRing-ProjectionAlgorithmThe1-DpatternobtainedfromtheRing-ProjectionalgorithmisinvarianttorotationsExtractionofrotation-invariantfeatures Ring-projection

Cumulativeangularfunction- Fourierdescriptor(CAF-FD) MomentInvariantCumulativeAngularFunction-

FourierDescriptors

(CAF-FD)Cumulativeangularfunction-Fourierdescriptor(CAF-FD)canproducerotation-invariantfeaturesWhentheobjectisrotatedwithdifferentangles,thefeaturearesameStep-1:Representapatternbyaboundary(closedcurve)Step-2:TracethecurveclockwiseovertheentireboundaryStep-3:Findtheangulardirection(t)ateachkeypointsStep-4:Findcumulativeangularfunction(t)Step-5:NormalizethecumulativeangularfunctionandproduceNCAF*(t)Step-6:ExpandNCAFintoFourierseriesAlgorithmofCAF-FDStep-1:

RepresentapatternbyaboundaryApatternisrepresentedbyaboundaryCumulativeangularfunction-Fourierdescriptor(CAF-FD)requireclosedcurvesAnypattern,thatcanbeapproximatedbyaboundarycurve,canbedescribedbyCAF-FDThecurveistracedclockwiseovertheentireboundaryAlgorithm:

(Boundarytracing)StartingpointThestartingpointofthecurveisarbitrarilychosenStep-2:

TracetheboundaryAlgorithm:(Boun