計(jì)算機(jī)圖形學(xué)cgimage processingCG圖像處理

ComputerComputer視網(wǎng)視網(wǎng)膜成像：上億個感光細(xì)ColorColorSpectralSpectralDistributionofSpectralSpectralDistributionofRGBRGBColorRGBRGBColorRGBRGBColorRGBRGBColorRGBColorRGBColor?=aR+bG+cRGBRGBColorOtherOtherColorHSVHSVColorHSVHSVColorCIECIEXYZColorCIECIECIECIE??????顏色空間派生于CIEXYZ??分量密切匹配人類亮度感知，可以通過修改??和??分量的輸???數(shù)字?jǐn)?shù)字圖光柵顯示光柵顯示設(shè)?逐個將“點(diǎn)”打在屏幕上的相應(yīng)位成像原成像原成像原成像原成像原成像原imageof成像原成像原digitalprojectionontodiscretesensor成像原成像原sampled成像原成像原discretereal-valued數(shù)字圖數(shù)字圖0.6R+0.3G+0.1數(shù)字圖??數(shù)字圖??像素的方陣每個元素稱為像素，存有一種顏彩色灰度圖像的圖像的種???Binaryimages(0orColorimagesindexedcolorfullcolorimages(24bitsperpixel,8-red,8-green,8-blue))AABinaryImage（二值圖像GrayImages（GrayImages（灰度圖像?8bitsperFullColorImagesFullColorImages（全彩圖像?24bitsperpixel,andthethreechannelsRGarethreegrayimages–Eachofthechannelsisencodedby8?32–(R,G,B,顏色分顏色分圖像文件的格?BMP:圖像文件的格?BMP:文件小，能存儲壓縮率JPEG更高壓縮率，支持漸近PSD,data，無壓縮，文????量化與壓Video:Video:Image圖像的連續(xù)數(shù)學(xué)圖像的連續(xù)數(shù)學(xué)模型平面區(qū)域上的向量值函區(qū)域內(nèi)每個點(diǎn)有個顏色?––每種顏色值是紅、綠、藍(lán)三個成分的線性組顏色空間是三維線性0.6R+0.3G+0.1圖像的離散圖像的離散數(shù)學(xué)模型：矩?分辨圖像分辨率:1024x 圖像處圖像處理軟??????Photoshop…ImageImage面向?qū)ο缶?面向?qū)ο缶?抽?對象?接圖像的抽圖像的抽?我們需要哪些信息可以決定一幅圖像寬、每個元素的?像素的矩陣圖像對象的數(shù)圖像對象的數(shù)據(jù)結(jié)????????class{intGetWidth();CColorGetPixelAt(intx,intSetPixelAt(intx,inty,CColor圖像圖像處理（圖像變換??????ReverseR,G,Bchannels–Gray=aR+bG+c–Gray=R*0.299+G*0.587+Add…??ApplicationsApplicationsof從數(shù)從數(shù)學(xué)的角度看圖像處從不同的角度來11、圖像是線性空間的數(shù)據(jù)點(diǎn)顏色：顏色：3D線性空????Example:RGB→Example:RGB→Example1:Example1:Color?使點(diǎn)云位置、形使點(diǎn)云位置、形狀相似（均值和方差變換?Example2:Example2:Problem:Problem:Dimension3D3D→PrincipalComponentPrincipalComponentPrincipalComponent?PCAisthemostcommonlyusedreductionPrincipalComponent?PCAisthemostcommonlyusedreduction(AlsocalledtheKarhunen-LoevePCA---datasamples??1,??2,?,????1Computethemean??Computethe1????????????PrincipalPrincipalComponentPrincipalComponentPrincipalComponentPrincipalPrincipalComponentColor2Gray:PreservingColor2Gray:PreservingNewExample3:Example3:Example4:Example4:Color22、圖像是一個矩AnAnimageisa數(shù)學(xué)工?數(shù)學(xué)工?矩陣分?低秩矩1.Matrix1.MatrixLUdecompositionQRCholeskydecompositionJordanDecompositionSpectraldecompositionSingularvaluedecomposition?????? Decompositionin MatrixFullcolumnLuNotalways Decompositionin MatrixFullcolumnLuNotalwaysQRThisimageisThisimageis600×465ImageCompressionPlotofthePlotofthesingularSingularvaluesofflowersRank-5Rank-1LowRank-5Rank-1LowrankApproximationtoflowersRank-20Rank-30Rank-20Rank-30LowrankApproximationtoflowersRank-50Rank-80Rank-50Rank-80LowrankApproximationtoflowersRank-100Rank-120Rank-100Rank-120LowrankApproximationtoflowersTrueRank-150TrueRank-150LowrankApproximationtoflowers2.Low2.LowRank高維數(shù)據(jù)往往具有低維結(jié)Visualdataexhibitlow-dimensionalstructures高維數(shù)據(jù)往往具有低維結(jié)Visualdataexhibitlow-dimensionalstructuresduetorichlocalregularities,globalsymmetries,repetitivepatterns,orredundantsampling.LowLowRank+Netflix?Netflix?WehavetoconsiderthecorrelationrowsandExample1:ImageLow-rankExample1:ImageLow-rankLow-rankLow-rank33、圖像是一個函圖像函?2D區(qū)域圖像函?2D區(qū)域上的向量值函DiscreteExampleExample1:四邊形域的四邊形域的三角形域的ExampleExample2:ImageExampleExample3:PoissonImage44、圖像是一個GraphGraphCut:Min-CutImageImageasExample:Example:Image55、圖像是一個MRFTextureTexture?TextureTexture?MarkovRandomFieldMarkovRandomField[Shannon,’48]proposedawaytogenerateEnglish-lookingtextusingN-grams:AssumeageneralizedMarkovUsealargetexttocomputeprobabilitydistributionsofeachlettergivenN-1previouslettersStartingfromaseedrepeatedlysamplethisMarkovchaintogeneratenewlettersAlsoworksforwholeSynthesizingOnefinitesampleGeneratedpSynthesizingOnefinitesampleGeneratedpPixel-BasedTexturePixel-BasedTextureStepninPixel-BasedTexturePixel-BasedTextureBuildL-shapedPixel-BasedTextureFindMatchingNeighborhood(s)inPixel-BasedTextureFindMatchingNeighborhood(s)inPixel-BasedTextureSelectBestNeighborhoodPixel-BasedTextureSelectBestNeighborhoodfromallPixel-BasedTextureCopySelectedPixel-BasedTextureCopySelectedPixeltoPixel-BasedTexturePixel-BasedTextureRepeatforallPixelsinthisPixel-BasedTexturePixel-BasedTexture...andallotherOutput從從更多的角度來看圖像Image?Image?ObjectObjectImageImageTourInto?TourInto?HybridHybridExposureexposuretimeExposureexposuretimeoutputexposuretimeinputFlashFlashNo-No-PhotoPhotoN