幾何運(yùn)算

幾何運(yùn)算平移旋轉(zhuǎn)放大縮小反轉(zhuǎn)延展幾何變形實(shí)例平移，旋轉(zhuǎn)三維的平移點(diǎn)擊圖片播放視頻PROBLEMSOLUTIONf(x’,y’)g(x,

y

)NearestneighbourBilinearBicubic,...NearestNeighbour(Zeroorder):Example:Fromwhichinputpixel(1,2,3or4)wouldyougetthegrayleveloftheoutputpixel?12341Interpolationmethods:f(x’,y’)g(x,

y

)Bilinear(First-Order)Interpolation:Graylevelatnon-integercoordinatesfoundbyinterpolatingvaluesoffour(4)neighbouringpixelsusingbilinearfunction.xyg(x,y)f(x’,y’)BilinearvsNearestNeighbour:OriginalNearestNeighbourBilinear幾何運(yùn)算線性內(nèi)插雙線性內(nèi)插雙線性內(nèi)插P118Eq.(2)雙線性方程雙線性內(nèi)插p.118上海交大學(xué)生作品透視F0108201張丹楓作品透視透視透視點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASHE.g.,imagewarping近朱者赤點(diǎn)擊圖片播放視頻變形的臉變形的狗嘴點(diǎn)擊圖片播放視頻幾何運(yùn)算幾何校正用于校正：透視失真枕形失真桶形失真GeometriccalibrationE.g.,barreldistortion(shownbelow);pin-cushiondistortionCorrectbyimagingaknowngridpatternanddesigningawarpingfunctionbasedonknownpatternandimagedpattern.ImagerectificationE.g.,polarscansinultrasound:convertfrom(r,

)coordinatesystemto(x,y)

rImagerectification(cont’d)Originalimage:Afterrectification:幾何校正P118Eq.(19)雙線性空間變換方程f(x’,y’)g(x,

y

)g(x,

y

)Gray-LevelInterpolation(1)ForwardMapping-computenewcoordinates-then“spread”grayleveloverfourneighbouringpixelsusinginterpolation(2)BackwardMappingE.g.,fortranslation-(i,

j)couldingeneralfallbetweennon-integercoordinates-obtaingray-levelatcoordinates(i,

j)usinginterpolationf(x’,y’)g(x,

y

)ManyinputpixelsmaymapoutsideborderofoutputimageEachoutputpixelmaybeaddressedmanytimes,withmanyinputpixelscontributingtofinalgraylevel(esp.fordemagnification)Forwardmappingiswasteful:f(x’,y’)g(x,

y

)Backwardmappingismorepractical:Inbackwardmapping,graylevelofeachoutputpixelisdeterminedbyoneinterpolationstepbetweenexactly4inputpixelsf(x’,y’)g(x,

y

)Backwardmappingismorepractical,althoughcalculatinginverseoperationmaybedifficult.p.122p.126p.127p.128p.123ControlPointpp.120-121平移放大變換公式旋轉(zhuǎn)Theaspectoftheorganmodel'sdeformation

ControlPointDataFusionSystemforSupportingtheSurgery

Timesequentialimageofwalking

ControlPoint—PositionMarker4-dimensionalmusculoskeletalmodel

點(diǎn)擊圖片播放視頻一個(gè)廣告的制作過(guò)程控制點(diǎn)的運(yùn)用怎樣讓骷髏動(dòng)得更逼真？點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASH點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASH點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASH幾何變換之大集成圖象配準(zhǔn)沒(méi)配準(zhǔn)的后果欲蓋彌彰的配準(zhǔn)ImageregistrationE.g.,mayimageatumorattwodifferentinstantsintimeandmaywanttocheckifitisgrowing.E.g.,Surveyingland:Image1showsanareaofMojavedesert;2showsadjacentarea;3formedbyregisteringoverlappingregionsandstitchingimagestogether.123MultispectralTissueClassificationT1T2

3DHistogramSegmentedImage配準(zhǔn)配準(zhǔn)點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASH圖象變形(Imagemorphing)p.137Figure8-17點(diǎn)擊圖片播放視頻ImagemorphingNote,wearewarpingfromoneimagetoadifferentimage.ComparewithEinsteinexample.

-usedinmotionpictures&animation反過(guò)來(lái)變換，豈不更好？點(diǎn)擊圖片播放視頻點(diǎn)擊圖片播放視頻哭笑不得的表情是怎樣生成的？點(diǎn)擊圖片播放視頻返老還童不是夢(mèng)（在屏幕上）成長(zhǎng)制圖學(xué)應(yīng)用對(duì)準(zhǔn)地球按住鼠標(biāo)左鍵移動(dòng)點(diǎn)擊圖片播放FLASH可按Alt+F4退出FLASHTermsGeometriccorrection,Geometriccalibration:幾何校正Spatialtransformation:空間變換Interpolation:內(nèi)插，插值Nearestneighborinterpolation:最近鄰點(diǎn)內(nèi)插Bilinearinterpolation:雙線性內(nèi)插Extrapolation:外插TermsZoomin:

放大Zoomout:縮小Hyperbolicparaboloid: