Chapter2Imageformation2.1Geometricprimitivesandtransformations...................292.1.1Geometricprimitives..........................292.1.22Dtransformations...........................332.1.33Dtransformations...........................362.1.43Drotations...............................372.1.53Dto2Dprojections..........................422.1.6Lensdistortions.............................522.2Photometricimageformation..........................542.2.1Lighting.................................542.2.2Reflectanceandshading........................552.2.3Optics..................................612.3Thedigitalcamera...............................652.3.1Samplingandaliasing.........................692.3.2Color..................................712.3.3Compression..............................802.4Additionalreading...............................822.5Exercises....................................82R.Szeliski,ComputerVision:AlgorithmsandApplications,TextsinComputerScience,27DOI10.1007/978-1-84882-935-0_2,©Springer-VerlagLondonLimited2011282Imageformationn^(a)(b)GRGRf=100mmBGBGdGRGRBGBGzi=102mmzo=5m(c)(d)Figure2.1Afewcomponentsoftheimageformationprocess:(a)perspectiveprojection;(b)lightscatteringwhenhittingasurface;(c)lensoptics;(d)Bayercolorfilterarray.2.1Geometricprimitivesandtransformations29Beforewecanintelligentlyanalyzeandmanipulateimages,weneedtoestablishavocabularyfordescribingthegeometryofascene.Wealsoneedtounderstandtheimageformationprocessthatproducedaparticularimagegivenasetoflightingconditions,scenegeometry,surfaceproperties,andcameraoptics.Inthischapter,wepresentasimplifiedmodelofsuchanimageformationprocess.Section2.1introducesthebasicgeometricprimitivesusedthroughoutthebook(points,lines,andplanes)andthegeometrictransformationsthatprojectthese3Dquantitiesinto2Dimagefeatures(Figure2.1a).Section2.2describeshowlighting,surfaceproperties(Fig-ure2.1b),andcameraoptics(Figure2.1c)interactinordertoproducethecolorvaluesthatfall