计算机视觉作业

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1、Problem1CCDtoCameraTransformation(a)FieldofView(FOV)i.ThefollowingdiagramshowstheperspectiveprojectionofacameraIfthewidthoftheimageisL,TheFieldofViewFOV=2a=2atan(L/2f)i.Forthegivencamera,FOV-vertical=2atan(8/24)=36.9°FOV-horizontal=2atan(6/24)=28.1°ii.Thereareonly

2、finitenumbersofpixelsinanimage・ThelargertheFOV,themoresceneisprojectedtotheimage.Hencetheresolutionforeverypixelisdecreased.(b)ApplicationLetthecamera-framecoordinatesofapointbe(Xc,Yc,Zc)andtheimageplanecoordinatesbe(x,y),thenLetthepixelcoordinatesw=(u，v),thenComb

3、inetogether:00f001000-ii.Assumetheoriginofcameraframeisatthecenteroftheimage,then(u0,vO)=(250,250)(ku,kv)=(500/12-500/16)=(41.67,-31.25)Itcanbecomputedthatw=(u,v)=(367,199)Problem2CameraProjection(a)LetXc=a+入b.thena茗+Ab工a、•+ax4-ax4-Abx=/(—-f-A(bxax-bxax),4-A(hyax-

4、flxfljItrepresentsalineina2DspaceMatlab,theprojectionisshownas(b)ThecameraframecoordinatesofsphereisXc=(rsin

5、320.18660.6283CamMatrix=0.0881-0.32640.08810.6010Itisnotacircleontheimageplane3a.0.00211—0.0002-0.0002-0.0002Afterdefininga2Nxl2matrixPasgiveninthereadingandcanbeseenexplicitlyinmycode,Ifoundthedesiredprojectionmatrixbyfindingtheeigenvectorcorrespondingtothesmalle

6、steigenvalueofP'*P，andreshapedthisvectorintoa3x4matrix,asinthemethoddescribedinsection3.1ofthetext.Printingouttheinput(u,v)valuesandthosegeneratedbyobtainedmatrix,bothareseentobeprojectionsofequivalentcubesinspace,sothematrixappearstobevalid.Idecomposedmymatrixint

7、oK[R,T],butIamafraidthatmyKmatrixisnotcorrect.Frommynotes,thereadings,andanoutsidearticle,IhavenotbeenabletodiscernwhatIammissing,buttheproductofmydecomposedmatricesisincorrect.GeneratingcodeisinthefileLinearCalib.mat.Iwas,however,abletofindseveraloftherelevantpar

8、ameters:rho=3.3134e+003uO=300.5vO=300.5theta=3.14/2alpha=1.1177e+003beta=1.1177e+003'0.70710.4150-0.5725、R=0.0000-0.8097-0.5869-0.7071.4150—0.5725丿T=(