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1、DigitalImageProcessingExamination1.Apreprocessingstepinanapplicationofmicroscopyisconcernedwiththeissueofisolatingindividualroundparticlesfromsimilarparticlesthatoverlapingroupsoftwoormore.Assumingthatallparticlesareofthesamesize,proposeamorphologicalalgorithmthatwillproduceanimagethatcontainson
2、lytheisolated(non-overlapping)particlesthatarenotincontactwiththeboundaryoftheimage.2.Animagerepresentedbyacontinuousfunctionf(x,y)isw=2cmwideandh=3cmhigh.Theimageistobeconvertedtoanarrayofpixelsbyascannerwhoseresponseiszeroabove80lines/centimeterinboththehorizontalandverticaldirections.Thediscr
3、eteimageisrepresentedbyanarrayˆf(n,m)wherenandmtakeonintegervalues,0~n~N-1,0~m~M-1.(a)DeterminesuitablevaluesforNandM.(b)Assumethatˆf(n,m)=f(na,mb).Determinethevaluesofaandb.(c)DetermineconstantsA,B,C,D,EsuchthattheDFToffˆcanbeexpressedasBC)−i(Dun+Evm)F(u,v)=A∑∑f(n,m)en==00m(d)Findnumbers(P1,P2)
4、suchthatF(u+jP1,v+kP2)=F(u,v)foranyintegersj,k,u,v.3.Thearithmeticdecodingprocessisthereverseoftheencodingprocedure.Decodethemessage0.23355giventhecodingmodel.SymbolProbabilitya0.2e0.3i0.1o0.2u0.1!0.14.Thegradientofafunctionf(x)isdefinedas⎡G⎤⎡∂f⎤x⎢⎥⎢∂x⎥∇f=⎢⎥=⎢∂f⎥⎢G⎥⎢⎥⎣y⎦⎢⎣∂y⎥⎦Computationally,the
5、firstderivativeisimplementedbycalculatingthedifferencebetweenadjacentpixels.(a)Isthefollowingalinearoperator?1⎡22⎤2⎛∂f⎞⎛∂f⎞∇f=⎢⎜⎟+⎜⎜⎟⎟⎥⎢⎣⎝∂x⎠⎝∂y⎠⎥⎦(b)Statehowwouldyouimplementtheaboveoperatorusingdifferencesbetweenpixels.(c)ASobeloperatorusestwomasks,HxandHytoprocessanimage.Explainwhyaretwomasks
6、neededandwhatdotheymeasure?(d)WritedownthemasksHxandHy,andidentifytheminthefollowingfigures:
7、Hx(u,v)
8、
9、Hy(u,v)
10、5.Thethreeimagesshownwereblurredusingsquareaveragingmasksofsizesn=23,25,and45,respectively.Theverticalbarsontheleftlowerpartof(a)and(c)areblurred,butaclearseparationexistsbetweenthem.How
11、ever,thebarshavemergedinimage(b),inspiteofthefactthatthemaskthatproducedthisimageissignificantlysmallerthanthemaskthatproducedimage(c).explainthis.
