Chapter3

IntensityTransformationand

SpatialFilteringPart3SpatialFiltering3.4FundamentalsofSpatialFilteringLinearnonlinearsmoothSmoothLinearFiltersSmoothnonlinearFiltersSharpeningSharpeningLinearfiltersSharpeningnonlinearfilters3.4FundamentalsofSpatialFilteringfloatr=0;for(intm=-M;m<=M;m++) for(intn=-N;n<=N;n++) { r+=f[x+m,y+n]*mask[M+m,N+n]; }g[x,y]=S(r);FundamentalsofSpatialFiltering*554474443#0-10-15-10-10*0*-1*0*-1*5*-1*0*-1*03.4FundamentalsofSpatialFiltering3.5SmoothingSpatialFilters3.5.1SmoothingLinearFilters3.5.1SmoothingLinearFiltersDirectionalBlur0.20.20.20.20.20.20.20.20.20.20.20.20.20.20.23.5.1SmoothingLinearFilters[Programmingofaveragefilter]GaussianBlurMask(x,y)=G(x,y)=exp(-(x*x+y*y)/(2*r*r)HowtomakeaGaussianFilterMask

(1)Sampling:G(x,y)=G[m,n];

(2)Normalized

s=∑G[m,n],G[m,n]=G[m,n]/s[ProgrammingofGaussianBlur]3.5.2Order-Statistic(Nonlinear)FiltersMedianFilterMedianFiltersareparticularlyeffectiveinthepresenceofimpulsenoise(alsocalledsalt-andpeppernoise)SaltandpeppernoiseRandomlocation;Dependentvalue;[ProgrammingofSaltandpeppernoise]Saltandpepper3.5.2Order-Statistic(Nonlinear)FiltersMedianOperationMedian{3,2,1,5,4}=?{3,2,1,5,4}=>(queue)=>{1,2,3,4,5}=>3[ProgrammingofMedianFilter]3.5.2Order-Statistic(Nonlinear)Filters3.6SharpeningSpatialFilters3.6.1Foundation1D:derivativefsubx.FirstderivativeMustbezerooftheareaofconstantintensity;MustbenonzeroattheonsetofanintensitysteporrampMustnonzeroalongramps.SecondderivativeMustbezeroinconstantareaMustbenonzeroattheonsetandendofanintensitysteporrampMustbezeroalongrampsofconstantslope3.6.1FoundationofSharpeningSpatialFilters3.6SharpeningSpatialFilters2D:Gx: partialderivativefsubx.Gy: partialderivativefsuby3.6.2Laplacian(SecondDerivative)3.6.2Laplacian(SecondDerivative)3.6.2Laplacian(SecondDerivative)input44477771-2103-300-12-10-3300HighPassfilter[Programmingofhighpassfilter]3.6.2Laplacian(SecondDerivative)[ProgrammingofLaplacian]SharpeningFilter3.6.2Laplacian(SecondDerivative)[ProgrammingofSharpeningFilter]-c-c1+4*c-c-c3.6.3UnsharpMaskingandHighboostFilteringUnsharpMaskingBlurtheoriginalImageSubtracttheblurredimagefromtheoriginal(theresultingdifferencecalledthemask)Addthemasktotheoriginal(10-10)3.6.3UnsharpMaskingandHighboostFiltering3.6.3UnsharpMaskingandHighboostFiltering3.6.4UsingtheFirst-OrderDerivativesfor(Nonlinear)ImageSharpening–TheGradientGradientMagnitudeofGradientGradientApproximateofmagnitude(suitablecomputationaly)First-OrderDerivativesQuestion:maxvalueof3.6.4UsingtheFirst-OrderDerivativesfor(Nonlinear)ImageSharpening–TheGradientSobelmaskGxGy-101-202-101-1-2-1000121YaxisProgrammingofSobelreliefeffectSunkenorRaised?3.6.4UsingtheFirst-OrderDerivativ