Math3360:MathematicalImagingLecture16:ImageenhancementinthefrequencydomainTheChineseUniversityof HongKong
Math 3360: Mathematical Imaging The Chinese University of Hong Kong Lecture 16: Image enhancement in the frequency domain
Key stepsforimage enhancementinthe freguency domainFrequency domain filleringcperaticnFilterInverseFourierfunctionFouriertransformH(u,t)transformF(u,t)H(u,t)F(ae)Pre-Post-processingprocessing(y)g(r.3)InputEnhancedimageimage
Key steps for image enhancement in the frequency domain
Relationshipbetween spatialandfreguencydomainf(x)[F(u)lAKMKpointsMpointsMpointsFlatfilterLowpassfiltering[F(u)]2AKMf(x)2KpointsMpointsMpoints
Relationship between spatial and frequency domain Flat filter Low pass filtering
Spatial and freguency domainaSEM:scanning electronbMicroscopeFIGURE4.4(a)SEMimageofadamagedinteeratedcircuit(b)Fourierspectrum of (a)(Original imagescotrtesyofDr.JM.Hudak.BrockhouseInstituteforMateriasResearch.MeMasterUniversity.Hamilton.OntarioCanada.)noticethe±45componentsandtheverticalcomponentwhich is slightly off-axistotheleft!Itcoirespondstotheprotrusion causedbythermalfailureabove.4.29
Spatial and frequency domain
ExamplesofLPandHPfiltersLinearFiltersLow-passHa,n)High-pass
Examples of LP and HP filters