Module 1.15-Spatial Sharpening Filters.pdf

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1. •Spatialfilteringchangethegreylevelofapixel(x,y)dependingonthe
pixelvaluesinasquareneighborhoodcenteredat(x,y)usinga
matrix(filter,mask,kernel/window).
•Therearemanythingsthatcanbeachievedbyneighborhood
processingwhicharenotpossiblewithpointprocessing.
Image Enhancement
Spatial domain Frequency domain
Point processing Neighbourhood processing
E.g. Negative Image, contrast
stretching, thresholding etc.
E.g. Averaging filter, median filtering
etc.
E.g. Image sharpening using Gaussian
high pass filters, unsharp masking,
highboost filtering etc.

2. Averaging filterWeighted averaging filter
Minimum filterMaximum filterMedian filter
Spatial filters
Smoothing spatial filters (LPF)
Sharpening spatial filters (HPF)
Linear filtersNon-linear(Order statistics) spatial filter
Laplacian linear filter

3. •Sharpeningfiltersareusedtohighlightfinedetails(e.g.edges)inanimage,or
enhancedetailsthatareblurredthrougherrorsorimperfectcapturingdevices.
•Sharpeningisoppositeofsmoothing(averaging).Henceinmathematics,itisgiven
bypartialderivatives(HPF)asaveragingisintegration(LPF).
•Whilelinearsmoothingisbasedontheweightedsummationorintegral
operationontheneighborhood,thesharpeningisbasedonthederivative
(gradient)orfinitedifference.
•Insmoothingwetrytosmoothnoiseandignoreedgesandinsharpeningwetry
toenhanceedgesandignorenoise.
❖Sharpening Spatial Filters:

4. •Thefirstorderpartialderivativeofthedigitalimagef(x,y)are:
❖Partial derivatives of digital image:
•Thefirstderivativemustbe:
(1)Zeroalongflatsegments(i.e.constantgreylevels)
(2)Non-zeroattheoutsetofgreylevelsteporramp(edgesornoise)
(3)Non-zeroalongsegmentsofcontinuingchanges(i.e.ramps)
•Thesecondorderpartialderivativesofthedigitalimagef(x,y)are:
•Thesecondderivativemustbe:
(1)Zeroalongflatsegments(i.e.constantgreylevels)
(2)Non-zeroattheoutsetofgreylevelsteporramp(edgesornoise)
(3)Zeroalongramps.

5. •Thefirstderivativedetectsthick
edgeswhilesecondderivativedetects
thinedges.
•Secondderivativehasmuchstronger
responseatgreylevelstepthanfirst
derivative.
•Thuswecanexpectasecondorder
derivativetoenhancefinedetail(thin
lines,edges,includingnoise)much
morethanafirstorderderivative.
f ' = f(x+1) -f(x)
f '' = f(x+1) + f(x-1) -2f(x)

6. •TheLaplacianoperatorofanimagef(x,y)is:
❖The Laplacian filter:
•Thisequationcanbeimplementedusingthe3x3mask:
•AstheLaplacianfilterisalinearspatialfilter,wecanapplyitusingthesame
mechanismofconvolution.ThiswillproduceaLaplacianimagethathasgrayish
edgelinesandotherdiscontinuities,allsuperimposedonadark,featureless
background.
•Backgroundfeaturescanbe“recovered”whilestillpreservingthesharpening
effectsoftheLaplaciansimplybyaddingtheoriginalandLaplacianimages.

7. Filter mask
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0-150-150
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Input image Output image