6.7. EDGEENHANCEMENT
69
Figure6.12:ResultofContrast-BasedEdgeDetector
Contrast-basededgedetectionis possiblewithanyedgedetector. . Asa
project,trymodifyingthehomogeneityedgedetectorbydividingitsresult
bytheaveragegraylevel|butrstmultiplytheresultofhomogeneityby
afactor(nineormore)sodividingdoesnotreduceedgestrengthstozero.
Modifyanyoftheotheredgedetectorsinasimilarmanner.
6.7 EdgeEnhancement
Agoodapplicationofedge detectors is toenhanceedges andimprovethe
appearanceofanoriginalimage. Detecttheedgesinanimageandoverlay
theseedgesontopoftheoriginalimagetoaccentitsedges.Thelastsection
ofListing6.1showstheenhance
edgesfunction,whichrepeatsthequick
edge
functionfromChapter5withafewaddedlinesofcode. Examinethecode
right after the loops over r a a and b. . If f the result t of f convolution (the sum
variable)isgreaterthanauser-chosenthreshold,theoutputimageisassigned
that value. . If f not, the output imageis assignedthe value from theinput
image. Theresultistheinputimagewithitsstrongedgesaccented.
Figure6.13shows theresultofenhancingtheedgesofFigure6.1. . The
edgesofthebricks,thesidingintheleft,andthelines onthegaragedoor
areallsharper.
Anyedgedetectorcanbeusedtoenhancetheedgesinaninputimage.
Simplyaddtheoptionoftakingtheedgedetectorresultoravaluefromthe
inputimage.Aninterestingprojectwouldbetousethe9x9Gaussianmask
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70
CHAPTER6. ADVANCEDEDGEDETECTION
Figure6.13:ResultofEdgeEnhancement
todetecttheedgesoflargeobjectsandthenusetheseedgestoenhancethe
inputimage.
6.8 VarianceandRange
Thechapterendswithtwoedgedetectorssimilartothedierenceedgede-
tector in n that they y look at t the image e numbers inside e a a small area. . The
variance operator,examines a3x3area andreplaces thecenter pixelwith
thevariance. The e varianceoperator subtractsthepixelnexttothecenter
pixel, squares s that dierence,adds up the squares of the dierences from
theeightneighbors,andtakesthesquareroot.Theotheredgedetector,the
rangeoperator,sorts the pixels in an nxn area andsubtractsthe smallest
pixelvaluefromthelargesttoproducetherange.
Figure6.14showstheresultsofapplyingthevarianceandrangeoperators
toanarrayofnumbers.Figures6.15and6.16showtheoutcomeofapplying
theseoperators.
6.9 Applications
Listing6.2showsthemedgeprogramthattiestogetheralltheedgedetectors
fromthisandthepreviouschapter.Theuserchoosesamong11dierentedge
detectors.Enteringthemedgecommandwithoutanyparameterscausesthe
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6.9. APPLICATIONS
71
Input
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
5 5 5 5 5 5 5 10 0 10 0 10 10 0 20 0 20 0 20 0 20
Variance Output
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
0 0 0 0 0 7 7 7 7 0 0 0 14 4 14 4 0 0 0 0
Range Output
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
0 0 0 0 0 5 5 5 5 0 0 0 10 0 10 0 0 0 0 0
Figure6.14:TheResultsofApplyingtheVarianceandRangeOperatorsto
anArrayofNumbers
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72
CHAPTER6. ADVANCEDEDGEDETECTION
Figure6.15:ResultofVarianceEdgeDetector
Figure6.16:ResultofRangeEdgeDetector
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6.10. CONCLUSIONS
73
usagemessagetoappearandgiveexamplesofeachoperator. Regardlessof
theoperatorchosen,theprogramdoestheusualcreatinganoutputimage
le,allocatingarrays,andreadinginputdata.Theprogramusesthesecond
commandlineparametertostepintoanifstatementtointerprettheother
parameters. It t then calls s the e desired edge detector andwrites the result
totheoutputimage. Themedge e programservesasapatternforprograms
inthefollowingchapters thatcollectanumberofrelatedimageprocessing
operations.
6.10 Conclusions
Thischapterhascontinuedthediscussionofedgedetectors.Thehomogene-
ity,dierence,variance,andrangeedgedetectorsworkbysubtractingpixel
valuesinsideasmallareaaroundanedge.TheGaussianedgedetectorcon-
volvesanimagewitha\Mexicanhat"imagepiece.Thecontrast-basededge
detectorcompensatesfordierencesinbrightnesslevelsindierentpartsof
animage. Theseedgedetectorswillbeusedagainduringthesegmentation
chapterslaterinthisbook.
6.11 References
6.1\RecognizingObjects inaNaturalEnvironment: : AContextualVision
System(CVS),"MartinA.Fischler,ThomasM.Strat,ProceedingsImage
UnderstandingWorkshop,pp.774-796,MorganKaufmannPublishers,May
1989.
6.2\DigitalImageProcessing,"KennethR.Castleman,Prentice-Hall,1979.
6.3\VisioninManandMachine,"MartinD.Levine,McGraw-Hill,1985.
6.4.\Contrast-BasedEdgeDetection,"R.P.Johnson,PatternRecognition,
Vol.23,No.3/4,pp.311-318,1990.
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74
CHAPTER6. ADVANCEDEDGEDETECTION
Chapter7
SpatialFrequencyFiltering
7.1 SpatialFrequencies
Allimagesandpicturescontainspatialfrequencies. Mostofusarefamiliar
withsometypeoffrequencysuchasthe60-cycle,110-voltelectricityinour
homes. Thevoltagevariesintimeasasinusoid,andthesinusoidcompletes
afullcycle60timesasecond|afrequencyof60Hertz.
Images have spatialfrequencies. . The e gray levelinthe image varies in
space(nottime),i.e.itgoesupanddown. Figure7.1showsthesideviewof
animagewithlowspatialfrequencies.Thegraylevelislowattheleftedge
ofthegure,stays constant for awhile,thenshiftstoahighergray level.
Thegraylevelisfairlyconstantthroughout(onlyonechangeinspace)and
sothegurehaslowspatialfrequencies.
Figure7.2showsthesideviewofanimagewithhighspatialfrequencies.
Thegraylevelchangesmanytimesinthespaceoftheimage. Therateor
frequencyofchangeinthespaceoftheimageishigh,sotheimagehashigh
spatialfrequencies.
7.2 Filtering
Filteringisalsoacommonconcept.Adjustingthebassandtrebleonstereos
ltersoutcertain audiofrequencies andamplies others. . High-passlters
pass highfrequenciesandstoplowfrequencies. . Low-pass s lters stophigh
frequenciesandpasslowfrequencies. Inthesamemanner,itispossibleto
lterspatialfrequenciesinimages. Ahigh-passlterwillamplifyor\pass"
75
76
CHAPTER7. SPATIALFREQUENCYFILTERING
Figure7.1: SideViewofanImagewithLowSpatialFrequencies
Figure7.2: SideViewofanImagewithHighSpatialFrequencies
7.3. APPLICATIONOFSPATIALIMAGEFILTERING
77
frequent changes s in gray y levels and a low-pass lter will reduce frequent
changesingraylevels.
Considerthenatureofafrequentorsharpchangeingraylevel.Figure7.1
showedanimagewithonlyonechangeingraylevel.Thatchange,however,
was very sharp|itwasanedge. . Ahigh-passlter r willpass,amplify,or
enhancetheedge.Alow-passlterwilltrytoremovetheedge.Insteadofan
instantmovefromonegrayleveltoanother,thelow-passlterwillproduce
agradualslopebetweenthetwolevels. Thetwograylevelswillstillexist,
butthetransitionwillbeslower.
7.3 ApplicationofSpatialImageFiltering
Spatial image e ltering has several l basic applications in image e processing.
Amongthesearenoiseremoval,smoothing,andedgeenhancement.Noisein
animageusuallyappearsassnow(whiteorblack)randomlysprinkledover
animage. Spikes,orverysharp,narrowedgesintheimagecausesnow. A
low-passltersmoothesandoftenremovesthesesharpedges.
Edgeenhancementimprovestheappearanceofanimagebysharpening
theoutlinesofobjects. Chapter6describedhowanedgedetectorenhanced
edges. The e detected edges s were overlaid d on top of the original image e to
emphasize the e edges. . A A high-pass lter r produces the same e result t in n one
operation.
7.4 Frequencyvs. . SpatialFiltering
Considersoundasnoisevaryinginthetimedomain,i.e.thepitchofthenoise
varieswithtime.Apuresinusoidcompletingacycle1000timesasecondisa
1KHztone.Inthefrequencydomain,thisisasinglevalueat1000.Tolter
itout,multiplyitbyalow-passlterthatonlypassesfrequenciesbelow900
cyclespersecond. Picturethelow-passlterasanarraywiththevalueof
oneinallplacesfromzerothrough900andthevaluezeroinallplacesabove
900.
Multiplicationinthefrequency domainisasimpleidea,however,there
isoneproblem. Peoplehearsoundinthetimedomain.Thesignal,however,
mustbetransformedtothefrequencydomainbeforemultiplication.Fourier
transformsdothistranformation[7.1].Fouriertransformsrequiresubstantial
78
CHAPTER7. SPATIALFREQUENCYFILTERING
0 1 1 0
1/6 * * 1 1 2 2 1
0 1 1 0
1 1 1 1
1/9 * * 1 1 1 1 1
1 1 1 1
1 1 1 1
1/10 * * 1 1 2 2 1
1 1 1 1
1 2 2 1
1/16 * * 2 2 4 4 2
1 2 2 1
Figure7.3:Low-PassFilterConvolutionMasks
computations,andinsomecasesisnotworththeeort.
Multiplicationinthefrequencydomaincorrespondstoconvolutioninthe
timeandthespatialdomain(suchasinChapter5).Usingasmallconvolution
mask,suchas3x3,andconvolvingthismaskoveranimageis mucheasier
andfasterthanperformingFouriertransformsandmultiplication.
7.5 Low-PassFiltering
Low-passlteringsmoothesoutsharptransitionsingraylevelsandremoves
noise. Figure7.3showsfourlow-passlterconvolutionmasks. . Convolving
theselterswithaconstantgraylevelareaofanimagewillnotchangethe
image. Notice e howthe secondconvolution mask replaces the center pixel
oftheinputimagewiththeaveragegraylevelofthearea. Theotherthree
maskshavethesamegeneralform|a\peak"inthecenterwithsmallvalues
atthecorners.
The next four gures s show numericalexamples of f how a low-pass l-
ter aectsanimage. . Figure e 7.4showsanimagesegment withlowspatial
frequencies. Theimagesegmentchangesgray y levelonce,but withasharp
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