11.8. ASHAPEOPERATIONSAPPLICATIONPROGRAM
179
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Figure11.30:ASquare,itsEuclideanDistanceMeasure,anditsMedialAxis
Transform(Part2)
11.8 A A Shape Operations s Application n Pro-
gram
Listing 11.3 shows application program mainsk k that t ties together r all the
routines thatmanipulateshapes. . Itcan n call14dierent operations. . The
formatofmainskisthesameastheotherapplicationspresentedinthistext.
11.9 Conclusions
Thischapterdiscussedshapeoperationsormorphologicallters.Thesetech-
niques helpyouimprovetheappearanceofsegmentationresults. . Theyare
alsousefulforothersituations.Aswithalltheimageprocessingoperatorsin
thissystem,youmustexperiment. Trythetechniquesandtoolsindierent
combinationsuntilyoundwhatworksfortheimageorclassofimagesat
hand.
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180
CHAPTER11. MANIPULATINGSHAPES
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Figure11.31:ARectangleanditsMedialAxisTransform
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11.10. REFERENCES
181
Figure11.32:(ClockwisefromUpperLeft)A,ItsOutline,MedialAxisTrans-
form,andThinning
11.10 References
11.1\TheImageProcessingHandbook,ThirdEdition,"JohnC.Russ,CRC
Press,1999.
11.2\Computer Imaging Recipes s in n C," Harley y R.Myler, , and Arthur r R.
Weeks,PrenticeHallPublishing,EnglewoodClis,NewJersey,1993.
11.3\VisioninManandMachine,"MartinD.Levine,McGraw-Hill,1985.
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182
CHAPTER11. MANIPULATINGSHAPES
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Chapter12
BooleanandOverlay
Operations
12.1 Introduction
ThischapterwilldiscussBooleanandoverlayoperations. Theseoperations
areusefulforcombiningimagesininterestingways. Theyarealsogoodfor
creating specialeects s in n images. . The e goal l is to combine e two images s to
produceathirdthathasfeaturesofthetwoinputs. TheBooleanoperations
use the functionsof Booleanalgebra. . The e overlay operations lay selected
pixels from one image on topof another. . These e are similartothe image
additionandsubtractionofChapter8.
12.2 BooleanOperations
TheBooleanoperationsexecutethebasicfunctions from Booleanalgebra.
Figure12.1shows thetruthtablefortheseoperations. . The e outputofthe
ANDisonewhenbothinputsareone.TheoutputoftheORisoneifeither
oftheinputsareone.Theoutputoftheexclusiveor(XOR)isoneifonebut
notbothoftheinputsisone. TheNANDistheoppositeoftheAND,the
NORisoppositeoftheOR,andtheNOTreversestheinput.
ItisasimplemattertoextendBooleanoperationsforgrayscaleimages.
Replacethe1sintheAandBcolumnsofthetruthtablewithanynon-zero
value. Replacethe1s s intheoutputcolumnswiththenon-zerovaluefrom
theAcolumn.Forexample,iftheAimagecontainsall200sandtheBimage
183
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184
CHAPTER12. BOOLEANANDOVERLAYOPERATIONS
a
b
a AND D b
a OR b
a XOR b
a NAND b
a NOR R b
NOT a
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Figure12.1:ExistingStandardTIFFTags
containsall100s,theoutputofAANDBwillbeall200s.
Listing 12.1showsthe subroutines that implementthe Booleanopera-
tions. Eachoftheroutines(and
image,or
image,xor
image,nand
image,
nor
image, not
image)follows theusualpattern. . They y combine the input
imagearraysusingthetruthtableandreturntheresult. Thesearesimple,
yetpowerfulroutines.
Listing12.2showsthebooleanprogram.Thisprogramallowstheuserto
applyanyoftheBooleanoperatorstoimages. It t follows thesamepattern
asallmainprogramsinthistext.
12.3 ApplicationsofBooleanOperations
Let’slookattwoapplicationsoftheBooleanoperations:maskingandlabel-
ingimages. Maskingplacesthegrayshadesofanimageontopofabinary
imagederivedfromit. Figure12.2showsanaerialimage,andFigure12.3
showsasegmentationofitfromChapter 10. . This s isafairlyaccurateseg-
mentation,butitisdiculttocorrelatethewhiteshapestoobjectsinthe
image. Isthelargerectangletotheleftgrassoraparkinglot? ? Onewayof
determiningthesourceoftheobjectsistomask theoriginalovertheseg-
mentationusingtheANDoperation.Figure12.4showstheresultofmasking
(ANDing). Itiseasytoseethatthelargerectangleisatenniscourt,some
oftheroadsarecement(white),andothersareasphalt(gray).
AnotheruseoftheBooleanoperationsistocreateandplacelabelsontop
ofimages. Listing12.3showsanimagelabelingprogramcalledilabel. This
programwritessimple9x7blockletterstoanimagele. Theusercallsthe
programbygivinganoutputimagename,alineandelementintheimage,
andthetexttogointheimage.Forexample,
ilabela.tif1020adam
placesthelettersADAMintheimagea.tifstartinginthetenthrow,twentieth
12.3. APPLICATIONSOFBOOLEANOPERATIONS
185
Figure12.2: OriginalAerialImage
Figure12.3:SegmentationofAerialImage(fromChapter10)
186
CHAPTER12. BOOLEANANDOVERLAYOPERATIONS
element.Mostofthelistingisthearraysdeningtheblockletters,numbers,
andafewpunctuationmarks. Theprogramitselfloopsthroughtheletters
inthetextandcopieseachletter’sarrayintotheimagearray.
Figure12.4:SegmentedAerialImageMaskedwithOriginal
TheleftsideoftheimageinFigure12.5showstheoutputoftheilabel
program. The e words s ADAM M PHILLIPS S are clear enough, , but t they y will
disappeariflaidontopofanimage. Theyneedabackground. Thecenter
sectionofFigure12.5shows theresultofdilatingthewordsasinChapter
11. TherightsideofFigure12.5showsthenallabel|blacklettersona
whitebackground.Thenallabelistheresultoftheexclusiveor(XOR)of
theletters andtheirdilation. . TheoutputoftheXORiswhiteonly y where
oneortheotherimageiswhite,butnotboth.
Figure12.6istheoutcomeoflabeling. ItistheresultofORingthenal
labelofFigure12.5withtheboyimage.ORingallowsustoseethroughthe
labeltotheimageunderneath. Itisalsopossibletolabeltheimageusing
thegreateroverlaydiscussedlater. Creatingthelabel,however,ispossible
onlyviatheXORoperation.
Theseareonly twopossibleuses of the Booleanoperations. . There e are
manymore,especiallywhenyoustartcombiningthem. Afterall,combining
Booleanoperationsishowpeoplebuildcomputers.
12.3. APPLICATIONSOFBOOLEANOPERATIONS
187
Figure12.5:ilabelOutputonLeft,DilationinCenter,XORofBothonRight
Figure12.6:LabeledBoyImage
188
CHAPTER12. BOOLEANANDOVERLAYOPERATIONS
12.4 OverlayOperations
The overlayoperations lay select pixels fromoneimageontopofanother
andplacethe outputintoathirdimage. . This s chaptershows vetypes of
pixeloverlayoperationsfromimageAontopofimageB.Theseare
1.overlaynon-zeropixelsfromAontoB,
2.overlayzeropixelsfromAontoB,
3.overlaypixelsfromAontoBiftheyaregreater,
4.overlaypixelsfromAontoBiftheyareless,and
5.averagethepixelsfromAandBandusethisastheoutput.
Figures12.7through12.12illustratetheseoperations.Figure12.7shows
twoimagearrays: AandB.Figure12.8showstheresultoflayingthenon-
zeropixelsofAontopofB.ThislookslikeimageAexceptfortheabsence
ofthe2x2areaof0sinthelowerright.Figure12.9showstheresultoflaying
the zero pixels of A on top of B.This looks like e image e B except for r the
additionofthe2x2areaof0s. Figure12.10shows s theresultofoverlaying
thepixelsinAthataregreaterthanthecorrespondingpixelsinB.Notethe
columnof100stothefarright. Figure12.11showstheresultofoverlaying
the pixels inAthatare less than the correspondingpixelsinB.Note the
predominanceof50sandthe0s. Figure12.12showstheresultofaveraging
imagesAandB.Figure12.12isnoteasytoperceiveorreadandisbetter
illustratedwiththeimagesdiscussedbelow.
Listing12.4showsthesubroutinesthatimplementtheoverlayoperations.
Thefollowingroutinesfollowtheusualmodel:non
zero
overlay,zero
overlay,
greater
overlay, less
overlay,andaverage
overlay. They y combine the input
imagearraysandreturntheresult.
12.5 ApplicationsofOverlayOperations
Let’s look attwo applicationsofimage overlaying. . Therst t isthedouble
exposure. Figure12.13showstwoimagessideby y side. . Figure12.14shows
theresultofaveragingthetwotogether. Thisresemblesadoubleexposure
image,asitcontainsbothimages.
Thistechniquecanalsoapplyapatternortexturetoanimage. Figure
12.15showsaleafytexture,andFigure12.16showsahouse.Figure12.17is
theresultofaveragingthetwo. Itiseasytorecognizethehouse,butparts
ofit(notablytheroofanddoor)haveatextureorpatterntothem.
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