9.2. HISTOGRAMPREPROCESSING
109
Figure9.7: ResultofHigh-PassFilteringonFigure9.6
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110
CHAPTER9. HISTOGRAM-BASEDSEGMENTATION
butthepeaksareshorterandthevalleysarelled.
Figure9.8:TheResultofSmoothingtheHistogramGiveninFigure9.2
Smoothingahistogramisaneasyoperation.Itreplaceseachpointwith
theaverageofitanditstwoneighbors.Listing9.1showsthesmooth
histogram
functionthatperformsthisoperation.
9.3 ThresholdingandRegionGrowing
Therearetwomoretopicscommontoallthemethodsofimagesegmenta-
tion: image e thresholdingandregiongrowing. . Imagethresholdingsets s the
pixels inthe image to one or zero. . Listing g 9.2 shows s allthe e subroutines
usedinthischapter’s segmentationtechniques. . It t beginswiththeroutine
threshold
image
arraythataccomplishesthistask.
Thediculttaskisregiongrowing.Figure9.9showstheresultofthresh-
oldingFigure9.1correctly. The\object"inFigure9.9is s ahappyface. . It
comprisesthreedierentregions(twoeyesandthesmile). Regiongrowing
takesthisimage,groupsthepixelsineachseparateregion,andgivesthem
uniquelabels. Figure9.10showstheresultofregiongrowingperformedon
Figure 9.9. . Region n growing grouped and labeled one eyeas region1, the
othereyeasregion2,andthesmileasregion3.
Figure9.11 shows the algorithmfor regiongrowing. . It t begins withan
imagearraygcomprisingzerosandpixelssettoavalue.Thealgorithmloops
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9.3. THRESHOLDINGANDREGIONGROWING
111
00000000000000000000
00000000000000000000
00011100000011111000
00011100000001110000
00111100000000100000
00001000000000000000
00000000000000000000
00000000000000000000
00001100000000100000
00011111000011110000
00001111100111000000
00000011111110000000
00000001111110000000
00000000110000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
Figure9.9:TheResultofCorrectlyThresholdingFigure9.1
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112
CHAPTER9. HISTOGRAM-BASEDSEGMENTATION
00000000000000000000
00000000000000000000
00011100000022222000
00011100000002220000
00111100000000200000
00001000000000000000
00000000000000000000
00000000000000000000
00003300000000300000
00033333000033330000
00003333300333000000
00000033333330000000
00000003333330000000
00000000330000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
Figure9.10:TheResultofRegionGrowingPerformedonFigure9.9
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9.4. HISTOGRAM-BASEDTECHNIQUES
113
throughtheimagearraylookingforag(i,j)==value.Whenitndssucha
pixel,itcallsthelabel
and
check
neighborroutine.label
and
check
neighbor
sets the pixeltog
label (the e region label) and examines the pixel’s eight
neighbors.Ifanyoftheneighborsequalvalue,theyarepushedontoastack.
Whencontrolreturnstothemainalgorithm,eachpixelonthestackispopped
andsenttolabel
and
check
neighbor. Allthe e points onthe stack equaled
value,sosetthemandchecktheirneighbors. Aftersettingallthepixelsin
therstregion,incrementg
labelandbeginlookingforthenextregion.
Listing9.2nextshowsthefunctionsthatimplementregiongrowingwith
growbeingtheprimaryroutine.growrunsthroughtheregion-growingalgo-
rithmandcallslabel
and
check
neighbor (shownnextinListing9.2). . The
growandlabel
and
check
neighborfunctionsfollowtheregion-growingal-
gorithmstepforstep.
9.4 Histogram-BasedTechniques
Thefollowingpagespresentfoursegmentationtechniques:manualtechnique,
histogram peak technique, , histogram m valley technique,andadaptive tech-
nique.
9.4.1 ManualTechnique
Inthemanualtechniquetheuserinspectsanimageanditshistogramman-
ually.Trialanderrorcomesintoplayandtheresultisasgoodasyouwant
ittobe.
Figure9.12istheinputforallthesegmentationexamples.Figures9.13,
9.14,and9.15showtheresultofsegmentationusingthreedierentthresh-
olds. The e resultinFigure9.14usedahighof255 andalowof 125. . The
segmentationincludedthewhitegravelroadsas wellas the house trailers
andsidewalks. The e resultinFigure 9.14usedahighof255anda lowof
175. Thegravelroads s begintodisappear,but the housetrailersandside-
walksremain.Figure9.15showstheresultusingahighof255andalowof
225. Thissegmentationonlyndsthefourdominanthousetrailers. Which
answeriscorrect?Thatdependsonwhatyouwantedtond.
Notethatallimage segmentations willappear rough. . Itis s possible to
perform additionalprocessingtomakethe resultmorepleasing totheeye
(see chapter r 11 1 for r erosion n and dilation n techniques), but that t is s not the
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114
CHAPTER9. HISTOGRAM-BASEDSEGMENTATION
1. Given an n image e g with m m rows and n n columns
g(i,j) for r i=1,m m j=1,n
g(i,j) = value e for r object
= 0 0 for r background
2. set t g_label=2 2 this s is s the e label l value
3.
for (i=0; ; i<m; i++)
scan ith row
for (j=0; j<n; j++)
check jth h element
stack_empty = = true
if g(i,j) ) == = value
label_and_check_neighbor(g(i,j),g_label)
while stack_empty = = false e do
pop element t (i,j) ) off f the stack
label_and_check_neighbor(g(i,j),g_label)
end while
g_label = = g_label l + + 1
end of f checking jth h element
end of scanning g ith row
4. The e End
---------------------------------------
procedure label_and_check_neighbor(g(r,e), g_label)
g(r,e) = g_label
for (R=r-1; r<=r+1; ; R++)
for (E=e-1; ; e<=e+1; ; e++)
if g(R,E) ) == = value e then
push (R,E) onto the stack
stack_empty = = false
end if
end loop over E
end loop over R
end procedure label_and_check_neighbor
Figure9.11:PseudocodeforRegionGrowing
9.4. HISTOGRAM-BASEDTECHNIQUES
115
Figure9.12:InputImageforSegmentationExamples
Figure9.13:ThresholdofFigure9.12withHigh=255andLow=125
116
CHAPTER9. HISTOGRAM-BASEDSEGMENTATION
Figure9.14:ThresholdofFigure9.12withHigh=255andLow=175
Figure9.15:ThresholdofFigure9.12withHigh=255andLow=225
9.4. HISTOGRAM-BASEDTECHNIQUES
117
purpose of segmentation. . The e purpose is to break the e image into pieces
so later computer r processing g can interpret t their r meaning. . The e output is
forcomputernothumanconsumption. Alsonotehowdicultitisforthe
computer,evenwithmanualaid,tondobjectsthataretrivialforhumans
to see. . Anyone e could trace over the input t image e and outline the objects
betterthanthesegmentationprocess.
Listing9.2nextshowsthecodethat implementsmanualsegmentation.
Thefunctionmanual
threshold
segmentationhasthesameformastheother
subroutines.
manual
threshold
segmentationhastheusualinputsaswellasthehigh
andlowthresholdvaluesandthevalueandsegmentparameters.Thevalue
parameterspecies thevalueat whichtoset apixelifitfalls betweenthe
highandlowthresholds. valueisusuallyonesincethosepixelsoutsidethe
high-lowrangearesettozero. Thesegmentparameterspecieswhetheror
nottogrowregionsafterthresholding.Sometimesyouonlywanttothreshold
animageandnotgrowregions. Thetwooperationsareidenticalexceptfor
the last t step. . If f segment t == = 1, , manual
threshold
segmentation calls s the
region-growingroutines.
Manualsegmentationisgoodfornetuningandunderstandingtheop-
eration. Its s trial-and-error nature,however,makes it time consumingand
impracticalfor many applications. . We e need d techniques that examine the
histogramandselectthresholdvaluesautomatically.
9.4.2 HistogramPeakTechnique
The rst technique to examine e the histogram and d select t threshold d values
automaticallyusesthepeaksofthehistogram.Thistechniquendsthetwo
peaksinthehistogramcorrespondingtothebackgroundandobjectofthe
image. Itsetsthethresholdhalfwaybetweenthetwopeaks. Lookbackat
thesmoothedhistograminFigure9.8. Thebackgroundpeakisattwoand
theobjectpeakisatseven.Themidpointisfour,sothelowthresholdvalue
isfourandthehighisnine.
Thepeaktechniqueisstraightforwardexceptfortwoitems. Inthehis-
tograminFigure9.8,you’llnotethepeakatsevenisthefourthhighestpeak.
Thepeaksatoneandthreearehigher,buttheyarepartofthebackground
mountainofthehistogramanddonotcorrespondtotheobject. Searching
the histogram for peaksrequirespeak spacingto ensurethehighestpeaks
areseparated. Ifthepeaktechniquedoesnot,thenitwouldchoosetwoas
118
CHAPTER9. HISTOGRAM-BASEDSEGMENTATION
----------*----*----
-------*--**--*--*--
--------------------
*--------*-------*--
------------------*-
-*-----*------------
--**------*-----*---
-*--*--*-----------*
----------------*---
-*------------------
-----------------*-*
--*-----------------
--------------*--*--
------------*-*-----
----*-*-------------
--*-------*----*-**-
-*-------*--*------*
----*-*-------------
-*--------*------*--
Figure9.16:ResultofIncorrectPeakSeparation
the background peak andone as the object peak. . Figure e 9.16 shows the
disastrouseectofthis.
Theseconditemtowatchcarefullyisdeterminingwhichpeakcorresponds
tothebackgroundandwhichcorrespondstotheobject. Supposeanimage
hadthe histogramshowninFigure 9.17. . Which h peak k corresponds to the
background?Thepeakforgrayleveleightisthehighest,butitcorresponds
totheobjectnotthebackground. Thereasonisthemountainsurrounding
thepeakatgrayleveltwohasamuchgreaterareathanthatnexttogray
leveleight. Therefore,graylevelszerothroughsixoccupythevastmajority
oftheimage,andtheyarethebackground.
Listing9.2nextshowsthesourcecodetoimplementthepeaktechnique.
peak
threshold
segmentationistheprimaryfunction.Next,itcallsnewfunc-
tionstondthehistogrampeaksanddeterminethehighandlowthreshold
values. Finally,itthresholdstheimage,performsregiongrowingifdesired,
andwritestheresultimagetotheoutputle.
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