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Image resizing using saliency strength map and seam carving for white blood cell analysis

De
14 pages
A new image-resizing method using seam carving and a Saliency Strength Map (SSM) is proposed to preserve important contents, such as white blood cells included in blood cell images. Methods To apply seam carving to cell images, a SSM is initially generated using a visual attention model and the structural properties of white blood cells are then used to create an energy map for seam carving. As a result, the energy map maximizes the energies of the white blood cells, while minimizing the energies of the red blood cells and background. Thus, the use of a SSM allows the proposed method to reduce the image size efficiently, while preserving the important white blood cells. Results Experimental results using the PSNR (Peak Signal-to-Noise Ratio) and ROD (Ratio of Distortion) of blood cell images confirm that the proposed method is able to produce better resizing results than conventional methods, as the seam carving is performed based on an SSM and energy map. Conclusions For further improvement, a faster medical image resizing method is currently being investigated to reduce the computation time, while maintaining the same image quality.
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Ko
etal
.
BioMedicalEngineeringOnLine
2010,
9
:54
http://www.biomedical-engineering-online.com/content/9/1/54

RESEARCH

OpenAccess

Imageresizingusingsaliencystrengthmapand
seamcarvingforwhitebloodcellanalysis
ByoungChulKo,SeongHoonKim,JaeYealNam
*

*Correspondence:jynam@kmu.ac.
rkDepartmentofComputer
Engineering,KeimyungUniversity,
Shindang-Dong,Dalseo-Gu,Daegu,
areKo

Abstract
Background:
Anewimage-resizingmethodusingseamcarvingandaSaliency
StrengthMap(SSM)isproposedtopreserveimportantcontents,suchaswhiteblood
cellsincludedinbloodcellimages.
Methods:
Toapplyseamcarvingtocellimages,aSSMisinitiallygeneratedusinga
visualattentionmodelandthestructuralpropertiesofwhitebloodcellsarethen
usedtocreateanenergymapforseamcarving.Asaresult,theenergymap
maximizestheenergiesofthewhitebloodcells,whileminimizingtheenergiesof
theredbloodcellsandbackground.Thus,theuseofaSSMallowstheproposed
methodtoreducetheimagesizeefficiently,whilepreservingtheimportantwhite
bloodcells.
Results:
ExperimentalresultsusingthePSNR(PeakSignal-to-NoiseRatio)andROD
(RatioofDistortion)ofbloodcellimagesconfirmthattheproposedmethodisable
toproducebetterresizingresultsthanconventionalmethods,astheseamcarvingis
performedbasedonanSSMandenergymap.
Conclusions:
Forfurtherimprovement,afastermedicalimageresizingmethodis
currentlybeinginvestigatedtoreducethecomputationtime,whilemaintainingthe
sameimagequality.

Background
Peripheralbloodcelldifferentialcountingprovidesvaluableinformationforaccurate
patientdiagnoses,yetthemicroscopicreviewislaborintensiveandrequiresahighly
trainedexpert.Currentautomatedcellcountersarebasedonlaser-lightscatterand
flow-cytochemicalprinciples,nonetheless,21%ofallprocessedbloodsamplesstill
requiremicroscopicreviewbyexperts[1].Therefore,variousefforts[1-5]havealready
beenmadetodevelopautomaticcellanalysissystemsusingimageprocessing.Blood
cellimagesconsistofbothwhiteandredbloodcellsscatteredacrosstheentireimage,
however,itisthewhitebloodcells(WBCs)thatprovidetheimportantinformationfor
patientdiagnoses,suchasleukemiaorcancer[2].Thus,inmostresearch,WBC
segmentationistheimportantprocedure,wheretheultimategoalistoextractallthe
WBCsfromacomplicatedbackgroundandthensegmenttheWBCsintotheir
morphologicalcomponents,suchasthenucleusandcytoplasm.
RepresentativeWBCanalysissystems,suchasCellarvisionDiffmasterOctavia[4]and
CellarvisionDM96[5],scanthewholeslideatalowmagnificationfirsttoidentify
potentialWBCsusingthespecificcharacteristicsofWBCs,suchastheircolor,size,and

©2010Koetal;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons
AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproductionin
anymedium,providedtheoriginalworkisproperlycited.

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shape,andthentakedigitalimagesatahighmagnification.Thereafter,pre-classification
isperformedusingonlythecroppeddigitalimages.Whilethismethodismoreefficient
thanscanningWBCsfromahigh-resolutionimageofthewholeslide,additionaltimeis
requiredfortheWBCsearch,especiallywhentheimagecontainsseveralWBCs.
Furthermore,additionalstorageisneededtosavetheindividualpotentialWBCsand
extratimerequiredtoclassifytheWBCs,asthesystemhastocheckallpotentialWBC
imagestoanalyzejustoneslide.
Meanwhile,othermethods[2,3]useonlyanoriginalhigh-resolutionimageforthe
WBCanalysis.However,analyzingWBCsfromthewholeimageistimeconsuming,
sincethesizeofbloodcellimagesisnormallyatleast800×600.Therefore,animage-
resizingmethodisneededthatretainsalltheWBCswithoutmorphologicaldistortion
inordertoreducethepost-segmentationclassificationtime.Furthermore,sinceresized
high-qualityimagesrequirelessstorage,thepost-imagesegmentationandclassification
canbemoreaccuratethanwithconventionalimagecompression,suchasJPEG.
Relatedworkcanbedividedintotwoparts;imagecompressionandimageresizing.
First,variouslosslesscompressiontechniquesalreadyexistthatcanpreservethe
characteristicsofanimage,yetwithalowcompressionrate.Forexample,several
researchers[6-8]haveproposedtransformcodingschemes,suchasaPrincipalCom-
ponentAnalysis(PCA)andDiscreteCosineTransform(DCT),whileKarrasetal.[9]
usedadiscretewavelettransformation(DWT)andfuzzyc-meansclusteringtechnique.
Plus,toachievehighercompressionrateswithoutdetractingfromthequality,region
ofinterest(ROI)methodswithaDCThavealsobeeninvestigated[6,10].Inparticular,
Gokturketal.[10]proposedahybridmodel,usinglosslesscompressioninregionsof
interestandhigh-ratemotion-compensatedlossycompressioninotherregionsinthe
caseofasequenceofCTimages.Nonetheless,eventhoughlosslesscompressionpro-
ducesahighercompressionratewithoutdistortingROIs,theexactpreservationofa
ROIisstilldifficultwhenthecompressionrateisaboveaspecificlimitation.Therefore,
anewalgorithmisneededthatcanefficientlypreserveROIs,regardlessofthecom-
pressionrate.
Inadditiontoimagecompressionmethodsthatmerelypreservetheoriginalimage
size,someresearchershaveattemptedtoresizeorcrop[11,12]imagesaccordingto
theimagecontents.Yet,asshowninFig.1-(b),standardresizinghomogeneously
reducestheimagesize,therebydamagingalltheimagecontentsbasedontheratioof
theresizing.Similarly,whilecroppingcanbeusedtodisplaythemostimportant
regioninanimage,asshowninFig.1-(c),cellimagescontainmanyROIs,making
croppinginappropriateforcellimagecompression.
Meanwhile,seamcarving[13]changesthesizeofanimagebysubtlyremovingor
insertingaconnectedpathofpixelsfromadifferentpartoftheimageaccordingtothe
measuredenergy,asshowninFig.2-(b).However,eventhoughseamcarvingcaneffi-
cientlyremovenon-ROIpixels,iftheoperationisappliedtooharshly(i.e.resizingan
800×600imageto200×120),importantROIscanstillbedamaged,asshowninFig.
2-(d).Furthermore,sinceseamcarvingwasoriginallydevelopedfornatureimages,its
applicationtomedicalimagesissomewhatlimited.Forexample,theenergydistribu-
tionofWBCsisnotdistinctiveinbloodimages,makingithardtoapplyaseamcar-
vingoperatortobloodcellimages,whichresultsinaninevitableremovalorinsertion
ofpixelsinWBCs.

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Figure1
Examplesofdifferentscaling-downmethods
.

Accordingly,thispaperpresentsanewmethodforresizingbloodcellimageswhile
preservingthesizeandshapeofWBCs.Inperipheralblood,WBCsaredividedinto
fiveclassesaccordingtotheirmaturationstage,makingitessentialtopreservethesize
andshapeofthenucleus.Thus,toprovideanefficientimage-resizingmethodthat
treatsWBCsasROIs,aSaliencyStrengthMap(SSM)isproposedusingavisualatten-
tionmodelandthestructuralpropertiesofWBCstogenerateanewenergymap.As
such,thismapmaximizestheenergiesoftheWBCs,whileminimizingtheenergiesof
theredbloodcellsandbackground.Therefore,incontrasttopreviousalgorithms,the
maincontributionofthisstudyistoimprovetheresizingperformancewithalower
filesize,whilepreservingtheWBCsusingtheproposedSSMwithanenergymap.
Fig.3showsthearchitectureofthecellimageresizingusingtheproposedSSMand
seamcarving.
Theremainderofthispaperisorganizedasfollows.
Methods
describesthealgo-
rithmsusedtocreatethesaliencystrengthmap,anEllipseAttentionWindow(EAW)
thatremovesuselessregionsfromtheimage,andtheseamremovalusinganenergy
mapbasedonthesaliencystrength.
ResultsandDiscussion
evaluatestheaccuracy

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Figure2
Exampleofseamcarving
:(a)originalimage,(b)energymapof(a),(c)reducedimageusing
seamcarvingthatpreservesshapeofimportantcontents(WBCs),(d)distortedimageusingharshseam
carving,whereshapesofWBCnucleiaredistorted.

Figure3
Architectureofproposedmethod
.

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andapplicabilityoftheproposedresizingmethodbasedonexperiments,andsome
finalconclusionsandareasforfutureworkarepresentedin
Conclusions
.
Methods
Thispaperproposesanewimage-resizingmethodwithalowerfilesizethatcanefficiently
preserveWBCsusingavisualsaliencymapbasedonthefollowingtwoassumptions:


thenucleiofWBCsarenearlyround.

thenucleiofWBCsarehighlightedinpurpleonawhitebackgroundwithmono-
chromaticredbloodcells.

Usingthesecharacteristics,aSaliencyStrengthMap(SSM)isproposedusingavisual
attentionmodel,whilethestructuralpropertiesofWBCsareusedtogeneratean
energymap.
Saliencymapgeneration
Incontrasttonatureimages,microscopicimages,especiallybloodcellimages,have
differentcharacteristicswithdistinctdiagnosticmeanings,suchasavaryingcolorand
saturationaccordingtofluorescencestaining.Forexample,inthecaseofbloodcell
images,thesalientparts,theWBCs,tendtobehighlysaturatedandpurpleincolor,
whiletheremainingparts,theredbloodcells,haveamoremonotonousappearance.
Thus,forsemanticseamcarving,knowledgeoftheexactpositionsoftherelevant
WBCsiscrucial.Therefore,toobtainthepositionofWBCs,amodifiedvisualatten-
tionmodelisused,asproposedinourpreviousresearch[14].
Theoriginalsaliency-basedvisualattentionmodelwasproposedbyIttietal.[15],
andusescolor,luminance,andorientation.Themostsalientareasarethenselected
basedonawinner-take-allcompetitionmap.However,inthisstudy,asaliencymapis
usedfortheinitialdetectionofAttentionWindowsbasedonaweightedlinearcombi-
nationofacolormap,saturationmap,andorientationmapasshowninFig.4.
Toproducethecolormap,thisstudyusesaCIELabcolormodel,whereeacha*and
b*imageisdown-sampledtohalfthesizeoftheoriginalimage.Differentsizedfilters
s
Î
{
1
×
1
,13×13}
arethenappliedtothedown-sampled
a
and
b
images.Thefilters
estimatethecenter-surrounddifferencebetweenthecenterpointandthesurrounding
pointswithinthefilterscale
s
usingtwocolors
c
Î
{a,b}
,andthisdifferenceyieldsthe
featuremap,
C(c,s)
.Thesizeofthefiltersistypicallychosenbasedonthenumberof
availableobservations.Inthisstudy,thesizeof
s
wassetat11×11and15×15based
onseveralexperimentsusingan800×600imagesize.Hence,thefiltersizecanbe
changedaccordingtotheimagesize,withahalfvaluewhenusinga400×300image
sizeandviceversa.InEq.(1),thenormalizedcolordifferencemap
C
isestimated
from
C(c,s)
s.
1C
=
(
∑∑
C
(
c
,
s
))
(1)
4
c

{
a
,
b
}
s

{11
×
11,13
×
13}
Inparallelwiththecolorfeaturemap,theorientationfeaturemapisproducedusing
asimplewavelettransform.Afteraone-levelwavelettransform,horizontally(LH),
vertically(HL),anddiagonally(HH)orientatedsub-imagesareobtainedfromthe

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Figure4
Flowdiagramofsaliencymap
:(a)sourceimage,(b)orientationmap,(c)colormap,(d)
saturationmap,and(e)saliencymap.
waveletsubbands.Theorientationfeaturemap,
O(c,s)
isthenproducedfromthethree
sub-images
c
Î
{HH,HL,LH}
andtwofilters
s
Î
{11×11,13×13}
usingthesame
methodasforthecolorfeaturemap.InEq.(2),thenormalizedorientationdifference
map
O
isestimatedfrom
O(c,s)
s.
1O
=
(
∑∑
O
(
c
,
s
))
(2)
6
c

{
HH
,
HL
,
LH
}
s

{11
×
11,13
×
13}
Thenormalizedsaturationfeaturemap
S
isprocessedinasimilarwaytothecolor
mapusingasaturationfeaturemap,
S(c,s)
fromHIScolorspaceandtwofilters
s
Î
{
1
×
1
,13×13}
basedonthefollowingEq.
1S
=
(

S
(
c
,
s
))
(3)
2c

{
s
}
s

{11
×
11,13
×
13}
Afterthethreefeaturemapsareproduced,theyarecombinedintoasaliencymap.
However,sincecellimageshaveahighercontrastforcolorthanfororientationand
saturation,asdistinctfromnaturescenes,differentweightsneedtobeappliedtoeach
featuremapwhentheyarecombinedintoasaliencymap.Inthepresentstudy,the
mostaccurateAttentionWindowswereproducedwhenthecolorweightwas0.6,the
orientationweightwas0.2,andthesaturationweightwas0.2.Finally,thethreefeature
mapsarenormalizedandsummedintoasinglesaliencymapusingtheirweightsand
Eq.(4).Aftergeneratingthesaliencymap
C
m
,itisup-sampledtotheoriginalsize.
C
m
=
w
1

C
(
x
,
y
)
+
w
2

L
(
x
,
y
)
+
w
3

O
(
x
,
y
)
(4)

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Saliencystrengthmapgeneration
Basedonthesaliencymap,AttentionWindows(AWs)arethendetectedtoremove
uselessregionsfromtheimage,suchasredbloodcellsandbackground,thereby
improvingthequalityoftheresizedimage.Todeterminetheproperlocationofthe
AWs,optimalthresholding[16]ofthesaliencymapisperformedfirst(Fig.5-(c)).This
thresholdingmethodisknowntoproducethebestperformancewhenanimageonly
containstwoprincipalregions(e.g.objectsandbackground)andthedistributionof
thegray-levelvaluesineachregionfollowsaGaussiandistribution[16].Morphological
closingisthenperformedtofilltheholesinthenucleioftheWBCs(Fig.5-(d)).Using
theresultingbinaryimage,regionlabelingisperformedandsmallregionsareconsid-
eredasnoiseandremoved(Fig.5-(e)).Atthesametime,theinitialAWpositions
(x,y)foreachremainingregionareestimatedbyX-Yprojection.Also,sinceWBCs
tendtohavearoundshape,theellipticalshapesoftheAWs(EAWs)arere-estimated
usingacentroidandtheradiusoftheinitialAW(Fig.5-(f)).Thereafter,adistance
transformusingtheEuclideandistanceisperformedtoboosttheintensitydifference
betweenthecentralandboundaryregions,termedthestrengthoftheEAW(
EAW
S
).
AsshowninFig.5-(g),theintensitystrengthoftheboundaryislowerthanthatofthe
centralregionineachnucleus.
ThesixstepsforextractingtheAWandestimatingthe
EAW
S
areasfollows:

tSep1:
Otsu[17]

soptimalthreshold
t
op
isappliedtothesaliencymap(
C
m
).
I
(
x
,
y
)
=⎧⎨
1
ifC
m
(
x
,
y
)
>
t
op
0
otherwise

⎩(5)

Figure5
SaliencystrengthusingEAWsandenergymap
:(a)originalimage(b)saliencymap,(c)
optimalthresholding,(d)morphologicalopening,(e)removalofsmallregions,(f)EAWs,(g)strengthof
EAWs,(h)SaliencyStrengthMap,(i)finalenergymapof(h),and(j)resizedimage.

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tSSetpe2p:3:Morphologicalopeningisperformedtofillanyholesinthecellnuclei.
Afterregionlabeling,smallregionsareremovedifthesizeofaregionis
belowapredefinedminimumthreshold(3%ofallimagepixels).Thispredefined
minimumthresholdwasdeterminedbyanalyzingtheminimumcellregionfrom
wholetrainingcellregions.
Step4:
TheinitialpositionoftheAWineachregionisestimatedusinganX-Y
projection.
Step5:
TheellipticalAWs(EAW)arere-estimatedusingthecentroidandradiusof
theinitialAW.
Step6:
AdistancetransformisperformedandthestrengthoftheEAW(
EAW
S
)
estimated.

ThesaliencymapandstrengthoftheEAWsarethensummedintoasinglesaliency
strengthmap(
S
M
)andnormalizedinto0~255,asshowninFig.5-(h).
1SSM
(
x
,
y
)
=
g
(

[
C
m
(
x
,
y
)
+
EAW
S
(
x
,
y
)])
(6)
2wheregrepresentsaGaussiansmoothingoperatortoreduceminornoise.
Finally,theresizedimagebasedontheSSManditsenergymapisshowninFig.5-(j).
Seamremovalusingenergymapbasedonsaliencystrengthmap
Aseamisamonotonicandconnectedpathofpixelsproceedingfromthetopofan
imagetothebottom,orfromlefttoright.Thus,whenaseamisremovedfroman
image,theimagesizeisreducedbyoneineitherthehorizontalorverticaldimension.
Likewise,seamcarvingusesanenergyfunctiondefinedbasedonthepixelstosucces-
sivelyremovetheminimumenergypathsfromanimage[17].Yet,asshownin6-(b),an
energymapusingonlythegradientmagnitudeintroducesvisualartifacts,regardlessof
theimportanceofthecells.WhereastheproposedenergymapsinFigs.5-(i)and6-(c)
showonlythehighestenergy,indicatingtheexistenceofWBCswithoutvisualartifacts.
Seamcarvingusestwotypesofenergyremovalstrategy:backwardandforward.
Backwardenergystrategiesarebasedonevaluatingtheenergy,yettheyintroduce
visualartifactsduetotheirseamremovalstrategy.Theseamscontainingthelowest
energyareremovedoneafteranother,however,theenergyinsertedintothenewedges
createdbypreviouslynon-adjacentpixelsthatbecomenewneighborsisignoredaftera

Figure6
Energymapcomparison
:(a)originalimage(b)energymapusingonlygradientmagnitude,
and(c)energymapusingsaliencystrengthofSSM.

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seamisremoved.Thus,toreducethesevisualartifacts,forwardenergystrategies[17]
substituteanenergyevaluationthatcalculatesthreepossibleseamstepcostsand
definestheminimalamountofenergyinsertedbytheremovalofaseam.
Intheseamremovalprocedureusedinthisstudy,thesaliencystrengthoftheSSM
isusedtocorrespondtothecomputingenergyforeachpixel.Computingthecostof
thesaliencystrengththenproducesthesameresultastheforwardenergystrategyof
Rubinsteinetal.[17].Asdistinctfrombackwardenergystrategies,threepossiblecases
arethencalculatedtoremoveseamswithforwardenergystrategiesusingthepixel
valuesof
S
M(i,j)
andthefollowingformula:
(
a
)
C
L
(
i
,
j
)
=
|
SSM
(
i
,
j
+
1)

SSM
(
i
,
j

1)|
+
|
SSM
(
i

1,
j
)

SSM
(
i
,
j

1)|
(
b
)
C
U
(
i
,
j
)
=
|
SSM
(
i
,
j
+
1)

SSM
(
i
,
j

1)|
(7)
(
c
)
C
R
(
i
,
j
)
=
|
SSM
(
i
,
j
+
1)

S
SM
(
i
,
j

1)|
+
|
SSM
(
i

1,
j
)

SSM
(
i
,
j
+
1)|
where
SSM
(
i
,
j
-1)isthenewpixelthatisreplacedafterremoving
S
M
(
i
,
j
),
SSM
(
i
,
j
+1)and
SSM
(
i
-1,
j
)arethenewrightandupperneighbors,respectively,and
C
L
,
C
U
,
and
CR
representthecostsofthethreepossibleverticalseams.
AcostmatrixMisthencreatedtocomputetheseams.

M
(
i

1,
j

1)
+
C
L
(
i
,
j
)
⎪M
(
i
,
j
)
=
P
(
i
,
j
)
+
min

M
(
i

1,
j
)
+
C
U
(
i
,
j
)
(8)
⎩⎪
M
(
i

1,
j
+
1)
+
C
R
(
i
,
j
)
where
P
(
i
,
j
)isthegradientvalueobtainedfrom
S
M(i,j)
,
M
(
i
-1,
j
-1)istheleftupper
neighbor,and
C
L
isitscost.Thecostofthecorrespondingupper
M
(
i
-1,
j
)neighbors
C
U
andrightupper
M
(
i
-1,
j
+1)neighbors
C
R
arecomputedinthesamemannerto
determinetheminimumenergyofthenewsaliencystrengthafterremoving
S
M
(
i
,
j
).
Oncethecostmatrixisconstructed,
M
(
i
,
j
)inarandompositionrepresentsapixel
(
i
,
j
)inapathcrossingtheimagefromtoptobottom,andisconnectedtootheradja-
centpixelscontainingtheminimalenergyaccordingtothesaliencystrength.Conse-
quently,theresizingisperformedbyiterativelycreatingacostmatrixafterblending
thegapsarisingfromseamremoval.
Fig.7showsacomparisonoftheresultsofseamcarvingwhenusingagradient-
basedenergymapandtheproposedenergymap.Whilethegradient-basedenergymap

Figure7
Comparisonofseamcarvingresults
:(b)resizedimageusingoriginalseamcarvingand(c)
resizedimageusingproposedmethod.

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distortstheWBCnucleiduetoaharshreductionoftheimagesize,theproposed
methodisabletopreservetheoriginalshapeoftheWBCnuclei.
Resultsanddiscussion
TheexperimentaltestsusedcolorperipheralbloodimagescollectedattheSeverance
Hospital,YonseiUniversity.The8testimageswerebasedonaslideofaperipheral
bloodsmearandtakenusingamicroscope,charge-coupleddevice(CCD)camera,and
24-bitdigitizerwithan800×600imagesize.
Asthereisnospecificmethodforevaluatingtheperformanceofimageresizing,the
PeakSignal-to-NoiseRatio(PSNR)wasusedfirsttoevaluatethecontentpreservation
oftheproposedmethod.Plus,theRatioofDistortion(ROD)wasappliedtoevaluate
thegeometricdistortionoftheresizedimages.Notethat,thesizeofthesourceimages
was800×600andthetargetsizewasautomaticallydeterminedaccordingtothesize
oftheEAWstoincludeallthenucleiwithoutdistortion.
PSNR(PeakSignal-to-NoiseRatio)comparison
Anexperimentalcomparisonofseamcarvingisgenerallyverydifficultasthereareno
standardcriteriaforperformancetests.Thus,tovalidatetheeffectivenessofthepro-
posedapproach,thisstudyusedthePeakSignal-to-NoiseRatio(PSNR).
ThePSNRoriginallycomesfromelectronicsandrepresentstheratiobetweenthe
maximumpossiblepowerofasignalandthepowerofthenoisethataffectsthefidelity
ofitsrepresentation.However,inthefieldofimageprocessing,thePSNRisusedto
measureofthequalityofanimageoritscompression.Inthecaseofimageprocessing,
themaximumvalue(
MAX
)ofintensitylevel255isusedinsteadofthemaximumpos-
siblepower.InEq.(9),theMSErepresentsthemeansquareerrorbetweentheoriginal
image
I(i,j)
andthetargetimage
K(i,j)
.
m

1
n

1
MSE
=
1
∑∑
||
I
(
i
,
j
)

K
(
i
,
j
)||
2
(9)
mn
i
=
0
j
=
0
Where
m
and
n
representwidthandheightoftheimage,respectively.
ThePSNRisthenestimatedbycomputingtheratioofthemaximumvaluetothe
MSEusingEq.(10).

MAX
2
⎞⎛
MAX

PSNR
=
10

log
10

I
⎟=
20

log
10

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MSE
⎟⎝
MSE

⎝⎠Fortheperformancetest,gradient-basedseamcarvingandtheproposedmethod
wereappliedtothesourceimagestocreatetargetimages.TheWBCnucleiwerethen
croppedmanuallyfromeachimagewithagraphictoolandusedforthePSNR
comparison.
Fig.8showstheimagequalityresultswhenusingaJPEGcompressionmethod,
imageresizingwithseamcarving,andimageresizingwiththeproposedmethod.
Clearly,theseamcarvingbasedonthegradientenergyproducedWBCnucleiwith
distortedshapesandsizes,whereastheJPEGcompressionandtheproposedmethod
preservedtheshapesandsizesoftheWBCnuclei.

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