ContentslistsavailableatScienceDirect
Food
and
Bioproducts
Processing
jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / f b p
Classification
modeling
based
on
surface
porosity
for
the
grading
of
natural
cork
stoppers
for
quality
wines
Vanda
Oliveira
∗,
Sofia
Knapic,
Helena
Pereira
UniversidadedeLisboa,InstitutoSuperiordeAgronomia,CentrodeEstudosFlorestais(CEF),TapadadaAjuda,
P-1349-017Lisboa,Portugal
a
b
s
t
r
a
c
t
Thenaturalcorkstoppersare commerciallygradedintoqualityclassesaccordingwiththehomogeneityofthe externalsurface.Theunderlyingcriteriaforthisclassificationaresubjectivewithoutquantifiedcriteriaandstandards definedbycorkindustryorconsumers.Imageanalysiswasappliedtopremium,goodandstandardqualityclassesto characterizethesurfaceofthecorkstoppersandstepwisediscriminantanalysis(SDA)wasusedtobuildpredictive classificationmodels.Thefinalgoalistoanalyzethecontributionofeachporosityfeatureandproposeanalgorithm forcorkstoppersqualityclassclassification.Thisstudyprovidestheknowledgebasedonalargesamplingtoan accurategradingofnaturalcorkstoppers.
Inaverageallthemodelspresentedaccuracyinrelationtothecommercialclassificationover68%withahigher mismatchinthemid-qualityrange.Colorshowedanimportantdiscriminatingpower,increasingtheaccuracyin 10%.Themaindiscriminantfeatureswereporositycoefficientandcolorvariables,calculatedforthelateralsurface.A qualityclassificationalgorithmwaspresentedbasedonasimplifiedmodelwithanaccuracyof75%.Theclassification basedoncolorvisionsystemscanensureimprovedqualityclassuniformityandahighertransparencyintrade.
©2013TheInstitutionofChemicalEngineers.PublishedbyElsevierB.V.Allrightsreserved.
Keywords: Naturalcorkstoppers;Qualityclasses;Imageanalysis;Porosity;Discriminantanalysis;Classification
algorithm
1.
Introduction
Naturalcorkisanoutstandingmaterialfortheclosureofwine bottlescombining physicalperformanceanddurability,and allowingabalanceddevelopmentofwineduringbottleaging throughitsoxygentransfercharacteristics(Lopesetal.,2005). Corkistheclosurematerialpreferredbywineconsumers,as shownby recentsurveys(Barber et al., 2009). Natural cork stoppershave alsoa veryfavorablefootprintand are asso-ciatedtocorkoakforests,asustainableecosystemwithhigh biodiversityrichness.
Corkisacellularmaterialwithchemicalinertiaandaset ofspecificphysicaland mechanicalpropertiesthatprovide anunmatchedclosureforbottlesandforhighperformance insulation,withnaturalcorkstoppersasthepremiumproduct ofthecorkindustry(Fortesetal.,2004;Pereira,2007).
∗ Correspondingauthor.Tel.:+351213653491;fax:+351213653338.
E-mailaddress:vandaoliveira@isa.ulisboa.pt(V.Oliveira).
Received18January2013;Receivedinrevisedform5November2013;Accepted15November2013 Availableonline24November2013
Natural cork stoppersare graded into qualityclasses in functionoftheapparenthomogeneityoftheirexternal sur-face,asseenbyhumanormachinevision(Fortesetal.,2004; Pereira,2007).Theheterogeneityofthecorksurfaceisgiven primarilybythepresenceoflenticularchannels,aswellasby woodyinclusions,smallfracturesorotherdefects,thatcan bevisuallyoutsingledfromthecorksurfaceandarenamed astheporosityofcork(Gonzalez-AdradosandPereira,1996; Pereiraetal.,1996).Thisevaluationismadeusingautomated image-basedinspectionsystemswithhighthroughputrates basedonline-scancamerasandacomputerembeddedinan industrialsortingmachinecapableofacquiringand process-inginreal-timethesurfaceimageofthestoppers(Limaand Costa,2006).Thesystemsallowanidentification ofsurface defectsandquantificationofporosityfeatures,e.g.totalarea, numberorconcentrationofpores(Changetal.,1997;Jordanov
0960-3085/$–seefrontmatter©2013TheInstitutionofChemicalEngineers.PublishedbyElsevierB.V.Allrightsreserved. http://dx.doi.org/10.1016/j.fbp.2013.11.004
qualityclassificationofcorkstoppersaresubjectivetosome extentandnostandardsweredefinedbythecorkindustryor theconsumerstogradesorting(Pereira,2007).The classifica-tionisusuallybasedonreferencesamplesshowingtherange ofqualityvariationthatcanbefoundintheconsignmentfor agivenclient(LopesandPereira,2000).
Several studies have been published on identifying the contribution of each porosity feature for the grading of cork stoppers (Costa and Pereira, 2005, 2006, 2007, 2009), aswell asofcork discs (Lopesand Pereira,2000)and cork planks(Benkiraneetal.,2001;Gonzalez-Adradosetal.,2000; Gonzalez-AdradosandPereira,1996;Pereiraetal.,1996).All thestudieshaveshownthatthereisoverlapbetweenclasses and thatthe role ofnon-quantified features, i.e.related to operatororindustryissignificant.However,thesamplingused inthesestudieswaslimited,e.g.innumberofcorkstoppers andinthesurfaceareacoveredbyimageanalysis,anddoubts mayremainregardingtheselectedfeaturessincethenatural variabilityincorkishigh.Arecentstudyanalyzedindetailthe porosityofalargesampleofnaturalcorkstoppers,showing thatvariationofsomeoftheporescharacteristicsthroughout thelateralsurfaceofthestopperisimportant(Oliveiraetal., 2012).
Otherstudieshavebeenpublishedfocusingonmodeling theclassificationofcorkstoppersanddiscs.Changetal.(1997) proposedacorkstopperqualityclassificationsystembasedon featuresextractionandafuzzyneuralnetwork,with6.7%of rejectionafterreevaluationoftheresultsbyhumanexperts. Vega-Rodríguez et al. (2001) presented a system for image processingusing reconfigurablehardwareandanalgorithm forthecorkstoppersclassificationthatusesasimplifiedset ofporosity features(defect area,size ofthe biggestdefect andareaoccupiedbydefectsofdifferentsizes)forthe two tops.Vitrià etal.(2007)presentedacork stopper classifica-tionmodelbasedonfeatureextractionandclass-conditional independentcomponentanalysis,reachinganaverageerror rate of2%. Paniagua et al. (2011) developed forcork discs aneurosystemtomodelthehumancorkquality classifica-tion.Othertechniqueshavebeenappliedtocorkclassification suchasX-rayComptontomography(Brunettietal.,2002)or terahertz/millimeterwavespectroscopy (Horet al.,2008)in ordertorefinethevisualclassificationwithinclusionof pos-siblevoids,cracks,anddefectsinsidethestopper.Recently, Gómez-Sánchezetal.(2013)usedcolorimetricimage analy-sistechniqueswithapplicationofsegmentationalgorithmsto measuretheporosityofcorksamples.Theyobtainedthebest NIRScalibrationsbymeasuringtheporosityintothreeclasses ofcolor,matchingtheresultsobtainedbyimageanalysis.
Thispaperanalysesindetailtheporosityfeaturesofcork stoppersinthegradesusedtodaybythequalitywinemarkets: threemajorqualitygrades,ofpremium,goodandstandard stoppers.Thestudywasmadeonthetotalexternalsurface (lateralsurfaceandtops)ofthestoppers,andwasbasedona largesampleinordertoencompassthecorknaturalvariability andtoallowbetterconfidenceintheresults.Thecontribution ofeachporosityfeaturetoqualityclassificationisanalyzed usingadequate statisticalvalidation, thesignificant indica-torsforthegradingselectedandaclassificationalgorithmis proposedforcorkstoppersqualityclassificationusingtoday’s qualitygrades.Thefinalgoalistodefineasimpleand objec-tiveclassificationthatcouldbeusedbytheindustryinorder to ensure improved quality class uniformity and a higher
2.
Materials
and
methods
2.1. Sampling
Thenaturalcorkstoppers(24mmdiameter×45mmlength) usedinthisstudywerecollectedfromonemajorPortuguese cork industrialunit. Thestopperswere randomly sampled (beforewashingandsurfacetreatment)afterafirststep grad-ing bythe automatedvision system used routinely in the industrial productionline. The criteria considered in such automatedgradingincludetotalareaandnumberofpores, area ofthelargest pores,pore concentrationlevel, location of defects, verticaland horizontal projectionofpores, and the presence of cracks. Subsequently they were inspected byskilledoperatorsandgradedintothreereferencesquality classesasrequiredtodaybythewinemarket,codedas pre-mium(includingthetraditional“flor”andextracommercial classes),good(superiorand1stcommercialclasses)and stan-dard(2ndand3rdcommercialclasses). Afterthis manually validatedclassification,asampleof200corkstoppersofeach qualityclasswasrandomlytakenandusedasthereference fortheclassificationmodeling.
2.2. Imageacquisition
The natural cork stoppers were individually analyzed and their image surface(cylindrical lateral surface and circular bases)acquiredwithanimageanalysissystemthatincluded a digital 7 megapixels inmacro stand solution set on an acquisition KaiserRS1 Boardwithacontrolledillumination apparatus,connectedtoacomputerusingAnalySIS®image processing software (Analysis Soft Imaging System GmbH Münster,Germany,version3.1).
Theimageacquisitioncovered100%ofthelateralareaby using eightsuccessiveframesofthe cylindricallateral sur-faceofthebody.Thefirstframewasacquiredparalleltocork growthringsandtheotherssubsequentlytakenbyrotating thestopper45◦(Fig.1).Twocircularframeswereacquiredfor thetwotopscorrespondingto96%ofthetotalarea.Duetothe waystoppersarepunchedout fromthecorkstrip,thetops correspond totransversal sectionsofcork whilethe lateral surfaceofthestopperincludestangentialandradialsections ofcorkandallthein-betweensections(Pereira,2007;Pereira etal.,1987).
Theobject extractionwas carriedout insidetwo prede-finedregionsofinterest,onerectangular,45.05mmlongand 9.41mmwide(area423.92mm2),forthelateralsurface,and another circular forthe topswith 23.51mm diameter(area 433.92mm2).Theimagethresholdwasadjustedindividually foreachimageandrangedinaRGBsystemfrom65to135for red,from60to115forgreen,andfrom65to120forblue.
2.3. Imagedataanalysis
Asetofvariableswascollectedautomaticallyforeachpore: area(mm2),calculatedbythenumberofpixelsoftheparticle timesthe calibrationfactors;meandiameter(mm),defined asthearithmeticmeanofalldiametersofaparticle(range anglesbetween0◦and179◦,withstepwidthof1◦);maximum diameter (mm),isthemaximum diameterofall maximum
Fig.1–Photographsofthecylindricallateralsurface(compositionofeightsuccessivepictures)andthetwocirculartops
(transversesection).FramesAandErepresenttangentialsectionwhileframesCandGrepresentscorkradialsection.
diametersdeterminedateachangle(variesin1◦steps);mean rectangle,definedasthearea ofthemean rectanglewhich sidesconsistoftangentstotheparticle borders;maximum rectangle,definedastheareaofthebiggestrectanglewhich sidesconsistoftangentstotheparticleborders;shapefactor, definedas(area/perimeter2)×4,measuringtheroundness ofthepores;convexity, definedasthe fractionofthe pore areaandtheareaofitsconvexhull(rangingbetween0and1); aspectratio,asthemaximumratiobetweenwidthandlength ofaboundingrectangleofthepore;sphericity,thatdescribes theelongationoftheporebyusingcentralmoments(value of1foraperfectcircularparticle);andmeanvalueofallred, greenandblueintensitiesineachpore.
Thesedatawerefilteredandonlyporeswithareaequal orsuperiorto0.1mm2wereconsideredfortheanalysis.The pixelsizewas0.05mmandthereforethelowestporeareathat could beconfidently resolved was 0.02mm2 corresponding toeightcontiguouspixels.Previousstudiesconsideredonly porositysuperiorto0.5mm2 on theassumptionthatsmall porosityisfunctionallyandestheticallyirrelevant,andonly bringshighervarianceandvariabilitytothesample(Costaand Pereira,2005,2006,2007,2009;Gonzalez-Adradosetal.,2000; LopesandPereira,2000;Pereiraetal.,1996).
Thevariablescollectedforeachporewereprocessedand originateseveralcalculatedvariablesforeachframe:porosity coefficient(%),definedastheproportionoftheareaoccupied bypores;totalnumberofporesandnumberofporesby dimen-sionclasses;totalareaofpores(mm2),sumoftheareaofall poresintheframe;averageporearea(mm2),calculatedasthe arithmeticmeanoftheareaofallporesintheframe; maxi-mumporearea(mm2),definedastheareaofthebiggestpore intheframe;meandiameter,calculatedasthemean diam-eteraverageofallpores;maximumdiameter,definedasthe biggestofallporesmaximumdiameter;meanrectangle, cal-culatedasthearithmeticmeanofthemeanrectangleofall poresintheframe;maximumrectangle, definedasbiggest ofallporesmaximumrectangle;theshape-variables(shape factor,sphericity,aspectratioandconvexity)andthe color-variables(red,greenandblue)fromporeswereaveragedinto framevariables.Moreover,thesevariableswereaveragedand transformedintocorkstoppertransverse(twotops), tangen-tial(framesAandE)andradial(framesCandG)sectionand corkstopperbodyvariables(consideringtheeightframesof thestopperslateralsurface).
2.4. Statisticalanalysis
Severalgraphicalanddescriptivestatisticalanalyseswere car-riedoutforthecharacterizationofthequalityclassesandof thestopperslateralsurface.
In order to differentiatebetween quality classes and to predict the classofafutureobservation, several predictive classificationmodels ofstopperswere built basedon their surface characteristics using stepwise discriminant analy-sis(SDA).Discriminantanalysisistheappropriatestatistical techniquewhenthedependentvariableiscategoricalandthe independentvariablesarequantitative.Discriminantanalysis assumesthatdatacomefrom amultivariate normal distri-bution and that the covariance matrices ofthe groupsare equal(Sharma,1996).Anothercharacteristicofthedatathat canaffecttheresultsismulticollinearityamongthe indepen-dentvariables.Thestepwisemethodcanbeusefulwhenin the presenceofmanypredictors byautomaticallyselecting the“best”variablestouseinthemodel.Thestepwise selec-tion begins withnovariables inthe discriminant function, andateachstepavariableiseitheraddedorremoved,ifit addsthemostdiscriminatingpowerorifitdoesnot signif-icantlylowerthediscriminatingpower,asmeasuredbythe statisticalcriterion.Theprocedurestopswhenatagivenstep novariableisaddedorremovedfromthediscriminant func-tions(Sharma,1996).Thestatisticalcriterionusedtomeasure variablediscriminatingpowerwasWilks’value(p<0.05).All thestatisticalanalysiswasperformedusingSPSS®statistical software(version19.0;SPSSInc.,ChicagoIL).
Thesamplewasrandomlydivided intotwogroups: 70% ofthecorkstopperswereusedtoestimatethediscriminant functionsandproducedtheclassificationmodels(modeling set),and30%ofthestopperswereusedforexternalvalidation ofthemodels(validationset).
These modelswereanalyzedand compared,anda sim-plifiedmodelandaclassificationalgorithmforcorkstoppers qualityclassclassificationwereproposed.
3.
Results
3.1. Characterizationofqualityclasses
Thethreequalityclassesofnaturalcorkstoppersare charac-terizedinTable1forthelateralsurface.
Premium Good Standard Porositycoefficient(>0.1mm2)(%) 2.4(0.8) 4.0(1.4) 5.6(2.0) Porositycoefficient(>0.5mm2)(%) 2.0(0.8) 3.5(1.4) 5.0(2.0) Numberofpores Total 135(48) 167(58) 193(54) 0.1–0.5mm2 86 99 112 0.5–1.0mm2 26 31 35 1.0–2.0mm2 15 20 23 2.0–5.0mm2 7 13 16 >5.0mm2 1 4 7
Totalareaofpores(mm2) 82.7(28.8) 135.1(47.6) 191.2(69.1)
Averageporearea(mm2) 0.6(0.2) 0.9(0.3) 1.1(0.4)
Maximumporearea(mm2) 6.5(3.2) 11.3(6.0) 18.0(9.9)
Averageporeshapefactor 0.6(0.1) 0.5(0.0) 0.5(0.1)
Averageporeaspectratio 2.0(0.3) 2.1(0.2) 2.1(0.2)
AverageporeRed 93(29) 96(21) 91(30)
AverageporeGreen 71(22) 77(16) 69(24)
AverageporeBlue 76(20) 80(14) 73(22)
Theaverageporositycoefficientincludingallporesabove 0.1mm2was2.4%,4.0%and5.6%,respectively,forpremium, goodandstandardclass.Whenconsideringonlyporesabove 0.5mm2,thevaluesdecreasedto2.0%,3.5%and5.0%, respec-tively.
Thesmallporosity(between0.1and0.5mm2)represented onaverageanincreaseof0.5%intheporositycoefficientand represented63.9%,59.4%and 58.1% ofthe totalnumber of poresfor thepremium, good andstandard quality classes, respectively.
Thestandard deviationoftheporositycoefficient ofthe lateral surface was 0.8%, 1.4% and 2.0% for the premium, good and standardquality class, respectively, regardlessof theminimumporeareaconsideredfortheporositycoefficient calculations(0.1or0.5mm2).
The maximum pore area in the lateral surface of cork stoppersdifferedsignificantlybetweenclasseswith6.5mm2, 11.3mm2 and 18.0mm2 for premium, good and standard classes,andtheaverageporeareaalsoincreasedfrom0.6mm2 to0.9mm2and1.1mm2,respectively.
Theshapevariables presentedidenticalvalues between qualityclasses.TheRGBoftheporeswas,onaverage,93red, 71greenand76blueforpremiumclass,96red,77greenand 80blueforgoodclassand91red,69greenand73blueforthe standardclass.
Fig.2presentsthevariationoftheporositycoefficientand theaverageporeareainthetransverse,tangentialandradial sectionsforthethreequalityclassesofnaturalcorkstoppers. These sections correspond respectively to the tops (trans-verse),framesAandE(tangential)andframesCandG(radial). Theporositycoefficientrangedbetween3.1%and6.2%in thetangential section,respectively,forpremiumand stan-dardqualityclass, and 1.9%and5.3%inthe radialsection (Fig.2a).Thepremiumclasshadaverageporeareasof0.6mm2, 0.8mm2and1.3mm2forthe,tangential,radialandtransverse section,respectively.Thecorrespondingvaluesforthe stan-dardqualityclasswere0.9,1.4and1.7mm2(Fig.2b).
3.2. Qualityclassificationmodels
Five predictive classification models ofstoppersinto qual-ityclasseswereanalyzedandtheirdifferencescharacterized. Table2 shows the variables selected bySDA tobuild each
modeland Table3presents theresultsoftheclassification ofcorkstoppersintothethreequalityclassesconsideredin thisstudy.
Themultivariatenormalityassumptionwasinvestigated bytheapplicationofKolmogorov–SmirnovtestwithLilliefors significancecorrectiontotheindependentvariablesandthere wasnoreasontobelievethatwasviolated.Box’sMtestwas usedtoverifyifthevariance–co-variancematricesare equiva-lent.AlthoughMwassignificant(p<0.00),withlargesamples, asignificantresultisnotregardedastooimportant.
Models1and2werebuiltwiththeapplicationofSDAto thevariablesusedtraditionallyintheautomatedimage-based inspectionsystems,i.e.dimension,concentrationandshape
0 1 2 3 4 5 6 7
Premium Good Standard
P oro si ty co e ff ic ien t ( %) Transverse Tangential Radial Mean Value a 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Premium Good Standard
Av erage pore area (m m 2) Tranverse Tangential Radial Mean Value b
Fig.2–Variationinthetransverse,tangentialandradial
sectionsandmeanvalueforthethreequalityclassesof
naturalcorkstoppers:(a)porositycoefficientand(b)
Table2–TypeandvariablesselectedbySDAforeachpredictiveclassificationmodel.
Variables Models
Model1 Model2 Model3 Model4 Model5
Body Body Tops Body Body Tops Tang Rad
Concentrationanddimension
Porositycoefficient x x x x x x x
Totalnumberofpores x x x x x
Meanporearea x x
Maximumporearea x x x x
Meandiameter x x x x x Maximumdiameter x x Meanrectangle x Maximumrectangle x x x Shape Shapefactor x x Sphericity x x x x Aspectratio x x x Convexity x x x Color
AverageporeRed x x x x
AverageporeGreen x x x x
AverageporeBlue x x x x
variablesaveraged forthebody lateralsurfaceand tops.In bothmodelsthebodyvariablesselectedbySDAwere poros-itycoefficient,shape-variables (shapefactor,sphericityand aspectratio)anddimension-variables(maximumporearea, mean and maximum diameter, total number ofpores and maximumrectangle).Inbothmodelstheaverageaccuracyfor modelingandvalidationsetwas69.5%and68.3%,respectively. Thegoodqualityclassshowedthelowestaccuracyof60.0% and62.9%for,respectively,models1and2,whilepremium andstandardqualityclasseshadaccuracyvaluesabove70%.
Models 3and4are comparabletomodels1and 2with theadditionofporescolor-variables.Theindependent vari-ablesselectedbySDAformodel4wereporositycoefficient, maximumporearea,meandiameter,totalnumberofpores, convexityandaverageporered,greenandblue.Thesecolor variableswereselectedbySDAleadingtoanaccuracyof80.0% formodel3and84.1%formodel4.Thegoodclassaccuracy increasedto70.7%and78.6%formodels3and4,respectively. Thevalidationsetshowedanaverageaccuracyover73%for bothmodelswiththehighestvalueof85.0%forthestandard
Table3–Classificationofcorkstoppersintothreequalityclassesusingdiscriminantanalysisinpercentageoftheinitial numberofstoppersineachqualityclass(modelingset).Inbracketsistheclassificationofthevalidationset.Bold correspondstothematchofclassifications.
Originalqualityclass Predictedqualityclass
Premium Good Standard Meanaccuracy
Model1 Premium 75.7(70.0) 20.7(30.0) 3.6(0.0) Good 21.4(20.0) 60.0(61.7) 18.6(18.3) Standard 5.7(8.3) 21.4(18.3) 72.9(73.3) 69.5(68.3) Model2 Premium 74.3(70.0) 22.9(30.0) 2.9(0.0) Good 20.0(20.0) 62.9(60.0) 17.1(20.0) Standard 5.0(6.7) 23.6(18.3) 71.4(75.0) 69.5(68.3) Model3 Premium 84.3(73.3) 13.6(25.0) 2.1(1.7) Good 23.6(23.3) 70.7(61.7) 5.7(15.0) Standard 10.7(10.0) 4.3(6.7) 85.0(83.3) 80.0(72.8) Model4 Premium 85.0(66.7) 12.9(30.0) 2.1(3.3) Good 17.1(21.7) 78.6(68.3) 4.3(10.0) Standard 7.1(8.3) 4.3(6.7) 88.6(85.0) 84.1(73.3) Model5 Premium 80.0(61.7) 15.7(31.7) 4.3(6.7) Good 20.0(20.0) 73.6(65.0) 6.4(15.0) Standard 13.6(10.0) 3.6(6.7) 82.9(83.3) 78.8(70.0) S.model Premium 84.3(70.0) 13.6(28.3) 2.1(1.7) Good 20.7(25.0) 68.6(63.3) 10.7(11.7) Standard 14.3(16.7) 10.0(5.0) 75.7(78.3) 76.2(70.6)
Porositycoefficient(>0.1mm2)(%) 0.762a 0.562
AverageporeRed −0.080 0.225a
AverageporeGreen −0.097 0.150a
AverageporeBlue −0.041 0.078a
a Largest absolute correlation between each variable and any
discriminantfunction.
classinmodel4.Inmodel3thegoodqualityclasshadthe low-estaccuracyof70.7%and61.7%forthevalidationsetandthe standardqualityclasshadthehighestaccuracyforvalidation setwith83.3%.
Model5considereddimension,concentration,shapeand colorvariablescalculatedforradialandtangentialsectionsof cork.Thevariablewiththehighestdiscriminatingpowerwas theporositycoefficientfrombothsections.Theothervariables ofthetangentialsectionselectedforthemodelbySDAwere: color(RGB),shape(sphericityandconvexity)andmean dimen-sionvariables(diameterandrectangle).Fortheradialsection thevariables selectedwere:totalnumber ofpores,average poreareaandmaximumrectangle.Theaverageaccuracyfor modelingandvalidationsetwas78.8%and70.0%,respectively. Twodiscriminatingfunctionswerefittedautomaticallyfor allthemodels,butnearlyallthevarianceexplainedinterms ofdifferencesbetweenclassesbythemodelswasduetothe firstdiscriminantfunction.Inallthemodelsbothfunctions wereconsideredrelevantforthediscriminatingpower.
3.3. Qualityclassificationalgorithm
Asimplifiedmodelwasmadeusingthemaindiscriminant fea-tures,i.e.porositycoefficientandtheRGBcolor-typevariables calculated forthebody lateral surface. Theanalysisofthe structurematrixtable(Table4)revealsthatporositycoefficient ishighlyrelated withfunction1 whilefunction2explains essentiallythecolorvariability.
Fig.3illustratesthedistributionofthediscriminant func-tions scores for each predicted group. Reading the scores rangeson the axesand the overlaps ofthe graphs,a sub-stantialdiscriminationisrevealed.Function1discriminates thestandardqualityclassfrompremiumandgoodstoppers (Fig.3a),whereasfunction2,thatrepresentscolorvariability, hasdiscriminatingpowerbetweenpremiumandgood stop-pers(Fig.3b).
Fisher’s classificationfunction coefficients were used to classifythecasesbetweenthequalityclasses.Thecoefficients oftheindependentvariablesshowninTable5wereusedto constructadiscriminant functionforeachquality class.To
Table5–Classificationfunctioncoefficients(Fisher’s lineardiscriminantfunctions).
Qualityclass Premium Good Standard Porositycoefficient
(>0.1mm2)(%)
1.283 1.727 2.695
AverageporeRed −1.689 −1.981 −1.332 AverageporeGreen −2.198 −1.854 −2.090 AverageporeBlue 4.948 4.995 4.312
(Constant) −34.033 −37.037 −32.853
Fig.3–Histogramsshowingthedistributionof discriminantscoresforeachpredictedcorkstoppers qualityclassbythesimplifiedmodel:(a)function1and(b) function2.
performclassificationthethreefunctionsarecomputedand anindividualisassignedtothegroupwiththehighestscore. Theclassificationresultsforthemodelingsetrevealthat 76.2%ofthecorkstopperswereclassifiedcorrectlyintoquality classes.Likethepreviousmodels,thegoodqualityclasshad thelowestaccuracyof68.6%.Itisimportanttohighlightthe accuracyof70.6%obtainedwiththevalidationset(Table3).
Whencomparingtoasimplisticmodelwiththeporosity coefficient as the onlyvariable, the inclusion ofcolor-type variables increasedthe overall accuracyin morethan10%. Themisclassificationcorresponded,onaverage,to13%ofthe totalityofthecorkstoppers,withhighervaluesforthegood qualityclass.Itisnoteworthythat14.3%ofthecorkstoppers originallyclassifiedasstandardqualitywerepredictedbythe modelaspremiumclassstoppers.
4.
Discussion
4.1. Characterizationofstoppersqualityclasses
Asexpected,thesurfaceofthecorkstoppersisnot homoge-neouswhencomparingthetransverse,tangentialandradial sections. The lenticular channels appear with a different
aspectinthethreesections:intheradialandtransverse sec-tionstheylooklikeelongatedrectangularchannelsandinthe tangentialsectiontheyhaveacirculartoellipticalform(Figs. 1and2).
Several porosityfeatures such asporosity coefficient or totalnumberofporespresentedanincreasingtrendfrom pre-miumtostandardqualityclass,forallsectionsinaccordance withthepublisheddata(CostaandPereira,2007).
Thetangentialsectionhadthehighestporositycoefficients (Fig. 2a)duetothehigh number ofporesevenif the aver-ageporeareawassmaller(Fig.2b).Pereiraetal.(1996)had alreadystatedthattheaverageporeareawashigherinthe transverse/radialsectionthaninthetangentialsection.Lopes andPereira(2000)reportedanaverageporeareaof0.25mm2 forcorkdiscscorrespondingtothetangentialsectionofcork. Poresinthetransversesectionhadahigheraspectratiothan intheradialandtangentialsections,andthereforeweremore elongatedorthinner.
Theshapevariables presented identicalvalues between qualityclasses,aspreviouslyreportedbyGonzalez-Adrados andPereira(1996),andCostaandPereira(2009).Ontheother hand,the color-type variables showed differences between classesalthoughwithoutatrend.
4.2. Qualityclassificationmodels
Several predictive classification models of stoppers into quality classes were built based on the presentedsurface characteristicsusingstepwisediscriminantanalysis(SDA)for selectionofaspecificsetofvariables(Table2).
All the fiveclassificationmodels presented, onaverage, accuracysuperiorto69.5%forthemodelingsetorsuperiorto 68.3%forthevalidationset.Theresultsachievedwiththe vali-dationsetaremuchbetterthanthosepresentedbyCostaand Pereira(2006)forsevenqualityclasseswiththeapplication oftheestablisheddecisionsrulesforclassificationstopperby stopper,onanindividualbasis.
Itisempiricallyknown that thequality classificationof stoppersissubjectivetosomeextentandthereforevarying betweenindividual expertsas demonstratedbyBarrosand Pereira(1987)whoreportedclassificationmatchvaluesof31% fortwooperators andhigher classificationdifficulty inthe mid-qualityclasses.Thislackofobjectivecriteriaforvisual classificationcontributestothehighermismatchfoundforthe mid-qualityrange;indeeditwasinthegoodclassofstoppers thatthelowestaccuracywasobtained(from60.0%inmodel1 to78.6%formodel4).
Intheanalysisofmodels1and2itisimportanttonotice thattheuniquevariable consideredbySDAwithsignificant power from tops was the porosity coefficient. Gonzalez-Adrados et al. (2000) reported that the first variable to be entered into classification models of cork planks was the porositycoefficientinthetransverse section.However,this variabledoesnothavethesamediscriminantpowerincork stoppersclassificationprobablybecausethetransversearea (ofthetops)issmallerandvisuallylessrelevantwhen com-paredwiththatincorkplanks.
Theaccuracyachievedwiththesemodelsiscomparable withthe65%and72%ofoverallaccuracyachievedbyCosta andPereira(2006)whentestedasimplifiedclassificationusing threequalityclassesandconsideringthesignificantvariables selectedbySDA.Theevaluationofmodels1and2suggests thatthe observation ofcork stopperstops isirrelevant for the construction and accuracy of the classification model,
andthereforefortheclassificationofcorkstoppersinquality classes.
In models3 and 4the color variables were selectedfor thediscriminatingfunctionsandleadtoahigheraccuracyin theclassificationwhencomparedwithmodels1and2.The accuracyobtainedforthevalidationset(72.8%and73.3%for, respectively,models3and4),despitebeingsmallerthanthose obtainedwhen buildingthe model(modeling set), improve thosepublishedtodatebyCostaandPereira(2006).Thecolor variationofporesrepresentsthe colorheterogeneityofthe fillingtissuesofporesandallowsabetterseparationofthe qualityclasses.Ingeneral“darker”poreswillleadtothe allo-cationofthecorrespondingstopperstoworsequalityclasses. Inmodel5thedifferentselectionofdiscriminating vari-ablesthatoccurredforbothsectionsreflectstheanisotropyof porosityfeaturesshownbycorkstoppers.
Overalltheporositycoefficientisthemostimportant vari-ablewithdiscriminantpowerforseparationofcorkstoppers qualityclassesandwasselectedinallthemodels.
Comparing the three “new” models (3, 4 and 5) that includedthecolortype-variableswiththe“traditional” mod-elsrepresentedbymodels1and2,itseemsthatcolorhasan importantdiscriminatingpowerconferringabetteraccuracy. Theclassificationbasedoncoloredvisionsystemscan there-foreensureimprovedqualityclassuniformityandahigher transparencyintrade.
4.3. Qualityclassificationalgorithm
Asimplifiedmodelusingthemaindiscriminantfeatures,i.e. porositycoefficient andthe RGBcolor-type variables calcu-latedforthebodylateralsurfacewerethereforeproposedhere. Thismodelminimizestheprocessingofdatabyreducingthe dimensionalityoftheproblemandsuppressinginformation redundancy.Moreover,theclassificationresultswereslightly betterthantheonesfoundfor“traditional”models.Most pub-lished studies,like Paniagua et al. (2011), assume that the classificationmadebyhumanexpertsisoptimal/perfectand the aimistoobtain themostsimilar classificationresults. Howeverthestoppersthatwereconsideredasmisclassified shouldbeanalyzed,becauseofthehumaninspection subjec-tivity alreadyreferred.Ablindbeliefinthe accuracyofthe presentin-useclassificationisthereforeanexaggeration.The 30%of“misclassification”shouldthereforebeconsideredonly asindicative,andthemodelclassificationprobablytranslates moreexactlythefeaturesandquantifiedappearanceofthe externalsurfaceofthestoppers.
Themostcommoncriteriaconsideredinautomated grad-ing includevariables like total area and number ofpores, area of the largest pores and concentration level ofpores, i.e. dimension and concentration variables. The inclusion of color-variables improves the classificationand probably approximates more the model to the presently used clas-sification related to visual appearance of cork stopper as perceivedbytheoperator,therebyapproximatingtheresults from manual and automated grading. The proposed qual-ity classification algorithm can be applied in the industry toensure improveduniformitywithineach stoppers’ qual-ityclass.Byusingmeasurableandquantifiedfeaturesofthe external surface ofthe naturalstoppers, this classification algorithmwillallowahighertransparencyintrade.Moreover, thehighlightonkeyfeaturesofcorkcanbeusedinresearch, development andenhancementofnewproductsthat have corkasrawmaterial.
ThisworkwassupportedbyFEDERfundsthroughthe Oper-ationalProgrammeforCompetitivenessFactors– COMPETE and by National Funds under the project FCOMP-01-0124-FEDER-005421.CentrodeEstudosFlorestais(ForestResearch Center) is a research unit supported by the National Research funding of Fundac¸ão para a Ciência e Tec-nologia (PEst-OE/AGR/UI0239/2011). Funding from FCT is acknowledged by Vanda Oliveira as a doctoral student (SFRH/BD/77550/2011), and Sofia Knapic as a post-doctoral researcher(SFRH/BPD/76101/2011).Theauthorsacknowledge thecollaborationofAmorim&Irmãos,S.A.inmaterials sup-plyandtheassistanceofourcolleagueLídiaSilvaintheimage analysis.
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