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ecauseasamplemodelwhichisontheedgeoftwoclustersisnotlikelytobeaclustercenter.Supposingthatthesetofclustercentersis,andthenumberofmodelsinkthclusteris.Theputationalplexityis,whiletheputationalplexityoforiginalapproachis.SimulationandResultAnalysis
Inordertoverifytheeffectivenessoftheproposedmethodproposed,6typesof3DmodelsareselectedfromthePrincetonlibrary[14].Theprojectionray-basedmethodisusedtogetthe256featurevectorsbyemitting1616rays,wherearetheindexnumberofgraticuleandisthemaximumdistancefromtheintersectionstoorigin.The3Dmodelsincludebottle,flange,gear,gun,helicopterandhumanbodymodel.ThepartsofthesamplemodelsareshowninFig.11.
Fig.11Partsofthesamplemodels
First,APalgorithmisadoptedtoclassifythe78modelsin6modelbasesinordertofindthecentermodelsofeachbasewhicharerepresentativeanddistinctive.ThetestenvironmentisWindowsXP.MATLAB7.1Softwareisusedforsimulation.Theclusteringerroriscalculatedasfollows:
(11)
whereisthecentermodelsofclassK(thereareseveralcentermodels),istheclusterK.
TheclusteringresultsareshowninTable2.
Table2Clusteringresults
ModelBottleFlangeGearGunHelicopterHumanbodyError(%)0022.037.538.95.0Theclusteringerrorsofgunandhelicoptermodelsarelarger.Thereasonisthatthegunandhelicoptermodelshavealotofdetailedcharacteristic.Asmentionedabove,araymayintersectseveralfacets,butonlythemaximumdistancefromtheintersectionstooriginisadoptedasthefeaturevector.Sothefeaturesextractedfromgunandhelicoptermodelscannotdescribethemodelsexactly.However,fortheconvexmodels,suchasthehumanbody,flangeandbottlemodels,theclusteringresultsarebetter.Thereforetheray-basedmethodsarenotsuitableforthe3Dmodelswithmoredetailcharacteristics.Theextractionmethodwithhigherprecisioncanbeusedinthissituation:suchaswaveletmoments[15],3DZernikmoments[16],Fourieranalysis[17],andsphericalharmonicanalysismethod[18-20]andother3Dmodelfeatureextractionmethods.
(1)Theanalysisofputationplexity.First,theEuclideandistancebetweentheretrievedmodelandthecentermodelsisutilizedtojudgewhichmodelbaseitmaybelongto.
,
Then,theretrievalalgorithmsearchesinthecorrespondingmodelbaseforthemostsimilar3Dmodel.Thetotalputationalplexityis:
whereisthemodelsinclusterK,.
However,ifretrievalfromallofthemodelbasesbytheoriginalmethod,thecalculationis.Dueto,therefore,thecalculationofthemethodismuchsmallerthanthatoforiginalmethod.
(2)Theanalysisofprecision.39bottle,bodyandflangemodelsareselectedfrom75samplesfortesting.AfterclusteringbyEq.(11),theclusteringerroris0.Thismeansthattheall39modelsareclassifiedtothecorrectmodelbase.Themostsimilarmodelandtheentiresimilarmodelswillberetrievedfromthecorrectmodelbase.Thereforetherecallandprecisionratesare100%.Ontheotherhand,the3Dretrievalsystemdevelopedbythepaperisusedtoretrievethesimilarmodelfromallthemodelbases.Withthe256featurevectorsextractedbytheprojectray-basedmethod,theretrievalprocessofthe3bottle,3humanbodyand3flangemodelsaredone(asshowninFigs.11-13).Theretrievalresultsarelistedindescendingorderofthesimilarity,andthefirst10retrievedmodelsaretakentocalculatetheprecisionratewhichisshowninTable3.
Fig.12InterfaceofbottleretrievalFig.13Interfaceofflangeretrieval
Fig.14Interfaceofhumanbodyretrieval
Table3Resultsofmodelretrieval
ModelBottleFlangeHumanbodyNamePrecision(%)NamePrecision(%)NamePrecision(%)Model1M48230Gb9113_120Humanm21960Model2M48330Gb9113_2100Humanm22160Model3M48460Gb9113_390Humanm23760
FromTable3,theretrievalprecisionsof3typesofmodelsarelow.Thereasonsarethatlessfeaturevectorsareextracted,andmoreover,thelimitationofray-basedmethoditself.Itisinaccuratethatonlythemaximumdistanceisextractedasthefeaturevectorfor3Dmodel.However,eveninthecaseoffewerfeatures,themethodproposedbythepapercanachievethehigherretrievalprecision,whichshowsthatthemethodisofthepracticabilityandeffectiveness.
Conclusions
Theprojectray-basedmethodwhichreducestheputationalplexityandimprovestheextractionefficiencyisproposedforfeatureextractionof3Dmodelsinthispaper.Infeatureextraction,multi-layerspheresmethodisproposedandthechoiceofraynumberandspherenumberarediscussed.Thetwo-layerspheresmethodisutilizedanditcanmakethefeaturevectormoreaccurateandimproveretrievalprecision.Semi-supervisedAffinityPropagation(S-AP)Clusteringisutilizedbecauseitcanbeappliedtodifferentclusterstructures.S-APalgorithmisadoptedtoclusterandfindthecentermodelswhichcanrepresentthemodellibrary.Thequerymodelisfirstlyclassifiedtocorrespondingmodelbase,andthen,themostsimilarmodelisretrievedinthemodelbase.TheS-APclusteringalgorithmisefficientanditsclusteringresultsaremoreaccurate.Infeatureextraction,themulti-layerspheresmethodcanextractaccuratefeaturesevenforplicated3Dmodels,andinmodelretrieval,theapplicationofS-APimprovestheretrievalefficiency.
References(格
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